Percolation transition: when all available channels open during a puff.

<p>A: Probability that all available IPR's become open, , as a function of the dimensionless radius of influence, , for (circles), (squares) and (triangles). B: (circles), (squares) and (triangles) as functions of . The values of and for the case with are indicated in A with one and two asterisks, respectively.</p

Change of behavior with event size.

<p>A: for data obtained with our model using , , and (solid circles). Complementary cumulative Poisson distributions, , for (inverted triangles), (triangles), (squares), (rhombes). B: Error of approximating by the various for (see text for definition) as a function of . Symbols are the same as in A. From this figure we choose as the one that provides the best fit to the tail of . The error in the case is larger than 0.02 in most cases and falls outside the region displayed in the figure. C: for the four values of that we tested. We see that .</p

Normalized waiting time distribution between bindings of a single enzyme.

<p>We show with squares the dwell time distribution estimated differentiating <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151132#pone.0151132.e019" target="_blank">Eq (10)</a> as prescribed in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151132#pone.0151132.e071" target="_blank">Eq (29)</a> and computing the integral numerically using <i>D</i>_<i>f</i> = 5<i>μm</i>² <i>s</i>⁻¹, <i>V</i>_<i>obs</i> = 5.6 × 10⁻³ <i>μm</i>³, [<i>S</i>_<i>T</i>] = 1/<i>V</i>_<i>obs</i>, <i>k</i>_<i>on</i> = 2<i>μM</i>⁻¹ <i>s</i>⁻¹, <i>k</i>₋₁ = 0.5<i>s</i>⁻¹ and, from top to bottom, the enzyme concentrations [<i>P</i>^(<i>f</i>)] = 10, 20, 50, 100 and 200<i>μM</i>. All the distributions are normalized with respect to their value at <i>τ</i> = 0. We also show the analytic <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151132#pone.0151132.e073" target="_blank">expression (30)</a> (solid curves) for all cases and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151132#pone.0151132.e074" target="_blank">Eq (31)</a> (dashed curves) for the three cases with the largest values of [<i>P</i>^(<i>f</i>)].</p

Correction: Fluctuations, Correlations and the Estimation of Concentrations inside Cells

<p>Correction: Fluctuations, Correlations and the Estimation of Concentrations inside Cells</p

Turing pattern obtained with the 5-variable Selkov model in two space dimensions.

<p>Stationary pattern in [<i>ATP</i>] achieved after 10 min from an initial condition randomly distributed around the Turing-unstable fixed point. White corresponds to [<i>ATP</i>] = 2.47 mM and black to 1.1 mM. The simulation was done for η = 1.3, ν = 0.0175, ε = 0.0005, α = 15, <i>K</i>₁ = 1500, <i>K</i>₃ = 1, and <i>d</i>₁ = <i>d</i>₂ = 0.01.</p

Comparison of different theoretical prescriptions of the fractional noise, , as time increases.

<p>(a) <i>vs</i> <i>T</i>_<i>obs</i> computed using <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151132#pone.0151132.e040" target="_blank">Eq (22)</a> with (dashed line) and with (dashed-dotted lines) and using the combination of Eqs <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151132#pone.0151132.e004" target="_blank">(3)</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151132#pone.0151132.e064" target="_blank">(27)</a> with (solid line). (b) Two of the curves displayed in (a) using the same symbols as in (a) but as functions of the mean of the accumulated mRNA produced. The curves correspond to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151132#pone.0151132.e096" target="_blank">Eq (38)</a> (dashed) and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151132#pone.0151132.e116" target="_blank">Eq (42)</a> (solid) with in both cases.</p

Relative error of the average number of bound particles as a function of time.

<p><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151132#pone.0151132.e008" target="_blank">Eq (7)</a> with <i>τ</i>^(<i>b</i>) given by <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151132#pone.0151132.e027" target="_blank">Eq (12)</a> (dashed-dotted curve) is plotted in all subfigures. (a) The <i>fr</i> limit holds. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151132#pone.0151132.e042" target="_blank">Eq (24)</a> (black solid curve) and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151132#pone.0151132.e043" target="_blank">Eq (25)</a> (dashed-dotted curve) are also plotted. (b) Same as (a) but with the vertical axis on a logarithmic scale. (c) The <i>fd</i> limit holds. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151132#pone.0151132.e040" target="_blank">Eq (22)</a> (black solid curve) and the combination of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151132#pone.0151132.e004" target="_blank">Eq (3)</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151132#pone.0151132.e064" target="_blank">Eq (27)</a> (gray solid curve) are also plotted. (d) Similar to (a) but for parameters such that goes below 10% for <i>T</i>_<i>obs</i> much smaller than the longest correlation time which is ∼1<i>s</i>.</p

Comparing the predictions of the analytic expresions with stochastic simulations.

<p>We show the time-dependence of the normalized average numbers of bound particles, <i>N</i>^(<i>b</i>), obtained from stochastic simulations (symbols) and of the region defined by with computed in various ways. The dashed-dotted curves correspond to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151132#pone.0151132.e008" target="_blank">Eq (7)</a> with <i>τ</i>^(<i>b</i>) given by <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151132#pone.0151132.e027" target="_blank">Eq (12)</a>. (a) The <i>fr</i> limit holds. The shaded area is computed using <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151132#pone.0151132.e042" target="_blank">Eq (24)</a>. (b) The <i>fd</i> limit holds. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151132#pone.0151132.e040" target="_blank">Eq (22)</a> is used to compute the shaded area. The error derived from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151132#pone.0151132.e064" target="_blank">Eq (27)</a> is also shown (dashed curve).</p

Parameters used in the stochastic simulations.

<p>The parameters of the first column were derived in [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151132#pone.0151132.ref010" target="_blank">10</a>] from an analysis of FCS experiments performed in <i>Drosophila</i> embryos. Those of the second column were chosen arbitrarily.</p

Parameters used to make the curves of Fig 1.

<p>These parameters were chosen arbitrarily.</p