First, using say AMBER, a trajectory is generated and a representative sample of n configurations (snapshots) i (i=1,…,n) is selected as mentioned earlier. In the case of a ligand-protein complex, each configuration consists of the conformations of the ligand and protein and the configuration of the surrounding water molecules; the ligand-ligand and ligand-protein interaction energies are calculated.
These simulations can easily be carried out with any of the available programs - AMBER, CHARMM, NAMD, etc. Here we use AMBER. Starting with configuration i=1 (i=1,…n) AMBER calculates for each reconstructed atom, k’, nf future chains (of the ligand), where their Cartesian coordinates are stored on a file denoted here by file.i.k’; thus for the molecule depicted in figure 1, 10 files will be created for each i. Notice that for file.i.k’ the coordinates for atoms 1,…k’-1 are constant (having their values in conformation i) while those for k’…,10 vary. These data are stored according to the default format of AMBER, which might be different for other programs (CHARMM, NAMD, etc.); thus, a user who applies, say CHARMM should change the reading format in the program accordingly.
To define the past and future atoms we use the file angles.dat.
angles.dat. This file provides a list of angles to be treated at each step of the reconstruction simulations (described above) and the reconstruction analysis (carried out by the program, see below). For example, the following data could be part of this file:
23 24 25 26
24 25 26 27
25 26 27 28
26 27 28 29
27 28 29 30
Each row in the file refers to a different step in the reconstruction process, where it defines the atom numbers (k’) which should be considered. Thus, the first three atoms are fixed, while the fourth atom is moving (together with future atoms with larger k’ values). The first line above means that we perform a (future) MD simulation where atoms 23, 24 and 25 are fixed while atom 26 is moving; thus the four atoms define the dihedral angle while the last three define the bond angle (from these angles the probabilities will be calculated, see Introduction). In the following reconstruction step, atoms 24, 25 and 26 will be fixed and 27 moving, which will define the dihedral and bond angles for atom 27, and so on.
RECONSTR_angles_list_amber.c: This program reads the files created by AMBER (described above) and calculates the bond and dihedral angles corresponding to the atoms listed in the input file angles.dat. These angles are stored on n new files, where a separate file is assigned for each i (i,..,n). Each of these files consists of several columns of size nf; the first column contains the nf bond angles related to atom k’=1 and the second column contains the nf dihedral angles of k’=1. The next two columns pertain to the second atom etc. thus if the number of atoms is 10, the file will contain 20 columns.
RECONSTR_count_amber.c: This program calculates the transition probabilities by reading the files containing the angles defined above, and counting their populations in bins of several sizes as defined in Eq. (1) of the theory. The bins’ sizes are obtained by first calculating for each angle αk its minimum and maximum values (αmin (k) and αmax(k) in the original sample of n snapshots, which leads to the difference Δαk= αmax(k) - αmin(k). The bins size is decreased as Δαk /l for increasing values of l. Notice that for the bond angles due to the Jacobian we use Δcos(αk) rather than Δαk. From the transition probabilities the entropies and their differences are calculated (see Equation (2)-(4) of Theory).
RECONSTR_analysis_manytraj_amber.bsh: This bash script, which calls the two previous programs, can be used to do the whole entropy analysis. For details on its use, see the tutorial.