Calculation of the entropy and free energy of peptides by molecular dynamics simulations using the hypothetical scanning molecular dynamics method

Abstract

Hypothetical scanning (HS) is a method for calculating the absolute entropy S and free energy F from a sample generated by any simulation technique. With this approach each sample configuration is reconstructed with the help of transition probabilities (TPs) and their product leads to the configuration's probability, hence to the entropy. Recently a new way for calculating the TPs by Monte Carlo (MC) simulations has been suggested, where all system interactions are taken into account. Therefore, this method--called HSMC--is in principle exact where the only approximation is due to insufficient sampling. HSMC has been applied very successfully to liquid argon, TIP3P water, self-avoiding walks on a lattice, and peptides. Because molecular dynamics (MD) is considered to be significantly more efficient than MC for a compact polymer chain, in this paper HSMC is extended to MD simulations as applied to peptides. Like before, we study decaglycine in vacuum but for the first time also a peptide with side chains, (Val)(2)(Gly)(6)(Val)(2). The transition from MC to MD requires implementing essential changes in the reconstruction process of HSMD. Results are calculated for three microstates, helix, extended, and hairpin. HSMD leads to very stable differences in entropy TDeltaS between these microstates with small errors of 0.1-0.2 kcal/mol (T=100 K) for a wide range of calculation parameters with extremely high efficiency. Various aspects of HSMD and plans for future work are discussed.

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

“…However, this good LS result might be accidental as unreliable differences were obtained by LS for the extended, helix, and hairpin microstates of decaglycine. 53,55 The similar results obtained for unit ) 2.5 and 10 ps suggest that already for unit )2.5 (n f )500) the coverage of both microstates by the future chains is adequate and that for unit ) 10 and n f ) 8000 the future chains still remain within these microstates. To get an idea about the extent of this coverage, we selected a structure from each of the two studied samples from which MD simulations of the entire loop were started (see the last paragraph of section II.6).…”

“…However, if S m A -S n A is found to be stable for significantly improving approximations, the constant value can be considered to be the correct difference. Indeed, in the previous application of HSMD to peptides 55 and in the present study of a loop (see section III), relatively small values of n′ f and j have already led to stable differences, meaning that systematic errors in both S m A and S n A are comparable and thus are cancelled in S m A -S n A . This cancellation of relatively large systematic errors (discussed further below) makes HSMD an efficient procedure for peptides/ loops.…”

“…53,54 Very recently HSMD has been extended to peptides with side chains simulated by MD. 55 We have found that reliable results for differences, ∆S mn and ∆F mn , can be obtained with considerable efficiency, ∼100 times faster (in term of computer time) than with MC. These results obtained for decaglycine and NH 2 (Val) 2 (Gly) 6 -(Val) 2 CONH 2 are very encouraging, suggesting that HSMD might become a highly efficient tool for calculating ∆F mn (our main interest) also for more complex systems such as loops.…”

“…Thus far we have studied by HSMD microstates of three systems, degaglycine, NH 2 (Val) 2 (Gly) 6 (Val) 2 CONH 2 , 55 and in this paper the 7-residue loop of R-amylase in vacuum and implicit solvent. In all these studies the cancellation of systematic errors has been found to occur for relatively small n f , which has been verified by comparing entropy differences obtained for a wide range of n f values.…”

“…In this context it should be pointed out that if one had tried to build loop structure i by selecting angles at random within the ranges R k ( δ/2, the constructed structure would differ from i and in the case of a loop would not satisfy the loop closure condition leading to a very high bond stretching energy. Therefore, the smallest bin chosen for a loop (∆R k /30) is smaller than that used for the linear peptides 55 (∆R k /15). Notice, however, that this structural deviation from i would affect both microstates, and the bins used are the largest that still lead to converging results of ∆S A .…”