Biomedical Engineering Reference
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chemicals that attract them and to swim away from other chemicals that repel
them ( chemotaxis ). The bacteria proceed in more or less straight lines for a cer-
tain period. This is called a "run." However, there is always a probability that the
bacteria will suddenly "tumble," which amounts to choosing a new run direction
at random. If the bacteria sense an increasing concentration of an attractant or a
decreasing concentration of a repellent, then the tumble probability decreases.
Thus, the bacteria persist longer in favorable behavior. This engenders a chemo-
tactic drift.
The described behavior of chemotactic bacteria has been suggested as the
basis for a mathematical algorithm for finding a point that maximizes some
function f of three variables x , y , z . (See (13) for a recent exposition.) A "chemo-
tactic" point ( x , y , z ) runs and tumbles until it approaches a maximum of f .
Suppose now that two different desiderata are simultaneously present, to
maximize a function f and also to maximize a second function g . Now let the
chemotactic point decrease its tumble probability if f is nondecreasing but g is
increasing, or if g is nondecreasing and f is increasing. Then one expects that the
point will approach the "Pareto optimum" set, where no change of ( x , y , z ) can
result in an increase of either f or g without decreasing the other. Of course, the
principles enunciated work for functions of arbitrary numbers of variables.
The suggested scheme could in principle improve the performance of a bio-
logical system in the face of multiple independent goals, goals that alter as con-
ditions change. (See (14) for examples of multiple goal systems, both biological
and nonbiological.) Random shifts in tactics could be tried, in attempts to do
better with respect to at least one goal and no worse with the others. A tactic that
accomplishes this persists longer before the inevitable random shift to something
new.
6.
RELEVANCE TO BIOMEDICINE
6.1. Cancer Chemotherapy
In principle, any advance in understanding immune system physiology
should eventually have medical relevance. In §2 a model of monocyte and PMN
hematopoiesis was shown to be of possible relevance to cancer chemotherapy.
Reciprocally, observations of the reaction to the chemotherapy supplied data
that were essential to calibrate the model.
6.2. Cytokine Therapy
There may be a "long-shot" impact on biomedicine of regarding cytokines
as bearers of information (§4.2).
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