Download Computational Modelling in Systems and Synthetic Biology

Computational Modelling in Systems
and Synthetic Biology
Fran Romero
Dpt Computer Science and Artificial Intelligence
University of Seville
[email protected]
www.cs.us.es/~fran
Models are Formal Statements
of 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)
How you select features, disambiguate and quantify
depends on the goals behind your modelling enterprise
Systems Biology
Synthetic Biology
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
Systems Biology and Synthetic Biology
Systems Biology
Synthetic Biology
• Understanding
• Integration
• Prediction
• Life as it is
Computational modelling to
elucidate and characterise
modular patterns exhibiting
robustness, signal filtering,
amplification, adaption,
error correction, etc.
• Control
Colonies
Cells
Networks
• Design
• Engineering
• Life as it could be
Computational modelling to
engineer and evaluate
possible cellular designs
exhibiting a desired
behaviour by combining well
studied and characterised
cellular modules
Stochasticity is important
in 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.
Spatial Localisation is
Important in Cellular Systems
Cellular Biology
Exhibits Modularity
2008 Nobel Prize in Chemistry for the
discovery and development of the Green
Fluorescence Protein
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.
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.
Petri Nets


π-calculus
Monika Heiner, David Gilbert, Robin Donaldson. Petri Nets for Systems and Synthetic Biology
SFM 2008, 215 – 264 (2008)
Aviv Regev, Ehud Shapiro. Modelling in Molecular Biology (2004)
P systems are Abstractions
of Single Cells
Abstraction of the structure and
functioning a single cell.
Objects
o Compartmental models
o Rule-based modelling approach
o Discrete and stochastic semantics
Membranes
Rewriting Rules
Stochastic P Systems
Molecular Species are represented
as objects or strings
 A molecular species can be represented using
individual objects.
LasR
 A molecular species with relevant internal structure
can be represented using a string.
cap ⋅ prom ⋅ op ⋅ lacZ1  lacZ 30 ⋅ lacY1  lacY12 ⋅ lacA1  lacA6
Molecular Interactions are
Represented as Rules
 Comprehensive and relevant rule-based schema for
the most common molecular interactions taking place in
living cells.
Protein-protein
interactions
{
Transformation/Degradation
Complex Formation and Dissociation
Diffusion in / out
Binding and Debinding
Recruitment and Releasing
{
Transcription Factor Binding/Debinding
Transcription/Translation
Gene expression
Molecular Interactions
Inside Compartments
Passive Diffusion
of Molecules
Signal Sensing and
Active Transport
Specification of Transcriptional
Regulatory Networks
Compartments / Cells are
Specified using Membranes
•
Compartments and regions are explicitly
specified using membrane structures.
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.
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.
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
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:
j




1
1
j0 = min  j / ai > r2 a0 
τ = ln 
a0  r1 
 i =0

∑

D. T. Gillespie. Stochastic simulation of chemical kinetics. Annual Review of Physical Chemistry,
58:35–55, 2007.
Rules are applied according to operational
semantics based on Gillespie Algorithm
1
3
r31,
…,r3n3
Local Gillespie
r11,
…,r1n1
( 1, τ1, r01)
M1
( 2, τ2, r02)
M3
r21,
…,r2n2
‘
2
( 3, τ3, r03)
Sort Compartments
τ2 < τ1 < τ3
M2
( 2, τ2’, r02)
( 1, τ1, r01)
τ2’’=τ2’+ tsim
( 1, τ1, r01)
( 2, τ2’ ’ , r02)
( 3, τ3, r03)
tsim =τ2
Insert new triplet
τ1 <τ2 ’ ’ < τ3
( 3, τ3, r03)
Update Global Time
( 2, τ2, r02)
( 1, τ1, r01)
( 3, τ3, r03)