Parallel Exact Stochastic Simulation in Biochemical Systems

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Parallel Exact Stochastic Simulation in
Biochemical Systems

• Jiangtian Li

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Introduction

• Overview of parallel exact stochastic simulation
• My summer work at Oak Ridge National Lab
• Joint work with Mike McCollum, Nagiza Samatova
• One of two research projects this summer

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Motivation for PESS

• Model large-scale biochemical systems such as
  gene regulatory network
• A single cell cycle of E.coli requires 10141016
  executions of reactions
• Accelerate simulation by parallelizing executions
  while preserving accuracy of stochastic
  simulation

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Gillespies stochastic simulation

• Event-driven simulation of random process
• Modeling spatially uniform mixture of N species
  (state variables) through M reaction channels
  (events)
• Probability of reaction scheduled is
  characterized by propensity function
• Simulation ends when species populations converge

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Simulation Framework
Simulation Application state variables code
modeling system behavior I/O and user
interface software
State variables Species A1000 Species
B500 Species C100
calls to schedule events
calls to event handlers
Event list (reactions) A B -gt C C D -gt E A
B -gt C
Simulation Executive event list management
managing advances in simulation time
Global clock 300
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Issues in Parallelization

• Inter-processor synchronization to avoid
  causality errors

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23
35
17
affect
processed event
42
26
14
unprocessed event
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Issues in Parallelization

• Model subdivision and processor mapping
• Reducing communications
• Load balancing

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Inter-processor Synchronization

• Optimistic synchronization protocol Time Warp
• To ensure correct execution order in whole
  simulation
• To exploit more parallelism in situation where
  causality errors dont occur
• natural and elegant implementation

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Time Warp

• Roll back state variables
• when a straggler message is received
• record a log of the modified state variables
• restore the state variables

straggler message
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processed event
12 A1 B2 C3
21 A4
35 A5 C9
unprocessed event
state variables log
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A0 B0 C0
A1
A4 C3
A4 C3
A1
A1 B2 C3
A5 B2 C9
rollback
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Time Warp (cont.)

• Unsend messages
• use anti-message logically identical copy of
  original message, with opposite sign
• anti-message stored in senders output queue and
  resent when rollback
• message/anti-message annihilated in receivers
  input queue

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Example unsend message
processed event
Input queue
unprocessed event
12
21
35
41
saved state
State queue
anti-message
Anti-message queue
42
19
18
send anti-message
Sender
Straggler message, rollback
Anti-message arrives, rollback Annihilate message
and anti-message
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Input queue
42
55
27
45
State queue
Receiver
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33
Anti-message queue
send anti-message
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Compute G.V.T

• Global virtual time
• Defined as minimum among unprocessed and
  partially processed events and anti-messages
• Serve as lower bound on time stamp of any future
  rollback
• Compute
• synchronous algorithm
• handle transient message message acknowledgement

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Model subdivision

• Goal - Efficient parallel execution
• Reduce communications
• Reduce rollbacks
• Maintain load balance
• Approach - Analyze interdependence among
  reactions

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Model subdivision (cont.)
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Model subdivision (cont.)

• Approach - Construct graph model
• vertex reaction
• vertex weight propensity function
• edge weight sum of vertices weights

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Model subdivision (cont.)

• Partition graph
• Objective - minimize messages communicated
  (cut-edge weights)
• Constraint balance executions
• Metis graph partition package
• University of Minnesota

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Results

• Tested on SGI Altix (Ram) at ORNL
• 256 Intel Itanium2 processors running at 1.5 GHz
  
• 8 GB of memory per processor

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Results
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Results
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Results
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Results
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Future work

• Dynamic model subdivision during simulation
• Trade-off how much is overhead?

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Conclusion

• Parallel Exact Stochastic Simulation has
  demonstrated to be efficient and effective in
  modeling biochemical systems
• Proper model subdivision significantly enhanced
  performance

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• Any question?