Survival Kinetics of Starving Bacteria Is Biphasic and Density-Dependent

<div><p>In the lifecycle of microorganisms, prolonged starvation is prevalent and sustaining life during starvation periods is a vital task. In the literature, it is commonly assumed that survival kinetics of starving microbes follows exponential decay. This assumption, however, has not been rigorously tested. Currently, it is not clear under what circumstances this assumption is true. Also, it is not known when such survival kinetics deviates from exponential decay and if it deviates, what underlying mechanisms for the deviation are. Here, to address these issues, we quantitatively characterized dynamics of survival and death of starving <i>E</i>. <i>coli</i> cells. The results show that the assumption – starving cells die exponentially – is true only at high cell density. At low density, starving cells <i>persevere</i> for extended periods of time, before dying rapidly exponentially. Detailed analyses show intriguing quantitative characteristics of the <i>density-dependent and biphasic</i> survival kinetics, including that the period of the perseverance is inversely proportional to cell density. These characteristics further lead us to identification of key underlying processes relevant for the perseverance of starving cells. Then, using mathematical modeling, we show how these processes contribute to the density-dependent and biphasic survival kinetics observed. Importantly, our model reveals a thrifty strategy employed by bacteria, by which upon sensing impending depletion of a substrate, the limiting substrate is conserved and utilized later during starvation to delay cell death. These findings advance quantitative understanding of survival of microbes in oligotrophic environments and facilitate quantitative analysis and prediction of microbial dynamics in nature. Furthermore, they prompt revision of previous models used to analyze and predict population dynamics of microbes.</p></div

A role of extracellular signaling and <i>rpoS</i> in the density-dependent survival kinetics.

<p>(A) A role of extracellular signaling: a high density of exponentially-growing cells (<i>N</i>_CFU ≈ 7·10⁸/ml) was transferred to a fresh medium without glycerol. <i>N</i>_CFU of cells in the fresh medium (green triangles) decreases similarly to that from the previous experiment (solid blue squares, re-plotted from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.g001" target="_blank">Fig. 1</a>). Next, a spent medium was prepared from a culture of a high density of cells. <i>N</i>_CFU of cells at low density in the spent medium (green inverse triangles) decreases similarly to that from the previous experiments (solid red circles, re-plotted from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.g001" target="_blank">Fig. 1</a>). The results indicate that extracellular signaling does not play a role for the density-dependent kinetics. See the text for details. (B) A role of <i>rpoS</i>: Under starvation, <i>N</i>_CFU of the Δ<i>rpoS</i> strain (open symbols) decreases faster than that of the wild type strain (solid symbols, re-plotted from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.g001" target="_blank">Fig. 1</a>); compare the slope of the dotted line −μ₀^ΔrpoS (= −0.035 hr ^-1) and the slope of the dashed line −<i>μ</i>₀ (= −0.018 hr ^-1). See also <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.s007" target="_blank">S6 Fig</a> for <i>N</i>_CFU of other densities of the Δ<i>rpoS</i> strain. Importantly, in the low cell-density cultures (e.g., open red circles), the periods during which <i>N</i>_CFU is maintained are much shorter for the Δ<i>rpoS</i> strain (brown region) than for the wild type strain (green region); note that here the brown and green regions are approximately determined as regions where the survival kinetics does not follow exponentially decay. This indicates that <i>rpoS</i> plays an important role for the wild type strain to maintain <i>N</i>_CFU for extended periods of time in low density under starvation.</p

A mechanistic account of the density-dependent, biphasic survival kinetics.

<p>(A) Cells consume substrates for cell growth and the substrate concentration decreases in the medium (green line). When the concentration decreases to the levels affecting the rate of cell growth, RpoS accumulates (blue line) [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.ref026" target="_blank">26</a>,<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.ref027" target="_blank">27</a>]. RpoS represses cell growth (red line) [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.ref030" target="_blank">30</a>–<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.ref032" target="_blank">32</a>], forming negative feedback. In the feedback scheme, at low substrate levels, RpoS strongly represses cell growth and hence, substrate consumption, allowing cells to <i>conserve</i> a small amount of the substrate before it is completely depleted by cell growth. See the text for details. (B) This feedback predicts that as the substrate concentration is reduced, the growth arrest occurs at a non-zero substrate concentration <i>S</i>₁, i.e., <i>λ</i> = 0 at <i>S</i> = <i>S</i>₁ > 0. This prediction agrees with previous studies [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.ref033" target="_blank">33</a>–<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.ref035" target="_blank">35</a>]. Importantly, further studies show that although the growth rate of the population is zero at <i>S</i> = <i>S</i>₁, the substrate consumption rate is not zero; see [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.ref036" target="_blank">36</a>] for review. This is commonly known as maintenance requirement; it requires continuous influx of the substrate to maintain a constant population size (<i>λ</i> = 0). If the influx of the substrate is less than the level needed for the maintenance, <i>λ</i> < 0 (green region) [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.ref037" target="_blank">37</a>,<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.ref038" target="_blank">38</a>]. Our model indicates that <i>λ</i>(0) = − <i>μ</i>₀; see the text for details. As a comparison, the relation of <i>λ</i> and <i>S</i> in the Δ<i>rpoS</i> strain is shown as a dashed line. Note that at intermediate substrate concentrations, <i>λ</i> of Δ<i>rpoS</i> strain is higher than that of the wild type strain [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.ref030" target="_blank">30</a>–<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.ref032" target="_blank">32</a>]. Also, note that when the substrate is completely exhausted, the culture of the Δ<i>rpoS</i> strain loses viability more rapidly than the wild type strain (see [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.ref018" target="_blank">18</a>,<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.ref025" target="_blank">25</a>] and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.g002" target="_blank">Fig. 2B</a>); thus, the value of <i>λ</i>(0) of Δ<i>rpoS</i> strain should be less than that of the wild type strain. (C, D) At the onset of growth arrest (time zero in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.s002" target="_blank">S1B Fig</a>), <i>S</i> = <i>S</i>₁; see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.g004" target="_blank">Fig. 4B</a>. Without additional influx of the substrate, <i>S</i> will continue to decrease over time due to the consumption for the maintenance (cyan line in green region in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.g004" target="_blank">Fig. 4C</a>). Following the relation between <i>λ</i> and <i>S</i> depicted in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.g004" target="_blank">Fig. 4B</a>, <i>λ</i> will continue to decrease over time too. This will result in gradual decrease of <i>N</i>_CFU (cyan line in green region in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.g004" target="_blank">Fig. 4D</a>). At some point (<i>T</i>₀), the substrate gets completely depleted (orange line in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.g004" target="_blank">Fig. 4C</a>) and <i>N</i>_CFU decreases exponentially at a fixed rate of <i>λ</i> (0) afterwards (orange line in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.g004" target="_blank">Fig. 4D</a>). For the culture with higher cell-densities, <i>S</i> will decrease faster because the substrate is consumed by more cells, leading to shorter periods of the first phase. Quantitative formulation of these processes straightforwardly leads to a mathematical solution equal to the empirical formulas (Eqs (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.e003" target="_blank">3</a>) and (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.e004" target="_blank">4</a>)). The solid lines in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.g001" target="_blank">Fig. 1</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004198#pcbi.1004198.s003" target="_blank">S2 Fig</a> show the fits of the solution to the data. See the text for details.</p