Conformational Energy Calculations on Polypeptides and Proteins

Vásquez, Maximiliano; Némethy, George; Scheraga, Harold A.

doi:10.1021/cr00032a002

Cited by 202 publications

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“…1, White and Meirovitch discuss the importance and difficulties of calculating the absolute free energy, F, and entropy, S; however, their role in computational structural biology should be further emphasized. The energy surface of a protein, commonly defined by a force field, is highly rugged, consisting of a tremendous number of local minima (2), where the native structure corresponds to the localized energy well with the lowest F. However, molecular dynamics simulations have shown (3,4) that even a protein with a well defined structure fluctuates significantly within a region called wide microstate (e.g., the conformational region of an ␣-helix of a peptide) that typically consists of many localized energy wells. A peptide or protein, or protein segments such as surface loops, can exhibit an intermediate flexibility, where several wide microstates are populated significantly at thermodynamic equilibrium.…”

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confidence: 99%

Simulation method for calculating the entropy and free energy of peptides and proteins

Cheluvaraja

Meirovitch

2004

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

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A method called complete hypothetical scanning Monte Carlo has been introduced for calculating the absolute entropy, S, and free energy, F, of fluids. Here, the method is extended to peptide chains in vacuum. Thus, S is calculated from a given sample by reconstructing each conformation step-by-step by using transition probabilities (TPs); at each step, part of the chain coordinates have already been determined (the ''frozen past''), and the TP is obtained from a Monte Carlo simulation of the (future) part of the chain whose TPs as yet have not been calculated. Very accurate results for S and F are obtained for the helix, extended, and hairpin microstates of a simplified model of decaglycine (Gly) 10 and (Gly)16. These results agree well with results obtained by the quasiharmonic approximation and the local states method. The complete HSMC method can be applied to a macromolecule with any degree of flexibility, ranging from local fluctuations to a random coil. Also, the difference in stability, ⌬F mn ‫؍‬ Fm ؊ Fn between significantly different microstates m and n can be obtained from two simulations only without the need to resort to thermodynamic integration. Our long-term goal is to extend this method to any peptide and apply it to a peptide immersed in a box with explicit water. I n ref. 1, White and Meirovitch discuss the importance and difficulties of calculating the absolute free energy, F, and entropy, S; however, their role in computational structural biology should be further emphasized. The energy surface of a protein, commonly defined by a force field, is highly rugged, consisting of a tremendous number of local minima (2), where the native structure corresponds to the localized energy well with the lowest F. However, molecular dynamics simulations have shown (3, 4) that even a protein with a well defined structure fluctuates significantly within a region called wide microstate (e.g., the conformational region of an ␣-helix of a peptide) that typically consists of many localized energy wells. A peptide or protein, or protein segments such as surface loops, can exhibit an intermediate flexibility, where several wide microstates are populated significantly at thermodynamic equilibrium. It is essential to be able to identify these wide microstates, m, and to calculate F m , which lead to their relative populations and to weighted averages of various quantities that can be compared with experimental values (5, 6). F m is useful particularly if m and n differ significantly; then, calculating the difference, ⌬F mn ϭ F m Ϫ F n is straightforward, whereas calculating it by thermodynamic integration might be prohibitive (see refs. 7-12 and references therein).In ref. 1, the hypothetical scanning (HS) method for calculating the absolute F and S (10) has been further developed and applied to liquid argon and water. This method, named complete hypothetical scanning Monte Carlo (HSMC), is extended here to a peptide in vacuum or peptide described by an implicit solvation. As a first step, we treat a simplified model...

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confidence: 99%

Simulation method for calculating the entropy and free energy of peptides and proteins

Cheluvaraja

Meirovitch

2004

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

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“…angles eq eq AMBER (1) r and θ are the actual values of the bond lengths and angles and r eq , and θ eq are their equilibrium values, respectively. r ij is the distance between atoms i and j and K r , K θ, Vn , n,γ, A ij , and B ij are constants.…”

Section: Protein Models and Energy Functionsmentioning

confidence: 99%

“…1 Identifying the lowest energy minima, in particular the global minimum, is the goal of protein folding studies, where the energy, rather than the free energy, is accepted as an approximate criterion of stability. A more rigorous criterion is minimum harmonic free energy, F har , where F har is obtained at an energy minimum from the harmonic entropy, S har that is proportional to the determinant of the Hessian, the matrix of second derivatives of the energy with respect to the molecular coordinates.…”

Section: Introductionmentioning

confidence: 99%

Performance of hybrid methods for large‐scale unconstrained optimization as applied to models of proteins

2003

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Energy minimization plays an important role in structure determination and analysis of proteins, peptides and other organic molecules; therefore, development of efficient minimization algorithms is important. Recently Morales and Nocedal have developed hybrid methods for large-scale unconstrained optimization that interlace iterations of the limited memory BFGS method (L-BFGS) and the Hessian-free Newton method (Computational Optimization and Applications (2002) 21, 143-154). We test the performance of this approach as compared to those of the L-BFGS algorithm of Liu and Nocedal and the truncated Newton (TN) with automatic preconditioner of Nash, as applied to the protein bovine pancreatic trypsin inhibitor (BPTI) and a loop of the protein Ribonuclease A. These systems are described by the all-atom AMBER force field with a dielectric constant ε=1 and a distance dependent dielectric function ε=2r, where r is the distance between two atoms. It is shown that for the optimal parameters, the hybrid approach is typically 2 times more efficient in terms of CPU time and function/gradient calculations than the two other methods. The advantage of the hybrid approach increases as the non-linearity of the energy function is enhanced, i.e., in going from ε=2r to ε=1, where the electrostatic interactions are stronger. However, no general rule that defines the optimal parameters has been found and their determination requires a relatively large number of trial and error calculations for each problem.

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“…[1]- [3]). For many years, the emphasis has been placed on how to find the global-minimum-energy conformation among a huge number of local-minimum states.…”

Section: Introductionmentioning

confidence: 99%

Free-Energy Calculations in Protein Folding by Generalized-Ensemble Algorithms

Sugita

Okamoto

2002

Lecture Notes in Computational Science and Engineering

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We review uses of the generalized-ensemble algorithms for free-energy calculations in protein folding. Two of the well-known methods are multicanonical algorithm and replicaexchange method; the latter is also referred to as parallel tempering. We present a new generalized-ensemble algorithm that combines the merits of the two methods; it is referred to as the replica-exchange multicanonical algorithm. We also give a multidimensional extension of the replica-exchange method. Its realization as an umbrella sampling method, which we refer to as the replica-exchange umbrella sampling, is a powerful algorithm that can give free energy in wide reaction coordinate space.

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Conformational Energy Calculations on Polypeptides and Proteins

Cited by 202 publications

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Simulation method for calculating the entropy and free energy of peptides and proteins

Simulation method for calculating the entropy and free energy of peptides and proteins

Performance of hybrid methods for large‐scale unconstrained optimization as applied to models of proteins

Free-Energy Calculations in Protein Folding by Generalized-Ensemble Algorithms

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