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

Cheluvaraja, Srinath; Meirovitch, Hagai

doi:10.1021/ct700116n

Cited by 12 publications

(101 citation statements)

References 82 publications

(233 reference statements)

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“…26). The Jacobian is also omitted for simplicity because we have shown 13 that it cancels out (within the error bars) in entropy and free-energy differences (this conclusion was checked again and verified in the present study). The Boltzmann probability density corresponding to Z [Eq.…”

Section: Statistical Mechanics Of a Loop In Internal Coordinatessupporting

confidence: 78%

“…In Ref. 13, we have shown that δα k and δα k+1 can be optimized. Notice that with HSMD the future loop conformations generated by MD at each step k' remain in general within the limits of m, which is represented by the analyzed MD sample.…”

Section: E the Hsmc(d) Methodsmentioning

confidence: 99%

“…S A loop [Eqs. (13) and (14)] constitutes a measure of a pure geometrical character for the loop flexibility, i.e., with no direct dependence on the interaction energy. When the converged or the best value of S A loop is considered, it will be denoted by S loop ; thus, F loop = E loop − TS loop is defined as the loop's contribution to the total free energy, where E loop is defined in Eq.…”

Section: E the Hsmc(d) Methodsmentioning

confidence: 99%

“…Also, with long simulations it is difficult to guarantee that the loop will remain in microstate m (see the discussion in Ref. 13). However, the exact scanning procedure provides the theoretical basis for HSMC(D).…”

Section: Exact Stochastic Future Scanning Proceduresmentioning

confidence: 99%

“…We studied initially the seven-residue surface loop, 304-310 (Gly-HisGly-Ala-Gly-Gly-Ser), of the enzyme porcine pancreatic α-amylase in vacuum and in the generalized Born surface area (GB/SA) implicit solvent. 13 In a subsequent paper, the loop was capped with 70 TIP3P water molecules and an HSMD-TI procedure was developed in which the contribution of water to F is calculated by a TI process, which is more efficient than HSMD. 14 Subsequently, HSMD-TI was applied to the loop 287-290 with the bulky residues, Ile, Phe, Arg, and Phe of acetylcholinesterase (AChE) from Torpedo California; 26 reaction of AChE with the inhibitor diisopropylphosphorofluoridate (DFP) leads to a displacement of the loop's backbone by roughly 4 Å, and experimental evidence suggests that the free-energy penalty for the loop displacement is on the order of 4 kcal/mol (i.e., F free -F bound ∼ −4 kcal/mol).…”

Section: Introductionmentioning

confidence: 99%

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Relative stability of the open and closed conformations of the active site loop of streptavidin

General

Meirovitch²

2011

The Journal of Chemical Physics

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The eight-residue surface loop, 45-52 (Ser, Ala, Val, Gly, Asn, Ala, Glu, Ser), of the homotetrameric protein streptavidin has a "closed" conformation in the streptavidin-biotin complex, where the corresponding binding affinity is one of the strongest found in nature ( G ∼ -18 kcal/mol). However, in most of the crystal structures of apo (unbound) streptavidin, the loop conformation is "open" and typically exhibits partial disorder and high B-factors. Thus, it is plausible to assume that the loop structure is changed from open to closed upon binding of biotin, and the corresponding difference in free energy, F = F open -F closed in the unbound protein, should therefore be considered in the total absolute free energy of binding. F (which has generally been neglected) is calculated here using our "hypothetical scanning molecular-dynamics" (HSMD) method. We use a protein model in which only the atoms closest to the loop are considered (the "template") and they are fixed in the x-ray coordinates of the free protein; the x-ray conformation of the closed loop is attached to the same (unbound) template and both systems are capped with the same sphere of TIP3P water. Using the force field of the assisted model building with energy refinement (AMBER), we carry out two separate MD simulations (at temperature T = 300 K), starting from the open and closed conformations, where only the atoms of the loop and water are allowed to move (the template-water and template-loop interactions are considered). The absolute F open and F closed (of loop + water) are calculated from these trajectories, where the loop and water contributions are obtained by HSMD and a thermodynamic integration (TI) process, respectively. The combined HSMD-TI procedure leads to total (loop + water) F = −27.1 ± 2.0 kcal/mol, where the entropy T S constitutes 34% of F, meaning that the effect of S is significant and should not be ignored. Also, S is positive, in accord with the high flexibility of the open loop observed in crystal structures, while the energy E is unexpectedly negative, thus also adding to the stability of the open loop. The loop and the 250 capped water molecules are the largest system studied thus far, which constitutes a test for the efficiency of HSMD-TI; this efficiency and technical issues related to the implementation of the method are also discussed. Finally, the result for F is a prediction that will be considered in the calculation of the absolute free energy of binding of biotin to streptavidin, which constitutes our next project.

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Section: Statistical Mechanics Of a Loop In Internal Coordinatessupporting

confidence: 78%

Section: E the Hsmc(d) Methodsmentioning

confidence: 99%

Section: E the Hsmc(d) Methodsmentioning

confidence: 99%

Section: Exact Stochastic Future Scanning Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Relative stability of the open and closed conformations of the active site loop of streptavidin

General

Meirovitch²

2011

The Journal of Chemical Physics

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The SAAP force field: Development of the single amino acid potentials for 20 proteinogenic amino acids and Monte Carlo molecular simulation for short peptides

et al. 2009

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Molecular simulation by using force field parameters has been widely applied in the fields of peptide and protein research for various purposes. We recently proposed a new all-atom protein force field, called the SAAP force field, which utilizes single amino acid potentials (SAAPs) as the fundamental elements. In this article, whole sets of the SAAP force field parameters in vacuo, in ether, and in water have been developed by ab initio calculation for all 20 proteinogenic amino acids and applied to Monte Carlo molecular simulation for two short peptides. The side-chain separation approximation method was employed to obtain the SAAP parameters for the amino acids with a long side chain. Monte Carlo simulation for Met-enkephalin (CHO-Tyr-Gly-Gly-Phe-Met-NH2) by using the SAAP force field revealed that the conformation in vacuo is mainly controlled by strong electrostatic interactions between the amino acid residues, while the SAAPs and the interamino acid Lennard-Jones potentials are predominant in water. In ether, the conformation would be determined by the combination of the three components. On the other hand, the SAAP simulation for chignolin (H-Gly-Tyr-Asp-Pro-Glu-Thr-Gly-Thr-Trp-Gly-OH) reasonably reproduced a native-like beta-hairpin structure in water although the C-terminal and side-chain conformations were different from the native ones. It was suggested that the SAAP force field is a useful tool for analyzing conformations of polypeptides in terms of intrinsic conformational propensities of the single amino acid units.

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Methods for calculating the absolute entropy and free energy of biological systems based on ideas from polymer physics

Meirovitch

2009

J of Molecular Recognition

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The commonly used simulation techniques, Metropolis Monte Carlo (MC) and molecular dynamics (MD) are of a dynamical type which enables one to sample system configurations i correctly with the Boltzmann probability, P i B while the value of P i B is not provided directly; therefore, it is difficult to obtain the absolute entropy, S ~ -ln P i B , and the Helmholtz free energy, F. With a different simulation approach developed in polymer physics, a chain is grown step-bystep with transition probabilities (TPs), and thus their product is the value of the construction probability; therefore, the entropy is known. Because all exact simulation methods are equivalent, i.e. they lead to the same averages and fluctuations of physical properties, one can treat an MC or MD sample as if its members have rather been generated step-by-step. Thus, each configuration i of the sample can be reconstructed (from nothing) by calculating the TPs with which it could have been constructed. This idea applies also to bulk systems such as fluids or magnets. This approach has led earlier to the "local states" (LS) and the "hypothetical scanning" (HS) methods, which are approximate in nature. A recent development is the hypothetical scanning Monte Carlo (HSMC) (or molecular dynamics, HSMD) method which is based on stochastic TPs where all interactions are taken into account. In this respect HSMC(D) can be viewed as exact and the only approximation involved is due to insufficient MC(MD) sampling for calculating the TPs. The validity of HSMC has been established by applying it first to liquid argon, TIP3P water, selfavoiding walks, and polyglycine models, where the results for F were found to agree with those obtained by other methods. Subsequently, HSMD was applied to mobile loops of the enzymes porcine pancreatic α-amylase and acetylcholineesterase in explicit water, where the difference of F between the bound and free states of the loop was calculated. Currently HSMD is being extended for calculating the absolute and relative free energy of ligand-enzyme binding. We describe the whole approach and discuss future directions.

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

Cited by 12 publications

References 82 publications

Relative stability of the open and closed conformations of the active site loop of streptavidin

Relative stability of the open and closed conformations of the active site loop of streptavidin

The SAAP force field: Development of the single amino acid potentials for 20 proteinogenic amino acids and Monte Carlo molecular simulation for short peptides

Methods for calculating the absolute entropy and free energy of biological systems based on ideas from polymer physics

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