New Directions Short Course in Cellular Physiology: A Participant's Perspective

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

1. Clear lectures on a diverse set of basic background topics in Cellular Physiology.
2. A seemingly limitless supply of open and often accessable problems in Cellular Physiology offered generously.
3. A series of lectures by invited Biologists.
4. 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 on fibrillation.

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.