(A) Hypothetical mechanism of cell clustering through slime-trail-following in reversing <i>M</i>. <i>xanthus</i> cells. (B) Circular cell aggregates observed in simulation for non-reversing agents with the slime-trail-following mechanism (<i>η</i> = 0.24, <i>L</i>_<i>s</i> = 11 <i>μm</i>, <i>ε</i>_<i>s</i> = 1.0).

<p>(A) Hypothetical mechanism of cell clustering through slime-trail-following in reversing <i>M</i>. <i>xanthus</i> cells. (B) Circular cell aggregates observed in simulation for non-reversing agents with the slime-trail-following mechanism (<i>η</i> = 0.24, <i>L</i>_<i>s</i> = 11 <i>μm</i>, <i>ε</i>_<i>s</i> = 1.0).</p

Clustering behavior of non-reversing flexible agents in simulations.

<p>(A-D) Snapshots of the simulation region at 180 min of simulation time for different cell densities, <i>η</i>. (A) <i>η</i> = 0.08, (B) <i>η</i> = 0.16, (C) <i>η</i> = 0.24, (D) <i>η</i> = 0.32. Flexible agents formed aligned clusters at moderate to high cell densities (<i>η</i> ≥ 0.16). (E) Mean cluster sizes, 〈<i>m</i>〉, from simulation as a function of cell density, <i>η</i>. The error bars indicate the standard deviation in the data. The results are averaged over 5 independent simulation runs. The mean cluster sizes increased with increases in cell density. (F) Orientation correlation 〈cos 2Δ<i>θ</i>_<i>r</i>〉 among cells as a function of neighbor cell distance, <i>r</i>. Δ<i>θ</i>_<i>r</i> is the angle deviation between orientations (<i>θ</i>) of a pair of neighbor cells separated by a distance <i>r</i>. Orientation correlation (cos 2Δ<i>θ</i>_<i>r</i>) values from all cell pairs are binned based on <i>r</i> (bin width = 1 <i>μm</i>) and averaged. Dashed and solid lines represent orientation correlation values at 1 min and 180 min of simulation time, respectively. Agents in clusters showed higher neighbor alignment at larger distances compared to the initial randomly oriented cells. Furthermore, the alignment increases with increases in cell density.</p

Comparison of cell clustering behavior in simulations with experiments.

<p>(A-B) Comparison of cluster size distributions (CSD) from simulations (lines) with experimental data (symbols, digitized from Starruẞ et al. [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004474#pcbi.1004474.ref016" target="_blank">16</a>]) for non-reversing (A) and reversing (B) cells. Probability, <i>p</i>(<i>m</i>), of finding a cell in a cluster is plotted as a function of the cluster size <i>m</i>. We use different sets of slime-trail-following mechanism parameters for non-reversing (<i>L</i>_<i>s</i> = 0.6 <i>μm</i>, <i>ε</i>_<i>s</i> = 0.5) and reversing (<i>L</i>_<i>s</i> = 11 μ<i>m</i>, <i>ε</i>_<i>s</i> = 0.2) agents. CSD results from simulations show a similar trend to that of the experimental data. (A) Non-reversing cells show a power-law-like CSD, whereas reversing cells show a monotonically decreasing CSD (B). (C-D) Heat maps of cell visit frequencies over the simulation region for 2 consecutive hours (<i>η</i> = 0.24). The color bar represents the number of cell visits per hour at a particular location. Non-reversing cells show a dynamic cluster pattern with changes in cell traces (C), whereas reversing cells show a static cluster pattern with the pattern of cell traces remaining approximately the same over time (D). (E) Probability of cell visits, <i>p</i>(<i>N</i>), as a function of visit frequency, <i>N</i>, for non-reversing (red) and reversing cells (green) over a 1-hr simulation time (120–180 min). Reversing cells show a large fraction of sites with high visit frequencies compared to non-reversing cells.</p

Clustering behavior of periodically reversing agents in simulations.

<p>(A) Snapshot of the simulation with periodically reversing agents (<i>η</i> = 0.24) at 180 min of simulation time. Reversing agents did not show significant clustering. (B) Mean cluster sizes, 〈<i>m</i>〉, in simulation as a function of cell density, <i>η</i>, for agents following slime trails (green line) and agents without slime trails (black line). Agents following slime trails showed a significant increase in mean cluster size compared to agents without slime-trail-following. (C) Snapshot of the simulation for periodically reversing cells with the slime-trail-following mechanism (<i>η</i> = 0.24, <i>L</i>_<i>s</i> = 11 <i>μm</i>, <i>ε</i>_<i>s</i> = 1.0, refer to <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004474#sec009" target="_blank">Methods</a> for details) at 180 min of simulation time. Agents show improved clustering compared to those without the slime-trail-following mechanism. (D) Orientation correlation 〈cos 2Δ<i>θ</i>_<i>r</i>〉 among agents for reversing cells (black) and reversing cells with the slime-trail-following mechanism (green). Dashed and solid lines are orientation correlation values at 1 min and 180 min of simulation time, respectively. Orientation correlation with neighbors improved for larger neighbor distances with the slime-trail-following mechanism.</p

An ultrasensitive response amplifies noise differences between cotranscribed and uncoupled linear metabolic pathway modules.

<p>A. When copy numbers of enzymes A and B are matched, transient changes in production and consumption flux are matched, resulting in maintenance of a low concentration of metabolic intermediate. An increase in expression of <i>A</i>, unmatched by a change in expression of B, can cause the production flux of metabolic intermediate to exceed the saturation point of flux through enzyme <i>B</i>, resulting in accumulation of metabolic intermediate. B. Simulated timecourse of metabolic intermediate in cotranscribed and uncoupled configurations of the linear metabolic pathway model. C. Steady state response of metabolic intermediate to changes in the ratio of production flux to consumption flux (solid line), with stochastic simulation timecourses of intermediate in cotranscribed and uncoupled linear metabolic pathway module configurations plotted with respect to changing flux balance. Results represent the single ribosome binding site model (translational coupling), but are qualitatively the same for multiple ribosome binding sites as well.</p

Dependence on expression level for frequencies of gene pairs of physically interacting proteins sharing operons.

<p>A dataset of single-cell protein and mRNA copy numbers in <i>E. coli </i><a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002672#pcbi.1002672-Taniguchi1" target="_blank">[43]</a> shows reduced frequency of coupling for abundant proteins (A) and mRNA (B). Error bars represent one standard deviation from bootstrapping the data 1,000 times. Significance levels were determined by a bootstrap test.</p

Noise levels in physiologically relevant variables depend on transcriptional coupling.

<p>We computed coefficient of variation [CV] = σ/μ, where σ is the standard deviation and μ is the mean, for simplified modules representing modes of interaction between two proteins: A) catalysis of subsequent steps in a linear metabolic pathway, B) redundant catalysis of the same metabolic step, C) catalysis of metabolic steps following a branch point, D) redundant regulation of a downstream gene <i>p</i> encoding protein <i>P</i>, E) physical interactions resulting in heterodimer formation, and F) covalent modification of one protein by another. In metabolic modules, S, I and P represent substrate, intermediate, and product, respectively. Complete reaction diagrams and parameters are given in supplemental tables (S4, S5, S6). Error bars represent one standard deviation from bootstrap resampling. Results correspond to the single ribosome binding site model (translational coupling), but hold qualitatively for multiple ribosome binding sites as well.</p

Negative feedback minimizes competition between stress σ factors for RNA polymerase.

<p><b>A,B.</b> Simplified network diagrams of stress σ-factors σ^B and σ^W and housekeeping σ-factor σ^A competing with each other for RNA polymerase. σ^B and σ^W activities are regulated by negative and positive feedbacks in (A) and (B) respectively. In both cases, signaling proteins P_B and P_W control the stress-signal driven activation of σ^B and σ^W respectively. <b>C, D.</b> Dependence of free σ^B and σ^W levels on P_B at fixed P_W (= 2μM). In the wildtype negative feedback system (C), increase in σ^B phosphatase leads to an increase in both free σ^B (green curve) and free σ^W (red curve). In the positive feedback system (D), increase in σ^B phosphatase leads to an increase in free σ^B (green curve) and a decrease in free σ^W (red curve). <b>E, F.</b> σ^B and σ^W target promoter activities as a function of P_B at fixed P_W in the wildtype negative feedback system (E), and the positive feedback system (F). <b>G, H.</b> RNA polymerase bound σ^B (Rpol-σ^B) as a function of P_B at fixed P_W in the wildtype negative feedback system (G) and the positive feedback system (H). Increase in σ^B phosphatase (P_B) leads to an increase in Rpol-σ^B (green curve) and corresponding decreases ΔRpol-σ^W (core complex with σ^W, red area) and ΔRpol-σ^A (complex with σ^A, blue area).</p

Operon organization trends in <i>E. coli</i> relate to noise-minimizing transcriptional coupling patterns.

a<p>Same operon pair fraction.</p>b<p>Numbers represent <i>p</i>-value vs rand.</p

Pulsatile response of the σ^B network to stochastic phosphatase bursts during energy stress.

<p>Model simulations for σ^B network response where energy stress leads to an increase in stress-sensing phosphatase RsbQP burst size (A-D) or RsbQP burst frequency (E-H). <b>A,E.</b> Simulations show stochastic bursts in levels of RsbQP lead to pulses of σ^B target promoter activity. Light and dark green curves are sample trajectory from stochastic simulation at high and low stress respectively. Note that σ^B target promoter activity pulse amplitude increases significantly with increasing stress for burst size modulation (A) but not for burst frequency modulation (E). <b>B,F.</b> Mean σ^B pulse amplitude increases linearly as a function of mean phosphatase level for burst size modulation (B) but is insensitive to mean phosphatase level for burst frequency modulation (F). Green circles and errorbars show means and standard deviations calculated from stochastic simulations. Black line is a linear fit. <b>C,G.</b> With increasing mean phosphatase level, mean σ^B pulse frequency increases ultrasensitively for burst size modulation (C) and linearly for burst frequency modulation (G). Green circles and errorbars show means and standard deviations calculated from stochastic simulations. Black curves are a Hill-equation fit with <i>n</i>_<i>Hill</i> = 5.6 in (C) and a linear fit in (G) respectively. <b>D,H.</b> Mean σ^B target expression increases ultrasensitively as a function of mean phosphatase level for both burst size (D) and burst frequency (H) modulation. Green circles are the mean σ^B target expression calculated from stochastic simulations. Black curve is a Hill-equation fit with <i>n</i>_<i>Hill</i> = 2 in (D) and in <i>n</i>_<i>Hill</i> = 1.2 (H).</p