Executable Biology Tutorial

A Gentle Introduction to Executable
Biology

Natalio Krasnogor
ASAP - Interdisciplinary Optimisation Laboratory
School of Computer Science and Information Technology

Centre for Integrative Systems Biology
School of Biology

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

University of Nottingham

www.cs.nott.ac.uk/~nxk
ECSB II, Sant Feliu de Guixols, Spain
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Main Contributors to this Tutorial
 Jonathan Blake
Integrated Environment

 Hongqing Cao Machine Learning & Optimisation

Modeling &
 Francisco Romero-Campero Model
Checking

 James Smaldon Dissipative Particle Dynamics

Stochastic
 Jamie Twycross Simulations

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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
•Conclusions
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Outline

•Conclusions
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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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InfoBiotics
There are good reasons to think that information processing is
an enabling viewpoint when modeling living systems

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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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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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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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

E. Klipp et al, Systems Biology in Practice, 2005

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Tools Suitability and Cost

Stochastic
ODE
uo
us Delay Eq.
in
Co
nt PDE
Cellular Automata
Time Dependent
Multi-agents
Spatially Structured
Monte Carlo
Petri Nets
te
re
Disc Π-calculus
P-systems
Deterministic

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

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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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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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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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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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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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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)
r3 1,…,r n3
3
Local Gillespie
M3 M1

2
r21,…,r2n2
M2

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Algorithm
1
3 r11,…,r1n1 ( 1, τ1, r01)
r3 1,…,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)
r3 1,…,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)
r3 1,…,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)
r3 1,…,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)
r3 1,…,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)
r3 1,…,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)
r3 1,…,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)
r3 1,…,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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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

 According to E. Davidson
functional cis-regulatory modules
are nonrandom clusters of target
binding sites for transcription
factors regulating the same gene
or operon.
 A library of modules
corresponding to promoters of
well studied genes. The activity of
these promoters have been
modelled mechanistically in terms
of rewriting rules representing TF
binding and debinding and
transcription initiation.

E. Davidson, The Regulatory Genome, Gene Regulatory Networks in Development and Evolution,
Elsevier.
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Representing transcriptional fusions and
synthetic gene regulatory networks
 Variables in our modules 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 modelled by the module.
 These genes can in turn codify other TFs that can interact with other modules
producing a synthetic gene regulatory network.

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Modelling Individual Cells
 An individual cell is represented as a P system, a set of compartments
where specific objects describing molecular species are placed.
 The gene regulatory networks in each cell are represented as a collection
of modules and rewriting rules.

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Modelling Multicellular Systems
 The geometry and topology of multicellular systems are described using
geometrical lattices over which many copies of the different P systems
representing individual cells are distributed.

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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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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
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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. Spatiotemporal control of gene expression with pulse generating
networks, PNAS, 101, 6355-6360

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Sending Cells

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Pulse Generating Cells

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An example: Ron Weiss' Pulse Generator
 A rectangular lattice is used over which P systems representing cells
sending AHL, cells with the previously introduced pulse generator and
environments are distributed.

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An example: Ron Weiss' Pulse Generator

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Outline

•Conclusions
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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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Outline

•Conclusions
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A (Proto)Cell as an Information
Processing Device

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

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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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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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‘Talking’ to cell-vesicle aggregates

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

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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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 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

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Conservative Force

i W
P

Dissipative Force
j W
P

Random Force

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 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.

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Liposome Formation in DPD

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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 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

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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 Logic
OR 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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Outline

•Conclusions
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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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Summary & Conclusions
 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

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Acknowledgements
 We would like to acknowledge EPSRC
grants EP/E017215/1 & EP/D021847/1 ,
BBSRC grant BB/F01855X/1 & BB/
D019613/1
 Our colleagues in the Centre for
Biomolecular Sciences and the Centre for
Plant Integrative Biology
 ESF for funding ECSB II

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Any Questions?
Vacancies:

• www.infobiotic.org • PhD in Computational Modeling
of root development

• Postdoc on Dissipative Particles
• www.synbiont.org Dynamics for ProtoCells

• ESF Summer School on Plants Bioinformatics,
Systems and Synthetic Biology
• Nottingham, UK between the 27th and 31st of July 2009
• EU students fully funded!
• Limited spaces! apply soon!!

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