Statistical Mechanical Theory of the Protein Conformation. I. General Considerations and the Application to Homopolymers

Wako, Hiroshi; Saitô, Nobuhiko

doi:10.1143/jpsj.44.1931

Cited by 108 publications

(118 citation statements)

References 15 publications

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“…This prediction should be investigated using singlemolecule observations of DHFR at equilibrium. However, with the original WSME model (18,35,36), the I α basin is absent from the calculated 2D free-energy surface (Fig. S4) because of overestimating the cooperativity among residues and the resulting overemphasis placed on chain connectivity.…”

Section: Resultsmentioning

confidence: 99%

“…Because experimental data for I 6 and I 5 became available (19,21,22) after this MD result was reported, we revisit the problem of the DHFR folding intermediates in this paper. To highlight the relationship between the topology of the native conformation and the folding pathway, we develop a simple theoretical model as an extension of the structure-based model first developed by Wako and Saito (35,36) that was systematically applied to proteins by Muñoz and Eaton (18). In this study, we apply the extended version of the Wako-Saito-Muñoz-Eaton (WSME) model to the early phases τ 7 , τ 6 , and τ 5 of DHFR folding, in which the effects of topology should be more evident than during the last τ 1 − τ 4 processes through which the atomic packing inside a protein should be realized.…”

Section: Significancementioning

confidence: 99%

“…Modifying the original model (18,35,36) by considering proline isomerization, energy in the WSME model is expressed as a function of fm i g,…”

Section: Significancementioning

confidence: 99%

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Folding pathway of a multidomain protein depends on its topology of domain connectivity

Inanami

Terada

Sasai

2014

Proc. Natl. Acad. Sci. U.S.A.

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How do the folding mechanisms of multidomain proteins depend on protein topology? We addressed this question by developing an Ising-like structure-based model and applying it for the analysis of free-energy landscapes and folding kinetics of an example protein, Escherichia coli dihydrofolate reductase (DHFR). DHFR has two domains, one comprising discontinuous N-and C-terminal parts and the other comprising a continuous middle part of the chain. The simulated folding pathway of DHFR is a sequential process during which the continuous domain folds first, followed by the discontinuous domain, thereby avoiding the rapid decrease in conformation entropy caused by the association of the N-and C-terminal parts during the early phase of folding. Our simulated results consistently explain the observed experimental data on folding kinetics and predict an off-pathway structural fluctuation at equilibrium. For a circular permutant for which the topological complexity of wild-type DHFR is resolved, the balance between energy and entropy is modulated, resulting in the coexistence of the two folding pathways. This coexistence of pathways should account for the experimentally observed complex folding behavior of the circular permutant.folding intermediates | internal friction | eWSME model

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Section: Resultsmentioning

confidence: 99%

Section: Significancementioning

confidence: 99%

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Folding pathway of a multidomain protein depends on its topology of domain connectivity

Inanami

Terada

Sasai

2014

Proc. Natl. Acad. Sci. U.S.A.

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“…We use a modified version of the native-centric WSME model [39][40][41][42] , with a suitable redefinition of the interactions to describe more realistically the chemical denaturation of gankyrin. The model has been used to study the kinetics and thermodynamics of several proteins, upon The equilibrium values of all thermodynamic quantities are calculated resorting to the exact solution of the model 89,90 .…”

Section: Theoretical Modeling and Simulationsmentioning

confidence: 99%

Mapping the Topography of a Protein Energy Landscape

et al. 2015

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Protein energy landscapes are highly complex, yet the vast majority of states within them tend to be invisible to experimentalists. Here, using site-directed mutagenesis and exploiting the simplicity of tandem-repeat protein structures, we delineate a network of these states and the routes between them. We show that our target, gankyrin, a 226-residue 7-ankyrin-repeat protein, can access two alternative (un)folding pathways. We resolve intermediates as well as transition states, constituting a comprehensive series of snapshots that map early and late stages of the two pathways and show both to be polarized such that the repeat array progressively unravels from one end of the molecule or the other. Strikingly, we find that the protein folds via one pathway but unfolds via a different one. The origins of this behavior can be rationalized using the numerical results of a simple statistical mechanics model that allows us to visualize the equilibrium behavior as well as single-molecule folding/unfolding trajectories, thereby filling in the gaps that are not accessible to direct experimental observation. Our study highlights the complexity of repeat-protein folding arising from their symmetrical structures; at the same time, however, this structural simplicity enables us to dissect the complexity and thereby map the precise topography of the energy landscape in full breadth and remarkable detail. That we can recapitulate the key features of the folding mechanism by computational analysis of the native structure alone will help towards the ultimate goal of designed amino-acid sequences with made-to-measure folding mechanisms -the Holy Grail of protein folding.

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“…This is the cooperativity arising from the connectivity of the chain. With this cooperativity, the residues that have the native-like configuration should tend to form contiguous domains in the sequence in the course of folding, and such tendency has been highlighted by the structurebased, coarse-grained models of folding (29)(30)(31)(32)(33)(34)(35)(36)(37)(38)(39). Success of these models in describing kinetic features of various small proteins showed that connectivity is an important factor to determine the cooperativity.…”

mentioning

confidence: 99%

Cooperativity, connectivity, and folding pathways of multidomain proteins

Itoh

Sasai

2008

Proc. Natl. Acad. Sci. U.S.A.

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Multidomain proteins are ubiquitous in both prokaryotic and eukaryotic proteomes. Study on protein folding, however, has concentrated more on the isolated single domains of proteins, and there have been relatively few systematic studies on the effects of domain-domain interactions on folding. We here discuss this issue by examining human ␥D-crystallin, spore coat protein S, and a tandem array of the R16 and R17 domains of spectrin as example proteins by using a structure-based model of folding. The calculated results consistently explain the experimental data on folding pathways and effects of mutational perturbations, supporting the view that the connectivity of two domains and the distribution of domain-domain interactions in the native conformation are factors to determine kinetic and equilibrium properties of cooperative folding.energy landscape theory ͉ structure-based model ͉ circular permutation O ur understanding of protein folding has been deepened by the combined efforts of experimental, theoretical, and computational studies of the last decade. Energy landscape theory describes folding as the stochastic relaxation process on the free energy surface of conformational change, where the free energy surface is determined by the compromise of conformational entropy of the polymer chain and interaction energies to stabilize the native conformation (1-3). Because proteins can fold when interactions that stabilize the native conformation dominate over the nonnative interactions that may trap the chain into the irrelevant structures, protein folding can be approximately simulated by using the interaction potentials that are derived from the knowledge of the native structure. With such structure-based models, folding of various small proteins has been simulated, and quantitative agreement between simulations and experiments has been reported (3). The agreement has been improved by simulations that further take account of the residue-dependent energetic differences (4), the atomistic packing (5-7), or the hydration structure (8), and such agreement has convinced us that the topology of the native structure is the primary determinant of the equilibrium and kinetic features of folding at least for small proteins (3) although the atomistic details perturb those features or they sometimes change the delicate balance among folding pathways (9, 10).These intensive studies on folding have been predominantly focused on small, single-domain proteins or isolated single domains of larger proteins. More than 70% of eukaryotic proteins, however, are composed of multiple domains, and hence we should ask whether the principles of folding found in single domains of proteins also apply to connected multidomain proteins as well (11). Anticorrelation between the contact order and the folding rate has been observed in multidomain proteins (12), and the structure-based simulations on multidomain proteins such as the ankyrin family (13-15) and CV-N (16) have provided consistent results with experiments. The importance of interactions...

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Statistical Mechanical Theory of the Protein Conformation. I. General Considerations and the Application to Homopolymers

Cited by 108 publications

References 15 publications

Folding pathway of a multidomain protein depends on its topology of domain connectivity

Folding pathway of a multidomain protein depends on its topology of domain connectivity

Mapping the Topography of a Protein Energy Landscape

Cooperativity, connectivity, and folding pathways of multidomain proteins

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