# Mov Lecture 31 - Simple Mathematical Models to Understand Evolution

Sumit Dec 31, 2013 By:

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Lecture 31 - Simple Mathematical Models to Understand Evolution

This video is part of the Module Biomathematics Lecture Series onBiomathematics by Dr. Ranjith Padinhateeri, Department of Biotechnology, IIT Bombay

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COURSE OUTLINE

Why Spoken English – Linguistic Aspects of Mishearing – Fluency - Speaking to Multicultural/Multidisciplinary Audience - Standard Varieties of Spoken English – Tempo of Speech & Phrasal Pause in English – English Rhythm - Stress on Simple and Derived Words in English – Long Vowels in English – Friction Consonants in English – Aspects of Theatre in Spoken Communication – Grooming, Eye Contact, Body Language, Amplitude – Preparing a Presentation : Charts, Graphs, Drawings, Maps, Diagrams, Tables, Etc – Research and Organization – Using Power Point Slides and Other Presentation Aids – Practice and Learning to Improve- Pronunciation of Numbers, Units of Weights, Distance, Etc. – Making Presentations and Self-Evaluation.

COURSE DETAIL

Sl. No.1

Topics in mathematics::Functions

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

Sl. No.2

Topics in mathematics::Derivative of a function,Techniques of differentiation

Eg. Concentration gradient; Pressure, entropy etc as derivatives of free energy

Sl. No.3

Topics in mathematics::Finding maxima, minima, Plotting functions

Minimum of free energy; Plotting Gaussian, exponential function etc using examples from biology, Energy landscape

Sl. No.4

Topics in mathematics::Integrals, Techniques of Integration

Integration as calculation of area under the curve.

Sl. No.5

Topics in mathematics::Scalars and vectors. Spherical polar coordinates and cylindrical coordinates

3-dimensional configuration of proteins, Structure of nucleosomes, 3D structure of chromatin

Sl. No.6

Topics in mathematics::Ordinary differential equations, Partial differential equations, Solving differential equations

Rate equations (eg. Actin polymerization), Diffusion etc

Sl. No.7

Topics in mathematics::Fourier series, Fourier transformation

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

Sl. No.8

Topics in mathematics::Introduction to probability

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

Sl. No.9

Topics in mathematics::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.

Sl. No.10

Topics in mathematics::Binomial distribution , Gaussian distribution , Poisson distribution

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

Sl. No.11

Topics in mathematics::Master equations

Eg. Modeling gene expression, polymerization of actin/microtubules