CFTI: conformational energy/free energy calculations * Menu: * Constraints:: Note on constrained optimization implementation * CFTINT:: Description and syntax of standard conformational free energy thermodynamic integration * CFTIM:: Description and syntax of multidimensional onformational free energy thermodynamic integration

Constraints: Energy minimization with holonomic constraints has been implemented. There are no special commands for this option. Charlie Brook's TSM module allows for MD simulations with constrained values of selected conformational coordinates - distances, atoms, dihedrals. This has been expanded to also allow energy minimization using several algorithms. The method is an alternative to using harmonic restraints in generating structures of flexible molecules with desired properties, or generating adiabatic profiles. To use this option, simply enter the 'TSM' module and give set of 'FIX' commands to define set of fixed internal coordinates (see perturb.doc for details). Next specify an energy minimization (see minmiz.doc). Algorithms that work: SD, CONJ, POWE (ABNR works also, for reasons unclear to me, KK)

CFTI: standard (one-dimensional) conformational thermodynamic integration Description of method Method expands the capabilities of the TSM module. The TSM module employs the Thermodynamic Perturbation (TP) approach to conformational free energy simulations. The basis of the calculation is a MD simulation with a constrained value of a conformational coordinate. With minimal modifications, the alternative Thermodynamic Integration (TI) method is added on. In the modified code the user has the option of using TP only (as previously) or activating TI, in which case the same simulation and data files are used to give both TP and TI results. [SYNTAX CFTI] All commands are parsed by the TSM command parser, so should be within a 'TSM ... END' block. CFTI command activates the thermodynamic integration calculation the context of use should be the same as for a thermodynamic perturbation run, i.e. some coordinates should be fixed by 'FIX ,,,', saving data to a disk file should be specified by 'SAVI ...', and one perturbation should be defined by 'MOVE ...' The derivative dA/dx is calculated for the coordinate defined in the 'MOVE ...' statement. This coordinate has to be also fixed with 'FIX ...'; other coordinates may also be fixed if desired. The formula for dA/dx involves only averaging over the corresponding derivative of the potential energy U, omitting the 'Jacobian term' realted to changes in phase space volume: dA/dx = <dU/dx> dU/dx = Sum(j=1,3N) (dU/dy_j)(dy_j/dx) y_j, j=1,...,3N - atomic Cartesian coordinates Notes: 1) The formatted data file generated by 'SAVI ...' may be read by both TI postprocessing command (CFTJ) and TP postprocessing (POST). The SAVI 'NWIN' keyword has meaning only for TP, it can be set to an arbitrary value if TI only is to be used. 2) For consistency with TP, the 'BY <real>' part of the 'MOVE' command was retained. The <real> value has meaning for TP only, it can be set to an arbitrary number if TI only is to be used. CFTJ [TEMP <real>] [UICP <int>] [CONT <int>] Command to calculate the conformational free energy derivative dA/dx = <dU/dx> as well as the energy-entropy components: d<U>/dx, -TdS/dx Data is read in from the formatted file generated by the 'SAVI ...' command TEMP - specifies temperature, needed for energy-entropy components UICP - specifies unit with data CONT - defines length of data block for error analysis e.g. if data file has 1000 entries, 'CONT 100' will divide data into 10 blocks and calculate the standard deviation of the mean of the block averages CFTA [FIRSt <int>] [NUNIt <int>] [BEGIn <int>] [STOP <int>] [SKIP <int>] [CONT <int>] [TEMP <real>] Command activates analysis of CFTI-generated trajectory. Trajectory coordinate file(s) should be in consecutive units FIRST, NUNI, BEGIN, STOP, SKIP - define trajectory reading CONT, TEMP - as in CFTJ Examples of usage : see test cases: cftidist.inp, cftiangl.inp, cftidihe.inp These test cases also compare the TI to TP results, showing the small size of the 'Jacobian term'.

CFTM: multidimensional conformational thermodynamic integration Description of method This is a new approach. MD simulations are performed with several conformational coordinates simultaneously constrained to fixed values. The partial derivatives of the conformational free energy with respect to all the coordinates in the fixed set are calculated from this one simulation. The free energy gradient may be used in different ways to explore conformational free energy surfaces of flexible molecules. Method expands the capabilities of the TSM module. Only TI calculations possible, no corresponding TP analysis possible. [SYNTAX CFTM] All commands are parsed by the TSM command parser, so should be within a 'TSM ... END' block. CFTM command activates the multidimensional TI method the context of use should be the same as for a thermodynamic perturbation run, i.e. several coordinates should be fixed by 'FIX ,,,', saving data to a disk file should be specified by 'SAVI ...'. and a perturbation should be defined by a 'MOVE ...' statement for each of the fixed coordinates. Only the average of the derivatives of the potential energy U are calculated, the 'Jacobian term' is ignored - see notes below and test cases. dA/dx_k = <dU/dx_k> x_k, k=1,...,m - fixed coordinates dU/dx_k = Sum(j=1,3N) (dU/dy_j)(dy_j/dx_k) y_j, j=1,...,3N - atomic Cartesian coordinates Notes: 1) The formated data file defined by 'SAVI ...' has a different format under CFTM than under CFTI. This file is only useful for CFTM post-processing. 2) For consistency with TP, the 'BY <real>' part of the 'MOVE' command was retained. The <real> value has no meaning in CFTM. 'INTE' keyword has to be specified within the 'MOVE' command. CFTC [TEMP <real>] [UICP <int>] [CONT <int>] Command to calculate the conformational free energy derivatives dA/dx_i = <dU/dx_i> as well as the energy-entropy components: d<U>/dx_i, -TdS/dx_i Data is read in from the formatted file generated by the 'SAVI ...' command TEMP - specifies temperature, needed for energy-entropy components UICP - specifies unit with data CONT - defines length of data block for error analysis e.g. if data file has 1000 entries, 'CONT 100' will divide data into 10 blocks and calculate the standard deviation of the mean of the block averages Output includes all individual partial derivatives, and optionally their analysis into groups. The derivative with respect to a path direction is also calculated. CFTB [FIRSt <int>] [NUNIt <int>] [BEGIn <int>] [STOP <int>] [SKIP <int>] [CONT <int>] [TEMP <real>] Command activates analysis of CFTM-generated trajectory. Trajectory coordinate file(s) should be in consecutive units FIRST, NUNI, BEGIN, STOP, SKIP - define trajectory reading CONT, TEMP - as in CFTJ Output is the free energy gradient with respect to the set of fixed coordinates, the derivative along a specified direction (see DIRE) and optionally a group contribution analysis. CFTS [FIRSt <int>] [NUNIt <int>] [BEGIn <int>] [STOP <int>] [SKIP <int>] [CONT <int>] [TEMP <real>] [DUNI <int>] Analogous to CFTB, additionally writes out potential energy and dU/dx_i to a disk file specified by DUNI. NCOR NUMB <int> NUMB specifies the number of internal coordinates involved (=NICP). Used in calculating the path derivative. DIRE LAMB <int> <real, real, ... , real> The LAMB value specifies number of step (progress along reaction path). The following line(s) contain NICP real numbers defining a path vector. The vector will be normalized automatically. The unit vector will be used to calculate derivatives of dA/dl, d<U>/dl, -TdS/dl along the path from the gradients. The real numbers correspond to weights of the fixed coordinates. Note: the vector components are read in free format CFTG NGRUp <int> <int, int, ..., int> <string,string,...,string> Define groups for group contribution analysis to free energy NGRUP is the number of groups. The following line(s) contain the integer group numbers of the coordinates (LGRUP(J),J=1,NICP) in free format After that follow line(s) with group symbols (i.e. tags that will be used to denote the groups) in (20A4) format (GSYM(J),J=1,NGRUP) Example of usage: The system is a decapeptide, we calculate derivatives with respect to all phi and psi backbone dihedrals (NICP=18). In the 18 'MOVE ...' commands we specify the 9 phi first and the 9 psi at the end. The following will calculate and print out an aggregate of all phi and all psi contributions labelled by the tags 'PHI' and 'PSI': cftg ngrup 2 1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2 PHI PSI cfts Examples of usage: see test cases cftmala10.inp, cftmtst1.inp Checks that 'Jacobian term' is small: cftmtst2.inp, cftmtst3.inp, cftmtst4.inp, cftmtst5.inp >NOTE on sign of derivatives: In both CFTI and CFTM it is possible to obtain a derivative value with incorrect sign by cleverly manipulating the atom selections in the 'MOVE ...' command. A simple way of checking the sign is to run a 1-D test case using both TI and TP postprocessing (see test cases cftidist.inp, cftiangl.inp, cftidihe.inp). A general rule is to think about how the coordinate is defined and how motions of fragments influence it. E.g. for a distance between atoms A and B, the coordinate is the length of the vector from A to B. Perturbations (TP) involve actual displacements of A and B along the =vector= from A to B; Derivative calculations (TI) do not involve actual motions of atoms, but rather predictions of how atomic positions will vary with infinitesimal coordinate changes. Moving B along this coordinate by delta > 0 will increase the coordinate, while moving A by delta will decrease the coordinate. Alternatively, we can distort the bond by delta by moving A by -delta/2 and B by + delta/2. To get correct sign of derivative you have to specify B as the moving part or specify both B and A, but maintaining that order (B first, A next). This is illustrated schematically below: Correct scheme 1: FIX DIST <spec atom A> <spec atom B> MOVE DIST <spec atom A> <spec atom B> BY 1.0 INTE - sele <atom B> end Correct scheme 2: FIX DIST <spec atom A> <spec atom B> MOVE DIST <spec atom A> <spec atom B> BY 1.0 INTE - sele <atom B> end sele <atom A> end Both give the same result (I tested this, KK). See test case cftidist.inp. The same holds true for a dihedral defined by atoms I-J-K-L. Mentally divide the molecule into two parts by cutting through the J-K bond. Atoms before the cut (I, J and all atoms bound to them except K) for the first part, the rest of the atoms form the second part. To distort the dihedral, we can either rotate second half by delta around J-K axis, or rotate first half by -delta/2 and second half by +delta/2. To get correct derivative either define the second part as moving or define both parts but in correct order: (second, first). Here is an example for the alanine dipeptide. The following defines the atoms (in toph19, see cftmtst1.inp): 1 1 ACE CH3 3.06258 0.64613 1.42088 ALA 1 0.00000 2 1 ACE C 2.33541 -0.68685 1.35313 ALA 1 0.00000 3 1 ACE O 2.01413 -1.29380 2.37725 ALA 1 0.00000 4 2 ALA N 2.07725 -1.18175 0.14371 ALA 2 0.00000 5 2 ALA H 2.45870 -0.76210 -0.65152 ALA 2 0.00000 6 2 ALA CA 1.35635 -2.43045 -0.00242 ALA 2 0.00000 7 2 ALA CB 0.69707 -2.49721 -1.37506 ALA 2 0.00000 8 2 ALA C 2.38192 -3.54475 0.11749 ALA 2 0.00000 9 2 ALA O 3.17467 -3.80389 -0.78914 ALA 2 0.00000 10 3 CBX N 2.41984 -4.12094 1.31507 ALA 3 0.00000 11 3 CBX H 1.92248 -3.68658 2.04150 ALA 3 0.00000 12 3 CBX CA 3.28397 -5.30373 1.59827 ALA 3 0.00000 The following is a correct set-up for a phi-psi gradient calculation using the single-selection variant: tsm fix dihe ala 1 c ala 2 n ala 2 ca ala 2 c toli 1.0e-5 fix dihe ala 2 n ala 2 ca ala 2 c ala 3 n toli 1.0e-5 maxi 100 cftm move dihe ala 1 c ala 2 n ala 2 ca ala 2 c by 1.0 - inte sele bynum 6:12 end move dihe ala 2 n ala 2 ca ala 2 c ala 3 n by 1.0 - inte sele bynum 8:12 end end And here is the correct alternative double-selection variant: tsm fix dihe ala 1 c ala 2 n ala 2 ca ala 2 c toli 1.0e-5 fix dihe ala 2 n ala 2 ca ala 2 c ala 3 n toli 1.0e-5 maxi 100 cftm move dihe ala 1 c ala 2 n ala 2 ca ala 2 c by 1.0 - inte sele bynum 6:12 end sele bynum 1:5 end move dihe ala 2 n ala 2 ca ala 2 c ala 3 n by 1.0 - inte sele bynum 8:12 end sele bynum 1:7 end end See test cases cftidihe.inp, cftmala10.inp. >NOTE on integrators: With CHARMM c30a2x I have tested LEAP, NOSE and NOSE VVER aproaches, which worked fine. The LANGevin integrator LED TO INCORRECT FORCES stored in the formatted data file (defined with 'SAVI ...'). Thus, post-processing using the 'CFTA' or 'CFTB' approaches worked fine, as this method re-reads the trajectory and re-calculates derivatives. The 'CFTJ' and/or 'CFTC' gave incorrect results! This is probably related to incorrect placement of the 'CALL DYNICT' and 'CALL DYNICM' commands within the dynamics files so that the energy gradient DX,DY,DZ does not agree with the coordinates X,Y,Z. I will look into this at a later date. KK

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Modified, updated and generalized by C.L. Brooks, III

The Scripps Research Institute