SHORT COURSES ON THE MATHEMATICS
OF BIOLOGICAL COMPLEXITY
University of Tennessee,
Knoxville
Supported by National Institutes
of Health Award GM5992402
For related NIH programs see NIGMS Complex
Systems Initiatives
2003 Short Courses
The 2003 series of Short Courses will
be held at the University of Tennessee and as with earlier ones, these are
oriented towards biologicallytrained individuals. The overall objective
is to provide a rapid introduction to the mathematical and computational
topics appropriate for understanding current research in biological complexity.
These Courses will each last four days. The Courses will be led by a group
of distinguished faculty with particular expertise in biological modeling.
Each Course will include computerbased workshops in addition to formal
lectures and discussion sessions. Each Course is organized separately, though
some individuals will benefit from attending two or more of them, depending
upon their research interests. Significant financial support for travel,
registration and housing expenses are available to qualified applicants
(particularly graduate students, postdoctoral fellows and faculty without
externallyfunded projects).
Course 1: Introduction to the Mathematics of Biological
Complexity:
March 30  April 2, 2003
Course 2: Optimal Control Theory in Application to Biology:
July 912, 2003
Course Home Page with Lecture Notes
Course 3: Modeling the evolutionary
genetics of complex phenotypes: a hierarchical approach from sequences to
populations:
September 710, 2003 (note changed date)
In addition to the above, the following Courses are planned to be held
over the next year, pending approval of funding:
4. Quantitative Assessment of Stress on Systems: Modeling, Risk and Decisons
(Dr. Thomas Hallam, organizer)
5. Nonlinear Dynamics, Bifurcations, and Chaos in Biology: an introduction
to the formulation, parameterization, analysis, and simulation of nonlinear
models of biological systems (Dr. Aaron King, organizer)
6. Statistical Data Mining in Biology (Dr. Hamparsum Bozdogan, organizer)
7. Bioinformatics and Computational Biology of Genome Sequences: compartive
analysis and evolution (Dr. Jay Snoddy, organizer)
8. Workshop: An Introduction to Biocomplexity and Quantitative Education
(Dr. Louis Gross, organizer)
Lecture notes and other materials from previous Short
Courses are at:
2002 Course Home
Page
2000 Courses Home
Page
2003 Courses
Attendance
Costs
The
Faculty
The Courses
Further Information
Application Form
Applicants
should complete the application form and email it to the
Director of the Courses as per instructions. Applicants will be notified
of their acceptance by email, and given details regarding travel and lodging
arrangements. Applicants for Course 1 will start to be accepted immediately
with a final deadline of March 20 for this Course  individuals are urged
not to delay in applying. Applicants for Courses 2 and 3 will start to be
accepted 3 months before the start of the Course, with a final application
deadline 1 month before the start of each of these Courses.
 Course
Organizer: Dr. Louis J. Gross
 Professor of Ecology and Evolutionary Biology and
Mathematics
 Director, The Institute for Environmental Modeling
 University of Tennessee
 Dr. Sharon Lubkin
 Assistant Professor of Statistics and Biomathematics
 North Carolina State University
 Dr. Holly Gaff
 Postdoctoral Fellow

 Department of Ecology and Evolutionary Biology
The Institute for Environmental Modeling
University of Tennessee
Course 2:
 Course Organizer: Dr. Suzanne Lenhart
 Professor of Mathematics
 University of Tennessee

 Dr. Renee Fister
 Associate Professor of Mathematics
 Murray State University




 Dr. Hem Raj Joshi
 Postdoctoral Fellow

 Department of Ecology and Evolutionary Biology
The Institute for Environmental Modeling
University of Tennessee

Course 3:
 Course Organizer: Dr. Jason Wolf
 Assistant Professor of Ecology and Evolutionary Biology
 University of Tennessee
 Dr. William Atchley
 Professor of Genetics and Statistics
 North Carolina State University
 Dr. Charles J. Goodnight
 Professor of Biology
 University of Vermont
Course 1: Introduction to
the Mathematics of Biological Complexity
This Course will provide an overview
of mathematical and computational approaches useful in analyzing complex
biological systems including: continuous dynamical systems, discrete dynamical
systems, matrix approaches including structured population models and Markov
chains, and stochastic process models. This is designed for biologists who
require a rapid, broad overview of modern quantitative techniques that appear
again and again in many biological contexts. The focus will be on modeling
methods, conceptual foundations and biological applications rather than detailed
computations. The concepts will be motivated by numerous biological examples,
chosen from physiology, genetics and infectious diseases. An objective is
to ensure that participants for whom the first short course is appropriate
would have been exposed to the basic mathematical background materials required
for either of the second or the third Courses. Another objective is to enable
attendees to read with comprehension the modeling literature in their own
fields of biological interest.
Topic coverage will include the
below, but will emphasize topics of particular interest to attendees. Accepted
attendees will be polled to ensure that topics of particular interest to
many attendees will be covered.
An overview of calculus with focus on differential equations in preparation for the section on dynamical systems and diffusion.
An overview of linear algebra in preparation for the section on Markov Chains and the section on dynamical systems.
An overview of basic probability in preparation for the section on stochastic models.
How to model it  examples of basic discrete and continuous models in application to chemostats, population genetics, and physiology. Application of nondimensionalization methods to reduce the number of parameters in a model.
Introduction to dynamical systems  Discrete and continuous compartment models, phaseplane analysis.
Transport and diffusion  partial differential equations, the conservation equation, steadystates and traveling waves.
Stochastic models  birth and death processes, branching processes, Markov Chains. Applications to genetics and evolutionary theory.
Course 2: Optimal Control Theory in Application
to Biology
This short course will focus on optimal control of systems of
ordinary differential equations modeling biological systems. Here the differential equations model the dynamics of system response with some component of the system
being under direct control, such as the rate of infusion of a drug. The
optimal control problem requires a criterion (the objective) that is to
maximized or minimized, such as minimizing tumor size, under constraints
such as a limited total infusion due to limited tolerance for the drug. The
mathematical theory then provides methods for how to best apply the control
in time (e.g. the timecourse of infusion) and stay within the constraints
of the problem. The basic ideas of optimal control theory will be covered,
and applications to disease, cancer and bioreactor models will be presented. Numerical solutions for simple control problems will be demonstrated in a computer lab setting.
Course 3: Modeling the evolutionary genetics of complex phenotypes: a hierarchical
approach from sequences to populations
The major goal of evolutionary and epidemiological genetics is
to understand the architecture of genetic variation in and among populations. In evolutionary analyses understanding this architecture allows one to predict or reconstruct evolutionary genetic changes in response to
selection at the level of phenotypes (e.g., Grant & Grant 1995). In
epidemiological analyses it allows one to predict the incidence and
distribution of various inherited pathologies (e.g., Sing & Boerwinkle
1987). However, understanding the genetic architecture underlying trait
variation, and its implications for various processes, can be extremely
difficult because there can be many levels of organization mediating the
mapping from DNA sequence to phenotype. As a result, researchers
studying
these complex phenotypes have relied heavily on theoretical models to
assess the implications of various patterns of genetic variation (e.g.,
Barton & Turelli 1991).
Because theoretical approaches have been so important in the advancement
of understanding of complex phenotypes it is critical that
nontheoreticians doing empirical genetics be able to comprehend the
models that are being developed. This course will provide these
researchers with the tools required to understand the various modeling
approaches that are being used in this area. In order to achieve this
goal we will utilize a hierarchical perspective, covering modeling
approaches that have examined the implications of variation at various
levels of organization. The course will span the hierarchy, from models
that focus on single loci and their RNA or protein products
(e.g., Atchley et al 2000) to those that include multilocus interactions
(see Wolf et al. 2000), developmental organization such as modularity
(Atchley et al. 1994) and the resulting modular interactions (Wolf et al.
2001), up to those that include phenomena above the level of the
individual such as genotype interactions (Moore et al, 1997), population
processes (e.g., founder events [Goodnight 1987]) and metapopulation
dynamics (Goodnight 2000).
Any questions about the Courses should be
directed to
Return to The Institute
for Environmental Modeling Home Page
http://www.tiem.utk.edu/
Last Modified: April 23, 2003