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Coarse-grained Molecular Dynamics of Micro-biological Systems

Крупно-зернистая Молекулярная Динамика Микро-биологических Систем

Molecular biology is relatively hard to study with analytical methods due to

  • such systems are usually open and non-homogeneous;
  • the exact form of interactions is unknown. Of course, there's no fundamentally new forces on molecular level — but they are mixed in a rather eccentric manner which leads to that instead of Coulomb law we get various polarization effects, steric interactions, excluded volume interactions, hydrophobic effect;
  • a relatively important role of kinetics compared to "energetics": so You can't neglect either of them;
  • finally: it's biology! You deal with living systems, which leads to effects absent in physics. For exapmle Levinthal's paradox: how does protein knows which way to fold? Answer: only proteins with a stable folding exist in surviving organisms.

Of course, there are phisics of polymers, perturbation theory, phisical kinetics, mean field theory... But neither is capable of predicting, say, secondary structure of the given protein.

Help comes from computational methods, such as molecular dynamics. The reasonably desired future prediction time range is about seconds. Modern supercomputers currently can do milliseconds, which is already sufficient for many problems.

In a nutshell molecular dynamics method consists of numerical integration equations of motion for particles composing the system. You first

  • set the coordinates of all system's particles;
  • set parameters of all particles: mass, charge, etc;
  • set the laws acting between particles: polarization, Coulomb, bonds, etc;
  • then You calculate forces, which You
  • set to be fixed for a small amount of time, say 50 picoseconds;
  • During that time particles move around the system;
  • Then You recalculate forces followed by
  • another period of particle movement.

See — this way You've prediceted the future of the system for the 100 picoseconds.

In case of large micro-biological systems it is often redundant to know movemnts of all atoms as all times. In order to save computational power — scientists split molecules in groups of 3-6 atoms each (so-called beads) and also the appropriate interactions. This is a called coarse-grained approach.

As an example of the problem that could be solved with molecular dynamics consider the following problem.

Suppose there's a protein which secondary structure is known from the x-ray experiments, but the way it is stucked into a lipid membrane is unknown.

We can perform a series of molecular dynamics runs (starting from different positions) to determine which position proteins adopts.

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