Michael Tabor

Principal Investigator
Professor and
Head Program in Applied Mathematics
Mathematics

Much of my research over the past five years has involved problems from the biological sciences. I have been particularly interested in issues of growth and form such as the evolution of patterns in bacterial colonies and the dynamics of bacterial filaments. My personal philosophy for interdisciplinary research such as this, involving the applications of mathematics to biology, is that

• it must involve the closest possible collaboration between the mathematician and the biologist
• that the research should be driven by the experimental data; and
• that it should also be "bi-directional" P that is not only should the mathematician be attempting to make contributions to the biology, but that the biologist should be making contributions to the mathematics by stimulating questions that are mathematically interesting in their own right. In addition to my own research this philosophy guides many of the activities in the BMPI program

The study of a mutant strain of the bacterium Bacillus subtilis by Prof. Neil Mendelson, of the Molecular and Cellular Department at the University of Arizona, is a perfect example of this type of research. The remarkable self-assembly dynamics of these bacterial filaments has led to the development of many new results in the mathematical description of elastic filaments. In collaboration with colleague Prof. Alain Goriely of the Program in Applied Mathematics and the Mathematics Department, we have been able to develop new dynamical models of the writhing instabilities of such filaments. In addition to providing insights into the behavior of Bacillus subtilis, these results are applicable to many other phenomena. In particular we have recently been able to use them to explain the phenomenon of tendril perversion in climbing plants. This effect corresponds to the way supporting outgrowths (the tendrils) on climbing plants (such as vines) undergo spontaneous reversal of handedn! ess as they form "twistless springs" that provide the plant with mechanically robust connections to supporting structures such as trellises and walls.

In the case of bacterial colonies we have again been stimulated by the work of Mendelson involving the patterns formed by growing colonies of a different strain of Bacillus subtilis. Although such pattern formation problems are a popular topics, the colonies studied here undergo particularly complicated morphogenesis. Furthermore, careful study of the experimental data suggests that the traditional models of chemotaxis (the motion engendered by response to a nutrient gradient) are far too simple to explain the sorts of pattern forming behavior seen. Thus, a more careful examination of this process and plausible mathematical models of it are required. This in turn will stimulate new mathematical issues as possible evolution equations for the patterns are developed.

Some recent references

"Nonlinear dynamics of filaments. IV. Spontaneous looping of twisted elastic rods", Proc. Roy. Soc. Lond. A (1998) in press, (with A. Goriely).

"Spontaneous helix-hand reversal and tendril perversion in climbing plants", Phys. Rev. Lett. 80, 1564 - 1567 (1998) ), (with A. Goriely).

"The nonlinear dynamics of filaments", Journal of Nonlinear Dynamics (1998) in press, (with A. Goriely).