Molecular dynamics (MD)

  • Molecular dynamics simulations predict the atomic-level motions of materials and processes using basic physical principles.
  • Continuum modeling accuracy is enriched by molecular dynamics (MD) simulations. These lower-scale simulations help us to unveil the behavior of molecules at the atomic scale.
  • Mimic what atoms do in real life, assuming a given potential energy function.
    • The energy function allows us to calculate the force experienced by any atom given the positions of the other atoms.
    • Newton’s laws tell us how those forces will affect the motions of the atoms.

Basic algorithm

  • Divide time into discrete time steps, no more than a few femtoseconds each.
  • At each time step:
    • Compute the forces acting on each atom, using a molecular mechanics force field.
    • Move the atoms a little bit: update position and velocity of each atom using Newton’s laws of motion. 

introduction to molecular dynamic simulation

Key properties of MD simulations

  • Atoms never stop jiggling.
  • In real life, and in an MD simulation, atoms are in constant motion.
    • They will not go to an energy minimum and stay there.
  • Given enough time, the simulation samples the Boltzmann distribution
    • That is, the probability of observing a particular arrangement of atoms is a function of the potential energy.
    • In reality, one often does not simulate long enough to reach all
      energetically favorable arrangements.
    • This is not the only way to explore the energy surface (i.e., sample the Boltzmann distribution), but it’s a pretty effective way to do so.
  • Energy conservation:
  • Total energy (potential + kinetic) should be conserved :
    • In atomic arrangements with lower potential energy, atoms move faster.
    • In practice, total energy tends to grow slowly with time due to numerical errors (rounding errors).
    • In many simulations, one adds a mechanism to keep the temperature roughly constant (a “thermostat”).

Sample applications

Determining where drug molecules bind, and how they exert their effects

  • We used simulations to determine where this molecule binds to its receptor, and how it changes the binding strength of molecules
    that bind elsewhere (in part by changing the protein’s structure). We then used that information to alter the molecule such that it has a
    different effect.

Dror et al., Nature 2013

Determining functional mechanisms of proteins 

  • We performed simulations in which a receptor protein transitions
    spontaneously from its active structure to its inactive structure.
  • We used these to describe the mechanism by which drugs binding to
    one end of the receptor cause the other end of the receptor to change shape (activate).

Rosenbaum et al., Nature 2010; Dror et al., PNAS 2011

Understanding the process of protein folding

  • For example, in what order do secondary structure elements form?
  • But note that MD is generally not the best way to predict the folded

Lindorff-Larsen et al., Science 2011

Limitations of MD simulations

  • Timescales
  • Force field accuracy
  • Covalent bonds cannot break or form during (standard) MD simulations.

Software packages

  • Multiple molecular dynamics software packages are available; their core functionality is similar – AMBER, NAMD, GROMACS, Desmond, OpenMM, CHARMM.
  • Dominant package for visualizing results of simulations: VMD (“Visual Molecular Dynamics”).

Force fields for molecular dynamics.

  • Three major force fields are used for MD – CHARMM, AMBER, OPLS-AA – Do not confuse CHARMM and AMBER force fields with CHARMM and AMBER software packages.
  • They all use strikingly similar functional forms – Common heritage: Lifson’s “Consistent force field”.

Monte Carlo simulation

  • An alternative method to discover low-energy regions of the space of atomic arrangements
  • Instead of using Newton’s laws to move atoms, consider random moves:
    • For example, consider changes to a randomly selected dihedral angle, or to multiple dihedral angles simultaneously.
    • Examine energy associated with resulting atom positions to decide whether or not to “accept” (i.e., make) each move you consider.
CS/CME/BioE/Biophys/BMI 279/Oct. 5 and 10, 2017
Ron Dror