25/10/20151Andrew Phillips Simulating Biological Systems in the Stochastic  -calculus Andrew Phillips with Luca Cardelli Microsoft Research, Cambridge UK

25/10/20152Andrew Phillips Biological Computing

25/10/20153Andrew Phillips 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...

25/10/20154Andrew Phillips Programming Biology Languages for complex, parallel computer systems: Languages for complex, parallel biological systems: stochastic  -calculus

25/10/20155Andrew Phillips Reactions vs. Components Traditional modelling: model individual reactions Stochastic  -calculus: model components

25/10/20156Andrew Phillips Build complex models incrementally, by direct composition of simpler components: Compositional Modelling

25/10/20157Andrew Phillips Model Analysis  A mathematical programming language  A range of analysis techniques (types, equivalences, model checking)  Could provide insight into fundamental properties of biological systems

25/10/20158Andrew Phillips 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]

25/10/20159Andrew Phillips Outline  Project Overview  Gene Networks  Immune System Pathway

25/10/201510Andrew Phillips Project Overview

25/10/201511Andrew Phillips 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

25/10/201512Andrew Phillips 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

25/10/201513Andrew Phillips 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...)

25/10/201514Andrew Phillips 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:

25/10/201515Andrew Phillips 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.

25/10/201516Andrew Phillips Gene Networks with Luca Cardelli (MSRC) Ralf Blossey (IRI Lille)

25/10/201517Andrew Phillips Gene with Negative Control let Neg(a,b) = do (Protein(b) | Neg(a,b)) or ?a; Neg(a,b) and Protein(b) = do !b; Protein(b) or rate(a,b,c) = 1.0 u = d = t = 0.1 Neg(a,b) ba  A gene that produces protein b and is blocked by protein a

25/10/201518Andrew Phillips Neg Gate  A Protein can be transcribed at t = 0.1 s -1

25/10/201519Andrew Phillips Neg Gate  Another Protein can be transcribed

25/10/201520Andrew Phillips Neg Gate  And another... x2

25/10/201521Andrew Phillips Neg Gate  A Protein can be degraded at d = s -1 x3

25/10/201522Andrew Phillips Neg Gate  Eventually an equilibrium is reached... x2

25/10/201523Andrew Phillips Neg Gate  Production of Protein stabilises at around 100

25/10/201524Andrew Phillips Repressilator [Elowitz and Leibler, 2000] © 2000 Elowitz, M.B., Leibler. S. A Synthetic Oscillatory Network of Transcriptional Regulators. Nature 403:

25/10/201525Andrew Phillips 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

25/10/201526Andrew Phillips Repressilator: Debugging (1)  One copy of Neg(a,b), Neg(b,c), Neg(c,a)  Any protein can be transcribed at rate 0.1

25/10/201527Andrew Phillips Repressilator: Debugging (2)  Protein(b) can block Neg(b,c) with fast rate 1.0

25/10/201528Andrew Phillips Repressilator: Debugging (3)  Neg(b,c) is blocked. No Protein(c) can be transcribed.

25/10/201529Andrew Phillips Repressilator: Debugging (4)  Protein(a) can block Neg(a,b) with fast rate 1.0

25/10/201530Andrew Phillips Repressilator: Debugging (5)  Neg(a,b) is blocked. No Protein(b) can be transcribed.

25/10/201531Andrew Phillips Repressilator: Debugging (363)  All of Protein(b) eventually degrades at rate  Meanwhile, lots of Protein(a) are transcribed

25/10/201532Andrew Phillips Repressilator: Debugging (2173)  Eventually, Neg(b,c) unblocks at rate  Protein(c) can now be transcribed...

25/10/201533Andrew Phillips Repressilator: Results  Alternate oscillation of proteins: a,c,b,a,c,b...

25/10/201534Andrew Phillips 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) © 2000 Elowitz, M.B., Leibler. S. A Synthetic Oscillatory Network of Transcriptional Regulators. Nature 403:

25/10/201535Andrew Phillips Refined Neg Gate let Neg(a,b) = ( new do (Protein(b) | Neg(a,b)) or !a(u1); Blocked(a,b,u1) ) and Blocked(a,b,u1) = ( new do ?u1; Neg(a,b) or !a(u2); ?u2; Blocked(a,b,u1) ) and Protein(b) = ( do or ?b(u); !u; Protein(b) )  Refined Neg gate with cooperative binding  Same main program: Neg(a,b) | Neg(b,c) | Neg(c,a)

25/10/201536Andrew Phillips Neg Gate with Inhibitor let Negp(a:chan,b:chan,r:chan) = do (Proteinp(b,r) | Negp(a,b,r)) or ?a; Negp(a,b,r) and Proteinp(b:chan,r:chan) = do !b; Proteinp(b,r) or ?r or let Inh(r:chan) = !r; Inh(r) rate(a,b,r) = 1.0 u = d = t = 0.1 Negp(a,b,r) ba r

25/10/201537Andrew Phillips 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):

25/10/201538Andrew Phillips 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):

25/10/201539Andrew Phillips 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)

25/10/201540Andrew Phillips Gene Networks Designed in Silico with Luca Cardelli (Microsoft Research)

25/10/201541Andrew Phillips 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

25/10/201542Andrew Phillips Stochastic  -calculus Model val tB = 0.37 val tB' = val dB = 0.002val unbind = 0.42 let b() = do ( B() | b() ) or ?inhibit(u); b_A(u) and b_A(u:chan) = do !u; b() or ( B() | b_A(u) ) and B() = do or ?bind(u); B_A(u) and B_A(u:chan) = () val tA = 0.20 val dA = val dAB = 0.53 new new let a() = ( A() | a() ) and A() = ( new do or !bind(u); A_B(u) or !inhibit(u); A_b(u) ) and A_b(u:chan) = ?u; A() and A_B(u:chan) = run (a() | b())

25/10/201543Andrew Phillips Bistable Network: Protein A  Gene a can transcribe a new protein A at rate tA

25/10/201544Andrew Phillips Bistable Network: Protein A  Protein A can bind to gene b to inhibit production of protein B

25/10/201545Andrew Phillips  More protein A is transcribed Bistable Network: Protein A u

25/10/201546Andrew Phillips  Protein A can unbind from gene b using private channel u Bistable Network: Protein A u

25/10/201547Andrew Phillips  High proportion of protein A Bistable Network: Protein A

25/10/201548Andrew Phillips  Gene b can transcribe a new protein B with rate tB Bistable Network: Protein B

25/10/201549Andrew Phillips Bistable Network: Protein B  Gene a can transcribe a new protein A at rate tA

25/10/201550Andrew Phillips Bistable Network: Protein B  Protein A can bind with protein B

25/10/201551Andrew Phillips Bistable Network: Protein B  More protein B is transcribed u

25/10/201552Andrew Phillips Bistable Network: Protein B  Complex AB can degrade with rate dAB u

25/10/201553Andrew Phillips Bistable Network: Protein B  High proportion of protein B

25/10/201554Andrew Phillips Bistable Network: Results  Random Initialisation:  Stable Switching:

25/10/201555Andrew Phillips Immune System Modelling: MHC I Antigen Presentation with Luca Cardelli (MSRC) Leonard Goldstein (Cambridge University) Tim Elliott (Southampton University) Joern Werner (Southampton University)

25/10/201556Andrew Phillips 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.

25/10/201557Andrew Phillips MHC I Antigen Presentation  [Copyright 2005 from Immunobiology, Sixth Edition by Janeway et al. Reproduced by permission of Garland Science/Taylor & Francis LLC.] [Copyright 2005 from Immunobiology, Sixth Edition by Janeway et al. Reproduced by permission of Garland Science/Taylor & Francis LLC.]

25/10/201558Andrew Phillips 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.

25/10/201559Andrew Phillips Peptide Selection: Flytrap Model  MHC I captures peptides like a Venus Flytrap. Sensitive to disease peptides only. peptide enters open MHC disease peptide is captured and presented at cell surface non disease peptide escapes

25/10/201560Andrew Phillips Flytrap Model:  -calculus x 200

25/10/201561Andrew Phillips Flytrap Model:  -calculus x 200 x 199 u

25/10/201562Andrew Phillips Flytrap Model:  -calculus x 200 x 199 u

25/10/201563Andrew Phillips Flytrap Model:  -calculus x 200 x 199 u

25/10/201564Andrew Phillips 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 TapasinTransient binding to Tapasin

25/10/201565Andrew Phillips Simplified Flytrap  Similar results obtained with a simpler model  Hypothesis: Tapasin is the 2 nd stage of a 2-stage filter  Perhaps an explanation of system function.

25/10/201566Andrew Phillips 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