The hypothetical scanning molecular dynamics (HSMD) method enables one to calculate the absolute entropy S and the absolute free energy, F of a peptide or any other “chain molecule” in any environment - vacuum, solvent or the active site of an enzyme. This method is part of a more general technique called HSMD-TI, where the entropy and free energy of the entire system (e.g., peptide + water) can be obtained; the contribution of the environment (e.g., solvent) to F is calculated by a thermodynamic integration (TI) procedure.
Notice, however, that in most applications we are interested in the free energy difference ΔFmn (and ΔSmn) between two states m and n (e.g., a helical and hairpin states of a peptide); such states are called in our papers “microstates”.
The software presented here is related only to the HSMD part of the entire method (HSMD-TI). To understand this part let’s assume a peptide in a box of explicit water (e.g., TIP3P) simulated by MD (e.g., using the software AMBER); we wish to calculate the contribution of the peptide to S. The method works as follows:
(a) From the above (initial) MD trajectory a sample of n equally spaced snapshots of the entire system are selected.
(b) For each snapshot i the conformation of the peptide should be “reconstructed” step-by-step by calculating transition probabilities (TPs) where their product leads to an approximation, Pi for the Boltzmann probability density of peptide’s conformation in i. This reconstruction is done in two stages:
Stage 1 is carried out again within AMBER. The data produced in stage 1 are stored on files which are read in stage 2 by the software provided here (this software consists of two programs, RECONSTR_angles_list_amber.c and RECONSTR_count_amber.c described later, which for brevity we denote as the program). This program calculates the TPs, their product, Pi and the entropy SA =-kBTlnPi related only to the peptide conformation of i (but not to the surrounding water which can be obtained by TI; the superscript “A” means that this entropy is approximate). Finally, SA is averaged over the sample of n snapshots.
The advantage of this two-stage procedure is that the raw data of the time consuming stage 1 is calculated only once and can be analyzed (typically) many times in stage 2 for different HSMD parameters. Also, the initial MD trajectory and the simulations of stage 1 can be carried out by any of the standard software packages – TINKER, CHARMM, etc., as well as AMBER discussed here.
The theoretical basis of HSMD