Quantitative Prediction of Protein Folding Behaviors from a Simple Statistical Model

Bruscolini, Pierpaolo; Naganathan, Athi N.

doi:10.1021/ja110884m

Cited by 34 publications

(54 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The two key assumptions of the Ising-like model are that amino acid interactions absent in the native structure play an insignificant role in determining the folding mechanism (23)(24)(25) and that native structure grows in only a few regions of the amino acid sequence as folding progresses. In the accompanying paper by Best et al (16), the MD simulations for nine proteins with clear two-state kinetics simulated by the Shaw group (10,11,14,15) are found to be consistent with the first assumption, which is also key to many other theoretical models (26)(27)(28)(29)(30)(31)(32)(33)(34)(35)(36)(37)(38)(39)(40)(41)(42) and numerous simulations of simplified representations of proteins (reviewed in refs. 1,43,44).…”

mentioning

confidence: 60%

Comparing a simple theoretical model for protein folding with all-atom molecular dynamics simulations

Henry

Best

Eaton

2013

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

109

View full text Add to dashboard Cite

Advances in computing have enabled microsecond all-atom molecular dynamics trajectories of protein folding that can be used to compare with and test critical assumptions of theoretical models. We show that recent simulations by the Shaw group (10,11,14,15) are consistent with a key assumption of an Ising-like theoretical model that native structure grows in only a few regions of the amino acid sequence as folding progresses. The distribution of mechanisms predicted by simulating the master equation of this native-centric model for the benchmark villin subdomain, with only two adjustable thermodynamic parameters and one temperature-dependent kinetic parameter, is remarkably similar to the distribution in the molecular dynamics trajectories. T heoretical models are essential for understanding the complex self-assembly reaction of protein folding, despite their reliance on apparently strong simplifying assumptions (1-5). In fact, the validated assumptions in a successful model point to the important features in protein folding. However, these assumptions are generally difficult to either justify or falsify by experiment. Fortunately, we can now examine them directly, thanks to recent advances in computing that allow us to study folding kinetics and mechanisms with all-atom molecular dynamics (MD) simulations (6-13). In particular, through the work of the Shaw group (10,11,14,15), many folding and unfolding transitions have been observed in long equilibrium trajectories. Here, and in the accompanying paper by Best et al. (16), we compare the key assumptions of a simple Ising-like model with the results from the all-atom MD simulations of the Shaw group (10,11,14,15). We also compare the distribution of folding mechanisms predicted by the model and the MD simulations.Ideally, to capture the full complexity of the process, a theoretical model for protein folding should enumerate all relevant conformations and specify the transition rates between them. To be useful, the model should also quantify the observables in equilibrium and kinetics experiments, and, like any theoretical model, be testable by new experiments. Among the very large number of proposed models (see bibliography in SI Text), a simple Ising-like model based on the contact map of the folded structure (17, 18), with just two adjustable thermodynamic parameters and a third parameter to set the time scale for kinetics, is of particular interest because it is the only one thus far that enumerates conformations and quantitatively explains so many different kinds of experimental results (19)(20)(21)(22). The two key assumptions of the Ising-like model are that amino acid interactions absent in the native structure play an insignificant role in determining the folding mechanism (23-25) and that native structure grows in only a few regions of the amino acid sequence as folding progresses. In the accompanying paper by Best et al. (16), the MD simulations for nine proteins with clear two-state kinetics simulated by the Shaw group (10,11,14,15) are found to be con...

show abstract

mentioning

confidence: 60%

Comparing a simple theoretical model for protein folding with all-atom molecular dynamics simulations

Henry

Best

Eaton

2013

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

109

View full text Add to dashboard Cite

show abstract

“…6(c) and (e)]. Recently, Bruscolini et al [30] extended the original model to the WSME-S model, which includes solvation effects explicitly. The authors addressed the solvation effects using an expression of the temperature-dependent parameters in the original WSME model, which can be adjusted to the phenomenological behavior of the heat capacity of any protein conformation.…”

Section: Discussionmentioning

confidence: 99%

“…Note that E = k B T 2 d ln Z dT is used in (30). According to the set of reduced partition functions derived and shown from (14) through (20), the heat capacity equations for systems with a different N can, in principle, be derived.…”

Section: Appendix C: the Single Foldon Unit Casementioning

confidence: 99%

“…It is worth noting that more complex multistate models, based on the generalization of the classical Potts model [19,26], can also be employed, though rare so far, to study protein folding [27,28]. Among the above-mentioned models, the Wako-Saitô-Muñoz-Eaton (WSME) model has been applied to study the folding of many proteins [6,7,18,29,30,33] and RNA molecules [31,32]. The WSME model is a topology-based model in which a protein state is represented topologically by {x 1 , x 2 , · · · , x i , · · · x N } ; x i is a binary variable and x i = 1 and x i = 0 indicate, respectively, the folded (native) or unfolded state at the i th local peptide bond.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Thermodynamics of protein folding using a modified Wako-Saitô-Muñoz-Eaton model

et al. 2012

View full text Add to dashboard Cite

Herein, we propose a modified version of the Wako-Saitô-Muñoz-Eaton (WSME) model. The proposed model introduces an empirical temperature parameter for the hypothetical structural units (i.e., foldons) in proteins to include site-dependent thermodynamic behavior. The thermodynamics for both our proposed model and the original WSME model were investigated. For a system with beta-hairpin topology, a mathematical treatment (contact-pair treatment) to facilitate the calculation of its partition function was developed. The results show that the proposed model provides better insight into the site-dependent thermodynamic behavior of the system, compared with the original WSME model. From this site-dependent point of view, the relationship between probe-dependent experimental results and model's thermodynamic predictions can be explained. The model allows for suggesting a general principle to identify foldon behavior. We also find that the backbone hydrogen bonds may play a role of structural constraints in modulating the cooperative system. Thus, our study may contribute to the understanding of the fundamental principles for the thermodynamics of protein folding.Keywords WSME model · Protein · Beta-hairpin · Backbone hydrogen bond · Thermodynamics · Probe-dependent thermodynamic behavior · Site-dependent behavior · Foldon

show abstract

“…17,[35][36][37] The original WSME model was proposed to explain the folding thermodynamics and kinetics of peptides 17 and proteins 34,37 about a decade ago. Because of its simplicity, it has been extended/modified to study not only a single isolated protein but also repeat proteins, 38 b-amyloid aggregation, 39 proteins under solvated condition, 40 and even RNA molecules. 41 Recently, we modified this model to include site-dependent folding properties for a b-hairpin, 42 aiming at understanding the probe-dependent experimental results in terms of the site-dependent properties in the peptide.…”

Section: Introductionmentioning

confidence: 99%

Molecular Dynamics Insight into the Diverse Thermodynamic Behavior of a Beta‐Hairpin Peptide

Tsai

Yuan

Yamaki

et al. 2013

J Chinese Chemical Soc

View full text Add to dashboard Cite

The b-hairpin is a building block in the b-sheet structure. Understanding the formation of the b-hairpin may provide insight into the formation of b-sheet structures in, for example, protein amyloids. In this study, we performed molecular dynamics (MD) simulations to investigate the temperature-dependent transition behaviors of the GB1 b-hairpin peptide. The simulated results are analysed in terms of distances between pairs of peptide bonds and site-dependent dihedral angles. Our results show that the properties of the hairpin can be site-dependent and that the dependency is primarily associated with the hairpin's geometrical shape and specific interactions, such as hydrophobic clustering. Thus our study provides a foundation for the interpretation of probe-dependent experimental results.

show abstract

Quantitative Prediction of Protein Folding Behaviors from a Simple Statistical Model

Cited by 34 publications

References 49 publications

Comparing a simple theoretical model for protein folding with all-atom molecular dynamics simulations

Comparing a simple theoretical model for protein folding with all-atom molecular dynamics simulations

Thermodynamics of protein folding using a modified Wako-Saitô-Muñoz-Eaton model

Molecular Dynamics Insight into the Diverse Thermodynamic Behavior of a Beta‐Hairpin Peptide

Contact Info

Product

Resources

About