The intersection of the mathematical sciences with topics at the forefront of current biology is a rich source of mathematical problems. Quantifying biological phenomena through simple and more complex models, as well as achieving a deeper, more systematic understanding of these models, is a challenge that draws upon multiple skills. Interested mathematicians and scientists must draw upon very disparate aspects of mathematics. These include nonlinear dynamical systems, partial differential equations (such as the Navier-Stokes equations for fluids or the equations that govern biological pattern formation), information theory,stochastics and probability, network models and discrete mathematics relevant to computation.
This AIS is among the first of its kind in India to introduce a broad audience consisting of applied and pure mathematicians, physicists, engineers and some biologists to this active field. It provides a selection of topics that are among the forefront of those being studied internationally. It is aimed at those pursuing (or intending to pursue) research in any related area of mathematics (interpreted in a broad sense). A basic facility with di↵erential equations and some elementary probability will be assumed, but otherwise there are no prerequisites.
|Speaker||No. of lectures||Syllabus|
Prof. Kavita Jain, JNCASR, Bengaluru
Mathematical Modelling in Population Biology:-
Lecture-2 Mutation rates are also subject to the action of evolutionary forces. I will discuss some
Lectures- 3 & 4 will introduce some basic results in quantitative genetics and discuss how one can
Tutorials-1 & 2:
Prof. Malay Banerjee, IIT Kanpur
A survey of Ecological Models:-
Lecture-2 Introduction to two species population models There are several types of population models of two interacting species - competitive,
Lecture-3 Stability and bifurcation analysis for multi-species population models Mathematical models of interacting species with three and higher trophic levels can
Lecture-4 Spatio-temporal model - Turing instability Spatio-temporal models of interacting populations are capable to capture the effect of heterogeneous distribution of various species over their habitats on the resulting
Prof. Leelavati Narlikar, NCL, Pune
Sequence Analysis :-
Lecture-1 Introduction to Algorithms and Probability Theory
Lecture-2 Modeling biological sequences I
Lecture-3 Modeling biological sequences II
Lecture-4: Meta Genomics
Prof. Gautam I Menon, IMSc, Chennai
The Mathematics of Infectious Diseases:-
Lecture-1 Introduction to the Modelling of Infectious Diseases This lecture provides the basic phenomena studied in infectious disease modelling, introduces the SI, SIR and more general compartmental models, and motivates the
Lecture-2 Host heterogeneities and multi-host, multi-pathogen models Populations are heterogeneous and the generalisation of simple compartmental models to study such heterogeneities will be discussed. Several diseases can infect multiple
Tutorial-3 Implementing SIR and related models in simple computer programs
Lecture-4 Temporal Forcing and Stochastic Models Many diseases undergo forcing from some external factor, such as climate, rainfall or temperature. The basics of the modelling of forced systems will be described, as also the
Lecture-5 Spatial and Network models Spatial and network generalizations of the classic disease models, as well as their generalizations to agent-based models will be described. The basics of the Gillespie method will also be described.
Tutorial-6 Implementing agent-based models in simple computer models
Prof. Mukund Thattai, NCBS, Bengaluru
Models in Systems Biology:-
Lecture-1 Gene regulatory networks. Models of transcriptional regulation
Prof. Mandar Inamdar, IIT Bombay
Mathematical Models for Continuous Media and Biological Applications :-
The broad scope of these lectures is to give the students basic understanding and implementable skill to model various phenomena in migration and mechanics of collective cell migration. To that end the lectures will be planned as follows. Each lecture/tutorial described below will be of 90 minutes duration.
Lecture-1 Introduction to continuum mechanics
Lecture-2 Application of continuum modelling for biological tissues
Lecture-3 Numerical techniques to solve continuum equations
Lecture-4/Tutorial: Solve mid-level to simple problems in the three topics discussed above.
Lecture-5 Discrete modelling of tissues and understanding the emergence of continuum level properties
Lecture-6/Tutorial Hands-on implementation of mesoscale modelling involving coarse-graining of the vertex model to continuum level description
Prof. Pranay Goel, IISER Pune
Electrophysiological Models :-
Lecture-1 Introduction to electrical phenomena in the nervous system . will introduce the basic biology of the nervous system; and the elementary ideas from circuit theory and their extensions that will be needed in later lectures. This will set the
Lecture-2 Modeling excitable media: The Hodgkin-Huxley equations of action potentials.We will develop the celebrated Hodgkin-Huxley model for electrical activity in nerves. We will then describe two broad classes of properties - Types I and II - that action potentials can be grouped into.
Tutorial-1 Introduction to XPP, and modelling excitable media. We will introduce XPP, a differential equations solutions package with a graphical interface. We will explore the Hodgkin-Huxley equations, and identify properties of Type I and II neurons using numerical experiments.
Lecture-3: Reduced models and phase-plane analysis of excitability. We will describe two-dimensional models that successfully reproduce the essential properties of Type I and II neurons. We will carry out a phase-plane analysis to understand
Lecture-4 Modeling neural networks. will investigate synapses, and the connectivity of neurons in networks. We will introduce questions of emergent behaviours in neural networks, and briefly touch upon some methods that been used to investigate these phenomena.
Tutorial 2 Neural networks.
Prof. Sitabhra Sinha, IMSc, Chennai
Lecture-1 Networks: An unifying framework for biology across scales
Tutorial-2 Identifying communities: Modularity, Graph partitioning and Synchronization & other collective dynamics in modular networks
Additional Resource persons
- Rahul Siddharthan (RS)
- Areejit Samal (AS)
- Sitabhra Sinha (SS)
The tutorials will be handled mostly by the lecturers with help from the resource persons listed above.
14:00 to 15:30