|
There was a time when the basic scientific needs of mathematical
biologists could be met--minimally--by typical graduate school
curricula and traditional conferences. But today's active mathematical
biologists must participate in--in addition to their traditional
conferences--annual meetings of major biological professional
societies, specialty conferences, as well as in focus groups (see Next
Wave's article by Fred Roberts,
and specialty workshops. Furthermore, a critical part of the training
of today's interdisciplinary scientists takes place at summer schools,
workshops, and more focused conferences. These nontraditional resources
must not be overlooked--indeed, they must be expanded--if we are to
meet the nation's hunger for interdisciplinary scientists and to
enhance the diversity of the scientific workforce.
Flexibility needed
Despite the success of training and mentorship models like University of Tennessee, Knoxville's Mathematical Ecology Program,
in an age of interdisciplinary science no single university model can
meet national and international scientific and educational needs.
Diverse, well supported, and above all flexible training and
research programs must be one of our nation's scientific priorities, as
flexibility often leads to innovation. One such flexible, innovative
program exists at Arizona State University (ASU).
At ASU, work in mathematical, theoretical, and computational biology is carried out in a variety of settings, including the department of mathematics and statistics, my current home. Our interdisciplinary applied mathematics program offers a Master in Natural Science and a Ph.D. in differential equations and mathematical biology.
One key to our program is that it offers the flexibility required to
meet the needs of students with a wide range of interests. Students are
encouraged to fulfill half of the Ph.D. course requirements by taking
approved courses in the biological sciences. Recent graduates of our
program include Purdue University associate professor Zilan Feng, University of Louisville associate professor Bingtuan Li, and University of Nebraska, Lincoln, assistant professor Irakli Loladze.
ASU also offers a Professional Science Master's degree within its Computational Biosciences degree
program. With its emphasis on quantitative approaches to biological
problems, this program aims to produce students capable of meeting the
demands of today's biotechnical and biomedical industries.
Our Ph.D. program in differential equations and mathematical biology
offers a wide range of opportunities. The strengths of this program lie
in a group of mathematical biologists with overlapping interests and
strong research groups in areas that provide excellent training
opportunities for our students. These scientists and research groups
have complementary expertise in numerical analysis, computational
science, dynamical systems, statistics, and stochastic processes. In
addition, our School of Life Sciences and Cancer Institute,
among other components, provide plenty of opportunities for the
training of undergraduates, graduate students, and postdocs interested
in theoretical, mathematical, and computational biology. Below, I
describe some of the research opportunities that are available at ASU
to qualified graduate student and postdoctoral candidates.
Faculty achievements
Recent work by Hal Smith
and collaborators involves the construction and analysis of
mathematical models of biofilms in fluid environments. Analysis of
these models has yielded answers to the question of why it is so
difficult to eradicate biofilms using biocides. More recently, their
research has turned to modeling the process of gene transfer between
bacteria in biofilms. Gene transfer typically occurs when a host
bacteria passes a plasmid, a small circular DNA not part of the host
genome, to another, not necessarily related bacteria, following
conjugation. Smith with graduate student M. Imran and collaborator D.
Jones have constructed a simple model of gene transfer in an immersed
biofilm. Genetic transfer in biofilms--with its relevance to the
transfer of antibiotic resistance--is an example of important phenomena
that have received little attention from mathematical modelers.
Horst Thieme
studies rapidly reproducing parasitic populations, which, as he notes,
"are ideal objects to study the principles of evolution; in turn, it is
important to understand these principles to control infectious diseases
effectively." Mathematical models, he notes, are essential in our
efforts to gain a deeper understanding of these phenomena and as a
theoretical laboratory to devise control and management strategies.
Such models are also needed to elucidate the role of parasites in
biocomplexity, as mediators of competition and coexistence. Thieme
works at the interface of differential equations, integral equations,
and dynamical systems (on the one hand), and ecology, population
biology, and epidemiology (on the other).
Yang Kuang's
research focuses, in part, on the identifications and characterization
of mechanisms of species coexistence or extinction. Individual
heterogeneity is critical to the evolutionary process, and yet most
population models tend to exclude or limit the level of heterogeneity.
Stoichiometry-based population models carefully imbed the natural
chemical heterogeneity that is innate to all life forms. Kuang, in
collaboration with Jim Elser
and others, have used these models to address specific biocomplexity
and biodiversity questions. Kuang is also involved in efforts to model
various aspects of tumor growth and management as part of ASU's efforts
on cancer research. Kuang has also maintained an active mathematics
research program on dynamical systems--particularly in the area of
functional differential equations.
One of Rosemary Renaut's
projects focuses on the development of reliable and sensitive
neuroimaging analysis tools for use with positron emission tomography
and magnetic resonance imaging. Her work is used in the assessment and
detection of functional and anatomical change in the human brain
through the course of Alzheimer's disease. The tools developed are
being enhanced and extended with the goal of developing a flexible
software package that provides an automated approach for neuroimaging
studies by Alzheimer's dementia researchers at the Good Samaritan
Medical Center in Phoenix.
Steve Baer's
research is in computational neuroscience. Current projects include
modeling the biophysical mechanisms underlying synaptic plasticity and
learning in dendritic trees, the dynamics of neuronal networks in the
outer plexiform layer of the retina, and modeling the integration of
multiple synaptic inputs in muscle fiber.
My research program
lies at the interface of the natural and social sciences, with its
emphasis on the role of dynamic social landscapes on pathogens'
evolution. In collaboration with many researchers (graduate students,
postdocs, and faculty elsewhere), we have examined the role of
cross-immunity on the evolution and dynamics of influenza; the impact
of behavioral changes, long periods of infectiousness, variable
infectivity, co-infections, prostitution, social networks, and vaccine
efficacy on HIV dynamics; the role of exogenous re-infection, variable
progression rates, vaccination, public transportation, close and casual
contacts on tuberculosis dynamics and control; the impact of
life-history vector dynamics on dengue epidemics; and on the
identification of time-response scales for epidemics of foot and mouth
disease.
More recently, I have worked on the role of dispersal and disease as
mechanisms that help support and maintain ecological diversity. Most
recently, we have started work on problems at the interface of homeland
security and disease invasions (natural or deliberate) and on models
for the spread of social "diseases" like alcoholism and
ecstasy. We have also worked on models for the spread of extreme
ideologies and their impact on cultural norms. The work on homeland
security is briefly described in my February column,
"Beyond Numbers and Proofs."
The recently organized ASU School of Life Sciences (SOLS) has as part
of its mission the instigation of collaborative research and training
in areas that need strong links between diverse groups, including
experimental, computational, theoretical, and mathematical biologists.
The school brings together a range of scholars from different
disciplines ranging from law, philosophy, ecology, and biogeochemistry
to biomedicine, bioinformatics, and genomics.
The school offers several opportunities for interdisciplinary
research involving the mathematical, statistical, and life
sciences--some provided by faculty with joint affiliation with the
mathematics department. The work of J. Marty Anderies
at the interface of biology, economics, and mathematics is but one
example of the type of collaborations that already exist between SOLS
and the mathematics department.
Carlos Castillo-Chavez is a Joaquin Bustoz Jr. Professor of
Mathematical Biology in the Department of Mathematics and Statistics at
Arizona State University. He can be reached at chavez@math.asu.edu.
|
