Liver metabolism is central to human physiology and influences the pathogenesis of common metabolic diseases. Yet, our understanding of human liver metabolism remains incomplete, with much of current knowledge based on animal or cell culture models that do not fully recapitulate human physiology. Here, we perform in-depth measurement of metabolism in intact human liver tissue ex vivo using global C-13 tracing, non-targeted mass spectrometry and model-based metabolic flux analysis. Isotope tracing allowed qualitative assessment of a wide range of metabolic pathways within a single experiment, confirming well-known features of liver metabolism but also revealing unexpected metabolic activities such as de novo creatine synthesis and branched-chain amino acid transamination, where human liver appears to differ from rodent models. Glucose production ex vivo correlated with donor plasma glucose, suggesting that cultured liver tissue retains individual metabolic phenotypes, and could be suppressed by postprandial levels of nutrients and insulin, and also by pharmacological inhibition of glycogen utilization. Isotope tracing ex vivo allows measuring human liver metabolism with great depth and resolution in an experimentally tractable system.

Introduction Cerebrovascular reactivity imaging (CVR) is a diagnostic method for assessment of alterations in cerebral blood flow in response to a controlled vascular stimulus. The principal utility is the capacity to evaluate the cerebrovascular reserve, thereby elucidating autoregulatory functioning. In CVR, CO2 gas challenge is the most prevalent method, which elicits a vascular response by alterations in inspired CO2 concentrations. While several systems have been proposed in the literature, only a limited number have been devised to operate in tandem with mechanical ventilation, thus constraining the majority CVR investigations to spontaneously breathing individuals. Methods We have developed a new method, denoted Additional CO2, designed to enable CO2 challenge in ventilators. The central idea is the introduction of an additional flow of highly concentrated CO2 into the respiratory circuit, as opposed to administration of the entire gas mixture from a reservoir. By monitoring the main respiratory gas flow emanating from the ventilator, the CO2 concentration in the inspired gas can be manipulated by adjusting the proportion of additional CO2. We evaluated the efficacy of this approach in (1) a ventilator coupled with a test lung and (2) in spontaneously breathing healthy subjects. The method was evaluated by assessment of the precision in attaining target inspired CO2 levels and examination of its performance within a magnetic resonance imaging environment. Results and discussion Our investigations revealed that the Additional CO2 method consistently achieved a high degree of accuracy in reaching target inspired CO2 levels in both mechanical ventilation and spontaneous breathing. We anticipate that these findings will lay the groundwork for a broader implementation of CVR assessments in mechanically ventilated patients.

Alcohol consumption is associated with a wide variety of preventable health complications and is a major risk factor for all-cause mortality in the age group 15-47 years. To reduce dangerous drinking behavior, eHealth applications have shown promise. A particularly interesting potential lies in the combination of eHealth apps with mathematical models. However, existing mathematical models do not consider real-life situations, such as combined intake of meals and beverages, and do not connect drinking to clinical markers, such as phosphatidylethanol (PEth). Herein, we present such a model which can simulate real-life situations and connect drinking to long-term markers. The new model can accurately describe both estimation data according to a χ2 -test (187.0 < Tχ2 = 226.4) and independent validation data (70.8 < Tχ2 = 93.5). The model can also be personalized using anthropometric data from a specific individual and can thus be used as a physiologically-based digital twin. This twin is also able to connect short-term consumption of alcohol to the long-term dynamics of PEth levels in the blood, a clinical biomarker of alcohol consumption. Here we illustrate how connecting short-term consumption to long-term markers allows for a new way to determine patient alcohol consumption from measured PEth levels. An additional use case of the twin could include the combined evaluation of patient-reported AUDIT forms and measured PEth levels. Finally, we integrated the new model into an eHealth application, which could help guide individual users or clinicians to help reduce dangerous drinking.

Alcohol consumption is associated with a wide variety of preventable health complications and is a major risk factor for all-cause mortality in the age group 15-47 years. To reduce dangerous drinking behavior, eHealth applications have shown promise. A particularly interesting potential lies in the combination of eHealth apps with mathematical models. However, existing mathematical models do not consider real-life situations, such as combined intake of meals and beverages, and do not connect drinking to clinical markers, such as phosphatidylethanol (PEth). Herein, we present such a model which can simulate real-life situations and connect drinking to long-term markers. The new model can accurately describe both estimation data according to a chi 2 -test (187.0 &lt; T-chi 2 = 226.4) and independent validation data (70.8 &lt; T-chi 2 = 93.5). The model can also be personalized using anthropometric data from a specific individual and can thus be used as a physiologically-based digital twin. This twin is also able to connect short-term consumption of alcohol to the long-term dynamics of PEth levels in the blood, a clinical biomarker of alcohol consumption. Here we illustrate how connecting short-term consumption to long-term markers allows for a new way to determine patient alcohol consumption from measured PEth levels. An additional use case of the twin could include the combined evaluation of patient-reported AUDIT forms and measured PEth levels. Finally, we integrated the new model into an eHealth application, which could help guide individual users or clinicians to help reduce dangerous drinking.

Current research on metabolic disorders and diabetes relies on animal models because multi-organ diseases cannot be well studied with standard in vitro assays. Here, we have connected cell models of key metabolic organs, the pancreas and liver, on a microfluidic chip to enable diabetes research in a human-based in vitro system. Aided by mechanistic mathematical modeling, we demonstrate that hyperglycemia and high cortisone concentration induce glucose dysregulation in the pancreas-liver microphysiological system (MPS), mimicking a diabetic phenotype seen in patients with glucocorticoid-induced diabetes. In this diseased condition, the pancreas-liver MPS displays beta-cell dysfunction, steatosis, elevated ketone-body secretion, increased glycogen storage, and upregulated gluconeogenic gene expression. Conversely, a physiological culture condition maintains glucose tolerance and beta-cell function. This method was reproducible in two laboratories and was effective in multiple pancreatic islet donors. The model also provides a platform to identify new therapeutic proteins, as demonstrated with a combined transcriptome and proteome analysis. A human-cell-based pancreas-liver microphysiological system serves as a preclinical platform for studying glucose-insulin homeostasis and disease mechanisms of glucose dysregulation, offering a tool for identifying targets and testing drugs.

Background & aims: Non-alcoholic fatty liver disease (NAFLD) is a common metabolic disorder, characterized by the accumulation of excess fat in the liver, and is a driving factor for various severe liver diseases. These multi -factorial and multi-timescale changes are observed in different clinical studies, but these studies have not been integrated into a uni fied framework. In this study, we aim to present such a uni fied framework in the form of a dynamic mathematical model. Methods: For model training and validation, we collected data for dietary or drug -induced interventions aimed at reducing or increasing liver fat. The model was formulated using ordinary differential equations (ODEs) and the mathematical analysis, model simulation, model formulation and the model parameter estimation were all performed in MATLAB. Results: Our mathematical model describes accumulation of fat in the liver and predicts changes in lipid fluxes induced by both dietary and drug interventions. The model is validated using data from a wide range of drug and dietary intervention studies and can predict both short-term (days) and long-term (weeks) changes in liver fat. Importantly, the model computes the contribution of each individual lipid flux to the total liver fat dynamics. Furthermore, the model can be combined with an established bodyweight model, to simulate even longer scenarios (years), also including the effects of insulin resistance and body weight. To help prepare for corresponding eHealth applications, we also present a way to visualize the simulated changes, using dynamically changing lipid droplets, seen in images of liver biopsies. Conclusion: In conclusion, we believe that the minimal model presented herein might be a useful tool for future applications, and to further integrate and understand data regarding changes in dietary and drug induced changes in ectopic TAG in the liver. With further development and validation, the minimal model could be used as a disease progression model for steatosis. (c) 2024 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Nuclear transport is an essential part of eukaryotic cell function. Here, we present scFRAP, a model-assisted fluorescent recovery after photobleaching (FRAP)-based method to determine nuclear import and export rates independently in individual live cells. To overcome the inherent noise of single-cell measurements, we performed sequential FRAPs on the same cell. We found large cell-to-cell variation in transport rates within isogenic yeast populations. For passive trans-port, the variability in NPC number might explain most of the variability. Using this approach, we studied mother-daughter cell asymmetry in the active nuclear shuttling of the transcription factor Ace2, which is specifically concentrated in daughter cell nuclei in early G1. Rather than reduced export in the daughter cell, as previously hypothesized, we found that this asymmetry is mainly due to an increased import in daughters. These results shed light on cell-to-cell variation in cellular dynamics and its sources.

BACKGROUND: The increased prevalence of insulin resistance is one of the major health risks in society today. Insulin resistance involves both short-term dynamics, such as altered meal responses, and long-term dynamics, such as the development of type 2 diabetes. Insulin resistance also occurs on different physiological levels, ranging from disease phenotypes to organ-organ communication and intracellular signaling. To better understand the progression of insulin resistance, an analysis method is needed that can combine different timescales and physiological levels. One such method is digital twins, consisting of combined mechanistic mathematical models. We have previously developed a model for short-term glucose homeostasis and intracellular insulin signaling, and there exist long-term weight regulation models. Herein, we combine these models into a first interconnected digital twin for the progression of insulin resistance in humans.

METHODS: The model is based on ordinary differential equations representing biochemical and physiological processes, in which unknown parameters were fitted to data using a MATLAB toolbox. RESULTS: The interconnected twin correctly predicts independent data from a weight increase study, both for weight-changes, fasting plasma insulin and glucose levels, and intracellular insulin signaling. Similarly, the model can predict independent weight-change data in a weight loss study with the weight loss drug topiramate. The model can also predict non-measured variables.

CONCLUSIONS: The model presented herein constitutes the basis for a new digital twin technology, which in the future could be used to aid medical pedagogy and increase motivation and compliance and thus aid in the prevention and treatment of insulin resistance.

BackgroundThe increased prevalence of insulin resistance is one of the major health risks in society today. Insulin resistance involves both short-term dynamics, such as altered meal responses, and long-term dynamics, such as the development of type 2 diabetes. Insulin resistance also occurs on different physiological levels, ranging from disease phenotypes to organ-organ communication and intracellular signaling. To better understand the progression of insulin resistance, an analysis method is needed that can combine different timescales and physiological levels. One such method is digital twins, consisting of combined mechanistic mathematical models. We have previously developed a model for short-term glucose homeostasis and intracellular insulin signaling, and there exist long-term weight regulation models. Herein, we combine these models into a first interconnected digital twin for the progression of insulin resistance in humans.MethodsThe model is based on ordinary differential equations representing biochemical and physiological processes, in which unknown parameters were fitted to data using a MATLAB toolbox.ResultsThe interconnected twin correctly predicts independent data from a weight increase study, both for weight-changes, fasting plasma insulin and glucose levels, and intracellular insulin signaling. Similarly, the model can predict independent weight-change data in a weight loss study with the weight loss drug topiramate. The model can also predict non-measured variables.ConclusionsThe model presented herein constitutes the basis for a new digital twin technology, which in the future could be used to aid medical pedagogy and increase motivation and compliance and thus aid in the prevention and treatment of insulin resistance.

BACKGROUND: Drug induced liver injury (DILI) is a major concern when developing new drugs. A promising biomarker for DILI is the hepatic uptake rate of the contrast agent gadoxetate. This rate can be estimated using a novel approach combining magnetic resonance imaging and mathematical modeling. However, previous work has used different mathematical models to describe liver function in humans or rats, and no comparative study has assessed which model is most optimal to use, or focused on possible translatability between the two species.

AIMS: Our aim was therefore to do a comparison and assessment of models for DILI biomarker assessment, and to develop a conceptual basis for a translational framework between the species.

METHODS AND RESULTS: We first established which of the available pharmacokinetic models to use by identifying the most simple and identifiable model that can describe data from both human and rats. We then developed an extension of this model for how to estimate the effects of a hepatotoxic drug in rats. Finally, we illustrated how such a framework could be useful for drug dosage selection, and how it potentially can be applied in personalized treatments designed to avoid DILI.

CONCLUSION: Our analysis provides clear guidelines of which mathematical model to use for model-based assessment of biomarkers for liver function, and it also suggests a hypothetical path to a translational framework for DILI.

Adipocyte signaling, normally and in type 2 diabetes, is far from fully understood. We have earlier developed detailed dynamic mathematical models for several well-studied, partially overlapping, signaling pathways in adipocytes. Still, these models only cover a fraction of the total cellular response. For a broader coverage of the response, large-scale phosphoproteomic data and systems level knowledge on protein interactions are key. However, methods to combine detailed dynamic models with large-scale data, using information about the confidence of included interactions, are lacking. We have developed a method to first establish a core model by connecting existing models of adipocyte cellular signaling for: (1) lipolysis and fatty acid release, (2) glucose uptake, and (3) the release of adiponectin. Next, we use publicly available phosphoproteome data for the insulin response in adipocytes together with prior knowledge on protein interactions, to identify phosphosites downstream of the core model. In a parallel pairwise approach with low computation time, we test whether identified phosphosites can be added to the model. We iteratively collect accepted additions into layers and continue the search for phosphosites downstream of these added layers. For the first 30 layers with the highest confidence (311 added phosphosites), the model predicts independent data well (70-90% correct), and the predictive capability gradually decreases when we add layers of decreasing confidence. In total, 57 layers (3059 phosphosites) can be added to the model with predictive ability kept. Finally, our large-scale, layered model enables dynamic simulations of systems-wide alterations in adipocytes in type 2 diabetes.

Adipocyte signaling, normally and in type 2 diabetes, is far from fully understood. We have earlier developed detailed dynamic mathematical models for several well-studied, partially overlapping, signaling pathways in adipocytes. Still, these models only cover a fraction of the total cellular response. For a broader coverage of the response, large-scale phosphoproteomic data and systems level knowledge on protein interactions are key. However, methods to combine detailed dynamic models with large-scale data, using information about the confidence of included interactions, are lacking. We have developed a method to first establish a core model by connecting existing models of adipocyte cellular signaling for: (1) lipolysis and fatty acid release, (2) glucose uptake, and (3) the release of adiponectin. Next, we use publicly available phosphoproteome data for the insulin response in adipocytes together with prior knowledge on protein interactions, to identify phosphosites downstream of the core model. In a parallel pairwise approach with low computation time, we test whether identified phosphosites can be added to the model. We iteratively collect accepted additions into layers and continue the search for phosphosites downstream of these added layers. For the first 30 layers with the highest confidence (311 added phosphosites), the model predicts independent data well (70-90% correct), and the predictive capability gradually decreases when we add layers of decreasing confidence. In total, 57 layers (3059 phosphosites) can be added to the model with predictive ability kept. Finally, our large-scale, layered model enables dynamic simulations of systems-wide alterations in adipocytes in type 2 diabetes.

BackgroundLiver cirrhosis, the advanced stage of many chronic liver diseases, is associated with escalated risks of liver-related complications like decompensation and hepatocellular carcinoma (HCC). Morbidity and mortality in cirrhosis patients are linked to portal hypertension, sarcopenia, and hepatocellular carcinoma. Although conventional cirrhosis management centered on treating complications, contemporary approaches prioritize preemptive measures. This study aims to formulate novel blood- and imaging-centric methodologies for monitoring liver cirrhosis patients.MethodsIn this prospective study, 150 liver cirrhosis patients will be enrolled from three Swedish liver clinics. Their conditions will be assessed through extensive blood-based markers and magnetic resonance imaging (MRI). The MRI protocol encompasses body composition profile with Muscle Assement Score, portal flow assessment, magnet resonance elastography, and a abbreviated MRI for HCC screening. Evaluation of lifestyle, muscular strength, physical performance, body composition, and quality of life will be conducted. Additionally, DNA, serum, and plasma biobanking will facilitate future investigations.DiscussionThe anticipated outcomes involve the identification and validation of non-invasive blood- and imaging-oriented biomarkers, enhancing the care paradigm for liver cirrhosis patients. Notably, the temporal evolution of these biomarkers will be crucial for understanding dynamic changes.Trial registrationClinicaltrials.gov, registration identifier NCT05502198. Registered on 16 August 2022. Link: https://classic.clinicaltrials.gov/ct2/show/NCT05502198.

BACKGROUND: Liver cirrhosis, the advanced stage of many chronic liver diseases, is associated with escalated risks of liver-related complications like decompensation and hepatocellular carcinoma (HCC). Morbidity and mortality in cirrhosis patients are linked to portal hypertension, sarcopenia, and hepatocellular carcinoma. Although conventional cirrhosis management centered on treating complications, contemporary approaches prioritize preemptive measures. This study aims to formulate novel blood- and imaging-centric methodologies for monitoring liver cirrhosis patients.

METHODS: In this prospective study, 150 liver cirrhosis patients will be enrolled from three Swedish liver clinics. Their conditions will be assessed through extensive blood-based markers and magnetic resonance imaging (MRI). The MRI protocol encompasses body composition profile with Muscle Assement Score, portal flow assessment, magnet resonance elastography, and a abbreviated MRI for HCC screening. Evaluation of lifestyle, muscular strength, physical performance, body composition, and quality of life will be conducted. Additionally, DNA, serum, and plasma biobanking will facilitate future investigations.

DISCUSSION: The anticipated outcomes involve the identification and validation of non-invasive blood- and imaging-oriented biomarkers, enhancing the care paradigm for liver cirrhosis patients. Notably, the temporal evolution of these biomarkers will be crucial for understanding dynamic changes.

TRIAL REGISTRATION: Clinicaltrials.gov, registration identifier NCT05502198. Registered on 16 August 2022. Link: https://classic. CLINICALTRIALS: gov/ct2/show/NCT05502198 .

Inflammation is one of the vital mechanisms through which the immune system responds to harmful stimuli. During inflammation, pro and anti-inflammatory cytokines interplay to orchestrate fine-tuned, dynamic immune responses. The cytokine interplay governs switches in the inflammatory response and dictates the propagation and development of the inflammatory response. Molecular pathways underlying the interplay are complex, and time-resolved monitoring of mediators and cytokines is necessary as a basis to study them in detail. Our understanding can be advanced by mathematical models which enable to analyze the system of interactions and their dynamical interplay in detail. We, therefore, used a mathematical modeling approach to study the interplay between prominent pro and anti-inflammatory cytokines with a focus on tumor necrosis factor (TNF) and interleukin 10 (IL-10) in lipopolysaccharide (LPS)-primed primary human monocytes. Relevant time-resolved data were generated by experimentally adding or blocking IL-10 at different time points. The model was successfully trained and could predict independent validation data and was further used to perform simulations to disentangle the role of IL-10 feedbacks during an acute inflammatory event. We used the insight to obtain a reduced predictive model including only the necessary IL-10-mediated feedbacks. Finally, the validated reduced model was used to predict early IL-10 - TNF switches in the inflammatory response. Overall, we gained detailed insights into fine-tuning of inflammatory responses in human monocytes and present a model for further use in studying the complex and dynamic process of cytokine-regulated acute inflammation.

Inflammation is one of the vital mechanisms through which the immune system responds to harmful stimuli. During inflammation, proinflammatory and anti-inflammatory cytokines interplay to orchestrate fine-tuned and dynamic immune responses. The cytokine interplay governs switches in the inflammatory response and dictates the propagation and development of the inflammatory response. Molecular pathways underlying the interplay are complex, and time-resolved monitoring of mediators and cytokines is necessary as a basis to study them in detail. Our understanding can be advanced by mathematical models that enable to analyze the system of interactions and their dynamical interplay in detail. We, therefore, used a mathematical modeling approach to study the interplay between prominent proinflammatory and anti-inflammatory cytokines with a focus on tumor necrosis factor and interleukin 10 (IL-10) in lipopolysaccharide-primed primary human monocytes. Relevant time-resolved data were generated by experimentally adding or blocking IL-10 at different time points. The model was successfully trained and could predict independent validation data and was further used to perform simulations to disentangle the role of IL-10 feedbacks during an acute inflammatory event. We used the insight to obtain a reduced predictive model including only the necessary IL-10-mediated feedbacks. Finally, the validated reduced model was used to predict early IL-10–tumor necrosis factor switches in the inflammatory response. Overall, we gained detailed insights into fine-tuning of inflammatory responses in human monocytes and present a model for further use in studying the complex and dynamic process of cytokine-regulated acute inflammation. © 2023 The Authors

Insulin resistance causes compensatory insulin production, which in humans can eventually progress to beta-cell failure and type 2 diabetes (T2D). This disease progression involves multi-scale processes, ranging from intracellular signaling to organ and whole-body level regulations, on timescales from minutes to years. T2D progression is commonly studied using overfed and genetically modified rodents. Available multi-scale data from rodents is too complex to fully comprehend using traditional analysis, not based on mathematical modelling. To help resolve these issues, we here present an in silico mouse model, featuring 38 ordinary differential equations and 78 parameters. This is the first mathematical model that simultaneously explains (chi-square cost=28.1 &lt;51 =cut-off, p = 0.05) multi-scale mouse insulin resistance data on all three levels - cells, organs, body - ranging from minutes to months. The model predicts new independent multi-scale simulations, on e.g., weight and meal response changes, which are corroborated by our own new experimental data. The thus validated model provides insights and non-trivial predictions regarding complex non-measured processes, such as the relation between insulin resistance and insulin-dependent glucose uptake for adipose tissue. Finally, we add a beta-cell failure module to the in silico mouse model to simulate different human-like scenarios of progression towards T2D. In summary, our in silico mouse model is an extendable and interactive knowledge-base for the study of T2D, which could help simulate treatment scenarios in rodents and translate results to the human situation.

Author summaryThe neurovascular coupling (NVC) is the basis for functional magnetic resonance imaging (fMRI), since the NVC connects neural activity with the observed hemodynamic changes. This connection is highly complex, which warrants a model-based analysis. However, even though NVC-data from several species and many relevant variables are available, a mathematical model for all these data is still missing. Herein, we combine experimental data from mice, monkeys, and humans, to develop a comprehensive model for NVC. Importantly, our new approach to modelling propagates the qualitative insights from each species to the subsequent analysis of data from other species. In mice, we unravel the role of different neuronal sub-populations when producing a biphasic response to prolonged sensory stimulations. The qualitative role of these sub-populations is preserved when analysing primate data. These primate data add knowledge on the interplay between local field potential (LFP) and vascular changes. Similarly, these pre-clinical qualitative insights are propagated to analysis of human data, which contain additional insights regarding blood flow and volume in arterioles and venules, during both positive and negative responses. This work illustrates how data with complementary information from different species can be combined, so that qualitative insights from animals are preserved in the quantitative analysis of human data. Neurons regulate the activity of blood vessels through the neurovascular coupling (NVC). A detailed understanding of the NVC is critical for understanding data from functional imaging techniques of the brain. Many aspects of the NVC have been studied both experimentally and using mathematical models; various combinations of blood volume and flow, local field potential (LFP), hemoglobin level, blood oxygenation level-dependent response (BOLD), and optogenetics have been measured and modeled in rodents, primates, or humans. However, these data have not been brought together into a unified quantitative model. We now present a mathematical model that describes all such data types and that preserves mechanistic behaviors between experiments. For instance, from modeling of optogenetics and microscopy data in mice, we learn cell-specific contributions; the first rapid dilation in the vascular response is caused by NO-interneurons, the main part of the dilation during longer stimuli is caused by pyramidal neurons, and the post-peak undershoot is caused by NPY-interneurons. These insights are translated and preserved in all subsequent analyses, together with other insights regarding hemoglobin dynamics and the LFP/BOLD-interplay, obtained from other experiments on rodents and primates. The model can predict independent validation-data not used for training. By bringing together data with complementary information from different species, we both understand each dataset better, and have a basis for a new type of integrative analysis of human data.

Type 2 diabetes (T2D) and hypertension increase the risk of cardiovascular diseases mediated by whole-body changes to metabolism, cardiovascular structure and haemodynamics. The haemodynamic changes related to hypertension and T2D are complex and subject-specific, however, and not fully understood. We aimed to investigate the haemodynamic mechanisms in T2D and hypertension by comparing the haemodynamics between healthy controls and subjects with T2D, hypertension, or both. For all subjects, we combined 4D flow magnetic resonance imaging data, brachial blood pressure and a cardiovascular mathematical model to create a comprehensive subject-specific analysis of central haemodynamics. When comparing the subject-specific haemodynamic parameters between the four groups, the predominant haemodynamic difference is impaired left ventricular relaxation in subjects with both T2D and hypertension compared to subjects with only T2D, only hypertension and controls. The impaired relaxation indicates that, in this cohort, the long-term changes in haemodynamic load of co-existing T2D and hypertension cause diastolic dysfunction demonstrable at rest, whereas either disease on its own does not. However, through subject-specific predictions of impaired relaxation, we show that altered relaxation alone is not enough to explain the subject-specific and group-related differences; instead, a combination of parameters is affected in T2D and hypertension. These results confirm previous studies that reported more adverse effects from the combination of T2D and hypertension compared to either disease on its own. Furthermore, this shows the potential of personalized cardiovascular models in providing haemodynamic mechanistic insights and subject-specific predictions that could aid in the understanding and treatment planning of patients with T2D and hypertension.

Microphysiological systems (MPS) are powerful tools for emulating human physiology and replicating disease progression in vitro. MPS could be better predictors of human outcome than current animal models, but mechanistic interpretation and in vivo extrapolation of the experimental results remain significant challenges. Here, we address these challenges using an integrated experimental-computational approach. This approach allows for in silico representation and predictions of glucose metabolism in a previously reported MPS with two organ compartments (liver and pancreas) connected in a closed loop with circulating medium. We developed a computational model describing glucose metabolism over 15 days of culture in the MPS. The model was calibrated on an experiment-specific basis using data from seven experiments, where HepaRG single-liver or liver-islet cultures were exposed to both normal and hyperglycemic conditions resembling high blood glucose levels in diabetes. The calibrated models reproduced the fast (i.e. hourly) variations in glucose and insulin observed in the MPS experiments, as well as the long-term (i.e. over weeks) decline in both glucose tolerance and insulin secretion. We also investigated the behaviour of the system under hypoglycemia by simulating this condition in silico, and the model could correctly predict the glucose and insulin responses measured in new MPS experiments. Last, we used the computational model to translate the experimental results to humans, showing good agreement with published data of the glucose response to a meal in healthy subjects. The integrated experimental-computational framework opens new avenues for future investigations toward disease mechanisms and the development of new therapies for metabolic disorders.

Adipocyte cellular signaling, normally and in type 2 diabetes, is far from fully studied. We have earlier developed detailed dynamic mathematical models for some well-studied, and partially overlapping, signaling pathways in adipocytes. Still, these models only cover a fraction of the total cellular response. For a broader coverage of the response, large-scale phosphoproteomic data is key. There exists such data for the insulin response of adipocytes, as well as prior knowledge on possible protein-protein interactions associated with a confidence level. However, methods to combine detailed dynamic models with large-scale data, using information about the confidence of included interactions, are lacking. In our new method, we first establish a core model by connecting our partially overlapping models of adipocyte cellular signaling with focus on: 1) lipolysis and fatty acid release, 2) glucose uptake, and 3) the release of adiponectin. We use the phosphoproteome data and prior knowledge to identify phosphosites adjacent to the core model, and then try to add the adjacent phosphosites to the model. The additions of the adjacent phosphosites is tested in a parallel, pairwise approach with low computation time. We then iteratively collect the accepted additions into a layer, and use the newly added layer to find new adjacent phosphosites. We find that the first 15 layers (60 added phosphosites) with the highest confidence can correctly predict independent inhibitor-data (70-90 % correct), and that this ability decrease when we add layers of decreasing confidence. In total, 60 layers (3926 phosphosites) can be added to the model and still keep predictive ability. Finally, we use the comprehensive adipocyte model to simulate systems-wide alterations in adipocytes in type 2 diabetes. This new method provide a tool to create large models that keeps track of varying confidence.Competing Interest StatementThe authors have declared no competing interest.

Today, there is great interest in diets proposing new combinations of macronutrient compositions and fasting schedules. Unfortunately, there is little consensus regarding the impact of these different diets, since available studies measure different sets of variables in different populations, thus only providing partial, non-connected insights. We lack an approach for integrating all such partial insights into a useful and interconnected big picture. Herein, we present such an integrating tool. The tool uses a novel mathematical model that describes mechanisms regulating diet response and fasting metabolic fluxes, both for organ-organ crosstalk, and inside the liver. The tool can mechanistically explain and integrate data from several clinical studies, and correctly predict new independent data, including data from a new study. Using this model, we can predict non-measured variables, e.g. hepatic glycogen and gluconeogenesis, in response to fasting and different diets. Furthermore, we exemplify how such metabolic responses can be successfully adapted to a specific individuals sex, weight, height, as well as to the individuals historical data on metabolite dynamics. This tool enables an offline digital twin technology.

Accurate measurements of metabolic fluxes in living cells are central to metabolism research and metabolic engineering. The gold standard method is model-based metabolic flux analysis (MFA), where fluxes are estimated indirectly from mass isotopomer data with the use of a mathematical model of the metabolic network. A critical step in MFA is model selection: choosing what compartments, metabolites, and reactions to include in the metabolic network model. Model selection is often done informally during the modelling process, based on the same data that is used for model fitting (estimation data). This can lead to either overly complex models (overfitting) or too simple ones (underfitting), in both cases resulting in poor flux estimates. Here, we propose a method for model selection based on independent validation data. We demonstrate in simulation studies that this method consistently chooses the correct model in a way that is independent on errors in measurement uncertainty. This independence is beneficial, since estimating the true magnitude of these errors can be difficult. In contrast, commonly used model selection methods based on the chi(2)-test choose different model structures depending on the believed measurement uncertainty; this can lead to errors in flux estimates, especially when the magnitude of the error is substantially off. We present a new approach for quantification of prediction uncertainty of mass isotopomer distributions in other labelling experiments, to check for problems with too much or too little novelty in the validation data. Finally, in an isotope tracing study on human mammary epithelial cells, the validation-based model selection method identified pyruvate carboxylase as a key model component. Our results argue that validation-based model selection should be an integral part of MFA model development.

The neurovascular and neurometabolic couplings (NVC and NMC) connect cerebral activity, blood flow, and metabolism. This interconnection is used in for instance functional imaging, which analyses the blood-oxygen-dependent (BOLD) signal. The mechanisms underlying the NVC are complex, which warrants a model-based analysis of data. We have previously developed a mechanistically detailed model for the NVC, and others have proposed detailed models for cerebral metabolism. However, existing metabolic models are still not fully utilizing available magnetic resonance spectroscopy (MRS) data and are not connected to detailed models for NVC. Therefore, we herein present a new model that integrates mechanistic modelling of both MRS and BOLD data. The metabolic model covers central metabolism, using a minimal set of interactions, and can describe time-series data for glucose, lactate, aspartate, and glutamate, measured after visual stimuli. Statistical tests confirm that the model can describe both estimation data and predict independent validation data, not used for model training. The interconnected NVC model can simultaneously describe BOLD data and can be used to predict expected metabolic responses in experiments where metabolism has not been measured. This model is a step towards a useful and mechanistically detailed model for cerebral blood flow and metabolism, with potential applications in both basic research and clinical applications. Author summary The neurovascular and neurometabolic couplings are highly central for several clinical imaging techniques since these frequently use blood oxygenation (the BOLD signal) as a proxy for neuronal activity. This relationship is described by the highly complex neurovascular and neurometabolic couplings, which describe the balancing between increased metabolic demand and blood flow, and which involve several cell types and regulatory systems, which all change dynamically over time. While there are previous works that describe the neurovascular coupling in detail, neither we nor others have developed connections to corresponding mechanistic models for the third aspect, the metabolic aspect. Furthermore, magnetic resonance spectroscopy (MRS) data for such modelling readily is available. In this paper we present a minimal mechanistic model that can describe the metabolic response to visual stimuli. The model is trained to describe experimental data for the relative change in metabolic concentrations of several metabolites in the visual cortex during stimulation. The model is also validated against independent validation data, that was not used for model training. Finally, we also connect this metabolic model to a detailed mechanistic model of the neurovascular coupling. Showing that the model can describe both the metabolic response and a neurovascular response simultaneously.

Glucose homeostasis is the tight control of glucose in the blood. This complex control is important, due to its malfunction in serious diseases like diabetes, and not yet sufficiently understood. Due to the involvement of numerous organs and sub-systems, each with their own intra-cellular control, we have developed a multi-level mathematical model, for glucose homeostasis, which integrates a variety of data. Over the last 10 years, this model has been used to insert new insights from the intra-cellular level into the larger whole-body perspective. However, the original cell-organ-body translation has during these years never been updated, despite several critical shortcomings, which also have not been resolved by other modeling efforts. For this reason, we here present an updated multi-level model. This model provides a more accurate sub-division of how much glucose is being taken up by the different organs. Unlike the original model, we now also account for the different dynamics seen in the different organs. The new model also incorporates the central impact of blood flow on insulin-stimulated glucose uptake. Each new improvement is clear upon visual inspection, and they are also supported by statistical tests. The final multi-level model describes &gt;300 data points in &gt;40 time-series and dose-response curves, resulting from a large variety of perturbations, describing both intra-cellular processes, organ fluxes, and whole-body meal responses. We hope that this model will serve as an improved basis for future data integration, useful for research and drug developments within diabetes.

Stroke is an example of a complex and multi-factorial disease involving multiple organs, timescales, and disease mechanisms. To deal with this complexity, and to realize Precision Medicine of stroke, mathematical models are needed. Such approaches include: 1) machine learning, 2) bioinformatic network models, and 3) mechanistic models. Since these three approaches have complementary strengths and weaknesses, a hybrid modelling approach combining them would be the most beneficial. However, no concrete approach ready to be implemented for a specific disease has been presented to date. In this paper, we both review the strengths and weaknesses of the three approaches, and propose a roadmap for hybrid modelling in the case of stroke care. We focus on two main tasks needed for the clinical setting: a) For stroke risk calculation, we propose a new two-step approach, where non-linear mixed effects models and bioinformatic network models yield biomarkers which are used as input to a machine learning model and b) For simulation of care scenarios, we propose a new four-step approach, which revolves around iterations between simulations of the mechanistic models and imputations of non-modelled or non-measured variables. We illustrate and discuss the different approaches in the context of Precision Medicine for stroke.

Lipolysis and the release of fatty acids to supply energy fuel to other organs, such as between meals, during exercise, and starvation, are fundamental functions of the adipose tissue. The intracellular lipolytic pathway in adipocytes is activated by adrenaline and noradrenaline, and inhibited by insulin. Circulating fatty acids are elevated in type 2 diabetic individuals. The mechanisms behind this elevation are not fully known, and to increase the knowledge a link between the systemic circulation and intracellular lipolysis is key. However, data on lipolysis and knowledge from in vitro systems have not been linked to corresponding in vivo data and knowledge in vivo. Here, we use mathematical modelling to provide such a link. We examine mechanisms of insulin action by combining in vivo and in vitro data into an integrated mathematical model that can explain all data. Furthermore, the model can describe independent data not used for training the model. We show the usefulness of the model by simulating new and more challenging experimental setups in silico, e.g. the extracellular concentration of fatty acids during an insulin clamp, and the difference in such simulations between individuals with and without type 2 diabetes. Our work provides a new platform for model-based analysis of adipose tissue lipolysis, under both non-diabetic and type 2 diabetic conditions.

Circulating levels of the adipocyte hormone adiponectin are typically reduced in obesity, and this deficiency has been linked to metabolic diseases. It is thus important to understand the mechanisms controlling adiponectin exocytosis. This understanding is hindered by the high complexity of both the available data and the underlying signaling network. To deal with this complexity, we have previously investigated how different intracellular concentrations of Ca2+, cAMP, and ATP affect adiponectin exocytosis, using both patch-clamp recordings and systems biology mathematical modeling. Recent work has shown that adiponectin exocytosis is physiologically triggered via signaling pathways involving adrenergic beta(3) receptors (beta(3)ARs). Therefore, we developed a mathematical model that also includes adiponectin exocytosis stimulated by extracellular epinephrine or the beta(3)AR agonist CL 316243. Our new model is consistent with all previous patch-clamp data as well as new data (collected from stimulations with a combination of the intracellular mediators and extracellular adrenergic stimuli) and can predict independent validation data. We used this model to perform new in silico experiments where corresponding wet lab experiments would be difficult to perform. We simulated adiponectin exocytosis in single cells in response to the reduction of beta(3)ARs that is observed in adipocytes from animals with obesity-induced diabetes. Finally, we used our model to investigate intracellular dynamics and to predict both cAMP levels and adiponectin release by scaling the model from single-cell to a population of cells-predictions corroborated by experimental data. Our work brings us one step closer to understanding the intricate regulation of adiponectin exocytosis.

BackgroundNon-alcoholic fatty liver disease (NAFLD) affects 20-30% of the general adult population. NAFLD patients with type 2 diabetes mellitus (T2DM) are at an increased risk of advanced fibrosis, which puts them at risk of cardiovascular complications, hepatocellular carcinoma, or liver failure. Liver biopsy is the gold standard for assessing hepatic fibrosis. However, its utility is inherently limited. Consequently, the prevalence and characteristics of T2DM patients with advanced fibrosis are unknown. Therefore, the purpose of the current study is to evaluate the prevalence and severity of NAFLD in patients with T2DM by recruiting participants from primary care, using the latest imaging modalities, to collect a cohort of well phenotyped patients.MethodsWe will prospectively recruit 400 patients with T2DM using biomarkers to assess their status. Specifically, we will evaluate liver fat content using magnetic resonance imaging (MRI); hepatic fibrosis using MR elastography and vibration-controlled transient elastography; muscle composition and body fat distribution using water-fat separated whole body MRI; and cardiac function, structure, and tissue characteristics, using cardiovascular MRI.DiscussionWe expect that the study will uncover potential mechanisms of advanced hepatic fibrosis in NAFLD and T2DM and equip the clinician with better diagnostic tools for the care of T2DM patients with NAFLD.Trial registration: Clinicaltrials.gov, identifier NCT03864510. Registered 6 March 2019, https://clinicaltrials.gov/ct2/show/NCT03864510.

BACKGROUND AND AIMS: Accurate biomarkers for quantifying liver fibrosis are important for clinical practice and trial end-points. We compared the diagnostic performance of magnetic resonance imaging (MRI), including gadoxetate-enhanced MRI and ³¹P-MR spectroscopy, with fibrosis stage and serum fibrosis algorithms in a clinical setting. Also, in a subset of patients, MR- and transient elastography (MRE and TE) was evaluated when available.

METHODS: Patients were recruited prospectively if they were scheduled to undergo liver biopsy on a clinical indication due to elevated liver enzyme levels without decompensated cirrhosis. Within a month of the clinical work-up, an MR-examination and liver needle biopsy were performed on the same day. Based on late-phase gadoxetate-enhanced MRI, a mathematical model calculated hepatobiliary function (relating to OATP1 and MRP2). The hepatocyte gadoxetate uptake rate (K_Hep) and the normalised liver-to-spleen contrast ratio (LSC_N10) were also calculated. Nine serum fibrosis algorithms were investigated (GUCI, King's Score, APRI, FIB-4, Lok-Index, NIKEI, NASH-CRN regression score, Forns' score, and NAFLD-fibrosis score).

RESULTS: The diagnostic performance (AUROC) for identification of significant fibrosis (F2-4) was 0.78, 0.80, 0.69, and 0.78 for MRE, TE, LSC_N10, and GUCI, respectively. For the identification of advanced fibrosis (F3-4), the AUROCs were 0.93, 0.84, 0.81, and 0.82 respectively.

CONCLUSION: MRE and TE were superior for non-invasive identification of significant fibrosis. Serum fibrosis algorithms developed for specific liver diseases are applicable in this cohort of diverse liver diseases aetiologies. Gadoxetate-MRI was sufficiently sensitive to detect the low function losses associated with fibrosis. None was able to efficiently distinguish between stages within the low fibrosis stages.Lay summaryExcessive accumulation of scar tissue, fibrosis, in the liver is an important aspect in chronic liver disease. To replace the invasive needle biopsy, we have explored non-invasive methods to assess liver fibrosis. In our study we found that elastographic methods, which assess the mechanical properties of the liver, are superior in assessing fibrosis in a clinical setting. Of interest from a clinical trial point-of-view, none of the tested methods was sufficiently accurate to distinguish between adjacent moderate fibrosis stages.

Both initiation and suppression of inflammation are hallmarks of the immune response. If not balanced, the inflammation may cause extensive tissue damage, which is associated with common diseases, e.g., asthma and atherosclerosis. Anti-inflammatory drugs come with side effects that may be aggravated by high and fluctuating drug concentrations. To remedy this, an anti-inflammatory drug should have an appropriate pharmacokinetic half-life or better still, a sustained anti-inflammatory drug response. However, we still lack a quantitative mechanistic understanding of such sustained effects. Here, we study the anti-inflammatory response to a common glucocorticoid drug, dexamethasone. We find a sustained response 22 hours after drug removal. With hypothesis testing using mathematical modeling, we unravel the underlying mechanism-a slow release of dexamethasone from the receptor-drug complex. The developed model is in agreement with time-resolved training and testing data and is used to simulate hypothetical treatment schemes. This work opens up for a more knowledge-driven drug development to find sustained anti-inflammatory responses and fewer side effects.

The neurovascular coupling (NVC) connects neuronal activity to hemodynamic responses in the brain. This connection is the basis for the interpretation of functional magnetic resonance imaging data. Despite the central role of this coupling, we lack detailed knowledge about cell-specific contributions and our knowledge about NVC is mainly based on animal experiments performed during anesthesia. Anesthetics are known to affect neuronal excitability, but how this affects the vessel diameters is not known. Due to the high complexity of NVC data, mathematical modeling is needed for a meaningful analysis. However, neither the relevant neuronal subtypes nor the effects of anesthetics are covered by current models. Here, we present a mathematical model including GABAergic interneurons and pyramidal neurons, as well as the effect of an anesthetic agent. The model is consistent with data from optogenetic experiments from both awake and anesthetized animals, and it correctly predicts data from experiments with different pharmacological modulators. The analysis suggests that no downstream anesthetic effects are necessary if one of the GABAergic interneuron signaling pathways include a Michaelis-Menten expression. This is the first example of a quantitative model that includes both the cell-specific contributions and the effect of an anesthetic agent on the NVC.

Estimation of liver function is important to monitor progression of chronic liver disease (CLD). A promising method is magnetic resonance imaging (MRI) combined with gadoxetate, a liver-specific contrast agent. For this method, we have previously developed a model for an average healthy human. Herein, we extended this model, by combining it with a patient-specific non-linear mixed-effects modeling framework. We validated the model by recruiting 100 patients with CLD of varying severity and etiologies. The model explained all MRI data and adequately predicted both timepoints saved for validation and gadoxetate concentrations in both plasma and biopsies. The validated model provides a new and deeper look into how the mechanisms of liver function vary across a wide variety of liver diseases. The basic mechanisms remain the same, but increasing fibrosis reduces uptake and increases excretion of gadoxetate. These mechanisms are shared across many liver functions and can now be estimated from standard clinical images.

Author summary

Being able to accurately and reliably estimate liver function is important when monitoring the progression of patients with liver disease, as well as when identifying drug-induced liver injury during drug development. A promising method for quantifying liver function is to use magnetic resonance imaging combined with gadoxetate. Gadoxetate is a liver-specific contrast agent, which is taken up by the hepatocytes and excreted into the bile. We have previously developed a mechanistic model for gadoxetate dynamics using averaged data from healthy volunteers. In this work, we extended our model with a non-linear mixed-effects modeling framework to give patient-specific estimates of the gadoxetate transport-rates. We validated the model by recruiting 100 patients with liver disease, covering a range of severity and etiologies. All patients underwent an MRI-examination and provided both blood and liver biopsies. Our validated model provides a new and deeper look into how the mechanisms of liver function varies across a wide variety of liver diseases. The basic mechanisms remain the same, but increasing fibrosis reduces uptake and increases excretion of gadoxetate.

Background: The possibility of non-invasively assessing load-independent parameters characterizing cardiac function is of high clinical value. Typically, these parameters are assessed during resting conditions. However, for diagnostic purposes, the parameter behavior across a physiologically relevant range of heart rate and loads is more relevant than the isolated measurements performed at rest. This study sought to evaluate changes in non-invasive estimations of load-independent parameters of left-ventricular contraction and relaxation patterns at rest and during dobutamine stress. Methods: We applied a previously developed approach that combines non-invasive measurements with a physiologically-based, reduced-order model of the cardiovascular system to provide subject-specific estimates of parameters characterizing left ventricular function. In this model, the contractile state of the heart at each time point along the cardiac cycle is modeled using a time-varying elastance curve. Non-invasive data, including four-dimensional magnetic resonance imaging (4D Flow MRI) measurements, were acquired in nine subjects without a known heart disease at rest and during dobutamine stress. For each of the study subjects, we constructed two personalized models corresponding to the resting and the stress state. Results: Applying the modeling framework, we identified significant increases in the left ventricular contraction rate constant [from 1.5 +/- 0.3 to 2 +/- 0.5 (p = 0.038)] and relaxation constant [from 37.2 +/- 6.9 to 46.1 +/- 12 (p = 0.028)]. In addition, we found a significant decrease in the elastance diastolic time constant from 0.4 +/- 0.04 s to 0.3 +/- 0.03 s = 0.008). Conclusions: The integrated image-modeling approach allows the assessment of cardiovascular function given as model-based parameters. The agreement between the estimated parameter values and previously reported effects of dobutamine demonstrates the potential of the approach to assess advanced metrics of pathophysiology that are otherwise difficult to obtain non-invasively in clinical practice.

Type 2 diabetes is characterized by insulin resistance, which arises from malfunctions in the intracellular insulin signaling network. Knowledge of the insulin signaling network is fragmented, and because of the complexity of this network, little consensus has emerged for the structure and importance of the different branches of the network. To help overcome this complexity, systems biology mathematical models have been generated for predicting both the activation of the insulin receptor (IR) and the redistribution of glucose transporter 4 (GLUT4) to the plasma membrane. Although the insulin signal transduction between IR and GLUT4 has been thoroughly studied with modeling and time-resolved data in human cells, comparable analyses in cells from commonly used model organisms such as rats and mice are lacking. Here, we combined existing data and models for rat adipocytes with new data collected for the signaling network between IR and GLUT4 to create a model also for their interconnections. To describe all data (amp;gt;140 data points), the model needed three distinct pathways from IR to GLUT4: (i) via protein kinase B (PKB) and Akt substrate of 160 kDa (AS160), (ii) via an AS160-independent pathway from PKB, and (iii) via an additional pathway from IR, e.g. affecting the membrane constitution. The developed combined model could describe data not used for training the model and was used to generate predictions of the relative contributions of the pathways from IR to translocation of GLUT4. The combined model provides a systems-level understanding of insulin signaling in rat adipocytes, which, when combined with corresponding models for human adipocytes, may contribute to model-based drug development for diabetes.

Lumped parameter models of the cardiovascular system have the potential to assist researchers and clinicians to better understand cardiovascular function. The value of such models increases when they are subject specific. However, most approaches to personalize lumped parameter models have thus far required invasive measurements or fall short of being subject specific due to a lack of the necessary clinical data. Here, we propose an approach to personalize parameters in a model of the heart and the systemic circulation using exclusively non-invasive measurements. The personalized model is created using flow data from four-dimensional magnetic resonance imaging and cuff pressure measurements in the brachial artery. We term this personalized model the cardiovascular avatar. In our proof-of-concept study, we evaluated the capability of the avatar to reproduce pressures and flows in a group of eight healthy subjects. Both quantitatively and qualitatively, the model-based results agreed well with the pressure and flow measurements obtained in vivo for each subject. This non-invasive and personalized approach can synthesize medical data into clinically relevant indicators of cardiovascular function, and estimate hemodynamic variables that cannot be assessed directly from clinical measurements.

The molecular mechanisms of insulin resistance in Type 2 diabetes have been extensively studied in primary human adipocytes, and mathematical modelling has clarified the central role of attenuation of mammalian target of rapamycin (mTOR) complex 1 (mTORC1) activity in the diabetic state. Attenuation of mTORC1 in diabetes quells insulin-signalling network-wide, except for the mTOR in complex 2 (mTORC2)-catalysed phosphorylation of protein kinase B (PKB) at Ser(473) (PKB-S473P), which is increased. This unique increase could potentially be explained by feedback and interbranch cross-talk signals. To examine if such mechanisms operate in adipocytes, we herein analysed data from an unbiased phosphoproteomic screen in 3T3-L1 adipocytes. Using a mathematical modelling approach, we showed that a negative signal from mTORC1-p70 S6 kinase (S6K) to rictor-mTORC2 in combination with a positive signal from PKB to SIN1-mTORC2 are compatible with the experimental data. This combined cross-branch signalling predicted an increased PKB-S473P in response to attenuation of mTORC1 - a distinguishing feature of the insulin resistant state in human adipocytes. This aspect of insulin signalling was then verified for our comprehensive model of insulin signalling in human adipocytes. Introduction of the cross-branch signals was compatible with all data for insulin signalling in human adipocytes, and the resulting model can explain all data network-wide, including the increased PKB-S473P in the diabetic state. Our approach was to first identify potential mechanisms in data from a phosphoproteomic screen in a cell line, and then verify such mechanisms in primary human cells, which demonstrates how an unbiased approach can support a direct knowledge-based study.

Recent technological advancements have made time-resolved, quantitative, multi-omics data available for many model systems, which could be integrated for systems pharmacokinetic use. Here, we present large-scale simulation modeling (LASSIM), which is a novel mathematical tool for performing large-scale inference using mechanistically defined ordinary differential equations (ODE) for gene regulatory networks (GRNs). LASSIM integrates structural knowledge about regulatory interactions and non-linear equations with multiple steady state and dynamic response expression datasets. The rationale behind LASSIM is that biological GRNs can be simplified using a limited subset of core genes that are assumed to regulate all other gene transcription events in the network. The LASSIM method is implemented as a general-purpose toolbox using the PyGMO Python package to make the most of multicore computers and high performance clusters, and is available at https://gitlab.com/Gustafsson-lab/lassim. As a method, LASSIM works in two steps, where it first infers a non-linear ODE system of the pre-specified core gene expression. Second, LASSIM in parallel optimizes the parameters that model the regulation of peripheral genes by core system genes. We showed the usefulness of this method by applying LASSIM to infer a large-scale non-linear model of naive Th2 cell differentiation, made possible by integrating Th2 specific bindings, time-series together with six public and six novel siRNA-mediated knock-down experiments. ChIP-seq showed significant overlap for all tested transcription factors. Next, we performed novel time-series measurements of total T-cells during differentiation towards Th2 and verified that our LASSIM model could monitor those data significantly better than comparable models that used the same Th2 bindings. In summary, the LASSIM toolbox opens the door to a new type of model-based data analysis that combines the strengths of reliable mechanistic models with truly systems-level data. We demonstrate the power of this approach by inferring a mechanistically motivated, genome-wide model of the Th2 transcription regulatory system, which plays an important role in several immune related diseases.

It is possible to estimate hepatic triglyceride content by calculating the proton density fat fraction (PDFF), using proton magnetic resonance spectroscopy (less thansuperscriptgreater than1less than/superscriptgreater thanH-MRS), instead of collecting and analyzing liver biopsies to detect steatosis. However, the current PDFF cut-off value (5%) used to define steatosis by magnetic resonance was derived from studies that did not use histopathology as the reference standard. We performed a prospective study to determine the accuracy of less thansuperscriptgreater than1less than/superscriptgreater thanH-MRS PDFF in measurement of steatosis using histopathology analysis as the standard. We collected clinical, serologic, less thansuperscriptgreater than1less than/superscriptgreater thanH-MRS PDFF, and liver biopsy data from 94 adult patients with increased levels of liver enzymes (6 months or more) referred to the Department of Gastroenterology and Hepatology at Linköping University Hospital in Sweden from 2007 through 2014. Steatosis was graded using the conventional histopathology method and fat content was quantified in biopsy samples using stereological point counts (SPCs). We correlated less thansuperscriptgreater than1less than/superscriptgreater thanH-MRS PDFF findings with SPCs (r = 0.92; P less than.001). less thansuperscriptgreater than1less than/superscriptgreater thanH-MRS PDFF results correlated with histopathology results (ρ = 0.87; P less than.001), and SPCs correlated with histopathology results (ρ = 0.88; P less than.001). All 25 subjects with PDFF values of 5.0% or more had steatosis based on histopathology findings (100% specificity for PDFF). However, of 69 subjects with PDFF values below 5.0% (negative result), 22 were determined to have steatosis based on histopathology findings (53% sensitivity for PDFF). Reducing the PDFF cut-off value to 3.0% identified patients with steatosis with 100% specificity and 79% sensitivity; a PDFF cut-off value of 2.0% identified patients with steatosis with 94% specificity and 87% sensitivity. These findings might be used to improve non-invasive detection of steatosis.

Pharmaceutical induction of metabolically active beige adipocytes in the normally energy storing white adipose tissue has potential to reduce obesity. Mitochondrial uncoupling in beige adipocytes, as in brown adipocytes, has been reported to occur via the uncoupling protein 1 (UCP1). However, several previous in vitro characterizations of human beige adipocytes have only measured UCP1 mRNA fold increase, and assumed a direct correlation with metabolic activity. Here, we provide an example of pharmaceutical induction of beige adipocytes, where increased mRNA levels of UCP1 are not translated into increased protein levels, and perform a thorough analysis of this example. We incorporate mRNA and protein levels of UCP1, time-resolved mitochondrial characterizations, and numerous perturbations, and analyze all data with a new fit-for-purpose mathematical model. The systematic analysis challenges the seemingly obvious experimental conclusion, i.e., that UCP1 is not active in the induced cells, and shows that hypothesis testing with iterative modeling and experimental work is needed to sort out the role of UCP1. The analyses demonstrate, for the first time, that the uncoupling capability of human beige adipocytes can be obtained without UCP1 activity. This finding thus opens the door to a new direction in drug discovery that targets obesity and its associated comorbidities. Furthermore, the analysis advances our understanding of how to evaluate UCP1-independent thermogenesis in human beige adipocytes.

Recent and rapidly evolving progress on high-throughput measurement techniques and computational performance has led to the emergence of new disciplines, such as systems medicine and translational systems biology. At the core of these disciplines lies the desire to produce multiscale models: mathematical models that integrate multiple scales of biological organization, ranging from molecular, cellular and tissue models to organ, whole-organism and population scale models. Using such models, hypotheses can systematically be tested. In this review, we present state-of-the-art multiscale modelling of bacterial and fungal infections, considering both the pathogen and host as well as their interaction. Multiscale modelling of the interactions of bacteria, especially Mycobacterium tuberculosis, with the human host is quite advanced. In contrast, models for fungal infections are still in their infancy, in particular regarding infections with the most important human pathogenic fungi, Candida albicans and Aspergillus fumigatus. We reflect on the current availability of computational approaches for multiscale modelling of host-pathogen interactions and point out current challenges. Finally, we provide an outlook for future requirements of multiscale modelling.

Functional magnetic resonance imaging (fMRI) of hemodynamic changes captured in the blood oxygen level-dependent (BOLD) response contains information of brain activity. The BOLD response is the result of a complex neurovascular coupling and comes in at least two fundamentally different forms: a positive and a negative deflection. Because of the complexity of the signaling, mathematical modelling can provide vital help in the data analysis. For the positive BOLD response, there are plenty of mathematical models, both physiological and phenomenological. However, for the negative BOLD response, no physiologically based model exists. Here, we expand our previously developed physiological model with the most prominent mechanistic hypothesis for the negative BOLD response: the neural inhibition hypothesis. The model was trained and tested on experimental data containing both negative and positive BOLD responses from two studies: 1) a visual-motor task and 2) a workin-gmemory task in conjunction with administration of the tranquilizer diazepam. Our model was able to predict independent validation data not used for training and provides a mechanistic underpinning for previously observed effects of diazepam. The new model moves our understanding of the negative BOLD response from qualitative reasoning to a quantitative systems-biology level, which can be useful both in basic research and in clinical use.

One of the most important properties of a mathematical model is the abilityto make predictions: to predict that which has not yet been measured. Suchpredictions can sometimes be obtained from a simple simulation, but that requiresthat the parameters in the model are known from before. In biology, theparameters are usually both not known from before and not identifiable, i.e.the parameter values cannot be determined uniquely from available data. Insuch cases of unidentifiability, the space of acceptable parameters is large, ofteninfinite in certain directions. For such large spaces, sampling-based approachesthat try to characterize the entire space have difficulties. Recently, a new type ofalternative approaches that circumvent this characterization problem has beenproposed: where one only searches those directions in the space of acceptable parametersthat are relevant for the uncertainty of a particular prediction. In thisreview chapter, these recently proposed methods are compared and contrasted,both regarding theoretical properties, and regarding user experience. The focusis on methods from the field of systems biology, but also methods from biostatistics,pharmacodynamics, and biochemometrics are discussed. The hope is thatthis review will increase the usefulness and understanding of already proposedmethods, and thereby help foster a tradition where predictions only are deemedinteresting if their uncertainties have been determined.

Parameter estimation – the assignment of values to the parameters in a model – is an important and time-consuming task in computational biology. Recent computational and algorithmic developments have provided novel tools to improve this estimation step. One of these improvements concerns the optimization step, where the parameter space is explored to find interesting regions. In this chapter we review the parameter estimation problem, with a special emphasis on the associated optimization methods. In relation to this, we also provide concepts and tools to help you select the appropriate methodology for a specific scenario.

Introduction

Over the past decades, several different non-invasive methods for staging hepatic fibrosis have been proposed. One such method is dynamic contrast enhanced MRI (DCE-MRI) using the contrast agent (CA) Gd-EOB-DTPA. Gd-EOB-DTPA is liver specific, which means that it is taken up specifically by the hepatocytes via the OATP3B1/B3 transporters and excreted into the bile via the MRP2 transporter. Several studies have shown that DCE-MRI and Gd-EOBDTPA can separate patients with advanced (F3-F4) from mild (F0-F2) hepatic fibrosis by measuring the signal intensity, where patients with advanced fibrosis have a lower signal intensity than the mild fibrosis cases.1 However, none of the studies up to date have been able to differentiate if the reduced signal intensity in the liver is because of an decreased uptake of CA or an increased excretion. Analyzing the DCE-MRI data with mechanistic mathematical modelling has the possibility of investigating such a differentiation.

Subjects and methods

88 patients with diffuse liver disease were examined using DCE-MRI (1.5 T Philips Achieva, two-point Dixon, TR=6.5 ms, TE=2.3/4.6 ms, FA=13) after a bolus injection of Gd-EOB-DTPA, followed by a liver biopsy. Regions of interest were placed within the liver, spleen and veins and a whole-body mechanistic pharmacokinetic model2 was fitted to the data. The fitted parameters in the model correspond to the rate of CA transport between different compartments, e.g. hepatocytes, blood plasma, and bile (Fig. 1).

Results

As can be seen in Fig. 2, the parameter corresponding to the transport of CA from the blood plasma to the hepatocytes, kph, is lower for patients with advanced fibrosis (p=0.01). Fig. 3 shows that the parameter corresponding to the CA excretion into the bile, khb, is higher for patients with advanced fibrosis (p<0.01).

Discussion/Conclusion

This work shows that the decreased signal intensity in DCE-MRI images in patients with advanced fibrosis depends on both a decreased uptake of CA in the hepatocytes and an increased excretion into the bile. Similar results have also been observed in a rat study3. In that study, rats with induced cirrhosis had a higher MRP2-activity than the healthy control rats.

References

1Norén et al: Eur. Radiol, 23(1), 174-181, 2013.

2Forsgren et al: PloS One, 9(4): e95700, 2014.

3Tsuda & Matsui: Radiol, 256(3): 767-773, 2010.

Functional magnetic resonance imaging (fMRI) measures brain activity by detecting the blood-oxygen-level dependent (BOLD) response to neural activity. The BOLD response depends on the neurovascular coupling, which connects cerebral blood flow, cerebral blood volume, and deoxyhemoglobin level to neuronal activity. The exact mechanisms behind this neurovascular coupling are not yet fully investigated. There are at least three different ways in which these mechanisms are being discussed. Firstly, mathematical models involving the so-called Balloon model describes the relation between oxygen metabolism, cerebral blood volume, and cerebral blood flow. However, the Balloon model does not describe cellular and biochemical mechanisms. Secondly, the metabolic feedback hypothesis, which is based on experimental findings on metabolism associated with brain activation, and thirdly, the neurotransmitter feed-forward hypothesis which describes intracellular pathways leading to vasoactive substance release. Both the metabolic feedback and the neurotransmitter feed-forward hypotheses have been extensively studied, but only experimentally. These two hypotheses have never been implemented as mathematical models. Here we investigate these two hypotheses by mechanistic mathematical modeling using a systems biology approach; these methods have been used in biological research for many years but never been applied to the BOLD response in fMRI. In the current work, model structures describing the metabolic feedback and the neurotransmitter feed-forward hypotheses were applied to measured BOLD responses in the visual cortex of 12 healthy volunteers. Evaluating each hypothesis separately shows that neither hypothesis alone can describe the data in a biologically plausible way. However, by adding metabolism to the neurotransmitter feed-forward model structure, we obtained a new model structure which is able to fit the estimation data and successfully predict new, independent validation data. These results open the door to a new type of fMRI analysis that more accurately reflects the true neuronal activity.

We are currently in the middle of a major shift in biomedical research: unprecedented and rapidly growing amounts of data may be obtained today, from in vitro, in vivo and clinical studies, at molecular, physiological and clinical levels. To make use of these large-scale, multi-level datasets, corresponding multi-level mathematical models are needed, i.e. models that simultaneously capture multiple layers of the biological, physiological and disease-level organization (also referred to as quantitative systems pharmacology-QSP-models). However, today's multi-level models are not yet embedded in end-usage applications, neither in drug research and development nor in the clinic. Given the expectations and claims made historically, this seemingly slow adoption may seem surprising. Therefore, we herein consider a specific example-type 2 diabetes-and critically review the current status and identify key remaining steps for these models to become mainstream in the future. This overview reveals how, today, we may use models to ask scientific questions concerning, e.g., the cellular origin of insulin resistance, and how this translates to the whole-body level and short-term meal responses. However, before these multi-level models can become truly useful, they need to be linked with the capabilities of other important existing models, in order to make them 'personalized' (e.g. specific to certain patient phenotypes) and capable of describing long-term disease progression. To be useful in drug development, it is also critical that the developed models and their underlying data and assumptions are easily accessible. For clinical end-usage, in addition, model links to decision-support systems combined with the engagement of other disciplines are needed to create user-friendly and cost-efficient software packages.

Insulin resistance is a major aspect of type 2 diabetes (T2D), which results from impaired insulin signaling in target cells. Signaling to regulate forkhead box protein O1 (FOXO1) may be the most important mechanism for insulin to control transcription. Despite this, little is known about how insulin regulates FOXO1 and how FOXO1 may contribute to insulin resistance in adipocytes, which are the most critical cell type in the development of insulin resistance. We report a detailed mechanistic analysis of insulin control of FOXO1 in human adipocytes obtained from non-diabetic subjects and from patients with T2D. We show that FOXO1 is mainly phosphorylated through mTORC2-mediated phosphorylation of protein kinase B at Ser(473) and that this mechanism is unperturbed in T2D. We also demonstrate a cross-talk from the MAPK branch of insulin signaling to stimulate phosphorylation of FOXO1. The cellular abundance and consequently activity of FOXO1 are halved in T2D. Interestingly, inhibition of mTORC1 with rapamycin reduces the abundance of FOXO1 to the levels in T2D. This suggests that the reduction of the concentration of FOXO1 is a consequence of attenuation of mTORC1, which defines much of the diabetic state in human adipocytes. We integrate insulin control of FOXO1 in a network-wide mathematical model of insulin signaling dynamics based on compatible data from human adipocytes. The diabetic state is network-wide explained by attenuation of an mTORC1-to-insulin receptor substrate-1 (IRS1) feedback and reduced abundances of insulin receptor, GLUT4, AS160, ribosomal protein S6, and FOXO1. The model demonstrates that attenuation of the mTORC1-to-IRS1 feedback is a major mechanism of insulin resistance in the diabetic state.

As our ability to measure the complexity of intracellular networks has evolved, it has become increasingly clear that we need new methods for data analysis: methods involving mathematical modeling. Nevertheless, it is still uncontroversial to publish and interpret experimental results without a model-based proof that the reasoning is correct. In the present study, we argue that this attitude probably needs to change in the future. We illustrate this need for modeling by considering the common experimental technique of using dominant-negative constructs. More specifically, we consider published time-series and dose-response data which previously have been used to argue that the protein S6 kinase does not phosphorylate insulin receptor substrate-1 at a specific serine residue. Using a presented general approach to interpret such data, we now demonstrate that the given dominant-negative data are not conclusive (i.e. that in the absence of other proofs, S6 kinase still may be the kinase). Using simulations with uncertainty analysis and analytical solutions, we show that an alternative explanation is centered around depletion of substrate, which can be tested experimentally. This analysis thus illustrates both the necessity and the benefits of using mathematical modeling to fully understand the implications of biological data, even for a small system and relatively simple data.

Background: Studies of cell-to-cell variation have in recent years grown in interest, due to improved bioanalytical techniques which facilitates determination of small changes with high uncertainty. Like much high-quality data, single-cell data is best analysed using a systems biology approach. The most common systems biology approach to single-cell data is the standard two-stage (STS) approach. In STS, data from each cell is analysed in a separate sub-problem, meaning that only data from the same cell is used to calculate the parameter values within that cell. Because only parts of the data are considered, problems with parameter unidentifiability are exaggerated in STS. In contrast, a related approach to data analysis has been developed for the studies of patient-to-patient variations. This approach, called nonlinear mixed-effects modelling (NLME), makes use of all data, when estimating the patient-specific parameters. NLME would therefore be advantageous compared to STS also for the study of cell-to-cell variation. However, no such systematic evaluation of the two approaches exists. Results: Herein, such a systematic comparison between STS and NLME has been performed. Different examples, both linear and nonlinear, and both simulated and real experimental data, have been examined. With informative data, there is no significant difference in the results for either parameter or noise estimation. However, when data becomes uninformative, NLME is significantly superior to STS. These results hold independently of whether the loss of information is due to a low signal-to-noise ratio, too few data points, or a bad input signal. The improvement is shown to come from both the consideration of a joint likelihood (JLH) function, describing all parameters and data, and from an a priori postulated form of the population parameters. Finally, we provide a small tutorial that shows how to use NLME for single-cell analysis, using the free and user-friendly software Monolix. Conclusions: When considering uninformative single-cell data, NLME yields more accurate parameter and noise estimates, compared to more traditional approaches, such as STS and JLH.

This work serves as a basis for a new type of fMRI analysis, which is based on a mechanistic interpretation of the hemodynamic response to synaptic activity. Activation was measured in the visual cortex of 12 healthy controls and ordinary differential equation models were fitted to the time series of the hemodynamic response. This allowed us to reject or refine previously proposed mechanistic hypotheses. This is the first attempt to describe the hemodynamic response quantitatively based on recent neurobiological findings. This mechanistic approach stands in contrast to the standard phenomenological description using the gamma variate function.

The beta-adrenergic response is impaired in failing hearts. When studying beta-adrenergic function in vitro, the half-maximal effective concentration (EC50) is an important measure of ligand response. We previously measured the in vitro contraction force response of chicken heart tissue to increasing concentrations of adrenaline, and observed a decreasing response at high concentrations. The classical interpretation of such data is to assume a maximal response before the decrease, and to fit a sigmoid curve to the remaining data to determine EC50. Instead, we have applied a mathematical modeling approach to interpret the full dose–response curvein a new way. The developed model predicts a non-steady-state caused by a short resting time between increased concentrations of agonist, which affect the dose–response characterization. Therefore, an improved estimate of EC50 may be calculated using steady-state simulations of the model. The model-based estimation of EC50 is further refined using additional time resolved data to decrease the uncertainty of the prediction. The resulting model-based EC50 (180–525 nM) is higher than the classically interpreted EC50 (46–191 nM). Mathematical modeling thus makes it possible to reinterpret previously obtained datasets, and to make accurate estimates of EC50 even when steady-state measurements are not experimentally feasible.

In metabolic diseases such as Type 2 Diabetes and Non-Alcoholic Fatty Liver Disease, the systemic regulation of postprandial metabolite concentrations is disturbed. To understand this dysregulation, a quantitative and temporal understanding of systemic postprandial metabolite handling is needed. Of particular interest is the intertwined regulation of glucose and non-esterified fatty acids (NEFA), due to the association between disturbed NEFA metabolism and insulin resistance. However, postprandial glucose metabolism is characterized by a dynamic interplay of simultaneously responding regulatory mechanisms, which have proven difficult to measure directly. Therefore, we propose a mathematical modelling approach to untangle the systemic interplay between glucose and NEFA in the postprandial period. The developed model integrates data of both the perturbation of glucose metabolism by NEFA as measured under clamp conditions, and postprandial time-series of glucose, insulin, and NEFA. The model can describe independent data not used for fitting, and perturbations of NEFA metabolism result in an increased insulin, but not glucose, response, demonstrating that glucose homeostasis is maintained. Finally, the model is used to show that NEFA may mediate up to 30-45% of the postprandial increase in insulin-dependent glucose uptake at two hours after a glucose meal. In conclusion, the presented model can quantify the systemic interactions of glucose and NEFA in the postprandial state, and may therefore provide a new method to evaluate the disturbance of this interplay in metabolic disease.

Regulation of nuclear transport is a key cellular function involved in many central processes, such as gene expression regulation and signal transduction. Rates of protein movement between cellular compartments can be measured by FRAP. However, no standard and reliable methods to calculate transport rates exist. Here we introduce a method to extract import and export rates, suitable for noisy single cell data. This method consists of microscope procedures, routines for data processing, an ODE model to fit to the data, and algorithms for parameter optimization and error estimation. Using this method, we successfully measured import and export rates in individual yeast. For YFP, average transport rates were 0.15 sec-1. We estimated confidence intervals for these parameters through likelihood profile analysis. We found large cell-to-cell variation (CV = 0.79) in these rates, suggesting a hitherto unknown source of cellular heterogeneity. Given the passive nature of YFP diffusion, we attribute this variation to large differences among cells in the number or quality of nuclear pores. Owing to its broad applicability and sensitivity, this method will allow deeper mechanistic insight into nuclear transport processes and into the largely unstudied cell-to-cell variation in kinetic rates.

Objectives: Diffuse liver disease (DLD), such as non-alcoholic fatty liver disease (NASH) and cirrhosis, is a rapidly growing problem throughout the Westernized world. Magnetic resonance imaging (MRI), based on uptake of the hepatocyte-specific contrast agent (CA) Gd-EOB-DTPA, is a promising non-invasive approach for diagnosing DLD. However, to fully utilize the potential of such dynamic measurements for clinical or research purposes, more advanced methods for data analysis are required. Methods: A mathematical model that can be used for such data-analysis was developed. Data was obtained from healthy human subjects using a clinical protocol with high spatial resolution. The model is based on ordinary differential equations and goes beyond local diffusion modeling, taking into account the complete system accessible to the CA. Results: The presented model can describe the data accurately, which was confirmed using chi-square statistics. Furthermore, the model is minimal and identifiable, meaning that all parameters were determined with small degree of uncertainty. The model was also validated using independent data. Conclusions: We have developed a novel approach for determining previously undescribed physiological hepatic parameters in humans, associated with CA transport across the liver. The method has a potential for assessing regional liver function in clinical examinations of patients that are suffering of DLD and compromised hepatic function.

Purpose: Aiming for non-invasive diagnostic tools to decrease the need for biopsy in diffuse liver disease and to quantitatively describe liver function, we applied a mechanistic pharmacokinetic modelling analysis of liver MRI with Gd-EOB-DTPA. This modelling method yields physiologically relevant parameters and was compared to previously developed methods in a patient group with diffuse liver disease. Materials and Methods: Using data from healthy volunteers undergoing liver MRI, an identifiable mechanistic model was developed, based on compartments described by ordinary differential equations and kinetic expressions, and validated with independent data including Gd-EOB-DTPA concentration measurements in blood samples. Patients (n=37) with diffuse liver disease underwent liver biopsy and MRI with Gd-EOB-DTPA. The model was used to derive pharmacokinetic parameters which were then compared with other quantitative estimates in their ability to separate mild from severe liver fibrosis. Results: The estimations produced by the mechanistic model allowed better separation between mild and severe fibrosis than previously described methods for quantifying hepatic Gd-EOB-DTPA uptake. Conclusions: With a mechanistic pharmacokinetic modelling approach, the estimation of liver uptake function and its diagnostic information can be improved compared to current methods.

Background: Model rejections lie at the heart of systems biology, since they provide conclusive statements: that the corresponding mechanistic assumptions do not serve as valid explanations for the experimental data. Rejections are usually done usinge.g. the chi-square test (χ2) or the Durbin-Watson test (DW). Analytical formulas for the corresponding distributions rely on assumptions that typically are not fulfilled. This problem is partly alleviated by the usage of bootstrapping, a computationally heavy approach to calculate an empirical distribution. Bootstrapping also allows for a natural extension to estimation of joint distributions, but this feature has so far been little exploited.

Results: We herein show that simplistic combinations of bootstrapped tests, like the max or min of the individual p-values, give inconsistent, i.e. overly conservative or liberal, results. A new two-dimensional (2D) approach based on parametric bootstrapping, on the other hand, is found both consistent and with a higher power than the individual tests, when tested on static and dynamic examples where the truth is known. In the same examples, the most superior test is a 2D χ2 vs χ2, where the second χ2-value comes from an additional help model, and its ability to describe bootstraps from the tested model. This superiority is lost if the help model is too simple, or too flexible. If a useful help model is found, the most powerful approach is the bootstrapped log-likelihood ratio (LHR). We show that this is because the LHR is one-dimensional, because the second dimension comes at a cost, and because LHR has retained most of the crucial information in the 2D distribution. These approaches statistically resolve a previously published rejection example for the first time.

Conclusions: We have shown how to, and how not to, combine tests in a bootstrap setting, when the combinatio is advantageous, and when it is advantageous to include a second model. These results also provide a deeper insight into the original motivation for formulating the LHR, for the more general setting of nonlinear and non-nested models. These insights are valuable in cases when accuracy and power, rather than computational speed, are prioritized.

The response to insulin is impaired in type 2 diabetes. Much information is available about insulin signaling, but understanding of the cellular mechanisms causing impaired signaling and insulin resistance is hampered by fragmented data, mainly obtained from different cell lines and animals. We have collected quantitative and systems-wide dynamic data on insulin signaling in primary adipocytes and compared cells isolated from healthy and diabetic individuals. Mathematical modeling and experimental verification identified mechanisms of insulin control of the MAPKs ERK1/2. We found that in human adipocytes, insulin stimulates phosphorylation of the ribosomal protein S6 and hence protein synthesis about equally via ERK1/2 and mTORC1. Using mathematical modeling, we examined the signaling network as a whole and show that a single mechanism can explain the insulin resistance of type 2 diabetes throughout the network, involving signaling both through IRS1, PKB, and mTOR and via ERK1/2 to the nuclear transcription factor Elk1. The most important part of the insulin resistance mechanism is an attenuated feedback from the protein kinase mTORC1 to IRS1, which spreads signal attenuation to all parts of the insulin signaling network. Experimental inhibition of mTORC1 using rapamycin in adipocytes from non-diabetic individuals induced and thus confirmed the predicted network-wide insulin resistance.

Insulin acutely controls metabolism in adipocytes, but also nuclear transcription through the “mitogenic” signaling pathway mediated by Map-kinases ERK1/2 (ERK). The cellular metabolic response to insulin is attenuated in insulin resistance and type 2 diabetes, but whether this involves also signaling through ERK is unclear. Based on experimental data from primary mature human adipocytes from diabetic and nondiabetic individuals, we demonstrate a network-wide, model-based analysis of insulin signaling through ERK to phosphorylation of transcription factor Elk1 integrated with signaling for “metabolic” control. We use minimal modeling to analyze the idiosyncratic phosphorylation dynamics of ERK, i.e. a slow phosphorylation response that returns to basal in response to insulin, and conclude that sequestration of ERK is the simplest explanation to data. We also demonstrate a significant cross-talk between ERK and mTORC1 signaling to ribosomal protein S6 for control of protein synthesis. A reduced sensitivity and reduced maximal phosphorylation of ERK in response to insulin in the diabetic state can be explained by the same mechanisms that generate insulin resistance in the control of metabolism.

Recent clinical studies suggest sustained treatment effects of interleukin-1β (IL-1β)-blocking therapies in type 2 diabetes mellitus. The underlying mechanisms of these effects, however, remain underexplored. Using a quantitative systems pharmacology modeling approach, we combined ex vivo data of IL-1β effects on β-cell function and turnover with a disease progression model of the long-term interactions between insulin, glucose, and β-cell mass in type 2 diabetes mellitus. We then simulated treatment effects of the IL-1 receptor antagonist anakinra. The result was a substantial and partly sustained symptomatic improvement in β-cell function, and hence also in HbA1C, fasting plasma glucose, and proinsulin-insulin ratio, and a small increase in β-cell mass. We propose that improved β-cell function, rather than mass, is likely to explain the main IL-1β-blocking effects seen in current clinical data, but that improved β-cell mass might result in disease-modifying effects not clearly distinguishable until >1 year after treatment.

Type 2 diabetes originates in an expanding adipose tissue that for unknown reasons becomes insulin resistant. Insulin resistance reflects impairments in insulin signaling, but mechanisms involved are unclear because current research is fragmented. We report a systems-level mechanistic understanding of insulin resistance in humans. We developed a dynamic mathematical model of insulin signaling – normally and in diabetes – based on quantitative steady-state and dynamic time-course data on signaling intermediaries in human mature adipocytes. At the core of insulin resistance is attenuation of a positive feedback from mammalian target of rapamycin in complex with raptor (mTORC1) to the insulin receptor substrate-1 (IRS1), which explains reduced sensitivity and signal strength throughout the signaling network. We demonstrate the potential of the model for identification of drug targets, e.g. increasing the feedback restores insulin signaling. Our findings suggest that insulin resistance in an expanded adipose tissue results from cell growth restriction to prevent cell necrosis.

It is often predicted that model-based data analysis will revolutionize biology, just as it has physics and engineering. A widely used tool within such analysis is hypothesis testing, which focuses on model rejections. However, the fact that a systems biology model is non-rejected is often a relatively weak statement, as such models usually are highly over-parametrized with respect to the available data, and both parameters and predictions may therefore be arbitrarily uncertain. For this reason, we formally define and analyse the concept of a core prediction. A core prediction is a uniquely identified property that must be fulfilled if the given model structure is to explain the data, even if the individual parameters are non-uniquely identified. It is shown that such a prediction is as strong a conclusion as a rejection. Furthermore, a new method for core prediction analysis is introduced, which is beneficial for the uncertainty of specific model properties, as the method only characterizes the space of acceptable parameters in the relevant directions. This avoids the curse of dimensionality associated with the generic characterizations used by previously proposed methods. Analysis on examples shows that the new method is comparable to profile likelihood with regard to practical identifiability, and thus generalizes profile likelihood to the more general problem of observability. If used, the concepts and methods presented herein make it possible to distinguish between a conclusion and a mere suggestion, which hopefully will contribute to a more justified confidence in systems biology analyses.

Signaling pathways that only a few years ago appeared simple and understandable, albeit far from complete, have evolved into very complex multi-layered networks of cellular control mechanisms, which in turn are integrated in a similarly complex whole-body level of control mechanisms. This complexity sets limits for classical biochemical reasoning, such that a correct and complete analysis of experimental data while taking the full complexity into account is not possible. In this Opinion we propose that mathematical modeling can be used as a tool in insulin signaling research, and we demonstrate how recent developments in modeling - and the integration of modeling in the experimental process - provide new possibilities to approach and decipher complex biological systems more efficiently.

Insulin signaling through insulin receptor (IR) and insulin receptor substrate-1 (IRS1) is important for insulin control of target cells. We have previously demonstrated a rapid and simultaneous overshoot behavior in the phosphorylation dynamics of IR and IRS1 in human adipocytes. Herein, we demonstrate that in murine adipocytes a similar overshoot behavior is not simultaneous for IR and IRS1. The peak of IRS1 phosphorylation, which is a direct consequence of the phosphorylation and the activation of IR, occurs earlier than the peak of IR phosphorylation. We used a conclusive modeling framework to unravel the mechanisms behind this counter-intuitive order of phosphorylation. Through a number of rejections, we demonstrate that two fundamentally different mechanisms may create the reversed order of peaks: (i) two pools of phosphorylated IR, where a large pool of internalized IR peaks late, but phosphorylation of IRS1 is governed by a small plasma membrane-localized pool of IR with an early peak, or (ii) inhibition of the IR-catalyzed phosphorylation of IRS1 by negative feedback. Although (i) may explain the reversed order, this two-pool hypothesis alone requires extensive internalization of IR, which is not supported by experimental data. However, with the additional assumption of limiting concentrations of IRS1, (i) can explain all data. Also, (ii) can explain all available data. Our findings illustrate how modeling can potentiate reasoning, to help draw nontrivial conclusions regarding competing mechanisms in signaling networks. Our work also reveals new differences between human and murine insulin signaling.

External control of tissues and cells, by hormones, nerves, and other stimuli, involves the transduction of signals from ligand-activated receptors to control of rate-limiting enzymes or proteins that affect key steps in metabolism, gene transcription or other processes within the cells. The signal transduction is carried out by a network of interacting signal mediators, i.e. proteins and small molecule transducers. Such signaling transduction networks display a high degree of complexity, which is due to the presence of feed-forward and feedback loops, both negative and positive, and to the fact that interactions change over time and according to intracellular location. In combination with multiple layers of control, redundancy, shared signal mediators, shared signal paths, and cross-talk between signals, this leads to a complexity that poses new challenges to progress in dissecting and understanding cellular control. Furthermore, many diseases, such as cancer, insulin resistance, and type 2 diabetes, are associated with malfunctioning in the complex signaling networks.

Intracellular signalling systems are highly complex. This complexity makes handling, analysis and visualisation of available knowledge a major challenge in current signalling research. Here, we present a novel framework for mapping signal-transduction networks that avoids the combinatorial explosion by breaking down the network in reaction and contingency information. It provides two new visualisation methods and automatic export to mathematical models. We use this framework to compile the presently most comprehensive map of the yeast MAP kinase network. Our method improves previous strategies by combining (I) more concise mapping adapted to empirical data, (II) individual referencing for each piece of information, (III) visualisation without simplifications or added uncertainty, (IV) automatic visualisation in multiple formats, (V) automatic export to mathematical models and (VI) compatibility with established formats. The framework is supported by an open source software tool that facilitates integration of the three levels of network analysis: definition, visualisation and mathematical modelling. The framework is species independent and we expect that it will have wider impact in signalling research on any system.

Type 2 diabetes is a metabolic disease that profoundly affects energy homeostasis. The disease involves failure at several levels and subsystems and is characterized by insulin resistance in target cells and tissues (i.e. by impaired intracellular insulin signaling). We have previously used an iterative experimental-theoretical approach to unravel the early insulin signaling events in primary human adipocytes. That study, like most insulin signaling studies, is based on in vitro experimental examination of cells, and the in vivo relevance of such studies for human beings has not been systematically examined. Herein, we develop a hierarchical model of the adipose tissue, which links intracellular insulin control of glucose transport in human primary adipocytes with whole-body glucose homeostasis. An iterative approach between experiments and minimal modeling allowed us to conclude that it is not possible to scale up the experimentally determined glucose uptake by the isolated adipocytes to match the glucose uptake profile of the adipose tissue in vivo. However, a model that additionally includes insulin effects on blood flow in the adipose tissue and GLUT4 translocation due to cell handling can explain all data, but neither of these additions is sufficient independently. We also extend the minimal model to include hierarchical dynamic links to more detailed models (both to our own models and to those by others), which act as submodules that can be turned on or off. The resulting multilevel hierarchical model can merge detailed results on different subsystems into a coherent understanding of whole-body glucose homeostasis. This hierarchical modeling can potentially create bridges between other experimental model systems and the in vivo human situation and offers a framework for systematic evaluation of the physiological relevance of in vitro obtained molecular/cellular experimental data.

Background: Models of biochemical systems are typically complex, which may complicate the discovery of cardinal biochemical principles. It is therefore important to single out the parts of a model that are essential for the function of the system, so that the remaining non-essential parts can be eliminated. However, each component of a mechanistic model has a clear biochemical interpretation, and it is desirable to conserve as much of this interpretability as possible in the reduction process. Furthermore, it is of great advantage if we can translate predictions from the reduced model to the original model. less thanbrgreater than less thanbrgreater thanResults: In this paper we present a novel method for model reduction that generates reduced models with a clear biochemical interpretation. Unlike conventional methods for model reduction our method enables the mapping of predictions by the reduced model to the corresponding detailed predictions by the original model. The method is based on proper lumping of state variables interacting on short time scales and on the computation of fraction parameters, which serve as the link between the reduced model and the original model. We illustrate the advantages of the proposed method by applying it to two biochemical models. The first model is of modest size and is commonly occurring as a part of larger models. The second model describes glucose transport across the cell membrane in bakers yeast. Both models can be significantly reduced with the proposed method, at the same time as the interpretability is conserved. less thanbrgreater than less thanbrgreater thanConclusions: We introduce a novel method for reduction of biochemical models that is compatible with the concept of zooming. Zooming allows the modeler to work on different levels of model granularity, and enables a direct interpretation of how modifications to the model on one level affect the model on other levels in the hierarchy. The method extends the applicability of the method that was previously developed for zooming of linear biochemical models to nonlinear models.

Insulin and other hormones control target cells through a network of signal-mediating molecules. Such networks are extremely complex due to multiple feedback loops in combination with redundancy, shared signal mediators, and cross-talk between signal pathways. We present a novel framework that integrates experimental work and mathematical modeling to quantitatively characterize the role and relation between coexisting submechanisms in complex signaling networks. The approach is independent of knowing or uniquely estimating model parameters because it only relies on (i) rejections and (ii) core predictions (uniquely identified properties in unidentifiable models). The power of our approach is demonstrated through numerous iterations between experiments, model-based data analyses, and theoretical predictions to characterize the relative role of co-existing feedbacks governing insulin signaling. We examined phosphorylation of the insulin receptor and insulin receptor substrate-1 and endocytosis of the receptor in response to various different experimental perturbations in primary human adipocytes. The analysis revealed that receptor endocytosis is necessary for two identified feedback mechanisms involving mass and information transfer, respectively. Experimental findings indicate that interfering with the feedback may substantially increase overall signaling strength, suggesting novel therapeutic targets for insulin resistance and type 2 diabetes. Because the central observations are present in other signaling networks, our results may indicate a general mechanism in hormonal control.

Background Systems biology models tend to become large since biological systems often consist of complex networks of interacting components, and since the models usually are developed to reflect various mechanistic assumptions of those networks. Nevertheless, not all aspects of the model are equally interesting in a given setting, and normally there are parts that can be reduced without affecting the relevant model performance. There are many methods for model reduction, but few or none of them allow for a restoration of the details of the original model after the simplified model has been simulated. Results We present a reduction method that allows for such a back-translation from the reduced to the original model. The method is based on lumping of states, and includes a general and formal algorithm for both determining appropriate lumps, and for calculating the analytical back-translation formulas. The lumping makes use of efficient methods from graph-theory and epsilon-decomposition and is derived and exemplified on two published models for fluorescence emission in photosynthesis. The bigger of these models is reduced from 26 to 6 states, with a negligible deviation from the reduced model simulations, both when comparing simulations in the states of the reduced model and when comparing back-translated simulations in the states of the original model. The method is developed in a linear setting, but we exemplify how the same concepts and approaches can be applied to non-linear problems. Importantly, the method automatically provides a reduced model with back-translations. Also, the method is implemented as a part of the systems biology toolbox for matlab, and the matlab scripts for the examples in this paper are available in the supplementary material. Conclusions Our novel lumping methodology allows for both automatic reduction of states using lumping, and for analytical retrieval of the original states and parameters without performing a new simulation. The two models can thus be considered as two degrees of zooming of the same model. This is a conceptually new development of model reduction approaches, which we think will stimulate much further research and will prove to be very useful in future modelling projects.

n/a

Systems biology and its usage of mathematical modeling to analyse biological data is rapidly becoming an established approach to biology. A crucial advantage of this approach is that more information can be extracted from observations of intricate dynamics, which allows nontrivial complex explanations to be evaluated and compared. In this minireview we explain this process, and review some of the most central available analysis tools. The focus is on the evaluation and comparison of given explanations for a given set of experimental data and prior knowledge. Three types of methods are discussed: (a) for evaluation of whether a given model is sufficiently able to describe the given data to be nonrejectable; (b) for evaluation of whether a slightly superior model is significantly better; and (c) for a general evaluation and comparison of the biologically interesting features in a model. The most central methods are reviewed, both in terms of underlying assumptions, including references to more advanced literature for the theoretically oriented reader, and in terms of practical guidelines and examples, for the practically oriented reader. Many of the methods are based upon analysis tools from statistics and engineering, and we emphasize that the systems biology focus on acceptable explanations puts these methods in a nonstandard setting. We highlight some associated future improvements that will be essential for future developments of model based data analysis in biology.

Type 2 diabetes is one of the most widespread and rapidly spreading diseases world-wide and has been subject of extensive research efforts. However, understanding the molecular basis of the disease is increasing piecemeal and a consensus regarding the overall picture of normal metabolic regulation and malfunction in diabetes has not emerged. A systems biology approach, combining mathematical modelling with simultaneous high-throughput measurements, can be of considerable help. On the whole-body level, this has been done in pharmacokinetic and pharmacodynamic models, which recently have started to mature into more physiologically realistic organ-based models. At the other end of the spectrum, detailed models for crucial cellular processes are starting to mature into complete modules that potentially can be fitted into such whole-body organ-based models. The result of such a merge is a multi-level hierarchical model, which is a model type that has been common in technical systems. In this review, we report and exemplify some of the recent progress that has been made to achieve such a hierarchical model, and we argue why it is only through such a model that a Complete picture of diabetes mellitus can be obtained.

Type II diabetes is one of the most common diseases afflicting people today. Understanding how this disease works, not only on a cellular level and between different organs and tissues, but also how it affects whole body level homeostasis is crucial for enhancement of its treatment. We use model-bases analysis as a tool for distinguishing different biological hypothesis on the system behavior.

The Insulin Receptor (IR), is located in the cell membrane as a dimer, and thus has the potential two bind two different insulin molecules. It can also undergo a series of phosphorylations, as well as having the ability to become internalized, and thus be removed from the cell’s censing area. However, it can then be recycled back to the membrane again. The major target of IR is the Insulin Receptor Substrate 1 (IRS1). IRS1 in turn mediates the signal further downstream through Protein Kinase B (PBK) and mammalian Target of Rapamycin (mTOR).  In adipocytes the end result is the translocation of internal vesicles containing Glucose Transporters (GLUT4) to the membrane, thus increasing the uptake of glucose. The liver, on the other hand, responds by down regulating the endogenous glucose production.

The activity of IRS1 is determined by its phospho-tyrosine composition. This in turn is regulated by at least two serine-phosphorylations, on ser307 and ser312. The serine levels of this protein are regulated by downstream kinases, of which only one is known, S6K. The ser307 phosphorylation appears to allow for a short term positive feedback while the ser312 phosphorylation has the dynamics of a more long term negative feedback.

The overall dynamics of the IRS1 tyrosine phosphorylation is a mirror of that of the Insulin Receptor. They both have a quick response to insulin within minutes, manifested as a high overshoot before declining to a steady state level. The overshoot behavior of this system can be explained either by a downstream negative feedback, or by having an advanced internalization and recycling model. Several hypotheses of the negative feedback mechanisms necessary to allow for the receptor to adopt such a behavior have previously been rejected by us. So has the hypothesis of internalization (unpublished data). The internalized Insulin Receptors can account for only a small fraction of the total amount of receptors, it however seems to be necessary for its own down regulation, since without it the overshoot behavior disappears.

The complexity of this system is immense and hence we keep to as minimal models as possible, only considering adding complexity to the system when data indicates so, or when a simpler model structure has been rejected. We model the system with a series of Ordinary Differential Equations (ODEs), optimize and estimate the parameters of a given model structure with the Systems Biology Toolbox (SBTB) and reject, or fail to reject, models based on their statistical agreement with our data. We search the entire approximated parameter space for a sample of all acceptable parameter values for any given parameter. We then look for commonalities shared between model simulations of all parameter sets in the sample. That is, a behavior of e.g. a state in the model that has to be above a certain threshold for it to be able to explain the data, while other states might be of arbitrary sizes. If we find such a commonality, we call it a core prediction. Assuming your data is correct and your analysis thorough, a Core Prediction has the same strength as a model rejection. The common aspect, shared between all acceptable parameter etc, is something that has to be true, no matter how much more data you acquire. One such core prediction, which led to the rejection of the internalization hypothesis, was that the amount of internalized IR had to be above 80% of the total receptor pool.  We subsequently rejected this experimentally.

Background: Biomedical research is changing due to the rapid accumulation of experimental data at an unprecedented scale, revealing increasing degrees of complexity of biological processes. Life Sciences are facing a transition from a descriptive to a mechanistic approach that reveals principles of cells, cellular networks, organs, and their interactions across several spatial and temporal scales. There are two conceptual traditions in biological computational-modeling. The bottom-up approach emphasizes complex intracellular molecular models and is well represented within the systems biology community. On the other hand, the physics-inspired top-down modeling strategy identifies and selects features of (presumably) essential relevance to the phenomena of interest and combines available data in models of modest complexity. Results: The workshop, "ESF Exploratory Workshop on Computational disease Modeling", examined the challenges that computational modeling faces in contributing to the understanding and treatment of complex multi-factorial diseases. Participants at the meeting agreed on two general conclusions. First, we identified the critical importance of developing analytical tools for dealing with model and parameter uncertainty. Second, the development of predictive hierarchical models spanning several scales beyond intracellular molecular networks was identified as a major objective. This contrasts with the current focus within the systems biology community on complex molecular modeling. Conclusion: During the workshop it became obvious that diverse scientific modeling cultures (from computational neuroscience, theory, data-driven machine-learning approaches, agent-based modeling, network modeling and stochastic-molecular simulations) would benefit from intense cross-talk on shared theoretical issues in order to make progress on clinically relevant problems.

Type 2 diabetes is characterized by insulin resistance of target organs, which is due to impaired insulin signal transduction. The skeleton of signaling mediators that provide for normal insulin action has been established. However, the detailed kinetics, and their mechanistic generation, remain incompletely understood. We measured time-courses in primary human adipocytes for the short-term phosphorylation dynamics of the insulin receptor (IR) and the IR substrate-1 in response to a step increase in insulin concentration. Both proteins exhibited a rapid transient overshoot in tyrosine phosphorylation, reaching maximum within 1 min, followed by an intermediate steady-state level after approximately 10 min. We used model-based hypothesis testing to evaluate three mechanistic explanations for this behavior: (A) phosphorylation and dephosphorylation of IR at the plasma membrane only, (B) the additional possibility for IR endocytosis, (C) the alternative additional possibility of feedback signals to IR from downstream intermediates. We concluded that (A) is not a satisfactory explanation, that (B) may serve as an explanation only if both internalization, dephosphorylation, and subsequent recycling are permitted, and that (C) is acceptable. These mechanistic insights cannot be obtained by mere inspection of the datasets, and they are rejections and thus stronger and more final conclusions than ordinary model predictions.

Biosimulation has the potential to drastically improve future drug development: mathematical models may be used to obtain maximal information from experimental data, and can be used to pin-point potential drug targets, in a much more systematic manner than is the case today. However, for this potential to be fulfilled, the developed models must themselves fulfill a number of requirements. For instance, the models must be trustworthy, and contain the necessary degree of mechanistic details. These two requirements are difficult to fulfill simultaneously, since a mechanistically detailed model typically becomes unidentifiable (i.e., over-parametrized with respect to existing data), which means that the model predictions are the result of arbitrary choices on a parameter manifold, and thus much less trustworthy. In this chapter, we review a recently developed modeling framework-core-box modeling-which has been developed to be able to fulfill both of the above requirements. A core-box model is a combination of two models: a core model and a gray-box model. The gray-box model is a mechanistically detailed description of the relevant biochemical processes, while the core model is a simplified version of the same processes, where all aspects that cannot uniquely be estimated from the data have been eliminated. The core-box model consists of both these models, and a translation between them. The translation allows the two sub-models to be considered as two degrees of zooming of the same core-box model, where changes in, for instance, parameters are preserved upon the zooming. A path is suggested for the development of a core-box model, including identifiability analysis, model reduction, system identification, and back-translation. All of these steps are reviewed, and the steps and advantages of the modeling framework are demonstrated on a core-box model for insulin signaling.

Motivation: The current trend in dynamical modelling of biochemical systems is to construct more and more mechanistically detailed and thus complex models. The complexity is reflected in the number of dynamic state variables and parameters, as well as in the complexity of the kinetic rate expressions. However, a greater level of complexity, or level of detail, does not necessarily imply better models, or a better understanding of the underlying processes. Data often does not contain enough information to discriminate between different model hypotheses, and such overparameterization makes it hard to establish the validity of the various parts of the model. Consequently, there is an increasing demand for model reduction methods. Results: We present a new reduction method that reduces complex rational rate expressions, such as those often used to describe enzymatic reactions. The method is a novel term-based identifiability analysis, which is easy to use and allows for user-specified reductions of individual rate expressions in complete models. The method is one of the first methods to meet the classical engineering objective of improved parameter identifiability without losing the systems biology demand of preserved biochemical interpretation. © The Author 2008. Published by Oxford University Press. All rights reserved.

Sensitivity of biochemical network models to uncertainties in the model structure, with a focus on autonomously oscillating systems, is addressed. Structural robustness, as defined here, concerns the sensitivity of the model predictions with respect to changes in the specific interactions between the network components and encompass, for instance, uncertain kinetic models, neglected intermediate reaction steps and unmodelled transport phenomena. Traditional parametric sensitivity analysis does not address such structural uncertainties and should therefore be combined with analysis of structural robustness. Here a method for quantifying the structural robustness of models for systems displaying sustained oscillations is proposed. The method adopts concepts from robust control theory and is based on adding dynamic perturbations to the network of interacting biochemical components. In addition to providing a measure of the overall robustness, the method is able to identify specific network fragilities. The importance of considering structural robustness is demonstrated through an analysis of a recently proposed model of the oscillatory metabolism in activated neutrophils. The model displays small parametric sensitivities, but is shown to be highly unrobust to small perturbations in some of the network interactions. Identification of specific fragilities reveals that adding a small delay or diffusion term in one of the involved reactions, likely to exist in vivo, completely removes all oscillatory behaviour in the model.

New experimental techniques in bioscience provide us with high-quality data allowing quantitative mathematical modelling. Parameter estimation is often necessary and, in connection with this, it is important to know whether all parameters can be uniquely estimated from available data, (i.e. whether the model is identifiable). Dealing essentially with models for metabolism, we show how the assumption of an algebraic relation between concentrations may cause parameters to be unidentifiable. If a sufficient data set is available, the problem with unidentifiability arises locally in individual rate expressions. A general method for reparameterisation to identifiable rate expressions is provided, together with a Mathematica code to help with the calculations. The general results are exemplified by four well-cited models for glycolysis.

One of the biggest problems when performing system identification of biological systems is that it is seldom possible to measure more than a small fraction of the total number of variables. If that is the case, the initial state, from where the simulation should start, has to be estimated along with the kinetic parameters appearing in the rate expressions. This is often done by introducing extra parameters, describing the initial state, and one way to eliminate them is by starting in a steady state. We report a generalisation of this approach to all systems starting on the centre manifold, close to a Hopf bifurcation. There exist biochemical systems where such data have already been collected, for example, of glycolysis in yeast. The initial value parameters are solved for in an optimisation sub-problem, for each step in the estimation of the other parameters. For systems starting in stationary oscillations, the sub-problem is solved in a straight-forward manner, without integration of the differential equations, and without the problem of local minima. This is possible because of a combination of a centre manifold and normal form reduction, which reveals the special structure of the Hopf bifurcation. The advantage of the method is demonstrated on the Brusselator.

The complexity of full-scale metabolic models is a major obstacle for their effective use in computational systems biology. The aim of model reduction is to circumvent this problem by eliminating parts of a model that are unimportant for the properties of interest. The choice of reduction