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Entropy and Free Energy of a Mobile Loop Based on the Crystal Structures of the Free and Bound Proteins.

ABSTRACT: A mobile loop changes its conformation from "open" (free enzyme) to "closed" upon ligand binding. The difference in the Helmholtz free energy, ?F(loop) between these states sheds light on the mechanism of binding. With our "hypothetical scanning molecular dynamics" (HSMD-TI) method ?F(loop) = F(free) - F(bound) where F(free) and F(bound) are calculated from two MD samples of the free and bound loop states; the contribution of water is obtained by a thermodynamic integration (TI) procedure. In previous work the free and bound loop structures were both attached to the same "template" which was "cut" from the crystal structure of the free protein. Our results for loop 287-290 of AcetylCholineEsterase agree with the experiment, ?F(loop)~ -4 kcal/mol if the density of the TIP3P water molecules capping the loop is close to that of bulk water, i.e., N(water) = 140 - 180 waters in a sphere of a 18 Å radius. Here we calculate ?F(loop) for the more realistic case, where two templates are "cut" from the crystal structures, 2dfp.pdb (bound) and 2ace.pdb (free), where N(water) = 40 - 160; this requires adding a computationally more demanding (second) TI procedure. While the results for N(water) ? 140 are computationally sound, ?F(loop) is always positive (18 ± 2 kcal/mol for N(water) = 140). These (disagreeing) results are attributed to the large average B-factor, 41.6 of 2dfp (23.4 Å(2) for 2ace). While this conformational uncertainty is an inherent difficulty, the (unstable) results for N(water) = 160 suggest that it might be alleviated by applying different (initial) structural optimizations to each template.

SUBMITTER: Mihailescu M

PROVIDER: S-EPMC3064000 | biostudies-literature | 2010 Aug

REPOSITORIES: biostudies-literature

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Entropy and Free Energy of a Mobile Loop Based on the Crystal Structures of the Free and Bound Proteins.

Mihailescu Mihail M Meirovitch Hagai H

Entropy (Basel, Switzerland) 20100801 8

A mobile loop changes its conformation from "open" (free enzyme) to "closed" upon ligand binding. The difference in the Helmholtz free energy, ΔF(loop) between these states sheds light on the mechanism of binding. With our "hypothetical scanning molecular dynamics" (HSMD-TI) method ΔF(loop) = F(free) - F(bound) where F(free) and F(bound) are calculated from two MD samples of the free and bound loop states; the contribution of water is obtained by a thermodynamic integration (TI) procedure. In pr ...[more]

PMID: 21448250

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Project description:Estimation of the energy from a given Boltzmann sample is straightforward since one just has to average the contribution of the individual configurations. On the other hand, calculation of the absolute entropy, S (hence the absolute free energy F) is difficult because it depends on the entire (unknown) ensemble. We have developed a new method called "the hypothetical scanning molecular dynamics" (HSMD) for calculating the absolute S from a given sample (generated by any simulation technique). In other words, S (like the energy) is "written" on the sample configurations, where HSMD provides a prescription of how to "read" it. In practice, each sample conformation, i, is reconstructed with transition probabilities, and 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 CarloHSMC) has been extended systematically to systems of increasing complexity, where the most recent is the seven-residue mobile loop, 304-310 (Gly-His-Gly-Ala-Gly-Gly-Ser) of the enzyme porcine pancreatic alpha-amylase modeled by the AMBER force field and AMBER with the implicit solvation GB/SA (paper I, Cheluvaraja, S.; Meirovitch, H. J. Chem. Theory Comput. 2008, 4, 192). In the present paper we make a step further and extend HSMD to the same loop capped with TIP3P explicit water at 300 K. As in paper I, we are mainly interested in entropy and free energy differences between the free and bound microstates of the loop, which are obtained from two separate MD samples of these microstates. The contribution of the loop to S and F is calculated by HSMD and that of water by a particular thermodynamic integration procedure. As expected, the free microstate is more stable than the bound microstate by a total free energy difference, Ffree-Fbound=-4.8+/-1, as compared to -25.5 kcal/mol obtained with GB/SA. We find that relatively large systematic errors in the loop entropies, Sfree(loop) and Sbound(loop) are cancelled in their difference which is thus obtained efficiently and with high accuracy, i.e., with a statistical error of 0.1 kcal/mol. This cancellation, which has been observed in previous HSMD studies, is in accord with theoretical arguments given in paper I.

Project description:The loop 287-290 (Ile, Phe, Arg, and Phe) of the protein acetylcholinesterase (AChE) changes its structure upon interaction of AChE with diisopropylphosphorofluoridate (DFP). Reversible dissociation measurements suggest that the free-energy (F) penalty for the loop displacement is DeltaF=Ffree-Fbound approximately -4 kcal/mol. Therefore, this loop has been the target of two studies by Olson's group for testing the efficiency of procedures for calculating F. In this paper, we test for the first time the performance of our "hypothetical scanning molecular dynamics" (HSMD) method and the validity of the related modeling for a loop with bulky side chains in explicit water. Thus, we consider only atoms of the protein that are the closest to the loop (they constitute the "template"), where the rest of the atoms are ignored. The template's atoms are fixed in the X-ray coordinates of the free protein, and the loop is capped with a sphere of TIP3P water molecules; also, the X-ray structure of the bound loop is attached to the free template. We carry out two separate MD simulations starting from the free and bound X-ray structures, where only the atoms of the loop and water are allowed to move while the template-water and template-loop (AMBER) interactions are considered. The absolute Ffree and Fbound (of the loop and water) are calculated from the corresponding trajectories. A main objective of this paper is to assess the reliability of this model, and for this several template sizes are studied capped with 80-220 water molecules. We find that consistent results for the free energy (which also agree with the experimental data above) require a template larger than a minimal size and a number of water molecules approximately equal to the experimental density of bulk water. For example, we obtain DeltaFtotal=DeltaFwater+DeltaFloop=-3.1+/-2.5 and -3.6+/-4 kcal/mol for a template consisting of 944 atoms and a sphere containing 160 and 180 waters, respectively. Our calculations demonstrate the important contribution of water to the total free energy. Namely, for water densities close to the experimental value, DeltaFwater is always negative leading thereby to a negative DeltaFtotal (while DeltaFloop is always positive). Also, the contribution of the water entropy TDeltaSwater to DeltaFtotal is significant. Various aspects related to the efficiency of HSMD are tested and improved, and plans for future studies are discussed.

Project description:Limitations in protein homology modeling often arise from the inability to adequately model loops. In this paper we focus on the selection of loop conformations. We present a complete computational treatment that allows the screening of loop conformations to identify those that best fit a molecular model. The stability of a loop in a protein is evaluated via computations of conformational free energies in solution, i.e., the free energy difference between the reference structure and the modeled one. A thermodynamic cycle is used for calculation of the conformational free energy, in which the total free energy of the reference state (i.e., gas phase) is the CHARMm potential energy. The electrostatic contribution of the solvation free energy is obtained from solving the finite-difference Poisson-Boltzmann equation. The nonpolar contribution is based on a surface area-based expression. We applied this computational scheme to a simple but well-characterized system, the antibody hypervariable loop (complementarity-determining region, CDR). Instead of creating loop conformations, we generated a database of loops extracted from high-resolution crystal structures of proteins, which display geometrical similarities with antibody CDRs. We inserted loops from our database into a framework of an antibody; then we calculated the conformational free energies of each loop. Results show that we successfully identified loops with a "reference-like" CDR geometry, with the lowest conformational free energy in gas phase only. Surprisingly, the solvation energy term plays a confusing role, sometimes discriminating "reference-like" CDR geometry and many times allowing "non-reference-like" conformations to have the lowest conformational free energies (for short loops). Most "reference-like" loop conformations are separated from others by a gap in the gas phase conformational free energy scale. Naturally, loops from antibody molecules are found to be the best models for long CDRs (> or = 6 residues), mainly because of a better packing of backbone atoms into the framework of the antibody model.

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Entropy and Free Energy of a Mobile Loop Based on the Crystal Structures of the Free and Bound Proteins.

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Entropy and Free Energy of a Mobile Loop Based on the Crystal Structures of the Free and Bound Proteins.

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