Calculation of the entropy and free energy by the hypothetical scanning Monte Carlo method: Application to peptides

Cheluvaraja, Srinath; Meirovitch, Hagai

doi:10.1063/1.1835911

Cited by 29 publications

(79 citation statements)

References 36 publications

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“…However, for forces larger than a small critical value a transition from the helix to the extended state occurs already in the early stage of the MC simulation and the entropy and free energy were therefore obtained for the extended state. The present results are more accurate than those obtained by the LS and QH methods, and it is of interest to compare them also to results obtained for the flexible model of (Gly) 10 in ref 25 at T ) 100 K without applying external forces. Thus, the accuracy of S A , the upper bound of the entropy, is better than that obtained there …”

Section: Discussionsupporting

confidence: 64%

Calculation of the Entropy and Free Energy from Monte Carlo Simulations of a Peptide Stretched by an External Force

Cheluvaraja

Meirovitch

2005

J. Phys. Chem. B

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Hypothetical scanning Monte Carlo (HSMC) is a method for calculating the absolute entropy, S, and free energy, F, from a trajectory generated by any simulation technique. HSMC was applied initially to fluids (argon and water) and later to peptides and self-avoiding walks on a lattice. In this paper we make a step further and apply it to a model of decaglycine (at T ) 300 K) in vacuum with constant bond lengths where external stretching forces are exerted at the end points; the changes in S and F are calculated as the forces are increased. The molecule is placed initially in a helical structure, which is changed to an extended structure after a short simulation time due to the exerted forces. This study has relevance to problems in polymers (e.g., rubber elasticity) and to the analysis of experiments where individual molecules are stretched by atomic force microscopy (AFM), for example. The results for S and F are accurate and are significantly better than those obtained by the quasi-harmonic approximation and the local states method. However, the molecule is quite stiff due to the strong bond angle potentials and the extensions are small even for relatively large forces. Correspondingly, as the force is increased the decrease in the entropy is relatively small while the potential energy is enhanced significantly. Still, differences, T∆S, for different forces are obtained with very good accuracy of ∼0.2 kcal/mol.

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Section: Discussionsupporting

confidence: 64%

Calculation of the Entropy and Free Energy from Monte Carlo Simulations of a Peptide Stretched by an External Force

Cheluvaraja

Meirovitch

2005

J. Phys. Chem. B

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“…Recently, the HS method has been extended to fluids and has been further developed by defining transition probabilities (TPs) that are calculated by an MC procedure and (unlike the TPs of HS) take into account all the long-range interactions [24,25]; this HSMC method has been applied very successfully to liquid argon, TIP3P water [25], and polyglycine molecules in helical, extended and hairpin states [26]. HSMC is significantly more accurate than HS, provides rigorous upper and lower bounds for F, which can be calculated from a relatively small sample and even from a single conformation.…”

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confidence: 99%

“…6)]. Also, it should be pointed out that an HSMC reconstruction for SAWs with attractions is practically the same, where, however, the MC acceptance criterion is determined by both, EV and the attractions [26].…”

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confidence: 99%

“…5) that are expected to increase efficiency further. Also, a chain with attractive interactions (a homopolymer or a heteropolymer consisting of monomers with different interactions) unlike SAWs would span (at low T) only a limited part of conformational space; to obtain the corresponding local F, the future chains should be limited to this region, which can be achieved only by local MC moves [26]. Moreover, in this work we have studied straight chains that are the easiest to reconstruct, where in practical applications non-straight SAWs will be treated.…”

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confidence: 99%

“…However, the applicability of HSMC to both, random coil SAWs and peptides that fluctuate locally [26] demonstrates applicability to all ranges of flexibility, versatility that is not shared by other methods. Thus, the harmonic and quasi-harmonic techniques [32,33] are limited to handle (at least approximately) local fluctuations (for which HS has failed), LS is very inefficient for SAWs, and calculating the absolute S (and F) of local fluctuations of peptides by TI is a standing problem.…”

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Calculation of the entropy of lattice polymer models from Monte Carlo trajectories

White

Funt

Meirovitch

2005

Chemical Physics Letters

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While lattice models are used extensively for macromolecules (synthetic polymers proteins, etc), calculation of the absolute entropy, S, and the free energy, F, from a given Monte Carlo (MC) trajectory is not straightforward. Recently we have developed the hypothetical scanning MC (HSMC) method for calculating S and F of fluids. Here we extend HSMC to self-avoiding walks on a square lattice and discuss its wide applicability to complex polymer lattice models. HSMC is independent of existing techniques and thus constitutes an independent research tool; it provides rigorous upper and lower bounds for F, which can be obtained from a very small sample and even from a single chain conformation.Lattice models have been utilized to study a wide range of phenomena in polymer physics [1][2][3][4][5] as well as in structural biology, mainly related to protein folding and stability [6-9] (Refs 1-9 constitute a very limited representation of hundreds of papers published in the last 15 years). Because of their simplicity these models have been invaluable tools for understanding global properties that do not depend strongly on molecular details. Such models vary in complexity, ranging from self-avoiding walks on a square lattice to chain models on enriched 3D lattices with a large effective coordination number.Commonly, these systems are simulated by variants of Metropolis Monte Carlo (MC) -a dynamical method that enables one to generate samples of chain configurations i distributed according to their Boltzmann probability, P i B , from which equilibrium information can be extracted [10]. Using MC it is straightforward to calculate properties that are measured directly from i, such as the potential energy E i . On the other hand, the value of P i B cannot be obtained in a straightforward manner, which makes it difficult to calculate the absolute entropy, S ~ -lnP i B directly, i.e., as a byproduct of the simulation (like E i ). There is a strong interest in S as a measure of order and as an essential ingredient of the free energy, F=E−TS, where T is the absolute temperature; F constitutes the criterion of stability, which is mandatory in structure determination of proteins, for example. Furthermore, because MC simulations constitute models for dynamical processes, one would seek to calculate changes in F and S during a relaxation process, by assuming local equilibrium in certain parts along the MC trajectory; a classic example is simulation of protein folding [11].S, and F are commonly calculated by thermodynamic integration (TI) techniques [12][13][14] that do not operate on a given MC sample but requires conducting a separate set of MC simulations. This is a robust approach that enables one to calculate differences, ΔS ab and ΔF ab , between two states a and b of a system; however, if the structural variance of such states is large (e.g., helical and hairpin states of a polypeptide) the integration from state a to b becomes difficult *Corresponding author

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The F130L mutation in streptavidin reduces its binding affinity to biotin through electronic polarization effect

et al. 2013

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Recently, Baugh et al. discovered that a distal point mutation (F130L) in streptavidin causes no distinct variation to the structure of the binding pocket but a 1000-fold reduction in biotin binding affinity. In this work, we carry out molecular dynamics simulations and apply an end-state free energy method to calculate the binding free energies of biotin to wild type streptavidin and its F130L mutant. The absolute binding affinities based on AMBER charge are repulsive, and the mutation induced binding loss is underestimated. When using the polarized protein-specific charge, the absolute binding affinities are significantly enhanced. In particular, both the absolute and relative binding affinities are in line with the experimental measurements. Further investigation indicates that polarization effect is indispensable in both the generation of structural ensembles and the calculation of interaction energies. This work verifies Baugh's conjecture that electrostatic polarization effect plays an essential role in modulating the binding affinity of biotin to the streptavidin through F130L mutation.

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Calculation of the entropy and free energy by the hypothetical scanning Monte Carlo method: Application to peptides

Cited by 29 publications

References 36 publications

Calculation of the Entropy and Free Energy from Monte Carlo Simulations of a Peptide Stretched by an External Force

Calculation of the Entropy and Free Energy from Monte Carlo Simulations of a Peptide Stretched by an External Force

Calculation of the entropy of lattice polymer models from Monte Carlo trajectories

The F130L mutation in streptavidin reduces its binding affinity to biotin through electronic polarization effect

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