Mathematical modeling has become an integral part of
different fields of biology, from ecology to cell biology. This
course will introduce students of biology to elementary mathematical
concepts and tools for dynamical models. The course will focus on
modeling using ordinary differential equations (ODEs). We will start
with basic mathematical concepts of ODE-based models and then
connect those with experimental biology. Mathematical models will be
on cellular and molecular processes in biology, like cell signaling,
and transcriptional networks. Students will learn basics of
analytical techniques, graphical techniques, and numerical
simulation.
Week
Topics
1.
L1: Introduction to mathematical modeling in
biology
L2: How to start modeling?
L3: Basic concepts of modeling using ODEs: Modeling the
spread of infectious disease
L4: Basic concepts of modeling using ODEs: Modeling
population growth
L5: Numerical solution of ODE-based models - I
L6: Numerical solution of ODE-based models - II
2.
L1: Simulating ODE-based models: Introduction to JSim
L2: Simulating ODE-based models: Examples of simulation in
JSim
L3: Steady state and stability analysis: Understanding
steady state
L4: Steady state and stability analysis: Stability of
steady states
L5: Phase plane analysis - I
L6: Phase plane analysis - II
3.
L1: Concepts of bifurcation
L2: Bifurcation in Biological systems
L3: Modeling molecular processes in cell
L4: Modeling molecular processes-I: Ligand-receptor
binding
L5: Modeling molecular processes-II: Enzymatic reaction
L6: Modeling molecular processes-III: Transcription and
translation
4.
L1: Modeling a signal transduction circuit: Negative
feedback
L2: Modeling a signal transduction circuit: Positive
feedback
L3: Modeling a signal transduction circuit: Incoherent
feedforward
L4: Modeling transcriptional circuits – I
L5: Modeling transcriptional circuits - II
L6: Online resources for mathematical modeling in biology
Must have studied Mathematics at 10+2 level. Have studied graduate-level Biochemistry and Molecular Biology. Knowledge of Computer Programming will be helpful but not a necessity.
Mathematical Modeling in Systems Biology: An Introduction, Brian P. Ingalls, MIT Press, 2013
Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Frederick R. Adler, Brooks/Cole, 2012
Biocalculus: Calculu
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