The Molecular Modelling Toolkit (MMTK) presents a new approach to molecular simulations. It is not a “simulation program” with a certain set of functions that can be used by writing more or less flexible “input files”, but a collection of library modules written in an easy-to-learn high-level programming language, Python. This approach offers three important advantages:
To further encourage collaborative code development, MMTK uses a very unrestrictive licensing policy. MMTK is free software, just like Python. Although MMTK is copyrighted, anyone is allowed to use it for any purpose, including commercial ones, as well as to modify and redistribute it (a more precise description is given in the copyright statement that comes with the code).
This manual describes version 2.7.9 of MMTK. The 2.x versions contain some incompatible changes with respect to earlier versions (1.x), most importantly a package structure that reduces the risk of name conflicts with other Python packages, and facilitates future enhancements. There are also many new features and improvements to existing functions.
Using MMTK requires a basic knowledge of object-oriented programming and Python. Newcomers to this subject should have a look at the introductory section in this manual and at the Python tutorial (which also comes with the Python interpreter). There are also numerous books on Python that are useful in getting started. Even without MMTK, Python is a very useful programming language for scientific use, allowing rapid development and testing and easy interfacing to code written in low-level languages such as Fortran or C.
This manual consists of several introductory chapters and a module reference. The introductory chapters explain how common tasks are handled with MMTK, but they do not describe all of its features, nor do they contain a full documentation of functions or classes. This information can be found in the module -reference, which describes all classes and functions intended for end-user applications module by module, using documentation extracted directly from the source code. References from the introductory sections to the module reference facilitate finding the relevant documentation.
This chapter explains the basic structure of MMTK and its view of molecular systems. Every MMTK user should read it at least once.
MMTK applications are ordinary Python programs, and can be written using any standard text editor. For interactive use it is recommended to use one of the many tools available for interactive Python programming.
MMTK tries to be as user-friendly as possible for interactive use. For example, lengthy calculations can usually be interrupted by typing Control-C. This will result in an error message (“Keyboard Interrupt”), but you can simply go on typing other commands. Interruption is particularly useful for energy minimization and molecular dynamics: you can interrupt the calculation at any time, look at the current state or do some analysis, and then continue.
MMTK is a package consisting of various modules, most of them written in Python, and some in C for efficiency. The individual modules are described in the module -reference. The basic definitions that almost every application needs are collected in the top-level module, MMTK. The first line of most applications is therefore:
from MMTK import *
The definitions that are specific to particular applications reside in submodules within the package MMTK. For example, force fields are defined in MMTK.ForceFields, and peptide chain and protein objects are defined in MMTK.Proteins.
Python provides two ways to access objects in modules and submodules. The first one is importing a module and referring to objects in it, e.g.:
import MMTK
import MMTK.ForceFields
universe = MMTK.InfiniteUniverse(MMTK.ForceFields.Amber99ForceField())
The second method is importing all or some objects from a module:
from MMTK import InfiniteUniverse
from MMTK.ForceFields import Amber99ForceField
universe = InfiniteUniverse(Amber99ForceField())
These two import styles can also be mixed according to convience. In order to prevent any confusion, all objects are referred to by their full names in this manual. The Amber force field object is thus called MMTK.ForceFields.Amber99ForceField. Of course the user is free to use selective imports in order to be able to use such objects with shorter names.
MMTK is an object-oriented system. Since objects are everywhere and everything is an object, it is useful to know the most important object types and what can be done with them. All object types in MMTK have meaningful names, so it is easy to identify them in practice. The following overview contains only those objects that a user will see directly. There are many more object types used by MMTK internally, and also some less common user objects that are not mentioned here.
These are the objects that represent the parts of a molecular system:
These objects form a simple hierarchy: complexes consist of molecules, molecules consist of groups and atoms, groups consist of smaller groups and atoms. All of these, except for groups, can be used directly to construct a molecular system. Groups can only be used in the definitions of other groups and molecules in the The chemical database.
A number of operations can be performed on chemical objects, which can roughly be classified into inquiry (constituent atoms, bonds, center of mass etc.) and modification (translate, rotate).
There are also specialized versions of some of these objects. For example, MMTK defines proteins as special complexes, consisting of peptide chains, which are special molecules. They offer a range of special operations (such as selecting residues or constructing the positions of missing hydrogen atoms) that do not make sense for molecules in general.
Collection objects represent arbitrary collections of chemical objects. They are used to be able to refer to collections as single entities. For example, you might want to call all water molecules collectively “solvent”. Most of the operations on chemical objects are also available for collections.
Force field objects represent a precise description of force fields, i.e. a complete recipe for calculating the potential energy (and its derivatives) for a given molecular system. In other words, they specify not only the functional form of the various interactions, but also all parameters and the prescriptions for applying these parameters to an actual molecular system.
Universes define complete molecular systems, i.e. they contain chemical objects. In addition, they describe interactions within the system (by a force field), boundary conditions, external fields, etc. Many of the operations that can be used on chemical objects can also be applied to complete universes.
A minimizer object is a special “machine” that can find local minima in the potential energy surface of a universe. You may consider this a function, if you wish, but of course functions are just special objects. Similarly, an integrator is a special “machine” that can determine a dynamical trajectory for a system on a given potential energy surface.
Minimizers and integrators can produce trajectories, which are special files containing a sequence of configurations and/or other related information. Of course trajectory objects can also be read for analysis.
Variable objects (not to be confused with standard Python variables) describe quantities that have a value for each atom in a system, for example positions, masses, or energy gradients. Their most common use is for storing various configurations of a system.
Normal mode objects contain normal mode frequencies and atomic displacements for a given universe. MMTK provides three kinds of normal modes which correspond to three different physical situations:
An MMTK application program will typically also make use of objects provided by Python or Python library modules. A particularly useful library is the package Scientific, which is also used by MMTK itself. The most important objects are
Of course MMTK applications can make use of the Python standard library or any other Python modules. For example, it is possible to write a simulation program that provides status reports via an integrated Web server, using the Python standard module SimpleHTTPServer.
For defining the chemical objects described above, MMTK uses a database of descriptions. There is a database for atoms, one for groups, etc. When you ask MMTK to make a specific chemical object, for example a water molecule, MMTK looks for the definition of water in the molecule database. A database entry contains everything there is to know about the object it defines: its constituents and their names, configurations, other names used e.g. for I/O, and all information force fields might need about the objects.
MMTK comes with database entries for many common objects (water, amino acids, etc.). For other objects you will have to write the definitions yourself. as described in the section Constructing the database.
MMTK contains everything necessary to use the Amber 99 force field on proteins, DNA, and water molecules. It uses the standard Amber parameter and modification file format. In addition to the Amber force field, there is a simple Lennard-Jones force field for noble gases, and a deformation force field for normal mode calculations on large proteins.
MMTK was designed to make the addition of force field terms and the implementation of other force fields as easy as possible. Force field terms can be defined in Python (for ease of implementation) or in Cython, C, or Fortran (for efficiency). This is described in the developer’s guide.
Since MMTK is not a black-box program, but a modular library, it is essential for it to use a consistent unit system in which, for example, the inverse of a frequency is a time, and the product of a mass and the square of a velocity is an energy, without additional conversion factors. Black-box programs can (and usually do) use a consistent unit system internally and convert to “conventional” units for input and output.
The unit system of MMTK consists mostly of SI units of appropriate magnitude for molecular systems:
| Measurement | Units |
|---|---|
| Length | nm |
| Time | ps |
| Mass | amu (g/mol) |
| Energy | kJ/mol |
| Frequency | THz (1/ps) |
| Temperature | K |
| Charge | e |
The module MMTK.Units contains convenient conversion constants for the units commonly used in computational chemistry. For example, a length of 2 Ångström can be written as 2*Units.Ang, and a frequency can be printed in wavenumbers with print frequency/Units.invcm.
The following simple example shows how a typical MMTK application might look like. It constructs a system consisting of a single water molecule and runs a short molecular dynamics trajectory. There are many alternative ways to do this; this particular one was chosen because it makes each step explicit and clear. The individual steps are explained in the remaining chapters of the manual.
# Import the necessary MMTK definitions.
from MMTK import *
from MMTK.ForceFields import Amber99ForceField
from MMTK.Trajectory import Trajectory, TrajectoryOutput, StandardLogOutput
from MMTK.Dynamics import VelocityVerletIntegrator
# Create an infinite universe (i.e. no boundaries, non-periodic).
universe = InfiniteUniverse(Amber99ForceField())
# Create a water molecule in the universe.
# Water is defined in the database.
universe.molecule = Molecule('water')
# Generate random velocities.
universe.initializeVelocitiesToTemperature(300*Units.K)
# Create an integrator.
integrator = VelocityVerletIntegrator(universe)
# Generate a trajectory
trajectory = Trajectory(universe, "water.nc", "w")
# Run the integrator for 50 steps of 1 fs, printing time and energy
# every fifth step and writing time, energy, temperature, and the positions
# of all atoms to the trajectory at each step.
t_actions = [StandardLogOutput(5), \
TrajectoryOutput("time", "energy", \
"thermodynamic", "configuration"), 0, None, 1]
integrator(delta_t = 1.*Units.fs, steps = 50, actions = t_actions)
# Close the trajectory
trajectory.close()
The construction of a complete system for simulation or analysis involves some or all of the following operations:
MMTK offers a large range of functions to deal with these tasks.
Chemical objects (atoms, molecules, complexes) are created from definitions in the Constructing the database. Since these definitions contain most of the necessary information, the subsequent creation of the objects is a simple procedure.
All objects are created by their class name (MMTK.ChemicalObjects.Atom, MMTK.ChemicalObjects.Molecule, and MMTK.ChemicalObjects.Complex) with the name of the definition file as first parameter. Additional optional parameters can be specified to modify the object being created. The following optional parameters can be used for all object types:
Some examples with additional explanations for specific types:
MMTK contains special support for working with proteins, peptide chains, and nucleotide chains. As described in the chapter Constructing the database, proteins can be described by a special database definition file. However, it is often simpler to create macromolecular objects directly in an application program. The classes are MMTK.Proteins.PeptideChain, MMTK.Proteins.Protein, and MMTK.NucleicAcids.NucleotideChain.
Proteins can be created from definition files in the database, from previously constructed peptide chain objects, or directly from PDB files if no special manipulations are necessary.
Examples:
Peptide chains are created from a sequence of residues, which can be a MMTK.PDB.PDBPeptideChain object, a list of three-letter residue codes, or a string containing one-letter residue codes. In the last two cases the atomic positions are not defined. MMTK provides several models for the residues which provide different levels of detail: an all-atom model, a model without hydrogen atoms, two models containing only polar hydrogens (using different definitions of polar hydrogens), and a model containing only the Cα atoms, with each Cα atom having the mass of the entire residue. The last model is useful for conformational analyses in which only the backbone conformations are important.
The construction of nucleotide chains is very similar. The residue list can be either a MMTK.PDB.PDBNucleotideChain object or a list of two-letter residue names. The first letter of a residue name indicates the sugar type (‘R’ for ribose and’D’ for desoxyribose), and the second letter defines the base (‘A’, ‘C’, and’G’, plus ‘T’ for DNA and’U’ for RNA). The models are the same as for peptide chains, except that the Cα model does not exist.
Most frequently proteins and nucleotide chains are created from a PDB file. The PDB files often contain solvent (water) as well, and perhaps some other molecules. MMTK provides convenient functions for extracting information from PDB files and for building molecules from them in the module MMTK.PDB. The first step is the creation of a MMTK.PDB.PDBConfiguration object from the PDB file:
from MMTK.PDB import PDBConfiguration
configuration = PDBConfiguration('some_file.pdb')
The easiest way to generate MMTK objects for all molecules in the PDB file is then
molecules = configuration.createAll()
The result is a collection of molecules, peptide chains, and nucleotide chains, depending on the contents of the PDB files. There are also methods for modifying the PDBConfiguration before creating MMTK objects from it, and for creating objects selectively. See the documentation for the modules MMTK.PDB and Scientific.IO.PDB for details, as well as the Proteins and DNA examples.
Sometimes it is necessary to generate objects (atoms or molecules) positioned on a lattice. To facilitate this task, MMTK defines lattice objects which are essentially sequence objects containing points or objects at points. Lattices can therefore be used like lists with indexing and for-loops. The lattice classes are MMTK.Geometry.RhombicLattice, MMTK.Geometry.BravaisLattice, and MMTK.Geometry.SCLattice.
The Python standard library and the Numerical Python package provide random number generators, and more are available in seperate packages. MMTK provides some convenience functions that return more specialized random quantities: random points in a universe, random velocities, random particle displacement vectors, random orientations. These functions are defined in module MMTK.Random.
Often it is useful to treat a collection of several objects as a single entity. Examples are a large number of solvent molecules surrounding a solute, or all sidechains of a protein. MMTK has special collection objects for this purpose, defined as MMTK.Collections.Collection. Most of the methods available for molecules can also be used on collections.
A variant of a collection is the partitioned collection, implemented in class MMTK.Collections.PartitionedCollection. This class acts much like a standard collection, but groups its elements by geometrical position in small sub-boxes. As a consequence, some geometrical algorithms (e.g. pair search within a cutoff) are much faster, but other operations become somewhat slower.
A universe describes a complete molecular system consisting of any number of chemical objects and a specification of their interactions (i.e. a force field) and surroundings: boundary conditions, external fields, thermostats, etc. The universe classes are defined in module MMTK:
Universes are created empty; the contents are then added to them. Three types of objects can be added to a universe: chemical objects (atoms, molecules, etc.), collections, and environment objects (thermostats etc.). It is also possible to remove objects from a universe.
MMTK comes with several force fields, and permits the definition of additional force fields. Force fields are defined in module MMTK.ForceFields.ForceField. The most important built-in force field is the Amber 99 force field, represented by the class MMTK.ForceFields.Amber.AmberForceField.Amber99ForceField. It offers several strategies for electrostatic interactions, including Ewald summation and cutoff with charge neutralization and optional screening [Wolf1999]..
In addition to the Amber 99 force field, there is the older Amber 94 forcefield, a Lennard-Jones force field for noble gases (Class MMTK.ForceFields.LennardJonesFF) and an Elastic Network Model force field for protein normal mode calculations (MMTK.ForceFields.DeformationFF.CalphaForceField).
Most MMTK objects (in fact all except for atoms) have a hierarchical structure of parts of which they consist. For many operations it is necessary to access specific parts in this hierarchy.
In most cases, parts are attributes with a specific name. For example, the oxygen atom in every water molecule is an attribute with the name “O”. Therefore if w refers to a water molecule, then w.O refers to its oxygen atom. For a more complicated example, if m refers to a molecule that has a methyl group called “M1”, then m.M1.C refers to the carbon atom of that methyl group. The names of attributes are defined in the database.
Some objects consist of parts that need not have unique names, for example the elements of a collection, the residues in a peptide chain, or the chains in a protein. Such parts are accessed by indices; the objects that contain them are Python sequence types. Some examples:
Peptide and nucleotide chains also allow the operation of slicing: if p refers to a peptide chain, then p[1:-1] is a subchain extending from the second to the next-to-last residue.
Since peptide and nucleotide chains are not constructed from an explicit definition file in the database, it is not evident where their hierarchical structure comes from. But it is only the top-level structure that is treated in a special way. The constituents of peptide and nucleotide chains, residues, are normal group objects. The definition files for these group objects are in the MMTK standard database and can be freely inspected and even modified or overriden by an entry in a database that is listed earlier in MMTKDATABASE.
Peptide chains are made up of amino acid residues, each of which is a group consisting of two other groups, one being called “peptide” and the other “sidechain”. The first group contains the peptide group and the C and H atoms; everything else is contained in the sidechain. The C atom of the fifth residue of peptide chain p is therefore referred to as p[4].peptide.C_alpha.
Nucleotide chains are made up of nucleotide residues, each of which is a group consisting of two or three other groups. One group is called “sugar” and is either a ribose or a desoxyribose group, the second one is called “base” and is one the five standard bases. All but the first residue in a nucleotide chain also have a subgroup called “phosphate” describing the phosphate group that links neighbouring residues.
Many inquiry and modification operations act at the atom level and can equally well be applied to any object that is made up of atoms, i.e. atoms, molecules, collections, universes, etc. These operations are defined once in a Mix-in class called MMTK.Collections.GroupOfAtoms, but are available for all objects for which they make sense. They include inquiry-type functions (total mass, center of mass, moment of inertia, bounding box, total kinetic energy etc.), coordinate modifications (translation, rotation, application of Coordinate transformations) and coordinate comparisons (RMS difference, optimal fits).
The most common coordinate manipulations involve translations and rotations of specific parts of a system. It is often useful to refer to such an operation by a special kind of object, which permits the combination and analysis of transformations as well as its application to atomic positions.
Transformation objects specify a general displacement consisting of a rotation around the origin of the coordinate system followed by a translation. They are defined in the module Scientific.Geometry, but for convenience the module MMTK contains a reference to them as well. Transformation objects corresponding to pure translations can be created with Translation(displacement); transformation objects describing pure rotations with Rotation(axis, angle) or Rotation(rotation_matrix). Multiplication of transformation objects returns a composite transformation.
The translational component of any transformation can be obtained by calling the method translation(); the rotational component is obtained analogously with rotation(). The displacement vector for a pure translation can be extracted with the method displacement(), a tuple of axis and angle can be extracted from a pure rotation by calling axisAndAngle().
Many properties in a molecular system are defined for each individual atom: position, velocity, mass, etc. Such properties are represented in special objects, defined in module MMTK: MMTK.ParticleProperties.ParticleScalar for scalar quantities, MMTK.ParticleProperties.ParticleVector for vector quantities, and MMTK.ParticleProperties.ParticleTensor for rank-2 tensors. All these objects can be indexed with an atom object to retrieve or change the corresponding value. Standard arithmetic operations are also defined, as well as some useful methods.
A configuration object, represented by the class MMTK.ParticleProperties.Configuration is a special variant of a MMTK.ParticleProperties.ParticleVector object. In addition to the atomic coordinates of a universe, it stores geometric parameters of a universe that are subject to change, e.g. the edge lengths of the elementary cell of a periodic universe. Every universe has a current configuration, which is what all operations act on by default. It is also the configuration that is updated by minimizations, molecular dynamics, etc. The current configuration can be obtained by calling the method configuration().
There are two ways to create configuration objects: by making a copy of the current configuration (with universe.copyConfiguration(), or by reading a configuration from a trajectory.
Minimization and dynamics algorithms produce sequences of configurations that are often stored for later analysis. In fact, they are often the most valuable result of a lengthy simulation run. To make sure that the use of trajectory files is not limited by machine compatibility, MMTK stores trajectories in netCDF files. These files contain binary data, minimizing disk space usage, but are freely interchangeable between different machines. In addition, there are a number of programs that can perform standard operations on arbitrary netCDF files, and which can therefore be used directly on MMTK trajectory files. Finally, netCDF files are self-describing, i.e. contain all the information needed to interpret their contents. An MMTK trajectory file can thus be inspected and processed without requiring any further information.
For illustrations of trajectory operations, see the examples.
Trajectory file objects are represented by the class MMTK.Trajectory.Trajectory. They can be opened for reading, writing, or modification. The data in trajectory files can be stored in single precision or double precision; single-precision is usually sufficient, but double-precision files are required to reproduce a given state of the system exactly.
A trajectory is closed by calling the method close(). If anything has been written to a trajectory, closing it is required to guarantee that all data has been written to the file. Closing a trajectory after reading is recommended in order to prevent memory leakage, but is not strictly required.
Newly created trajectories can contain all objects in a universe or any subset; this is useful for limiting the amount of disk space occupied by the file by not storing uninteresting parts of the system, e.g. the solvent surrounding a protein. It is even possible to create a trajectory for a subset of the atoms in a molecule, e.g. for only the Cα atoms of a protein. The universe description that is stored in the trajectory file contains all chemical objects of which at least one atom is represented.
When a trajectory is opened for reading, no universe object needs to be specified. In that case, MMTK creates a universe from the description contained in the trajectory file. This universe will contain the same objects as the one for which the trajectory file was created, but not necessarily have all the properties of the original universe (the description contains only the names and types of the objects in the universe, but not, for example, the force field). The universe can be accessed via the attribute universe of the trajectory.
If the trajectory was created with partial data for some of the objects, reading data from it will set the data for the missing parts to “undefined”. Analysis operations on such systems must be done very carefully. In most cases, the trajectory data will contain the atomic configurations, and in that case the “defined” atoms can be extracted with the method atomsWithDefinedPositions().
MMTK trajectory files can store various data: atomic positions, velocities, energies, energy gradients etc. Each trajectory-producing algorithm offers a set of quantities from which the user can choose what to put into the trajectory. Since a detailed selection would be tedious, the data is divided into classes, e.g. the class “energy” stands for potential energy, kinetic energy, and whatever other energy-related quantities an algorithm produces.
For optimizing I/O efficiency, the data layout in a trajectory file can be modified by the block_size parameter. Small block sizes favour reading or writing all data for one time step, whereas large block sizes (up to the number of steps in the trajectory) favour accessing a few values for all time steps, e.g. scalar variables like energies or trajectories for individual atoms. The default value of the block size is one.
Every trajectory file contains a history of its creation. The creation of the file is logged with time and date, as well as each operation that adds data to it with parameters and the time/date of start and end. This information, together with the comment and the number of atoms and steps contained in the file, can be obtained with the function MMTK.Trajectory.trajectoryInfo().
It is possible to read data from a trajectory file that is being written to by another process. For efficiency, trajectory data is not written to the file at every time step, but only approximately every 15 minutes. Therefore the amount of data available for reading may be somewhat less than what has been produced already.
Minimizers and dynamics integrators accept various optional parameter specifications. All of them are selected by keywords, have reasonable default values, and can be specified when the minimizer or integrator is created or when it is called. In addition to parameters that are specific to each algorithm, there is a general parameter actions that specifies actions that are executed periodically, including trajectory and console output.
Periodic actions are specified by the keyword parameter actions whose value is a list of periodic actions, which defaults to an empty list. Some of these actions are applicable to any trajectory-generating algorithm, especially the output actions. Others make sense only for specific algorithms or specific universes, e.g. the periodic rescaling of velocities during a Molecular Dynamics simulation.
Each action is described by an action object. The step numbers for which an action is executed are specified by three parameters. The parameter first indicates the number of the first step for which the action is executed, and defaults to 0. The parameter last indicates the last step for which the action is executed, and default to None, meaning that the action is executed indefinitely. The parameter skip speficies how many steps are skipped between two executions of the action. The default value of 1 means that the action is executed at each step. Of course an action object may have additional parameters that are specific to its action.
The output actions are defined in the module MMTK.Trajectory and can be used with any trajectory-generating algorithm. They are:
The other periodic actions are meaningful only for Molecular Dynamics simulations:
During the course of a minimization or molecular dynamics algorithm, the atoms move to different positions. It is possible to exclude specific atoms from this movement, i.e. fixing them at their initial positions. This has no influence whatsoever on energy or force calculations; the only effect is that the atoms’ positions never change. Fixed atoms are specified by giving them an attribute fixed with a value of one. Atoms that do not have an attributefixed, or one with a value of zero, move according to the selected algorithm.
MMTK has two energy minimizers using different algorithms: steepest descent (MMTK.Minimization.SteepestDescentMinimizer) and conjugate gradient (MMTK.Minimization.ConjugateGradientMinimizer) . Steepest descent minimization is very inefficient if the goal is to find a local minimum of the potential energy. However, it has the advantage of always moving towards the minimum that is closest to the starting point and is therefore ideal for removing bad contacts in a unreasonably high energy configuration. For finding local minima, the conjugate gradient algorithm should be used.
Both minimizers accept three specific optional parameters:
There are three classes of trajectory data: “energy” includes the potential energy and the norm of its gradient, “configuration” stands for the atomic positions, and “gradients” stands for the energy gradients at each atom position.
The following example performs 100 steps of steepest descent minimization without producing any trajectory or printed output:
from MMTK import *
from MMTK.ForceFields import Amber99ForceField
from MMTK.Minimization import SteepestDescentMinimizer
universe = InfiniteUniverse(Amber99ForceField())
universe.protein = Protein('insulin')
minimizer = SteepestDescentMinimizer(universe)
minimizer(steps = 100)
See also the example file modes.py.
The techniques described in this section are illustrated by several examples.
The integration of the classical equations of motion for an atomic system requires not only positions, but also velocities for all atoms. Usually the velocities are initialized to random values drawn from a normal distribution with a variance corresponding to a certain temperature. This is done by calling the method initializeVelocitiesToTemperature() on a universe. Note that the velocities are assigned atom by atom; no attempt is made to remove global translation or rotation of the total system or any part of the system.
During equilibration of a system, it is common to multiply all velocities by a common factor to restore the intended temperature. This can done explicitly by calling the method scaleVelocitiesToTemperature() on a universe, or by using the action object MMTK.Dynamics.VelocityScaler.
A common technique to eliminate the fastest (usually uninteresting) degrees of freedom, permitting a larger integration time step, is the use of distance constraints on some or all chemical bonds. MMTK allows the use of distance constraints on any pair of atoms, even though constraining anything but chemical bonds is not recommended due to considerable modifications of the dynamics of the system [vanGunsteren1982], [Hinsen1995].
MMTK permits the definition of distance constraints on all atom pairs in an object that are connected by a chemical bond by calling the method setBondConstraints. Usually this is called for a complete universe, but it can also be called for a chemical object or a collection of chemical objects. The removeDistanceConstraints() removes all distance constraints from the object for which it is called.
Constraints defined as described above are automatically taken into account by Molecular Dynamics integrators. It is also possible to enforce the constraints explicitly by calling the method enforceConstraints() for a universe. This has the effect of modifying the configuration and the velocities (if velocities exist) in order to make them compatible with the constraints.
A standard Molecular Dynamics integration allows time averages corresponding to the NVE ensemble, in which the number of molecules, the system volume, and the total energy are constant. This ensemble does not represent typical experimental conditions very well. Alternative ensembles are the NVT ensemble, in which the temperature is kept constant by a thermostat, and the NPT ensemble, in which temperature and pressure are kept constant by a thermostat and a barostat. To obtain these ensembles in MMTK, thermostat and barostat objects must be added to a universe. In the presence of these objects, the Molecular Dynamics integrator will use the extended-systems method for producing the correct ensemble. The classes to be used are MMTK.Environment.NoseThermostat and MMTK.Environment.AndersenBarostat.
A Molecular Dynamics integrator based on the “Velocity Verlet” algorithm [Swope1982], which was extended to handle distance constraints as well as thermostats and barostats [Kneller1996], is implemented by the class MMTK.Dynamics.VelocityVerletIntegrator. It has two optional keyword parameters:
There are three classes of trajectory data: “energy” includes the potential energy and the kinetic energy, as well as the energies of thermostat and barostat coordinates if they exist, “time” stands for the time, “thermodynamic” stand for temperature and pressure, “configuration” stands for the atomic positions, “velocities” stands for the atomic velocities, and “gradients” stands for the energy gradients at each atom position.
The following example performs a 1000 step dynamics integration, storing every 10th step in a trajectory file and removing the total translation and rotation every 50th step:
from MMTK import *
from MMTK.ForceFields import Amber99ForceField
from MMTK.Dynamics import VelocityVerletIntegrator, \
TranslationRemover, \
RotationRemover
from MMTK.Trajectory import TrajectoryOutput
universe = InfiniteUniverse(Amber99ForceField())
universe.protein = Protein('insulin')
universe.initializeVelocitiesToTemperature(300.*Units.K)
actions = [TranslationRemover(0, None, 50), \
RotationRemover(0, None, 50), \
TrajectoryOutput("insulin.nc", \
("configuration", "energy", "time"), \
0, None, 10)]
integrator = VelocityVerletIntegrator(universe, delta_t = 1.*Units.fs, \
actions = actions)
integrator(steps = 1000)
A snapshot generator allows writing the current system state to a trajectory. It works much like a zero-step minimization or dynamics run, i.e. it takes the same optional arguments for specifying the trajectory and protocol output. A snapshot generator is created using the class MMTK.Trajectory.SnapshotGenerator.
Normal mode analysis provides an analytic description of the dynamics of a system near a minimum using an harmonic approximation to the potential. Before a normal mode analysis can be started, the system must be brought to a local minimum of the potential energy by energy minimization, except when special force fields designed only for normal mode analysis are used (e.g. MMTK.ForceFields.CalphaFF.CalphaForceField). See also the Normal Modes examples.
A standard normal mode analysis is performed by creating a normal modes object, implemented in the classes MMTK.NormalModes.EnergeticModes.EnergeticModes, MMTK.NormalModes.VibrationalModes.VibrationalModes, and MMTK.NormalModes.BrownianModes.BrownianModes. A normal mode object behaves like a sequence of mode objects, which store the atomic displacement vectors corresponding to each mode and the associated force constant, vibrational frequency, or inverse relaxation time.
For short-ranged potentials, it is advantageous to store the second derivatives of the potential in a sparse-matrix form and to use an iterative method to determine some or all modes. This permits the treatment of larger systems that would normally require huge amounts of memory.
Another approach to deal with large systems is the restriction to low-frequency modes which are supposed to be well representable by linear combinations of a given set of basis vectors. The basis vectors can be obtained from a basis for the full Cartesian space by elimination of known fast degrees of freedom (e.g. bonds); the module MMTK.Subspace contains support classes for this approach. It is also possible to construct a suitable basis vector set from small-deformation vector fields (e.g. MMTK.FourierBasis.FourierBasis).
Analysis is the most non-standard part of molecular simulations. The quantities that must be calculated depend strongly on the system and the problem under study. MMTK provides a wide range of elementary operations that inquire the state of the system, as well as several more complex analysis tools. Some of them are demonstrated in the example section.
Many operations access and modify various properties of an object. They are defined for the most general type of object: anything that can be broken down to atoms, i.e. atoms, molecules, collections, universes, etc., i.e. in the class MMTK.Collections.GroupOfAtoms.
The most elementary operations are inquiries about specific properties of an object: number of atoms, total mass, center of mass, total momentum, total charge, etc. There are also operations that compare two different conformations of a system. Finally, there are special operations for analyzing conformations of peptide chains and proteins.
Geometrical operations in periodic universes require special care. Whenever a distance vector between two points in a systems is evaluated, the minimum-image convention must be used in order to obtain consistent results. MMTK provides routines for finding these distance vectors as well as distances, angles, and dihedral angles between any points. Because these operations depend on the topology and geometry of the universe, they are implemented as methods in class MMTK.Universe.Universe and its subclasses. Of course they are available for non-periodic universes as well.
Universes also provide methods for obtaining atom property objects that describe the state of the system (configurations, velocities, masses), and for restoring the system state from a trajectory file.
Energy evaluation requires a force field, and therefore all the methods in this section are defined only for universe objects, i.e. in class MMTK.Universe.Universe. However, they all take an optional arguments (anything that can be broken down into atoms) that indicates for which subset of the universe the energy is to be evaluated. In addition to the potential energy, energy gradients and second derivatives (force constants) can be obtained, if the force field implements them. There is also a method that returns a dictionary containing the values for all the individual force field terms, which is often useful for analysis.
Surfaces and volumes can be analyzed for anything consisting of atoms. Both quantities are defined by assigning a radius to each atom; the surface of the resulting conglomerate of overlapping spheres is taken to be the surface of the atom group. Atom radii for surface determination are usually called “van der Waals radii”, but there is no unique method for determining them. MMTK uses the values from [Bondi1964]. However, users can change these values for each individual atom by assigning a new value to the attribute vdW_radius.
The operations provided in MMTK.MolecularSurface include basic surface and volume calculation, determination of exposed atoms, and identification of contacts between two objects.
MMTK provides an easy way to store (almost) arbitrary objects in files and retrieve them later. All objects of interest to users can be stored, including chemical objects, collections, universes, normal modes, configurations, etc. It is also possible to store standard Python objects such as numbers, lists, dictionaries etc., as well as practically any user-defined objects. Storage is based on the standard Python module pickle.
Objects are saved with MMTK.save() and restored with MMTK.load(). If several objects are to be stored in a single file, use tuples: save((object1, object2), filename) and object1, object2 = load(filename) to retrieve the objects.
Note that storing an object in a file implies storing all objects referenced by it as well, such that the size of the file can become larger than expected. For example, a configuration object contains a reference to the universe for which it is defined. Therefore storing a configuration object means storing the whole universe as well. However, nothing is ever written twice to the same file. If you store a list or a tuple containing a universe and a configuration for it, the universe is written only once.
Frequently it is also useful to copy an object, such as a molecule or a configuration. There are two functions (which are actually taken from the Python standard library module copy) for this purpose, which have a somewhat different behaviour for container-type objects (lists, dictionaries, collections etc.). MMTK.copy() returns a copy of the given object. For a container object, it returns a new container object which contains the same objects as the original one. If the intention is to get a container object which contains copies of the original contents, then MMTK.deepcopy(object) should be used. For objects that are not container-type objects, there is no difference between the two functions.
MMTK can write objects in specific file formats that can be used by other programs. Three file formats are supported: the PDB format, widely used in computational chemistry, the DCD format for trajectories, written by the programs CHARMM, X-Plor, and NAMDm, and read by many visualization programs, and the VRML format, understood by VRML browsers as a representation of a three-dimensional scene for visualization. MMTK also provides a more general interface that can generate graphics objects in any representation if a special module for that representation exists. In addition to facilitating the implementation of new graphics file formats, this approach also permits the addition of custom graphics elements (lines, arrows, spheres, etc.) to molecular representations.
Any chemical object, collection, or universe can be written to a PDB or VRML file by calling the method writeToFile, defined in class MMTK.Collections.GroupOfAtoms. PDB files are read via the class MMTK.PDB.PDBConfiguration. DCD files can be read by a MMTK.DCD.DCDReader object. For writing DCD files, there is the function MMTK.DCD.writeDCDPDB(), which also creates a compatible PDB file without which the DCD file could not be interpreted.
Special care must be taken to ensure a correct mapping of atom numbers when reading from a DCD file. In MMTK, each atom object has a unique identity and atom numbers, also used internally for efficiency, are not strictly necessary and are not used anywhere in MMTK’s application programming interface. DCD file, however, simply list coordinates sorted by atom number. For interpreting DCD files, another file must be available which allows the identification of atoms from their number and vice versa; this can for example be a PDB file.
When reading DCD files, MMTK assumes that the atom order in the DCD file is identical to the internal atom numbering of the universe for which the DCD file is read. This assumption is in general valid only if the universe has been created from a PDB file that is compatible with the DCD file, without any additions or removals.
The most common need for file export is visualization. All objects that can be visualized (chemical systems and subsets thereof, normal mode objects, trajectories) provide a method view which creates temporary export files, starts a visualization program, and deletes the temporary files. Depending on the object type there are various optional parameters.
MMTK also allows visualization of normal modes and trajectories using animation. Since not all visualization programs permit animation, and since there is no standard way to ask for it, animation is implemented only for the programs XMol and VMD. Animation is available for normal modes, trajectories, and arbitrary sequences of configurations (see function MMTK.Visualization.viewSequence()).
For more specialized needs, MMTK permits the creation of graphical representations of most of its objects via general graphics modules that have to be provided externally. Suitable modules are provided in the package Scientific.Visualization and cover VRML (version 1), VRML2 (aka VRML97), and the molecular visualization program VMD. Modules for other representations (e.g. rendering programs) can be written easily; it is recommended to use the existing modules as an example. The generation of graphics objects is handled by the method graphicsObjects, defined in the class MMTK.Visualization.Viewable, which is a Mix-in class that makes graphics objects generation available for all objects that define chemical systems or parts thereof, as well as for certain other objects that are viewable.
The explicit generation of graphics objects permits the mixture of different graphical representations for various parts of a system, as well as the combination of MMTK-generated graphics objects with arbitrary other graphics objects, such as lines, arrows, or spheres. All graphics objects are finally combined into a scene object (also defined in the various graphics modules) in order to be displayed. See also the visualization examples.
For analyzing or visualizing atomic properties that change little over short distances, it is often convenient to represent these properties as functions of position instead of one value per atom. Functions of position are also known as fields, and mathematical techniques for the analysis of fields have proven useful in many branches of physics. Such a field can be obtained by averaging over the values corresponding to the atoms in a small region of space. MMTK provides classes for scalar and vector field in module MMTK.Field. See also the example vector_field.py.
A frequent problem in determining force field parameters is the determination of partial charges for the atoms of a molecule by fitting to the electrostatic potential around the molecule, which is obtained from quantum chemistry programs. Although this is essentially a straightforward linear least-squares problem, many procedures that are in common use do not use state-of-the-art techniques and may yield erroneous results. MMTK provides a charge fitting method that is numerically stable and allows the imposition of constraints on the charges. It is implemented in module MMTK.ChargeFit. See also the example charge_fit.py.
MMTK uses a database of chemical entities to define the properties of atoms, molecules, and related objects. This database consists of plain text files, more precisely short Python programs, whose names are the names of the object types. This chapter explains how to construct and manage these files. Note that the standard database already contains many definitions, in particular for proteins and nucleic acids. You do not need to read this chapter unless you want to add your own molecule definitions.
MMTK’s database does not have to reside in a single place. It can consist of any number of subdatabases, each of which can be a directory or a URL. Typically the database consists of at least two parts: MMTK’s standard definitions and a user’s personal definitions. When looking up an object type in the database, MMTK checks the value of the environment variable MMTKDATABASE. The value of this variable must be a list of subdatabase locations seperated by white space. If the variable MMTKDATABASE is not defined, MMTK uses a default value that contains the path ”.mmtk/Database” in the user’s home directory followed by MMTK’s standard database, which resides in the directory Database within the MMTK package directory (on many Unix systems this is /usr/local/lib/python2.x/site-packages/MMTK). MMTK checks the subdatabases in the order in which they are mentioned in MMTKDATABASE.
Each subdatabase contains directories corresponding to the object classes, i.e. Atoms (atom definitions), Groups (group definitions), Molecules (molecule definitions), Complexes (complex definitions), Proteins (protein definitions), and PDB (Protein Data Bank files). These directories contain the definition files, whose names may not contain any upper-case letters. These file names correspond to the object types, e.g. the call MMTK.Molecule('Water') will cause MMTK to look for the file Molecules/water in the database (note that the names are converted to lower case).
The remaining sections of this chapter explain how the individual definition files are constructed. Keep in mind that each file is actually a Python program, so of course standard Python syntax rules apply.
An atom definition in MMTK describes a chemical element, such as “hydrogen”. This should not be confused with the “atom types” used in force field descriptions and in some modelling programs. As a consequence, it is rarely necessary to add atom definitions to MMTK.
Atom definition files are short and of essentially identical format. This is the definition for carbon:
name = 'carbon'
symbol = 'C'
mass = [(12, 98.90), (13.003354826, 1.10)]
color = 'black'
vdW_radius = 0.17
The name should be meaningful to users, but is not used by MMTK itself. The symbol, however, is used to identify chemical elements. It must be exactly equal to the symbol defined by IUPAC, including capitalization (e.g. ‘Cl’ for chlorine). The mass can be either a number or a list of tuples, as shown above. Each tuple defines an isotope by its mass and its percentage of occurrence; the percentages must add up to 100. The color is used for VRML output and must equal one of the color names defined in the module VRML. The van der Waals radius is used for the calculation of molecular volumes and surfaces; the values are taken from [Bondi1964].
An application program can create an isolated atom with Atom('c') or, specifying an initial position, with Atom('c', position=Vector(0.,1.,0.)). The element name can use any combination of upper and lower case letters, which are considered equivalent.
Group definitions in MMTK exist to facilitate the definition of molecules by avoiding the frequent repetition of common combinations. MMTK doesn’t give any physical meaning to groups. Groups can contain atoms and other groups. Their definitions look exactly like molecule definitions; the only difference between groups and molecules is the way they are used.
This is the definition of a methyl group:
name = 'methyl group'
C = Atom('C')
H1 = Atom('H')
H2 = Atom('H')
H3 = Atom('H')
bonds = [Bond(C, H1), Bond(C, H2), Bond(C, H3)]
pdbmap = [('MTH', {'C': C, 'H1': H1, 'H2': H2, 'H3': H3})]
amber_atom_type = {C: 'CT', H1: 'HC', H2: 'HC', H3: 'HC'}
amber_charge = {C: 0., H1: 0.1, H2: 0.1, H3: 0.1}
The name should be meaningful to users, but is not used by MMTK itself. The following lines create the atoms in the group and assign them to variables. These variables become attributes of whatever object uses this group; their names can be anything that is a legal Python name. The list of bonds, however, must be assigned to the name bonds. The bond list is used by force fields and for visualization.
The name pdbmap is used for reading and writing PDB files. Its value must be a list of tuples, where each tuple defines one PDB residue. The first element of the tuple is the residue name, which is used only for output. The second element is a dictionary that maps PDB atom names to the actual atoms. The pdbmap entry of any object can be overridden by an entry in a higher-level object. Therefore the entry for a group is only used for atoms that do not occur in the entry for a molecule that contains this group.
The remaining lines in the definition file contain information specific to force fields, in this case the Amber force field. The dictionary amber_atom_type defines the atom type for each atom; the dictionary amber_charge defines the partial charges. As for pdbmap entries, these definitions can be overridden by higher-level definitions.
Molecules are typically used directly in application programs, but they can also be used in the definition of complexes. Molecule definitions can use atoms and groups.
This is the definition of a water molecule:
name = 'water'
structure = \
" O \n" + \
" / \ \n" + \
"H H \n"
O = Atom('O')
H1 = Atom('H')
H2 = Atom('H')
bonds = [Bond(O, H1), Bond(O, H2)]
pdbmap = [('HOH', {'O': O, 'H1': H1, 'H2': H2})]
pdb_alternative = {'OH2': 'O'}
amber_atom_type = {O: 'OW', H1: 'HW', H2: 'HW'}
amber_charge = {O: -0.83400, H1: 0.41700, H2: 0.41700}
configurations = {
'default': ZMatrix([[H1], \
[O, H1, 0.9572*Ang], \
[H2, O, 0.9572*Ang, H1, 104.52*deg]])
}
The name should be meaningful to users, but is not used by MMTK itself. The structure is optional and not used by MMTK either. The following lines create the atoms in the group and assign them to variables. These variables become attributes of the molecule, i.e. when a water molecule is created in an application program by w = Molecule('water'), then w.H1 will refer to its first hydrogen atom. The names of these variables can be any legal Python names. The list of bonds, however, must be assigned to the name bonds. The bond list is used by force fields and for visualization.
The name pdbmap is used for reading and writing PDB files. Its value must be a list of tuples, where each tuple defines one PDB residue. The first element of the tuple is the residue name, which is used only for output. The second element is a dictionary that maps PDB atom names to the actual atoms. The pdbmap entry of any object can be overridden by an entry in a higher-level object, i.e. in the case of a molecule a complex containing it. The name pdb_alternative allows to read PDB files that use non-standard names. When a PDB atom name is not found in the pdbmap, an attempt is made to translate it to another name using pdb_alternative.
The two following lines in the definition file contain information specific to force fields, in this case the Amber force field. The dictionary amber_atom_type defines the atom type for each atom; the dictionary amber_charge defines the partial charges. As for pdbmap entries, these definitions can be overridden by higher-level definitions.
The name configurations can be defined to be a dictionary of configurations for the molecule. During the construction of a molecule, a configuration can be specified via an optional parameter, e.g. w = Molecule('water', configuration='default'). The names of the configurations can be arbitrary; only the name “default” has a special meaning; it is applied by default if no other configuration is specified when constructing the molecule. If there is no default configuration, and no other configuration is explicitly specified, then the molecule is created with undefined atomic positions.
There are three ways of describing configurations:
By a Z-Matrix:
ZMatrix([[H1], \
[O, H1, 0.9572*Ang], \
[H2, O, 0.9572*Ang, H1, 104.52*deg]])
By Cartesian coordinates:
Cartesian({O: ( 0.004, -0.00518, 0.0),
H1: (-0.092, -0.00518, 0.0),
H2: ( 0.028, 0.0875, 0.0)})
By a PDB file:
PDBFile('water.pdb')
The PDB file must be in the database subdirectory PDB, unless a full path name is specified for it.
Complexes are defined much like molecules, except that they are composed of molecules and atoms; no groups are allowed, and neither are bonds.
Protein definitions can take many different forms, depending on the source of input data and the type of information that is to be stored. For proteins it is particularly useful that database definition files are Python programs with all their flexibility.
The most common way of constructing a protein is from a PDB file. This is an example for a protein definition:
name = 'insulin'
# Read the PDB file.
conf = PDBConfiguration('insulin.pdb')
# Construct the peptide chains.
chains = conf.createPeptideChains()
# Clean up
del conf
The name should be meaningful to users, but is not used by MMTK itself. The second command reads the sequences of all peptide chains from a PDB file. Everything which is not a peptide chain is ignored. The following line constructs a PeptideChain object (a special molecule) for each chain from the PDB sequence. This involves constructing positions for any missing hydrogen atoms. Finally, the temporary data (“conf”) is deleted, otherwise it would remain in memory forever.
The net result of a protein definition file is the assignment of a list of molecules (usually PeptideChain objects) to the variable “chains”. MMTK then constructs a protein object from it. To use the above example, an application program would use the command p = Protein('insulin'). The construction of the protein involves one nontrivial (but automatic) step: the construction of disulfide bridges for pairs of cystein residues whose sulfur atoms have a distance of less then 2.5 Ångström.
This chapter explains the use of threads by MMTK and MMTK’s parallelization support. This is an advanced topic, and not essential for the majority MMTK applications. You need to read this chapter only if you use multiprocessor computers, or if you want to implement multi-threaded programs that use MMTK.
Threads are different execution paths through a program that are executed in parallel, at least in principle; real parallel execution is possible only on multiprocessor systems. MMTK makes use of threads in two ways, which are conceptually unrelated: parallelization of energy evaluation on shared-memory multiprocessor computers, and support for multithreaded applications. Thread support is not available on all machines; you can check if yous system supports threads by starting a Python interpreter and typing import threading. If this produces an error message, then your system does not support threads, otherwise it is available in Python and also in MMTK. If you do not have thread support in Python although you know that your operating system supports threads, you might have compiled your Python interpreter without thread support; in that case, MMTK does not have thread support either.
Another approach to parallelization is message passing: several processors work on a program and communicate via a fast network to share results. A standard library, called MPI (Message Passing Interface), has been developped for sharing data by message passing, and implementations are available for all parallel computers currently on the market. MMTK contains elementary support for parallelization by message passing: only the energy evaluation has been paralellized, using a data-replication strategy, which is simple but not the most efficient for large systems. MPI support is disabled by default. Enabling it involves modifying the file Src/Setup.template prior to compilation of MMTK. Furthermore, an MPI-enabled installation of ScientificPython is required, and the mpipython executable must be used instead of the standard Python interpreter.
Threads and message passing can be used together to use a cluster of shared-memory machines most efficiently. However, this requires that the thread and MPI implementations being used work together; sometimes there are conflicts, for example due to the use of the same signal in both libraries. Refer to your system documentation for details.
The use of threads for parallelization on shared-memory systems is very simple: Just set the environment variable MMTK_ENERGY_THREADS to the desired value. If this variable is not defined, the default value is 1, i.e. energy evaluations are performed serially. For choosing an appropriate value for this environment variable, the following points should be considered:
Parallelization via message passing is somewhat more complicated. In the current MMTK parallelization model, all processors execute the same program and replicate all tasks, with the important exception of energy evaluation. Energy terms are divided evenly between the processors, and at the end the energy and gradient values are shared by all machines. This is the only step involving network communication. Like thread-based parallelization, message-passing parallelization does not support the evaluation of second derivatives.
A special problem with message-passing systems is input and output. The MMTK application must ensure that output files are written by only one processor, and that all processors correctly access input files, especially in the case of each processor having its own disk space. See the example md.py for illustration.
Multithreaded applications are applications that use multiple threads in order to simplify the implementation of certain algorithms, i.e. not necessarily with the goal of profiting from multiple processors. If you plan to write a multithreaded application that uses MMTK, you should first make sure you understand threading support in Python. In particular, you should keep in mind that the global interpreter lock prevents the effective use of multiple processors by Python code; only one thread at a time can execute interpreted Python code. C code called from Python can permit other threads to execute simultaneously; MMTK does this for energy evaluation, molecular dynamics integration, energy minimization, and normal mode calculation.
A general problem in multithreaded applications is access to resources that are shared among the threads. In MMTK applications, the most important shared resource is the description of the chemical systems, i.e. universe objects and their contents. Chaos would result if two threads tried to modify the state of a universe simultaneously, or even if one thread uses information that is simultaneously being modified by another thread. Synchronization is therefore a critical part of multithreaded application. MMTK provides two synchronization aids, both of which described in the documentation of the class MMTK.Universe.Universe: the configuration change lock (methods acquireConfigurationChangeLock() and releaseConfigurationChangeLock()), and the universe state lock (methods acquireReadStateChangeLock(), releaseReadStateChangeLock(), acquireWriteStateChangeLock(), and releaseWriteStateChangeLock()). Only a few common universe operations manipulate the universe state lock in order to avoid conflicts with other threads; these methods are marked as thread-safe in the description. All other operations should only be used inside a code section that is protected by the appropriate manipulation of the state lock. The configuration change lock is less critical; it is used only by the molecular dynamics and energy minimization algorithms in MMTK.
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