25/10/20151andrew phillips - 2006 simulating biological systems in the stochastic -calculus andrew...

20/04/23 1Andrew Phillips - 2006

Simulating Biological Systems in the Stochastic

-calculusAndrew Phillips

with Luca Cardelli

Microsoft Research, Cambridge UKhttp://research.microsoft.com/~aphillip/spim


Biological Computing


Modelling Biology The Human Genome project:

Scientists hoped that DNA code would help predict system behaviour Functional meaning of the code is still a mystery

Systems Biology: Understand and precisely describe the behaviour of biological systems

Two complementary approaches: Look at experimental results and “infer” general system properties Build detailed models of systems and test these in the lab

Biological Modelling: Need tools for modelling complex parallel systems. Should also scale up to very large systems. The beginnings of a biological programming language...


Programming BiologyLanguages for complex, parallel computer systems:

Languages for complex, parallel biological systems:

stochastic -calculus


Reactions vs. ComponentsTraditional modelling: model individual reactions

Stochastic -calculus: model components


Build complex models incrementally, by direct composition of simpler components:

Compositional Modelling


Model Analysis A mathematical programming language

A range of analysis techniques (types, equivalences, model checking)

Could provide insight into fundamental properties of biological systems


Related Work Stochastic -calculus proposed by [Priami, 1995]

Used to model and simulate a range of biological systems: RTK MAPK pathway [Regev et al., 2001] Gene Regulation by positive Feedback [Priami et al., 2001] Cell Cycle Control in Eukaryotes [Lecca and Priami, 2003]

First simulator for stochastic -calculus [BioSPI] A subset of -calculus with limited choice Compiles a calculus process to an FCP procedure Executed by the FCP Logix platform [Silverman et al., 1987]


Outline Project Overview

Gene Networks

Immune System Pathway


Project Overview


Graphical Stochastic -calculus

Display stochastic -calculus models as graphs [Phillips and Cardelli, Bioconcur 2005] Helps make the stochastic -calculus more accessible Defined a graphical calculus and graphical execution model Proved equivalent to the stochastic -calculus [Phillips, Cardelli and Castagna, TCSB 2006]

PROVED EQUIVALENT


The Stochastic Pi Machine A simulation algorithm for stochastic -calculus

[Phillips and Cardelli, Bioconcur 2004] Based on standard theory of chemical kinetics [Gillespie 1977] The probability of a reaction is proportional to the rate of the reaction

times the number of reactants. Proved correct with respect to the stochastic -calculus.

PROVED CORRECT


The SPiM Simulator Simulation algorithm mapped to functional code (OCaml / F#)

Used as the basis for implementing the SPiM simulator. [Phillips, SPiM 2006] Correct specification improves confidence in simulation results Close correspondence between formal algorithm and functional code Used in various research centres (UK, France, Italy, Sweden...)

http://research.microsoft.com/~aphillip/spim


Gene Networks Library Proposed a combinatorial library of gene gates

[Blossey, Cardelli, Phillips, TCSB 2006] Used as building blocks to model complex gene networks Explain behaviour of controversial gene networks engineered

in vivo

© 2000 Elowitz, M.B., Leibler. S. A Synthetic Oscillatory Network of Transcriptional Regulators. Nature 403:335-338.


Immune System Modelling Model of MHC Class I Antigen Presentation

A key pathway in the immune system [Goldstein, MPhil Dissertation 2005] Ongoing collaboration with Immunologists at Southampton University [Cardelli, Elliott, Goldstein, Phillips, Werner. In preparation]

© 2003 Nature Reviews Immunology, 3(12):952–96.© 2003 Current Opinion in Immunology, 15:75–81.


Gene Networks

with

Luca Cardelli (MSRC)

Ralf Blossey (IRI Lille)


Gene with Negative Control

let Neg(a,b) = do delay@t; (Protein(b) | Neg(a,b)) or ?a; delay@u; Neg(a,b)

and Protein(b) = do !b; Protein(b) or delay@d

Graph.txt

rate(a,b,c) = 1.0u = 0.0001

d = 0.001t = 0.1

Source.txt

Neg(a,b)

ba

A gene that produces protein b and is blocked by protein a


Neg Gate

A Protein can be transcribed at t = 0.1 s-1


Neg Gate

Another Protein can be transcribed


Neg Gate

And another...

x2


Neg Gate

A Protein can be degraded at d = 0.001 s-1

x3


Neg Gate

Eventually an equilibrium is reached...

x2


Neg Gate

Production of Protein stabilises at around 100

Results


Repressilator [Elowitz and Leibler, 2000]



Repressilator Combination of Neg gates Program: Neg(a,b) | Neg(b,c) | Neg(c,a)

b

Neg(a,b)

Neg(c,a)

Neg(b,c)

ca


Repressilator: Debugging (1)

One copy of Neg(a,b), Neg(b,c), Neg(c,a) Any protein can be transcribed at rate 0.1

Graph.txt



Protein(b) can block Neg(b,c) with fast rate 1.0



Neg(b,c) is blocked. No Protein(c) can be transcribed.



Protein(a) can block Neg(a,b) with fast rate 1.0



Neg(a,b) is blocked. No Protein(b) can be transcribed.



All of Protein(b) eventually degrades at rate 0.001 Meanwhile, lots of Protein(a) are transcribed



Eventually, Neg(b,c) unblocks at rate 0.0001 Protein(c) can now be transcribed...


0

20

40

60

80

100

120

140

0 20000 40000 60000 80000 100000 120000 140000 160000 180000 200000

!a

!b

!c

Repressilator: Results Alternate oscillation of proteins: a,c,b,a,c,b...

Results


Repressilator [Elowitz and Leibler, 2000]

A gene network engineered in live bacteria. Modelled as a simple combination of Neg gates:

Neg(LacI,TetR)

| Neg(TetR,LambdacI)

| Neg(LambdacI,LacI)

| Neg(TetR,GFP)

Source.txt

0

20

40

60

80

100

120

140

160

0 20000 40000 60000 80000 100000 120000 140000 160000 180000 200000

!TetR

!LambdacI

!LacI

!GFP

Results



Refined Neg Gate

let Neg(a,b) = (

new [email protected]

do delay@t; (Protein(b) | Neg(a,b))

or !a(u1); Blocked(a,b,u1)

)

and Blocked(a,b,u1) = (

new [email protected]

do ?u1; Neg(a,b)

or !a(u2); ?u2; Blocked(a,b,u1)

)

and Protein(b) = (

do delay@d

or ?b(u); !u; Protein(b)

)

Graph.txt

Source.txt Refined Neg gate with cooperative binding Same main program: Neg(a,b) | Neg(b,c) | Neg(c,a)


Neg Gate with Inhibitor

let Negp(a:chan,b:chan,r:chan) =

do delay@t; (Proteinp(b,r) | Negp(a,b,r))

or ?a; delay@u; Negp(a,b,r)

and Proteinp(b:chan,r:chan) =

do !b; Proteinp(b,r)

or ?r

or delay@d

let Inh(r:chan) = !r; Inh(r)

Graph.txt

rate(a,b,r) = 1.0u = 0.0001

d = 0.001t = 0.1

Source.txt

Negp(a,b,r)

ba

r


Bacteria Logic Gates [Guet et al., 2002]

3 genes: tetR, lacI, cI 5 promoters: PL1, PL2, PT, P-, P+ 125 possible networks consisting of 3 promoter-gene units 2 inputs: IPTG (represses Tet), aTc (represses Lac) 1 output: GFP (linked to P-)

© 2002 Guet et al. Combinatorial Synthesis of Genetic Networks. Science 296 (5572): 1466 - 1470


Bacteria Logic Gates [Guet et al., 2002]

IPTG and aTc as boolean inputs, GFP as boolean output

© 2002 Guet et al. Combinatorial Synthesis of Genetic Networks. Science 296 (5572): 1466 - 1470


Combinatorial Library of Genes

Model complex gene networks from simpler building blocks. Use simulation to formulate hypotheses about system behaviour.

D038() = tet() | lac() | cI() | gfp()tet() = Negp(TetR,TetR,aTc)lac() = Negp(TetR,LacI,IPTG)cI() = Neg(LacI,lcI)gfp() = Neg(lcI,GFP)

D038() D038() | Inh(aTc)D038() | Inh(IPTG)D038() | Inh(aTc) | Inh(IPTG)


Gene Networks Designed in Silico

with

Luca Cardelli (Microsoft Research)


Evolution in Silico [Francois and Hakim, 2004]

Gene networks can be evolved in silico to perform specific functions, e.g. a bistable switch:

Genes a and b can produce proteins A and B respectively: A and B can bind irreversibly to produce AB, which degrades. A can also bind reversibly to gene b, to inhibit transcription of B


Stochastic -calculus Model

val tB = 0.37 val tB' = 0.027

val dB = 0.002 val unbind = 0.42

let b() =

do delay@tB; ( B() | b() )

or ?inhibit(u); b_A(u)

and b_A(u:chan) =

do !u; b()

or delay@tB'; ( B() | b_A(u) )

and B() =

do delay@dB

or ?bind(u); B_A(u)

and B_A(u:chan) = ()

val tA = 0.20

val dA = 0.002 val dAB = 0.53

new [email protected] new [email protected]

let a() = delay@tA; ( A() | a() )

and A() = (

new u@unbind:chan

do delay@dA

or !bind(u); A_B(u)

or !inhibit(u); A_b(u)

)

and A_b(u:chan) = ?u; A()

and A_B(u:chan) = delay@dAB

run (a() | b())


Bistable Network: Protein A

Gene a can transcribe a new protein A at rate tA



Protein A can bind to gene b to inhibit production of protein B


More protein A is transcribed


u


Protein A can unbind from gene b using private channel u


u


High proportion of protein A



Gene b can transcribe a new protein B with rate tB

Bistable Network: Protein B



Gene a can transcribe a new protein A at rate tA



Protein A can bind with protein B



More protein B is transcribed

u



Complex AB can degrade with rate dAB

u



High proportion of protein B


Bistable Network: Results Random Initialisation:

Stable Switching:


Immune System Modelling:

MHC I Antigen Presentationwith

Luca Cardelli (MSRC)Leonard Goldstein (Cambridge University)

Tim Elliott (Southampton University)Joern Werner (Southampton University)


MHC I Antigen Presentation

A key pathway of the immune system:

MHC I complexes can signal when a cell is infected.

They present peptides (small pieces of virus or bacteria) at the surface of infected cells.

A way of marking infected cells for destruction.

© 2003 Jonathan W. Yewdell, Eric Reits, and Jacques Neefjes. Making sense of mass destruction: quantitating MHC class I antigen presentation. Nature Reviews Immunology, 3(12):952–96.


MHC I Antigen Presentation [Copyright 2005 from Immunobiology, Sixth Edition by Janeway et al. Repro

duced by permission of Garland Science/Taylor & Francis LLC.]


MHC I Assembly MHC I complexes follow an assembly line:

© 2003 Antony N Antoniou, Simon J Powis, and Tim Elliott. Assembly and export of MHC class I peptide ligands. Current Opinion in Immunology, 15:75–81.


Peptide Selection: Flytrap Model

MHC I captures peptides like a Venus Flytrap. Sensitive to disease peptides only.

peptide enters open MHC

disease peptide is capturedand presented at cell surface

non diseasepeptide escapes


Flytrap Model: -calculusx 200

x 200



x 199

u


Simulation Results A specific molecule called Tapasin allows disease peptides to be

rapidly selected in favour of non-disease peptides.

Next steps: Investigate influence of tapasin in the lab. Incrementally build a more detailed immune system model. Construct a minimal functional model of the system.

No Tapasin Always with Tapasin Transient binding to Tapasin


Simplified Flytrap Similar results obtained with a simpler model Hypothesis: Tapasin is the 2nd stage of a 2-stage filter Perhaps an explanation of system function.


Future Plans Improve core SPiM algorithm (scalability, debugging, analysis) Immune System Modelling (Southampton University) Improve the graphical interface for SPiM (ENS Paris) Extend SPiM with membranes Stochastic -calculus and ODEs (IRI Lille, CCBI Cambridge.) Interface SPiM with stochastic analysis tools (Birmingham

University) Collaborate with medical researchers to model and simulate a

range of biological systems Collaborate with pharmaceutical industry to design a next-

generation programming language for Systems Biology

25/10/20151andrew phillips - 2006 simulating biological systems in the stochastic -calculus andrew...

Documents

equivalentandrew phillips

aphillipspimandrew phillips

correctandrew phillips

stochastic pcalculusphillips

stochastic pcalculus

subset of p

graphical calculus

parallel biological