Lecture 3.4

Structural analysis

Learning objectives

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

Account for why a consensus spelling cannot locate a binding site in a genome, and propose what has to be added to find one.

  1. Given \(4^n\) supplied as a power of ten, determine roughly how many times an \(n\)-base consensus turns up by chance in a genome of stated length.
  2. Attribute the symptoms of a failed promoter scan to the right limit.
  3. Defend the claim that a validated model of a single site still cannot find that site in a genome, and propose what has to be added.

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. Explain why the energy an energy function reports for one arrangement of atoms is not a free-energy difference between two states, and name what the second accounts for that the first does not.
  2. 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.

Determine how two structures of one molecule differ once they are superposed, and distinguish a difference in shape from a difference in which atoms were compared.

  1. Define the root-mean-square deviation between two superposed structures, and state what its single value reports.
  2. State what superposing two structures does, and why two sets of coordinates cannot be compared before it is done.
  3. Explain why one deviation value reported for a whole structure can hide a large movement confined to a few residues.
  4. Explain what the root-mean-square fluctuation reports for one residue across a trajectory, and compare it with a deviation measured between two structures.
  5. Given the per-atom displacements between two superposed structures, determine which atoms set the value of the reported deviation.
  6. Given per-residue fluctuation values from a trajectory, read off which regions move most, and compare that ranking with the B-factors reported for the same regions.
  7. Given one pair of structures and two different sets of atoms chosen for the superposition, differentiate the deviation values the two choices report and state which claim each one supports.

Read a free-energy surface built by counting the frames of a trajectory, and relate its basins to the states and populations the trajectory reports.

  1. Explain why a bin holding no frames is not a region of infinite energy, and state what its emptiness reports instead.
  2. Explain how counting the frames falling in each bin of a measured coordinate turns a trajectory into a free-energy surface.
  3. Given a free-energy surface along one coordinate, read off how many states it shows, which one lies lowest, and from which side the barrier between them is the higher climb.
  4. Predict how widening the bins changes the surface, and what a surface drawn from too few frames per bin looks like.
  5. Given the frame counts in two bins, state which bin lies lower on the free-energy surface, and predict how the free-energy difference between them changes when the ratio of their counts is multiplied by ten or inverted.
  6. Given two free-energy surfaces built from one trajectory along different measured coordinates, differentiate what each one supports about the states the molecule occupies.

Account for how overlaying several complexes of one target with different partners produces a consensus volume, and interpret what the occupancy of a cell records and how it responds when partners are added or removed.

  1. Name what has to be in hand before a consensus volume can be built: several complexes of the target with different partners, one common reference frame, and any symmetry the target has.
  2. Explain why a consensus volume is defined by how many partners occupy a cell rather than by the region every partner shares, and state what the strictly shared region would cost.
  3. Explain why every complex has to be superposed on the same part of the target before the partners can be compared with one another.
  4. Explain what a symmetry axis in the target implies about where an equivalent partner could sit, and why that bears on how the cells are counted.
  5. Explain what the occupancy count of a cell records when several partners are overlaid on one grid, and predict how the counts change when one partner is added, removed, or shifted by one cell.
  6. Given the number of complexes behind a consensus volume, distinguish the parts of the volume that number supports from the parts one further complex could change.
  7. Given a grid of occupancy counts and two candidate thresholds for admitting a cell to the volume, differentiate the volumes the two choices produce and state which cells the disagreement falls on.

Compare how far ligands reach outside a consensus volume, and account for what the protruding volume counts and what it leaves confounded.

  1. Define the protruding volume of a ligand against a consensus volume, and name the two things its value depends on.
  2. Interpret \(V_{\mathrm{out}} = (v/N)\sum_i (N - g_i)\) as a sum, over the cells a ligand fills, of how many of the \(N\) overlaid partners are absent from each cell.
  3. Explain why the division by \(N\) makes a protrusion value comparable across ligands, and why this quantity carries no logarithm when most of the course’s scores do.
  4. Given the protruding volumes of two ligands measured against one consensus volume, determine which one asks more of the target than its own partners do.
  5. Given a grid of occupancy counts and the cells one ligand fills, determine which of those cells add to the protruding volume and which add nothing to it.
  6. Distinguish a large protruding volume produced by a ligand reaching into cells few partners occupy from one produced only by the ligand being large, and state what has to be held constant to tell them apart.

Relate the failure of a per-position sequence model to the shape requirement a consensus volume represents, and account for why that volume is the part of a target its function requires.

  1. State the design rule that follows from a function-constrained volume, and name what it predicts about a ligand that reaches outside it.
  2. Explain why the volume a target’s own partners occupy is the part of the target that its function requires it to keep.
  3. Explain why a model that scores each sequence position independently cannot represent a requirement that is one three-dimensional volume.
  4. Explain how partners sharing little sequence with one another can all satisfy one shape requirement.
  5. Determine what the method used to capture a target holding an uncleaved partner costs the set of complexes a consensus volume is built from.
  6. Relate the ranking failure of a per-column matrix on known sites to the shape requirement a consensus volume captures, and state which observations each of the two models accounts for.

Judge what a published analysis establishes, given the evidence standing behind it, what it leaves out, and where its claims are disputed.

  1. Compare what a volume that accounts for cases already known establishes with what one that predicted a case before it was observed establishes.
  2. Relate a reported correlation between protrusion and a measured outcome to the number of ligands behind it, and determine how much weight the relation can carry.
  3. Given a published consensus-volume analysis, distinguish the construction choices it reports from the ones it leaves unstated, and identify which omission most limits reuse of the volume.
  4. Judge the claim that a ligand staying inside a consensus volume will keep working, and state what evidence would settle it.
  5. Given a target you have not studied and several complexes of it with different partners, find the flaw in a proposed plan for building a consensus volume for it, such as a skipped construction step or a missing test before the volume is trusted.
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