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
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