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Survival kinetics of starving bacteria is biphasic and density-dependent.

Phaiboun A, Zhang Y, Park B, Kim M - PLoS Comput. Biol. (2015)

Bottom Line: The results show that the assumption--starving cells die exponentially--is true only at high cell density.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, Emory University, Atlanta, Georgia, United States of America.

ABSTRACT
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 E. coli cells. The results show that the assumption--starving cells die exponentially--is true only at high cell density. At low density, starving cells persevere for extended periods of time, before dying rapidly exponentially. Detailed analyses show intriguing quantitative characteristics of the density-dependent and biphasic 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.

No MeSH data available.


Related in: MedlinePlus

A mechanistic account of the density-dependent, biphasic survival kinetics.(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) [26,27]. RpoS represses cell growth (red line) [30–32], forming negative feedback. In the feedback scheme, at low substrate levels, RpoS strongly represses cell growth and hence, substrate consumption, allowing cells to conserve 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 S1, i.e., λ = 0 at S = S1 > 0. This prediction agrees with previous studies [33–35]. Importantly, further studies show that although the growth rate of the population is zero at S = S1, the substrate consumption rate is not zero; see [36] for review. This is commonly known as maintenance requirement; it requires continuous influx of the substrate to maintain a constant population size (λ = 0). If the influx of the substrate is less than the level needed for the maintenance, λ < 0 (green region) [37,38]. Our model indicates that λ(0) = − μ0; see the text for details. As a comparison, the relation of λ and S in the ΔrpoS strain is shown as a dashed line. Note that at intermediate substrate concentrations, λ of ΔrpoS strain is higher than that of the wild type strain [30–32]. Also, note that when the substrate is completely exhausted, the culture of the ΔrpoS strain loses viability more rapidly than the wild type strain (see [18,25] and Fig. 2B); thus, the value of λ(0) of ΔrpoS strain should be less than that of the wild type strain. (C, D) At the onset of growth arrest (time zero in S1B Fig), S = S1; see Fig. 4B. Without additional influx of the substrate, S will continue to decrease over time due to the consumption for the maintenance (cyan line in green region in Fig. 4C). Following the relation between λ and S depicted in Fig. 4B, λ will continue to decrease over time too. This will result in gradual decrease of NCFU (cyan line in green region in Fig. 4D). At some point (T0), the substrate gets completely depleted (orange line in Fig. 4C) and NCFU decreases exponentially at a fixed rate of λ (0) afterwards (orange line in Fig. 4D). For the culture with higher cell-densities, S 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 (3) and (4)). The solid lines in Fig. 1 and S2 Fig show the fits of the solution to the data. See the text for details.
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pcbi.1004198.g004: A mechanistic account of the density-dependent, biphasic survival kinetics.(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) [26,27]. RpoS represses cell growth (red line) [30–32], forming negative feedback. In the feedback scheme, at low substrate levels, RpoS strongly represses cell growth and hence, substrate consumption, allowing cells to conserve 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 S1, i.e., λ = 0 at S = S1 > 0. This prediction agrees with previous studies [33–35]. Importantly, further studies show that although the growth rate of the population is zero at S = S1, the substrate consumption rate is not zero; see [36] for review. This is commonly known as maintenance requirement; it requires continuous influx of the substrate to maintain a constant population size (λ = 0). If the influx of the substrate is less than the level needed for the maintenance, λ < 0 (green region) [37,38]. Our model indicates that λ(0) = − μ0; see the text for details. As a comparison, the relation of λ and S in the ΔrpoS strain is shown as a dashed line. Note that at intermediate substrate concentrations, λ of ΔrpoS strain is higher than that of the wild type strain [30–32]. Also, note that when the substrate is completely exhausted, the culture of the ΔrpoS strain loses viability more rapidly than the wild type strain (see [18,25] and Fig. 2B); thus, the value of λ(0) of ΔrpoS strain should be less than that of the wild type strain. (C, D) At the onset of growth arrest (time zero in S1B Fig), S = S1; see Fig. 4B. Without additional influx of the substrate, S will continue to decrease over time due to the consumption for the maintenance (cyan line in green region in Fig. 4C). Following the relation between λ and S depicted in Fig. 4B, λ will continue to decrease over time too. This will result in gradual decrease of NCFU (cyan line in green region in Fig. 4D). At some point (T0), the substrate gets completely depleted (orange line in Fig. 4C) and NCFU decreases exponentially at a fixed rate of λ (0) afterwards (orange line in Fig. 4D). For the culture with higher cell-densities, S 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 (3) and (4)). The solid lines in Fig. 1 and S2 Fig show the fits of the solution to the data. See the text for details.

Mentions: As cells grow and consume substrates, the concentration of substrates in the medium will decrease (green line in Fig. 4A). When the concentration falls to the level reducing the rate of cell growth, the expression of RpoS is activated (blue line; note that higher RpoS levels at lower substrate concentrations were previously established [26,27]). The RpoS expression subsequently leads to expression of other new genes (i.e., RpoS regulon) and the expression of these genes protects cells from stress [7–10]. Importantly, this protection is expected to be density-independent, because RpoS expression itself is independent of cell density [26,27]. In Fig. 3G, we see that in the second phase of the survival kinetics, NCFU decreases at the rate of −μo (= −0.018 hr -1, dashed line) independently of cell density. This is lower than the rate of decrease in the ΔrpoS strain, −μoΔrpoS (= −0.035 hr -1, see Fig. 2B), suggesting that the protection lowers the rate of viability loss during the second phase independently of cell density. This protection, however, is not likely to be a major cause for the extension of the first phase at low density, because the extension is strongly dependent on cell density; see Fig. 1 and Fig. 3E. (There are studies suggesting that RpoS expression may be possibly higher at higher cell density [28,29]. Even if this is true, it cannot account for our observation that the first phase is extended further at lower cell density.)


Survival kinetics of starving bacteria is biphasic and density-dependent.

Phaiboun A, Zhang Y, Park B, Kim M - PLoS Comput. Biol. (2015)

A mechanistic account of the density-dependent, biphasic survival kinetics.(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) [26,27]. RpoS represses cell growth (red line) [30–32], forming negative feedback. In the feedback scheme, at low substrate levels, RpoS strongly represses cell growth and hence, substrate consumption, allowing cells to conserve 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 S1, i.e., λ = 0 at S = S1 > 0. This prediction agrees with previous studies [33–35]. Importantly, further studies show that although the growth rate of the population is zero at S = S1, the substrate consumption rate is not zero; see [36] for review. This is commonly known as maintenance requirement; it requires continuous influx of the substrate to maintain a constant population size (λ = 0). If the influx of the substrate is less than the level needed for the maintenance, λ < 0 (green region) [37,38]. Our model indicates that λ(0) = − μ0; see the text for details. As a comparison, the relation of λ and S in the ΔrpoS strain is shown as a dashed line. Note that at intermediate substrate concentrations, λ of ΔrpoS strain is higher than that of the wild type strain [30–32]. Also, note that when the substrate is completely exhausted, the culture of the ΔrpoS strain loses viability more rapidly than the wild type strain (see [18,25] and Fig. 2B); thus, the value of λ(0) of ΔrpoS strain should be less than that of the wild type strain. (C, D) At the onset of growth arrest (time zero in S1B Fig), S = S1; see Fig. 4B. Without additional influx of the substrate, S will continue to decrease over time due to the consumption for the maintenance (cyan line in green region in Fig. 4C). Following the relation between λ and S depicted in Fig. 4B, λ will continue to decrease over time too. This will result in gradual decrease of NCFU (cyan line in green region in Fig. 4D). At some point (T0), the substrate gets completely depleted (orange line in Fig. 4C) and NCFU decreases exponentially at a fixed rate of λ (0) afterwards (orange line in Fig. 4D). For the culture with higher cell-densities, S 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 (3) and (4)). The solid lines in Fig. 1 and S2 Fig show the fits of the solution to the data. See the text for details.
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Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC4383377&req=5

pcbi.1004198.g004: A mechanistic account of the density-dependent, biphasic survival kinetics.(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) [26,27]. RpoS represses cell growth (red line) [30–32], forming negative feedback. In the feedback scheme, at low substrate levels, RpoS strongly represses cell growth and hence, substrate consumption, allowing cells to conserve 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 S1, i.e., λ = 0 at S = S1 > 0. This prediction agrees with previous studies [33–35]. Importantly, further studies show that although the growth rate of the population is zero at S = S1, the substrate consumption rate is not zero; see [36] for review. This is commonly known as maintenance requirement; it requires continuous influx of the substrate to maintain a constant population size (λ = 0). If the influx of the substrate is less than the level needed for the maintenance, λ < 0 (green region) [37,38]. Our model indicates that λ(0) = − μ0; see the text for details. As a comparison, the relation of λ and S in the ΔrpoS strain is shown as a dashed line. Note that at intermediate substrate concentrations, λ of ΔrpoS strain is higher than that of the wild type strain [30–32]. Also, note that when the substrate is completely exhausted, the culture of the ΔrpoS strain loses viability more rapidly than the wild type strain (see [18,25] and Fig. 2B); thus, the value of λ(0) of ΔrpoS strain should be less than that of the wild type strain. (C, D) At the onset of growth arrest (time zero in S1B Fig), S = S1; see Fig. 4B. Without additional influx of the substrate, S will continue to decrease over time due to the consumption for the maintenance (cyan line in green region in Fig. 4C). Following the relation between λ and S depicted in Fig. 4B, λ will continue to decrease over time too. This will result in gradual decrease of NCFU (cyan line in green region in Fig. 4D). At some point (T0), the substrate gets completely depleted (orange line in Fig. 4C) and NCFU decreases exponentially at a fixed rate of λ (0) afterwards (orange line in Fig. 4D). For the culture with higher cell-densities, S 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 (3) and (4)). The solid lines in Fig. 1 and S2 Fig show the fits of the solution to the data. See the text for details.
Mentions: As cells grow and consume substrates, the concentration of substrates in the medium will decrease (green line in Fig. 4A). When the concentration falls to the level reducing the rate of cell growth, the expression of RpoS is activated (blue line; note that higher RpoS levels at lower substrate concentrations were previously established [26,27]). The RpoS expression subsequently leads to expression of other new genes (i.e., RpoS regulon) and the expression of these genes protects cells from stress [7–10]. Importantly, this protection is expected to be density-independent, because RpoS expression itself is independent of cell density [26,27]. In Fig. 3G, we see that in the second phase of the survival kinetics, NCFU decreases at the rate of −μo (= −0.018 hr -1, dashed line) independently of cell density. This is lower than the rate of decrease in the ΔrpoS strain, −μoΔrpoS (= −0.035 hr -1, see Fig. 2B), suggesting that the protection lowers the rate of viability loss during the second phase independently of cell density. This protection, however, is not likely to be a major cause for the extension of the first phase at low density, because the extension is strongly dependent on cell density; see Fig. 1 and Fig. 3E. (There are studies suggesting that RpoS expression may be possibly higher at higher cell density [28,29]. Even if this is true, it cannot account for our observation that the first phase is extended further at lower cell density.)

Bottom Line: The results show that the assumption--starving cells die exponentially--is true only at high cell density.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, Emory University, Atlanta, Georgia, United States of America.

ABSTRACT
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 E. coli cells. The results show that the assumption--starving cells die exponentially--is true only at high cell density. At low density, starving cells persevere for extended periods of time, before dying rapidly exponentially. Detailed analyses show intriguing quantitative characteristics of the density-dependent and biphasic 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.

No MeSH data available.


Related in: MedlinePlus