Download Boolean Networks and Biology

Boolean Networks and Biology
Peter Lee
Shaun Lippow
BE.400 Final Project
December 10, 2002
Introduction
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Need quantitative analysis to understand
complex biological networks
What mathematical framework is appropriate for
analysis? Depends...
Case 1: Detailed knowledge of biochemical
mechanisms
Case 2: Data imply connectivities, but molecular
details unknown
Causes
Biochemical
Mechanisms
Effects
Where does Boolean fit in?
Case 1: Detailed knowledge of
biochemical mechanisms
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Model with system of differential equations
2 types of dynamics
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Analog: ODE crucial to describe key features
Discrete: steady-states capture behavior; ODE is
sufficient but not necessary
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Can be abstracted to Boolean algebra, where new
framework offers new insights while retaining
analysis capabilities
Where does Boolean fit in?
Case 2: Data imply connectivities, but
molecular details unknown
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When data show only two steady-states, cause
and effect relationships can be modeled with
Boolean logic functions
A
B
C
A B
State 1 State 1 State 1
State 1 State 2 State 2
B
C
State 2 State 1 State 1
State 2 State 2 State 1
A
C
Outline
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A model biochemical network (Case 1)
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Boolean network modeling (Case 2)
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Demonstrate that biochemical kinetics can produce
Boolean behavior at the steady-state, input-output
level
Motivates use of Boolean algebra framework when
cause/effect data shows 2 states
Caspase cascade
Boolean with HT Experiments
The Biochemical Network
Overview
I1
E1
X1
X1+I1
kin1
X1
X1I1
kdeg1
I2
S1
E2
S2
X2
E3
S3
E1+2X3
X3
E4
ka1
kd1
ki1
X4
E1X3
kr1
2
E2+2X1 E2X1
2
k-i1
+
E1+2X1
Governing Equations
Inputs: I1, I2
Output: x4
Simulation
Mathematical Analysis
Conclusions from Biochemical
Network
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Network was based on known biochemical
mechanisms
Demonstrated feasibility of a biochemical
network performing Boolean operations
Motivates use of Boolean framework for
analyzing data that shows two discrete
steady-state levels
Caspase Cascade in Apoptosis
Intrinsic
•Missing some
mechanistic
detail
•Data show 2
steady-states
Death
Extrinsic
Previous Caspase Modeling
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Details of underlying mechanisms and
important parameters were unknown, but
Bailey attempted to model the cascade with a
set of differential equations coupled with
specialized functions.
Their goal was to obtain qualitative results in
the form of identifying combinations of drug
targets to inhibit apoptosis despite both
intrinsic and extrinsic death signals.
Previous Results
Boolean Network
Our Updated Model (Boolean)
Analysis
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Mathematical manipulation
Extract how output depends on input
Blake Canonical Form
Caspase-Dependent Death =
External Death Signal AND not FLIPs AND not IAPs
OR
Cell Damage AND not ARC AND not IAPs
Model with Drug Targets
Drug Target Analysis
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without drugs: ab’d’ ۷ cd’e’
with drugs: ab’d’ ۷ [cd’e’ ۸ (f1’ ۷ f2’)]
a = external death signal
b = FLIPs
c = cell damage
d = decoy substrates
e = ARC
f1 = knockout drug 1
f2 = knockout drug 2
Our Opinion
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Yes, we actually think that this is useful
and applies to some biological systems.
Governing Equations
Parameter Set 2
5 x32
dx1
 x1  10 x1 I 1

2
dt 1  5 x3
dx 2
10
 x 2  10 x 2 I 2

2
dt 1  x1
Inputs: I1, I2
dx3
10
 x3

2
dt 1  x 2
Output: x4
dx 4
10
 x4

2
dt 1  x3
Simulation
Mathematical Analysis
Imagine…
Boolean with HT Experiments