MD Simu....Theory

March 23, 2018 | Author: bedibedi | Category: Molecular Dynamics, Force Field (Chemistry), Chemistry, Applied And Interdisciplinary Physics, Mechanics
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IntroductionOne of the principal tools in the theoretical study of biological molecules is the method of  molecular dynamics simulations (MD). This computational method calculates the time  dependent   behavior   of   a   molecular   system.   MD   simulations   have   provided   detailed  information   on   the   fluctuations   and   conformational   changes   of   proteins   and   nucleic  acids.   These methods are now routinely used to investigate the structure, dynamics and  thermodynamics of biological molecules and their complexes. They are also used in the  determination of structures from x­ray crystallography and from NMR experiments. Biological   molecules   exhibit   a   wide   range   of   time   scales   over  which specific processes occur; for example • o o o • o o o • o o o Local Motions (0.01 to 5 Å, 10­15 to 10­1 s) Atomic fluctuations Sidechain Motions Loop Motions Rigid Body Motions (1 to 10Å, 10­9 to 1s) Helix Motions Domain Motions (hinge bending) Subunit motions Large­Scale Motions (> 5Å, 10­7 to 104 s) Helix coil transitions Dissociation/Association Folding and Unfolding An overview of the theoretical foundations of classical molecular dynamics simulations, to  discuss   some   practical   aspects   of   the   method   and   to   provide   several   specific   applications  within the framework of the CHARMM program. Although the applications will be presented  in   the   framework   of   the   CHARMM   program,   the   concepts   are   general   and   applied   by   a  number of different molecular dynamics simulation programs. The CHARMM program is a  research program developed at Harvard University for the energy minimization and dynamics  simulation of proteins, nucleic acids and lipids in vacuum, solution or crystal environments  (Harvard CHARMM Web Page http://yuri.harvard.edu/). Section   I   of   this   course   will   focus   on   the   fundamental   theory   followed   by   a   brief  discussion of classical mechanics.  In section II, the potential energy function and some  related   topics   will   be   presented.   Section   III   will   discuss   some   practical   aspects   of  molecular dynamics simulations and some basic analysis. The remaining sections will  present the CHARMM program and provide some tutorials to introduce the user to the  program. This course will concentrate on the classical simulation methods (i.e., the most  common) that have contributed significantly to our understanding of biological systems.  Molecular   dynamics   simulations   permit   the   study   of   complex,  dynamic processes that occur in biological systems. These include,  for example, Protein stability Conformational changes Protein folding Molecular   recognition:   proteins,   DNA,   membranes,  complexes • Ion transport in biological systems • • • • and provide the mean to carry out the following studies, • • Drug Design Structure determination: X­ray and NMR Historical Background The molecular dynamics method was first introduced by Alder and Wainwright in the  late 1950's (Alder and Wainwright, 1957,1959) to study the interactions of hard spheres.  Many important insights concerning the behavior of simple liquids emerged from their  studies.   The   next   major   advance   was   in   1964,   when   Rahman   carried   out   the   first  simulation using a realistic potential for liquid argon (Rahman, 1964). The first molecular  dynamics simulation of a realistic system was done by Rahman and Stillinger in their  simulation   of   liquid   water   in   1974   (Stillinger   and   Rahman,   1974).   The   first   protein  simulations   appeared   in   1977   with   the   simulation   of   the   bovine   pancreatic   trypsin  inhibitor (BPTI) (McCammon,  et al, 1977). Today in the literature, one routinely finds  molecular dynamics simulations of solvated proteins, protein­DNA complexes as well as  lipid  systems   addressing   a variety  of issues  including  the  thermodynamics   of  ligand  binding   and  the   folding  of  small  proteins.   The  number   of  simulation   techniques   has  greatly expanded; there exist now many specialized techniques for particular problems,  including mixed quantum mechanical ­ classical simulations, that are being employed to  study   enzymatic   reactions   in   the   context   of   the   full   protein.   Molecular   dynamics  simulation   techniques   are   widely   used   in   experimental   procedures   such   as   X­ray  crystallography and NMR structure determination.   References Alder, B. J. and Wainwright, T. E. J. Chem. Phys. 27, 1208  (1957) Alder, B. J. and Wainwright, T. E.  J. Chem. Phys.  31, 459  (1959) Rahman, A. Phys. Rev. A136, 405 (1964) Stillinger, F. H. and Rahman, A.  J. Chem. Phys.  60, 1545  (1974) McCammon, J. A., Gelin, B. R., and Karplus, M.  Nature   (Lond.) 267, 585 (1977) 3. STATISTICAL MECHANICS Molecular   dynamics   simulations   generate   information   at   the   microscopic   level,  including atomic positions and velocities. The conversion of this microscopic information  to   macroscopic   observables   such   as   pressure,   energy,   heat   capacities,   etc.,   requires  statistical   mechanics.   Statistical   mechanics   is   fundamental   to   the   study   of   biological  systems by molecular dynamics simulation. In this section, we provide a brief overview  of   some   main  topics.  For  more  detailed   information,  refer   to  the   numerous   excellent  books available on the subject. INTRODUCTION TO STATISTICAL MECHANICS: In   a   molecular   dynamics   simulation,   one   often   wishes   to   explore   the   macroscopic  properties   of   a   system   through   microscopic   simulations,   for   example,   to   calculate  changes in the binding free energy  of a particular drug candidate, or to examine the  energetics   and   mechanisms   of   conformational   change.   The   connection   between  microscopic   simulations   and   macroscopic   properties   is   made   via  statistical   mechanics  which provides the rigorous mathematical expressions that relate macroscopic properties  to   the   distribution   and   motion   of   the   atoms   and   molecules   of   the   N­body   system;  molecular dynamics simulations provide the means to solve the equation of motion of  the   particles   and   evaluate   these   mathematical   formulas.   With   molecular   dynamics  simulations,   one   can   study   both   thermodynamic   properties   and/or   time   dependent  (kinetic) phenomenon. Reference Textbooks on Statistical Mechanics D.   McQuarrie,   Statistical   Mechanics   (Harper   &   Row,   New  York, 1976) D.   Chandler,   Introduction   to   Modern   Statistical   Mechanics  (Oxford University Press, New York, 1987) R. E. Wilde and S. Singh, Statistical Mechanics, Fundamentals  and Modern Applications (John Wiley & Sons, Inc, New York,  1998)      Statistical mechanics is the branch of physical sciences that studies macroscopic systems  from a molecular point of view. The goal is to understand and to predict macroscopic  phenomena   from   the   properties   of   individual   molecules   making   up   the   system.   The   these can also be considered as coordinates in a multidimensional space  called phase space.  p. T. N. V. N. and they  correspond to the different conformations of the system and their respective momenta. P.   the   pressure. V. For a system of N particles.   Other  thermodynamic   properties   may   be   derived   from   the   equations   of   state   and   other  fundamental thermodynamic equations. time  independent   statistical   averages   are   often   introduced. In order to connect the macroscopic system to the microscopic system.   P.  and a fixed temperature.   T. and a fixed temperature. for  example.   the   temperature. a fixed volume. • Microcanonical ensemble (NVE) : The thermodynamic state  characterized by a fixed number of atoms. and a fixed temperature. A single  point in phase space. this space has 6N dimensions. An ensemble is a collection of all possible systems which have different microscopic  states but have an identical macroscopic or thermodynamic state. An  ensemble  is a  collection   of   points   in   phase   space   satisfying   the   conditions   of   a   particular  thermodynamic state.system could range from a collection of solvent molecules to a solvated protein­DNA  complex.  Several different ensembles are described below.   and   the   number   of   particles. This corresponds to an isolated system. V. A molecular dynamics simulations generates a sequence of points  in phase space as a function of time. N. and  a fixed energy. • Canonical Ensemble (NVT): This is a collection of all systems  whose thermodynamic state is characterized by a fixed number of  atoms. describes the state of the system. T. E. denoted by  Γ . these points belong to the same ensemble. The mechanical or microscopic state of a system is defined by the atomic positions.   N. . a fixed volume. • Isobaric­Isothermal   Ensemble   (NPT):   This   ensemble   is  characterized by a fixed number of atoms. and  momenta. Definitions The thermodynamic state of a system is usually defined by a small set of parameters. • Grand canonical Ensemble (µ VT): The thermodynamic state  for this ensemble is characterized by a fixed chemical potential. T. q. There exist different ensembles with different characteristics.  a fixed volume. µ .   We   start   this   discussion   by  introducing a few definitions. a fixed pressure.  averages corresponding to experimental observables are defined in  terms   of   ensemble   averages. The ensemble average is given by where is the observable of interest and it is expressed as a function of the momenta. p.   one   justification   for   this   is   that   there   has   been   good  agreement with experiment. and the  .CALCULATING AVERAGES FROM A MOLECULAR DYNAMICS SIMULATION An experiment is usually made on a macroscopic sample that contains an extremely  large number of atoms or molecules sampling an enormous number of conformations. average values are defined as ensemble averages. An ensemble average is average taken over a large number  of replicas of the system considered simultaneously. In  statistical mechanics.   In statistical mechanics.  the  molecular dynamics simulations must pass through all possible states corresponding to  the particular thermodynamic constraints. The integration is over all possible variables of r and p. The probability density of the ensemble is given by where H is the Hamiltonian. so to calculate an ensemble average. which  is expressed as where  τ   is the simulation time.   but   the   experimental   observables   are   assumed   to   be   ensemble   averages. which states that the time average equals the ensemble average.   In   a   molecular   dynamics   simulation. The dilemma appears to be that one can calculate time averages by molecular dynamics  simulation. The Ergodic hypothesis states . r.  the ergodic hypothesis. M is the number of time steps in the simulation and  A(pN. kB is Boltzmann’s constant and Q is  the partition function   This integral is generally  extremely  difficult to calculate because one must calculate all  possible   states   of   the   system. Another way. of the system. is to determine a time average of A.   the   points   in   the  ensemble are calculated sequentially in time. as done in an MD simulation.rN) is the instantaneous value of A.  Resolving this leads us to one of the most fundamental axioms of statistical mechanics.positions. T is the temperature.  F=ma. experimentally relevant information concerning  structural.  one must be certain to sample a sufficient amount of phase space. where F is the force exerted on the particle.Ensemble average = Time average The basic idea is that if one allows the system to evolve in time indefinitely.   therefore. N is the number of atoms in  the system.   of   a   molecular  dynamics simulation is to generate enough representative conformations such that this  equality is satisfied. that system  will   eventually   pass   through   all   possible   states. AVERAGE KINETIC ENERGY where M is the number of configurations in the simulation. If this is the case. Because the simulations are of fixed duration. mi is the mass of the particle i and vi is the velocity of particle i. m is its mass and  .   One   goal. Some examples of time averages: AVERAGE POTENTIAL ENERGY where M is the number of configurations in the molecular dynamics trajectory and Vi is  the potential energy of each configuration.   dynamic   and   thermodynamic   properties   may   then   be   calculated   using   a  feasible amount of computer resources. 4. CLASSICAL MECHANICS The molecular dynamics simulation method is based on Newton’s second law or the  equation of motion. A   molecular   dynamics   simulation   must   be   sufficiently   long   so   that   enough  representative conformations have been sampled.  Integration of the equations of  motion then yields a trajectory that describes the positions. the state of the system can be predicted at any time in the future or the  past. computers are getting faster and cheaper.   it   is   possible   to  determine the acceleration of each atom in the system.  mi  is   the   mass   of   particle  i  and  ai  is   the  acceleration of particle i. From this trajectory. the average values of properties  can be determined. The method is deterministic. Combining these two equations yields where  V  is the potential energy of the system. simulations into the  millisecond regime have been reported.  Newton’s  equation of motion can then  relate the derivative of the potential energy to the changes in position as a function of  time. NEWTON’S SECOND LAW OF MOTION: A SIMPLE APPLICATION . However. Simulations of solvated  proteins are calculated up to the nanosecond time scale.   Newton’s equation of motion is given by where  Fi  is   the   force   exerted   on   particle  i.a  is   its   acceleration. once the positions and velocities of each  atom are known.   Molecular   dynamics   simulations   can   be   time   consuming   and   computationally  expensive. velocities and accelerations of  the particles as they vary with time. The force can also be expressed as the gradient of the potential  energy. however.   From   a   knowledge   of   the   force   on   each   atom.  to calculate a trajectory. The acceleration is given as the derivative of the potential energy with respect to the  position. Therefore. we obtain the following  relation which gives the value of x at time t as a function of the acceleration. x0 . we obtain an expression for the velocity after integration and since we can once again integrate to obtain Combining this equation with the expression for the velocity. one only needs the initial positions of the atoms. r. which is determined by the gradient  . and the initial velocity. the initial  position. v0. an  initial distribution of velocities and the acceleration.Taking the simple case where the acceleration is constant.. a. INTEGRATION ALGORITHMS The potential energy is a function of the atomic positions (3N) of all the atoms in the  system. The initial positions can be obtained from experimental structures. they must be solved numerically. t. Due to the complicated nature of this function.   The   equations   of   motion   are   deterministic. The velocities.g.   e. i.e.   the  positions and the velocities at time zero determine the positions and velocities at all other  times. which gives the probability that an atom i has a  velocity vx in the x direction at a temperature T.. Numerous numerical algorithms have been developed for integrating the equations of  . there is no analytical solution to the  equations of motion. such as the x­ ray   crystal   structure   of   the   protein   or   the   solution   structure   determined   by   NMR  spectroscopy.of   the   potential   energy   function..  are often chosen randomly from a Maxwell­Boltzmann or Gaussian  distribution at a given temperature. The initial distribution of velocities are usually determined from a random distribution  with the magnitudes conforming to the required temperature and corrected so there is  no overall momentum. The temperature can be calculated from the velocities using the relation where N is the number of atoms in the system.  vi.  a is  the acceleration (the second derivative with respect to time). To derive the Verlet algorithm one can write .   one   should   consider   the   following  criteria: • • • The algorithm should conserve energy and momentum. velocities and accelerations can be  approximated by a Taylor series expansion: Where r is the position. • • • •   Verlet algorithm      Leap­frog algorithm      Velocity Verlet      Beeman’s algorithm    Important:   In   choosing   which   algorithm   to   use. We list several here.motion. etc. v is the velocity (the first derivative with respect to time). It should be computationally efficient It should permit a long time step for integration. INTEGRATION ALGORITHMS All the integration algorithms assume the positions.  The disadvantage is that the algorithm is of moderate  precision. and ii) the  storage requirements are modest . these are used to  calculate the positions. The advantages of the Verlet algorithm are. the velocities are first calculated at time  t+1/2δ t. The velocities at time t can be approximated  .  then the positions  leap  over the velocities. one obtains The Verlet algorithm uses positions and accelerations at time  t  and the positions from  time t­δ t to calculate new positions at time t+δ t. i) it is straightforward.   the   disadvantage   is   that   they   are   not  calculated at the same time as the positions. the velocities leap over the positions. The Verlet algorithm uses no explicit  velocities. THE LEAP­FROG ALGORITHM In this algorithm. In this way.   however.Summing these two equations. The advantage of this algorithm is that the  velocities   are   explicitly   calculated. at time t+δ t. r.   velocities   and   accelerations   at   time  t.   There   is   no  compromise on precision.by the relationship: THE VELOCITY VERLET ALGORITHM This   algorithm   yields   positions. BEEMAN’S ALGORITHM This algorithm is closely related to the Verlet algorithm . binding) • (free energy Modeling tool • structure prediction / modeling . The disadvantage is that the more complex  expressions make the calculation more expensive.The advantage of this algorithm is that it provides a more accurate expression for the  velocities and better energy conservation. allosteric mechanisms • Protein folding • Equilibrium ensemble sampling Flexibility • thermodynamics changes. Use of Molecular Dynamics Sim ulation Kinetics and irreversible processes chemical reaction kinetics (with QM) • conformational changes. • Dynamics are important because Biological systems are compartmentalized and are FAR FROM EQUILIBRIUM.• • • solvent effects NMR/crystallography (refinement) Electron microscopy (flexible fitting) Why use molecular dynamics? MD is a sampling method. • . but MD gives you a movie. So why u se MD? • MD gives you DYNAMICS. Other methods can give you the ensemble (smeared picture). But there are other sampling methods like MonteCarlo (MC). The average (ensemble) picture of the two doesn’t help the poor frog trying to get across the highway. midday and at 2 in the morning. And can the molecule influence the dynamics during its contact time? • Consider highway traffic at rush hour.From a small molecule’s standpoint. Instead the molecule cares about the protein’s structures over the time it can diffusively sample (about a nsec). it doesn’t matter what the list of potential structures of a protein are. • Atomic Detail Computer Simulation Model System Molecular Mechanics Potential Energy Surface → . ro )2 Bonded Interactions: Bending .ij ( rij .Exploration by Simulation. ro. and the energy required to stretch or compress it can be approximated by the Hookean potential for an ideal spring: Estr = ½ ks.. © Jeremy Smith Bonded Interactions: Stretching Estr represents the energy required to stretch or compress a covalent bond: A bond can be thought of as a spring having its own equilibrium length. and the energy is given by the Hookean potential with respect to planar angle: Eimproper = ½ ko. usually equal to zero: Again this system can be modeled by a spring.ijk (θ ijk -θ o )2 Bonded Interactions: Improper Torsio n Eimproper is the energy required to deform a planar group of atoms from its equilibrium angle. θ o: Again this system can be modeled by a spring. and the energy is given by the Hookean potential with respect to angle: Ebend = ½ kb. Shattuck ijkl -ω o )2 ω .Ebend is the energy required to bend a bond from its equilibrium angle.ijkl (ω © Thomas W. ω o. cos 3 φ ) Etor ½ ktor.cos φ ) + φ ) + ½ ktor. Shattuck Torsional interactions are modeled by the potential: = ½ ktor.3 ( 1 .cos 2 asymmetry (butane) 2-fold groups e.i j l k Bonded Interactions: Torsion Etor is the energy of torsion needed to rotate about bonds: © Thomas W.2 (1 .1 (1 .g. COO.standard tetrahedral torsions . Non-Bonded Interactions: van der Waals EvdW is the steric exclusion and long-range attraction energy (QM origins): © Thomas W. Shattuck Two frequently used formulas: E E Non-Bonded Interactions: Coulomb Eqq is the Coulomb potential function for electrostatic interactions of charges: © Thomas W. Shattuck . For gas phase calculations ε is normally set to 1. k is a units conversion constant. Larger values of ε are used to approximate the dielectric effect of intervening solute (ε ∼ 60-80) or solvent atoms in solution. Newton’s Law Newton’s Law: Esteric energy = Estr + Ebend + Eimproper + Etor + EvdW + Eqq Verlet’s Numeric Integration Method . k=2086.Formula: The Qi and Qj are the partial atomic charges for atoms i and j separated by a distance rij. ε is the relative dielectric constant.4. for kcal/mol. micro/milliseconds (10-6-10-3 s) • Conformational transitions pico/nanoseconds (10-12-10-9 s) • Collective vibrations • 1 picosecond (10-12 s) • Bond vibrations - 1 femtosecond (10-15 s) .Taylor expansion: Verlet’s Method Timescale Limitations Protein Folding .milliseconds/seconds (10-3-1s) • Ligand Binding .micro/milliseconds (106 -10-3 s) • Enzyme catalysis . 4 .1 fs. Accessible timescale: about 10 nanoseconds.Timescale Limitations Molecular dynamics: Integration timestep .3 PME. Schlick 9. Cutting Corners SHAKE. Schlick 12. set by fastest varying force. Schlick 13.5 MTS. etc) • An input script for the MD program (. amber.psf) • A force field (.Input files for MD simulation A starting structure (. gromacs.conf) • Input Files: PDB atomic structures Input Files: PDB .par) for the atom types (charmm.pdb) • A description of structural connections and atom types (. data Input Files: Topology Files blueprints for building a PSF file Input Files: Topology Files The topology file represents residues in internal coordinates . Then view it using vmd.We will use ubiquitin (1UBQ) as an example. take a look at the file. The pdb structure is available in the protein bank. First. .Input Files: Topology Files Take a look at the charmm/xplor topology file top_all27_prot_lipi d.inp Input Files: PSF Use information in topology file to “fill in the gaps” of the pdb structure: • • • Patch residues Add hydrogens Add waters NAMD/VMD uses the utility psfgen to construct the psf file. Input Files: Parameter Files defining the MM energy terms Input Files: Parameter Files defining the MM energy terms . ubq. that uses psfgen to render the psf file.Input Files: PSF Input Files: PSF Look at the Tcl script.pgn. conf .Take a look at the charmm force field par_all27_prot_lipid. Input Files: MD run script defining the MM energy terms NAMD input script ubq_wb_eq.inp Production Run Protocol Different protocols: • One can do constrained dynamics at the final temp Or • Do free dynamics with a temp ramp-up. one calculates average properties within a sin • . Depending on input script.Output is a trajectory (mcd) in binary format. mcd may contain trajectory coordinates and trajectory velocities. • More commonly. Data reduction and analysis MD runs. by virtue of temperature coupling are stochastic. Can use vmd to visualize the trajectory. One can calculate average trajectories by summing over mu ltiple runs to get an AVERAGE TRAJECTORY . This gives information on nonequilibrium systems. One recovers an ENSEMBLE AVERAGE. IFF the MD run has sampled the entire configurational phase space ( is ergotic). then the time average = ensemb le average. entropy. Ensemble properties of interest include: t hermodynamic state functions: free energy (partition fun ction). • And . enthalpy Data reduction and analysis Averaging is done by constructing a correlation matrix. where Off-diagonal terms give correlations between atoms.gle run. sampling a local basin . and order param eters from NMR. • RMSD MD . RMSD from MD can be compared to B-factors from X-ray chrystallography. H/D protecti on factors from NMR data. (ex: the RMSD of a residue). EPR.Diagonal elements give an average property of an atom. or fluorescence.energies energies: kinetic and potential MD . Biased . To cover configurational phase space. one needs to be able to do two things well: explore canyons and jump over energy barriers.exploring conformations Biased MD .jumping barriers exploring conformations Biased MD exploring conformations MD simulations are generally bad at sampling phase space. Whereas it is possible to take "still snapshots" of crystal structures and probe features of the motion of molecules through NMR.accelerated collective motions (ACM) T4 lysozyme example. Molecular dynamics is a specialized discipline of molecular modeling and computer simulation based on statistical mechanics. no current experimental technique allows access to all the time scales of motion with atomic resolution. giving a view of the motion of the particles.info. It is tempting. Molecular dynamics simulation is frequently used in the study of proteins and biomolecules. known as the ergodic hypothesis. search Molecular dynamics (MD) is a form of computer simulation in which atoms and molecules are allowed to interact for a period of time by approximations of known physics. • http://cmm. Richard Feynman once said that "If we were to name the most powerful assumption of all. though not entirely accurate.MD algorithms have been devised to overco me these deficiencies. which leads one on and on in an attempt to understand life. Explore canyons . MD has also been termed "statistical mechanics by numbers" and "Laplace's vision of Newtonian mechanics" of predicting the future by animating nature's . and that everything that living things do can be understood in terms of the jigglings and wigglings of atoms.nih. the free encyclopedia Jump to: navigation. to describe the technique as a "virtual microscope" with high temporal and spatial resolution." Molecular dynamics lets scientists peer into the motion of individual atoms in a way which is not possible in laboratory experiments. as well as in materials science. the main justification of the MD method is that statistical ensemble averages are equal to time averages of the system. it is that all things are made of atoms.gov/intro_simulation MOLECULAR DYNAMICS From Wikipedia. movement and function. . physics. current potential energy functions (also called force-fields) are. J. in 1962: ". I took a number of rubber balls and stuck them together with rods of a selection of different lengths ranging from 2."[3] Fortunately. now computers keep track of bonds during a simulation. not sufficiently accurate to reproduce the dynamics of molecular systems.75 to 4 inches. It represents an interface between laboratory experiments and theory. However. I tried to do this in the first place as casually as possible.. some undertook the hard work of trying it with physical models such as macroscopic spheres. Before it became possible to simulate molecular dynamics with computers. Molecular dynamics is a multidisciplinary method. MD simulation circumvents the analytical intractability by using numerical methods. long MD simulations are mathematically ill-conditioned. The idea was to arrange them to replicate the properties of a liquid. being interrupted every five minutes or so and not remembering what I had done before the interruption. When the number of particles interacting is higher than two. generating cumulative errors in numerical integration that can be minimized with proper selection of algorithms and parameters. working in my own office. but not eliminated entirely. and can be understood as a "virtual experiment". in many cases. It was originally conceived within theoretical physics in the late 1950s[4] and early 1960s [5]. Bernal said. MD probes the relationship between molecular structure. and chemistry. and it employs algorithms from computer science and information theory.forces[1][2] and allowing insight into molecular motion on an atomic scale. it is in general impossible to find the properties of such complex systems analytically. Because molecular systems generally consist of a vast number of particles.. the result is chaotic motion (see n-body problem). Nevertheless. Its laws and theories stem from mathematics. Furthermore. so the much more computationally demanding Ab Initio Molecular Dynamics method must be used. but is applied today mostly in materials science and the modeling of biomolecules.D. molecular dynamics techniques allow detailed time and space resolution into representative behavior in phase space for carefully selected systems. . including two steps (predictor and corrector) in solving the equations of motion and many additional steps for e. Highly simplified description of the molecular dynamics simulation algorithm.g. In practise. almost all MD codes use much more complicated versions of the algorithm. note that the actual atomic interactions used in current simulations are more complex than those of 2dimensional hard spheres. temperature and pressure control. The simulation proceeds iteratively by alternatively calculating forces and solving the equations of motion based on the accelerations obtained from the new forces. analysis and output. Each circle illustrates the position of a single atom.Example of a molecular dynamics simulation in a simple system: deposition of a single Cu atom on a Cu (001) surface. It has also been applied with limited success as a method of refining protein structure predictions. the interaction between the particles is either described by a "force field" (classical MD). These terms are not used in physics.1 General references 11 External links [EDIT ] AREAS OF APPLICATION There is a significant difference between the focus and methods used by chemists and physicists. In physics. MD serves as an important tool in protein structure determination and refinement using experimental tools such as X-ray crystallography and NMR.4 Generalized ensembles 3 Potentials in MD simulations 3.1 Empirical potentials 3. or a mix between the two. and this is reflected in differences in the jargon used by the different fields.4 Polarizable potentials 3.2 Pair potentials vs. Beginning in theoretical physics.2 Canonical ensemble (NVT) 2. In chemistry.2 Short-range interaction algorithms 5.3 Semi-empirical potentials 3.3 Long-range interaction algorithms 5. many-body potentials 3. where the interactions are usually described by the name of the theory or approximation being used and called the potential energy. MD is used to examine the dynamics of atomic-level phenomena that cannot be observed directly. the method of MD gained popularity in materials science and since the 1970s also in biochemistry and biophysics. a quantum chemical model.5 Ab-initio methods 3.CONTENTS [hide] • • o o o o • o o o o o o o • • o o o o • • • • • o • 1 Areas of Application 2 Design Constraints 2.4 Parallelization strategies 6 Major software for MD simulations 7 Related software 8 Specialized hardware for MD simulations 9 See also 10 References 10.1 Integrators 5.3 Isothermal-Isobaric (NPT) ensemble 2. such as thin film . or just the "potential".7 Coarse-graining and reduced representations 4 Examples of applications 5 Molecular dynamics algorithms 5.1 Microcanonical ensemble (NVE) 2. In chemistry and biophysics.6 Hybrid QM/MM 3. The concepts of energy conservation and molecular entropy come from thermodynamics.e.growth and ion-subplantation. Simulation size (n=number of particles). Multiple . the most expensive one is the non-bonded or non-covalent part. with the size of their van der Waals radii. [EDIT ] DESIGN CONSTRAINTS Design of a molecular dynamics simulation should account for the available computational power. Otherwise. Another factor that impacts total CPU time required by a simulation is the size of the integration timestep. Typical timesteps for classical MD are in the order of 1 femtosecond (1E-15 s). This is the time length between evaluations of the potential. The timestep must be chosen small enough to avoid discretization errors (i. Also. Some techniques to calculate conformational entropy such as principal components analysis come from information theory. In Big O notation. In applied mathematics and theoretical physics. common molecular dynamics simulations scale by O(n2) if all pair-wise electrostatic and van der Waals interactions must be accounted for explicitly. there is a large community of mathematicians working on volume preserving. This computational cost can be reduced by employing electrostatics methods such as Particle Mesh Ewald ( O(nlog(n)) ). Most scientific publications about the dynamics of proteins and DNA use data from simulations spanning nanoseconds (1E-9 s) to microseconds (1E-6 s). smaller than the fastest vibrational frequency in the system). Mathematical techniques such as the transfer operator become applicable when MD is seen as a Markov chain. the time span simulated should match the kinetics of the natural process. which fix the vibrations of the fastest atoms (e. This value may be extended by using algorithms such as SHAKE. several CPU-days to CPU-years are needed.g. it is analogous to making conclusions about how a human walks from less than one footstep. Parallel algorithms allow the load to be distributed among CPUs. ergodic theory and statistical mechanics in general. the most CPU intensive task is the evaluation of the potential (force field) as a function of the particles' internal coordinates. an example is the spatial or force decomposition algorithm [1]. During a classical MD simulation. Within that energy evaluation. MD can also be seen as a special case of the discrete element method (DEM) in which the particles have spherical shape (e. hydrogens) into place. To obtain these simulations. However. P3M or good spherical cutoff techniques ( O(n) ). molecular dynamics is a part of the research realm of dynamical systems.) Some authors in the DEM community employ the term MD rather loosely. To make statistically valid conclusions from the simulations. the simulations should be long enough to be relevant to the time scales of the natural processes being studied. It is also used to examine the physical properties of nanotechnological devices that have not or cannot yet be created. even when their simulations do not model actual molecules.g. timestep and total time duration must be selected so that the calculation can finish within a reasonable time period. symplectic integrators for more computationally efficient MD simulations. In all kinds of molecular dynamics simulations. Commonly we have experience with macroscopic temperatures.g. [EDIT ] MICROCANONICAL ENSEMBLE (NVE) In the microcanonical. a choice should be made between explicit solvent and implicit solvent. The time evolution of X and V is called a trajectory. Boundary conditions are often treated by choosing fixed values at the edges (which may cause artifacts). each particle's position X and velocity V may be integrated with a symplectic method such as Verlet. Explicit solvent particles (such as the TIP3P. This is especially important to reproduce kinetics. mimicking a bulk phase. If there is a large enough number of atoms. But temperature is a statistical quantity. which is . we can calculate all future (or past) positions and velocities. or NVE ensemble. randomized Gaussian). But the granularity and viscosity of explicit solvent is essential to reproduce certain properties of the solute molecules. For a system of N particles with coordinates X and velocities V. It corresponds to an adiabatic process with no heat exchange. It is referred to simply as the "potential" in Physics. One frequent source of confusion is the meaning of temperature in MD. or by employing periodic boundary conditions in which one side of the simulation loops back to the opposite side. while implicit solvents use a mean-field approach. Using an explicit solvent is computationally expensive. the following pair of first order differential equations may be written in Newton's notation as The potential energy function U(X) of the system is a function of the particle coordinates X. which allow for extended times between updates of slower long-range forces. with total energy being conserved. from theoretical knowledge) and velocities (e. the system is isolated from changes in moles (N). volume (V) and energy (E). or the "force field" in Chemistry. statistical temperature can be estimated from the instantaneous temperature. A microcanonical molecular dynamics trajectory may be seen as an exchange of potential and kinetic energy. the simulation box size must be large enough to avoid boundary condition artifacts. For every timestep.time scale methods have also been developed. requiring inclusion of roughly ten times more particles in the simulation. the force F acting on each particle in the system can be calculated as the negative gradient of U(X). which involve a huge number of particles.[6][7][8] For simulating molecules in a solvent. The first equation comes from Newton's laws. SPC/E and SPC-f water models) must be calculated expensively by the force field.g. Given the initial positions (e. In NVT. approximating the canonical ensemble. It was originally created to deal with the slow dynamics of disordered spin systems. The temperature of the system in NVE is naturally raised when macromolecules such as proteins undergo exothermic conformational changes and binding. the 100 eV from the deposited atom would rapidly be transported through and shared among a large number of atoms (1010 or more) with no big change in temperature. It is not trivial to obtain a canonical distribution of conformations and velocities using these algorithms. In the real world. pressure control occurs under constant membrane area (NPAT) or constant surface tension "gamma" (NPγT). time step and integrator is the subject of many articles in the field. Note that the Berendsen thermostat might introduce the flying ice cube effect. a barostat is needed. It is also called parallel tempering. A variety of thermostat methods is available to add and remove energy from the boundaries of an MD system in a more or less realistic way. the energy of endothermic and exothermic processes is exchanged with a thermostat. moles (N). the NoséHoover thermostat. It corresponds most closely to laboratory conditions with a flask open to ambient temperature and pressure. however. [EDIT ] ISOTHERMAL-ISOBARIC (NPT) ENSEMBLE In the isothermal-isobaric ensemble. [EDIT ] GENERALIZED ENSEMBLES The replica exchange method is a generalized ensemble. [EDIT ] CANONICAL ENSEMBLE (NVT) In the canonical ensemble. How this depends on system size. thermostat parameters. Popular techniques to control temperature include velocity rescaling. A temperature-related phenomenon arises due to the small number of atoms that are used in MD simulations. It is also sometimes called constant temperature molecular dynamics (CTMD).found by equating the kinetic energy of the system to nkBT/2 where n is the number of degrees of freedom of the system. When there are only 500 atoms. Nosé-Hoover chains. In addition to a thermostat. Something similar happens in biophysical simulations. the Berendsen thermostat and Langevin dynamics. The replica exchange MD (REMD) formulation [9] tries to overcome the multiple-minima . the substrate is almost immediately vaporized by the deposition. thermostat choice. isotropic pressure control is not appropriate. For example. consider simulating the growth of a copper film starting with a substrate containing 500 atoms and a deposition energy of 100 eV. pressure (P) and temperature (T) are conserved. moles (N). In the simulation of biological membranes. For lipid bilayers. which leads to unphysical translations and rotations of the simulated system. volume (V) and temperature (T) are conserved. These potentials contain free parameters such as atomic charge. usually representing the ground state. Most force fields in chemistry are empirical and consist of a summation of bonded forces associated with chemical bonds. force fields employ . angle. while those used in materials physics are called just empirical or analytical potentials. those most commonly used in chemistry are based on molecular mechanics and embody a classical treatment of particle-particle interactions that can reproduce structural and conformational changes but usually cannot reproduce chemical reactions. van der Waals parameters reflecting estimates of atomic radius. which states that the dynamics of electrons is so fast that they can be considered to react instantaneously to the motion of their nuclei. Its calculation is normally the bottleneck in the speed of MD simulations. and non-bonded forces associated with van der Waals forces and electrostatic charge. these are obtained by fitting against detailed electronic calculations (quantum chemical simulations) or experimental physical properties such as elastic constants. as point particles that follow classical Newtonian dynamics. To lower the computational cost. and equilibrium bond length. Potentials may be defined at many levels of physical accuracy. As a consequence. Empirical potentials represent quantum-mechanical effects in a limited way through ad-hoc functional approximations. The reduction from a fully quantum description to a classical potential entails two main approximations. The second one treats the nuclei. or a description of the terms by which the particles in the simulation will interact. [EDIT ] POTENTIALS IN MD SIMULATIONS Main articles: Force field and Force field implementation A molecular dynamics simulation requires the definition of a potential function. potentials based on quantum mechanics are used. The first one is the Born-Oppenheimer approximation. they may be treated separately. Because of the non-local nature of non-bonded interactions. bond angles. and dihedral. lattice parameters and spectroscopic measurements. they involve at least weak interactions between all particles in the system. and bond dihedrals. [EDIT ] EMPIRICAL POTENTIALS Empirical potentials used in chemistry are frequently called force fields. When finer levels of detail are required. In chemistry and biology this is usually referred to as a force field. In classical molecular dynamics the effect of the electrons is approximated as a single potential energy surface. some techniques attempt to create hybrid classical/quantum potentials where the bulk of the system is treated classically but a small region is treated as a quantum system. which are much heavier than electrons. usually undergoing a chemical transformation.problem by exchanging the temperature of non-interacting replicas of the system running at several temperatures. Examples of such potentials include the Brenner potential[10] for hydrocarbons and its further developments for the C-Si-H and C-OH systems. Chemistry force fields commonly employ preset bonding arrangements (an exception being ab-initio dynamics). particle mesh Ewald summation. silicon and germanium and has since been used for a wide range of other materials. employed in many popular force fields. although sometimes the quadrupolar term is included as well. the dependency between the variables cannot in general be expressed using only pairwise products of the degrees of freedom. involves a sum over groups of three atoms. The ReaxFF potential[11] can be considered a fully reactive hybrid between bond order potentials and chemistry force fields. the second term is the short-range repulsion explained by Pauli's exclusion principle and the final term is the dispersion interaction term.numerical approximations such as shifted cutoff radii. many of the potentials used in physics. In simulations with pairwise potentials. with the angles between the atoms being an important factor in the potential. In the statistical view. the potential energy includes the effects of three or more particles interacting with each other. used for calculating van der Waals forces. which was originally used to simulate carbon. In manybody potentials. or the newer Particle-Particle Particle Mesh (P3M). On the other hand. Usually. Other examples are the embedded-atom method (EAM)[13] and the Tight-Binding Second Moment . reaction field algorithms. The simplest choice. MANY-BODY POTENTIALS The potential functions representing the non-bonded energy are formulated as a sum over interactions between the particles of the system. and thus are unable to model the process of chemical bond breaking and reactions explicitly. For example. the Tersoff potential[12]. An example of such a pair potential is the non-bonded Lennard-Jones potential (also known as the 6-12 potential). in which the total potential energy can be calculated from the sum of energy contributions between pairs of atoms. In many-body potentials. as these interactions are calculated explicitly as a combination of higher-order terms. a simulation only includes the dipolar term. but they occur only through pairwise terms. [EDIT ] PAIR POTENTIALS VS. the potential energy cannot be found by a sum over pairs of atoms. is the "pair potential". Another example is the Born (ionic) model of the ionic lattice. global interactions in the system also exist. The first term in the next equation is Coulomb's law for a pair of ions. such as those based on the bond order formalism can describe several different coordinations of a system and bond breaking. This allows for a dynamic redistribution of charge between atoms which responds to the local chemical environment. However. and the potential energy contribution is then a function of this sum. This is known as Ab Initio Molecular Dynamics (AIMD). a single potential energy surface (usually the ground state) is represented in the force field. Due to the cost of treating the electronic degrees of freedom.g. For many years. increased accuracy has been achieved through the inclusion of polarizability. and empirical formulae are used once again to determine the energy contributions of the orbitals. by scaling up the partial charges obtained from quantum chemical calculations. [EDIT ] POLARIZABLE POTENTIALS Main article: Force field Most classical force fields implicitly include the effect of polarizability. such as Drude particles or fluctuating charges. the values of the matrix elements are found through empirical formulae that estimate the degree of overlap of specific atomic orbitals. where the electron density of states in the region of an atom is calculated from a sum of contributions from surrounding atoms. In excited states.[15] Some promising results have also been achieved for proteins. the computational cost of this simulations is much higher than classical molecular dynamics. These partial charges are stationary with respect to the mass of the atom. This calculation is usually . e. [citation needed] [EDIT ] AB-INITIO METHODS In classical molecular dynamics. For homogenous liquids such as water. This implies that AIMD is limited to smaller systems and shorter periods of time. polarizable MD simulations have been touted as the next generation. The matrix is then diagonalized to determine the occupancy of the different atomic orbitals. it is still uncertain how to best approximate polarizability in a simulation. known as tight-binding potentials. This is a consequence of the Born-Oppenheimer approximation. such as Density Functional Theory. Ab-initio quantum-mechanical methods may be used to calculate the potential energy of a system on the fly. But molecular dynamics simulations can explicitly model polarizability with the introduction of induced dipoles through different methods.Approximation (TBSMA) potentials[14]. [16] However. There are a wide variety of semi-empirical potentials. chemical reactions or a more accurate representation is needed. electronic behavior can be obtained from first principles by using a quantum mechanical method. as needed for conformations in a trajectory. [EDIT ] SEMI-EMPIRICAL POTENTIALS Semi-empirical potentials make use of the matrix representation from quantum mechanics. which vary according to the atoms being modeled. This allows generation of hydrogen wave-functions (similar to electronic wave-functions). A significant advantage of using ab-initio methods is the ability to study reactions that involve breaking or formation of covalent bonds. The methodology for such techniques was introduced by Warshel and coworkers. Sharon Hammes-Schiffer (The Pennsylvania State University). Weitao Yang (Duke University). such as density of electronic states or other electronic properties.made in the close neighborhood of the reaction coordinate. where N is the number of atoms in the system. and are limited in their abilities for providing accurate details regarding the chemical environment). as it determines the reaction rate. These methods are known as mixed or hybrid quantum-mechanical and molecular mechanics methods (hybrid QM/MM). However. In more sophisticated implementations.7)).[17] . The most important advantage of hybrid QM/MM methods is the speed. use of cutoff radius. energy estimates obtained are not very accurate. This methodology has been useful in investigating phenomena such as hydrogen tunneling. tunneling is important for the hydrogen. they are computationally expensive. not on empirical fitting. Donald Truhlar and Jiali Gao (University of Minnesota) and Kenneth Merz (University of Florida). To overcome the limitation. However. In the recent years have been pioneered by several groups including: Arieh Warshel (University of Southern California). while the MM (classical or molecular mechanics) methods are fast but suffer from several limitations (require extensive parameterization. a small part of the system is treated quantum-mechanically (typically activesite of an enzyme) and the remaining system is treated classically. these are based on theoretical considerations. [EDIT ] HYBRID QM/MM QM (quantum-mechanical) methods are very powerful. Ab-Initio calculations produce a vast amount of information that is not available from empirical methods. One example where QM/MM methods have provided new discoveries is the calculation of hydride transfer in the enzyme liver alcohol dehydrogenase. On the other hand the simplest ab-initio calculations typically scale O(n3) or worse (Restricted Hartree-Fock calculations have been suggested to scale ~O(n2. This is mainly due to electrostatic interactions term (every particle interacts with every other particle). In other words. Although various approximations may be used. which correspond to multiple electronic states. periodic pair-list updates and more recently the variations of the particle-mesh Ewald's (PME) method has reduced this between O(N) to O(n2). A new class of method has emerged that combines the good points of QM (accuracy) and MM (speed) calculations. A popular software for ab-initio molecular dynamics is the Car-Parrinello Molecular Dynamics (CPMD) package based on the density functional theory. cannot be used to simulate reactions where covalent bonds are broken/formed. The cost of doing classical molecular dynamics (MM) in the most straightforward case scales O(n2). In this case. QM/MM methods exist to treat both light nuclei susceptible to quantum effects (such as hydrogens) and electronic states. if a system with twice as many atoms is simulated then it would take between two to four times as much computing power. angles. because they require so many timesteps. An example of this is the Charmm 19 force-field. • The simplest form of coarse-graining is the "united atom" (sometimes called "extended atom") and was used in most early MD simulations of proteins. This pseudo-atom must. of course. In these cases. by matching the behavior of the model to appropriate experimental data or all-atom simulations. be properly parameterized so that its van der Waals interactions with other groups have the proper distance-dependence. one typically eliminates all explicit hydrogen atoms except those that have the capability to participate in hydrogen bonds ("polar hydrogens"). • RNA structure in the ribosome and other large systems has been modeled with one pseudo-atom per nucleotide. and torsions in which the pseudo-atom participates. When coarse-graining is done at higher levels. one represents the whole group with a single pseudo-atom. Similarly. simulations of processes on long timescales (beyond about 1 microsecond) are prohibitively expensive. Similar considerations apply to the bonds. one uses "pseudo-atoms" to represent groups of atoms. The aliphatic tails of lipids are represented by a few pseudo-atoms by gathering 2 to 4 methylene groups into each pseudo-atom. • DNA supercoiling has been investigated using 1-3 pseudo-atoms per basepair. In this kind of united atom representation.[EDIT ] COARSE-GRAINING AND REDUCED REPRESENTATIONS At the other end of the detail scale are coarse-grained and lattice models. Instead of explicitly representing every atom of the system. Coarse-graining is done sometimes taking larger pseudoatoms. Examples for coarse graining (CG) methods are discontinuous molecular dynamics (CGDMD)[18][19] and Go-models[20]. and at even lower resolution. lipids and nucleic acids. MD simulations on very large systems may require such large computer resources that they cannot easily be studied by traditional all-atom methods. For example. one can sometimes tackle the problem by using reduced representations. . Examples of applications of coarse-graining in biophysics: protein folding studies are often carried out using a single (or a few) pseudo-atoms per amino acid. • Packaging of double-helical DNA into bacteriophage has been investigated with models where one pseudo-atom represents one turn (about 10 basepairs) of the double helix. Such united atom approximations have been used in MD simulations of biological membranes. But very coarsegrained models have been used successfully to examine a wide range of questions in structural biology. the accuracy of the dynamic description may be less reliable. The parameterization of these very coarse-grained models must be done empirically. instead of treating all four atoms of a CH3 methyl group explicitly (or all three atoms of CH2 methylene group). these parameters should account for both enthalpic and entropic contributions to free energy in an implicit way. which are also called coarse-grained models. Ideally. which measures the probability of folding before unfolding of a specific starting conformation. because proper treatment of hydrogen bonds requires a reasonably accurate description of the directionality and the electrostatic interactions between the donor and acceptor groups. program: NAMD) This virus is a small. for example.0092 ns. Simulation time: 500 µs = 500. Molecular dynamics simulations were used to probe the mechanisms of viral assembly. These computers had the folding@home program installed. Size: 20. and it would be impossible to treat this with a single OH pseudo-atom. The entire STMV particle consists of 60 identical copies of a single protein that make up the viral capsid (coating). One key finding is that the capsid is very unstable when there is no RNA inside. Its simulation published in Nature magazine paved the way for understanding protein motion as essential in function and not just accessory. Program: folding@home) This simulation was run in 200. Program: CHARMM precursor) Protein: Bovine Pancreatic Trypsine Inhibitor.000 CPU's of participating personal computers around the world. Pfold gives information about transition state structures and an ordering of conformations along the folding pathway. but many independent trajectories are needed. Size: 500 atoms. Simulation Time: 9.[22][23] • The following two biophysical examples are not run-of-the-mill MD simulations. the effects that energetic neutron and ion irradiation have on solids an solid surfaces.000 atoms.[24] • Folding Simulations of the Villin Headpiece in All-Atom Detail (2006. Note that about half the atoms in a protein or nucleic acid are nonpolar hydrogens. The simulation would take a single 2006 desktop computer around 35 years to complete. Each trajectory in a Pfold calculation can be relatively short. icosahedral plant virus which worsens the symptoms of infection by Tobacco Mosaic Virus (TMV).2 ps=0. Size: 1 million atoms. • First macromolecular MD simulation published (1977. short trajectories run by CPU's without continuous real-time communication.[21] MD is the standard method to treat collision cascades in the heat spike regime. It was thus done in many processors in parallel with continuous communication between them.The polar hydrogens are usually retained in the model.e. so the use of united atoms can provide a substantial savings in computer time. A hydroxyl group. i. This is one of the best studied proteins in terms of folding and kinetics. One technique employed was the Pfold value analysis. [EDIT ] EXAMPLES OF APPLICATIONS Molecular dynamics is used in many fields of science. They illustrate notable efforts to produce simulations of a system of very large size (a complete virus) and very long simulation times (500 microseconds): • MD simulation of the complete satellite tobacco mosaic virus (STMV) (2006.000 ns. The kinetic properties of the Villin Headpiece protein were probed by using many independent. a large-scale distributed computing effort coordinated by Vijay Pande at Stanford University. can be both a hydrogen bond donor and a hydrogen bond acceptor.[25] [EDIT ] MOLECULAR DYNAMICS ALGORITHMS . Simulation time: 50 ns. and a 1063 nucleotide single stranded RNA genome. Dreiding. parallelization with up to thousands of CPU's) Culgi (classical.Parallel Algorithms [EDIT ] MAJOR SOFTWARE FOR MD SIMULATIONS Main article: List of software for molecular mechanics modeling • • • • • • • • • • • • • • • • AutoDock suite of automated docking tools. implicit water) ABINIT (DFT) ACEMD (running on NVIDIA GPUs: heavily optimized with CUDA) ADUN (classical. Autodock Vina improved local search algorithm. P2P database for simulations) AMBER (classical) Ascalaph (classical. extensive analysis tools) COSMOS (classical and hybrid QM/MM.[EDIT ] INTEGRATORS • • • • • • Verlet-Stoermer integration Runge-Kutta integration Beeman's algorithm Gear predictor . Nerd. Abalone (classical. quantum-mechanical atomic charges with Desmond (classical. and TraPPE-UA force fields) DL_POLY (classical) BPT) . the pioneer in MD simulation. suite of automated docking tools.corrector Constraint algorithms (for constrained systems) Symplectic integrator [EDIT ] SHORT-RANGE INTERACTION ALGORITHMS • • • Cell lists Verlet list Bonded interactions [EDIT ] LONG-RANGE INTERACTION ALGORITHMS • • • • Ewald summation Particle Mesh Ewald (PME) Particle-Particle Particle Mesh P3M Reaction Field Method [EDIT ] PARALLELIZATION STRATEGIES • • Domain decomposition method (Distribution of system data for parallel computing) Molecular Dynamics . OPLS-AA. GPU accelerated) CASTEP (DFT) CPMD (DFT) CP2K (DFT) CHARMM (classical. MC in OPLS esra Lightweight molecular modeling and analysis library (Java/Jython/Mathematica). massively parallel supercomputer designed to execute MD simulations. parallel) • MOLDY (classical. • MacroModel (classical) • MDynaMix (classical. • VMD .A specialized. large-scale with spatial-decomposition of simulation domain for parallelism) • LPMD Las Palmeras Molecular Dynamics: flexible an modular MD.Molecular Visualization software written in python.3d visualization and analysis software. Dreiding. etc. analysis and visualization of MD trajectories. coarse-grained.ESPResSo (classical.MD simulation trajectories can be visualized and analyzed. • PyMol . surface-hopping dynamics) • ORAC (classical) • ProtoMol (classical. extensible) Fireball (tight-binding DFT) GROMACS (classical) GROMOS (classical) GULP (classical) Hippo (classical) HOOMD-Blue (classical. BOSS . parallelization with up to thousands of CPU's) • nano-Material Simulation Toolkit • NEWTON-X (ab initio. parallel) latest release • Materials Studio (Forcite MD using COMPASS. • Punto is a freely available visualisation tool for particle simulations. heavily optimized with CUDA) • Kalypso MD simulation of atomic collisions in solids • LAMMPS (classical. • Sirius . includes multigrid electrostatics) • PWscf (DFT) • RedMD (coarse-grained simulations package on GNU licence) • S/PHI/nX (DFT) • SIESTA (DFT) • VASP (DFT) • TINKER (classical) • YASARA (classical) • XMD (classical) [EDIT ] RELATED SOFTWARE Avizo . extensible.) • MOSCITO (classical) • NAMD (classical. [EDIT ] SPECIALIZED HARDWARE FOR MD SIMULATIONS • Anton . accelerated by NVIDIA GPUs. cvff and pcff forcefields in serial or parallel. • Packmol Package for building starting configurations for MD in an automated fashion. • • • • • • • • • • . • Molecular Workbench . ONESTEP (DFT).Interactive molecular simulations on your desktop. parallel. QMERA (QM+MD). Universal.Molecular modeling. especially protein structure prediction.A special purpose system built for molecular dynamics simulations.• MDGRAPE . .
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