"The time needed to set up a gradient: detailed calculations"

Date:
1970-1971
Reference:
PP/CRI/H/4/25
Catalogue details

Licence: In copyright

Credit: "The time needed to set up a gradient: detailed calculations". Source: Wellcome Collection.

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    maximum value of 1.5 for the sigmoid pump. These take comparable times to set up a linear gradient. A comparison of Tables 2 and 3 shows that, as expected, the sigmoid pump is the more efficient, since it can reach a given value of t* for a lower value of the initial flux. However, the important point to notice is that for all the cases considered y the time V is not increased grossly above the value for the mathematical model described first. The results presented in Tables 2 and 3 were calculated on a computer, for a model with twenty cells between_x.= o and x = L. The diffusion equation =1) ,-P 9 (where C is concentration; D, diffusion MM iu constant at point x at time t ) was approximated as a finite difference srn. . equation _c(x, t +6t) = c(x, t) +_Dôt fc(x +6x, _t) + t) - 2 c(x, t)]/(7) (6 x) 2/ L where c(x, t) is the concentration at time t and the point x, _¿t is the time interval between each step, and __Sc_the distance between each point. We took D =0 .01, J .X =û. 05L_and ¿t =0 .01 (the conversion to dimensionless time gave fSTzr ì K;'^ y * t ='d t =0.01 t \ The concentrations c(o, t) and c(L, t) at the source and sink were changed according to the specifications for the flux of each model. In the simple diffusion model, where it was possible to calculate the constant easily algebraically, we compared the result with those obtained by the reiterative process using equation (7). These are shown in Table 4.
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