Computational Modelling in Systems and Synthetic Biology

Fran RomeroDpt Computer Science and Artificial Intelligence

University of Seville

fran@us.eswww.cs.us.es/~fran

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Models are Formal Statementsof Our Current Knowledge

A non ambiguous description of our understanding of the elements of a system of interest, their states and interactions.

Feature selection is key in model development.

According to the semantics used in the simulations: Denotational Semantics Models: Set of equations showing relationships

between aggregates of components and how they change over time (i.e. DE).

Operational Semantics Models: Algorithm executable by an abstract machine whose computation resembles the behaviour of the system (I.e. Finite State Machine)

Fisher et al (2008) Executable cell biology. Nature Biotechnology, 25, 11, 1239-1249 (2008)

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How you select features, disambiguate and quantify

depends on the goals behind your modelling enterprise

Basic goal: to clarify current understandings by formalising what the constitutive elements of a system are and how they interact

Intermediate goal: to test current understandings against experimental data; calculate/simulate

Advanced goal: to predict beyond current understanding and available data; calculate/simulate + analyse

Dream goal: (1) to combinatorially combine in silico well-understood

components/models for the design and generation of novel experiments and hypothesis and ultimately

(2) to design, program, optimise & control (new) biological systems

Sys

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Systems Biology Synthetic Biology

• Understanding• Integration• Prediction• Life as it is

• Control• Design• Engineering• Life as it could be

Computational modelling toelucidate and characterisemodular patterns exhibitingrobustness, signal filtering,amplification, adaption, error correction, etc.

Computational modelling toengineer and evaluate possible cellular designsexhibiting a desiredbehaviour by combining well studied and characterised cellular modules

Networks

Cells

Colonies

Systems Biology and Synthetic Biology

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Stochasticity is importantin Cellular Systems

Sources of noise are low number of molecules and slow molecular interactions.

Over 80% of genes in E. coli express fewer than a hundred proteins .

Mesoscopic, discrete and stochastic approaches are more suitable: Only relevant molecules are taken into account. Focus on the statistics of the molecular interactions and how often they take

place.

Mads Karn et al. Stochasticity in Gene Expression: From Theories to Phenotypes. Nature Reviews, 6, 451-464 (2005)Purnananda Guptasarma. Does replication-induced transcription regulate synthetis of the myriad low copy number

proteins in E. Coli. BioEssays, 17, 11, 987-997.

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Spatial Localisation is Important in Cellular Systems

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Cellular Biology Exhibits Modularity

2008 Nobel Prize in Chemistry for the discovery and development of the Green Fluorescence Protein

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We Look for Specific Requirements in our Modelling Formalism

o Individual cells as the elementary unit in the system.

o Explicit representation of their compartmental structures.

o Spatial and geometric information in multicellular systems.

o The molecular interactions as discrete and stochastic processes. Executable semantics.

o Modularity in cellular systems, especially in gene regulatory networks.

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There exists different Computational Frameworks

Most computational models are implemented in custom programs. Computational formalisms which cope with complex, concurrent,

interactive systems has been successfully applied.

Monika Heiner, David Gilbert, Robin Donaldson. Petri Nets for Systems and Synthetic BiologySFM 2008, 215 – 264 (2008)

Aviv Regev, Ehud Shapiro. Modelling in Molecular Biology (2004)

π-calculusPetri Nets

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P systems are Abstractions of Single Cells

Abstraction of the structure and functioning a single cell.

o Compartmental modelso Rule-based modelling approacho Discrete and stochastic semantics

Membranes

Objects

Rewriting Rules

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Stochastic P Systems

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Molecular Species are represented as objects or strings

A molecular species can be represented using individual objects.

A molecular species with relevant internal structure can be represented using a string.

61121301 lacAlacAlacYlacYlacZlacZoppromcap ⋅⋅⋅⋅⋅

LasR

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Molecular Interactions are Represented as Rules Comprehensive and relevant rule-based schema for

the most common molecular interactions taking place in living cells.

Transformation/Degradation Complex Formation and Dissociation Diffusion in / out Binding and Debinding Recruitment and Releasing

Transcription Factor Binding/Debinding Transcription/Translation

{{

Protein-proteininteractions

Gene expression

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Molecular Interactions Inside Compartments

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Passive Diffusion of Molecules

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Signal Sensing and Active Transport

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Specification of Transcriptional Regulatory Networks

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Compartments / Cells are

Specified using Membranes • Compartments and regions are explicitly

specified using membrane structures.

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Colonies / Tissues are Represented using Collections of P systems

Colonies and tissues are representing as collection of P

systems distributed over a lattice.

v

Objects can travel around the lattice through translocation rules.

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Lattice Population P Systems

LPP = (Σ, Lat, (Π1, ... , Πp), Pos, (T1,…,Tp) )

Σ is an alphabet of objects representing molecular species.

Lat is a finite geometrical lattice in R2 or R3

Π1, ... , Πp are individual stochastic P systems

Pos : Lat (Π1, ... , Πp) associates a specific P system with each position in the lattice.

T1,…,Tp are translocation rules added to the skin membrane of each P system.

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Stochastic P Systems Are Executable Programs

The virtual machine running these programs is a “Gillespie Algorithm (SSA)”. It generates trajectories of a stochastic syste:

A stochastic constant is associated with each rule.A propensity is computed for each rule by multiplying the

stochastic constant by the number of distinct possible combinations of the elements on the left hand side of the rule.

F. J. Romero-Campero, J. Twycross, M. Camara, M. Bennett, M. Gheorghe, and N. Krasnogor. Modular assembly of cell systems biology models using p systems. International Journal of Foundations of Computer Science, 2009

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Stochastic P Systems Maximal parallelism and non determinism fails to accurately replicate

the rate of molecular interactions.

Gillespie Stochastic Simulation Algorithm (SSA) generates exact trajectories of a stochastic system in a single volume:

1) A stochastic constant ci is associated with each rule.2) A propensity ai is computed for each rule. 3) The rule to apply j0 and the waiting time τ for its application are

computed by generating two random numbers r1,r2 ~ U(0,1) and using the formulas:

=

10

1ln

1

raτ

>= ∑=

j

ii arajj

0020 /min

D. T. Gillespie. Stochastic simulation of chemical kinetics. Annual Review of Physical Chemistry, 58:35–55, 2007.

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1

2

3 r11,…,r1n1

M1

r21,…,r2n2

M2

r31,…,r3n3

M3

( 1, τ1, r01)

( 2, τ2, r02)

( 3, τ3, r03)

( 2, τ2, r02)

( 1, τ1, r01)

( 3, τ3, r03)

Sort Compartments τ2 < τ1 < τ3

Local Gillespie

( 1, τ1, r01)

( 3, τ3, r03)

Update Global Time

( 2, τ2’, r02)

( 1, τ1, r01)

( 2, τ2’ ’ , r02)

( 3, τ3, r03) Insert new triplet τ1 <τ2 ’ ’ < τ3

‘

tsim =τ2τ2’’=τ2’+ tsim

Rules are applied according to operational semantics based on Gillespie Algorithm