Free Energy Via Molecular Simulation: Applications to Chemical and Biomolecular Systems

Beveridge, David L.; DiCapua, Frank M.

doi:10.1146/annurev.bb.18.060189.002243

Cited by 1,071 publications

(857 citation statements)

References 135 publications

(187 reference statements)

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“…In most cases, however, one is interested in free energy differences ∆F mn , which are somewhat easier to obtain than F m and F n themselves. [13][14][15][16][17][18][19] I.3. Calculation of ∆F mn by the Counting Method and Thermodynamic Integration.…”

Section: I1 the Role Of Free Energy In Structural Biologymentioning

confidence: 99%

Stability of the Free and Bound Microstates of a Mobile Loop of α-Amylase Obtained from the Absolute Entropy and Free Energy

Cheluvaraja

Meirovitch

2007

J. Chem. Theory Comput.

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Abstract:The hypothetical scanning molecular dynamics (HSMD) method is a relatively new technique for calculating the absolute entropy, S, and free energy, F, from a given sample generated by any simulation procedure. Thus, each sample conformation, i, is reconstructed by calculating transition probabilities that their product leads to the probability of i, hence to the entropy. HSMD is an exact method where all interactions are considered, and the only approximation is due to insufficient sampling. In previous studies HSMD (and HS Monte Carlo -HSMC) has been applied very successfully to liquid argon, TIP3P water, self-avoiding walks, and peptides in a R-helix, extended, and hairpin microstates. In this paper HSMD is developed further as applied to the flexible 7-residue surface loop, 304-310 (Gly-His-Gly-Ala-Gly-GlySer) of the enzyme porcine pancreatic R-amylase. We are mainly interested in entropy and free energy differences ∆S ) S free -S bound (and ∆F)F free -F bound ) between the free and bound microstates of the loop, which are obtained from two separate MD samples of these microstates without the need to carry out thermodynamic integration. As for peptides, we find that relatively large systematic errors in S free and S bound (and F free and F bound ) are cancelled in ∆S (∆F) which is thus obtained efficiently with high accuracy, i.e., with a statistical error of 0.1-0.2 kcal/mol (T)300 K) using the AMBER force field and AMBER with the implicit solvation GB/SA. We provide theoretical arguments in support of this cancellation, discuss in detail the problems involved in the computational definition of a microstate in conformational space, suggest potential ways for enhancing efficiency further, and describe the next development where explicit water will replace implicit solvation.

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Section: I1 the Role Of Free Energy In Structural Biologymentioning

confidence: 99%

Stability of the Free and Bound Microstates of a Mobile Loop of α-Amylase Obtained from the Absolute Entropy and Free Energy

Cheluvaraja

Meirovitch

2007

J. Chem. Theory Comput.

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“…Free energy perturbation (FEP) 30,40 can be performed to evaluate free energy change caused by a small structural change. The FEP method, in combination with MD simulation, has been used to study protein-ligand interaction [41][42][43] and protein stability.…”

Section: Free Energy Simulationmentioning

confidence: 99%

Free Energy Perturbation (FEP) Simulation on the Transition States of Cocaine Hydrolysis Catalyzed by Human Butyrylcholinesterase and Its Mutants

et al. 2007

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A novel computational protocol based on free energy perturbation (FEP) simulations on both the free enzyme and transition state structures has been developed and tested to predict the mutation-caused shift of the free energy change from the free enzyme to the rate-determining transition state for human butyrylcholinesterase (BChE)-catalyzed hydrolysis of (-)-cocaine. The calculated shift, denoted by ΔΔG(1→2), of such kind of free energy change determines the catalytic efficiency (k cat /K M ) change caused by the simulated mutation transforming enzyme 1 to enzyme 2. By using the FEP-based computational protocol, the ΔΔG(1→2) values for the mutations A328W/Y332A → A328W/Y332G and A328W/Y332G → A328W/Y332G/A199S were calculated to be -0.22 and -1.94 kcal/mol, respectively. The calculated ΔΔG(1→2) values predict that the change from the A328W/Y332A mutant to the A328W/Y332G mutant should slightly improve the catalytic efficiency and that the change from the A328W/Y332G mutant to the A328W/Y332G/A199S mutant should significantly improve the catalytic efficiency of the enzyme for the (-)-cocaine hydrolysis. The predicted catalytic efficiency increases are supported by the experimental data showing that k cat /K M = 8.5 × 10 6 , 1.4 × 10 7 , and 7.2 × 10 7 min -1 M -1 for the A328W/Y332A, A328W/Y332G, and A328W/Y332G/A199S mutants, respectively. The qualitative agreement between the computational and experimental data suggests that the FEP simulations may provide a promising protocol for rational design of highactivity mutants of an enzyme. The general computational strategy of the FEP simulation on a transition state can be used to study the effects of a mutation on the activation free energy for any enzymatic reaction.

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“…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…”

mentioning

confidence: 99%

“…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 and in many cases unfeasible.…”

mentioning

confidence: 99%

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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Free Energy Via Molecular Simulation: Applications to Chemical and Biomolecular Systems

Cited by 1,071 publications

References 135 publications

Stability of the Free and Bound Microstates of a Mobile Loop of α-Amylase Obtained from the Absolute Entropy and Free Energy

Stability of the Free and Bound Microstates of a Mobile Loop of α-Amylase Obtained from the Absolute Entropy and Free Energy

Free Energy Perturbation (FEP) Simulation on the Transition States of Cocaine Hydrolysis Catalyzed by Human Butyrylcholinesterase and Its Mutants

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

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