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Macroscopic Modeling of Metabolic Reaction Networks and Dynamic Identification of Elementary Flux Modes by Column Generation
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this work an intersection between optimization methods and animal cell culture modeling is considered. We present optimization based methods for analyzing and building models of cell culture; models that could be used when designing the environment cells are cultivated in, i.e., medium. Since both the medium and cell line considered are complex, designing a good medium is not straightforward. Developing a model of cell metabolism is a step in facilitating medium design.

In order to develop a model of the metabolism the methods presented in this work make use of an underlying metabolic reaction network and extracellular measurements. External substrates and products are connected via the relevant elementary flux modes (EFMs). Modeling from EFMs is generally limited to small networks, because the number of EFMs explodes when the underlying network size increases. The aim of this work is to enable modeling with more complex networks by presenting methods that dynamically identify a subset of the EFMs.

In papers A and B we consider a model consisting of the EFMs along with the flux over each mode. In paper A we present how such a model can be decided by an optimization technique named column generation. In paper B the robustness of such a model with respect to measurement errors is considered. We show that a robust version of the underlying optimization problem in paper A can be formed and column generation applied to identify EFMs dynamically.

In papers C and D a kinetic macroscopic model is considered. In paper C we show how a kinetic macroscopic model can be constructed from the EFMs. This macroscopic model is created by assuming that the flux along each EFM behaves according to Michaelis-Menten type kinetics. This modeling method has the ability to capture cell behavior in varied types of media, however the size of the underlying network is a limitation. In paper D this limitation is countered by developing an approximation algorithm, that can dynamically identify EFMs for a kinetic model.

Abstract [sv]

I denna avhandling betraktar vi korsningen mellan optimeringsmetoder och modellering av djurcellodling.Vi presenterar optimeringsbaserade metoder för att analysera och bygga modeller av cellkulturer. Dessa modeller kan användas vid konstruktionen av den miljö som cellerna ska odlas i, dvs, medium.Eftersom både mediet och cellinjen är komplexa är det inte okomplicerat att utforma ett bra medium. Att utveckla en modell av cellernas ämnesomsättning är ett steg för att underlätta designen av mediet.

För att utveckla en modell av metabolismen kommer de metoder som används i detta arbete att utnyttja ett underliggande metaboliskt reaktions\-nätverk och extracellulära mätningar. Externa substrat och produkter är sammankopplade via de relevanta elementära metaboliska vägarna (EFM).Modellering med hjälp av EFM är i allmänhet begränsad till små nätverk eftersom antalet EFM exploderar när de underliggande nätverket ökar i storlek. Målet med detta arbete är att möjliggöra modellering med mer komplexa nätverk genom att presentera metoder som dynamiskt identifierar en delmängd av EFM.

I artikel A och B betraktar vi en modell som består av EFM och ett flöde över varje EFM.I artikel A presenterar vi hur en sådan modell kan bestämmas med hjälp av en optimeringsteknik som kallas kolumngenerering.I artikel A undersöker vi hur robust en sådan modell är med avseende till mätfel. Vi visar att en robust version av det underliggande optimeringsproblemet i artikel A kan konstrueras samt att kolumngenerering kan appliceras för att identifiera EFM dynamiskt.

Artikel C och D behandlar en kinetisk makroskopisk modell. Vi visar i artikel C hur en sådan modell kan konstrueras från EFM.Denna makroskopiska modell är skapad genom att anta att flödet genom varje EFM beter sig enligt Michaelis-Menten-typ av kinetik. Denna modelleringsmetod har förmågan att fånga cellernas beteende i olika typer av media, men storleken på nätverket är en begränsning.I artikel D hanterar vi denna begränsing genom att utveckla en approximationsalgoritm som identifierar EFM dynamiskt för en kinetisk modell.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2015. , xii, 27 p.
Series
TRITA-MAT-A, 2015:08
Keyword [en]
Metabolic Network; Optimization; Robust Optimization; Least-squares; Column Generation; Modeling; Algorithm; Elementary Flux Mode, Metabolic Flux Analysis, Chinese Hamster Ovary Cell, Amino Acid Metabolism
National Category
Computational Mathematics
Research subject
Applied and Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-172367ISBN: 978-91-7595-634-3 (print)OAI: oai:DiVA.org:kth-172367DiVA: diva2:847421
Public defence
2015-09-21, F3, Lindstedtsvägen 26, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Funder
Swedish Research Council
Note

QC 20150827

Available from: 2015-08-27 Created: 2015-08-20 Last updated: 2015-08-27Bibliographically approved
List of papers
1. On dynamically generating relevant elementary flux modes in a metabolic network using optimization
Open this publication in new window or tab >>On dynamically generating relevant elementary flux modes in a metabolic network using optimization
2014 (English)In: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416Article in journal (Refereed) Published
Abstract [en]

Elementary flux modes (EFMs) are pathways through a metabolic reaction network that connect external substrates to products. Using EFMs, a metabolic network can be transformed into its macroscopic counterpart, in which the internal metabolites have been eliminated and only external metabolites remain. In EFMs-based metabolic flux analysis (MFA) experimentally determined external fluxes are used to estimate the flux of each EFM. It is in general prohibitive to enumerate all EFMs for complex networks, since the number of EFMs increases rapidly with network complexity. In this work we present an optimization-based method that dynamically generates a subset of EFMs and solves the EFMs-based MFA problem simultaneously. The obtained subset contains EFMs that contribute to the optimal solution of the EFMs-based MFA problem. The usefulness of our method was examined in a case-study using data from a Chinese hamster ovary cell culture and two networks of varied complexity. It was demonstrated that the EFMs-based MFA problem could be solved at a low computational cost, even for the more complex network. Additionally, only a fraction of the total number of EFMs was needed to compute the optimal solution.

Keyword
Metabolic network, Optimization, Algorithm, Elementary flux mode, Metabolic flux analysis, Chinese hamster ovary cell
National Category
Mathematics
Research subject
Biotechnology; Mathematics
Identifiers
urn:nbn:se:kth:diva-165581 (URN)10.1007/s00285-014-0844-1 (DOI)000360851700006 ()2-s2.0-84941359801 (Scopus ID)
Funder
Swedish Research CouncilVINNOVA
Note

QC 20150518

Available from: 2015-04-29 Created: 2015-04-29 Last updated: 2017-12-04Bibliographically approved
2. On the Robustness of Elementary-Flux-Modes-based Metabolic Flux Analysis
Open this publication in new window or tab >>On the Robustness of Elementary-Flux-Modes-based Metabolic Flux Analysis
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Elementary flux modes (EFMs) are vectors defined from a metabolic reaction network, giving the connections between substrates and products. EFMs-based metabolic flux analysis (MFA) estimates the flux over each EFM from external flux measurements through least-squares data fitting. The measurements used in the data fitting are subject to errors. A robust optimization problem includes information on errors and gives a way to examine the sensitivity of the solution of the EFMs-based MFA to these errors. In general, formulating a robust optimization problem may make the problem significantly harder. We show that in the case of the EFMs-based MFA the robust problem can be stated as a convex quadratic programming problem. We have previously shown how the data fitting problem may be solved in a column-generation framework. In this paper, we show how column generation may be applied also to the robust problem. Furthermore, the option to indicate intervals on metabolites that are not measured is introduced in this column generation framework. The robustness of the data is evaluated in a case-study, which indicated that the solutions of our non-robust problems are in fact near-optimal also when robustness is considered, implying that the errors in measurement do not have a large impact on the optimal solution. Furthermore, we showed that the addition of intervals on unmeasured metabolites resulted in a change in the optimal solution.

Keyword
Metabolic Network; Robust Optimization; Least-squares; Elementary Flux Mode; Chinese Hamster Ovary Cell
National Category
Computational Mathematics Bioinformatics and Systems Biology
Identifiers
urn:nbn:se:kth:diva-172372 (URN)
Funder
Swedish Research CouncilVINNOVA
Note

QS 2015

Available from: 2015-08-20 Created: 2015-08-20 Last updated: 2015-08-27Bibliographically approved
3. Poly-pathway model, a novel approach to simulate multiple metabolic states by reaction network-based model - Application to CHO cell culture
Open this publication in new window or tab >>Poly-pathway model, a novel approach to simulate multiple metabolic states by reaction network-based model - Application to CHO cell culture
Show others...
(English)Manuscript (preprint) (Other academic)
National Category
Bioinformatics and Systems Biology
Identifiers
urn:nbn:se:kth:diva-172374 (URN)
Note

QS 2015

Available from: 2015-08-20 Created: 2015-08-20 Last updated: 2015-08-27Bibliographically approved
4. On dynamically identifying elementary flux modes for a poly-pathway model of metabolic reaction networks
Open this publication in new window or tab >>On dynamically identifying elementary flux modes for a poly-pathway model of metabolic reaction networks
(English)Manuscript (preprint) (Other academic)
Abstract [en]

he aim with poly-pathway models is to model variations in the metabolic behavior of cells in response to changes in their external environment.By considering the elementary flux modes of a metabolic network, the network can be reduced to a set of macroscopic reactions. The macroscopic reactions connect external substrates to products, where each reaction is associated with a kinetic equation.Since enumerating all elementary flux modes is prohibitive for complex networks, these types of models are usually limited to simple networks. In this work we consider an algorithm for identifying elementary flux modes for a poly-pathway model. First we consider a dynamic identification of elementary flux modes and model parameters using column generation. However, due to non-linearity in one optimization problem involved in column generation, elementary flux mode identification can not be guaranteed with that column generation approach. In order to still be able to identify elementary flux modes, an approximation algorithm is derived and tested for the model identification. In a case study, the algorithm is shown to work well in practice and obtains a near-optimal solution compared to a method in which all elementary flux modes are enumerated beforehand.

National Category
Bioinformatics and Systems Biology Computational Mathematics
Research subject
Applied and Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-172376 (URN)
Funder
Swedish Research CouncilVINNOVA
Note

QS 2015

Available from: 2015-08-20 Created: 2015-08-20 Last updated: 2015-08-27Bibliographically approved

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