Mobile Process Algebras in Systems Biology

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Mobile Process Algebras in Systems Biology
Corrado Priami University of Trento

• New Challenges and Opportunities

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AGENDA

• 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

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What we can do
In Silico Virtual Distributed Lab for Systems
Biology

• Modeling dynamic evolution of bio-systems
• Not only structures (genome), but functions

• Simulation of time/space evolution
• Stochastic run-time of languages/Parameter
  fitness and exploration

• 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

• 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

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A possible architecture

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

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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
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Why we want to do it
Shapiro, Cardelli
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
E.coli smaller than Pentium gate, 1M
molecules, 1M ROM, 1M aminoacids PS
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 COMPUTER is BUILDING A SOFTWARE
INTERPRETATION
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DOE vision
Systems Biology Gain a comprehensive and
predictive understanding of the dynamic,
interconnected processes underlying living systems
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
LONG-TERM IMPACT predictive and preventive
medicine, rationale drug discovery and
design, cell models and simulation, cell
programming and repair, biocomputing and
biocomputers
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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)

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How we can do it
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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
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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.
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Mobile process algebras
Meredith
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Formal models of Bio-Systems

• Process Algebras for Mobility
• Compositionality
• Simple Abstractions
• Well-developed theory for analysis and
  verification
• Tools already developed and available

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Compositionality

• Assign meaning to the basic graphical notations
• Interpret them as process calculi primitives
• Compose the processes to formally specify the
  whole system

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The pi-calculus
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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.
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Molecule --- ProcessesCompartments --- Private
names and scope
Shapiro
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Interaction capability --- Global channelsChange
of future interactions --- mobility
Shapiro
Molecular interaction and modification
Communication and change of channel names
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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
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Syntax and semantics

• We associate the single parameter r in (0, 8 of
  an exponential distribution to each
• prefix p it describes the stochastic behavior of
  the activity
• p.P is replaced by (p, 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.

Race condition is defined in a probabilistic
competitive context all the activities that are
enabled in a state compete and the fastest one
succeeds.
Bang ! is replaced by constant definition and
the structural congruence accordingly extended
with A(y) congruent to Py/x if
A(x) P is the unique defining equation of
constant A with x fn(P)
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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.
Simple Graph Manipulation
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Biochemical stochastic pi-calculus
Shapiro

• Gillespie (1977) Accurate stochastic simulation
  of
• chemical reactions
• Modification of the race condition and actual
  rate
• calculation according to
  biochemical principles

The actual rate of a reaction between
two proteins is determined according to a basal
rate and the concentrations or quantities of the
reactants
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Biochemical stochastic pi-calculus
Reduction Semantics
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Biochemical stochastic pi-calculus
Inductively counts the number of receive
operations Enabled on the channel x.
Computing rates according to bio intuition
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The BioPSI system
Compiles (full) pi calculus to FCP/Logix Incorpor
ates Gillespies algorithm in the runtime engine
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Transcriptionalregulationby positivefeedback
BioSPI
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Eukaryotic cell cycle

• Interphase
• G1 growth phase, synthesis of organelles
• S synthesis of DNA (replication)
• G2 growth synthesis of proteins essential to
  cell division

• Mitosis
• prophase
• methaphase
• anaphase
• telophase

Cycle duration in human liver cells
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Nasmyths model (1996)
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.
Cycle with two states (G1 and S-G2-M) separated
by two irreversible transitions START and FINISH.
START is triggered by the activity of a protein
kinase (CDK) associated with a cyclin subunit.
When DNA replication is complete and all the
chromosomes are aligned, the second transition of
the cycle (FINISH) drives the cell in anaphase.
FINISH is accomplished by proteolytic machinery
(APC) that inhibits the activity of cyclin/CDK
dimer.
CDK Cyclin-Dependent Kinase APC
Anaphase-Promoting Complex
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The molecular mechanism
CDK activity drives cell through S phase, G2
phase and up to the metaphase
CDK and APC are antagonistic proteins

• APC destroys CDK activity degrading cyclin and
• cyclin/CDK dimers inactivate APC by
  phosphorilating some of its subunits.

Moreover, cyclin/CDK dimers can be put out of
commission also by the stoichiometric binding
with an inhibitor (CKI)
CDK Cyclin Dependent Kinase APC Anaphase
Promoting Complex CKI Cyclin-dependent Kinase
Inhibitor
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Fundamental antagonism
CDC20
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.

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CDK APC antagonism specification
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BioSPI specification specification
SYSTEM CYCLIN CDK CDH1 CDC14 CKI CLOCK
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BioSPI Simulations
CYCLIN_BOUND
Fictious values for the initial number of
molecules
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The RTK-MAPK pathway

• 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

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A success story
A simulation of extra-vasation in multiple
sclerosis has highlighted a new behavior of
leukocytes proved in lab experiments a posteriori
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Implementation
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Simulation
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Results
Prediction of rolling cells percentage as a
function of vessel diameters
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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
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Conclusions
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
Unique opportunity to change future life
science, but also future computer science
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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
www.dit.unitn.it/bioinfo