Boolean Networks and Boolean Networks and BiologyBiology

Peter LeePeter Lee

Shaun LippowShaun Lippow

BE.400 Final ProjectBE.400 Final Project

December 10, 2002December 10, 2002

IntroductionIntroduction Need quantitative analysis to understand Need quantitative analysis to understand

complex biological networkscomplex biological networks What mathematical framework is What mathematical framework is

appropriate for analysis? Depends...appropriate for analysis? Depends... Case 1: Detailed knowledge of biochemical Case 1: Detailed knowledge of biochemical

mechanismsmechanisms Case 2: Data imply connectivities, but Case 2: Data imply connectivities, but

molecular details unknownmolecular details unknown

BiochemicalMechanismsCauses Effects

Model with system of differential equationsModel with system of differential equations 2 types of dynamics2 types of dynamics

Analog: ODE crucial to describe key featuresAnalog: ODE crucial to describe key features Discrete: steady-states capture behavior; Discrete: steady-states capture behavior;

ODE is sufficient but not necessaryODE is sufficient but not necessary Can be abstracted to Boolean algebra, where Can be abstracted to Boolean algebra, where

new framework offers new insights while new framework offers new insights while retaining analysis capabilitiesretaining analysis capabilities

Where does Boolean fit in?Where does Boolean fit in? Case 1: Detailed knowledge ofCase 1: Detailed knowledge of

biochemical mechanismsbiochemical mechanisms

Where does Boolean fit in?Where does Boolean fit in? Case 2: Data imply connectivities, but Case 2: Data imply connectivities, but

molecular details unknownmolecular details unknown When data show only two steady-states, When data show only two steady-states,

cause and effect relationships can be cause and effect relationships can be modeled with Boolean logic functionsmodeled with Boolean logic functions

AA BB CC

State State 11

State State 11

State State 11

State State 11

State State 22

State State 22

State State 22

State State 11

State State 11

State State 22

State State 22

State State 11

A B

C

A B

C

OutlineOutline

A model biochemical network (Case 1)A model biochemical network (Case 1) Demonstrate that biochemical kinetics can Demonstrate that biochemical kinetics can

produce Boolean behavior at the steady-state, produce Boolean behavior at the steady-state, input-output levelinput-output level

Motivates use of Boolean algebra framework Motivates use of Boolean algebra framework when cause/effect data shows 2 stateswhen cause/effect data shows 2 states

Boolean network modeling (Case 2)Boolean network modeling (Case 2) Caspase cascadeCaspase cascade

Boolean with HT ExperimentsBoolean with HT Experiments

The Biochemical NetworkThe Biochemical NetworkOverviewOverview

E1X1

I1

E3

X2

I2E2

S1

X3S2

E4X4S3

E1+2X3 E1X3 E1+2X1

ka1

kd1

kr1

E2+2X1 E2X1

ki1

k-i1+

X1+I1 X1I1kin1 X1

kdeg1

2

2

Governing EquationsGoverning Equations

Inputs: I1, I2

Output: x4

SimulationSimulation

Mathematical AnalysisMathematical Analysis

Conclusions from Biochemical Conclusions from Biochemical NetworkNetwork

Network was based on known Network was based on known biochemical mechanismsbiochemical mechanisms

Demonstrated feasibility of a Demonstrated feasibility of a biochemical network performing biochemical network performing Boolean operationsBoolean operations

Motivates use of Boolean framework Motivates use of Boolean framework for analyzing data that shows two for analyzing data that shows two discrete steady-state levelsdiscrete steady-state levels

Caspase Cascade in Caspase Cascade in ApoptosisApoptosis

Intrinsic Extrinsic

Death

•Missing some mechanistic detail

•Data show 2 steady-states

Previous Caspase ModelingPrevious Caspase Modeling

Details of underlying mechanisms and Details of underlying mechanisms and important parameters were unknown, but important parameters were unknown, but Bailey attempted to model the cascade Bailey attempted to model the cascade with a set of differential equations coupled with a set of differential equations coupled with specialized functions.with specialized functions.

Their goal was to obtain qualitative results Their goal was to obtain qualitative results in the form of identifying combinations of in the form of identifying combinations of drug targets to inhibit apoptosis despite drug targets to inhibit apoptosis despite both intrinsic and extrinsic death signals.both intrinsic and extrinsic death signals.

Previous ResultsPrevious Results

Boolean NetworkBoolean Network

Our Updated Model Our Updated Model (Boolean)(Boolean)

AnalysisAnalysis

Mathematical manipulationMathematical manipulation Extract how output depends on inputExtract how output depends on input Blake Canonical FormBlake Canonical Form

Caspase-Dependent Death =Caspase-Dependent Death =External Death Signal External Death Signal ANDAND not FLIPs not FLIPs ANDAND not IAPs not IAPs

ORORCell Damage Cell Damage ANDAND not ARC not ARC ANDAND not IAPs not IAPs

Model with Drug TargetsModel with Drug Targets

Drug Target AnalysisDrug Target Analysis

without drugs: ab’d’ without drugs: ab’d’ ۷۷ cd’e’cd’e’ with drugs: ab’d’ with drugs: ab’d’ ۷۷ [cd’e’[cd’e’۸ ۸ (f(f11’ ’ ۷۷ ff22’)]’)]

a = external death signala = external death signal ff11 = knockout drug 1 = knockout drug 1

b = FLIPsb = FLIPs ff22 = knockout drug 2 = knockout drug 2

c = cell damagec = cell damage

d = decoy substratesd = decoy substrates

e = ARCe = ARC

Our OpinionOur Opinion

Yes, we actually think that this is Yes, we actually think that this is useful and applies to some biological useful and applies to some biological systems.systems.

Governing EquationsGoverning EquationsParameter Set 2Parameter Set 2

423

4

322

3

22221

2

11123

231

1

10

1

10

101

10

1051

5

xxdt

dx

xxdt

dx

Ixxxdt

dx

Ixxx

x

dt

dx

Inputs: I1, I2

Output: x4

SimulationSimulation

Mathematical AnalysisMathematical Analysis

Imagine…Imagine…

Boolean with HT Boolean with HT ExperimentsExperiments