Single-Gradient Model in <i>d</i> = 2

<div><p>(A) Variation of the estimated threshold position with averaging time, with <i>x_T</i> = 2 μm and <i>λ</i> = 2 μm.</p><p>(B) Variation of the width as a function of averaging time.</p><p>(C) Data collapse of the width at large <i>τ</i> for a range of parameter values. Full line shows the prediction of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030078#pcbi-0030078-e007" target="_blank">Equation 7</a> with <i>k</i>_2<i>d</i> = 0.40 and <i>α</i> = 2.5.</p><p>(D) <i>w</i>(<i>τ</i>) as a function of decay length, with <i>x_T</i> = 2 μm. Results for three different averaging times are shown: ×, <i>τ</i> = 10 s; circle, <i>τ</i> = 15 s; and +, <i>τ</i> = 22.5 s. The full line shows the prediction from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030078#pcbi-0030078-e007" target="_blank">Equation 7</a>. At large <i>λ</i>, the simulation results deviate from the prediction since the assumption that <i>L</i> ≫ <i>λ</i> is no longer valid.</p><p>(E) Plot of the probability distribution for measuring the threshold at position <i>x</i> with an averaging time <i>τ</i> = 45 s. The full line shows a normal distribution.</p><p>(F) Scaling of the crossover time, <i>τ_×</i>, according to <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030078#pcbi-0030078-e013" target="_blank">Equation 13</a>.</p><p>In (A), (B), and (E), the standard parameter values given in the text were used. In (C) and (F), * indicates the standard parameter values. For the other datasets, one parameter value was changed as follows: open circle, <i>D</i> = 0.5 μm²s⁻¹; open square, <i>J</i> = 6.25 μm⁻¹s⁻¹; ×, Δ<i>x</i> = 0.02 μm; closed circle, <i>μ</i> = 1 s⁻¹; +, <i>μ</i> = 0.11 s⁻¹; open diamond, <i>x_T</i> = 1 μm; and inverted triangle, <i>x_T</i> = 3 μm.</p>