New Directions Short Course in Cellular Physiology:
A Participant's Perspective
(Donald A. French, University of Cincinnati)
Today, there is an extensive interest in the use of mathematical
models to study physiology. Indeed, the "participation of the
Mathematical Sciences is indispensable" in order to further advance
research in the biomedical sciences according to P. Tondeur while he
was the director at NSF (2001). A serious problem, however, is that
the biologists who study physiological systems only rarely have the
appropriate mathematical background while the engineers, physicists,
and mathematicians who do have that background speak a very different
language and are seldom in a position to apply their skills to the
solution of physiological problems. The New Directions Short Course
at the IMA which took place on June 16-27 was, from this participant's
point of view, a successful attempt to facilitate the transition of a
broad range of mathematicians to work in the Mathematical Biosciences.
This was accomplished by the program's teachers James Keener and
Alexander Mogilner through their
- Clear lectures on a diverse set of basic background topics in
- A seemingly limitless supply of open and often accessable problems
in Cellular Physiology offered generously.
- A series of lectures by invited Biologists.
- The creation of lab groups consisting of 5-7 participants to foster work
on the open problems.
The short course was sometimes referred to as a "Mid-Career
Transition Course" and, except for a handful of younger
mathematicians, did indeed have primarily full and associate
mathematics professors. Most had backgrounds in Applied Mathematics;
Seth Oppenheimer from Mississippi State who works in Partial
Differential Equations and Modeling or Bjorn Sandstedt who works in
Dynamical Systems and Pattern Formation were a typical examples.
There were a few people with backgrounds that were less applied such
as Alex Himonas (Regularity Theory for Partial Differential Equations)
and Maurice Rojas (Algebraic Geometry). Another small group already had
some experience with Biology; Vassilios Alexides had participated in a
serious project on phototransduction in the retina and this author had
spent the last year working with Neuroscientists.
In the opening lecture, James Keener, who is one of the authors of the
award winning book Mathematical Physiology (1998 Association of
American Publishers "Best New Title in Mathematics"), encouraged the
participants to start working on biological problems right away and
followed up that day and every day thereafter with a set of open
research problems he had prepared for the conference. The problems,
in general, involved setting up ordinary differential equation (ODE)
models for biological systems.
A big challenge in this work is choosing the right cell processes to
include; one has to balance enough detail to reflect the biology
accurately but keep the equations to a minimum to begin to understand
the mathematical structure of the system. One project involved
modeling enzymatic oscillations in the bacterium E. Coli and 6-7
participants started modeling this on the first day. The dangerous
pathogen Vibrio Vulnificus which is implicated in wound
infections was another example of a project that a group of 3-4
started modeling early in the workshop. Learning was elevated to a
new level of intensity the second week when the participants were
divided into labs and instructed to discuss their progress on the
suggested problems. On the last day of the workshop the labs made
progress reports. The organizers generosity and enthusiasm paid off
as nearly all the participants demonstrated a clear understanding of
the biological problems they had chosen to tackle. The majority of
the labs had made a good start on their problem and some of the more
experienced groups had made substantial progress.
Biologists usually understand the processes they are studying on a
qualitative level; for example they frequently produce "cartoons" of
certain signaling pathways. One way mathematicians can contribute is
by attempting to interpret these processes quantitatively and
simplifying them to identify the key mechanisms. Often identification
of fixed points in the ODE systems provides useful insight into the
structure of the mechanisms and can lead to predictions on the
behavior of the biological system.
For example: is there hysteresis in the system or some other type of
switch? A major obstacle in this analysis is that the value of many
key rate constants are not known.
Many of the mathematical models of biological systems currently used
involve ODE's. J. Keener noted, however, that now, spatial location
is being recognized as an integral part of many of these biological
processes. Chemicals found in one compartment of a cell (e.g. ATP in
the mitocondria) may have to be transported via diffusion or some type
of molecular motor to another part of the cell and this movement is a
crucial part of the mechanisms involved. Thus, many of the ODE
studies may need to be enhanced by partial differential equation
models which include the spatial effects. This is, of course, a place
where mathematics is likely to have a substantial impact.
Keener and Mogilner presented two different sets of topics. Keener
focused on the background basic topics from his book which he
explained had been modeled after Physiology texts.
Mogilner presented a series of lectures on cell migration sprinkled
with advice on joining the biosciences community; how to read a
biological paper (save the materials and methods section for later and
look for "cartoons on the cellular mechanisms''), how to deal with a
lab hierarchy (talk to the "boss'' first even though you may
ultimately be referred to a Postdoc), how to structure and format a
biological manuscript, etc.
Keener specifically covered mass balance equations, Hodgkin-Huxley
equations, Michaelis-Menten enzyme kinetics, as well as a wide range
of cellular processes such as glycolysis, cell cycle, carrier mediated
transport, etc. He finished with lectures on biofilms and gels which
is a more recent area of research for him and an overview of his work
Mogilner first provided lectures on actin filaments and microtubules
that are used in cell division (mitosis), cell movement in general,
and for intercellular transport. He then presented an an overview on
bacterium swimming and how they search for food. He discussed the
flagella that power the single cells movement and then covered in
depth how the bacterium's chemical sensory mechanism works. The next
two lectures were on segmentation and patterning in the fruitfly
drosophila and he finished with a lecture on a finite element model of
the movement of the nematode sperm cell.
Finally, this author cannot help but compare this new directions
workshop to Industrial Mathematics workshops that occur at the IMA as
well as at places such as RPI and NC State. On the first one-half day
of an Industrial Mathematics workshop the invited industry scientists
present some real world problems. The mathematicians then spend the
rest of the workshop trying to solve the problems. They present their
results at the end. The ND workshop was, of course, quite similar
except that the participant also had to learn some of the physiology
before they could begin their problems.