A THEORY OF THE SURVIVAL VALUE OF MOTILITY 141 



effective value of R at which the concentration of nutrient is reduced 

 to zero, and hence increase there maximum flux available. 



I submit, therefore, that there may be cells which possess flagella, or 

 other similar structures, which beat asynchronously and do noth- 

 ing more than stir the surrounding" fluid and thereby increase the 

 steady-state flux rate of nutrients to the cell surface. Indeed, this 

 may even be the major function of flagella. It is my guess that such 

 a stirring mechanism might be expected to produce an increase of as 

 much as an order of magnitude or so in the steady-state flux rate, for 

 if the stirring structures have roughly the same dimensions as the cell 

 and their motion is characterized by a low Reynolds number they 

 will, in the first approximation, stir effectively only that solution which 

 is not too far removed from the region through which they sweep. 



THE CASE OF THE MOVING CELL 



It has been seen that, faced with a steadily decreasing supply of 

 food, that is, a drop in C , a given steady-state influx of nutrient 

 can be maintained by increasing the effective radius of the cell, all 

 other things being held constant. What else can be done? The only 

 other term in the expression for the flux of nutrient across the cell 

 surface which is available for manipulation is the diffusion coefficient 

 of the nutrient. At first sight it would seem that there is nothing much 

 that can be done about this except for the cell to evolve in such a 

 way that it requires only those molecules which have the highest 

 values for their diffusion coefficients, namely the smallest molecular 

 species. It turns out, however, that there is something that can be 

 done to increase the effective D n and that is to move. 



First let us consider the simple case of an organism which moves 

 with a constant linear velocity, v. In addition to those molecules 

 which reach it by diffusion, it, will collide with and capture those 

 molecules which lie within the volume that it sweeps out in a unit of 

 time. The volume swept out per unit time is x • R 2 ■ v. By assuming 

 100% capture efficiency the number of molecules intercepted per 

 unit of time <£„ is given by the volume swept out times the concen- 

 tration, that is, 



<f> = 7T • R 2 • v ■ Co 



