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Biomolecular Processes as Concurrent Computation:
Modeling Molecular Processes in the -calculus
Process Algebra
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Intracellular biochemical processes
Metabolic pathways
Signal transduction
Transcriptional regulation
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Signal transduction (ST) pathways
Pathways of molecular interactions that provide communication between thecell membrane and intracellular end-points, leading to some change in the
cell.
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Modularat
domain, compone
nt and pathway
level
MAPKKK
MAPKK
MAPK
Multiple connection
s:
feedback, cross talk
G protein receptors Cytokine receptors DNA damage, stress sensorsRT
K
RT
K
RhoA
GCK
RAB
PAK
RAC/Cdc42
?
JNK1/2/3
MKK4/7
MEKK1,2,3,4MAPKKK5
C-ABL
HPK
P38 ///
MKK3/6
MLK/DLK ASK1
G
GG
Ca+2
PYK2
Cell division, Differentiation
Rsk, MAPKAP’s
Kinases, TFs
Inflammation, Apoptosis
TFs, cytoskeletal proteins
PP2A
MOS TLP2
PKA
GAP
GRB2SHC
SOS
RAS
ERK1/2
MKK1/2
RAF
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What is missing from the picture?
Information about Dynamics
Molecular structure
Biochemical detail of interaction
The Power to simulate
analyze
compare
Formal semantic
s
Script:
Characters +PlotMovie
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Our Goal
A formal representation language for molecular processes
• Powerful and essential
• Dynamic and executable (simulation)
• Analyzable (comparative and functional studies)
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The molecule as a computational process
•Represent a structure by its potential behavior: by the process in which it can participate
•Example: An enzyme as the enzymatic reaction process, in which it may participate
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Example: ERK1 Ser/Thr kinase
Binding MP1 molecules
Regulatory T-loop: Change conformation
Kinase site: Phosphorylate Ser/Thr residues
(PXT/SP motifs)
ATP binding site: Bind ATP, and use it for
phsophorylation
Binding to substrates
Structure Process
COOH
Nt lo
be
Cata
lytic co
reC
t lobe
NH2
p-Y
p-T
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The correspondence between molecular and computational
processes
STConcurrent
communicationsystems
Multiple moleculesParallel (concurrent)
computationalprocesses
Molecular interaction(signaling)
Communication
The eff ect of interaction (communication) is tochange future interaction (communication)capabilities of the interacting components
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The -calculus
• A program specifies a network of interacting processes
• Processes are defined by their potential communication activities
• Communication occurs via channels, defined by names
• Communication content: Change of channel names (mobility)
(Milner, Walker and Parrow)
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The -calculus: Formal structure
• Syntax How to formally write a specification?
• Congruence laws When are two specifications the same?
• Reaction rules How does communication occur?
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Syntax: Channels
Channel names x , y
Input x ? y Receiving a channelname y on a channel x
Output x ! y Sending a channelname y on a channel x
Restriction (new x) The scope of channelsmay be restricted
All communication events, input or output, occur on channels
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Syntax: Processes
Processnames
P , Q
Emptyprocess
0 No current or futureactivity
Normalprocess
. P Input or outputpreceding (guarding)process P
Summedprocess
. P + . Q Two mutual exclusiveprocesses
Parallelcomposition(PAR)
P | Q Two processes occur inparallel
Processes are composed of communication events and of other processes
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The -calculus: Reduction rules
COMM:
z replaces y in P
Actions consumed;Alternative
choices discarded
Ready to send
z on x
( … + x ! z . Q ) | (… + x ? y . P) Q | P {z/y}
Ready to
receive y
on x
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Principles for mapping ST to -calculus
Domains, molecules, systems Processes
SYSTEM ::= ERK1 | ERK1 | …ERK1 ::= (new internal_channels)
(Nt_LOBE |CATALYTIC_LOBE |Ct_LOBE)
Y
ERK1
Molecular determinants Global (free) channel names and co-names
T_LOOP (tyr )::= tyr ? (tyr’ ).T_LOOP(tyr’)
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Principles for mapping ST to -calculus
Molecular integrity (molecule) Local channels as unique identifiers
ERK1 ::= (new backbone)(Nt_LOBE |CATALYTIC_LOBE |Ct_LOBE)
ERK1
MEK1
Y
ERK1
MP1
Molecule binding Exporting local channels
mp1 ! {backbone} . backbone ! { … } | mp1 ? {cross_backbone} . cross_backbone ? {…}
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Principles for mapping ST to -calculus
Molecular interaction and modification Communication and change of channel names
tyr ! p-tyr . KINASE_ACTIVE_SITE | … + tyr ? Tyr’ . T_LOOP
KINASE_ACTIVE_SITE | T_LOOP {p-tyr / tyr }
Y
Y
Applied to the RTK-Ras-MAPK mitogenic pathway
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Stochastic -calculus (Priami, 1995)
• Stochastic effects on molecular interaction
• Every channel x or internal communication attached with a delay parameter d
• Delay for each communication is chosen from an exponential distribution with d
• At each time step all enabled communications occur
• (s)PiFCP simulation system
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Circadian Clocks: Implementations
J. Dunlap, Science (1998) 280 1548-9
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The circadian clock machinery(Barkai and Leibler, Nature 2000)
PA PR
UTRA UTRR
RA
A R
A_GENE
A_RNA
R_GENE
R_RNAtranscription
translation
transcription
translation
degradationdegradation
Appropriate behavior requires different rates
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The machinery in -calculus: “A” molecules
Agene_a::= PROMOTED_A + BASAL_A
PROMOTED_A::= pA ? {e} . ACTIVATED_TRANSCRIPTION_A(e)
BASAL_A::= bA ? []. ( Agene_a | AmRNA_a)
ACTIVATED_TRANSCRIPTION_A::=
1 . (ACTIVATED_TRANSCRIPTION_A | AmRNA_a) + e ? [] . Agene_a
AmRNA_a::= TRANSLATION_A + DEGRADATION_mA
TRANSLATION_A::= utrA ? [] . (AmRNA_a | Aprot_A)
DEGRADATION_mA::= degmA ? [] . 0
Aprot_A::= (new e1,e2,e3) PROMOTION_A-R + BINDING_R + DEGRADATION_A
PROMOTION_A-R ::= pA ! {e2} . e2 ! [] . Aprot_A +
pR ! {e3} . e3 ! [] . Aprot_A
BINDING_R ::= rbs ! {e1} . BOUND_Aprot_A
BOUND_Aprot_A::= e1 ! [] . Aprot_A + degpA ? [] .e1 ![] . 0
DEGRADATION_A::= degpA ? [] . 0
Gene
RNA
Protein
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The machinery in -calculus: “R” molecules
Rgene_r::= PROMOTED_R + BASAL_R
PROMOTED_R::= pR ? {e} . ACTIVATED_TRANSCRIPTION_R(e)
BASAL_R::= bR ? []. ( Rgene_r | RmRNA_r)
ACTIVATED_TRANSCRIPTION_R::=
2 . (ACTIVATED_TRANSCRIPTION_R | RmRNA_r) + e ? [] . Rgene_r
RmRNA_r::= TRANSLATION_R + DEGRADATION_mR
TRANSLATION_R::= utrR ? [] . (RmRNA_r | Rprot_R)
DEGRADATION_mR::= degmR ? [] . 0
Rprot_R::= BINDING_R + DEGRADATION_A
BINDING_A ::= rbs ? {e} . BOUND_Rprot_R
BOUND_Rprot_R::= e1 ! [] . Rprot_R
DEGRADATION_R::= degpR ? [] . 0
Gene
RNA
Protein
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sPiFCP simulation
A-R complex
Free A protein Free R protein
R mRNAA mRNA
Robust to a wide range of parameters
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Modular Cell Biology
How to identify and compare modules and prove their function?
• Semantic concept: Two processes are equivalent if can be exchanged within any context without changing system behavior
• Build two representations in the -calculus molecular level (implementation)
functional module level (specification)
• Show the equivalence of both representations by computer simulation
by formal verification
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The circadian clock hysteresis module
A
R
ON
OFF
FastFast
Internal actionCommunication
(reaction)Transition
Rapid accumulation of A(creation+degradation)
OFF ON:CA>= Threshold1
Slow accumulation of A
Inhibition of A(binding with R) ON OFF:
CA<= Threshold2
A
R
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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
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sPiFCP simulation
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R mRNABound R
A module (ON) Free R protein
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The homology of process:Biological formal verification
• Homologous pathways share both components and interaction structure
• The -calculus model includes both structure and dynamics
• Two models can be formally compared to determine the degree of mutual similarity of their behavior (bisimulation)
• A homology measure of molecular processes could determined based on such bisimilarity
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WIS
• Udi Shapiro
• Bill Silverman
• Naama Barkai
TAU
• Eva Jablonka
• Yehuda Ben-Shaul