Mobile Process Algebras in Systems Biology New Challenges and Opportunities Corrado Priami University of Trento

1. What we can do 2. Why we want to do it 3. Where we are 4. How we can do it 5. The stochastic pi 6. Its biochemical version 7. The BioSPI tool 8. A success story 9. Concluding remarks AGENDA

What we can do “In Silico” Virtual Distributed Lab for Systems Biology Modeling dynamic evolution of bio-systems Not only structures (genome), but functions Analysis of their properties Causality, Locality, Concurrency, feedback loops Comparison for similar/equivalent behavior Bisimulation based equivalences/Modular Cell Biology Application of knowledge to similar classes of diseases Simulation of time/space evolution Stochastic run-time of languages/Parameter fitness and exploration Predicting behavior Looking at the computational space of models Data bases of (behavior) functionalities Programs as data + a run time engine Connection with high-throughput tools Specifications inferred from actual data

A possible architecture We need biologists to use our tools and this implies 1.We must hide as much formal details as possible from the user, 2.We must include in the framework all the tools they usually work with

A man on the moon vision Programming the cell New computational paradigms, new primitives for programming, new software development tools, new (living) hardware. New drugs development, new genetic therapies, new cell repairing tools, predictive, preventive, personalized medicine First step: complete understanding of living matter functions

Why we want to do it High impact on health and quality of life environmental protection (reduction of in vivo and in vitro experiments) software development (new primitives and paradigms) social and economical models of evolution Living devices: machine are already there (bacteria, eukaryotic cells, etc.). Once we completely understand their physical layer, we only need a hierarchy of software on top of them BUILDING A CELL COMPUTERBUILDING A SOFTWARE INTERPRETATION BUILDING A CELL COMPUTER is BUILDING A SOFTWARE INTERPRETATION ResultInterpretation of the new behavior/ new states ExecutionPerturbation of normal behavior E.coli: smaller than Pentium gate, ~ 1M molecules, ~ 1M ROM, ~ 1M aminoacids PS “Shapiro, Cardelli”

DOE vision goal 1 Identify and characterize the molecular machines of life goal 2 Characterize gene regulatory network goal 3 Characterize the functional repertoire of complex microbial communities in their natural environments at the molecular level goal 4 Develop the computational capabilities to advance understanding of complex biological systems and predict their behavior Systems Biology Gain a comprehensive and predictive understanding of the dynamic, interconnected processes underlying living systems LONG-TERM IMPACT: predictive and preventive medicine, cell models and simulation rationale drug discovery and design, cell models and simulation, cell programming and repair, biocomputing and biocomputers

Where we are On the starting blocks, but … we developed the first tool (BioSPI and Stochastic pi) we applied it to a real case study (inflammatory processes in brain vessels)

How we can do it

What is Systems Biology Leroy Hood (invented systems biology) Building models of biological systems and then tuning/validating them via (high-throughput) experiments that provide feedback. Reductionism is replaced by hypothesis driven investigation. Robin Milner (invented mobile process algebras) Computer science as an experimental science. Computer systems are first modeled (generation of hypothesis), then implemented and tested (experiments) to refine/validate the model (feedback loop). Abstracting from experiments, Systems Biology is Computer Science in the applicative domain of life science

From structures to functions in Biology New vision of biological systems Bio-components as information and computational devices Millions of simultaneous computational threads active (e.g., metabolic networks, gene regulatory networks, signaling pathways). Components interaction changes the future behavior Interactions occur only if components are correctly located (e.g., they are close enough or they are not divided by membranes). Interpreting Bio-components as Processes, Concurrent, Distributed, Mobile Systems have the above characteristics.

Mobile process algebras CompletenessCompositionalityConcurrencyCost TM -calculus -calculus Petri Nets  CCS/CSP Mobile process algebras “Meredith”

Formal models of Bio-Systems Process Algebras for Mobility Compositionality Simple Abstractions Well-developed theory for analysis and verification Tools already developed and available

Compositionality 1. Assign meaning to the basic graphical notations 2. Interpret them as process calculi primitives 3. Compose the processes to formally specify the whole system

The pi-calculus

MoleculeProcess Interaction capability Channel InteractionCommunication Modification State and/or channel change Modeling paradigm of bio-components With the same principles specify chemistry, organic chemistry, enzymatic reactions, metabolic pathways, signal-transduction pathways… and ultimately the entire cell.

Molecule --- Processes Compartments --- Private names and scope SYSTEM ::= … | ERK1 | ERK1 | … | MEK1 | MEK1 | … ERK1 ::= ( new internal_channels) (Nt_LOBE |CATALYTIC_CORE |Ct_LOBE) ERK1 Domains, molecules, systems ~ Processes Compartments, membranes ~ Restriction “Shapiro”

Interaction capability --- Global channels Change of future interactions --- mobility “Shapiro” Molecular interaction and modification ~ Communication and change of channel names p-tyr replaces tyr KINASE_ACTIVE_SITE | T_LOOP {p-tyr / tyr} Actions consumed alternatives discarded tyr ! [p-tyr]. KINASE_ACTIVE_SITE + … | … + tyr ? [tyr]. T_LOOP Y ERK1MEK1 Ready to send p-tyr on tyr ! Ready to receive on tyr ? pY

The stochastic pi-calculus Biology is driven by quantities (e.g., energy, time, affinity, distance, amount of components). Stochastic variant of process algebras must be considered Simulation techniques come into play

Syntax and semantics We associate the single parameter r in (0, ∞] of an exponential distribution to each prefix  ; it describes the stochastic behavior of the activity .P is replaced by ( , r).P The delay of the activity (x, r) is a random variable with an exponential distribution. Exponential distribution guarantees the memoryless property: the time at which a change of state occurs is independent of the time at which the last change of state occurred. Bang “!” is replaced by constant definition and the structural congruence accordingly extended with A(y) congruent to P{y/x} if A(x) = P is the unique defining equation of constant A with x = fn(P) Race condition is defined in a probabilistic competitive context: all the activities that are enabled in a state compete and the fastest one succeeds.

Stochastic TS and CTMC A transition system is an oriented graph that connects the states through which a process can pass with arcs called transitions and possibly labeled with information on the activities that causes the state change. TS resembles stochastic (Markov) processes except that TS can have pair of states connected by more than one transition. (A, r) TS (A, 2r) CTMC Simple Graph Manipulation

Biochemical stochastic pi-calculus Gillespie (1977): Accurate stochastic simulation of chemical reactions Modification of the race condition and actual rate calculation according to biochemical principles “Shapiro” The actual rate of a reaction between two proteins is determined according to a basal rate and the concentrations or quantities of the reactants

Biochemical stochastic pi-calculus Reduction Semantics

Biochemical stochastic pi-calculus Computing rates according to bio intuition Inductively counts the number of receive operations Enabled on the channel x.

The BioPSI system Compiles (full) pi calculus to FCP/Logix Incorporates Gillespie’s algorithm in the runtime engine

BioSPI Transcriptional regulation by positive feedback

 Interphase  G1: growth phase, synthesis of organelles  S: synthesis of DNA (replication)  G2: growth; synthesis of proteins essential to cell division Cycle duration in human liver cellsG1 9 h S 10 h G2 2 h M 50 min Eukaryotic cell cycle  Mitosis  prophase  methaphase  anaphase  telophase

Nasmyth’s model (1996) START At START a cells confirms that internal and external conditions are favorable for a new round of DNA synthesis and division and commits itself to the process. STARTFINISH Cycle with two states (G1 and S-G2-M) separated by two irreversible transitions START and FINISH. FINISH When DNA replication is complete and all the chromosomes are aligned, the second transition of the cycle (FINISH) drives the cell in anaphase. CDK = Cyclin-Dependent Kinase; APC = Anaphase-Promoting Complex START START is triggered by the activity of a protein kinase (CDK) associated with a cyclin subunit. FINISH FINISH is accomplished by proteolytic machinery (APC) that inhibits the activity of cyclin/CDK dimer.

The molecular mechanism  APC destroys CDK activity degrading cyclin and  cyclin/CDK dimers inactivate APC by phosphorilating some of its subunits. CDK = Cyclin Dependent Kinase APC = Anaphase Promoting Complex CKI = Cyclin-dependent Kinase Inhibitor degraded cyclin degraded CKI START FINISH CDK activity drives cell through S phase, G2 phase and up to the metaphase Moreover, cyclin/CDK dimers can be put out of commission also by the stoichiometric binding with an inhibitor (CKI) CDK and APC are antagonistic proteins:

Fundamental antagonism The APC extinguishes CDK activity by destroying its cyclin partners, whereas cyclin/CDK dimers inhibit APC activity by phosphorilating CDH1. Two alternative stable steady states of the cell cycle:  G1 state with high CDH1/APC activity and low cyclin/CDK activity  S-G2-M state with high cyclin/CDK activity and low CDH1/APC activity. 12 polypeptides + 2 auxiliary proteins CDH1 and CDC20 APC CDC20

CDK – APC antagonism specification

BioSPI specification specification SYSTEM = CYCLIN | CDK | CDH1 | CDC14 | CKI | CLOCK

BioSPI Simulations Time (min) N. of molecules CYCLIN_BOUND Fictious values for the initial number of molecules !

16 molecular species 24 domains; 15 sub-domains Four cellular compartments Binding, dimerization, phosphorylation, de-phosphorylation, conformational changes, translocation ~100 literature articles 250 lines of code ERK1 RAF GRB2 RTK SHC SOS RAS GAP PP2A MKK1 GF MP1 MKP1 IEG IEP JF The RTK-MAPK pathway

A success story A simulation of extra-vasation in multiple sclerosis has highlighted a new behavior of leukocytes proved in lab experiments a posteriori Selectins/Mucins PSGL -1/E & P-Selectin Integrins a 4 b 1 / VCAM-1 LFA-1/ICAM-1 lymphocyte 1. Tethering and rolling 2. Firm arrest 3. Diapedesis Activation of G protein Activation of integrins Hematic flow Endotheliu m

Implementation

Simulation

Results Prediction of rolling cells percentage as a function of vessel diameters

Recent evolutions First attempt: lambda-calculus Buss, Fontana -- no concurrency Second attempt: (stochastic) pi-calculus Priami, Regev, Shapiro, Silvermann Then: BioAmbients, Brane Calculi -- Cardelli et al. Core Formal Biology, CCS-R -- Danos et al. Beta binders -- Priami, Quaglia

Conclusions Unique opportunity to change future life science, but also future computer science We have a lot to do, but we are in the position to win the challenge, if we establish a P2P collaboration between BIO and IT we find a common language and common expectations we set up interdisciplinary curricula and carry out interdisciplinary research projects

Acknowledgements: Bioinformatics group at the University of Trento: Corrado Priami, Paola Quaglia Daniel Errampalli, Katerina Pokozy Federica Ciocchetta, Claudio Eccher, Paola Lecca, Radu Mardare, Davide Prandi, Debora Schuch da Rosa, Alex Vagin Alessandro Romanel