Course Co-ordinated by IIT Guwahati
 Coordinators IIT Guwahati

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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.

1. Mathematical Modeling in Systems Biology: An Introduction, Brian P. Ingalls, MIT Press, 2013
2. Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Frederick R. Adler, Brooks/Cole, 2012
3. Biocalculus: Calculu

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