synthetic biology - modeling and optimisation

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Natalio KrasnogorASAP - Interdisciplinary Optimisation LaboratorySchool of Computer Science

Centre for Integrative Systems BiologySchool of Biology

Centre for Healthcare Associated InfectionsInstitute of Infection, Immunity & Inflammation

University of Nottingham

Synthetic Biology: Modelling and Optimisation

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.

1

Thursday, 9 July 2009

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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

•Conclusions2


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•Conclusions3


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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.5


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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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Cells

DNA/RNA

OrganCell colony

Proteins

Individual

RegulatoryNetworks

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

Time

Progress

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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.

• 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?

& Integrative

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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 LThe simulation clock ticks every Δt units for a total of T units

We can simulate processes: as fast as Δt for as long as T units ranging from Δx to L sizes.


Δx

L

L

ΔtT

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

Temporal scale (log)

Spa

tial s

cale

(log

)

1

23.1 3.2

0

A ξA

τA

B ξB

τB

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Spa

tial s

cale

(log

)

1

23.1 3.2

0

A ξA

τAB ξB

τB

• Region 0: A and B overlap single scale multi-science model• Region 1: ξA ≈ ξB ^ τA > τB

temporal scale separation• Region 2: ξA > ξB ^ τB ≈ τA coarse and fine structures 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 large process (e.g. Blood flood and artery repair)

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Spa

tial s

cale

(log

)

1

23.1 3.2

0

A ξA

τA

B ξB

τB

• Region 0: A and B overlap single scale multi-science model• Region 1: ξA ≈ ξB ^ τA > τB

temporal scale separation• Region 2: ξA > ξB ^ τB ≈ τA coarse and fine structures 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 large process (e.g. Blood flood and artery repair)

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Even within a single cell the space & time scale separations are important

[F.J. Romero Campero, 2007]

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.

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Spa

tial s

cale

(log

)

• With sufficient data each process can be assigned its space-time region unambiguously

• A given process may well have its Δx (respectively Δt) > than another’s ξA (respectively τA)

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

Couplings, e.g. F


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Modelling Approaches

There exist many modelling approaches, each with its advantages and disadvantages.

Macroscopic, Microscopic and MesoscopicQuantitative and qualitativeDiscrete and ContinuousDeterministic and StochasticTop-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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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, e

rror

C, cost of modelling

Synthetic Biologist

Computer Scientist/Mathematician

Tools Suitability and Cost

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Tools Suitability and Cost

Low cost/High error

High cost/Low error

Unarticulatedwisdom

ArticulatedQualitativemodels

Dimensionalmodels

Facetwisemodels

EquationsOf motion

ChemicalMarkup Language

(CML)

BioinformaticSequence MarkupLanguage (BSML)

BiopolimerMarkup Language

(BioML)

Microarrays and G.E. Markup Language

(MAGEML)

Cell Markup Language

(MathML)

Systems Biology Markup Language

(SBML)

Mathematics Markup Language

(MathML)

Adapted from [Goldberg 2002]

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Formalism-independent errors Formalism-dependent errors

Low cost/High error

High cost/Low error

Unarticulatedwisdom

Dimensionalmodels

Facetwisemodels

EquationsOf motion

From [Di Ventura et al., Nature, 2006]

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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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“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

Towards Executable Modells for SBs

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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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InfoBioticswww.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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http://www.infobiotic.net

http://www.infobiotic.net

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Cells

Colonies

Modeling in Systems & Synthetic Biology

Networks

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

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• 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

Model Design in Systems/Synthetic Biology

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How you select features, disambiguate and quantify depends on the goals behind your modelling enterprise.

Sys

tem

s B

iolo

gy

Syn

thet

ic B

iolo

gy

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

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 problem2. Verification of available information3. Selection of model structure4. Establishing a simple model5. Sensitivity analysis6. Experimental tests of the model predictions7. Stating the agreements and divergences between

experimental and modelling results8. Iterative refinement of model

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•Conclusions34


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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 EntitiesContainer

• 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.

Compartments

Objects

Rewriting Rules

• Computational universality and efficiency.

• Modelling Framework

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Cell-like P systems

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

Intuitive Visual representation as a Venn diagram with a unique superset and without intersected sets.

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Cell-like P systems

1

23

4

75

8

6

9

formally equivalent to a tree:



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Cell-like P systems

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

[7 ]7 ]4 ]1

1

23

4

75

8

6

9

formally equivalent to a tree:



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P-Systems: Modelling PrinciplesMoleculesStructured Molecules

ObjectsStrings

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

a b

Symport channel

a

a

b

b

Antiport channel

ab

a b

Promoted symport channel (trap)

c

Transport Modalities

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1

5

4 3

2

Endocitosys

Pinocitosys

Phagocitosys

Exocitosys


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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

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.

LuxRAHL

CI

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 EvolutionVariables for stochastic constants can be instantiated

with specific values in order to represent directed evolution.

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Representing Directed EvolutionVariables 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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1

2

3

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1

2

3 r11,…,r1

n1

M1

r21,…,r2

n2

M2

r31,…,r3

n3

M3

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1

2

3 r11,…,r1

n1

M1

r21,…,r2

n2

M2

r31,…,r3

n3

M3

Local Gillespie

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1

2

3 r11,…,r1

n1

M1

r21,…,r2

n2

M2

r31,…,r3

n3

M3

( 1, τ1, r01)

Local Gillespie

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1

2

3 r11,…,r1

n1

M1

r21,…,r2

n2

M2

r31,…,r3

n3

M3

( 1, τ1, r01)

( 2, τ2, r02)

Local Gillespie

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1

2

3 r11,…,r1

n1

M1

r21,…,r2

n2

M2

r31,…,r3

n3

M3

( 1, τ1, r01)

( 2, τ2, r02)

( 3, τ3, r03)

Local Gillespie

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1

2

3 r11,…,r1

n1

M1

r21,…,r2

n2

M2

r31,…,r3

n3

M3

( 1, τ1, r01)

( 2, τ2, r02)

( 3, τ3, r03)

Sort Compartments τ2 < τ1 < τ3

Local Gillespie

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1

2

3 r11,…,r1

n1

M1

r21,…,r2

n2

M2

r31,…,r3

n3

M3

( 1, τ1, r01)

( 2, τ2, r02)

( 3, τ3, r03)

( 2, τ2, r02)

( 1, τ1, r01)

( 3, τ3, r03)


Local Gillespie

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1

2

3 r11,…,r1

n1

M1

r21,…,r2

n2

M2

r31,…,r3

n3

M3

( 1, τ1, r01)

( 2, τ2, r02)

( 3, τ3, r03)

( 2, τ2, r02)

( 1, τ1, r01)

( 3, τ3, r03)


Local Gillespie

‘

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1

2

3 r11,…,r1

n1

M1

r21,…,r2

n2

M2

r31,…,r3

n3

M3

( 1, τ1, r01)

( 2, τ2, r02)

( 3, τ3, r03)

( 2, τ2, r02)

( 1, τ1, r01)

( 3, τ3, r03)


Local Gillespie

( 1, τ1-τ2, r01)

( 3, τ3-τ2, r03)

Update Waiting Times

‘

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1

2

3 r11,…,r1

n1

M1

r21,…,r2

n2

M2

r31,…,r3

n3

M3

( 1, τ1, r01)

( 2, τ2, r02)

( 3, τ3, r03)

( 2, τ2, r02)

( 1, τ1, r01)

( 3, τ3, r03)


Local Gillespie

( 1, τ1-τ2, r01)

( 3, τ3-τ2, r03)


( 2, τ2’, r02)

‘

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1

2

3 r11,…,r1

n1

M1

r21,…,r2

n2

M2

r31,…,r3

n3

M3

( 1, τ1, r01)

( 2, τ2, r02)

( 3, τ3, r03)

( 2, τ2, r02)

( 1, τ1, r01)

( 3, τ3, r03)


Local Gillespie

( 1, τ1-τ2, r01)

( 3, τ3-τ2, r03)


( 2, τ2’, r02)

Insert new triplet τ1-τ2 <τ2’ < τ3-τ2

‘

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1

2

3 r11,…,r1

n1

M1

r21,…,r2

n2

M2

r31,…,r3

n3

M3

( 1, τ1, r01)

( 2, τ2, r02)

( 3, τ3, r03)

( 2, τ2, r02)

( 1, τ1, r01)

( 3, τ3, r03)


Local Gillespie

( 1, τ1-τ2, r01)

( 3, τ3-τ2, r03)


( 2, τ2’, r02)( 1, τ1-τ2, r0

1)

( 2, τ2’, r02)

( 3, τ3-τ2, r03)

Insert new triplet τ1-τ2 <τ2’ < τ3-τ2

‘

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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 geneTime-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 genep = 1

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When repression is weak(dissociation rate = 10)

No obvious oscillatory behaviour in single simulation75


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When repression is weak(dissociation rate = 10)

Mean of 100 runs shows convergence to steady state76


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When repression is strong(dissociation rate = 0.1)

Oscillations evident in single simulation77


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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

Oscillations are steady and protein levels are controlled

target

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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.

An example: Ron Weiss' Pulse Generator

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

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Sending Cells

Pconst luxI

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Sending Cells

Pconst

Pconst({X = luxI },…)

luxI

85


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Sending Cells

Pconst

LuxI AHL

AHL

Pconst({X = luxI },…)

PostTransc({X=LuxI},{c1=3.2,…})

Diff({X=AHL},{c=0.1})

luxI

85


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Pulse Generating Cells

86


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luxRPconst

LuxR


86


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luxRPconst

LuxRAHL

AHL


86


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luxRPconst gfp

PluxOR1

LuxR GFPAHL

AHL


86


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luxRPconst

cIPlux

gfpPluxOR1

LuxR GFPAHL

AHL


86


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luxRPconst

cIPlux

gfpPluxOR1

LuxR

CI

GFPAHL

AHL


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luxRPconst

cIPlux

gfpPluxOR1

LuxR

CI

GFPAHL

AHL

Pconst({X=luxR},…)

PluxOR1({X=gfp},…)

Plux({X=cI},…)

…

…

Diff({X=AHL},…)


86


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Spatial Distribution of Senders and Pulse Generators

luxIPconst

LuxI AHL

AHL

87

luxRPconst

cIPlux

gfpPluxOR1

LuxR

CI

GFPAHL


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Spatial Distribution of Senders and Pulse Generators

luxIPconst

LuxI AHL

AHL

AHL

87

luxRPconst

cIPlux

gfpPluxOR1

LuxR

CI

GFPAHL

AHL


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Wave propagation simulation I

SIMULATION I

88


http://www.cs.nott.ac.uk/~nxk/pulseGenerator2.swf




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Pulse Generating Cells With Relay

luxRPconst

cIPlux

gfpPluxOR1

LuxR GFPAHL

AHL

CI

89


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luxRPconst

cIPlux

gfpPluxOR1

LuxR GFPAHL

AHL

luxIPlux

LuxI

AHL

CI

89


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luxRPconst

cIPlux

gfpPluxOR1

LuxR GFPAHL

AHL

luxIPlux

LuxI

AHL


CI

89


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luxRPconst

cIPlux

gfpPluxOR1

LuxR GFPAHL

AHL

luxIPlux

LuxI

AHL



CI

89


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luxRPconst

cIPlux

gfpPluxOR1

LuxR GFPAHL

AHL

luxIPlux

LuxI

AHL



Plux({X=cI},…)

CI

89


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luxRPconst

cIPlux

gfpPluxOR1

LuxR GFPAHL

AHL

luxIPlux

LuxI

AHL



Plux({X=cI},…)

…

CI

89


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luxRPconst

cIPlux

gfpPluxOR1

LuxR GFPAHL

AHL

luxIPlux

LuxI

AHL



Plux({X=cI},…)

…

…CI

89


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luxRPconst

cIPlux

gfpPluxOR1

LuxR GFPAHL

AHL

luxIPlux

LuxI

AHL



Plux({X=cI},…)

…

…

Diff({X=AHL},…)CI

89


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luxRPconst

cIPlux

gfpPluxOR1

LuxR GFPAHL

AHL

luxIPlux

LuxI

AHL



Plux({X=cI},…)

…

…

Diff({X=AHL},…)Plux({X=luxI},…)

CI

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Wave propagation simulation II

90

SIMULATION II






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Spatial Distribution of Pulse Generators and Seed

luxRPconst

cIPlux

gfpPluxOR1

LuxR

CI

GFPAHL

AHL

luxI

LuxI

AHL

Plux CI

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Wave propagation with Four Droplets of Signal

92

SIMULATION III


http://www.cs.nott.ac.uk/~nxk/fourDroplets.swf




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luxRPconst

cIPlux

PluxOR1

LuxR

CI

AHL

AHL

luxIPlux

LuxI

AHL

PulseGenerator(X ) =

{ Pconst({X=luxR},…) ,

PluxOR1({X},…) ,

Plux({X=cI},…) ,

…

Diff({X=AHL},…) ,

Plux({X=luxI},…) }

93


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Combining Complex Modules

luxRPconst

Plac

lacIPluxOR1

LuxR

LacI

AHL

AHL

Inverter(X ) =


PluxOR1({X=lacI},…) ,

Plac({X},…) ,

…

Diff({X=AHL},…)}

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Combining Complex Modules

luxRPconst

Plac

lacIPluxOR1

LuxR

LacI

AHL

AHL

Inverter(X ) =


PluxOR1({X=lacI},…) ,

Plac({X},…) ,

…

Diff({X=AHL},…)}

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

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Inversion Through a Propagating Wave

SIMULATION IV

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•Conclusions96


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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.

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P Systems and PRISMP System Component PRISM Component

Membrane ModuleMultisets 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]

98

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


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Post-transcriptional Regulation

Post-transcriptionalregulation

[ gene ]b [ gene + rna ]b ctrc

[ rna ]b [ ]b c2=0.3465

[ rna ]b [ rna + Protein ]b ctrl

[ Protein ]b [ ]b c4=0.3465

ctrc*ctrl = 1.13

10 proteins in steady State

99


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Post-transcriptional RegulationR = ? [ I = 240 ]

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

100


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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

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

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

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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.

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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

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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.

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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.

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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

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•Conclusions108


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A (Proto)Cell as an Information Processing Device

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

109


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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

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Vesicle Biorecognition

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

111


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‘Talking’ to cell-vesicle aggregates

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

112


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•Conclusions113


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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

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Dissipative Particle Dynamics 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.

H HO

H HO

H HO

W

115


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Dissipative Particle Dynamics

W

W

i

j

P

P

i

j

Conservative Force

Dissipative Force

Random Force

116


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Dissipative Particle Dynamics 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


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Liposome Formation in DPD

118


/203119


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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.

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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

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Case Study One: Vesicle DiffusionTagged 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


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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.

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Case Study Two: Liposome LogicOR gate results for different inputs: (¬X,¬Y) (¬X,Y) (X,¬Y) (X,Y)

J. Smaldon, N. Krasnogor, M. Gheorghe, and A. Cameron. Liposome logic. In Proceedings of the 2009 Genetic and Evolutionary Computation Conference (GECCO 2009), 2009

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Parallel DPD In order to simulate large systems, the

DPD method can be parallelised using spatial decomposition techniques

Each processor is assigned a subvolume of the 3D simulation space

Communication required when particles move between subvolumes

Communication performed using MPI 10x-15x faster than the single processor

version of DPD (Jupiter implementation)

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Compute Unified Device Architecture (CUDA) DPD

Algorithms can be written in C code for execution on an Nvidia G8X/GT200 GPU.

Modern CPUs have 2-4 cores, modern GPUs have hundreds. Highly parallel SIMD computing.

Several orders of magnitude calculation speed increase for MD.

The DPD algorithm was expressed in a manner enabling parallel execution with CUDA.

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CUDA DPD Implementation

CUDA DPD is ~27 times faster than single processor

129


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•Conclusions130


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Automated Model Synthesis and Optimisation

Modeling is an intrinsically difficult process

It involves “feature selection” and disambiguation

Model Synthesis requires design the topology or structure of the system in

terms of molecular interactions estimate the kinetic parameters associated with

each molecular interaction

All the above iterated131


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Once a model has been prototyped, whether derived from existing literature or “ab initio” ➡ Use some optimisation method to fine tune parameters/model structure

adopts an incremental methodology, namely starting from very simple P system modules (BioBricks) specifying basic molecular interactions, more complicated modules are produced to model more complex molecular systems.

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Large Literature on Model Synthesis• Mason et al. use a random Local Search (LS) as the mutation to

evolve electronic networks with desired dynamics

• Chickarmane et al. use a standard GA to optimize the kinetic parameters of a population of ODE-based reaction networks having the desired topology.

• Spieth et al. propose a memetic algorithm to find gene regulatory networks from experimental DNA microarray data where the network structure is optimized with a GA and the parameters are optimized with an Evolution Strategy (ES).

• Etc

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Evolutionary Algorithms for Automated Model Synthesis and Optimisation

EA are potentially very useful for AMSO There’s a substantial amount of work on:

using GP-like systems to evolve executable structures

using EAs for continuous/discrete optimisation

An EA population represents alternative models (could lead to different experimental setups)

EAs have the potential to capture, rather than avoid, evolvability of models

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• The main idea is to use a nested evolutionary algorithm where the first layer evolves model structures while the inner layer acts as a local search for the parameters of the model. • It uses stochastic P systems as a computational, modular and discrete-stochastic modelling framework.

• It adopts an incremental methodology, namely starting from very simple P system modules specifying basic molecular interactions, more complicated modules are produced to model more complex molecular systems.

•Successfully validated evolved models can then be added to the models library

Evolving Executable Biology Models

135


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Nested EA for Model Synthesis

F. Romero-Campero, H.Cao, M. Camara, and N. Krasnogor. Structure and parameter estimation for cell systems biology models. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2008), pages 331-338. ACM Publisher, 2008.

Best Paper award at the Bioinformatics track.

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Fitness Evaluation

137


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Representation

138


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Structural Operators

140


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Structural Operators

141


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Parameter Optimisation

142


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Parameter Optimisation

143


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Simple Illustrative Case studies

• Case 1: molecular complexation

• Case 2: enzymatic reaction

• Case 3: autoregulation in transcriptional networks

•Case 3.1. negative autoregulation•Case 3.2. positive autoregulation

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Case 1: Molecular ComplexationTarget P System Model Structure

Target P System Model Parameters

c1

c2

145


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Case 1: Experimental Results

50/50 runs found the same P system model structure as the target one

Target and Evolved Time Series 146


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50/50 runs found the same P system model structure as the target one

Best Model Parameters

Target Model Parameters

Target and Evolved Time Series 147


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Case 2: Enzymatic ReactionTarget P System Model Structure

Target P System Model Parameters

c1

c2

c3

148


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Case 2: Experimental ResultsTarget and Evolved Time Series

149


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Best Model Parameters

Target Model Parameters Target and Evolved Time Series

Two Approaches Using Basic Modules

Adding the Newly Found in Case 1

Number of runs the target P system model was

found

12/50 39/50

Mean RMSE 3.8 2.85150


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Case 3.1: Negative AutoregulationTarget P System Model Structure Target P System Model Parameters

c1

c2

c3

c4

c5

c6

151


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Case 3.1: Experimental Results

Best Model in Design 1

Design Design 1 Design 2

Model

Number of runs 46/50 4/50

Mean +/- STD 4.11+/- 11.73 4.63 +/- 2.91


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Case 3.2: Positive AutoregulationTarget P System Model Structure Target P System Model Parameters

c1

c2

c3

c4

c5

c6

c7

153


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Case 3.2: Experimental ResultsDesign Design 1 Design 2

Model

Number of runs 30/50 20/50

Mean +/- STD 16.36 +/- 3.03 20.14 +/- 5.13


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Revisiting the Fitness Function• Multiple time-series per target

• Different time series have very different profiles, e.g., response time or maxima occur at different times/places

• Transient states (sometimes) as important as steady states

•RMSE will mislead search

H. Cao, F. Romero-Campero, M.Camara, N.Krasnogor. Analysis of Alternative Fitness Methods for the Evolutionary Synthesis of Cell Systems Biology Models. Submitted (2009)

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Four Fitness FunctionsN time seriesM time points in each time series Simulated data Target data

F1

F2

F2 normalises whithin a time series between [0,1]

156


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Four Fitness FunctionsN time seriesM time points in each time series Simulated data Target data Randomly generated normalised

vector with:

F3

F3, unlike F1, does not assume an equal weighting of all the errors. It produces a randomised average of weights.

157


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Four Fitness FunctionsN time seriesM time points in each time series Simulated data Target data

F4

F4 simply multiplies errors hence even small ones within a set with multiple orders of maginitudes can still have an effect. Indeed, this might lead to numerical instabilities due to nonlinear effects.

158


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Further Case Studies

159


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/203162


/203163


/203164


/203165


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Results Study Case 1

167


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168


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169


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Alternative, biologically valid, modules

Target model

170


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172


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Comparisons of the constants between the best fitness models obtained by F1, F4 and the target model for Test Case 4 (Values different from the target are in bold and underlined)

173


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Target

179


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Target

180


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The evolving curve of average fitness by four fitness methods (F1 ∼ F4) in 20 runs for Test Case 4.

181


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The evolving curve of average model diversity by four fitness methods (F1 ∼ F4) in 20 runs for Test Case 4

182


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Multi-Objective Optimisation in Morphogenesis

The following slides are based on

Rui Dilão, Daniele Muraro, Miguel Nicolau, Marc Schoenauer. Validation of a morphogenesis model of Drosophila early development by a multi-objective evolutionary optimization algorithm. Proc. 7th European Conference on Evolutionary Computation, ML and Data Mining in BioInformatics (EvoBIO'09), April 2009.

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• The authors investigate the use of MOEA for modeling morphogenesis

• The model organism is drosophila embrios Rui Dilão, Daniele Muraro, Miguel Nicolau, Marc Schoenauer. Validation of a morphogenesis model of Drosophila early development by a multi-objective evolutionary optimization algorithm. Proc. 7th European Conference on Evolutionary Computation, ML and Data Mining in BioInformatics (EvoBIO'09), April 2009

185


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Initial Conditions

PDE model

186


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Target

By Evolving:abcd, acad, Dbcd/Dcad, r, mRNA distributions and t

However: Goal is not perfect fit but rather robust fit

187


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• The authors use both Single and Multi-objective optimisation• CMA-ES is at the core of both• CMA-ES is a (µ,λ)-ES that employs multivariate Gaussian

distributions • Uses “cumulative path” for co-variantly adapting this

distribution• For the MO case it uses the global pareto dominance based

selection

Bi-Objective Function

Objective Function

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•Conclusions192


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Summary & Conclusions This talk has focused on an integrative methodology,

InfoBiotics, for Systems & Synthetic Biology Executable Biology/DPD Parameter and Model Structure Discovery Model Checking

Computational models (or executable in Fisher & Henzinger’s jargon) adhere to (a degree) to an operational semantics.

Refer to the excellent review [Fisher & Henzinger, Nature Biotechnology, 2007]

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The gap present in mathematical models between the model and its algorithmic implementation disappears in computational models as all of them are algorithms.

A new gap appears between the biology and the modelling technique and this can be solved by a judicious “feature selection”, i.e. the selection of the correct abstractions

Good computational models are more intuitive and analysable

Summary & Conclusions

194


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Computational models can thus be executed (quite a few tools out there, lots still missing)

Quantitative VS qualitative modelling: computational models can be very useful even when not every detail about a system is known.

Missing Parameters/model structures can sometimes be fitted with of-the-shelf optimisation strategies (e.g. COPASI, GAs, etc)

Computational models can be analysed by model checking: thus they can be used for testing hypothesis and expanding experimental data in a principled way


195


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A nested evolutionary algorithm is proposed to automatically develop and optimise the modular structure and parameters of cellular models based on stochastic P systems. Several case studies with incremental model complexity demonstrate the effectiveness of our algorithm.

The fact that this algorithm produces alternative models for a specific biological signature is very encouraging as it could help biologists to design new experiments to discriminate among competing hypothesis (models).

Comparing results by only using the elementary modules and by adding newly found modules to the library shows the obvious advantage of the incremental methodology with modules. This points out the great potential to automatically design more complex cellular models in the future by using a modular approach.


196


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Synthetising Synthetic Biology Models is more like evolving general GP programs and less like fitting regresion or inter/extra-polation

We evolve executable structures, distributed programs(!) These are noisy and expensive to execute Like in GP programs, executable biology models might achieve

similar behaviour through different program “structure” Prone to bloat Like in GP, complex relation between diversity and solution

quality However, diverse solutions of similar fit might lead to interesting

experimental routes Co-desig of models and wetware.


197


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Summary & Conclusions Some really nice tutorials and other sources:

Luca Caderlli’s BraneCalculus & BioAmbients Simulating Biological Systems in the Stochastic π−calculus by Phillips and Cardelli

From Pathway Databases to Network Models by Aguda and Goryachev

Modeling and analysis of biological processes by Brane Calculi and Membrane Systems by Busi and Zandron

D. Gilbert’s website contain several nice papers with related methods and tutorials

198


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Other SourcesF. 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, (to appear), 2009.

F.J. Romero-Camero and N. Krasnogor. An approach to biomodel engineering based on p systems. In Proceedings of Computation In Europe (CIE 2009), 2009.

J. Smaldon, N. Krasnogor, M. Gheorghe, and A. Cameron. Liposome logic. In Proceedings of the 2009 Genetic and Evolutionary Computation Conference (GECCO 2009), 2009

F. Romero-Campero, H.Cao, M. Camara, and N. Krasnogor. Structure and parameter estimation for cell systems biology models. In Maarten Keijzer et.al, editor, Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2008), pages 331-338. ACM Publisher, 2008. This paper won the Best Paper award at the Bioinformatics track.

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.

199


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Other SourcesPăun, Gh. Computing with membranes. Journal of Computer and System Sciences 61 (2000) 108-143

P Systems Web Page http://psystems.disco.unimib.it/ Bianco L. Membrane Models of Biological Systems PhD thesis 2007

Bernardini F, Gheorghe M, Krasnogor N, Terrazas G. Membrane Computing - Current Results and Future Problems. CiE 2005 49-53

Bernardini F, Gheorghe M, Krasnogor N. Quorum sensing P systems. Theoretical Computer Science 371 (2007) 20-33

Miguel Nicolau, Marc Schoenauer. Evolving Specific Network Statistical Properties using a Gene Regulatory Network Model. In ECCS 2008, 5th European Conference on Complex Systems, 2008. Miguel Nicolau, Marc Schoenauer. Evolving Scale-Free Topologies using a Gene Regulatory Network Model. CEC 2008, IEEE Congress on Evolutionary Computation, pp. 3748-3755, IEEE Press, 2008.

200


http://psystems.disco.unimib.it/

http://psystems.disco.unimib.it/

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A. Ridwan. A parallel implementation of Gillespie's Direct Method. Proc. of the International Conference on Computational Science, p.284-291, Krakow, Poland, June 2004.

G. C. Ewing et al. Akaroa2: Exploiting network computing by distributing stochastic simulation. Proc. of the European Simulation Multiconference, p.175-181, Warsaw, June 1999.

P. Hellekalek. Don't trust parallel Monte Carlo! ACM SIGSIM Simulation Digest, 28(1):82-89, 1998.

M. Schwehm. Parallel stochastic simulation of whole cell models. Proc. of the Second International Conference on Systems Biology, p.333-341, CalTech, C.A., November 2001

Other Sources

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Acknowledgements

Jonathan Blake

Hongqing Cao

Francisco Romero-Campero

James Smaldon

Jamie Twycross

Integrated Environment

Machine Learning & Optimisation

Modeling & Model Checking

Dissipative Particle Dynamics

Stochastic Simulations

Members of my team working on SB2

EP/E017215/1

EP/D021847/1

BB/F01855X/1

BB/D019613/1

My colleagues in the Centre for Biomolecular Sciences and the Centre for Plant Integrative Biology at Nottingham

• GECCO 2009 organisers for inviting this tutorial, specially Martin Butz and Gunther Raidl

• You for listening!202


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Any Questions?

•www.infobiotic.org

•www.synbiont.org Become a member and have access to $$$ forengaging in SB research. Contact me if interested

203


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