Boolean Networks and Biology Peter Lee Shaun Lippow BE.400 Final Project December 10, 2002

Introduction Need quantitative analysis to understand complex biological networks Need quantitative analysis to understand complex biological networks What mathematical framework is appropriate for analysis? Depends... What mathematical framework is appropriate for analysis? Depends... Case 1: Detailed knowledge of biochemical mechanisms Case 1: Detailed knowledge of biochemical mechanisms Case 2: Data imply connectivities, but molecular details unknown Case 2: Data imply connectivities, but molecular details unknown Biochemical Mechanisms Causes Effects

Model with system of differential equations Model with system of differential equations 2 types of dynamics 2 types of dynamics Analog: ODE crucial to describe key features Analog: ODE crucial to describe key features Discrete: steady-states capture behavior; ODE is sufficient but not necessary Discrete: steady-states capture behavior; ODE is sufficient but not necessary Can be abstracted to Boolean algebra, where new framework offers new insights while retaining analysis capabilities Can be abstracted to Boolean algebra, where new framework offers new insights while retaining analysis capabilities Where does Boolean fit in? Case 1: Detailed knowledge of biochemical mechanisms

Where does Boolean fit in? Case 2: Data imply connectivities, but molecular details unknown When data show only two steady-states, cause and effect relationships can be modeled with Boolean logic functions When data show only two steady-states, cause and effect relationships can be modeled with Boolean logic functions ABC State 1 State 2 State 1 State 2 State 1 A B C AB C

Outline A model biochemical network (Case 1) A model biochemical network (Case 1) Demonstrate that biochemical kinetics can produce Boolean behavior at the steady-state, input-output level 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 Motivates use of Boolean algebra framework when cause/effect data shows 2 states Boolean network modeling (Case 2) Boolean network modeling (Case 2) Caspase cascade Caspase cascade Boolean with HT Experiments Boolean with HT Experiments

The Biochemical Network Overview E1E1 X1X1 I1I1 E3E3 X2X2 I2I2 E2E2 S1S1 X3X3 S2S2 E4E4 X4X4 S3S3 E 1 +2X 3 E 1 X 3 E 1 +2X 1 k a1 k d1 k r1 E 2 +2X 1 E 2 X 1 k i1 k -i1 + X 1 +I 1 X 1 I 1 k in1 X1X1 k deg1 2 2

Governing Equations Inputs: I 1, I 2 Output: x 4

Simulation

Mathematical Analysis

Conclusions from Biochemical Network Network was based on known biochemical mechanisms Network was based on known biochemical mechanisms Demonstrated feasibility of a biochemical network performing Boolean operations Demonstrated feasibility of a biochemical network performing Boolean operations Motivates use of Boolean framework for analyzing data that shows two discrete steady-state levels Motivates use of Boolean framework for analyzing data that shows two discrete steady-state levels

Caspase Cascade in Apoptosis Intrinsic Extrinsic Death Missing some mechanistic detail Data show 2 steady-states

Previous Caspase Modeling 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. 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. 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 Mathematical manipulation Mathematical manipulation Extract how output depends on input Extract how output depends on input Blake Canonical Form 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 without drugs: ab’d’ ۷ cd’e’ without drugs: ab’d’ ۷ cd’e’ with drugs: ab’d’ ۷ [cd’e’۸ (f 1 ’ ۷ f 2 ’)] with drugs: ab’d’ ۷ [cd’e’۸ (f 1 ’ ۷ f 2 ’)] a = external death signalf 1 = knockout drug 1 b = FLIPsf 2 = knockout drug 2 c = cell damage d = decoy substrates e = ARC

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

Governing Equations Parameter Set 2 Inputs: I 1, I 2 Output: x 4

Simulation

Mathematical Analysis

Imagine…

Boolean with HT Experiments