Analysis of PIN1 WW domain through a simple statistical mechanics model

Bruscolini, Pierpaolo; Cecconi, Fabio

doi:10.1016/j.bpc.2004.12.020

Cited by 6 publications

(7 citation statements)

References 30 publications

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“…These findings suggest that the mean-field approach could be used to further simplify the system and that the possibility of its application should be examined. The mean-field theory has been widely used to study protein systems, including the relationship between probe-dependent experiments and models [15,16,48]; the free energy landscape and the dynamic behavior of the WSME model [36]; and the thermodynamic properties of the Galzitskaya-Finkelstein (GF) model and its applications [74,76]. It is worth noting that, in some cases, the mean-field approach can relate thermodynamics and statistical mechanical models, thereby adding insight into the relationship between experimentally determined parameters and theoretical models [15].…”

Section: Discussionmentioning

confidence: 99%

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

et al. 2012

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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

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Section: Discussionmentioning

confidence: 99%

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

et al. 2012

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“…For each interaction matrix, we determine the temperature of midtransition T m and compute the free energy profile at that temperature, obtaining the free energy barrier Δ F †−( f,u ) as the difference between the absolute maximum in between the profile and the deepest minimum corresponding to the unfolded state. We evaluate the barrier at T m , inspired by previous results that show that the barrier calculated with the mean‐field model is more reliable in the region of temperatures around the transition temperature T m 33. We then obtain the folding and unfolding rates as k f , u = k 0 exp(−βΔ F †−( f,u ) ), assuming that k 0 is substantially independent of T in the range of temperatures considered, a reasonable hypothesis if the heterogeneity does not shift T m too much.…”

Section: Methodsmentioning

confidence: 99%

Sequence determinants of protein folding rates: Positive correlation between contact energy and contact range indicates selection for fast folding

2012

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In comparison with intense investigation of the structural determinants of protein folding rates, the sequence features favoring fast folding have received little attention. Here, we investigate this subject using simple models of protein folding and a statistical analysis of the Protein Data Bank (PDB). The mean-field model by Plotkin and coworkers predicts that the folding rate is accelerated by stronger-than-average interactions at short distance along the sequence. We confirmed this prediction using the Finkelstein model of protein folding, which accounts for realistic features of polymer entropy. We then tested this prediction on the PDB. We found that native interactions are strongest at contact range l = 8. However, since short range contacts tend to be exposed and they are frequently formed in misfolded structures, selection for folding stability tends to make them less attractive, that is, stability and kinetics may have contrasting requirements. Using a recently proposed model, we predicted the relationship between contact range and contact energy based on buriedness and contact frequency. Deviations from this prediction induce a positive correlation between contact range and contact energy, that is, short range contacts are stronger than expected, for 2/3 of the proteins. This correlation increases with the absolute contact order (ACO), as expected if proteins that tend to fold slowly due to large ACO are subject to stronger selection for sequence features favoring fast folding. Our results suggest that the selective pressure for fast folding is detectable only for one third of the proteins in the PDB, in particular those with large contact order.

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“…1). The design principles [37,38] and folding kinetics [25,29,33,[39][40][41][42][43][44][45][46][47] of WW domains and other three-stranded β-sheet proteins have been studied extensively. Because of their small size and abundance as protein domains, WW domains are important model systems for understanding β-sheet folding and stability.…”

Section: φ =mentioning

confidence: 99%

Transition States in Protein Folding Kinetics: Modeling Φ-Values of Small β-Sheet Proteins

Weikl

2008

Biophysical Journal

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Small single-domain proteins often exhibit only a single free-energy barrier, or transition state, between the denatured and the native state. The folding kinetics of these proteins is usually explored via mutational analysis. A central question is which structural information on the transition state can be derived from the mutational data. In this article, we model and structurally interpret mutational Phi-values for two small beta-sheet proteins, the PIN and the FBP WW domains. The native structure of these WW domains comprises two beta-hairpins that form a three-stranded beta-sheet. In our model, we assume that the transition state consists of two conformations in which either one of the hairpins is formed. Such a transition state has been recently observed in molecular dynamics folding-unfolding simulations of a small designed three-stranded beta-sheet protein. We obtain good agreement with the experimental data 1), by splitting up the mutation-induced free-energy changes into terms for the two hairpins and for the small hydrophobic core of the proteins; and 2), by fitting a single parameter, the relative degree to which hairpins 1 and 2 are formed in the transition state. The model helps us to understand how mutations affect the folding kinetics of WW domains, and captures also negative Phi-values that have been difficult to interpret.

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Analysis of PIN1 WW domain through a simple statistical mechanics model

Cited by 6 publications

References 30 publications

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

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

Sequence determinants of protein folding rates: Positive correlation between contact energy and contact range indicates selection for fast folding

Transition States in Protein Folding Kinetics: Modeling Φ-Values of Small β-Sheet Proteins

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