144 FRANCIS D. CARLSON 



THE BALANCE OF ENERGY EXPENDITURE 

 AND ENERGY ACCUMULATION 



Having developed relationships for the dependence of the rate 

 of nutrient accumulation and the rate of energy expenditure on 

 velocity with which the cell moves, we are in a position to examine 

 the conditions of energy balance for the moving cell. 



This is most easily done with the aid of some graphical plots of the 

 relations 



$ s = 4tt • RC (D n + A' • v) 



and 



p = p + Av*/E 



A plot of $ s as a function of v is a straight line with a slope, 4?r • RC\ ■ K; 

 a >;-axis intercept, y = 4tt • RC ■ D n ; and an .v-axis intercept, v = 

 — DJK. A plot of P as a function of v is a parabola with a y-axis 

 intercept of P . In Fig. la, $ s and P are plotted against z>. In this 

 plot Co is such that the intercept y = 4nrRC D„ is greater than P - 

 This simply means that the concentration is such that the maximum 

 rate at which nutrient can diffuse to the cell is greater than the basal 

 metabolic rate P„ . The cell is not limited in its supply of nutrient by 

 diffusion; hence growth is possible. Movement is not necessary in 

 order to increase the influx of nutrient. The cell can, however, move 

 with velocities v m or less and remain in energy balance, although 

 there is a velocity somewhat less than v m which if exceeded will 

 result in a decrease in the influx of nutrient over that which can be 

 attained at rest. 



In Fig. lb the concentration has decreased so that now y = P • 

 The stationary cell receives, by diffusion, barely enough nutrient to 

 survive. There is no nutrient left over for growth. Under these cir- 

 cumstances the cell can increase its influx of nutrient by moving at 

 velocities less than v m . 



In Fig. lc the concentration has dropped still farther and now y 

 is less than P . The flux of nutrient by diffusion to the stationary 

 cell is insufficient for survival. The cell must move with a velocity 

 v h if it is to survive and with a velocity greater than v b but less than 

 v m if it is to grow. 



In Fig. Id the concentration of nutrient has dropped to the point 



