UCI ICS IGB SISL

The Sigmoid Biological Pathway Modeling System

Eric Mjolsnessemj@uci.edu

Scientific Inference Systems Laboratory

Institute for Genomics and Bioinformatics, and

Department of Computer Science

University of California, Irvine USA

http://www.ics.uci.edu/~emj

Based on joint work with Pierre Baldi, Lee Bardwell, Jianlin Cheng, Ben Compani, Andre Levchenko, Lucas Scharenbroich, Trent Su

UCI ICS IGB SISL

Rationale

• Mathematics is still the language of nature– Even in biology, after physical science

• Smooth the process of biology to mathematics to computation and back

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E.g. MAP Kinase Cascade

K3⇒K4K3

*

K2⇒K3

*

K2*⇒K3

*

K2**

K1 ⇒K2

**

K1* ⇒K2

**

K1**

With A. Levchenko, B. Shapiro, B. Wold

J. Ferrell model w/o scaffold

UCI ICS IGB SISL

Biosynthesis of Valine, Leucine and Isoleucine

With Yang, Shapiro, Najdi, Hatfield

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CLV3CLV1

?

Fletcher et al., Science v. 283, 1999

Brand et. al., Science 289, 617-619, (2000)

WUS

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Software architectures for systems biology: Sigmoid & Cellerator

www.sigmoid.org + sourceforgeCheng et al., IEEE Intelligent Systems, May/June 2005

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Autogeneration Architecture

• Schema (UML) to database (SQL, Java)– Reactions, reactants, models, knowledge sources

• Compound reactions to elementary ones• Reactions to dynamical systems

– ODE systems

– Stochastic model sims

• Equilibrium models to dynamical systems

UCI ICS IGB SISL

Reaction type hierarchies

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Multivalued mapping

www.sigmoid.org

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Specialized Cellerator ArrowsCellerator Form Differential Equation Terms {{A1,A2,...,An}aB,hill[options]} d[B]dt=r+vi[Ai]i=1n∑( )nKn+vi[Ai]i=1n∑( )n {{A1,A2,...,AN}aB,GRN[options]} d[B]dt=r1+exp{−(h+Ti[Ai]nii=1N∑)} {{A1,A2,...,AN}aB,GRN[...,Sigmoid→f]} d[B]dt=rf(h+TgAn) {{A1,A2,...,AN}aB, SSystem[options]}

d[B]dt=1τk+[Ai]Ci+i=1n∏−k−[Ai]Ciii=1n∏⎛⎝⎜ ⎞⎠⎟ {S1,S2,...}⇒{P1,P2,...{{A1,A2,...},{I1,I2,...}}E} d[Pi]dt=kcat[E]1+aq()nq∏sqq∏(1+sq)n−1q∏+L(csq)q∏(1+csq)n−1q∏(1+iq)nq∏1+aq()nq∏(1+sq)nq∏+L(1+csq)nq∏(1+iq)nq∏

Cellerator: Shapiro et al., Bioinformatics 19(5):677-678, 2003www.cellerator.info

UCI ICS IGB SISL

SIGMOID Model Explorer (SME)

JGraph

SigmoidPathway DatabasePostgreSQL

Cellerator/kMechSimulation

EngineMathematicaTM

The Internet

Future Expansion:Parameter Optimization,Data Mining, …

DatabaseSchema

UML

SIGMOID Architecture:A Service-Oriented Distributed Computing System for Systems Biology

SBML

AX

gen

Da

tab

as

e

Ac

ce

ss

Mo

de

l T

ran

sla

tio

n

MiddlewareWeb Services (SOAP)

...

Biologists

Bioinformaticians

OJ

B

JL

ink

UCI ICS IGB SISL“Sigmoid” Architecture

UCI ICS IGB SISL

Sigmoid ModelExplorer (SME)

Cheng et al., IEEE Intelligent Systems, May/June 2005

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Connect Reactions and Reactants by Defining the Reactants’ Roles

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Filtered List of Appropriate Biological Reaction Assignments Appears in the Left Panel

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Using the Same Mechanism to Expand the Model

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Graphically Constructed MAP Kinase Model

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MAPK/Scaffold Modeling

MAPKKK (K3)

MAPKK (K2)

MAPK (K1)

Input(s)

Output

Shapiro et al., 1st Int. Conf. Systems Biology, 2000; in Foundations of Systems Biology, MIT Press 2001

UCI ICS IGB SISLReactions in ScaffoldedMAP Kinase Cascade

• Phosphorylation in Solution

• Binding to Scaffold

• Phosphorylation in Scaffold

Kij ⇔

Phi

Ki+1ai+1

K ij+1 i =1,K ,n−1, j =0,K ,aj −1

⎧⎨⎩⎪

⎫⎬⎭⎪

Sp1 ,L , pi =ε,L ,pn

+ K ij ↔ Sp1 ,L ,pi =j ,L ,pn{ } , pi =

ε,0,1,K ,ai , i ≠ j0,1,K ,ai , i = j

⎧⎨⎩

Sp1 ,L , pi−1=j<ai−1, pi =ai ,L ,pn+ K ⇔ Sp1 ,L ,pi−1=j+1, pi =ai ,L ,pn{ }

Sp1 ,L ,pi−1=j<ai−1, pi =ai ,L ,pn→ Sp1 ,L ,pi−1=j+1, pi =ai ,L ,pn{ }

Shapiro et al., 1st Int. Conf. Systems Biology, 2000; in Foundations of Systems Biology, MIT Press 2001

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NFB Oscillations in Cellerator

Hoffmann, Levchenko, Scott, Baltimore. Science 298:1241, 2003A. Levchenko, Cellerator notebook.

UCI ICS IGB SISL

Amino Acid Syntheses

Asp

Thr

KB

Pyr

Leu

Val

Ile

GlycolysisGlucose TCA cycleAla

+

tRNA-Leu

tRNA-Val

tRNA-Ile

tRNA-Ala

tRNA-ThrLys Met

Kmech: Yang, et al. Bioinformatics 21: 774-780, 2005

UCI ICS IGB SISLBiosynthesis of Valine, Leucine

and Isoleucine

Yang et al., Journal of Biological Chemistry, 280(12):11224-32, Mar 25 2005

UCI ICS IGB SISL

∏∏∏ ∏

+++++

+++++=

−−

q

nq

nq

q

nq

nq

q q

nqq

nq

nqq

nq

f icsLas

icscsLass

Y])1()1[(])1()1[(

])1)(()1[(])1()1[( 11

A GeneralizedMWC Modelfor multiple substrates, inhibitors and activators

T R

L Substrate 1

Inhibitor 1

Activator

. ... .. . . ... ..... .. ...

Substrate 2

.. .. ... .. ... .... .... .

Inhibitor 2

GMWC model: Yang et al: to appear, CSB conference 2005MWC: Cf. Changeux and Edelstein, Science 3 June 2005; 308: 1424-142

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Amino Acid Biosynthesis in SME

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Amino Acid Biosynthesis Command Translation

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A Model for the Bifunctional Enzyme AKI-HDHI

UCI ICS IGB SISL

UCI ICS IGB SISL

CLV3/WUS networks

V. Agrawal, B. Shapiro, Caltech

Z

wusclv1

clv3Xdiffusive

YL1diffusive

Jönsson et al., Bioinformatics 21(Suppl. 1):i232-i240 June 2005 (ISMB, 4:35pm Sunday)

UCI ICS IGB SISL

Forthcoming Sigmoid Features• new reaction types

– e.g. for CLV3, calcineurin, p53 models

• model search web page• fixed point/Jacobian/critical point algebra• phase plot options• stochastic simulation• param fitting• p:p interaction database• * federate with other databases

UCI ICS IGB SISL

Autogeneration Architecture

• Schema (UML) to database (SQL, Java)– Reactions, reactants, models, knowledge sources

• Compound reactions to elementary ones• Reactions to dynamical systems

– ODE systems

– Stochastic model sims

• Equilibrium models to dynamical systems

UCI ICS IGB SISL

For more information …• Papers

– Sigmoid: Cheng et al., IEEE Intelligent Systems, May/June 2005– Kmech: Yang, et al. Bioinformatics 21: 774-780, 2005

– Cellerator: Shapiro et al., Bioinformatics 19(5):677-678, 2003

– Amino acid synthesis: Yang et al., Journal of Biological Chemistry, 280(12):11224-32, Mar 25 2005

– Plant Gene Regulatory Nets: Jönsson et al., Bioinformatics 21(Suppl. 1):i232-i240 June 2005

– MAPK Scaffold: Shapiro et al., in Foundations of Systems Biology, MIT Press 2001

• URLs– www.sigmoid.org– www.ics.uci.edu/~emj– www.cellerator.info– www.igb.uci.edu/servers/sb.html

• Sigmoid Sponsor: NIGH BISTI (GM069013)

UCI ICS IGB SISL