Coupled Flip-Flop Model for REM Sleep Regulation in the Rat

Recent experimental studies investigating the neuronal regulation of rapid eye movement (REM) sleep have identified mutually inhibitory synaptic projections among REM sleep-promoting (REM-on) and REM sleep-inhibiting (REM-off) neuronal populations that act to maintain the REM sleep state and control its onset and offset. The control mechanism of mutually inhibitory synaptic interactions mirrors the proposed flip-flop switch for sleep-wake regulation consisting of mutually inhibitory synaptic projections between wake- and sleep-promoting neuronal populations. While a number of synaptic projections have been identified between these REM-on/REM-off populations and wake/sleep-promoting populations, the specific interactions that govern behavioral state transitions have not been completely determined. Using a minimal mathematical model, we investigated behavioral state transition dynamics dictated by a system of coupled flip-flops, one to control transitions between wake and sleep states, and another to control transitions into and out of REM sleep. The model describes the neurotransmitter-mediated inhibitory interactions between a wake- and sleep-promoting population, and between a REM-on and REM-off population. We proposed interactions between the wake/sleep and REM-on/REM-off flip-flops to replicate the behavioral state statistics and probabilities of behavioral state transitions measured from experimental recordings of rat sleep under ad libitum conditions and after 24 h of REM sleep deprivation. Reliable transitions from REM sleep to wake, as dictated by the data, indicated the necessity of an excitatory projection from the REM-on population to the wake-promoting population. To replicate the increase in REM-wake-REM transitions observed after 24 h REM sleep deprivation required that this excitatory projection promote transient activation of the wake-promoting population. Obtaining the reliable wake-nonREM sleep transitions observed in the data required that activity of the wake-promoting population modulated the interaction between the REM-on and REM-off populations. This analysis suggests neuronal processes to be targeted in further experimental studies of the regulatory mechanisms of REM sleep.     

The consequences of volatile organic compound mediated bacterial and fungal interactions

Microbial interactions via infochemicals are fundamental to the development of spatial distribution and activity variations in ecosystems. Microorganisms produce a wide range of infochemicals, frequently secondary metabolites, most of which are soluble and many volatile. Volatile organic compounds (VOCs) have been identified in soil atmospheres and related to community structure and function. VOC profiles produced by microorganisms are consistent, relating to cultural conditions, environment and inputs, and so to population and function dynamics. VOC-mediated interactions can result in functional responses by the organisms involved that result in selective advantage to some community members. Positive, negative or neutral interactions can occur between a very wide range of soil bacteria and fungi. These effects include both stimulation and inhibition of growth, by 40 and 60%, respectively, and enzyme production. These effects are usually transient, e.g. removal of an antagonist is followed by complete recovery. Up- and down-regulation of gene expression, by mRNA and protein profiling has been demonstrated. VOCs have played an important role during the evolution of microorganisms in the context of their communities. This revised version was published online in August 2006 with corrections to the Cover Date.     

Temporal variation can facilitate niche evolution in harsh sink environments

We examine the impact of temporal variation on adaptive evolution in "sink" environments, where a species encounters conditions outside its niche. Sink populations persist because of recurrent immigration from sources. Prior studies have highlighted the importance of demographic constraints on adaptive evolution in sinks and revealed that adaptation is less likely in harsher sinks. We examine two complementary models of population and evolutionary dynamics in sinks: a continuous-state quantitative-genetics model and an individual-based model. In the former, genetic variance is fixed; in the latter, genetic variance varies because of mutation, drift, and sampling. In both models, a population in a constant harsh sink environment can exist in alternative states: local maladaptation (phenotype comparable to immigrants from the source) or adaptation (phenotype near the local optimum). Temporal variation permits transitions between these states. We show that moderate amounts of temporal variation can facilitate adaptive evolution in sinks, permitting niche evolution, particularly for slow or autocorrelated variation. Such patterns of temporal variation may particularly pertain to sinks caused by biotic interactions (e.g., predation). Our results are relevant to the evolutionary dynamics of species' ranges, the fate of exotic invasive species, and the evolutionary emergence of infectious diseases into novel hosts.     

Noise-driven stem cell and progenitor population dynamics

Background

The balance between maintenance of the stem cell state and terminal differentiation is influenced by the cellular environment. The switching between these states has long been understood as a transition between attractor states of a molecular network. Herein, stochastic fluctuations are either suppressed or can trigger the transition, but they do not actually determine the attractor states.

Methodology/Principal Findings

We present a novel mathematical concept in which stem cell and progenitor population dynamics are described as a probabilistic process that arises from cell proliferation and small fluctuations in the state of differentiation. These state fluctuations reflect random transitions between different activation patterns of the underlying regulatory network. Importantly, the associated noise amplitudes are state-dependent and set by the environment. Their variability determines the attractor states, and thus actually governs population dynamics. This model quantitatively reproduces the observed dynamics of differentiation and dedifferentiation in promyelocytic precursor cells.

Conclusions/Significance

Consequently, state-specific noise modulation by external signals can be instrumental in controlling stem cell and progenitor population dynamics. We propose follow-up experiments for quantifying the imprinting influence of the environment on cellular noise regulation.     

Enzymatic reactions in small spatial volumes: comment on a model of Hess and Mikhailov

Recently Hess and Mikhailov pointed out that in small subcellular compartments diffusion is so fast that mixing is instantaneous on the time scale of many enzymatic reactions. This opens the possibility for synchronizing individual reaction events. To illustrate this fact they discuss as example an irreversible enzymatic reaction with allosteric product activation. Under appropriate conditions their model shows coherent spiking in the number of product molecules, caused by the strong correlation between reaction events. In this model only substrate binding is an indeterministic process, all other subsequent transitions between different enzyme states being deterministic, contrary to real processes. The purpose of the present paper was to investigate this interesting phenomenon by means of a more realistic modification of the original model, with only probabilistic transitions. In an attempt to obtain spiking, which was not observed under these conditions, the model was extended to make a clear distinction between allosteric high and low affinity substrate binding, in contrast to the original model using a product dependent mean binding probability. However no periodic signal was detectable in the indeterministic version of the Hess Mikhailov model or the extended version, either by means of direct visualization or on autocorrelation or Fourier analysis. Reasons why spiking is not observed in indeterministic enzyme models are discussed.     

Analysis of fluctuation in protein abundance without promoter regulation based on Escherichia coli continuous culture

Fluctuation of protein abundance of isogenic Escherichia coli cells in uniform environment was studied. Based on a continuous culture system, which provides homogeneous culture environment, we investigated the fluctuation in GlnA protein abundance regardless of known glnALG promoter regulation. As results by flow cytometer, we found that the GlnA protein abundance in the cells exhibit a large fluctuation, even though GlnA protein is an essential factor for cell growth and the environment is homogeneous. Furthermore, among several steady states, transient processes of such heterogeneous cell population were investigated, by changing the environmental conditions. The results showed that the expression of GlnA protein can be controlled, depending on its necessity, even though there is no known regulatory machinery. These results may provide a clue to understand the nature of regulation of protein expression dynamics with the stochastic fluctuation.     

Analysis of fluctuation in protein abundance without promoter regulation based on Escherichia coli continuous culture

Fluctuation of protein abundance of isogenic Escherichia coli cells in uniform environment was studied. Based on a continuous culture system, which provides homogeneous culture environment, we investigated the fluctuation in GlnA protein abundance regardless of known glnALG promoter regulation. As results by flow cytometer, we found that the GlnA protein abundance in the cells exhibit a large fluctuation, even though GlnA protein is an essential factor for cell growth and the environment is homogeneous. Furthermore, among several steady states, transient processes of such heterogeneous cell population were investigated, by changing the environmental conditions. The results showed that the expression of GlnA protein can be controlled, depending on its necessity, even though there is no known regulatory machinery. These results may provide a clue to understand the nature of regulation of protein expression dynamics with the stochastic fluctuation.     

Moderate disturbances accelerate forest transition dynamics under climate change in the temperate–boreal ecotone of eastern North America

Several temperate tree species are expected to migrate northward and colonize boreal forests in response to climate change. Tree migrations could lead to transitions in forest types, but these could be influenced by several non‐climatic factors, such as disturbances and soil conditions. We analysed over 10,000 forest inventory plots, sampled from 1970 to 2018 in meridional Québec, Canada, to identify what environmental conditions promote or prevent regional‐scale forest transitions. We used a continuous‐time multi‐state Markov model to quantify the probabilities of transitions between forest states (temperate, boreal, mixed, pioneer) as a function of climate (mean temperature and climate moisture index during the growing season), soil conditions (pH and drainage) and disturbances (severity levels of natural disturbances and logging). We further investigate how different disturbance types and severities impact forests' short‐term transient dynamics and long‐term equilibrium using properties of Markov transition matrices. The most common transitions observed during the study period were from mixed to temperate states, as well as from pioneer to boreal forests. In our study, transitions were mainly driven by natural and anthropogenic disturbances and secondarily by climate, whereas soil characteristics exerted relatively minor constraints. While major disturbances only promoted transitions to the pioneer state, moderate disturbances increased the probability of transition from mixed to temperate states. Long‐term projections of our model under the current environmental conditions indicate that moderate disturbances would promote a northward shift of the temperate forest. Moreover, disturbances reduced turnover and convergence time for all transitions, thereby accelerating forest dynamics. Contrary to our expectation, mixed to temperate transitions were not driven by temperate tree recruitment but by mortality and growth. Overall, our results suggest that moderate disturbances could catalyse rapid forest transitions and accelerate broad‐scale biome shifts.     

Diversity in times of adversity: probabilistic strategies in microbial survival games

Population diversification strategies are ubiquitous among microbes, encompassing random phase-variation (RPV) of pathogenic bacteria, viral latency as observed in some bacteriophage and HIV, and the non-genetic diversity of bacterial stress responses. Precise conditions under which these diversification strategies confer an advantage have not been well defined. We develop a model of population growth conditioned on dynamical environmental and cellular states. Transitions among cellular states, in turn, may be biased by possibly noisy readings of the environment from cellular sensors. For various types of environmental dynamics and cellular sensor capability, we apply game-theoretic analysis to derive the evolutionarily stable strategy (ESS) for an organism and determine when that strategy is diversification. We find that: (1) RPV, effecting a sort of Parrondo paradox wherein random alternations between losing strategies produce a winning strategy, is selected when transitions between different selective environments cannot be sensed, (2) optimal RPV cell switching rates are a function of environmental lifecycle asymmetries and environmental autocorrelation, (3) probabilistic diversification upon entering a new environment is selected when sensors can detect environmental transitions but have poor precision in identifying new environments, and (4) in the presence of excess additive noise, low-pass filtering is required for evolutionary stability. We show that even when RPV is not the ESS, it may minimize growth rate variance and the risk of extinction due to 'unlucky' environmental dynamics.     

A diffusion-based theory of organism dispersal in heterogeneous populations

We develop a general theory of organism movement in heterogeneous populations that can explain the leptokurtic movement distributions commonly measured in nature. We describe population heterogeneity in a state-structured framework, employing advection-diffusion as the fundamental movement process of individuals occupying different movement states. Our general analysis shows that population heterogeneity in movement behavior can be defined as the existence of different movement states and among-individual variability in the time individuals spend in these states. A presentation of moment-based metrics of movement illustrates the role of these attributes in general dispersal processes. We also present a special case of the general theory: a model population composed of individuals occupying one of two movement states with linear transitions, or exchange, between the two states. This two-state "exchange model" can be viewed as a correlated random walk and provides a generalization of the telegraph equation. By exploiting the main result of our general analysis, we characterize the exchange model by deriving moment-based metrics of its movement process and identifying an analytical representation of the model's time-dependent solution. Our results provide general and specific theoretical explanations for empirical patterns in organism movement; the results also provide conceptual and analytical bases for extending diffusion-based dispersal theory in several directions, thereby facilitating mechanistic links between individual behavior and spatial population dynamics.     

Transients and attractors in epidemics

Historical records of childhood disease incidence reveal complex dynamics. For measles, a simple model has indicated that epidemic patterns represent attractors of a nonlinear dynamic system and that transitions between different attractors are driven by slow changes in birth rates and vaccination levels. The same analysis can explain the main features of chickenpox dynamics, but fails for rubella and whooping cough. We show that an additional (perturbative) analysis of the model, together with knowledge of the population size in question, can account for all the observed incidence patterns by predicting how stochastically sustained transient dynamics should be manifested in these systems.     

Modelling effects of high product and substrate inhibition on oscillatory behavior in continuous bioreactors

In this study we consider a model for continuous bioreactors which incorporates the effects of high product and substrate inhibition on the kinetics as well as biomass and product yields. We theoretically investigate the possibility of various dynamic behaviors in the bioreactor over different ranges of operating parameters to determine the delineating process conditions which may lead to oscillatory behavior. Application of the singular perturbation technique allows us to derive explicit conditions on the system parameters which specifically ascertain the existence of limit cycles composed of concatenations of catastrophic transitions occurring at different speeds. We discover further that the interactions between the limiting substrate and the growing microorganisms can give rise to high frequency oscillations which can arise during the transients toward the attractor or during the low-frequency cycle. Such a study not only can describe more fully the kinetics in a fermentor but also assist in formulating optimum fermentor operating conditions and in developing control strategy for maintaining optimum productivity.     

Effect of denaturant and protein concentrations upon protein refolding and aggregation: a simple lattice model.

We present a study of the competition between protein refolding and aggregation for simple lattice model proteins. The effect of solvent conditions (i.e., the denaturant concentration and the protein concentration) on the folding and aggregation behavior of a system of simple, two-dimensional lattice protein molecules has been investigated via (dynamic Monte Carlo simulations. The population profiles and aggregation propensities of the nine most populated intermediate configurations exhibit a complex dependence on the solution conditions that can be understood by considering the competition between intra- and interchain interactions. Some of these configurations are not even seen in isolated chain simulations; they are observed to be highly aggregation prone and are stabilized primarily by the aggregation reaction in multiple-chain systems. Aggregation arises from the association of partially folded intermediates rather than from the association of denatured random-coil states. The aggregation reaction dominates over the folding reaction at high protein concentration and low denaturant concentration, resulting in low refolding yields at those conditions. However, optimum folding conditions exist at which the refolding yield is a maximum, in agreement with some experimental observations.     

Integrating Evolution into Ecological Modelling: Accommodating Phenotypic Changes in Agent Based Models

Evolutionary change is a characteristic of living organisms and forms one of the ways in which species adapt to changed conditions. However, most ecological models do not incorporate this ubiquitous phenomenon. We have developed a model that takes a ‘phenotypic gambit’ approach and focuses on changes in the frequency of phenotypes (which differ in timing of breeding and fecundity) within a population, using, as an example, seasonal breeding. Fitness per phenotype calculated as the individual’s contribution to population growth on an annual basis coincide with the population dynamics per phenotype. Simplified model variants were explored to examine whether the complexity included in the model is justified. Outputs from the spatially implicit model underestimated the number of individuals across all phenotypes. When no phenotype transitions are included (i.e. offspring always inherit their parent’s phenotype) numbers of all individuals are always underestimated. We conclude that by using a phenotypic gambit approach evolutionary dynamics can be incorporated into individual based models, and that all that is required is an understanding of the probability of offspring inheriting the parental phenotype.     

Irregular dynamics in up and down cortical states

Complex coherent dynamics is present in a wide variety of neural systems. A typical example is the voltage transitions between up and down states observed in cortical areas in the brain. In this work, we study this phenomenon via a biologically motivated stochastic model of up and down transitions. The model is constituted by a simple bistable rate dynamics, where the synaptic current is modulated by short-term synaptic processes which introduce stochasticity and temporal correlations. A complete analysis of our model, both with mean-field approaches and numerical simulations, shows the appearance of complex transitions between high (up) and low (down) neural activity states, driven by the synaptic noise, with permanence times in the up state distributed according to a power-law. We show that the experimentally observed large fluctuation in up and down permanence times can be explained as the result of sufficiently noisy dynamical synapses with sufficiently large recovery times. Static synapses cannot account for this behavior, nor can dynamical synapses in the absence of noise.     

Preemptive spatial competition under a reproduction-mortality constraint

Spatially structured ecological interactions can shape selection pressures experienced by a population's different phenotypes. We study spatial competition between phenotypes subject to antagonistic pleiotropy between reproductive effort and mortality rate. The constraint we invoke reflects a previous life-history analysis; the implied dependence indicates that although propagation and mortality rates both vary, their ratio is fixed. We develop a stochastic invasion approximation predicting that phenotypes with higher propagation rates will invade an empty environment (no biotic resistance) faster, despite their higher mortality rate. However, once population density approaches demographic equilibrium, phenotypes with lower mortality are favored, despite their lower propagation rate. We conducted a set of pairwise invasion analyses by simulating an individual-based model of preemptive competition. In each case, the phenotype with the lowest mortality rate and (via antagonistic pleiotropy) the lowest propagation rate qualified as evolutionarily stable among strategies simulated. This result, for a fixed propagation to mortality ratio, suggests that a selective response to spatial competition can extend the time scale of the population's dynamics, which in turn decelerates phenotypic evolution.     

Costs,benefits, and loss of vertically transmitted symbionts affect host population dynamics

The costs and benefits of symbiotic interactions may vary with host and symbiont ontogeny. Effects of symbionts at different stages of host development or on different host demographic rates do not contribute equally to fitness. Although rarely applied, a population dynamics approach that integrates over the host life cycle is therefore necessary for capturing the net costs or benefits and, thus, the mutualistic or parasitic nature of symbioses. Using the native, disturbance‐specialist grass Agrostis hyemalis, we asked how a symbiotic endophyte affected the population dynamics of its host and how imperfect vertical transmission influenced symbiont frequency in a late successional environment. A size‐structured integral projection model (IPM) parameterized with experimental field data showed that greater rates of individual growth and reproduction for endophyte‐symbiotic (E+) hosts outweighed their lower rates of survival, leading to a net positive effect of symbiosis on equilibrium plant population growth (slower rate of extinction). Given that populations under going successional transitions are unlikely to be at an equilibrium size structure, we also conducted transient analysis that showed an initial short‐term cost to endophyte symbiosis. We used a megamatrix approach to link E? and E+ IPMs via imperfect vertical transmission and found that this parameter strongly influenced the frequency of symbiosis via complex interactions with host demographic rates. Overall, our population dynamics approach improves the ability to characterize the outcome of symbiotic interactions, and results suggest that particular attention should be paid to interactions between the rate of vertical transmission and host demography.     

Dynamics of a plant-herbivore-predator system with plant-toxicity

A system of ordinary differential equations is considered that models the interactions of two plant species populations, an herbivore population, and a predator population. We use a toxin-determined functional response to describe the interactions between plant species and herbivores and use a Holling Type II functional response to model the interactions between herbivores and predators. In order to study how the predators impact the succession of vegetation, we derive invasion conditions under which a plant species can invade into an environment in which another plant species is co-existing with a herbivore population with or without a predator population. These conditions provide threshold quantities for several parameters that may play a key role in the dynamics of the system. Numerical simulations are conducted to reinforce the analytical results. This model can be applied to a boreal ecosystem trophic chain to examine the possible cascading effects of predator-control actions when plant species differ in their levels of toxic defense.     

Transient sensitivities of non-indigenous shrub species indicate complicated invasion dynamics

As biological invasions increasingly affect natural systems, the need for methods that can quantify the processes responsible for invasion success has increased. Further, methods should be geared to the formulation of management strategies. Demographic analyses are designed to explore the causes and properties of population change. Matrix population models, a commonly used technique for demographic analysis, have been applied to the analysis of stage-structured populations. However, most commonly, analyses have focused on long-term outcomes dynamics (ergodic dynamics). The methods available for analysis of matrix population models have recently been extended to facilitate analysis of the transient dynamics most important to invasion analysis. In this paper we analyze the transient population dynamics of three invasive shrubs and compare them to ergodic dynamics. Cytisus scoparius, Clidemia hirta, and Ardisia elliptica come from different parts of the world and are all now found in the United States of America. They also have published transition matrices that measure the probabilities that any one life-history stage will transition to another over an annual time step. These matrices have been estimated from multi-year data collected from plots in various environments. Our comparative study of transient and ergodic dynamics of invasive shrubs shows that, for all the considered shrub species, there was a clear difference between the sensitivities drawn from these two approaches. The transient sensitivities of earlier life-history transitions showed magnified importance relative to ergodic sensitivities. This was especially true of A. elliptica for which the stable population structure was most different from the starting structure analyzed in detail here. For other species, as stable population structures were heavily weighted towards early stages, the differences in the importance of early transitions transiently and ergodically were less dramatic. Late life transitions showed magnified importance in areas towards the center of the invasion or in older invasion areas. Finally, populations with shorter estimated generation times show greater transient sensitivity to early life-history stages; but the pattern was complex and varied according to species, and was also observed across other life-history transitions. Overall, the ambiguity and complexity of the results highlight the power of considering transient population dynamics for invading species, as well as the importance of specific biological and ecological knowledge of the invading species. Although there may be commonalities across invasions, important decisions on control or inference on population dynamics should treat invasions as individual, unique events.