Fundamental Limits to Position Determination by Concentration Gradients
Figure 2
(A) The mean threshold position fluctuates about L/2 due to the symmetry of the system.
(B) Variation of the width w as a function of averaging time.
(C) Data collapse of the width as a function of averaging time, at long times, for a range of parameter values. The full line shows Equation 19 with k~2d = 0.63 and Α~ = 2.5. * indicates the standard parameter values. For the other datasets, parameter values were changed as follows: open circle, D = 0.5 μm2s−1; open square, J = 9 μm−1s−1; ×, Δx = 0.02 μm; closed circle, μ = 1 s−1; +, μ = 0.25 s−1; diamond, L = 7.5 μm; and inverted triangle, L = 15 μm and Δx = 0.02 μm.
(D) Plot of width as a function of decay length for averaging times: ×, τ = 30 s; open circle, τ = 45 s; and +, τ = 60 s. The full line shows the prediction from Equation 19.