Biomolecular Processes as Concurrent Computation:

Modeling Molecular Processes in the -calculus

Process Algebra

Intracellular biochemical processes

Metabolic pathways

Signal transduction

Transcriptional regulation

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.

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

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

Our Goal

A formal representation language for molecular processes

• Powerful and essential

• Dynamic and executable (simulation)

• Analyzable (comparative and functional studies)

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

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

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

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)

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?

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

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

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

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’)

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 ? {…}

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

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

Circadian Clocks: Implementations

J. Dunlap, Science (1998) 280 1548-9

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

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

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

sPiFCP simulation

A-R complex

Free A protein Free R protein

R mRNAA mRNA

Robust to a wide range of parameters

0 1000 2000 3000 4000 5000 6000 70000

50

100

150

200

250

300

350

400

0 1000 2000 3000 4000 5000 6000 70000

100

200

300

400

500

600

0 1000 2000 3000 4000 5000 6000 70000

10

20

30

40

50

60

70

0 1000 2000 3000 4000 5000 6000 70000

10

20

30

40

50

60

70

80

90

0 1000 2000 3000 4000 5000 6000 70000

50

100

150

200

250

300

350

400

450

500

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

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

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

sPiFCP simulation

0 1000 2000 3000 4000 5000 60000

50

100

150

200

250

300

350

400

0 1000 2000 3000 4000 5000 60000

50

100

150

200

250

300

350

400

450

0 1000 2000 3000 4000 5000 60000

10

20

30

40

50

60

70

0 1000 2000 3000 4000 5000 60000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

R mRNABound R

A module (ON) Free R protein

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

WIS

• Udi Shapiro

• Bill Silverman

• Naama Barkai

TAU

• Eva Jablonka

• Yehuda Ben-Shaul