Gliding motility: anticipating the next move with a molecular clock

FrzS protein is important for normal social motility in myxobacteria, which includes periodic reversals in the direction of cell motion. Recent results show that cell reversal correlates with the migration of FrzS from the old leading pole of the cell to the new leading pole.     

The contributions of interlocking loops and extensive nonlinearity to the properties of circadian clock models

Background

Sensitivity and robustness are essential properties of circadian clock systems, enabling them to respond to the environment but resist noisy variations. These properties should be recapitulated in computational models of the circadian clock. Highly nonlinear kinetics and multiple loops are often incorporated into models to match experimental time-series data, but these also impact on model properties for clock models.

Methodology/Principal Findings

Here, we study the consequences of complicated structure and nonlinearity using simple Goodwin-type oscillators and the complex Arabidopsis circadian clock models. Sensitivity analysis of the simple oscillators implies that an interlocked multi-loop structure reinforces sensitivity/robustness properties, enhancing the response to external and internal variations. Furthermore, we found that reducing the degree of nonlinearity could sometimes enhance the robustness of models, implying that ad hoc incorporation of nonlinearity could be detrimental to a model''s perceived credibility.

Conclusion

The correct multi-loop structure and degree of nonlinearity are therefore critical in contributing to the desired properties of a model as well as its capacity to match experimental data.     

Entrainment of the mammalian cell cycle by the circadian clock: modeling two coupled cellular rhythms

The cell division cycle and the circadian clock represent two major cellular rhythms. These two periodic processes are coupled in multiple ways, given that several molecular components of the cell cycle network are controlled in a circadian manner. For example, in the network of cyclin-dependent kinases (Cdks) that governs progression along the successive phases of the cell cycle, the synthesis of the kinase Wee1, which inhibits the G2/M transition, is enhanced by the complex CLOCK-BMAL1 that plays a central role in the circadian clock network. Another component of the latter network, REV-ERBα, inhibits the synthesis of the Cdk inhibitor p21. Moreover, the synthesis of the oncogene c-Myc, which promotes G1 cyclin synthesis, is repressed by CLOCK-BMAL1. Using detailed computational models for the two networks we investigate the conditions in which the mammalian cell cycle can be entrained by the circadian clock. We show that the cell cycle can be brought to oscillate at a period of 24 h or 48 h when its autonomous period prior to coupling is in an appropriate range. The model indicates that the combination of multiple modes of coupling does not necessarily facilitate entrainment of the cell cycle by the circadian clock. Entrainment can also occur as a result of circadian variations in the level of a growth factor controlling entry into G1. Outside the range of entrainment, the coupling to the circadian clock may lead to disconnected oscillations in the cell cycle and the circadian system, or to complex oscillatory dynamics of the cell cycle in the form of endoreplication, complex periodic oscillations or chaos. The model predicts that the transition from entrainment to 24 h or 48 h might occur when the strength of coupling to the circadian clock or the level of growth factor decrease below critical values.     

Clines in clock genes: fine-tuning circadian rhythms to the environment

The dissection of the circadian clock into its molecular components represents the most striking and well-studied example of a gene regulatory network underlying a complex behavioural trait. By contrast, the evolutionary analysis of the clock has developed more slowly. Here we review studies that have surveyed intraspecific clock gene variation over large geographical areas and have discovered latitudinal clines in gene frequencies. Such spatial patterns traditionally suggest that natural selection shapes genetic variation, but it is equally possible that population history, or a mixture of demography and selection, could contribute to the clines. We discuss how population genetics, together with functional assays, can illuminate these possible cases of natural selection in Drosophila clock genes.     

Modeling the circadian clock: from molecular mechanism to physiological disorders

Based on genetic and biochemical advances on the molecular mechanism of circadian rhythms, a computational model for the mammalian circadian clock is used to examine the dynamical bases of circadian-clock-related physiological disorders in humans. Entrainment by the light-dark cycle with a phase advance or a phase delay is associated with the Familial advanced sleep phase syndrome (FASPS) or the Delayed sleep phase syndrome (DSPS), respectively. Lack of entrainment corresponding to the occurrence of quasiperiodic oscillations with or without phase jump can be associated with the non-24 h sleep-wake syndrome. In the close vicinity of the entrainment domain, the model uncovers the possibility of infradian oscillations of very long period. Perturbation in the form of chronic jet lag, as used in mice, prevents entrainment of the circadian clock and results in chaotic or quasiperiodic oscillations. It is important to clarify the conditions for entrainment and for its failure because dysfunctions of the circadian clock may lead to physiological disorders, which pertain not only to the sleep-wake cycle but also to mood and cancer.     

Photic entrainment of the circadian clock: from Drosophila to mammals.

Entrainment is as fundamental to an organism's circadian timing as are the molecular mechanisms involved in the functioning of the intracellular clock oscillator. In nature, one of the principle, although not the only, circadian entraining stimulus (Zeitgeber) is provided by the daily light--dark cycles. In animals, the visual processing apparatus alone is inadequate to accomplish the task of transducing circadian photic signals to the clockwork machinery. In fact, it is ever more appreciated by circadian biologists that organisms as divergent as plants and mammals have evolved a wonderfully complex array of partly redundant specializations which can guarantee the precise alignment of biological and environmental time. Research in circadian biology is cruising at such a rate that attempts to review the state of the art can only hope, at best, to provide a snapshot of the speeding cruiser from its wake. This paper will hopefully provide a reasonably sharp portrayal of what is at hand.     

Development of a two-dimension manifold to represent high dimension mathematical models of the intracellular Mammalian circadian clock

A new focus for mathematical models of the circadian pacemaker involves the encapsulation within the models of detailed biological processes responsible for generating those circadian rhythms. Representing greater biological detail requires more mathematical equations, which pose a greater challenge for the analysis of such systems. Development of a method that retains the predominant dynamics while still providing biologically detailed information is advantageous. Two high-dimension mathematical models of intracellular mammalian circadian pacemakers, Leloup-Goldbeter and Forger-Peskin, with 19 and 73 differential equations, respectively, have been published. The authors projected each of these high-dimension models onto their respective manifold using proper orthogonal functions (POFs) obtained from the empirical decomposition of the model's phase space to obtain a 2-dimension model. The resulting 2-dimension model, represented by 2 differential equations, predicts most of the salient characteristics of a biological clock including approximately 24-h oscillations, entrainment to an LD cycle, phase response curves, and the amplitude recovery dynamics that emerge following amplitude suppression. The manifold representation simplifies the mathematical analysis, since only 2 variables need to be observed and analyzed to understand the behavior of the biological clock. This reduced model derived from a model based on biological variables can be used for the development and analysis of mathematical models of the coupled mammalian oscillators to understand the dynamics of the integrated circadian pacemaker.     

Oscillator model reduction preserving the phase response: application to the circadian clock

Mathematical model reduction is a long-standing technique used both to gain insight into model subprocesses and to reduce the computational costs of simulation and analysis. A reduced model must retain essential features of the full model, which, traditionally, have been the trajectories of certain state variables. For biological clocks, timing, or phase, characteristics must be preserved. A key performance criterion for a clock is the ability to adjust its phase correctly in response to external signals. We present a novel model reduction technique that removes components from a single-oscillator clock model and discover that four feedback loops are redundant with respect to its phase response behavior. Using a coupled multioscillator model of a circadian clock, we demonstrate that by preserving the phase response behavior of a single oscillator, we preserve timing behavior at the multioscillator level.     

Lab mice in the field: unorthodox daily activity and effects of a dysfunctional circadian clock allele

Daily patterns of animal behavior are potentially of vast functional importance. Fitness benefits have been identified in nature by the association between individual timing and survival or by the fate of individuals after experimental deletion of their circadian pacemaker. The recent advances in unraveling the molecular basis of circadian timing enable new approaches to natural selection on timing. The investigators report on the effect and fate of the mutant Per2(Brdm1) allele in 4 replicate populations of house mice in a seminatural outside environment over 2 years. This allele is known to compromise circadian organization and entrainment and to cause multiple physiological disturbances. Mice (N=250) bred from Per2(Brdm1) heterozygotes were implanted subcutaneously with transponders and released in approximately Mendelian ratios in four 400 m(2) pens. An electronic system stored the times of all visits to feeders of each individual. The study first demonstrates that mice are not explicitly nocturnal in this natural environment. Feeding activity was predominantly and sometimes exclusively diurnal and spread nearly equally over day and night under the protective snow cover in winter. The effect of Per2(Brdm1) on activity timing is negligible compared to seasonal changes in all genotypes. Second, the Per2(Brdm1) allele did not have persistent negative effects on fitness. In the first year, the allele gradually became less frequent by reducing survival. New cohorts captured had the same Per2(Brdm1) frequency as the survivors from previous cohorts, consistent with an absence of an effect on reproduction. In the second year, the allele recovered to about its initial frequency (0.54). These changes in selective advantage were primarily due to female mice, as females lived longer and the sex ratio dropped to about 25% males in the population. While it is unknown which selective advantage led to the recovery, the results caution against inferences from laboratory experiments on fitness consequences in the natural environment. It also demonstrates that the activity of mice, while strictly nocturnal in the laboratory, may be partially or completely diurnal in the field. The new method allows assessment of natural selection on specific alleles on a day-today basis.     

Statistical approach to combining the results of similar experiments, with application to the hematologic effects of extremely-low-frequency electric field exposures

A large proportion of scientific effort in investigating the possible biological effects of exposure to extremely-low-frequency (ELF) fields consists of laboratory studies on experimental animals. Most experiments in which hematologic properties are measured show no statistically significant effect due to exposure. However, some studies show significant effects which, in general, are not clearly reproducible. A difficult question must then be addressed: Are these relatively few indications of ELF effects statistical artifacts due to the increased risk of a type I error in multiple studies, or is there a real biological effect that is undetected in most studies due to the relatively small sample sizes commonly used? A statistical approach for examining the accumulated results of multiple experiments which results in a single test for treatment effect is presented. The technique requires very mild assumptions, and is valid for experiments that vary widely in specific characteristics such as exposure level, duration, and laboratory. The method is applied to the results of a collection of hematologic and serum chemistry experiments, and the combined results indicate the existence of experimental effects on some end points.     

Combining field experiments and individual-based modeling to identify the dynamically relevant organizational scale in a field system

Community ecologists continually strive to build analytical models that realistically describe long‐term dynamics of the systems they study. A key step in this process is identifying which details are relevant for predicting dynamics. Currently, this remains a limiting step in development of analytical theory because experimental field ecology, which provides the key empirical insight, and theoretical ecology, which translates empirical knowledge into analytical theory, remain weakly linked. I illustrate how an individual‐based computational model of species interactions is a useful way to bridge the gulf between empirical research and theory development. I built a computational model that reproduced key natural history and biological detail of an old‐field interaction web composed of a predator species, a herbivore species and two plant groups that had been the subject of extensive previous field research. I examined, using simulation experiments, how individual behavior of herbivores in response to changing resource and predator abundance scaled to long‐term population‐level and community‐level dynamics. The simulation experiments revealed that the long‐term community dynamics could be highly predictable because of two counterintuitive reasons. First, seasonality was a strong forcing variable on the system that removed the possibility of serial dependence in population abundance over time. Second, because of seasonality, short‐term behavioral responses of herbivores played a much stronger role in shaping community structure than longer‐term processes such as density responses. So, simply knowing the short‐term responses of herbivores at the evolutionary ecological level was sufficient to forecast the long‐term outcome of experimental manipulations. This study shows that an individual‐based model, once it is calibrated to the real‐world field system, can provide key insight into the biological detail that analytical models should include to predict long‐term dynamics.     

Control systems models for the circadian clock of the New Zealand weta, Hemideina thoracica (Orthoptera: Stenopelmatidae)

The New Zealand weta, Hemideina thoracica, is a nocturnal orthopteran insect which emerges from holes in trees or from under bark soon after sunset to forage for several hours on plant and animal material before returning to its refuge before dawn. In tests of the internal clock hypothesis it exhibits clear circadian locomotor rhythms in which the period is initially somewhat less than 24 h, but frequently spontaneously increases to over 25 h. The rhythms are entrainable by light and temperature cycles, obey Aschoff's Law and are temperature compensated. A single oscillator feedback model accounts for these basic properties of the weta clock, but does not explain a variety of examples of rhythm lability, such as day skipping, spontaneous change in period, scalloping and desynchrony typically found in the real data. To account for these characteristics the model is expanded into two linked populations of oscillators, which retain the basic properties of the simple model and in addition interact through their coupling to show the various types of free-run lability. To make these control systems models compatible with the molecular interpretation of circadian biology, each of the components in the feedback loop is matched with molecular function and structure.     

Concordance of the circadian clock with the environment is necessary to maximize fitness in natural populations

The ubiquity of endogenous, circadian (daily) clocks among eukaryotes has long been held as evidence that they serve an adaptive function, usually cited as the ability to properly time biological events in concordance with the daily cycling of the environment. Herein we test directly whether fitness is a function of the matching of the period of an organism's circadian clock with that of its environment. We find that fitness, measured as the per capita expectation of future offspring, a composite measure of fitness incorporating both survivorship and reproduction, is maximized in environments that are integral multiples of the period of the organism's circadian clock. Hence, we show that organisms require temporal concordance between their internal circadian clocks and their external environment to maximize fitness and thus the long-held assumption is true that, having evolved in a 24-h world, circadian clocks are adaptive.