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
The talk has three parts:
1. Briefly introduce molecular biology
2. Computer-based consolidation of molecular biology
3. Our work on helping this happen
Part IBrief Introduction to
Molecular Biology
Pentium II E. Coli
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
Pentium II E. Coli
Pentium II E. Coli
1 micron
Pentium II E. Coli
1 micron1 micron
Inside E. Coli
(1Mbyte)
Inside E. Coli
Ribosomes in operation
Ribosomes translate RNA to Proteins
RNA Polymerase transcribes DNA to RNA
Computationally: A stateless string transducer from the RNA alphabet of nucleic acids to the Protein alphabet of amino acids
(= protein)
Ribosomes in operation
Ribosome operation
Ribosome operation
Ribosome operation
Ribosome operation
Seqeunces and String Transducers
Ribosomes translate RNA to Proteins
RNA Polymerase transcribes DNA to RNA
Molecular Biology in One Slide Sequence: Sequence of DNA and Proteins
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
The talk has three parts:
1. Briefly introduce molecular biology
2. Computer-based consolidation of molecular biology
3. Our work on helping this happen
Part IBrief Introduction to
Molecular Biology
Pentium II E. Coli
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
What about “The Rest” of biology: the function, activityand interaction of molecular systems in cells?
?
Part III An Abstraction for Molecular
Systems
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?
“We have no real ‘algebra’ for describing regulatory circuits across different systems...”
- T. F. Smith (TIG 14:291-293, 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 22:325-326, 1997)
Our Proposal: Molecule as Computational Process
“Cellular Abstractions: Cells as Computation”,
to appear in Nature, September 26th, 2002
A system of interacting molecular entities is described and modelled by a system of interacting computational entities.
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
Towards “Molecule as Process”
1. Use the -calculus process algebra as molecule description language
The -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
-calculus key constructs
Parallel A | B
Choice A ; B
Communication X ! M or X ? Y
Recursion, with state change
P :- … P’…
Molecules as Processes
Molecule Process
Interaction capability Channel
Interaction Communication
Modification State change
Na + Cl < 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.
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
ERK1RAF
GRB2
RTK
RTK
SHC
SOS
RAS
GAP
PP2A
MKK1
GF GF
MP1
MKP1
IEG
IEP
IEP
J F
Molecular systems with -calculus
Can express, qualitatively, the behavior of many complex molecular systems
Cannot express quantitative aspects
Towards “Molecule as Process”
1. Use the -calculus process algebra as molecule description language
2. Provide a biochemistry-oriented stochastic extension (with Corrado Priami)
Stochastic -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(A+B C) = BaseRate *[A]*[B]
[A] = number of A’s willing to communicate with B’s.
[B] = number of B’s willing to communicate with A’s.
BioSPI implementation: -calculus + Gillespie’s algorithm
Gillespie (1977): Accurate stochastic simulation of chemical reactions
The BioSPI system: Compiles (full) calculus
Runtime incorporates Gillespie’s algorithm
0 0.005 0.01 0.015 0.02 0.025 0.030
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global(e1(100),e2(10)).
Na::= e1 ! [] , Na_plus .
Na_plus::= e2 ? [] , Na .
Cl::= e1 ? [] , Cl_minus .
Cl_minus::= e2 ! [] , Cl .
0 0.5 1 1.5 2 2.5 3 3.5 4
x 10-3
0
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100Na + Cl < Na+ + Cl-
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…
Circadian Clocks
J. Dunlap, Science (1998) 280 1548-9
The circadian clock machinery (Barkai and Leibler, Nature 2000)
PR
UTRR
R
R
R_GENE
R_RNAtranscription
translation
degradation
PA
UTRA
A
A
A_GENE
A_RNAtranscription
translation
degradation
Differential rates: Very fast, fast and slow
The machinery in -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::=
1 . (ACTIVATED_TRANSCRIPTION_A | A_RNA) +e ? [] . A_GENE
RNA_A::= TRANSLATION_A + DEGRADATION_mATRANSLATION_A::= utrA ? [] . (A_RNA | A_PROTEIN)DEGRADATION_mA::= degmA ? [] . 0
A_PROTEIN::= (new e1,e2,e3) PROMOTION_A-R + BINDING_R + DEGRADATION_A
PROMOTION_A-R ::= pA!{e2}.e2![]. A_PROTEIN + pR!{e3}.e3![]. A_PRTOEIN
BINDING_R ::= rbs ! {e1} . BOUND_A_PRTOEIN BOUND_A_PROTEIN::= e1 ? [].A_PROTEIN + degpA ? [].e1 ![].0DEGRADATION_A::= degpA ? [].0
A_Gene
A_RNA
A_protein
The machinery in -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::=
2 . (ACTIVATED_TRANSCRIPTION_R | R_RNA) +e ? [] . R_GENE
RNA_R::= TRANSLATION_R + DEGRADATION_mRTRANSLATION_R::= utrR ? [] . (R_RNA | R_PROTEIN)DEGRADATION_mR::= degmR ? [] . 0
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_Gene
R_RNA
R_protein
BioSPI simulation
Robust to random perturbations
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000
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0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000
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A R
The A hysteresis module
The entire population of A molecules (gene, RNA, and protein) behaves as one bi-stable module
A
R
ON
OFF
FastFast
0 100 200 300 400 500 6000
100
200
300
400
500
600A
R
Hysteresis moduleON_H-MODULE(CA)::=
{CA<=T1} . OFF_H-MODULE(CA) + {CA>T1} . (rbs ! {e1} . ON_DECREASE + e1 ! [] . ON_H_MODULE + pR ! {e2} . (e2 ! [] .0 | ON_H_MODULE) + 1 . ON_INCREASE)ON_INCREASE::= {CA++} . ON_H-MODULEON_DECREASE::= {CA--} . ON_H-MODULE
OFF_H-MODULE(CA)::=
{CA>T2} . ON_H-MODULE(CA) + {CA<=T2} . (rbs ! {e1} . OFF_DECREASE + e1 ! [] . OFF_H_MODULE + 2 . OFF_INCREASE )OFF_INCREASE::= {CA++} . OFF_H-MODULEOFF_DECREASE::= {CA--} . OFF_H-MODULE
ON
OFF
Modular cell biology
Build two representations in the -calculus Implementation (how?): molecular level
Specification (what?): functional module level
The circadian specification
R (gene, RNA, protein) processes are unchanged (modular;compositional)
PR
UTRR
R
R
R_GENE
R_RNAtranscription
translation
degradation
ONOFF
Counter_A
BioSPI simulation
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Module, R protein and R RNA
7500 8000 8500 9000 9500 100000
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R (module vs. molecules)
Modular cell biology
Build two representations in the -calculus Implementation (how?): molecular level
Specification (what?): functional module level
Ascribing a function to a biomolecular system ~ equivalence between specification and implementation
Limitation of stochastic - 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
Towards “Molecule as Process”
1. Use the -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)
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
Multi-molecular complexes
Form and break Bind and unbind to molecular scaffolds
The ambient calculus (Cardelli and Gordon)
An ambient is a bounded place where computation happens
Ambient Processes
The ambient calculus (Cardelli and Gordon)
The ambient’s boundary restricts process interactions across it
Ambient Processes
The ambient calculus (Cardelli and Gordon)
Processes can move in and out of ambients
Ambient Processes
Ambient are mobile processes, too !
Compartments as ambients
Cells, vesicles, compartments ~ Ambients
Cell
NucleusP
QR
Rcell [ P | Q | R | nuc [R] ]
Synchronized ambient movement
enter/accept exit/expel merge+/merge-
vesicle[merge- c. P|Q] | lysozome [merge+ c . R|S]
lysozome [P|Q|R|S]
Lysozome
vesicle
Enter, exit, merge ~ Budding-in or -out, endo- or exo-cytosis
merge
enter
exit
merge
Molecules and complexes
Merge, enter, exit (with private channels) ~ Complex formation and breakage,
molecule re-localization
Complex
Mol1
P Q
Mol2
R S
P Q R S
Mol1 [P|merge+ c.Q]Mol2[merge- c. R|S] |
Complex [P|Q|R|S]
enter/accept exit/expel merge+/merge-
Vesicle merging
Vesicle
Cell
Cell
Single substrate reactions:Enzyme and substrate as ambients
Enzyme
S X P
enter
enter
exit
exit
Bi-substrate reactions: Inter-ambient communication
Enzyme
S1 X P1
enter
enter
exit
exit
S2 Y P2
enter
enter
exit
exit
s2s
Example: Multi-cellular system (hypothalamic body
weight control system)
IRS-1
IR
tub
1st ord
er
ARCVMNPVN
2nd
ord
er
PVN PFA LHA
Uterinefunction
Eff
ere
nt
signal
Fat cell mass
Leptin expression
Insulin expression
Insulin resistanceGlucose utilization in adipocytes
POMC*/CART*POMC CART
MSH expressioncleavage
NPY*/AgRP*NPY/AgRP expression
Orexin
PFA
MCHLHA
TRH* CRH* OXY
PVN
Thyroid axis
Hypothalamic Pituitary
Adrenal axis
Energy expenditureFood intake
Aff
ere
nt
signal
Weight gain / Weight loss
Contro
lled
syste
m 2
MSH
MC4
Gs
cAMP,PKA
Gi
NPY
NPYR
AgRP
IRS-1 tub
IR LR
JAK
STAT
LR
JAKSTAT
Inp
ut
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”
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