Microsoft Research Faculty Summit 2007

Colonies Of Colonies Of Synchronizing Agents:Synchronizing Agents:Molecules, Cells, Molecules, Cells, And TissuesAnd TissuesMatteo Cavaliere – MSR – UNITN CoSBi (Trento, Italy)Giuditta Franco - University of Verona, ItalyNatasha Jonoska – University of South FloridaSean Sedwards – MSR – UNITN CoSBi (Trento, Italy)

Model Model

intuitiveness, intuitiveness, transparency, transparency,

scalability, scalability, composability, composability,

expressivity, simplicity, expressivity, simplicity, analysability …analysability …

MotivationMotivation

RealityReality

Formalization…Formalization…

Petri nets process algebraPetri nets process algebra

ODE statistical mechanicsODE statistical mechanics

rewriting automatarewriting automata

Formalization…Formalization…

Petri nets process algebraPetri nets process algebra

ODE statistical mechanicsODE statistical mechanics

rewriting automatarewriting automata

UnderstandiUnderstandingngand and

PredictionPrediction

AnalysisAnalysisInterpretatiInterpretationon

Efficient simulation…Analytical solution…

Role Of Computer ScienceRole Of Computer Science

ComputationComputationalal

ModelModel

MathematicMathematicalal

modelmodelExperimentsExperiments CSCS

Intuition

IntuitioIntuitionn

The problem:Human intuition is the limiting step

MathematicMathematicalal

ModelModelCSCS

ComputationComputationalal

ModelModelExperimentsExperiments AnalysisAnalysis

Inference

Role Of Computer ScienceRole Of Computer Science

The goal:Formalise and automate

A Membrane SystemA Membrane System

a a b

c c a

b

a a b + a a + ca b

a + b c

b + c b + a

hierarchical system of compartments with membranes

multisets of floating objects local to regions

local ‘chemical’ rules based on multiset rewriting

system environment

a b

multisets of objects attached to membranes plus transport rules

a + b c

c

b

conflicts between rules areresolved non-deterministically

0

1

23

4

Knee InjuryKnee InjuryThe important actors:B', C' lining cellsaltered hyaluronan (HA) molecules h’activated macrophages D’

Knee tissue after injury

Knee tissue in healthy state

Knee Injury ModelKnee Injury ModelRegular cell turnover of the system in a homeostatic state

Knee Injury ModelKnee Injury Model

G. Franco, N. Jonoska, B. Osborn, A. Plaas, Knee Joint Injury and Repair Modeled by Membrane Systems, Biosystems, to appear.

Gravity signals s (injury)instigates a cascade ofbiochemical interactions(the healing process)

Computational IssuesComputational Issues

Formal description andanalysis of the healing process

Confirmed structural importance of hyaluronan for tissue repair

Analysis using techniques from symbolic dynamicsThe system is non-deterministic

Represents lack of knowledge and innate stochasticityCreates complexity for analysis

Potential parallelization (e.g., on a cluster)

Generalized version of Membrane SystemsPopulation of enclosed regions (agents) in 3D containing objects

Internal rewriting rules (chemistry)

Pairwise synchronization rulesSynchronized rewriting (synchronized chemistry)

Passage of objects (molecules) between regions

Plus movement, division and deletion rules

Agents may represent molecules or cellsA colony may be a tissue or a solution

Colonies Of Synchronizing Colonies Of Synchronizing AgentsAgents

Agents (cells) contain multisets of objects (molecules) and are acted upon by rules (reactions)

chemistry [a,b] [c,d]synchronization[a] [b] [c] [d]deletion [a] λ

Colonies Of Synchronizing Colonies Of Synchronizing AgentsAgents

a bb a a

b b a a c

a b c c

10 100 26

Number of agents of type

Initial contents of agent

movement [a] (,,)[b]division [a] [c] [d]

Having space, movement and division allows us to model complex spatio-temporal behaviour and structures, e.g., morphogenesis, quorum sensing…

[a,b,c,a] → [b,a]

a b c

b c

a b

b

a b c

b a

a b c

b c

a b

b

b a

b

Internal Rules Internal Rules

Intracellular mechanisms, e.g., chemistry

Synchronization Rules Synchronization Rules

[a,b,c] [c,c] [a,b,c] [c,c] → [a,a] [c,b]→ [a,a] [c,b]

a b c

b c

a b

b

a b c

b a

a b

b

a a

b a

a b c

b b

Intercellular mechanisms, e.g., signalling

Evolution Of ColoniesEvolution Of Colonies

Global behaviour of a colony is obtained using just internal rules + synchronization rules

Overall behaviour is more complex than the sum of the individual components

Robustness Of ColoniesRobustness Of Colonies

Robust behaviour is biologically important

A robust colonyThe behaviour does not change critically if one or more agents cease to exist or if one or more rules stop working

There are (efficient) algorithms to check if a colony is robust*

M. Cavaliere, R. Mardare, S. Sedwards, Colonies of Synchronizing Agents: An Abstract Model of M. Cavaliere, R. Mardare, S. Sedwards, Colonies of Synchronizing Agents: An Abstract Model of Intracellular and Intercellular Processes, Int. Work. on Automata for Cellular and Molecular Intracellular and Intercellular Processes, Int. Work. on Automata for Cellular and Molecular Computing, Budapest, 2007.Computing, Budapest, 2007.

Why Simulate?Why Simulate?

Modelling Behavioural Need topower complexity simulate

maximal……minimal

Difficulty of deciding properties

(analysability)

Simulation ComplexitySimulation Complexity

Complexity of each step of a stochastic simulation

Membrane system with M reactions: O(M)CSA with N agents, no synchronization: O(NM)CSA with N agents, space and synchronization: O(N2M)

Optimised algorithm: O(NM)

Optimised and distributed algorithm: O(NM½)

ProspectsProspects

More complex biological modelsE.g., immune system, cell cycle, evolution

Model checking algorithms

Distributed implementation of CSAs

Thank You For Your Thank You For Your AttentionAttention

Contributors:

Matteo Cavaliere – MSR – UNITN CoSBi (Trento, Italy)

Sean Sedwards – MSR – UNITN CoSBi (Trento, Italy)

Giuditta Franco - Department of Computer Science, University of Verona, Italy

Natasha Jonoska – Department of Computer Science, University of South Florida

Barbara Osborn - Department of Internal Medicine, University of South Florida

Anna Plaas - Department of Internal Medicine, University of South Florida

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