Conformational Entropy Calculation

CENCALC Users’ Manual

##Preface This software has been designed to estimate the conformational entropy of single molecules from extended computer simulations, especially Molecular Dynamics (MD) simulations. On input CENCALC needs both trajectory coordinates and topology information in order to characterize the conformational states of the molecule of interest. The molecular conformers are identified by discretizing the time evolution of internal rotations. After this transformation, CENCALC determines the probability mass functions of the individual torsions and uses them for conformational entropy estimations. CENCALC can use up to four different methodologies for approaching to the full conformational entropy: the classical Mutual Information Expansion (MIE), the Approximate MIE (AMIE), the so-called Multibody Local Approximation (MLA), and the default method that corresponds to the correlation corrected MLA (CC-MLA). All of these techniques can also be combined with a distance-based cutoff criterion. In this case, CENCALC requires as additional input an inter-atomic distance matrix containing the mean distance values derived from the MD trajectory in order to include only correlation effects among torsion angles whose mean separation is below a predefined cutoff. The best cutoff for a given amount of sampling can be determined using the CC-MLA method.

All the assumptions and equations defining the various techniques available in CENCALC have been discussed in the literature as well as in the accompanying paper. Users are therefore encouraged to consult those references cited below before using the software.

##0-License and Citation Copyright (C) 2012 Ernesto Suárez Álvarez CENCALC is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/. Any use of the CENCALC software or derivative should include at least the following citation: 1) E. Suárez, N. Díaz, J. Méndez and D. Suárez. CENCALC: A Computational Tool for Conformational Entropy Calculations from Molecular Simulations. Submitted. The methods implemented in CENCALC are fully described in the following references: 2) E. Suárez, N. Díaz and D. Suárez. Entropy Calculations of Single Molecules by Combining the RigidRotor and Harmonic-Oscillator Approximations with Conformational Entropy Estimations from Molecular Dynamics Simulations J. Chem. Theor. Comput. 2011, 7, 2638-2653. 3) E. Suárez, D. Suárez. Multibody Local Approximation: Application to Conformational Entropy Calculations on Biomolecules. J. Chem. Phys. 2012, 137, 084115. All questions regarding the usage and distribution of CENCALC or bug reports should be addressed to Ernesto Suárez ([email protected] ; [email protected] ). The software, which is distributed under the GNU public license, together with numerical examples and this user’s manual are available in the Supporting Information of reference 1.

##1-Compliling the code The CENCALC software consists mainly of two standalone codes written in the FORTRAN90 language, cencalc_prep.f90 and cencalc_omp.f90. The first program carries out various preparatory tasks prior to the main entropy calculations that are performed by cencalc_omp.f90. As the bulk of the effort to obtain the conformational entropy values is expended by cencalc_omp.f90, this program takes advantage of shared-memory parallel computers through the OpenMP Application Program Interface.

Important notice: The FORTRAN90 codes in CENCALC have been compiled and fully tested using the Linux version of the gfortran compiler (v. 4.4.5):

>>  gfortran  cencalc_prep_0.2.2.f90 -o cencalc_prep 
>>  gfortran  -fopenmp cencalc_omp_0.2.2.f90 -o cencalc_omp 

##2-Running the code

##2.1-Files needed to perform conformational entropy calculations
The following Table describes the data files, in plain text format, that are needed by CENCALC in order to carry out conformational entropy calculations.

Content	Filenames*	Observations
Time series of torsion angles	d0001.dat, d0002.dat ...	Mandatory
Distance matrix	distance_matrix.dat (Format: F9.3)	Only for calculations with cutoff
ID numbers of the central atoms involved in the M torsions	atoms_in_tor.info	Only for calculations with cutoff
(*) Default filenames are indicated, but users can choose other filenames using command line options (see below).

In principle the d0001.dat, d0002.dat, ... , d000M.dat files have each two columns corresponding to the time counter and the torsion angle value, respectively. In any case CENCALC reads only one column per file whose column index can be specified using a command line option (see below). Torsion angles must be specified as dihedral angles measured in degrees. Of course the d0001.dat, d0002.dat, ... files should all have the same number N of lines corresponding to the number of MD snapshots being considered. It may be noted that a time space of 1ps between the MD snapshots seems appropriate for most applications of CENCALC. On the other hand, the value of N will depend on the dimensionality of the problem as well as on the conformational flexibility of the molecular system: for medium-sized systems one should expect that millions of configurations would be required to reach converged entropies.

The file atoms_in_tor.info must have M lines, with M being the number of torsion data files. If, for example, d0001.dat and d0002.dat store the time series of the torsion angles defined by the 1-2-3-4 and 2-3-4-5 atom ID numbers, then the first two lines in atoms_in_tor.info should be simply 2 3 and 3 4, respectively. On the other hand, the file distance_matrix.dat should contain, in format F9.3, the inter-atomic mean distance matrix of the solute, or at least, the inter-atomic mean distance matrix of the first K atoms in the topology, where K is greater or equal than the highest atom ID number in atoms_in_tor.info. Note that coordinates of solvent molecules and counterions should be better removed before generating distance_matrix.dat, otherwise the resulting distance matrix could be huge and very expensive to compute.

Of course CENCALC assumes that a mutually consistent atom numbering is used in the construction of the atoms_in_tor.info and distance_matrix.dat files.

##2.2-Runing cencalc_prep The cencalc_prep code estimates first the probability density functions of the M torsion angles and characterizes their maxima and minima critical points. Basing on these data, cencalc_prep transforms subsequently the initial time series of N real numbers per torsion angle $\theta$ into a set of N integer numbers labeling the conformational states populated by $\theta$. On output, all the information is saved in a file named MATRIX.dat, which has N rows (i.e, the number of MD snapshots) and M columns (the number of rotatable bonds). Thus, the ith row of MATRIX.dat is an array of integer numbers that represent the conformational state at the ith-snapshot. In principle, MATRIX.dat should have as many columns as times series read on input (d0001.dat, d0002, ...). However, cencalc_prep removes by default all the frozen torsions because they do not represent conformational changes and do not affect the conformational entropy and, consequently, M could be lower on output than on input. In addition cencalc_prep reads the atoms_in_tor.info and distance_matrix.dat files and generates a new distance matrix file named reduced_dist_matrix.dat that contains the mean distance between every pair of torsions. These distance values are derived by applying the following rules: a) The distance d(A,A) between every torsion A and itself is zero; b) the distance d(A,B) between two different torsions A1-A2-A3-A4 and B1-B2-B3-B4 is the mean distance d(Ai,Bj) between the central pair of atoms of both torsions.

A typical execution of cencalc_prep assuming default filenames looks like:

>>  cencalc_prep  d????.dat 

Any other regular expression besides d????.dat can be used. 
The program will also look for atoms_in_tor.info and distance_matrix.dat. 

or without cutoff:

>> cencalc_prep -nocut d????.dat

Calculations with no cutoff. The program will not look for the atoms_in_tor.info 
and distance_matrix.dat files.

For the more general case, we provide the full help of cencalc_prep:

---

Usage of cencalc_prep:

SYNOPSIS:

cencalc_prep [OPTIONS] file1.dat file2.dat ... (Default names: d0001.dat, d0002.dat ...)

OPTIONS:

-u/-usecol COLNUM Default: 2

Column number in file1.dat, file2.dat that contains the times series of the torsion variable. 
This value is normally 2 since first column often corresponds to the time  or the snapshot 
number variable. 

-dist DIST_MATRIX_FILE_NAME Default: distance_matrix.dat

This variable specifies the filename of the inter-atomic mean distance matrix. 

-i/-info TOR_INFO_FILE_NAME Default: atoms_in_tor.info

This file specifies the atoms involved in the torsion angles (only the two central atoms).  
For example, if the first row in *TOR_INFO_FILE_NAME*  reads as 3 4,  then file1.dat contains 
the time series for rotation about the 3-4 bond.

-nocut Default: Use cutoff

Using this option no cutoff will be applied and the options -dist/-info  are thereby not needed.  

-s/-simplify yes/no Default: yes

Remove all frozen torsions.

-k K_VALUE Default: 1.0

The k_value (k) sets the smoothing parameter vin the von-Mises kernel density estimation as 
proposed in Eq.(7) in Computational Statistics & Data Analysis, 2008, 52, 34933500. By 
default ˆ1 as this value ensures slightly over-smoothed Probability Density Functions (PDFs) 
of individual torsion angles, what is convenient for searching critical points.

-ag yes/no Default: no

If yes then analytic gradients are used for locating the minima critical points of the von-Mises
PDFs of individual torsion angles. The default option (no) uses instead a sufficiently accurate 
and fast linear interpolation scheme for PDF gradient evaluation. 

-step STEP_SIZE Default: 5 (degrees)

PDF minimization step size:  xn+1=xn - STEP_SIZE * GRADIENT 

-crit CONVERGENCE_THRESHOLD Default: 1.e-4

Gradient convergence threshold for the PDF minimizations.

-maxitr MAX_NUMBER_OF_ITERATIONS Default: 1000

Maximum number of iteration for PDF minimizations. 

-maxconf MAX_NUMBER_OF_CONFORMERS Default: 3

Maximum number of conformers (from 2 to 9) generated by internal rotation about a single bond. 

-help Print this quick help

---