Molecule as Computation

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Molecule as Computation
Ehud Shapiro Weizmann Institute of Science Joint
work with Aviv Regev and Bill Silverman In
collaboration with Corrado Priami, Naama Barkai
and Luca Cardelli
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The talk has three parts

1. Briefly introduce molecular biology
2. Computer-based consolidation of molecular biology
3. Our work on helping this happen

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Part IBrief Introduction to Molecular Biology
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Pentium II E. Coli
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Pentium II E. Coli

• 1 million macromolecules
• 1 million bytes of static genetic memory
• 1 million amino-acids per second

• 3 million transistors
• 1/4 million bytes of memory
• 80 million operations per second

Comparison courtesy of Eric Winfree
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Pentium II E. Coli
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Pentium II E. Coli
1 micron
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Pentium II E. Coli
1 micron
1 micron
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Inside E. Coli
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Inside E. Coli
(1Mbyte)
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Ribosomes in operation

• Ribosomes translate RNA to Proteins
• RNA Polymerase transcribes DNA to RNA

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Ribosomes in operation
( protein)
Computationally A stateless string transducer
from the RNA alphabet of nucleic acids to the
Protein alphabet of amino acids
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Ribosome operation
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Ribosome operation
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Ribosome operation
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Ribosome operation
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Seqeunces and String Transducers

• Ribosomes translate RNA to Proteins
• RNA Polymerase transcribes DNA to RNA

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Molecular Biology in One Slide

• Sequence Sequence of DNA and Proteins

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Molecule as Computation
Ehud Shapiro Weizmann Institute of Science Joint
work with Aviv Regev and Bill Silverman In
collaboration with Corrado Priami, Naama Barkai
and Luca Cardelli
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The talk has three parts

1. Briefly introduce molecular biology
2. Computer-based consolidation of molecular biology
3. Our work on helping this happen

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Part IBrief Introduction to Molecular Biology
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Pentium II E. Coli
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Pentium II E. Coli

• 1 million macromolecules
• 1 million bytes of static genetic memory
• 1 million amino-acids per second

• 3 million transistors
• 1/4 million bytes of memory
• 80 million operations per second

Comparison courtesy of Eric Winfree
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What about The Rest of biology the function,
activityand interaction of molecular systems in
cells?
?
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Part III An Abstraction for Molecular Systems
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The New Biology

• The cell as an information processing device
• Cellular information processing and passing are
  carried out by networks of interacting molecules
• Ultimate understanding of the cell requires an
  information processing model
• Which?

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• We have no real algebra for describing
  regulatory circuits across different systems...
• - T. F. Smith (TIG 14291-293, 1998)
• The data are accumulating and the computers are
  humming, what we are lacking are the words, the
  grammar and the syntax of a new language
• - D. Bray (TIBS 22325-326, 1997)

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Our Proposal Molecule as Computational Process
A system of interacting molecular entities is
described and modelled by a system of interacting
computational entities.
Cellular Abstractions Cells as Computation,
to appear in Nature, September 26th, 2002
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Composition of two processes is a process,
therefore

• Molecular ensembles as processes
• Molecular networks as processes
• Cells as processes (virtual cell)
• Multi-cellular organisms as processes
• Collections of organisms as processes

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Towards Molecule as Process

1. Use the p-calculus process algebra as molecule
   description language

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The p-calculus (Milner, Walker and Parrow 1989)

• A program specifies a network of interacting
  processes
• Processes are defined by their potential
  communication activities
• Communication occurs on complementary channels,
  identified by names
• Message content Channel name

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p-calculus key constructs
Parallel A B
Choice A B
Communication X ! M or X ? Y
Recursion, with state change P - P
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Molecules as Processes
Molecule Process
Interaction capability Channel
Interaction Communication
Modification State change
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Na Cl lt? Na Cl-

• Na Na Na Cl Cl Cl
• Na e ! , Na_plus .
• Na_plus e ? , Na .
• Cl e ? , Cl_minus .
• Cl_minus e ! , Cl .

Processes, guarded communication, alternation
between two states.
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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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Molecular systems with p-calculus

• Can express, qualitatively, the behavior of many
  complex molecular systems
• Cannot express quantitative aspects

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Towards Molecule as Process

1. Use the p-calculus process algebra as molecule
   description language
2. Provide a biochemistry-oriented stochastic
   extension (with Corrado Priami)

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Stochastic p-Calculus (Priami, 1995, Regev,
Priami, Shapiro, Silverman 2000)

• Every channel x attached with a base rate r
• A global (external) clock is maintained
• The clock is advanced and a communication is
  selected according to a race condition
• Rate calculation and race condition adapted for
  chemical reactions
• Rate(AB ? C) BaseRate AB
• A number of As willing to communicate with
  Bs.
• B number of Bs willing to communicate with
  As.

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BioSPI implementation p-calculus Gillespies
algorithm

• Gillespie (1977) Accurate stochastic simulation
  of chemical reactions
• The BioSPI system
• Compiles (full) p-calculus
• Runtime incorporates Gillespies algorithm

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Na Cl lt? Na Cl-

• global(e1(100),e2(10)).
• Na e1 ! , Na_plus .
• Na_plus e2 ? , Na .
• Cl e1 ? , Cl_minus .
• Cl_minus e2 ! , Cl .

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Programming Experience with Stochastic Pi
Calculus

• Taught semesterial M.Sc. Course (available
  online) with lots of examples, exercises and
  final projects
• Textbook examples from chemistry, organic
  chemistry, enzymatic reactions, metabolic
  pathways, signal-transduction pathways

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Circadian Clocks
J. Dunlap, Science (1998) 280 1548-9
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The circadian clock machinery (Barkai and
Leibler, Nature 2000)
Differential rates Very fast, fast and slow
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The machinery in p-calculus A molecules
A_GENE PROMOTED_A BASAL_APROMOTED_A pA ?
e.ACTIVATED_TRANSCRIPTION_A(e)BASAL_A bA ?
.( A_GENE A_RNA)ACTIVATED_TRANSCRIPTION_A
t1 . (ACTIVATED_TRANSCRIPTION_A A_RNA) e ?
. A_GENE
A_Gene
RNA_A TRANSLATION_A DEGRADATION_mATRANSLATIO
N_A utrA ? . (A_RNA A_PROTEIN)DEGRADATION
_mA degmA ? . 0
A_RNA
A_PROTEIN (new e1,e2,e3)
PROMOTION_A-R BINDING_R DEGRADATION_APROMOTIO
N_A-R pA!e2.e2!. A_PROTEIN
pR!e3.e3!. A_PRTOEINBINDING_R rbs !
e1 . BOUND_A_PRTOEIN BOUND_A_PROTEIN e1 ?
.A_PROTEIN degpA ? .e1 !.0DEGRADATION_A
degpA ? .0
A_protein
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The machinery in p-calculus R molecules
R_GENE PROMOTED_R BASAL_RPROMOTED_R pR ?
e.ACTIVATED_TRANSCRIPTION_R(e)BASAL_R bR ?
.( R_GENE R_RNA)ACTIVATED_TRANSCRIPTION_R
t2 . (ACTIVATED_TRANSCRIPTION_R R_RNA) e ?
. R_GENE
R_Gene
RNA_R TRANSLATION_R DEGRADATION_mRTRANSLATIO
N_R utrR ? . (R_RNA R_PROTEIN)DEGRADATION
_mR degmR ? . 0
R_RNA
R_PROTEIN BINDING_A DEGRADATION_RBINDING_R
rbs ? e . BOUND_R_PRTOEIN
BOUND_R_PROTEIN e1 ? . A_PROTEIN degpR
? .e1 !.0DEGRADATION_R degpR ? .0
R_protein
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BioSPI simulation
A
R
Robust to random perturbations
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The A hysteresis module
A
A
ON
Fast
Fast
OFF
R
R

• The entire population of A molecules (gene, RNA,
  and protein) behaves as one bi-stable module

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Hysteresis module
ON_H-MODULE(CA) CAltT1 . OFF_H-MODULE(CA)
CAgtT1 . (rbs ! e1 . ON_DECREASE
e1 ! . ON_H_MODULE pR ! e2 . (e2 !
.0 ON_H_MODULE) t1 . ON_INCREASE) ON_INCRE
ASE CA . ON_H-MODULEON_DECREASE CA--
. ON_H-MODULE
ON
OFF_H-MODULE(CA) CAgtT2 . ON_H-MODULE(CA)
CAltT2 . (rbs ! e1 . OFF_DECREASE
e1 ! . OFF_H_MODULE t2 .
OFF_INCREASE ) OFF_INCREASE CA .
OFF_H-MODULEOFF_DECREASE CA-- . OFF_H-MODULE
OFF
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Modular cell biology

• Build two representations in the p-calculus
• Implementation (how?) molecular level
• Specification (what?) functional module level

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The circadian specification
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BioSPI simulation
Module, R protein and R RNA
R (module vs. molecules)
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Modular cell biology

• Build two representations in the p-calculus
• Implementation (how?) molecular level
• Specification (what?) functional module level
• Ascribing a function to a biomolecular system
  equivalence between specification and
  implementation

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Limitation of stochastic p- calculus Lack of
location information

• Membranes Cells and cellular compartments,
  inside and outside
• Molecular proximity The identity of complexes
  and single molecules
• Limited solution programming tricks

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Towards Molecule as Process

1. Use the p-calculus process algebra as molecule
   description language
2. Provide a biochemistry-oriented stochastic
   extension (with Corrado Priami)
3. Provide an Ambient Calculus extension (with Luca
   Cardelli)

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Mobile compartments
Compartment Compartment mobility Process mobility
Cells Cell movement Trans-membranal molecules (receptors, channels, transporters) Molecule entry and exit
Organelles and vesicles Merging, budding, bursting Trans-membranal molecules (receptors, channels, transporters) Molecule entry and exit
Multi-molecular complexes Form and break Bind and unbind to molecular scaffolds
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The ambient calculus (Cardelli and Gordon)

• An ambient is a bounded place where computation
  happens

Ambient
Processes
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The ambient calculus (Cardelli and Gordon)

• The ambients boundary restricts process
  interactions across it

Ambient
Processes
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The ambient calculus (Cardelli and Gordon)

• Processes can move in and out of ambients

Ambient
Processes
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Compartments as ambients
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Synchronized ambient movement
enter/accept exit/expel merge/merge-
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Molecules and complexes
enter/accept exit/expel merge/merge-
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Vesicle merging
Vesicle
Cell
Cell
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Single substrate reactionsEnzyme and substrate
as ambients
Enzyme
enter
exit
S
X
P
exit
enter
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Bi-substrate reactions Inter-ambient
communication
Enzyme
enter
exit
S1
X
P1
exit
enter
s2s
enter
exit
S2
Y
P2
exit
enter
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Example Multi-cellular system (hypothalamic body
weight control system)
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2
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Conclusions

• The most advanced tools for computer process
  description seem to be also the best tools for
  the description of biomolecular systems
• This intellectual economy validates the
  decades-long study of concurrency in computer
  science
• An essential foundation for the forthcoming
  Virtual Cell Project