Stochastic roadmap simulation for the study of ligand-protein interactions

1
Stochastic roadmap simulation for the study of
ligand-protein interactions

• Mehmet Serkan Apaydin, Carlos E. Guestrin, Chris
  Varma, Douglas L. Brutlag and Jean-Claude Latombe
  (Stanford Departments of Computer Science and
  Biochemistry)

Presented by Max Shneider
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Definitions

• Stochastic - Random, probabilistic
• Roadmap - Compact graph structure
• Torsional twisting or turning
• Putative binding sites different cavities on a
  protein where a ligand could potentially bind
• Funnel of Attraction all ligand conformations
  within 10 Å RMSD of a binding site conformation

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Monte Carlo Simulation (MC)

• Generate paths corresponding to potential motions
  of the ligand and protein
• Select initial conformation of interest
• Sample new conformation according to move set
• Accept or reject new conformation based on energy
  difference with original
• Drawbacks
• Only generates one simulation path at a time
• Can get stuck in local minima of the energy
  function (repeatedly sampling many similar
  conformations)

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Stochastic Roadmap Simulation (SRS)

• Example conformation representation - ligand and
  protein parameters specified as vector (?1, ?2,
  , ?d)
• Ligand parameters 3D coordinates of one atom,
  torsional angles of remaining atoms
• Protein parameters backbone torsional angles
• Conformational parameters determine interaction
  between atoms of molecule and between molecules
  and the medium (ie. van der Waals, electrostatic)
• Assumes that interactions are described by an
  energy function that depends only on the
  conformation of the molecules

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SRS Roadmap

• Encode many pathways as a directed graph
• Node conformation with each ?i sampled randomly
  from allowed range according to some distribution
• Find nearest neighbors using some metric (ie.
  RMS, Euclidean Distance)
• Edge probability of the molecules transitioning
  from a node i to one of its neighbors j
• Roadmap contains many simultaneous MC paths
• Can get individual MC path by starting with top
  node, choosing successor node at random according
  to edge probabilities (note you never need to do
  this with SRS)

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SRS Roadmap (cont.)
PAA
A
E
A
A
PAB
PAC
B
F
PCC
PBB
B
C
B
C
C
G
PBD
PBE
PCF
PCG
D
D
D
E
E
F
F
G
G
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SRS - Properties

• Implicitly defines a Markov chain that captures
  stochastic nature of molecular motion
• Markov property probability of where the system
  will go next depends only on its current states,
  not where it has been
• Doesnt suffer from MCs drawbacks
• No local minimization problems
• Orders of magnitude speed-up (can process paths
  simultaneously in closed form using linear
  algebra methods)

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Escape Time

• Measure of binding affinity (expected number of
  MC simulation steps for ligand to escape the
  funnel of attraction of the proteins binding
  site)
• Longer escape time high energy barriers around
  catalytic site
• Averaged over many molecular motion pathways
• Naïve approach perform many simulation runs on
  roadmap (start from potential bound conformation,
  end when ligand escapes from funnel), average
  number of steps taken in each run
• Slow, and only provides estimate of escape time!

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Escape Time (cont.)

• Better solution use first-step analysis (from
  Markov chain theory)
• Each of the neighboring nodes is either
• In the funnel (expected number of further steps
  that nodes escape time)
• Not in the funnel (stop)
• Can define a linear system with one equation for
  each roadmap node, solve all escape times
  simultaneously
• Very fast, and computes escape times exactly!

I
F
PIJ2
PIJ1
J1
J2
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Ligand-Protein Modeling

• Proteins rigid, ligand flexible
• One atom in ligand designated as the base with 5
  DOF, each additional atom had 1 torsional DOF
• Bonds in a ring were rigid, no DOF
• Bond angles and lengths assumed constant
• Potential function used to calculate free energy
  incorporated electrostatic, van der Walls, and
  solvation free energies (resolution of 1 Å or 0.5
  Å)
• Modeled solvent with dielectric of 80, solute
  with dielectric of 1
• Repeated experiments with 6 Å and 8 Å funnels,
  obtained similar results

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Study 1 - Effects of Mutations

• Site-directed mutagenesis biological method in
  which a few amino acids are deleted, replaced by
  other amino acids, or have their side chains
  altered
• Computational mutagenesis same as above, but
  using computers (faster/easier, but less accurate)

• Lactate dehydrogenase (LDH) catalyzes reduction
  of pyruvate to lactate when bound to NADH
• Mutated residues near LDHs catalytic site
  (computational mutagenesis), observed effects on
  binding affinity (via escape time)

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Study 1 Mutations

• His193?Ala, Arg106?Ala, both of these together
• Cause large reduction in energetic structure of
  active site
• Show sensitivity of SRS to coarse changes in
  system
• Asp195?Asn, Gln101?Arg, Thr245?Gly
• Cause small or no reduction in energetic
  structure of active site
• Show sensitivity of SRS to fine changes in system
• Generated roadmaps contained 4,000 nodes sampled
  over whole conformation space, 100 extra nodes
  sampled around bound conformation
• Other sampling schemes gave similar results

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Study 1 Results

?
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Study 2 Distinguishing Catalytic Site

• Shape and electrostatic complementarity between
  catalytic site and ligand ? tight bond
• Singh et al. (1999) Studied 3 different
  ligand-protein complexes
• Bound state energy not good at discriminating
  catalytic site from other putative sites
• Instead compared average path weight of most
  energetically stable paths entering and leaving
  the sites ? energy barrier around catalytic site
• Study expands on this idea
• SRS/first-step analysis measures whole energy
  barrier, not just small part corresponding to
  most feasible paths
• Escape time more precise than average path weight

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Study 2 - Methods

• Each test conducted with true bound conformation
  and 4 other putative conformations with
• Lowest energies, close to protein surface (lt
  5 Å), and distant from each other (gt 10 Å)
• 20 roadmaps/complex, each with set of random
  conformations and 100 extra conformations around
  each putative binding site conformation
• Took lt 4 mins. to generate roadmaps, and lt 4.5
  mins to compute escape times on desktop computer

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Study 2 - Results
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Summary

• Can compute escape time efficiently with SRS to
  analyze ligand-protein interactions
• Study 1 showed high sensitivity of SRS by
  performing computational mutagenesis on catalytic
  site of protein
• In all 6 cases, SRS simulation results agreed
  with expected biological interpretation of
  mutation
• Study 2 used escape time as metric to
  distinguish catalytic site from 4 other putative
  sites
• In 5/7 cases, escape time distinguished the
  catalytic site by over 2 orders of magnitude
  difference from other putative binding sites

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Future

• SRS is a general tool, and could be used to
  efficiently compute other interesting metrics in
  addition to escape time (binding time, total
  energy difference along binding paths, etc.)
• Combine SRS with other techniques to model
  simultaneously interactions of many molecules
  (current representation only models one
  ligand-protein complex)

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Discussion Questions

• What are some explanations for why the escape
  times of the putative sites were higher than the
  catalytic site in study 2s failed cases?
• The paper showed that escape time could be useful
  in distinguishing the catalytic site. What are
  other possible applications of escape time?
• Did the way in which they modeled ligands and
  proteins affect the results of the studies?