DEPARTMENT OF MATHEMATICAL &
UNIVERSITY OF ALBERTA
MATHEMATICAL BIOLOGY SEMINAR
MONDAY February 2, 2004
Dr. Janet A.W. Elliott
Canada Research Chair in Interfacial Thermodynamics, University of Alberta
Currently Visiting Professor, Chemical Engineering and Mechanical Engineering, M.I.T.
The challenge in using fundamentals from the physical sciences to model biological systems is to have enough complexity in the mathematical model to capture the behaviour of interest while at the same time having a simple enough biological model that the problem is tractable. Particular applications of thermodynamics in cryobiology will be used to illustrate this point. Cryobiology is the study of the effects of extremely low temperature on biological systems with a major application being preserving cells and tissues for transplantation or research.
An example of a ubiquitous rudimentary thermodynamic model is the Boyle van’t Hoff equation used to relate equilibrium cell volume to the osmolality of the surrounding solution. This relationship is used extensively in cryobiological calculations. The Boyle van’t Hoff equation is only valid if the cell contents form a thermodynamically ideal dilute solution (i.e. osmolality linear in concentration). This is a rather extreme requirement and one consequence of the inappropriate use of the Boyle van’t Hoff equation is the unreasonably large value obtained for the osmotically inactive fraction of many types of cells, such as human red blood cells. When a replacement for the Boyle van’t Hoff equation is combined with a hemoglobin-plus-salt osmotic virial equation (i.e. osmolality given by a polynomial expansion in concentration rather than being linear), the inferred osmotically inactive fraction for human red blood cells is reduced by 25%.
We are putting various mathematical models such as the above into a computer simulation tool being developed to predict transport and freezing during the cooling of cells and their environment. The simulations are becoming so accurate that we are beginning to use them in a predictive way to find and optimize novel cryoprotection protocols. In addition, current mathematical research involves examining the stability of coupled flux equations using the osmotic virial equation that may be relevant to cryobiology.
(with L. E. McGann, J. D. Benson, R. Bannerman, L. Ross-Rodriguez, H. Y. Elmoazzen)