Lecture 3.3

Molecular dynamics

Learning objectives

After this lecture, you should be able to do the following.

Interpret a potential energy surface as the object a structural model sits on, and relate its minima and barriers to what the molecule does.

  1. Explain why a molecule with many rotatable degrees of freedom has an energy surface holding many minima, and state what that implies about any one optimized structure.
  2. Explain why one set of coordinates is a single point on an energy surface rather than a description of the surface, and state what the surface says that the point cannot.
  3. Given a one-dimensional energy curve with two minima and a barrier between them, read off which minimum is deeper, which barrier is higher from each side, and which state is occupied more of the time.
  4. Given a claim that a molecule prefers one shape, supported by a single minimized structure, diagnose what the energy surface would have to look like for the claim to hold and which feature of it the evidence leaves unmeasured.

Relate a free-energy difference to the equilibrium it implies through \(\Delta G = -RT\ln K\), and predict how that energy responds when the fold change it corresponds to grows, shrinks, or inverts.

  1. Given the free-energy difference between two states, predict which state is more populated, and how the population ratio changes when that difference doubles or changes sign.
  2. Relate one free-energy difference to the three ratios it can be read as: an equilibrium constant, the relative populations of two states, and a fold change in a measured potency.

Judge whether a reported number supports the claim drawn from it, given how the number was produced and how large the uncertainty of that method is.

  1. Explain what running a simulation a second time from different starting velocities tests, and why one long run and several shorter independent runs support different claims.
  2. Compare the error stated for a free-energy difference taken from a simulation with the energy that corresponds to a tenfold change in population.
  3. Given the duration of a simulation and the time a stated motion is known to take, determine whether the run could have sampled that motion at all.
  4. Given two reported populations differing tenfold, the error stated for the method, and the number of independent runs behind each, determine whether the difference is a result.
  5. Given a claim about how a molecule works and one simulation offered in support, judge whether the evidence supports the claim and state what further evidence would settle it.

Account for how a simulation turns an energy function into motion, and determine what the timestep and the number of steps each limit about the result.

  1. Define the timestep of a simulation, and name the kind of atomic motion whose speed sets how large it may be.
  2. Explain how the slope of the energy at an atom’s position sets the force on that atom, and state which way the force points.
  3. Explain how repeating one small update of positions and velocities produces a trajectory, and compare that update with the downhill-only update of a geometry optimization.
  4. Explain why a simulation run at a temperature can leave the basin it started in while a downhill optimization cannot.
  5. Predict how the duration a simulation covers changes when the timestep or the number of steps is changed by a stated factor with the other held fixed.
  6. Predict what happens to a simulation when the timestep is set larger than the fastest motion in the system allows.

Read a trajectory as an ensemble of sampled structures, and account for what one frame of it can and cannot support.

  1. Define an ensemble of structures, and state what it reports about a molecule that one structure cannot.
  2. Define a trajectory, a frame, and the saving interval, and state what one frame holds.
  3. Compare what an ensemble of frames reports about a flexible region with what one deposited structure reports about the same region.
  4. Explain why the early part of a trajectory is set aside before any frames are counted, and state what the choice of where to start counting changes.
  5. Explain why one frame taken from a trajectory supports no claim about the molecule, and name what makes a frame unrepresentative of the run it came from.
  6. Explain how sorting the frames of a trajectory by one measured geometric value turns them into a distribution of that value, and given such a distribution, read off which range of it is occupied most.
  7. Predict what is lost when frames are saved too rarely and what is wasted when they are saved too often.
  8. Given two independent simulations of one system whose distributions of the same measured value disagree, differentiate too little sampling from a difference in how the two runs were set up.

Relate a functional conformational change to what deposited structures and a trajectory each report about the states involved.

  1. Define a conformational state, and state what makes two states of one molecule different from two different molecules.
  2. Compare the ensemble of a protein on its own with the ensemble of the same protein holding a partner, and state what the comparison reports about whether the bound shape existed before binding.
  3. Explain why one measured distance or angle can stand in for a whole conformational change, and state what choosing that one measurement commits you to.
  4. Explain why a protein whose job requires a region to open and close cannot do that job from a single fixed conformation.
  5. Given two deposited structures of one molecule in different conformations, determine what a trajectory would have to show for them to be two states of one ensemble rather than two unrelated models.
  6. Given a distribution of frames along one measured coordinate and two candidate cut points dividing it into states, differentiate the populations the two choices report and state which features of the distribution make the choice matter.

Relate the population ratio of two conformational states to counted frames or to a free-energy difference, predict which way it moves when either changes, and account for what the ratio depends on.

  1. Compare what a population reports about two states with what a rate reports, and state why the state occupied least of the time can carry most of the traffic through a process.
  2. Explain why a state that appears in a small fraction of frames can still be the state that matters for what the molecule does.
  3. Predict how the population ratio of two states counted from a trajectory’s frames changes when frames shift from one state to the other, and state what that ratio assumes about the run it was counted from.
  4. Given two published population values for one conformational switch obtained by different methods, differentiate the choices that could produce the disagreement.
  5. Relate a population ratio counted from frames to the same ratio obtained from a free-energy difference, and distinguish the inputs each route depends on.
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