Synthetic Biology - Modeling and Optimisation

Synthetic Biology: Modelling and
Optimisation
Natalio Krasnogor
ASAP - Interdisciplinary Optimisation Laboratory
School of Computer Science

Centre for Integrative Systems Biology
School of Biology

Centre for Healthcare Associated Infections
Institute of Infection, Immunity & Inflammation

University of Nottingham
Copyright is held by the author/owner(s).
GECCO’09, July 8–12, 2009, Montréal Québec, Canada.
ACM 978-1-60558-505-5/09/07.

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Thursday, 9 July 2009

Outline
•Brief Introduction to Computational Modeling
•Modeling for Top Down SB
•Executable Biology
•A pinch of Model Checking
•Modeling for the Bottom Up SB
•Dissipative Particle Dynamics
•Automated Model Synthesis and Optimisation
•Conclusions
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Outline
•Conclusions
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Synthetic Biology
• Aims at designing, constructing and developing artificial biological
systems

•Offers new routes to ‘genetically modified’ organisms, synthetic living
entities, smart drugs and hybrid computational-biological devices.

• Potentially enormous societal impact, e.g., healthcare, environmental
protection and remediation, etc

• Synthetic Biology's basic assumption:
• Methods commonly used to build non-biological systems could
also be use to specify, design, implement, verify, test and deploy
novel synthetic biosystems.
• These method come from computer science, engineering and
maths.
• Modelling and optimisation run through all of the above.
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Models and Reality
•The use of models is intrinsic to any
scientific activity.

•Models are abstractions of the real-world
that highlight some key features while
ignoring others that are assumed to be not
relevant.

•A model should not be seen or presented
as representations of the truth, but instead
as a statement of our current knowledge.
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What is modelling?
• Is an attempt at describing in a
precise way an understanding of the
elements of a system of interest, their
states and interactions

• A model should be operational, i.e. it
should be formal, detailed and
“runnable” or “executable”.
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•“feature selection” is the first issue one
must confront when building a model

•One starts from a system of interest
and then a decision should be taken as
to what will the model include/leave out

•That is, at what level the model will be
built
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The goals of Modelling
•To capture the essential features of
a biological entity/phenomenon
•To disambiguate the understanding
behind those features and their
interactions
•To move from qualitative knowledge
towards quantitative knowledge

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•There is potentially a distinction between modelling for Synthetic Biology
and Systems Biology:
•Systems Biology is concerned with Biology as it is
•Synthetic Biology is concerned with Biology as it could be

“Our view of engineering biology focuses on the abstraction and
standardization of biological components” by R. Rettberg @ MIT newsbite
August 2006.
“Well-characterized components help lower the barriers to modelling. The
use of control elements (such as temperature for a temperature-sensitive
protein, or an exogenous small molecule affecting a reaction) helps model
validation” by Di Ventura et al, Nature, 2006

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•There is potentially a distinction between modelling for Synthetic Biology
and Systems Biology:
•Systems Biology is concerned with Biology as it is
•Synthetic Biology is concerned with Biology as it could be

“Our view of engineering biology focuses on the abstraction and
standardization of biological components” by R. Rettberg @ MIT newsbite
August 2006.
“Well-characterized components help lower the barriers to modelling. The
use of control elements (such as temperature for a temperature-sensitive
protein, or an exogenous small molecule affecting a reaction) helps model
validation” by Di Ventura et al, Nature, 2006

Co-design of parts and their models hence improving
and making both more reliable

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Thus, Multi-Scale Modelling in the 2 SBs seek
to produce computable understanding
integrating massive datasets at various levels
of details simultaneously

Progress
Organ Individual
Cell colony

Cells

Regulatory
Networks

Proteins

DNA/RNA
Time

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The Pragmalogical Problem of
Modelling in XXI century Biology
• XXI century Biology brings to the fore the ubiquitous philosophical
questions in complex systems, that of emergent behavior and the
tension between reductionism and holistic approaches to science.

• Synthetic Biology (and SysBio) has, however, a very pragmatic
agenda: the engineering and control of novel biological systems

• The pragmalogical problem: If each subcomponent of a living system
(and processes/components therein) are understood… Can we say that
the system is understood? That is, can we assume that the system =
∑parts ?

• More importantly: can we control that biosystem?

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The Pragmalogical Problem of
Modelling in XXI century Biology
• XXI century Biology brings to the fore the ubiquitous philosophical
questions in complex systems, that of emergent behavior and the
tension between reductionism and holistic approaches to science.
& Integrative

• Synthetic Biology (and SysBio) has, however, a very pragmatic
agenda: the engineering and control of novel biological systems

• The pragmalogical problem: If each subcomponent of a living system
(and processes/components therein) are understood… Can we say that
the system is understood? That is, can we assume that the system =
∑parts ?

• More importantly: can we control that biosystem?

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 Modelling relies on rigorous computational,
engineering and mathematical tools &
techniques
 However, the act of modelling remains at the
interface between art and science
 Undoubtedly, a multidisciplinary endeavour

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Modelling as a constrained
scientific art
 Although modelling lies at the interface of art
and science there are guidelines we can
follow
 Some examples:
 The scale separation map [Hoekstra et al, LNCS 4487, 2007]
 Tools suitability & cost [Goldberg, 2002]

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The Scale Separation Map
 The Scale Separation Map is an
abstraction recently proposed by Hoekstra
and co-workers [Hoekstra et al, LNCS
4487, 2007]
 Introduced in the context of Multi-scale
modelling with cellular automata but the
core concepts still valid for other modelling
techniques

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 A Cellular Automata is defined as:
C= < A(Δx, Δt,L,T), S, R, G, F >

A is a spatial domain made of cells of size Δx with a total size of L
The simulation clock ticks every Δt units for a total of T units

T
We can simulate processes: Δt

 as fast as Δt for as long as T units

 ranging from Δx to L sizes. Δx

L

L
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 A Scale Separation Map (SSM) is a two dimensional
map with horizontal axis representing time and vertical
axis representing space

1 0 B ξB

A ξA τB
Spatial scale (log)

τA

3.1 2 3.2

Temporal scale (log)

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• Region 0: A and B overlap
 single scale multi-science
1 0 model
A ξA • Region 1: ξA ≈ ξB ^ τA > τB
B ξB  temporal scale separation
Spatial scale (log)

τA • Region 2: ξA > ξB ^ τB ≈ τA
τB  coarse and fine structures
3.1 2 3.2 in similar timescales
• Region 3.1: ξA > ξB ^ τB <
τA  familiar micro-macro
models
• Region 3.2: ξA > ξB ^ τB >
τA  small and slow
process linked to a fast and
Temporal scale (log) large process (e.g. Blood
flood and artery repair)

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1 0 model
 temporal scale separation
Spatial scale (log)

 coarse and fine structures
models
B ξB • Region 3.2: ξA > ξB ^ τB >
τB τA  small and slow
process linked to a fast and

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1 0 model
 temporal scale separation
Spatial scale (log)

 coarse and fine structures
models
• Region 3.2: ξA > ξB ^ τB >
B ξB
τA  small and slow
τB process linked to a fast and

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Even within a single cell the space & time
scale separations are important
E.g.:

• Within a cell the dissociation
constants of DNA/ transcription
factor binding to specific/non-
specific sites differ by 4-6 orders of
magnitude

• DNA protein binding occurs at 1-10s
time scale very fast in comparison
to a cell’s life cycle.

[F.J. Romero Campero, 2007]
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• With sufficient data each process can be
assigned its space-time region
unambiguously

Couplings, e.g. F • A given process may well have its Δx
(respectively Δt) > than another’s ξA
(respectively τA)
Spatial scale (log)

• Hence different processes in the SSM might
require different modelling techniques

Temporal scale (log)

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Modelling Approaches

There exist many modelling approaches, each with its
advantages and disadvantages.
Macroscopic, Microscopic and Mesoscopic
Quantitative and qualitative
Discrete and Continuous
Deterministic and Stochastic
Top-down or Bottom-up

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Modelling Frameworks
•Denotational Semantics Models:
Set of equations showing relationships between molecular
quantities and how they change over time.
They are approximated numerically.
(I.e. Ordinary Differential Equations, PDEs, etc)

•Operational Semantics Models:
Algorithm (list of instructions) executable by an abstract
machine whose computation resembles the behaviour of the
system under study. (i.e. Finite State Machine)

Jasmin Fisher and Thomas Henzinger. Executable cell biology. Nature Biotechnology, 25, 11, 1239-1249
(2008)

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Tools Suitability and Cost
 From [D.E Goldberg, 2002] (adapted):
“Since science and math are in the description
business, the model is the thing…The engineer
or inventor has much different motives. The
engineered object is the thing”
ε, error

Synthetic Biologist

Computer Scientist/Mathematician

C, cost of modelling

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Tools Suitability and Cost
Low cost/ High cost/
High error Low error
Adapted from [Goldberg 2002]

Unarticulated Articulated Dimensional Facetwise Equations
wisdom Qualitative models models Of motion
models

Chemical Bioinformatic Biopolimer Microarrays and G.E.
Markup Language Sequence Markup Markup Language Markup Language
(CML) Language (BSML) (BioML) (MAGEML)

Cell Systems Biology Mathematics
Markup Language Markup Language Markup Language
(MathML) (SBML) (MathML)

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From [Di Ventura et al., Nature, 2006]
Low cost/ High cost/
High error Low error

Unarticulated Dimensional Facetwise Equations
wisdom models models Of motion

 Formalism-independent errors
 Formalism-dependent errors

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Stochasticity in Cellular Systems
 Most commonly recognised sources of noise in cellular system are low
number of molecules and slow molecular interactions.

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

 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 synthesis of the myriad low
copy number poteins of E. Coli. BioEssays, 17, 11, 987-997

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Towards Executable Modells for SBs
“Although the road ahead is long and winding, it leads to a
future where biology and medicine are transformed into
precision engineering.” - Hiroaki Kitano.

 Synthetic Biology and Systems biology promise more than
integrated understanding: it promises systematic control of
biological systems:
1. From an experimental viewpoint: Improved data acquisition
2. From a bioinformatics viewpoint: Improved data analysis tools
3. From a conceptual viewpoint: move from a science of mass-action/
energy-conversion to a science of information processing through
multiple heterogeneous medium

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There are good reasons to think that information
processing is a key viewpoint to take when modeling

Life as we know is:
• coded in discrete units (DNA, RNA, Proteins)
• combinatorially assembles interactions (DNA-RNA, DNA-
Proteins,RNA-Proteins , etc) through evolution and self-organisation
• Life emerges from these interacting parts
• Information is:
• transported in time (heredity, memory e.g. neural, immune
system, etc)
• transported in space (molecular transport processes, channels,
pumps, etc)
• Transport in time = storage/memory  a computational process
• Transport in space = communication  a computational process
• Signal Transduction = processing  a computational process

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 It thus makes sense to use methodologies
designed to cope with complex,
concurrent, interactive systems of parts as
found in computer sciences (e.g.):
 Petri Nets
 Process Calculi
 P-Systems

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InfoBiotics
www.infobiotic.net
•The utilisation of cutting-edge information
processing techniques for biological modelling and
synthesis
•The understanding of life itself as multi-scale
(Spatial/Temporal) information processing systems
•Composed of 3 key components:
•Executable Biology (or other modeling
techniques)
•Automated Model and Parameter Estimation
•Model Checking (and other formal analysis)
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Modeling in Systems & Synthetic Biology

Systems Biology Synthetic Biology
Colonies
• Understanding •Control
• Integration • Design
• Prediction • Engineering
• Life as it is •Life as it could be
Cells

Computational modelling to Computational modelling to
elucidate and characterise engineer and evaluate
modular patterns exhibiting possible cellular designs
robustness, signal filtering, exhibiting a desired
amplification, adaption, behaviour by combining well
error correction, etc. studied and characterised
Networks cellular modules

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Model Design in Systems/Synthetic Biology
• It is a hard process to design suitable models in systems/
synthetic biology where one has to consider the choice of the
model structure and model parameters at different points
repeatedly.

• Some use of computer simulation has been mainly focused on
the computation of the corresponding dynamics for a given
model structure and model parameters.

• Ultimate goal: for a new biological system (spec) one would like
to estimate the model structure and model parameters (that
match reality/constructible) simultaneously and automatically.

• Models should be clear & understandable to the biologist
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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
Systems Biology

are and how they interact
Intermediate goal: to test current understandings
Synthetic Biology

against experimental data

Advanced goal: to predict beyond current
understanding and available data

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

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Model Development
 From [E. Klipp et al, Systems Biology in Practice,
2005]
1. Formulation of the problem
2. Verification of available information
3. Selection of model structure
4. Establishing a simple model
5. Sensitivity analysis
6. Experimental tests of the model predictions
7. Stating the agreements and divergences between
experimental and modelling results
8. Iterative refinement of model

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Outline
•Conclusions
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Executable Biology with P systems
 Field of membrane computing initiated by
Gheorghe Păun in 2000
 Inspired by the hierarchical membrane structure
of eukaryotic cells
 A formal language: precisely defined and
machine processable
 An executable biology methodology

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Functional Entities
Container
• A boundary defining self/non-self (symmetry breaking).
• Maintain concentration gradients and avoid environmental damage.

Metabolism
• Confining raw materials to be processed.
• Maintenance of internal structures (autopoiesis).

Information

• Sensing environmental signals / release of signals.
• Genetic information

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Distributed and parallel rewritting systems in
compartmentalised hierarchical structures.

Objects

Compartments

Rewriting Rules

• Computational universality and efficiency.

• Modelling Framework

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Cell-like P systems
Intuitive Visual representation
as a Venn diagram with a
unique superset and without
intersected sets.

the classic P system diagram appearing in most papers
(Păun)

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Cell-like P systems
intersected sets.

formally equivalent to a tree:
1

2 4
3
7
5 6
(Păun)
8 9

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Cell-like P systems
intersected sets.

formally equivalent to a tree:
1

2 4
3
7
5 6
(Păun)
8 9

• a string of matching parentheses: [ 1 [2 ] 2 [ 3 ] 3 [4 [5 ] 5 [6 [ 8 ] 8 [9 ] 9 ]6
[7 ]7 ]4 ]1

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P-Systems: Modelling Principles
Molecules Objects
Structured Molecules Strings
Molecular Species Multisets of objects/
strings
Membranes/organelles Membrane

Biochemical activity rules

Biochemical transport Communication rules

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Stochastic P Systems

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Rewriting Rules

used by Multi-volume Gillespie’s algorithm
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Molecular Species
 A molecular species can be represented using
individual objects.

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

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Molecular Interactions
 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

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Compartments / Cells
 Compartments and regions are explicitly
specified using membrane structures.

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Colonies / Tissues
 Colonies and tissues are representing as
collection of P systems distributed over a lattice.

 Objects can travel around the lattice through
translocation rules.

v

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Molecular Interactions
Inside Compartments

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Passive Diffusion of Molecules

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a b Transport Modalities

a b Antiport channel
a b

Symport channel

a
c b a b

Promoted symport channel (trap)

a b
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Transport Modalities

5 2
1

4
3
Phagocitosys

Endocitosys

Pinocitosys
Exocitosys

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Transport Modalities

Highly specific:
cell specific & topology specific

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Signal Sensing and
Active Transport

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Specification of Transcriptional
Regulatory Networks

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Transcription as Rewriting Rules on
Multisets of Objects and Strings

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Translation as Rewriting Rules on
Multisets of Objects and Strings

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Post-Transcriptional Processes
 For each protein in the system, post-transcriptional processes like
translational initiation, messenger and protein degradation, protein
dimerisation, signal sensing, signal diffusion etc are represented using
modules of rules.
 Modules can have also as parameters the stochastic kinetic constants
associated with the corresponding rules in order to allow us to explore
possible mutations in the promoters and ribosome binding sites in order to
optimise the behaviour of the system.

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Scalability through Modularity

 Cellular functions arise from orchestrated
interactions between motifs consisting of
many molecular interacting species.

 A P System model is a set of rules
representing molecular interactions motifs
that appear in many cellular systems.

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Basic P System Modules Used

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Modularity in Gene Regulatory
Networks
 Cis-regulatory modules
are nonrandom clusters of
target binding sites for
transcription factors
regulating the same gene
or operon.

 A P system module is a
set of rewriting rules
containing variables that
can be instantiated with
specific objects, stochastic
constants and membrane
labels.

E. Davidson (2006) The Regulatory Genome, Gene Regulation Networks in Development and
Evolution, Elsevier

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Modularity in Gene Regulatory
Networks AHL
LuxR CI
 Cis-regulatory modules
are nonrandom clusters of
target binding sites for
transcription factors
regulating the same gene
or operon.

 A P system module is a
set of rewriting rules
containing variables that
can be instantiated with
specific objects, stochastic
constants and membrane
labels.

E. Davidson (2006) The Regulatory Genome, Gene Regulation Networks in Development and
Evolution, Elsevier

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Representing transcriptional
fusions
 Objects Variables can be instantiated with the name of specific genes to
represent a construct where the gene is fused to the promoter or cluster of TF
binding sites specified by the module.

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Representing Directed Evolution
 Variables for stochastic constants can be instantiated
with specific values in order to represent directed
evolution.

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Representing Directed Evolution
 Variables for stochastic constants can be instantiated
with specific values in order to represent directed
evolution.

A

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Representing synthetic
transcriptional networks
 The genes used to instantiate variables in our modules can
codify other TFs that interact with other modules or promoters
producing a synthetic gene regulatory network.

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Stochastic P Systems
 Gillespie Algorithm (SSA) generates trajectories of a stochastic
system consisting of modified for multiple compartments/volumes:

1) A stochastic constant is associated with each rule.
2) 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.
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:

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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Multicompartmental Gillespie
Algorithm

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Algorithm
1
3

2

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Algorithm
1
3 r11,…,r1n1
r31,…,r3n3
M3 M1

2
r21,…,r2n2
M2

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Algorithm
1
3 r11,…,r1n1
r31,…,r3n3
Local Gillespie
M3 M1

2
r21,…,r2n2
M2

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Algorithm
1
3 r11,…,r1n1 ( 1, τ1, r01)
r31,…,r n3
3
Local Gillespie
M3 M1

2
r21,…,r2n2
M2

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Algorithm
1
3 r11,…,r1n1 ( 1, τ1, r01)
r31,…,r n3
3
Local Gillespie
M3 M1 ( 2, τ2, r02)

2
r21,…,r2n2
M2

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Algorithm
1
3 r11,…,r1n1 ( 1, τ1, r01)
r31,…,r n3
3
Local Gillespie
M3 M1 ( 2, τ2, r02)

2 ( 3, τ3, r03)
r21,…,r2n2
M2

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Algorithm
1
3 r11,…,r1n1 ( 1, τ1, r01)
r31,…,r n3
3
Local Gillespie
M3 M1 ( 2, τ2, r02)

2 ( 3, τ3, r03)
r21,…,r2n2
Sort Compartments
M2
τ2 < τ1 < τ3

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Algorithm
1
3 r11,…,r1n1 ( 1, τ1, r01)
r31,…,r n3
3
Local Gillespie
M3 M1 ( 2, τ2, r02)

2 ( 3, τ3, r03)
r21,…,r2n2
Sort Compartments
M2
τ2 < τ1 < τ3

( 2, τ2, r02)

( 1, τ1, r01)

( 3, τ3, r03)

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Algorithm
1
3 r11,…,r1n1 ( 1, τ1, r01)
r31,…,r n3
3
Local Gillespie
M3 M1 ( 2, τ2, r02)

2 ( 3, τ3, r03)
r21,…,r2n2
‘ Sort Compartments
M2
τ2 < τ1 < τ3

( 2, τ2, r02)

( 1, τ1, r01)

( 3, τ3, r03)

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Algorithm
1
3 r11,…,r1n1 ( 1, τ1, r01)
r31,…,r n3
3
Local Gillespie
M3 M1 ( 2, τ2, r02)

2 ( 3, τ3, r03)
r21,…,r2n2
M2
τ2 < τ1 < τ3

( 2, τ2, r02)
( 1, τ1-τ2, r01)
( 1, τ1, r01)
( 3, τ3-τ2, r03)
( 3, τ3, r03)
Update Waiting Times

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Algorithm
1
3 r11,…,r1n1 ( 1, τ1, r01)
r31,…,r n3
3
Local Gillespie
M3 M1 ( 2, τ2, r02)

2 ( 3, τ3, r03)
r21,…,r2n2
M2
τ2 < τ1 < τ3

( 2, τ2, r02)
( 2, τ2’, r02)
( 1, τ1-τ2, r01)
( 1, τ1, r01)
( 3, τ3-τ2, r03)
( 3, τ3, r03)
Update Waiting Times

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Algorithm
1
3 r11,…,r1n1 ( 1, τ1, r01)
r31,…,r n3
3
Local Gillespie
M3 M1 ( 2, τ2, r02)

2 ( 3, τ3, r03)
r21,…,r2n2
M2
τ2 < τ1 < τ3

( 2, τ2, r02)
( 2, τ2’, r02)
( 1, τ1-τ2, r01)
( 1, τ1, r01)
( 3, τ3-τ2, r03)
Insert new triplet ( 3, τ3, r03)
τ1-τ2 <τ2’ < τ3-τ2 Update Waiting Times

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Algorithm
1
3 r11,…,r1n1 ( 1, τ1, r01)
r31,…,r n3
3
Local Gillespie
M3 M1 ( 2, τ2, r02)

2 ( 3, τ3, r03)
r21,…,r2n2
M2
τ2 < τ1 < τ3

( 2, τ2, r02)
( 1, τ1-τ2, r01) ( 2, τ2’, r02)
( 1, τ1-τ2, r01)
( 1, τ1, r01)
( 2, τ2’, r02)
( 3, τ3-τ2, r03)
( 3, τ3-τ2, r03) Insert new triplet ( 3, τ3, r03)
τ1-τ2 <τ2’ < τ3-τ2 Update Waiting Times

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 Using P systems modules one can model a large variety of
commonly occurring BRN:

 Gene Regulatory Networks
 Signaling Networks
 Metabolic Networks

 This can be done in an incremental way.

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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InfoBiotics
Pipeline

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SBML from CellDesigner

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Runs simulations and extract data

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Plot Timeseries

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in time and space

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Synthetic Biology Examples

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Multi-component negative-
feedback oscillator

Oscillations caused by time-delayed negative-feedback:
Negative-feedback: gene-product that represses it's gene
Time-delay: mRNA export, translation and repressor import
Novak & Tyson: Design Principles of Biochemical Oscillators. Nat. Rev. Mol. Cell. Biol. 9: 981-991 (2008)

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Multi-component negative-
feedback oscillator
 Mathematical model
− Xc = [mRNA in cytosol]
− Yc = [protein in cytosol]
− Xn = [mRNA in nucleus]
− Yn = [protein in nucleus]
− E = [total protease]
− p = “integer indicating
whether Y binds to DNA as a
monomer, trimer, or so on”
Executable Biology makes this more obvious:
we can vary the value of p and the sequence of binding...

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Single protein represses gene
p=1

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When repression is weak
(dissociation rate = 10)

No obvious oscillatory behaviour in single simulation
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When repression is weak
(dissociation rate = 10)

Mean of 100 runs shows convergence to steady state
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When repression is strong
(dissociation rate = 0.1)

Oscillations evident in single simulation
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When repression is strong
(dissociation rate = 0.1)

Averging 100 runs dampens oscillations due to different
phases but observable. Protein levels steady.
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Repressor binding sequence
 When p=2 there are two possible scenarios:
– First protein binds to second protein weakly then
protein-dimer binds to gene strongly
– First protein binds to gene weakly then second
protein binds to protein-gene dimer strongly
 In the following only the model structure is
changed, not the parameters
 First dissociation rate = 10
 Second dissociation rate = 0.1
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1. Protein represses as dimer

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1. Protein represses as dimer

target

mRNA levels oscillate ready but protein
accumulates in the cytosol
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2. Proteins repress cooperatively

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2. Proteins repress cooperatively

target

Oscillations are steady and protein levels are controlled
83 /203


An example: Ron Weiss' Pulse Generator

 Two different bacterial strains carrying specific synthetic
gene regulatory networks are used.

 The first strain produces a diffusible signal AHL.

 The second strain possesses a synthetic gene regulatory
network which produces a pulse of GFP after AHL sensing.

 These two bacterial strains and their respective synthetic
networks are modelled as a combination of modules.

 S. Basu, R. Mehreja, et al. (2004) Spatiotemporal control of gene expression with pulse
generating networks, PNAS, 101, 6355-6360

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Sending Cells

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Sending Cells

Pconst

85 /203


Sending Cells

Pconst
luxI

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Sending Cells

Pconst({X = luxI },…)

Pconst
luxI

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Sending Cells
AHL

Pconst({X = luxI },…)
LuxI AHL PostTransc({X=LuxI},{c1=3.2,…})
Diff({X=AHL},{c=0.1})
Pconst
luxI

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Pulse Generating Cells

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LuxR

Pconst
luxR

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AHL

AHL
LuxR

Pconst
luxR

86 /203


AHL

AHL
LuxR GFP

PluxOR1
Pconst gfp
luxR

86 /203


AHL

AHL
LuxR GFP

PluxOR1
Pconst gfp
luxR

Plux
cI

86 /203


AHL

AHL
LuxR GFP

PluxOR1
Pconst gfp
luxR

CI

Plux
cI

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AHL

AHL Pconst({X=luxR},…)
LuxR GFP
PluxOR1({X=gfp},…)
PluxOR1 Plux({X=cI},…)
Pconst gfp
luxR
…
…
CI
Diff({X=AHL},…)
Plux
cI

86 /203


Spatial Distribution of Senders
and Pulse Generators
AHL
GFP AHL
LuxR

Pconst PluxOR1
luxR gfp LuxI AHL

CI Pconst luxI
Plux
cI

87 /203


AHL
Spatial Distribution of Senders
and Pulse Generators
AHL
GFP AHL
LuxR

Pconst PluxOR1
luxR gfp LuxI AHL

CI Pconst luxI
Plux
cI

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Wave propagation
simulation I

SIMULATION I

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AHLWith Relay
AHL
LuxR GFP

PluxOR1
Pconst gfp
luxR

CI

Plux
cI

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AHLWith Relay
AHL
LuxR GFP

PluxOR1
Pconst gfp
luxR

Plux CI
luxI

LuxI
Plux
cI

AHL

89 /203


AHLWith Relay
LuxR GFP

PluxOR1
Pconst gfp
luxR

Plux CI
luxI

LuxI
Plux
cI

AHL

89 /203


AHLWith Relay
LuxR GFP
PluxOR1
Pconst gfp
luxR

Plux CI
luxI

LuxI
Plux
cI

AHL

89 /203


AHLWith Relay
LuxR GFP
Pconst gfp
luxR

Plux CI
luxI

LuxI
Plux
cI

AHL

89 /203


AHLWith Relay
LuxR GFP
Pconst gfp
luxR
…

Plux CI
luxI

LuxI
Plux
cI

AHL

89 /203


AHLWith Relay
LuxR GFP
Pconst gfp
luxR
…
…
Plux CI
luxI

LuxI
Plux
cI

AHL

89 /203


AHLWith Relay
LuxR GFP
Pconst gfp
luxR
…
…
Plux CI
luxI Diff({X=AHL},…)

LuxI
Plux
cI

AHL

89 /203


AHLWith Relay
LuxR GFP
Pconst gfp
luxR
…
…
Plux CI
luxI Diff({X=AHL},…)
Plux Plux({X=luxI},…)
LuxI cI

AHL

89 /203


Wave propagation
simulation II

SIMULATION II

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36

AHL
Spatial Distribution of
Pulse Generators and Seed
AHL
LuxR GFP

Pconst PluxOR1
luxR gfp

Plux CI
luxI
Plux
cI
LuxI

AHL

91 /203


Wave propagation with
Four Droplets of Signal

SIMULATION III

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38

AHLWith Relay
LuxR
AHL
PulseGenerator(X ) =

PluxOR1
{ Pconst({X=luxR},…) ,
Pconst
luxR PluxOR1({X},…) ,
Plux({X=cI},…) ,

Plux …
CI
luxI Diff({X=AHL},…) ,

LuxI
Plux
cI Plux({X=luxI},…) }
AHL

93 /203


Combining Complex Modules
AHL

AHL Inverter(X ) =
LuxR
PluxOR1({X=lacI},…) ,
Pconst PluxOR1 Plac({X},…) ,
luxR lacI
…

LacI Diff({X=AHL},…)}

Plac

94 /203


Combining Complex Modules
AHL

AHL Inverter(X ) =
LuxR
PluxOR1({X=lacI},…) ,
Pconst PluxOR1 Plac({X},…) ,
luxR lacI
…

LacI Diff({X=AHL},…)}

Plac
PulseGenerator({X=lacI})
Inverter({X=gfP})

94 /203


Inversion Through a
Propagating Wave

SIMULATION IV

95 /203
41

Outline
•Conclusions
96 /203


Probabilistic Model Checking
 A precise computational/mathematical model allows
us to perform formal verification techniques:
Probabilistic model checking.

 Properties are expressed formally using temporal
logic and analysed.

 The fundamental components of the PRISM language
are modules, variables and commands.
• A model is composed of a number of modules which can
interact with each other.
• A module contains a number of local variables and commands.

97 /203


P Systems and PRISM
P System Component PRISM Component
Membrane Module
Multisets of Objects Local Variables
Rewriting rules Commands

 Rewards/Costs are associated with states and transitions representing
the number of objects and the application of rules.

 Some Properties:

 Expected Number of objects over time: R = ? [ I = T ]
 Expected Number of rule application over time: R = ? [ C <= T ]
 Expected Time to reach a state: R = ? [ F molec_1 = K ]
 Transient properties: P = ? [ true U[t_1 t_2] molec_1 >= K_1 ]
 Steady State/Long run properties: S = ? [ molec_1 >= K_1]

PRISM is used as an example. Other model checkers are more appropriate for larger systems
98 /203


Post-transcriptional Regulation

Post-transcriptional
regulation

[ gene ]b  [ gene + rna ]b ctrc
ctrc*ctrl = 1.13
[ rna ]b  [ ]b c2=0.3465
10 proteins in
[ rna ]b  [ rna + Protein ]b ctrl steady State

[ Protein ]b  [ ]b c4=0.3465

99 /203


Post-transcriptional Regulation
R = ? [ I = 240 ]

P = ? [ true U[240,240] Proteins = N ]

100 /203


Positive Regulation

[ TF + gene ] b  [ TF.gene ] b con

[ TF.gene ] b  [ TF + gene ] b coff

[ gene ]b  [ gene + rna ]b ctrc

[ rna ]b  [ ]b c2

[ rna ]b  [ rna + Protein ]b ctrl

[ Protein ]b  [ ]b c4
101 /203


Positive Regulation
R = ? [ C <= 100 ] R = ? [ C <= 100 ]

P = ? [ true U[60,60] Proteins = N ]

102 /203


Model Checking on the Pulse
Generator
 The simulation of the Pulse Generator show some interesting
properties that were subsequently analysed using model checking.
 Due to the complexity of the system (state space explosion) we
perform approximate model checking with a precision of 0.01 and a
confidence of 0.001 which needed to run 100000 simulations.

103 /203


Model Checking on the Pulse
Generator
 The simulations show that although the number of signals
reaches eventually the same level in all the cells in the lattice
those cells that are far from the sending cells produce fewer
number of GFP molecules.
 The difference between cells close to and far from the
sending cells is the rate of increase of the signal AHL.
 We study the effect of the rate of increase of the signal AHL
in the number of GFP produced.

S. Basu, R. Mehreja, et al. Spatiotemporal control of gene expression with pulse generating
networks, PNAS, 101, 6355-6360

104 /203


 We studied the expected number of GFP molecules produced over time for
different increase rates of AHL.

R = ? [ I = 60 ]

rewards
molecule = 1 : proteinGFP;
endrewards

The system is expected to
produce longer pulses with
lower amplitudes for slow
increase rates of AHL
signals.

105 /203


 In order to get a clearer idea, the probability distribution of the number of
GFP molecules at 60 minutes was computed.

P = ? [ true U[60,60] ((proteinGFP > N) & (proteinGFP <= (N + 10))) ]

Note that for slow
increase rates of AHL
the probability of having
NO GFP molecules at
all is high.

106 /203


 Finally, assuming that for a cell to be fluorescence it needs to have a given
number of GFP for an appreciable period of time we studied the expected
amount of time a cell have more than 50 GFP molecules during the first 60
minutes after the signals arrive to the cell.

R = ? [ C <= 60 ]

rewards
true : proteinGFP;
endrewards

107 /203


Outline
•Conclusions
108 /203


A (Proto)Cell as an Information
Processing Device

LeDuc et al. Towards an in vivo biologically inspired nanofactory. Nature (2007)

109 /203


Towards a synthetic cell from
the bottom up
 Biocompatible vesicles as long-circulating carriers
 Polymer self-assembly into higher-order structures
 Cell-mimics with hydrophobic ‘cell-wall’ and glycosylated
surfaces
 Potential for cross-talk with biological cells

Pasparakis, G. Angew Chem Int Ed. 2008 47 (26), 4847-4850

110 /203


Vesicle Biorecognition

Pasparakis, G. et al, Angew Chem Int Ed. 2008 47 (26), 4847-4850

111 /203


‘Talking’ to cell-vesicle aggregates

Pasparakis, G. Angew Chem Int Ed. 2008 47 (26), 4847-4850

112 /203


Outline
•Conclusions
113 /203


Dissipative Particle Dynamics
 Simulate movement of particles which represent several
atoms / molecules
 Calculate forces acting on particles, integrate equations of
motion
 Used extensively for investigating the self-assembly of lipid
membrane structures at the mesoscale
 Typical simulations contain ~105-106 particles, for ~105-106 time
steps
 Particles interact with each other within a finite radius much
smaller than the simulation space, algorithmic optimisations of
force calculations are possible

114 /203


 First introduced by Hoogerbrugge and Koelmann in 1992.
 Statistical mechanics of the model derived by espanol and warren in
1995.
 A coarse graining approach is used so that one simulation particle
represents a number of real molecules of a given type.
 Since the timescale at which interactions occur is longer than in MD,
fewer time-steps are required to simulation the same period of real time.
 The short force cut-off radius enables optimisation of the force calculation
code to be performed.

O
H H W
O O
H H H H

115 /203


Conservative Force

i W
P

Dissipative Force
j W
P

Random Force

116 /203


 Polymers
 A number of simulation beads are tied together to
represent the original molecule.
 Two new forces are introduced between polymer
particles, a Hookean spring force and a bond angle
force.

117 /203


Liposome Formation in DPD

118 /203


119 /203


Case Study One: Vesicle Diffusion
Polar heads

Non polar tails

Pores

J. Smaldon, J. Blake, D. Lancet, and N. Krasnogor. A multi-scaled approach to artificial life simulation
with p systems and dissipative particle dynamics. In Proceedings of the Genetic and Evolutionary
Computation Conference (GECCO-2008), ACM Publisher, 2008.

120 /203


Case Study One: Vesicle
Diffusion
 The regions were formed by allowing vesicles to self-
assemble from phospholipids in the presence of pore
inclusions
 Pores are simple channels with an exterior mimicking
the hydrophobic/hydrophilic profile of the bilayer

121 /203


122 /203


Case Study One: Vesicle Diffusion
Tagged solvent particles were placed within the liposome inner
volume, the change in concentration due to diffusion of solvent
through the membrane pores was measures

123 /203


Case Study Two: Liposome
Logic
 The behaviour of some prokaryotic RNA
transcription motifs matches that of
boolean logic gates[1]
 DPD was extended with mesoscale
collision based reactions.
 transcriptional logic gates were simulated
in bulk solvent and within a liposome core
volume.

124 /203


125 /203


Synthetic Biology - Modeling and Optimisation

Synthetic Biology - Modeling and Optimisation

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