executable biology tutorial

www.cs.nott.ac.uk/~nxkECSB II, Sant Feliu de Guixols, Spain /94

Natalio KrasnogorASAP - Interdisciplinary Optimisation LaboratorySchool of Computer Science and Information Technology

Centre for Integrative Systems BiologySchool of Biology

Centre for Healthcare Associated InfectionsInstitute of Infection, Immunity & Inflammation

University of Nottingham

A Gentle Introduction to Executable Biology

1

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



Main Contributors to this Tutorial Jonathan Blake

Hongqing Cao

Francisco Romero-Campero

James Smaldon

Jamie Twycross

2

Integrated Environment

Machine Learning & Optimisation

Modeling & Model Checking

Dissipative Particle Dynamics

StochasticSimulations




Outline

3

•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




Outline

4





•Conclusions




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)

5



http://www.infobiotic.net

http://www.infobiotic.net


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

InfoBiotics

6




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”.

7




Cells

Colonies

Modeling in Systems & Synthetic Biology

Networks

8

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




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

9




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

10

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




Modelling ApproachesThere 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

11




Tools Suitability and Cost

Time DependentSpatially Structured

Determ

inistic

Sto

chas

tic

Discrete

Continuous

ODEDelay Eq.PDECellular AutomataMulti-agentsMonte Carlo Petri NetsΠ-calculusP-systems

12

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




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)

13

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




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

14




Outline

15





•Conclusions




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

16




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

17




Distributed and parallel rewritting systems in compartmentalised hierarchical structures.

Compartments

Objects

Rewriting Rules

• Computational universality and efficiency.

• Modelling Framework

18




P-Systems: Modelling PrinciplesMoleculesStructured Molecules

ObjectsStrings

Molecular Species Multisets of objects/strings

Membranes/organelles Membrane

Biochemical activity rules

Biochemical transport Communication rules

19




Stochastic P Systems

20




Rewriting Rules

21

used by Multi-volume Gillespie’s algorithm




Molecular Species A molecular species can be represented using

individual objects.

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

22




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

23




Compartments / Cells Compartments and regions are explicitly

specified using membrane structures.

24




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

25




Molecular Interactions Inside Compartments

26




Passive Diffusion of Molecules

27




Signal Sensing and Active Transport

29




Specification of Transcriptional Regulatory Networks

30




Transcription as Rewriting Rules on Multisets of Objects and Strings

31




Translation as Rewriting Rules on Multisets of Objects and Strings

32




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:

33

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




Multicompartmental Gillespie Algorithm

34





1

2

3

34





1

2

3 r11,…,r1

n1

M1

r21,…,r2

n2

M2

r31,…,r3

n3

M3

34





1

2

3 r11,…,r1

n1

M1

r21,…,r2

n2

M2

r31,…,r3

n3

M3

Local Gillespie

34





1

2

3 r11,…,r1

n1

M1

r21,…,r2

n2

M2

r31,…,r3

n3

M3

( 1, τ1, r01)

Local Gillespie

34





1

2

3 r11,…,r1

n1

M1

r21,…,r2

n2

M2

r31,…,r3

n3

M3

( 1, τ1, r01)

( 2, τ2, r02)

Local Gillespie

34





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

34





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

34





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

34





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

‘

34





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

‘

34





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)

‘

34





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

‘

34





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

‘

34




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.

35




Basic P System Modules Used

36




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.




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.




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.




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.


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.

41

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




InfoBiotics Pipeline

42




SBML from CellDesigner

43




Runs simulations and extract data

44




Plot Timeseries

45




in time and space

46




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)

47




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...

48




Single protein represses genep = 1

49




When repression is weak(dissociation rate = 10)

No obvious oscillatory behaviour in single simulation

50




When repression is weak(dissociation rate = 10)

Mean of 100 runs shows convergence to steady state

51




When repression is strong(dissociation rate = 0.1)

Oscillations evident in single simulation

52




When repression is strong(dissociation rate = 0.1)

Averging 100 runs dampens oscillations due to different phases but observable. Protein levels steady.

53




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

54




1. Protein represses as dimer

55




1. Protein represses as dimer

target

mRNA levels oscillate ready but protein accumulates in the cytosol

56




2. Proteins repress cooperatively

57




2. Proteins repress cooperatively

Oscillations are steady and protein levels are controlled

target

58




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




Sending Cells




Pulse Generating Cells




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.


An example: Ron Weiss' Pulse Generator




Outline

64





•Conclusions




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.




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




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.




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.




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




Outline

70





•Conclusions




A (Proto)Cell as an Information Processing Device

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

71




a b

a b

Symport channel

a

a

b

b

Antiport channel

ab

a b

Promoted symport channel (trap)

c

Transport Modalities

72




1

5

4 3

2

Endocitosys

Pinocitosys

Phagocitosys

Exocitosys


73





Highly specific:cell specific & topology specific

74




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

75




‘Talking’ to cell-vesicle aggregates

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

76




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

77




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

78




Dissipative Particle Dynamics

W

W

i

j

P

P

i

j

Conservative Force

Dissipative Force

Random Force

79




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.

80




Liposome Formation in DPD

81




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.

83




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

84




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

86




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.

87




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

89




Outline

90





•Conclusions




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]

91




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

Summary & Conclusions

92




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

93




Any Questions?

•www.infobiotic.org

•www.synbiont.org

•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!!

94

Vacancies:

• PhD in Computational Modeling of root development

• Postdoc on Dissipative Particles Dynamics for ProtoCells



http://www.infobiotic.org

http://www.infobiotic.org

http://www.synbiont.org

http://www.synbiont.org

executable biology tutorial

Education

sant feliu

nxk ecsb

systems life

understanding of life

computational modelingmodeling

dna proteins

brief introduction

information technology