c42b1

pnm

Plastic Network Model (PNM) -------------------------------------------- Jingzhi Pu (pu@tammy.harvard.edu) Paul Maragakis (Paul.Maragakis@deshaw.com) Martin Karplus (marci@tammy.harvard.edu) Victor Ovchinnikov (ovchinnv/at/georgetown/dot/edu) The PNM module provides an implementation of the plastic network model (Maragakis and Karplus, 2005) for studying conformational changes at a coarse-grained level. * Description / Description of the PNM method * Syntax / Syntax of the PNM commands * Options / Command-line Options * Examples / Usage examples * Installation / Compiling CHARMM with PNM * Status / Status of the code * References / References
Top Description of the PNM method For a system with multiple energy basins, with each basin described by an elastic network model, a combined energy function can be represented by the plastic network model (PNM). PNMs can be used to model pathways and dynamics between metastable states. For example, for a system expressed as a PNM of two conformations (labeled 1 and 2), we can construct a phenomenological energy Hamiltonian in a diabatic representation (a 2 x 2 matrix): H = [ G11 G12 ] [ G21 G21 ] where G11 and G22 are the configurational free energy functionals for conformer 1 and 2, respectively. Following Tirion's elastic network model (ENM), G11 and G22 can be calculated as a harmonic deformation of each conformer with respect to its equilibrium network configuration: G11 = G_0(1) + 1/2 Sum { D_ab(1) C(1) [r_ab(1) - r_ab,0(1)]^2 } a,b G22 = G_0(2) + 1/2 Sum { D_ab(2) C(2) [r_ab(1) - r_ab,0(2)]^2 } a,b where G_0(i) represents the equilibrium free energy of the conformer i; D_a,b(i) is the network connectivity matrix for the conformer i, whose element is 1 for an atom pair (a,b) if their distance is smaller than a cutoff distance, 0 otherwise; C(i) is a uniform elastic constant for elastic i; r_ab(i) and r_ab,0(i) denote the distance between atoms (a,b) in the network i obtained from the instantaneous and equilibrium positions, respectively. Given a constant coupling term (G12=G21=epsilon), the adiabatic free energy (G) of the PNM is expressed as the lowest eigen-energy of the eigen-states that diagonalize the above energy Hamiltonian: (G11 + G22) - sqrt[(G11 - G22)^2 + 4 epsilon^2] G = ------------------------------------------------ 2 More generally, for a system with n>2 metastable basins and n corresponding elastic energy functions, the above Hamiltonian matrix will be of size n x n. As for the case with n=2, the PNM energy corresponds to the smallest eigenvalue of the matrix, which can be obtained by numerical matrix diagonalization. Alternative mixing models that do not involve diagonalization are also possible. One such model available in the present implementation (as of comprised of N elastic models, the network free energy is computed as: G = - 1 / \beta * log ( \Sum_{i=1}^n exp [ - \beta Gii ] ) Note that the inverse temperature \beta will generally be much higher than the room temperature value ( ~ 1.7 ) to facilitate transitions between the constituent ENMs on relatively short simulation timescales. Values \beta are typically be explored by trial and error. In addition to its utility for modeling conformational changes at a coarse-grained level, the PNM potential function can be added as an additional (`rigidification`) potential to standard force fields. This can be useful in an all-atom transition simulations, whereby the two (or more) conformational states are connected via coarse-grained PNM potentials, while the fine-grain interatomic forces are computed by the underlying force field. The syntax of PNM invocation has been changed in CHARMM v. c39 to allow greater functionality and flexibility.
Top Syntax of the PNM commands PNM < [{ INITialize int }] | [{ DONE }] | [{ NEWModel }] | [{ EXP <on|true|t|yes|off|false|f|no> [TEMP real] }] | [{ ADD [FORC real] [CUT real] [ZERO real] [PMIX real] [atom-selection] [REMO atom-selection atom-selection] [COMP] }] | [ { PARA <on|true|t|yes|off|false|f|no> } ] [ { HELP } ] > Note: the PNM energy can be conditionally skipped by the 'SKIP' command in CHARMM, e.g., 'SKIP PNME' will remove the PNM energy and related force from the energy calculation.
Top PNM Command Options 1) INIT : initialize PNM module with a maximum number of networks (default=2); can be called multiple times 2) DONE : finalize PNM module; can be called multiple times 3) ADD : add a new elastic model with the following optional parameters: FORC real : elastic spring constant (default 2) CUT real : cutoff for constructing nearest neighbors (default 10) ZERO : equilibrium value of elastic energy function (default 0) PMIX : the mixing constant (eps) for this elastic model (default 0.5) the (i,j) off-diagonal entry in the Hamiltonian matrix is computed as Gij = 1/2 ( eps_i + eps_j ) REMO : remove the connections between two groups of atoms specified in a double selection following this keyword (all atoms selected by default) atom-selection: define the atom selection that PNM nodes reside on COMP : when specified, equilibrium coordinates for the elastic network will be taken from the comparison set (the main set is used by default) 4)NEWM : construct a new PNM model (in addition to the ones present, if any); the elastic models that are ADDed after this command will be part of the new PNM model (e.g. they correspond to a separate Hamiltonian matrix); with this functionality it is possible to simulate multiple interacting molecules, each described by a separate PNM. 5)EXP : specify whether the exponential mixing is to be used for the active network model (default : EXP = off) and supply an optional temperature in K (default: 300K) 6)PARA : turn on or off parallel force computation in PNM (on by default) 7)HELP : print usage syntax
Top Examples of using PNM An example is provided in the test suite to demonstrate the usage of the PNM command: pnm_test1.inp This testcase shows a MD simulation for one beta subunit in the open conformation of the F1-ATPase. The coarse-grained potential used for PNM is defined by CA atom positions in the conformation taken from PDB:1BMF. The system is simulated for 1000 MD steps. Energy and first derivatives are also tested. pnm_test2.inp A test case designed to demonstrate the flexibility of the PNM code. Sets up and performs a MD simulation of a hexameric AAA protein machine, with each monomer described by a separate PNM with six constituent ENMs (for a total of 36 ENMs). The six individual monomers interact via LJ and electrostatic forces. The BLOCK module is used to switch off unwanted monomer self-interactions. pnm_test3.inp Identical to pnm_test3.inp except that the exponential version of mixing is used.
Top Installation of PNM Currently, the PNM module is not activated by default in a standard installation. To compile the PNM code under the CHARMM environment, the 'PNM' keyword needs to be specified in the build/host-machine-type/pref.dat file. The modification of the pref.dat file can be done by providing the '+PNM' argument to the installation script "install.com" when CHARMM is installed: ./install.com host-machine-type size +PNM Here the '+PNM' option will adds the 'PNM' keyword into the pref.dat file for a given compilation.
Top Status of the PNM code The PNM energy calculations are parallelized under the atom decomposition model in CHARMM. However, because of the simplicity of the elastic energy networks that constitute the PNMs and the communication overhead associated with parallelization, the serial version of the code may actually run faster for some (usually smaller) systems.
Top References [1]. Maragakis, P.; Karplus, M. J. Mol. Biol. 2005, 352, 807. [2]. Tirion, M. M. Phys. Rev. Lett. 1996, 77, 1905. [3]. Schlitter, J.; Engels, M.; Kruger, P. J. Mol. Graphics 1994, 12, 84. [4]. Pu, J.; Karplus, M., PNAS, 2008, 105, 1192