Kinetic scheme for the gene expression with general arrival time distributions.

<p>Bursts of mRNAs arrive with a general arrival time distributions <i>f</i>(<i>t</i>). Each mRNA produces proteins with rate <i>k</i>_<i>p</i> and mRNAs and proteins decay with rates <i>μ</i>_<i>m</i> and <i>μ</i>_<i>p</i>, respectively.</p

Schematic representation of the general kinetic scheme with promoter switching.

<p>Thick line from inactive state <i>D</i>₀ to active state <i>D</i>_<i>a</i> represents a general kinetic scheme with <i>g</i>(<i>t</i>) as the waiting-time distribution for the promoter to switch to the ON state.</p

Estimation of mean burst size from sequence size function <i>ϕ</i>(<i>τ</i>).

<p>For the transcriptional scheme shown in (a), the variations of <i>ϕ</i>″(<i>τ</i>) and <i>ϕ</i>(<i>τ</i>) as a function of time <i>τ</i> (scaled by 10³) are shown in (b) and (c) respectively. The three lines correspond to three different values of <i>β</i>, 50 (dashed line), 100 (dotted line) and 200 (dashed-dotted line), while keeping <i>k</i>_<i>m</i> = 500: Exact burst size for these three cases are 11, 6 and 3.5, respectively. Estimated mean burst size has been indicated by filled symbols and the inflexion points in the sequence size function are shown by empty symbols. Other parameters: <i>α</i>₁ = 1,<i>α</i>₂ = 0.5,<i>α</i>₃ = 0.25,<i>α</i>₄ = 0.75,<i>β</i>₁ = 0.1,<i>β</i>₂ = 0.2,<i>β</i>₃ = 0.5.</p

Steady state moments for proteins.

<p>(a) Kinetic scheme for the two-state random telegraph model. For this model, steady state variance (scaled by 10⁻⁵) and third central moment <i>ν</i>₃ (scaled by 10⁻⁶) of proteins as a function of <i>μ</i>_<i>m</i>/<i>μ</i>_<i>p</i> are plotted in (b) and (c) respectively: lines represent analytic estimates and points correspond to the simulation results. Parameters are: <i>α</i> = 0.5, <i>β</i> = 0.25, <i>k</i>_<i>m</i> = 2, ⟨<i>m</i>_<i>b</i>⟩ = 5, <i>k</i>_<i>p</i> = 0.5.</p

Signatures for non-Poisson arrival.

<p>The quantities <math><msub><mi>D</mi><mi>m</mi></msub></math>, <math><msub><mi>D</mi><mi>p</mi></msub></math> and <math><msub><mi>D</mi><mrow><mi>m</mi><mi>p</mi></mrow></msub></math> are plotted for the model shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004292#pcbi.1004292.g002" target="_blank">Fig 2a</a> as a function of <i>off</i> rate <i>β</i>. Analytic estimates are shown by lines whereas points correspond to the simulation results with parameters: <i>α</i> = 0.25, <i>k</i>_<i>m</i> = 2, ⟨<i>m</i>_<i>b</i>⟩ = 5, <i>k</i>_<i>p</i> = 0.5, <i>μ</i>_<i>m</i> = 1, <i>μ</i>_<i>p</i> = 0.01.</p

Effects of extrinsic noise on burst estimation.

<p>For the transcriptional scheme shown in the inset, the relative error Δ_<i>σ</i>(⟨<i>m</i>_<i>b</i>⟩) = (⟨<i>m</i>_<i>b</i>⟩₀−⟨<i>m</i>_<i>b</i>⟩_<i>σ</i>)/⟨<i>m</i>_<i>b</i>⟩₀ is plotted. Parameters as <i>α</i>₁ = 1, <i>α</i>₂ = 0.5, <i>β</i> = 50, ⟨<i>k</i>_<i>m</i>⟩ = 500 and <i>μ</i>_<i>m</i> = 1.</p

Fungal phylogenetic composition within the Daring Lake soil at the Order level.

<p>Samples include soil that had been incubated for 86 days without NPs or MPs (Cont), soil incubated with 0.066% NPs (NP_L), soil with 6.6% NPs (NP_H), soil with 0.066% MPs (MP_L) and soil with 6.6% MPs (MP_H). Sequence identity was determined after pyrosequencing of the partial 18S rRNA genes, classified into genus, and the means of duplicate, replicate samples of those with >0.5% abundance (for either treatment or control groups) presented in separate categories, with groupings of less abundant Orders shown as ‘Others’.</p

A hierarchical clustering dendogram obtained using Ward's method, an agglomerative clustering algorithm.

<p>Phylogenic composition at the Order level for both bacteria and fungi (present at >0.5% abundance) were subjected to clustering analysis, calculating the total sum of the squared deviations from the mean of the cluster. Clusters collapsed into treatment-groups irrespective of the microbe type. Treatment groups had been incubated for 86 days without NPs or MPs treatment (Control), soil incubated with 0.066% NPs (NP_L), soil with 6.6% NPs (NP_H), soil with 0.066% MPs (MP_L) and soil with 6.6% MPs (MP_H).</p

Freeze-Casting of Multifunctional Cellular 3D-Graphene/Ag Nanocomposites: Synergistically Affect Supercapacitor, Catalytic, and Antibacterial Properties

Developments of new and highly effective multifunctional materials have been shown great interest in recent years. Herein, we report a simple, cost efficient, one-step, surfactant-free cellular 3D-graphene/Ag nanocomposite using the freeze-casting method and explore it further for supercapacitor, catalytic, and antibacterial applications. FE-SEM and HRTEM analyses of nanocomposites revealed a 3D-cellular network structure having continuous micrometer size open pores with uniformly decorated Ag nanoparticles of an average size of 25 nm. An electrochemical study exhibited the highest specific capacitance at 845 Fg^–1 at 5 mV s^–1 and excellent cyclic retention ∼97% even after 1000 cycles. Further, 3D-graphene/Ag nanocomposites are applied as catalyst to reduce methylene blue using NaBH₄. A rate of reduction above 99% was attained for 3D-graphene/Ag (40%) nanocomposites, which is significantly higher than that of pristine 3D-graphene. The network like structure of the 3D-graphene/Ag nanocomposite filtered out 37% of the population from total bacterial strains. Also, the 3D-graphene/Ag nanocomposite killed almost 100% of the bacterial strains after 3 h of incubation due to a merging effect of Ag ions and 3D-graphene

Relative amounts (mol%) of extracted fatty acids (see Methods) in control untreated (Cont) and treated soils: silver nanoparticles at 0.066% (w/v; NP_L) and 6.6% (w/v; NP_H), and silver microparticles at 0.066% (w/v; MP_L) and 6.6% (w/v; MP_H) concentrations.

<p>The bars represent the means of three independent fatty acid assessments and the standard errors. The fatty acids are grouped according to their most-frequently associated categories. “Non-signature” fatty acids are indicated as saturated or unnamed.</p