Survival of Phenotypic Information during Cellular Growth Transitions

Phenotypic memory can predispose cells to physiological outcomes, contribute to heterogeneity in cellular populations, and allow computation of environmental features, such as nutrient gradients. In bacteria and synthetic circuits in general, memory can often be set by protein concentrations: because of the relative stability of proteins, the degradation rate is often dominated by the growth rate, and inheritance is a significant factor. Cells can then be primed to respond to events that recur with frequencies faster than the time to eliminate proteins. Protein memory can be extended if cells reach extremely low growth rates or no growth. Here we characterize the necessary time scales for different quantities of protein memory, measured as relative entropy (Kullback–Leibler divergence), for a variety of cellular growth arrest transition dynamics. We identify a critical manifold in relative protein degradation/growth arrest time scales where information is, in principle, preserved indefinitely because proteins are trapped at a concentration determined by the competing time scales as long as nongrowth-mediated protein degradation is negligible. We next asked what characteristics of growth arrest dynamics and initial protein distributions best preserve or eliminate information about previous environments. We identified that sharp growth arrest transitions with skewed initial protein distributions optimize flexibility, with information preservation and minimal cost of residual protein. As a result, a nearly memoryless regime, corresponding to a form of bet-hedging, may be an optimal strategy for storage of information by protein concentrations in growth-arrested cells

A framework for population growth dynamics in the presence of metabolic risk.

<p>(A). Growth conditions, gene expression, replication, and regulatory factors determine timescales for switching between different types of growth. On a characteristic timescale <i>τ</i>_<i>1</i>, cells stochastically switch from balanced growth (<i>g</i>) to a condition of rapidly changing growth rate (<i>ĝ</i>) and escape on a timescale of <i>τ</i>_<i>-1</i>. Growth arrest arises from the growth shift state on a timescale of <i>τ</i>_<i>2</i>. Escape from growth arrest permits cells to resume growth on a timescale of <i>τ</i>_<i>-2</i>, or die on a timescale of <i>τ</i>_<i>3</i>. (B) In the limit of large <i>τ</i>_<i>1</i> or small <i>τ</i>_<i>-1</i>, populations have classical balanced growth. (C) In the limit of small <i>τ</i>_<i>1</i> and <i>τ</i>_<i>2</i> with large <i>τ</i>_<i>-1</i> and <i>τ</i>_<i>-2</i>, the metastable population model holds.</p

Three discrete growth phases in metabolic pathways.

<p>(A) A metabolic pathway consists of enzymes <i>A</i> and <i>B</i> that produce and consume the intracellular metabolite <i>M</i>, respectively. (B) Mathematical models predict three growth phases for combinations of metabolite production rate and demand <i>δ</i>. Color bar indicates normalized growth rate. Colored spots correspond to the colored lines in panel C. The black line represents the effect of experimental conditions changing extracellular lactose concentrations in <i>E</i>. <i>coli</i> causing intracellular lactose concentration changes because of LacY activity. Results are for two models of toxicity: metabolite buildup (left) and permease proton symport (right). (C) Mathematical models predict that growth is maximized below a threshold production rate (dashed line between cyan and yellow) past which no steady state exists. Increasing the rate of metabolite production (<i>V</i>⁺) translates the rate curves upward. When the rate is beyond the dashed line, there is a runaway buildup of metabolite and consequent toxic effects. Results are for two models of toxicity: metabolite buildup (left) and permease proton symport (toxic byproduct; right). The toxic byproduct model has two variables; we plot only the rate of toxic byproduct buildup for simplicity because it crosses the threshold at a lower <i>V</i>⁺.</p

Cellular Growth Arrest and Persistence from Enzyme Saturation

<div><p>Metabolic efficiency depends on the balance between supply and demand of metabolites, which is sensitive to environmental and physiological fluctuations, or noise, causing shortages or surpluses in the metabolic pipeline. How cells can reliably optimize biomass production in the presence of metabolic fluctuations is a fundamental question that has not been fully answered. Here we use mathematical models to predict that enzyme saturation creates distinct regimes of cellular growth, including a phase of growth arrest resulting from toxicity of the metabolic process. Noise can drive entry of single cells into growth arrest while a fast-growing majority sustains the population. We confirmed these predictions by measuring the growth dynamics of <i>Escherichia coli</i> utilizing lactose as a sole carbon source. The predicted heterogeneous growth emerged at high lactose concentrations, and was associated with cell death and production of antibiotic-tolerant persister cells. These results suggest how metabolic networks may balance costs and benefits, with important implications for drug tolerance.</p></div

Reactions, propensities and parameter values used for stochastic simulations.

<p>Reactions, propensities and parameter values used for stochastic simulations.</p

Protection from antibiotics in growth-arrest-prone media.

<p>(A) Survival curves of bacteria grown at indicated lactose concentrations in ampicillin-treated cultures (100 μg/ml). (B) Culture conditions favoring growth arrest enhance the presence of antibiotic tolerant cells after 20 h treatment of 32 μg/ml doxycycline (blue bars; ANOVA <i>p</i> = 0.003) or 100 μg/ml ampicillin (yellow bars; ANOVA <i>p</i> = 0.004). Survival ratios are normalized by cell densities of untreated cultures in corresponding conditions. <i>N</i> = 3 for each condition and the survival curve points, reporting mean ± SEM. In the final timepoint of the survival curve for 0.1 mg/ml lactose, two of the replicates were below the level of detection; the remaining replicate value is plotted.</p

Characterization of <i>lac</i> operon regulation.

<p>A) Examples of the range of evolved LacZ activity phenotypes present in the four evolution environments. Degree of blue coloration on TGX plates gives a qualitative measure of LacZ activity. B) Schematic of <i>lac</i> operon and reporters used to measure <i>lac</i> operon regulation. <i>lacZ</i> encodes the β-galactosidase responsible for lactose catabolism and <i>lacY</i> encodes a lactose permease. The expression of <i>lacZYA</i> is directly controlled by LacI and CRP. LacI is a negative regulator, binding to operator sites within the <i>lacZYA</i> promoter (P_lac). LacI binding is inhibited by lactose and gratuitous inducers, such as TMG. CRP is a positive regulator, activating <i>lacZYA</i> expression when cAMP levels are elevated in response to low glucose concentrations. High levels of glucose also repress <i>lac</i> expression by inhibiting import of lactose through LacY. Two reporters were designed to measure LacI and CRP inputs into <i>lac</i> operon regulation. The native <i>lac</i> promoter drives expression of GFP and is subject to regulation by both LacI and CRP. A second reporter utilizes a mutant <i>lac</i> promoter that cannot bind LacI to drive expression of DsRedExpress2. This reporter is only subject to regulation by CRP. Solid lines indicate positive (arrows) and negative (blunt arrow) regulatory interactions; dotted lines indicate the transfer of metabolites; blue lines indicate the production of proteins; open arrows indicate expression start sites. Figure adapted from Ozbudak et al. 2004. C) Ancestral inducer response profile. Shown are flow cytometry histograms for the ancestor grown in a range of TMG concentrations. P_lac-GFP and P_lac(O-)-RFP measurements were taken simultaneously from the same cultures.</p

Fitness effect of <i>lacI</i> and <i>lacO1</i> mutations depend on genetic background.

<p>The fitness effect of <i>lacO1</i> and <i>lacI</i> mutations were measured in the ancestor and the G+L3-1 evolved genetic backgrounds when competed in the G+L environment. Gray points indicate fitness effect in competitions against the corresponding progenitor strains that do not have the added <i>lac</i> mutation; black points indicate fitness of <i>lacI</i> and <i>lacO1</i> mutations competed directly against each other. Lines connect competitions of the same type but in different genetic backgrounds.</p

Population and individual cell fitness of <i>E</i>. <i>coli</i> (<i>lacI</i>⁻ B REL606) in varying growth conditions.

<p>(A) Mean ± SEM (<i>N</i> = 3) growth rate (<i>p</i> < 10⁻⁶ for no trend in lactose concentrations > 1 mg/ml) and fraction of propidium iodide-stained (PI+) cells (<i>p</i> = 0.0051 for no PI+ trend in lactose concentrations > 1 mg/ml) at various lactose concentrations. Dashed lines indicate quadratic regression models, which fit significantly better than do linear models (see text for details). PI+ fractions at low lactose concentrations are shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004825#pcbi.1004825.s005" target="_blank">S4c Fig</a>. (B) Mean ± SEM (<i>N</i> = 3) expression of GFP at various lactose concentrations (<i>p</i> = 0.00016 for no trend). CV, coefficient of variation (<i>p</i> < 10⁻⁶ for no trend). Dashed lines indicate fits of statistical models used as a guide to the eye (fitted model is: ). (C) PI-stained <i>E</i>. <i>coli</i> grown in a microfluidic device perfused with the indicated concentration of lactose (mg/ml). Note the patchy distribution of fast growing (low GFP) and slow- or non-growing (high GFP) cells at 50 mg/ml lactose. Brightfield alone is shown below. PI staining identifies dead cells and appears red or yellow, depending on the amount of GFP in the same cell. Dark spots are silicone support structures.</p

Contribution of <i>lac</i> mutations to evolved inducer responses.

<p>A) Inducer response histograms for reconstructed <i>lacI</i>^ΔTGGC and <i>lacO1</i>^G11A mutants. The <i>lacI</i> mutation confers constitutive <i>lac</i> expression, whereas the <i>lacO1</i> mutation confers a lower induction threshold and a graded response to inducer. B) Effect of the <i>lacO1</i> mutation on the maximum <i>lac</i> expression level. Mean P_lac-GFP expression levels during growth in saturating levels of inducer (100 µM TMG) are shown for the ancestor, evolved clone G+L3-1, <i>lacO1</i>^G11A single mutant and the G+L3-1 clone with <i>lacO1</i> reverted to the ancestral sequence (G+L3-1 <i>lacO1^anc</i>). Standard error is shown, n = 4.</p