Mathematical Modeling of Signal Transduction Pathways Biplab Bose IIT Guwahati

Cellular Communication Ligand Receptor Relay Output Message Function Encoding/Decoding Image: BioCarta

Encoding-decoding in Dynamics Nat Rev Mol Cell Biol. 2011, 12(2): Cell. 1995, 80(2):

Why Model? To understand empirical observations To generate new hypothesis

Linear Network Network with Negative Feedback Signaling beyond saturation PLoS Comput Biol 4(10): e

Weber’s Law Weber’s Law in Signaling Circuit that senses only fold change Mol Cell. 2009, 36(5):724-7

Deterministic Modeling Assumes that the system is large Uses Law of Mass Action Homogenous system: Ordinary Differential Equation (ODE) Non-homogenous system: Partial Differential Equation (PDE)

productiondegradation Deterministic Modeling System of ODEs [A], [B] and [E] considered constant

Deterministic Modeling Solve the ODEs Analytical solution Numerical solution [C] [pD]

Modeling Strategy Model Data Estimate parameters Simulate to predict Images: Mol Cell. 2012, 46(6):

X Yp Sustained signaling: both X and Yp reach steady state Simple but Complex

The system has memory Can lead to two population of cells Simple but Complex

IRS1 PI3K Akt mTOR Insulin/IGF-1 The mTor Story Nat Rev Drug Discov. 2007,6(11):871-80

DatabaseWeb Address KEGG REACTOMEhttp:// ypoint.html PATHWAY INTERACTION DATABASE (PID) PANTHERhttp:// WikiPathwayshttp:// SMPDBhttp:// Pathway Database

The parameters

DatabaseWeb Address BioModelshttp:// CellMLhttp:// JWS Onlinehttp://jjj.biochem.sun.ac.za/index.html Model Database

Tools for Dynamic Simulation JSim COPASI GEPASI CellDesigner MATLAB Mathematica Extended list: Biochimie. 2006, 88(3-4):

Stochasticity in Chemical Reaction Conventional reactions involve large number of molecules A + B  C Follows Law of Mass Action When number of molecules is low Can not apply Law of Mass Action Uncertainty in reactions

Some misconceptions about random/stochastic process: Any thing can happen. Things are mixed-up Does not have cause-and-effect relation. We can not make predictions. What is Random?

Random walk in Brownian motion 1.Water molecules are in motion. 2.Hit each other and the pollen. 3.Classical mechanics can be used to understand (approximately) trajectories due to collisions. Facts: Problem: We do not (or can not have) have exact information of the system (ie. position and momentum of each particle) Consequence: 1.Can not predict exact trajectory. 2.Get surprised by the movement of the pollen 3.Call this random or stochastic process Image source: wikipedia

Beyond uncertainties 1.We can calculate average behaviour 2.We can calculate probability of an outcome 3.We can calculate distribution of outcomes Frequency  Displacement  Can not calculate exact displacement of a pollen in a particular duration But Can calculate the PROBABILITY of a particular amount of displacement. What is Random?

Protein expression similar to coin toss: You may get Head or Tail in a toss At one moment cell may make one copy protein or not Cell 1 Cell 2 YYY Y Y Y Y NN N time Protein number Protein Expression Like Coin Toss

Stochasticity in Gene Expression

Linear Circuit Positive feedback Transcriptional Circuit Affects Expression Heterogeneity PLoS ONE (2): e

Modeling Stochastic Systems Kinetic Monte Carlo Gillespie algorithm MATLAB Dizzy StochSim STOCKS

Constrains of Dynamic Modeling Difficult to model very large system Difficulty in parameter estimation: How to design experiment? How to estimate parameters? Problem in connecting different scales

@bose_biplab FlowPy How a cell handles information