# Mov Simple Mathematical Models to Understand Evolution

Sumit Jun 30, 2013 By:

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**Last modified:** 03 May 2013

Lecture -30- Simple Mathematical Models to Understand Evolution of Biomathematics Biomathematics by Dr. Ranjith Padinhateeri, Department of Biotechnology, IIT Bombay.For more details on NPTEL visit http://nptel.iitm.ac.in

Course Detail :

Functions : Introduce the idea of functions using examples from Biology. Eg. Velocity of molecular motors as a function of ATP concentration

Derivative of a function,Techniques of differentiation : Eg. Concentration gradient; Pressure, entropy etc as derivatives of free energy

Finding maxima, minima, Plotting functions : Minimum of free energy; Plotting Gaussian, exponential function etc using examples from biology, Energy landscape

Integrals, Techniques of Integration : Integration as calculation of area under the curve.

Scalars and vectors. Spherical polar coordinates and cylindrical coordinates : 3-dimensional configuration of proteins, Structure of nucleosomes, 3D structure of chromatin

Ordinary differential equations, Partial differential equations, Solving differential equations : Rate equations (eg. Actin polymerization), Diffusion etc

Fourier series, Fourier transformation : Discussion of the use of Fourier transformation in X-ray crystallography and in optics, Examples from neurobiology

Introduction to probability : Discussion of stochastic processes in biology (Eg. bacterial motion), Application in statistical thermodynamics

Probability distributions, Average, variance, standard deviation etc : Eg. length distribution of microtubules with dynamics instability. Finding average length and standard deviation of the filament lengths; DNA loop formation probability.

Binomial distribution , Gaussian distribution , Poisson distribution : Eg. End-to-end distance distribution of proteins/DNA/RNA; Run and tumble motion of bacteria etc

Master equations : Eg. Modeling gene expression, polymerization of actin/microtubules

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