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Introduction to computational cell biology Spring 2007
Course
Overview
In this class we'll combine some
biology and some math to understand how cells and tissue work, with an
emphasis on electrophysiology. We'll
study the structure and function of ion channels and how they combine to
determine the behavior of a whole cell.
We'll also develop mathematical descriptions of this behavior and do
computer simulations using MATLAB and/or similar programs.
Prerequisites
The prerequisite for Math and BME
students is Math 366, Differential Equations, or equivalent.
General
Information
Leaders in the National
Institutes of Health and the National Science Foundation believe that
computational and mathematical methods increasingly will provide the
foundation for advances in the biological sciences. This course is intended
to provide an introduction to mathematical modeling of the biological and
electrical processes involved in the cell function. The course will begin
with a brief introduction to differential equations and the basic biology
underlying the electrical processes in cardiac cells. Classical systems
of differential equations, such as those of Hodgkin-Huxley, FitzHugh-Nagumo,
and Morris-Lecar, used to describe firing of action potentials in cardiac
cells and their propagation through networks will be developed and analyzed.
These ideas and these models describe a diverse set of biological systems and
organisms, from action potentials in cardiac cells and in the giant axon of
the squid, to control of insulin production in pancreatic beta cells, to
understanding the effect of dopamine in the thalamus of Parkinson's patients.
The course will introduce ideas from dynamical systems to understand the
behavior of these models, especially the ways in which the behavior changes
as the inputs and biological parameters change. Since systems of differential
equations of biological importance do not (usually) have closed form
solutions, software packages MATLAB and XPPAUT will be used to do modeling
and computations with the resulting models. The course will emphasize setting
up the models of cardiac systems and interpreting the computed solutions in
the context in which the models arose and the dependence of the predicted
behavior on the inputs. An important goal of the course is to help prepare
students to work in an interdisciplinary environment that includes both
biological and mathematical scientists.
Textbooks
BIOL
595N and MATH 490N will both use Computational Cell Biology, by C. P. Fall,
E. S. Marland, J. M. Wagner, and J. J. Tyson, editors, Springer, 2002.
Grading
The course grade will be based on
a midterm exam, a final exam, homework assignments that include computation
using XPPAUT or MATLAB, and a group report on a
published model (chosen by the group members) that was not covered in the
lectures.
Comments
This course does NOT assume that
students bring both mathematical and biological sophistication to the course,
but it is assumed that students are at the junior level or above in one of
these areas. It is expected that students will gain an appreciation for the
kinds of information that mathematical and computational approaches can add
to understanding the functioning of a neural system, for example, to realize
that some systems are inherently more sensitive to changes in the input
parameters than others. It is hoped that students who have completed the
course will be more willing and more able to incorporate mathematical or
computational approaches into their own biological work or see ways in which
their own mathematical work can be used in the biological sciences.
Software for the Course
There are several
pieces of software that we will use in the course. WINPP
is a version of the program XPPAUT developed by
mathematical biologist Bard Ermentrout at the There are other programs that can
solve systems of differential equations and do other kinds of related
computations and graphics that are not free but are available on the ITAP
machines. These programs include MATLAB, MAPLE, and MATHEMATICA. The Computational
Cell Biology website has .ode files for many of the illustrations of the
book and a description of how to use Virtual Cell.
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