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Protein Folding Simulations in Kink Model
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

The structure of protein is essentially important for life activities. Proteins can perform their functions only by specific structures. In this thesis, the kink and multi-kink model for protein description are reviewed. It is shown that most of the loop parts in Protein Databank (PDB) can be described by very limited number of kinks within the experimental precision. Furthermore, by applying the model into two well studied real proteins (myoglobin and villin headpiece HP35), it is shown that the multi-kink model gives correct folding pathway and thermal dynamical properties compared with the experimental results for both proteins. In particular, the kink model is computationally inexpensive compared with other existing models. In the last chapter, a new visualization method for the heavy atoms in the side-chain is presented.

##### Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2014. , 56 p.
##### Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1184
##### Keyword [en]
protein folding, kink model, soliton
Biophysics
##### Research subject
Physics with specialization in Biophysics
##### Identifiers
ISBN: 978-91-554-9043-0 (print)OAI: oai:DiVA.org:uu-232562DiVA: diva2:748739
##### Public defence
2014-11-07, 80101, Ångström Laboratory, Lägerhyddsvägen 1, Uppsala, 13:15 (English)
##### Supervisors
Available from: 2014-10-14 Created: 2014-09-22 Last updated: 2015-01-23
##### List of papers
1. Towards quantitative classification of folded proteins in terms of elementary functions
Open this publication in new window or tab >>Towards quantitative classification of folded proteins in terms of elementary functions
2011 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 83, no 4, 041907- p.Article in journal (Refereed) Published
##### Abstract [en]

A comparative classification scheme provides a good basis for several approaches to understand proteins, including prediction of relations between their structure and biological function. But it remains a challenge to combine a classification scheme that describes a protein starting from its well-organized secondary structures and often involves direct human involvement, with an atomary-level physics-based approach where a protein is fundamentally nothing more than an ensemble of mutually interacting carbon, hydrogen, oxygen, and nitrogen atoms. In order to bridge these two complementary approaches to proteins, conceptually novel tools need to be introduced. Here we explain how an approach toward geometric characterization of entire folded proteins can be based on a single explicit elementary function that is familiar from nonlinear physical systems where it is known as the kink soliton. Our approach enables the conversion of hierarchical structural information into a quantitative form that allows for a folded protein to be characterized in terms of a small number of global parameters that are in principle computable from atomary-level considerations. As an example we describe in detail how the native fold of the myoglobin 1M6C emerges from a combination of kink solitons with a very high atomary-level accuracy. We also verify that our approach describes longer loops and loops connecting alpha helices with beta strands, with the same overall accuracy.

Natural Sciences
##### Identifiers
urn:nbn:se:uu:diva-152823 (URN)10.1103/PhysRevE.83.041907 (DOI)000289354500006 ()
Available from: 2011-05-03 Created: 2011-05-02 Last updated: 2017-12-11
2. Soliton concepts and protein structure
Open this publication in new window or tab >>Soliton concepts and protein structure
2012 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 85, no 3, 031906Article in journal (Refereed) Published
##### Abstract [en]

Structural classification shows that the number of different protein folds is surprisingly small. It also appears that proteins are built in a modular fashion from a relatively small number of components. Here we propose that the modular building blocks are made of the dark soliton solution of a generalized discrete nonlinear Schrödinger equation. We find that practically all protein loops can be obtained simply by scaling the size and by joining together a number of copies of the soliton, one after another. The soliton has only two loop-specific parameters, and we compute their statistical distribution in the Protein Data Bank (PDB). We explicitly construct a collection of 200 sets of parameters, each determining a soliton profile that describes a different short loop. The ensuing profiles cover practically all those proteins in PDB that have a resolution which is better than 2.0 Å, with a precision such that the average root-mean-square distance between the loop and its soliton is less than the experimental B-factor fluctuation distance. We also present two examples that describe how the loop library can be employed both to model and to analyze folded proteins.

APS, 2012
Biophysics
##### Research subject
Theoretical Physics
##### Identifiers
urn:nbn:se:uu:diva-196716 (URN)10.1103/PhysRevE.85.031906 (DOI)000209132200002 ()22587122 (PubMedID)
Available from: 2013-03-13 Created: 2013-03-13 Last updated: 2017-12-06Bibliographically approved
3. On the role of thermal backbone fluctuations in myoglobin ligand gate dynamics
Open this publication in new window or tab >>On the role of thermal backbone fluctuations in myoglobin ligand gate dynamics
2013 (English)In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 138, no 17, 175101- p.Article in journal (Refereed) Published
##### Abstract [en]

We construct an energy function that describes the crystallographic structure of sperm whale myoglobin backbone. As a model in our construction, we use the Protein Data Bank entry 1ABS that has been measured at liquid helium temperature. Consequently, the thermal B-factor fluctuations are very small, which is an advantage in our construction. The energy function that we utilize resembles that of the discrete nonlinear Schrodinger equation. Likewise, ours supports topological solitons as local minimum energy configurations. We describe the 1ABS backbone in terms of topological solitons with a precision that deviates from 1ABS by an average root-mean-square distance, which is less than the experimentally observed Debye-Waller B-factor fluctuation distance. We then subject the topological multi-soliton solution to extensive numerical heating and cooling experiments, over a very wide range of temperatures. We concentrate in particular to temperatures above 300 K and below the Theta-point unfolding temperature, which is around 348 K. We confirm that the behavior of the topological multi-soliton is fully consistent with Anfinsen's thermodynamic principle, up to very high temperatures. We observe that the structure responds to an increase of temperature consistently in a very similar manner. This enables us to characterize the onset of thermally induced conformational changes in terms of three distinct backbone ligand gates. One of the gates is made of the helix F and the helix E. The two other gates are chosen similarly, when open they provide a direct access route for a ligand to reach the heme. We find that out of the three gates we investigate, the one which is formed by helices B and G is the most sensitive to thermally induced conformational changes. Our approach provides a novel perspective to the important problem of ligand entry and exit.

Natural Sciences
##### Identifiers
urn:nbn:se:uu:diva-203304 (URN)10.1063/1.4801330 (DOI)000319289600056 ()
Available from: 2013-07-08 Created: 2013-07-08 Last updated: 2017-12-06Bibliographically approved
4. Soliton driven relaxation dynamics and protein collapse in the villin headpiece
Open this publication in new window or tab >>Soliton driven relaxation dynamics and protein collapse in the villin headpiece
2013 (English)In: Journal of Physics: Condensed Matter, ISSN 0953-8984, E-ISSN 1361-648X, Vol. 25, no 32, 325103- p.Article in journal (Refereed) Published
##### Abstract [en]

Protein collapse from a random chain to the native state involves a dynamical phase transition. During the process, new scales and collective variables become excited while old ones recede and fade away. The presence of different phases and many scales causes formidable computational bottle-necks in approaches that are based on full atomic scale scrutiny. Here we propose a way to describe the folding and unfolding processes effectively, using only the biologically relevant time and distance scales. We merge a coarse grained Landau theory that models the static collapsed protein in the low-temperature limit with a Glauber protocol that describes finite-temperature relaxation dynamics in a statistical system which is out of thermal equilibrium. As an example we inspect the collapse of a HP35 chicken villin headpiece subdomain, a paradigm specimen in protein folding studies. We simulate the folding and unfolding process by repeated heating and cooling cycles between a given low-temperature, i.e. bad solvent, environment where the protein is collapsed and various different high-temperature, i.e. good solvent, environments. We find that as long as the high temperature value stays below a value in the range that separates the random walk phase from the self-avoiding walk phase, we consistently recover the native state upon cooling. But, when heated to sufficiently high temperatures, the native state practically never recurs. Our result confirms Anfinsen's thermodynamical hypothesis and estimates a temperature range for its validity, in the case of villin.

Natural Sciences
##### Identifiers
urn:nbn:se:uu:diva-207013 (URN)10.1088/0953-8984/25/32/325103 (DOI)000322227600003 ()
Available from: 2013-09-10 Created: 2013-09-09 Last updated: 2017-12-06Bibliographically approved
5. Collective motions and structural self-organisation along the myoglobin folding pathway
Open this publication in new window or tab >>Collective motions and structural self-organisation along the myoglobin folding pathway
##### Abstract [en]

We develop a highly predictive energy function to describe the low temperature crystallographic structure of myoglobin with sub-\AA ngstr\"om precision. We use the energy function to investigate the way how myoglobin folds.For this we employ the Glauber protocol, with a variable ambient temperature. We first increase the temperature so that the structure unfolds into a random coil. We then lower thetemperature back to its original value, and monitor how the myoglobin folds towards its native state.We find that the folding proceeds by $\alpha$-helix nucleation, and that the ordering of helix formation parallels experimental observations. There is also a molten globule folding intermediate, with a radius of gyration that matches the experimentally measured value. We estimate the relative folding times between a random chain and molten globule, and between molten globule and the native state, and we find that the ratio is consistentwith the experimentally measured values. We also propose a number of novel experimental characteristics that could be measured in future experiments.

Biophysics
##### Identifiers
urn:nbn:se:uu:diva-232561 (URN)
Available from: 2014-09-22 Created: 2014-09-22 Last updated: 2015-01-23Bibliographically approved
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