FDA Manual

Force Distribution Analysis with Gromacs Wolfram Stacklies October 21, 2009 Contents 1 Patching and installation 2 Force distribution Analysis 2.1 When (and why) should I use FDA . . . 2.2 Usage of the FDA code . . . . . . . . . . 2.3 Analysis of the FDA results . . . . . . . 2.4 Analysis with the FDAtools package in R 2.5 Noise and normalization . . . . . . . . . 2.6 Limitations . . . . . . . . . . . . . . . . 3 Implementation details 3.1 Approximations for multi body forces . . 3.2 The force
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  Force Distribution Analysis with Gromacs Wolfram StackliesOctober 21, 2009 Contents 1 Patching and installation22 Force distribution Analysis2 2.1 When (and why) should I use FDA. . . . . . . . . . . . . . . 32.2 Usage of the FDA code. . . . . . . . . . . . . . . . . . . . . . 32.3 Analysis of the FDA results. . . . . . . . . . . . . . . . . . . 52.4 Analysis with the FDAtools package in R. . . . . . . . . . . . 72.5 Noise and normalization. . . . . . . . . . . . . . . . . . . . . 92.6 Limitations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3 Implementation details10 3.1 Approximations for multi body forces. . . . . . . . . . . . . . 113.2 The force matrix file format (version 1.2). . . . . . . . . . . . 123.3 ASCII representation of the force-matrix. . . . . . . . . . . . 133.4 Where do I find the FDA code?. . . . . . . . . . . . . . . . . 13 A Files modified for the FDA implementation15 1  1 Patching and installation Currently we only provide a .tar file with the modified code; a patch willfollow soon. Installation should work as normal, see the Gromacs website 1 for details. 2 Force distribution Analysis Force distribution analysis (FDA) is a method to detect stress propagation inproteins, reminiscent of finite element analysis used to engineer macroscopicstructures. The method is based on molecular dynamics simulations duringwhich we directly calculate forces between each atom pair in a system. Themost recent version of FDA is now implemented in Gromacs-4.0.5 [1].What the FDA code basically does is to write out forces F  ij between eachatom pair i and j in a molecule. Forces include contributions of individualbonded (bond, angle, dihedral) and non-bonded (electrostatic and van derWaals) terms below the cutoff distance, which are stored separately for fur-ther analysis. The force between each atom pair is represented as the normof the force vector and thus is a scalar. Attractive and repulsive forces areassigned opposite signs (negative for attractive, positive for repulsive). It isimportant to make yourself clear about the concept of pair wise forces. Apair wise force is the force an atom exerts on another atom. It is NOT thetotal force acting on a certain atom. By considering the direct force betweeneach atom pair, the equilibrium force between these atoms can be differentfrom zero, even for the theoretical case of a system without any motion. Wehereby obtain the advantage to be able to observe signal propagation eventhrough stiff materials, where, by definition, forces propagate without caus-ing major atomic displacement. Atomic forces, i.e. the sum over the forcevectors acting on an atom, instead average out to zero over time and are notof interest here. A real world example for such force propagation is Newton’scradle, where atomic forces would only see the first and the last beat moving.But when using pair wise forces one is able to see the whole force propagationpathway.The careful reader may have noticed that we do not write out forces be-yond the cutoff distance. This basically only affects Coulomb interactions,as the VdW potential quickly decays to zero. Due to the nature of thenon-bonded potentials, pairwise forces are most significant for atom pairsin relative close proximity. At distances > 1nm the Coulomb potential be-comes very flat, i.e. slight changes in atomic distances have little effect on 1 2  the force between them. For this reason we would anyway end up with aforce-propagation network comprised of a series of short to medium rangedconnections, and thus it is no problem to ignore forces beyond the cutoff distance. The long range interactions are important for a proteins overallstability, but they play only a minor role in propagating forces. 2.1 When (and why) should I use FDA FDA is a valuable tool to investigate allostery, or more general, the propaga-tion of mechanical signals within molecules. It is particularly useful to followsignal propagation in stiff allosteric proteins or crystalline materials [2, ? ]. Inthese structures, by definition, allosteric signals propagate without causingmajor atomic rearrangements, making it impossible to follow the signal withconventional methods. In other cases, such as e.g. molecular motors, me-chanical tension caused by an allosteric event may build up and eventuallyresult in a conformational change, e.g. a rotation. These changes are slowand generally not accessible in simulation time-scales. Even if we cannotsee the actual transition, FDA still is able to tell you where tension buildsup. Thereby it can identify crucial residues of a protein and help you tounderstand the underlying machinery.Another case we used FDA for is the debugging of force field parameters,or to find errors in the initial system setup (oh my god, my system explodedagain!!). Getting the forces acting between each atom pair allows to quicklyidentify and hopefully eliminate the srcin of unrealistically high forces.Pair wise forces are very sensitive to even minor conformational rearrange-ments. This normally is an advantage, but may become a problem if anallosteric event involves large conformational changes. In this case it mightbe appropriate to use other methods. For the same reason I strongly discour-age you to compare forces obtained from different crystal structures. Evenif both structures have very low RMSD, the changes between the structuresare most likely stronger than the changes you observe upon a certain pertur-bation of your system. 2.2 Usage of the FDA code It is theoretically possible to write out pair wise forces directly during yourMD simulation, and in rare cases this might make sense. The caveat of thatis that Gromacs uses assembly loops optimized for performance, and turningon the FDA code will force Gromacs to fallback to the slow C inner loops.3  Another caveat is that FDA currently does not support domain decomposi-tion, what will slow your simulation down further. Hence, the best solutionis to perform a standard MD simulation and afterwards calculate pair wiseforces during a rerun MD. For now I strongly suggest to only use oneCPU when doing FDA, I will not guarantee for any results donein parallel! Usage of the FDA code is straightforward. You will notice that mdrun nowsupports four new parameters, which are: ã -fi ( ) - The input parameters for FDA (explained in detaillater on). ã -fo ( ) The parsed FDA parameters (output). ã -fm ( ) The matrix containing pair wise forces, a binaryfile. ã -fn ( pforce.ndx ) An index file defining the atoms for which pair wiseforces are written out.After the simulation you will end up with a three dimensional matrix of size N  × N  × S  where N  is the number of atoms and S  the number of write steps.The matrix is stored in a binary sparse matrix representation, see Section3for more information.But let’s have a look at the input parameters given in the .fi file. Cur-rently there are only four options, namely the output frequency (in simulationsteps), the index group for which forces are written out, the option to writevariances in forces instead of the forces themselves and, last but not least aflag that indicates if the (slower) pair-wise force inner loops should be used.This should only be enabled if you really intend to to FDA for waters, whatmakes sense in only few cases, see also Section2.6.A typical input file wouldthen look like: output_freq = 10group = Proteinvariance = nowater = no In this example we would average forces for Protein atoms over every 10simulation steps and then write them out. Setting output_freq to -1 willaverage forces over the whole simulation time. If we would set variance to yes we would end up with a matrix containing only one frame storing thevariances in forces over time.4
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