Hysteresis Can Grant Fitness in Stochastically Varying Environment

Although the existence of multiple stable phenotypes of living organisms enables random switching between phenotypes as well as non-random history dependent switching called hysteresis, only random switching has been considered in prior experimental and theoretical models of adaptation to variable environments. This work considers the possibility that hysteresis may also evolve together with random phenotype switching to maximize population growth. In addition to allowing the possibility that switching rates between different phenotypes may depend not only on a continuous environmental input variable, but also on the phenotype itself, the present work considers an opportunity cost of the switching events. This opportunity cost arises as a result of a lag phase experimentally observed after phenotype switching and stochastic behavior of the environmental input. It is shown that stochastic environmental variation results in maximal asymptotic growth rate when organisms display hysteresis for sufficiently slowly varying environmental input. At the same time, sinusoidal input does not cause evolution of memory suggesting that the connection between the lag phase, stochastic environmental variation and evolution of hysteresis is a result of a stochastic resonance type phenomenon.     

Cloning and characterization of the trpC gene from an aflatoxigenic strain of Aspergillus parasiticus

The trpC gene in the tryptophan biosynthetic pathway was isolated from an aflatoxigenic Aspergillus parasiticus by complementation of an Escherichia coli trpC mutant lacking phosphoribosylanthranilate isomerase (PRAI) activity. The cloned gene complemented an E. coli trpC mutant deficient in indoleglycerolphosphate synthase (IGPS) activity as well as an Aspergillus nidulans mutant strain that was defective in all three enzymatic activities of the trpC gene (glutamine amidotransferase, IGPS, and PRAI), thus indicating the presence of a complete and functional trpC gene. The location and organization of the A. parasiticus trpC gene on the cloned DNA fragment were determined by deletion mapping and by hybridization to heterologous DNA probes that were prepared from cloned trpC genes of A. nidulans and Aspergillus niger. These experiments suggested that the A. parasiticus trpC gene encoded a trifunctional polypeptide with a functional domain structure organized identically to those of analogous genes from other filamentous fungi. The A. parasiticus trpC gene was expressed constitutively regardless of the nutritional status of the culture medium. This gene should be useful as a selectable marker in developing a DNA-mediated transformation system to analyze the aflatoxin biosynthetic pathway of A. parasiticus.     

Cloning and characterization of the trpC gene from an aflatoxigenic strain of Aspergillus parasiticus.

The trpC gene in the tryptophan biosynthetic pathway was isolated from an aflatoxigenic Aspergillus parasiticus by complementation of an Escherichia coli trpC mutant lacking phosphoribosylanthranilate isomerase (PRAI) activity. The cloned gene complemented an E. coli trpC mutant deficient in indoleglycerolphosphate synthase (IGPS) activity as well as an Aspergillus nidulans mutant strain that was defective in all three enzymatic activities of the trpC gene (glutamine amidotransferase, IGPS, and PRAI), thus indicating the presence of a complete and functional trpC gene. The location and organization of the A. parasiticus trpC gene on the cloned DNA fragment were determined by deletion mapping and by hybridization to heterologous DNA probes that were prepared from cloned trpC genes of A. nidulans and Aspergillus niger. These experiments suggested that the A. parasiticus trpC gene encoded a trifunctional polypeptide with a functional domain structure organized identically to those of analogous genes from other filamentous fungi. The A. parasiticus trpC gene was expressed constitutively regardless of the nutritional status of the culture medium. This gene should be useful as a selectable marker in developing a DNA-mediated transformation system to analyze the aflatoxin biosynthetic pathway of A. parasiticus.     

Kinetics of Genetic Switching into the State of Bacterial Competence

Nonlinear amplification of gene expression of master regulators is essential for cellular differentiation. Here we investigated determinants that control the kinetics of the genetic switching process from the vegetative state (B-state) to the competent state (K-state) of Bacillus subtilis, explicitly including the switching window which controls the probability for competence initiation in a cell population. For individual cells, we found that after initiation of switching, the levels of the master regulator [ComK](t) increased with sigmoid shape and saturation occurred at two distinct levels of [ComK]. We analyzed the switching kinetics into the state with highest [ComK] and found saturation after a switching period of length 1.4 ± 0.3 h. The duration of the switching period was robust against variations in the gene regulatory network of the master regulator, whereas the saturation levels showed large variations between individual isogenic cells. We developed a nonlinear dynamics model, taking into account low-number stochastic effects. The model quantitatively describes the probability and timescale of switching at the single cell level and explains why the ComK level in the K-state is highly sensitive to extrinsic parameter variations. Furthermore, the model predicts a transition from stochastic to deterministic switching at increased production rates of ComK in agreement with experimental data.     

The trpC gene of Phanerochaete chrysosporium is unique in containing an intron but nevertheless maintains the order of functional domains seen in other fungi

The Phanerochaete chryososporium trpC gene has been isolated by complementation of an Escherichia coli trpC mutant. The full extent of the fungal gene, determined by sequence analysis, was found to be 2414bp. This includes a single intron of 50bp, the presence of which was confirmed by RNA-primed polymerase chain reaction analysis. This features makes the P. chrysosporium gene unique when compared to equivalent genes from other filamentous fungi. The P. chrysosporium trpC gene encodes a single protein containing three enzyme activities involved in tryptophan biosynthesis arranged in the order: NH2-GAT-IGPS-PRAI-COOH. This order is conserved in all filamentous fungi so far examined and, indeed, is the gene order within the E. coli trp operon.     

Cloning in Bacillus subtilis cells of the Bacillus mesentericus genes that determine the enzyme synthesis of tryptophan metabolism

In this work, we tried to clone some Bacillus mesentericus genes coding for tryptophan synthesis in Bacillus subtilis cells. We succeeded in obtaining two identical plasmids carrying some genes of Bac. mesentericus and complementing the trpC2 and trpF mutations of Bac. subtilis. The cloned genes of Bac. mesentericus completely replaced the functions of trpC2 and trpF genes.     

The impact of bottlenecks on microbial survival,adaptation, and phenotypic switching in host–pathogen interactions

Microbial pathogens and viruses can often maintain sufficient population diversity to evade a wide range of host immune responses. However, when populations experience bottlenecks, as occurs frequently during initiation of new infections, pathogens require specialized mechanisms to regenerate diversity. We address the evolution of such mechanisms, known as stochastic phenotype switches, which are prevalent in pathogenic bacteria. We analyze a model of pathogen diversification in a changing host environment that accounts for selective bottlenecks, wherein different phenotypes have distinct transmission probabilities between hosts. We show that under stringent bottlenecks, such that only one phenotype can initiate new infections, there exists a threshold stochastic switching rate below which all pathogen lineages go extinct, and above which survival is a near certainty. We determine how quickly stochastic switching rates can evolve by computing a fitness landscape for the evolutionary dynamics of switching rates, and analyzing its dependence on both the stringency of bottlenecks and the duration of within‐host growth periods. We show that increasing the stringency of bottlenecks or decreasing the period of growth results in faster adaptation of switching rates. Our model provides strong theoretical evidence that bottlenecks play a critical role in accelerating the evolutionary dynamics of pathogens.     

Inactivation and partial degradation of phosphoribosylanthranilate isomerase-indoleglycerol phosphate synthetase in nongrowing cultures of Escherichia coli.

The stability of tryptophan biosynthetic enzyme activities was examined in cultures of repressor-negative (trpR) strains of Escherichia coli K-12 incubated under conditions of nutrient starvation of chloramphenicol inhibition. The results show that four of the five activities examined are stable under most nongrowing conditions, whereas one activity, indoleglycerol phosphate (InGP) synthetase, carried by the trpC protein, is unstable under most conditions tested. Phosphoribosylanthranilate (PRA) isomerase activity, which is also carried by the trpC protein, is unstable during starvation for ammonium, cysteine, or sulfate but is stable under other nongrowing conditions where InGP synthetase is not. InGP synthetase activity but not PRA isomerase activity is also diminished about twofold in cultures using glycerol as a carbon-energy source. These results indicate that one or both activities of the trpC protein is specifically inactivated under several culture conditions. Experiments with antibodies to the trpC protein show that sulfate-starved and ammonium-starved cultures contain 20 to 40% less immunologically reactive trpC protein than unstarved cultures. This indicates that the trpC protein is probably partially degraded under these conditions. During recovery from sulfate starvation or ammonium starvation, cultures slowly regain normal levels of InGP synthetase and PRA isomerase activities, suggesting that inactivation may be reversible.     

Fitness and entropy production in a cell population dynamics with epigenetic phenotype switching

Motivated by recent understandings in the stochastic natures of gene expression, biochemical signaling, and spontaneous reversible epigenetic switchings, we study a simple deterministic cell population dynamics in which subpopulations grow with different rates and individual cells can bi-directionally switch between a small number of different epigenetic phenotypes. Two theories in the past, the population dynamics and thermodynamics of master equations, separately defined two important concepts in mathematical terms: the fitness in the former and the (non-adiabatic) entropy production in the latter. Both of them play important roles in the evolution of the cell population dynamics. The switching sustains the variations among the subpopulation growth, thus sustains continuous natural selection. As a form of Price’s equation, the fitness increases with (i) natural selection through variations and (ii) a positive covariance between the per capita growth and switching, which represents a Lamarchian-like behavior. A negative covariance balances the natural selection in a fitness steady state --- “the red queen” scenario. At the same time the growth keeps the proportions of subpopulations away from the “intrinsic” switching equilibrium of individual cells, thus leads to a continuous entropy production. A covariance, between the per capita growth rate and the “chemical potential” of subpopulation, counteracts the entropy production. Analytical results are obtained for the limiting cases of growth dominating switching and vice versa.     

Evolution and population dynamics in stochastic environments

Inter-generational temporal variability of the environment is important in the evolution and adaptation of phenotypic traits. We discuss a population-dynamic approach which plays a central role in the analysis of evolutionary processes. The basic principle is that the phenotypes with the greatest long-term average growth rate will dominate the entire population. The calculation of longterm average growth rates for populations under temporal stochasticity can be highly cumbersome. However, for a discrete non-overlapping population, it is identical to the geometric mean of the growth rates (geometric mean fitness), which is usually different from the simple arithmetic mean of growth rates. Evolutionary outcomes based on geometric mean fitness are often very different from the predictions based on the usual arithmetic mean fitness. In this paper we illustrate the concept of geometric mean fitness in a few simple models. We discuss its implications for the adaptive evolution of phenotypes, e.g. foraging under predation risks and clutch size. Next, we present an application: the risk-spreading egg-laying behaviour of the cabbage white butterfly, and develop a two-patch population dynamic model to show how the optimal solution diverges from the ssual arithmetic mean approach. The dynamics of these stochastic models cannot be predicted from the dynamics of simple deterministic models. Thus the inclusion of stochastic factors in the analyses of populations is essential to the understanding of not only population dynamics, but also their evolutionary dynamics.