When to wake up? The optimal waking-up strategies for starvation-induced persistence.

Prolonged lag time can be induced by starvation contributing to the antibiotic tolerance of bacteria. We analyze the optimal lag time to survive and grow the iterative and stochastic application of antibiotics. A simple model shows that the optimal lag time can exhibit a discontinuous transition when the severeness of the antibiotic application, such as the probability to be exposed the antibiotic, the death rate under the exposure, and the duration of the exposure, is increased. This suggests the possibility of reducing tolerant bacteria by controlled usage of antibiotics application. When the bacterial populations are able to have two phenotypes with different lag times, the fraction of the second phenotype that has different lag time shows a continuous transition. We then present a generic framework to investigate the optimal lag time distribution for total population fitness for a given distribution of the antibiotic application duration. The obtained optimal distributions have multiple peaks for a wide range of the antibiotic application duration distributions, including the case where the latter is monotonically decreasing. The analysis supports the advantage in evolving multiple, possibly discrete phenotypes in lag time for bacterial long-term fitness.

Modeling slow-processing of toxin messenger RNAs in type-I toxin-antitoxin systems: post-segregational killing and noise filtering.

In type-I toxin-antitoxin (TA) systems, the action of growth-inhibiting toxin proteins is counteracted by the antitoxin small RNAs (sRNAs) that prevent the translation of toxin messenger RNAs (mRNAs). When a TA module is encoded on a plasmid, the short lifetime of antitoxin sRNA compared to toxin mRNAs mediates post-segregational killing (PSK) that contribute the plasmid maintenance, while some of the chromosomal encoded TA loci have been reported to contribute to persister formation in response to a specific upstream signal. Some of the well studied type-I TA systems such as hok/sok are known to have a rather complex regulatory mechanism. Transcribed full-length toxin mRNAs fold such that the ribosome binding site is not accessible and hence cannot be translated. The mRNAs are slowly processed by RNases, and the truncated mRNAs can be either translated or bound by antitoxin sRNA to be quickly degraded. We analyze the role of this extra processing by a mathematical model. We first consider the PSK scenario, and demonstrate that the extra processing compatibly ensures the high toxin expression upon complete plasmid loss, without inducing toxin expression upon acquisition of a plasmid or decrease of plasmid number to a non-zero number. We further show that the extra processing help filtering the transcription noise, avoiding random activation of toxins in transcriptionally regulated TA systems as seen in chromosomal ones. The present model highlights impacts of the slow processing reaction, offering insights on why the slow processing reactions are commonly identified in multiple type-I TA systems.

Enzyme oscillation can enhance the thermodynamic efficiency of cellular metabolism: consequence of anti-phase coupling between reaction flux and affinity.

Cells generally convert nutrient resources to products via energy transduction. Accordingly, the thermodynamic efficiency of this conversion process is one of the most essential characteristics of living organisms. However, although these processes occur under conditions of dynamic metabolism, most studies of cellular thermodynamic efficiency have been restricted to examining steady states; thus, the relevance of dynamics to this efficiency has not yet been elucidated. Here, we develop a simple model of metabolic reactions with anabolism-catabolism coupling catalyzed by enzymes. Through application of external oscillation in the enzyme abundances, the thermodynamic efficiency of metabolism was found to be improved. This result is in strong contrast with that observed in the oscillatory input, in which the efficiency always decreased with oscillation. This improvement was effectively achieved by separating the anabolic and catabolic reactions, which tend to disequilibrate each other, and taking advantage of the temporal oscillations so that each of the antagonistic reactions could progress near equilibrium. In this case, anti-phase oscillation between the reaction flux and chemical affinity through oscillation of enzyme abundances is essential. This improvement was also confirmed in a model capable of generating autonomous oscillations in enzyme abundances. Finally, the possible relevance of the improvement in thermodynamic efficiency is discussed with respect to the potential for manipulation of metabolic oscillations in microorganisms.

Evolution of hierarchy and irreversibility in theoretical cell differentiation model.

The process of cell differentiation in multicellular organisms is characterized by hierarchy and irreversibility in many cases. However, the conditions and selection pressures that give rise to these characteristics remain poorly understood. By using a mathematical model, here we show that the network of differentiation potency (differentiation diagram) becomes necessarily hierarchical and irreversible by increasing the number of terminally differentiated states under certain conditions. The mechanisms generating these characteristics are clarified using geometry in the cell state space. The results demonstrate that the hierarchical organization and irreversibility can manifest independently of direct selection pressures associated with these characteristics, instead they appear to evolve as byproducts of selective forces favoring a diversity of differentiated cell types. The study also provides a new perspective on the structure of gene regulatory networks that produce hierarchical and irreversible differentiation diagrams. These results indicate some constraints on cell differentiation, which are expected to provide a starting point for theoretical discussion of the implicit limits and directions of evolution in multicellular organisms.

Distinct Survival, Growth Lag, and rRNA Degradation Kinetics during Long-Term Starvation for Carbon or Phosphate.

The stationary phase is the general term for the state a bacterial culture reaches when no further increase in cell mass occurs due to exhaustion of nutrients in the growth medium. Depending on the type of nutrient that is first depleted, the metabolic state of the stationary phase cells may vary greatly, and the subsistence strategies that best support cell survival may differ. As ribosomes play a central role in bacterial growth and energy expenditure, ribosome preservation is a key element of such strategies. To investigate the degree of ribosome preservation during long-term starvation, we compared the dynamics of rRNA levels of carbon-starved and phosphorus-starved Escherichia coli cultures for up to 28 days. The starved cultures' contents of full-length 16S and 23S rRNA decreased as the starvation proceeded in both cases, and phosphorus starvation resulted in much more rapid rRNA degradation than carbon starvation. Bacterial survival and regrowth kinetics were also quantified. Upon replenishment of the nutrient in question, carbon-starved cells resumed growth faster than cells starved for phosphate for the equivalent amount of time, and for both conditions, the lag time increased with the starvation time. While these results are in accordance with the hypothesis that cells with a larger ribosome pool recover more readily upon replenishment of nutrients, we also observed that the lag time kept increasing with increasing starvation time, also when the amount of rRNA per viable cell remained constant, highlighting that lag time is not a simple function of ribosome content under long-term starvation conditions. IMPORTANCE The exponential growth of bacterial populations is punctuated by long or short periods of starvation lasting from the point of nutrient exhaustion until nutrients are replenished. To understand the consequences of long-term starvation for Escherichia coli cells, we performed month-long carbon and phosphorus starvation experiments and measured three key phenotypes of the cultures, namely, the survival of the cells, the time needed for them to resume growth after nutrient replenishment, and the levels of intact rRNA preserved in the cultures. The starved cultures' concentration of rRNA dropped with starvation time, as did cell survival, while the lag time needed for regrowth increased. While all three phenotypes were more severely affected during starvation for phosphorus than for carbon, our results demonstrate that neither survival nor lag time is correlated with ribosome content in a straightforward manner.

Epigenetic Ratchet: Spontaneous Adaptation via Stochastic Gene Expression.

Adaptation to unforeseen environmental changes is one of the most prominent features that characterize the living system. Although signal transduction and gene regulation networks evolved to adapt specific environmental conditions that they frequently experience, it is also reported that bacteria can modify their gene expression patterns to survive a huge variety of environmental conditions even without such pre-designed networks to adapt specically to each environment. Here we propose a general mechanism of cells for such "spontaneous" adaptation, on the basis of stochastic gene expression and epigenetic modication. First, a variety of gene expression states that are marginally stable states are generated by epigenetic modication. Then by taking advantage of stochastic gene expression and dilution by cellular growth, it is shown that, a gene expression pattern that achieves greater cell growth is generically selected, as conrmed by simulations and analysis of several models. The mechanism does not require any design of gene regulation networks. General relevance of the mechanism to cell biology is also discussed.

Entropy production of a steady-growth cell with catalytic reactions.

Cells generally convert external nutrient resources to support metabolism and growth. Understanding the thermodynamic efficiency of this conversion is essential to determine the general characteristics of cellular growth. Using a simple protocell model with catalytic reaction dynamics to synthesize the necessary enzyme and membrane components from nutrients, the entropy production per unit-cell-volume growth is calculated analytically and numerically based on the rate equation for chemical kinetics and linear nonequilibrium thermodynamics. The minimal entropy production per unit-cell growth is found to be achieved at a nonzero nutrient uptake rate rather than at a quasistatic limit as in the standard Carnot engine. This difference appears because the equilibration mediated by the enzyme exists only within cells that grow through enzyme and membrane synthesis. Optimal nutrient uptake is also confirmed by protocell models with many chemical components synthesized through a catalytic reaction network. The possible relevance of the identified optimal uptake to optimal yield for cellular growth is also discussed.