34 research outputs found

    Population dynamics.

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    <p>The simulated model has <i>N</i> = 20 species and <i>γ</i> = 10<sup>−4</sup>. (A) Time-courses of populations of all species. The color denotes population size (see the color scale on the right) with the dominating species visible as red horizontal bands. Note five diversity waves ending at purple dashed lines. Transitions between these waves were triggered by extinctions of the dominating species # 5, 15, 6, 19, 16 correspondingly. (B) The time-course of the species # 6 with the logarithmic y-axis. Note the pattern of intermittent periods of exponential growth fueled by local extinctions.</p

    Average population vs species’ properties in the “Resilience model” variant #7.

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    <p>Time-averaged population of a species (see color scale on the right) plotted as a function of its re-population growth rate Ω<sub><i>i</i></sub> (x-axis) and population drop after collapses <i>γ</i><sub><i>i</i></sub> (y-axis). in a variant of our model with fitness differences between species. Note that the population increase with both Ω<sub><i>i</i></sub> and <i>γ</i><sub><i>i</i></sub>. Populations and fitness parameters of <i>N</i> = 1000 species were taken from 50 million snapshots of the model.</p

    Memory of population size distribution is preserved across several diversity waves.

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    <p>Time course of jumps −log[1 − <i>P</i><sub><i>collapsed</i></sub>(<i>t</i>)] in the logarithm of surviving populations following a collapse of a substantial population <i>P</i><sub><i>collapsed</i></sub>(<i>t</i>) > 10<sup>−10</sup> in A) the simplified model in which at the start of each wave all populations are set equal to each other; B) our basic model. Both were simulated at <i>N</i> = 1000 and <i>γ</i> = 10<sup>−20</sup>. Note that our basic model, unlike its simplified counterpart, preserves memory of population sizes distribution across several subsequent diversity waves. This is manifested e.g. in similar fractal structure of jumps sizes in waves #2-6 shown in panel B). Colors of symbols (see colorbar below) represent the <i>log</i>10 of the number of substantial populations during the the previous wave, when a given population originated at the small size <i>γ</i>. Thus red dots mark populations originated at the very end of the previous wave, while yellow dots—those originated when there were two large populations left in the previous wave. Finally, green, blue, and purple dots refer to older populations in the previous wave.</p

    Diversity dynamics.

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    <p>The grey shaded area shows the the time course of the population diversity <math><mrow><mi>D</mi><mo>=</mo><mn>1</mn><mo>/</mo><msub><mo>∑</mo><mi>i</mi></msub><msubsup><mi>P</mi><mi>i</mi><mn>2</mn></msubsup></mrow></math> in our model with <i>N</i> = 1000 and <i>γ</i> = 10<sup>−12</sup>. Purple dashed lines mark the beginnings of diversity waves when a collapse of the dominant species with <i>P</i><sub><i>max</i></sub> ≃ 1 leads to an abrupt increase in population diversity from ∼ 1 to ∼ <i>N</i>. The diversity subsequently decreases ∝ exp(−<i>t</i>/<i>N</i>) (dash-dotted line).</p

    Time-aggregated distributions for different values of <i>N</i> and <i>γ</i>.

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    <p>Time-aggregated distributions of population sizes in our model with A) <i>γ</i> = 10<sup>−10</sup> and <i>N</i> = 100 (blue), <i>N</i> = 1000 (red), and <i>N</i> = 10,000 (green). B) <i>N</i> = 1000 and varying <i>γ</i> ranging between 10<sup>−4</sup> (green) to 10<sup>−10</sup> (red) in ten-fold decrements. Note the emergence of a nearly universal scale-free tail of the distribution fitted with <i>τ</i> ≃ 1.7 (dashed line).</p

    At steady state, protein A can be present either as a mixture of misfolded monomers and insoluble oligomers (U), a folded monomer F, or in a complex with its interaction partners (D).

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    <p>At steady state, protein A can be present either as a mixture of misfolded monomers and insoluble oligomers (U), a folded monomer F, or in a complex with its interaction partners (D).</p

    The equilibrium between the folded state of protein A (blue protein) and its unfolded/insoluble state (blue coil) is affected by the interactions of the folded state with its interaction partner B (red).

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    <p>The formation of the AB dimer lowers the population of the unfolded/insoluble state of protein A and effectively stabilizes the folded state.</p

    The spearman correlation coefficient between interaction-induced stability and inherent stability as a function of effective population size (See supplementary Text S1).

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    <p>Population size is in arbitrary units. The blue region identifies the location of real life proteomes (See <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003023#pcbi-1003023-g003" target="_blank">Fig. 3</a>).</p

    SOS Response to Prolonged UV Exposure

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    <div><p>(A) LexA (blue) and RecA* (red) levels as a function of time in the presence of a continuous source of UV, which in 300 min (i.e., five cell generations) produces as many lesions as an instantaneous pulse of 20 J/m<sup>2</sup>.</p><p>(B) The presence or absence of mutagenesis in our model in response to a pulse of UV radiation of a given integral intensity (<i>y</i>-axis) and duration (<i>x</i>-axis). Mutagenesis was detected in the colored regions. The criterion for its detection was the Pol V level crossing a specified threshold: 0.1 nM (yellow region), 1 nM (orange region), and 10 nM (brown region).</p></div

    Temporal Profile of Pol V Following a UV Dose of 20 J/m<sup>2</sup> as a Function of Various Parameters

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    <div><p>(A) The three curves refer, respectively, to strong (<i>K<sub>dd′</sub></i> = 0.01 nM, blue), medium (<i>K<sub>dd′</sub></i> = 1 nM, red), and weak (<i>K<sub>dd′</sub></i> = 100 nM, black) binding between UmuD and UmuD′.</p><p>(B) The effects of changing the binding constant between the UmuD′ homodimer and UmuC: as binding strength 1/<i>K</i> in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030041#pcbi-0030041-e012" target="_blank">Equation 12</a> increases (<i>K</i> = 100,10,1 nM for the green, blue, and red curves, respectively), the Pol V concentration saturates at the 200 nM value set by the maximum cellular level of UmuC.</p><p>(C) For strong binding (<i>K<sub>dd′</sub></i> = 0.01 nM), the three curves show the effect of increasing the degradation rate <i>γ<sub>dd′</sub></i> of UmuD′ by ClpX. As a default, the degradation rate is set equal to the dilution rate <i>γ<sub>dil</sub></i> (blue). The rate is half of the dilution rate for the red curve, whereas it is zero for the black curve. For the green curve, the degradation rate is double that of the dilution rate, which—at this level of UV damage—results in almost no Pol V.</p><p>(D) The effect of removing the Pol V to RecA* feedback. The blue curve is when there is feedback (as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030041#pcbi-0030041-g007" target="_blank">Figure 7</a> A–C). The green curve is when there is no feedback, i.e., τ<i><sub>stalled</sub></i> = τ<i>stalled</i>(0), irrespective of the Pol V level.</p></div
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