Transcript Max1
Stochastic roadmap
simulation for the study of
ligand-protein interactions
Mehmet Serkan Apaydin, Carlos E. Guestrin,
Chris Varma, Douglas L. Brutlag and JeanClaude Latombe (Stanford Departments of
Computer Science and Biochemistry)
Presented by Max Shneider
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
Monte Carlo Simulation (MC)
Generate paths corresponding to potential motions
of the ligand and protein:
1.
2.
3.
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)
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
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:
ij
P
1
Ni
e
Eij / k Bt
1
Ni
if Eij 0
otherwise
Pii 1 Pij
i 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)
SRS Roadmap (cont.)
A
E
B
F
C
PAA
A
A
PAB
B
G
PCC
PBB
C
PAC
B
PBD
C
PBE
PCF
PCG
D
D
E
F
G
D
E
F
G
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
Doesn’t suffer from MC’s drawbacks
No local minimization problems
Orders of magnitude speed-up (can process
paths simultaneously in closed form using
linear algebra methods)
Escape Time
Measure of binding affinity (expected number of MC
simulation steps for ligand to escape the “funnel of
attraction” of the protein’s 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!
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 node’s escape time)
Not in the funnel (stop)
i 1
Pij 0
jF i
Pij j
jF i
F
I
PIJ1 PIJ2
J1
J2
Can define a linear system with one equation for each
roadmap node, solve all escape times simultaneously
Very fast, and computes escape times exactly!
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
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 LDH’s
catalytic site (computational
mutagenesis), observed
effects on binding affinity (via
escape time)
Study 1 – Mutations
His193Ala, Arg106Ala, both of these together
Cause large reduction in energetic structure of active
site
Show sensitivity of SRS to coarse changes in system
Asp195Asn, Gln101Arg, Thr245Gly
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
Study 1 – Results
=
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
Study 2 - Methods
Each test conducted with true bound
conformation and 4 other putative
conformations with:
Lowest energies, close to protein surface
(< 5 Å), and distant from each other (> 10 Å)
20 roadmaps/complex, each with set of
random conformations and 100 extra
conformations around each putative binding
site conformation
Took < 4 mins. to generate roadmaps, and
< 4.5 mins to compute escape times on
desktop computer
Study 2 - Results
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
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)
Discussion Questions
What are some explanations for why the
escape times of the putative sites were higher
than the catalytic site in study 2’s 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?