Stochastic noise interferes coherently with a model biological clock and produces specific dynamic behaviour

Cut the noise or couple up: Coordinating circadian and synthetic clocks

Circadian clocks are important to much of life on Earth and are of inherent interest to humanity, implicated in fields ranging from agriculture and ecology to developmental biology and medicine. New techniques show that it is not simply the presence of clocks, but coordination between them that is critical for complex physiological processes across the kingdoms of life. Recent years have also seen impressive advances in synthetic biology to the point where parallels can be drawn between synthetic biological and circadian oscillators. This review will emphasize theoretical and experimental studies that have revealed a fascinating dichotomy of coupling and heterogeneity among circadian clocks. We will also consolidate the fields of chronobiology and synthetic biology, discussing key design principles of their respective oscillators.

Adaptive Estimation of Biological Rhythm in Crassulacean Acid Metabolism with Critical Manifold

The mechanism of endogenous circadian photosynthesis oscillations of plants performing crassulacean acid metabolism (CAM) is investigated in terms of a nonlinear theoretical model. Blasius et al. used throughout continuous time differential equations which adequately reflect the CAM dynamics. The model shows regular endogenous limit cycle oscillations that are stable for a wide range of temperatures in a manner that complies well with experimental data. In this paper, we pay attention to the approximation of the fast modes of the CAM dynamics. Using the zero-epsilon approximation of the slow manifold, we derive the critical manifold that is defined by two algebraic nonlinear equations. The critical manifold allows us to give the algebraic estimate of the order of the tonoplast membrane. The dynamic equation of the order of the tonoplast membrane includes the nonlinear function that gives the equilibrium value of the lipid order of tonoplast functions as a hysteresis switch. We identify the nonlinear function with the measurement signals. Using the basis function expansion of the nonlinear and the critical manifold, we propose an adaptive observer to estimate the tonoplast order and the nonlinear function.

Weak noise in neurons may powerfully inhibit the generation of repetitive spiking but not its propagation

Many neurons have epochs in which they fire action potentials in an approximately periodic fashion. To see what effects noise of relatively small amplitude has on such repetitive activity we recently examined the response of the Hodgkin-Huxley (HH) space-clamped system to such noise as the mean and variance of the applied current vary, near the bifurcation to periodic firing. This article is concerned with a more realistic neuron model which includes spatial extent. Employing the Hodgkin-Huxley partial differential equation system, the deterministic component of the input current is restricted to a small segment whereas the stochastic component extends over a region which may or may not overlap the deterministic component. For mean values below, near and above the critical values for repetitive spiking, the effects of weak noise of increasing strength is ascertained by simulation. As in the point model, small amplitude noise near the critical value dampens the spiking activity and leads to a minimum as noise level increases. This was the case for both additive noise and conductance-based noise. Uniform noise along the whole neuron is only marginally more effective in silencing the cell than noise which occurs near the region of excitation. In fact it is found that if signal and noise overlap in spatial extent, then weak noise may inhibit spiking. If, however, signal and noise are applied on disjoint intervals, then the noise has no effect on the spiking activity, no matter how large its region of application, though the trajectories are naturally altered slightly by noise. Such effects could not be discerned in a point model and are important for real neuron behavior. Interference with the spike train does nevertheless occur when the noise amplitude is larger, even when noise and signal do not overlap, being due to the instigation of secondary noise-induced wave phenomena rather than switching the system from one attractor (firing regularly) to another (a stable point).

Cycles, phase synchronization, and entrainment in single-species phytoplankton populations

Complex dynamics, such as population cycles, can arise when the individual members of a population become synchronized. However, it is an open question how readily and through which mechanisms synchronization-driven cycles can occur in unstructured microbial populations. In experimental chemostats we studied large populations (>10(9) cells) of unicellular phytoplankton that displayed regular, inducible and reproducible population oscillations. Measurements of cell size distributions revealed that progression through the mitotic cycle was synchronized with the population cycles. A mathematical model that accounts for both the cell cycle and population-level processes suggests that cycles occur because individual cells become synchronized by interacting with one another through their common nutrient pool. An external perturbation by direct manipulation of the nutrient availability resulted in phase resetting, unmasking intrinsic oscillations and producing a transient collective cycle as the individuals gradually drift apart. Our study indicates a strong connection between complex within-cell processes and population dynamics, where synchronized cell cycles of unicellular phytoplankton provide sufficient population structure to cause small-amplitude oscillations at the population level.

Noise-induced coherence in multicellular circadian clocks

In higher organisms, circadian rhythms are generated by a multicellular genetic clock that is entrained very efficiently to the 24-h light-dark cycle. Most studies done so far of these circadian oscillators have considered a perfectly periodic driving by light, in the form of either a square wave or a sinusoidal modulation. However, in natural conditions, organisms are subject to nonnegligible fluctuations in the light level all through the daily cycle. In this article, we investigate how the interplay between light fluctuations and intercellular coupling affects the dynamics of the collective rhythm in a large ensemble of nonidentical, globally coupled cellular clocks modeled as Goodwin oscillators. On the basis of experimental considerations, we assume an inverse dependence of the cell-cell coupling strength on the light intensity, in such a way that the larger the light intensity, the weaker the coupling. Our results show a noise-induced rhythm generation for constant light intensities at which the clock is arrhythmic in the noise-free case. Importantly, the rhythm shows a resonancelike phenomenon as a function of the noise intensity. Such improved coherence can be only observed at the level of the overt rhythm and not at the level of the individual oscillators, thus suggesting a cooperative effect of noise, coupling, and the emerging synchronization between the oscillators.

Internal noise-sustained circadian rhythms in a Drosophila model

Circadian rhythmic processes, mainly regulated by gene expression at the molecular level, have inherent stochasticity. Their robustness or resistance to internal noise has been extensively investigated by most of the previous studies. This work focuses on the constructive roles of internal noise in a reduced Drosophila model, which incorporates negative and positive feedback loops, each with a time delay. It is shown that internal noise sustains reliable oscillations with periods close to 24 h in a region of parameter space, where the deterministic kinetics would evolve to a stable steady state. The amplitudes of noise-sustained oscillations are significantly affected by the variation of internal noise level, and the best performance of the oscillations could be found at an optimal noise intensity, indicating the occurrence of intrinsic coherence resonance. In the oscillatory region of the deterministic model, the coherence of noisy circadian oscillations is suppressed by internal noise, while the period remains nearly constant over a large range of noise intensity, demonstrating robustness of the Drosophila model for circadian rhythms to intrinsic noise. In addition, the effects of time delay in the positive feedback on the oscillations are also investigated. It is found that the time delay could efficiently tune the performance of the noise-sustained oscillations. These results might aid understanding of the exploitation of intracellular noise in biochemical and genetic regulatory systems.

E-photosynthesis: a comprehensive modeling approach to understand chlorophyll fluorescence transients and other complex dynamic features of photosynthesis in fluctuating light

Plants are exposed to a temporally and spatially heterogeneous environment, and photosynthesis is well adapted to these fluctuations. Understanding of the complex, non-linear dynamics of photosynthesis in fluctuating light requires novel-modeling approaches that involve not only the primary light and dark biochemical reactions, but also networks of regulatory interactions. This requirement exceeds the capacity of the existing molecular models that are typically reduced to describe a partial process, dynamics of a specific complex or its particular dynamic feature. We propose a concept of comprehensive model that would represent an internally consistent, integral framework combining information on the reduced models that led to its construction. This review explores approaches and tools that exist in engineering, mathematics, and in other domains of biology that can be used to develop a comprehensive model of photosynthesis. Equally important, we investigated techniques by which one can rigorously reduce such a comprehensive model to models of low dimensionality, which preserve dynamic features of interest and, thus, contribute to a better understanding of photosynthesis under natural and thus fluctuating conditions. The web-based platform www.e-photosynthesis.org is introduced as an arena where these concepts and tools are being introduced and tested.

Carbon dioxide signalling in plant leaves

The role of carbon dioxide (CO(2)) as a signal in biochemical regulation networks of plants is fathomed. Transport mechanisms of CO(2) and HCO3- are surveyed, which are the prerequisite for signalling. A CO(2) sensor is not known to date, but any reaction where CO(2)/HCO3- is a substrate can be a candidate. Carbon concentrating mechanisms, e.g., in higher plants C(4)-photosynthesis and crassulacean acid metabolism (CAM), generate high internal CO(2) concentrations, important for photosynthesis, but also as a basis for signalling via diffusion of CO(2). Spatiotemporal dynamics of desynchronization/synchronization of photosynthetic activity over leaves can be followed by chlorophyll fluorescence imaging. One example of desynchronization is based on patchiness of stomatal opening/closing in heterobaric leaves due to anatomic constraints of lateral CO(2) diffusion. During CAM, largely different internal CO(2) concentrations prevail in the leaves, offering opportunities to study the effect of lateral diffusion of CO(2) in synchronizing photosynthetic activity over the entire leaves.

Constructive effects of fluctuations in genetic and biochemical regulatory systems

Biochemical and genetic regulatory systems that involve low concentrations of molecules are inherently noisy. This intrinsic stochasticity has received considerable interest recently, leading to new insights about the sources and consequences of noise in complex systems of genetic regulation. However, most prior work was devoted to the reduction of fluctuation and the robustness of cellular function with respect to intrinsic noise. Here, we focus on several scenarios in which the inherent molecular fluctuations are not merely a nuisance, but act constructively and bring about qualitative changes in the dynamics of the system. It will be demonstrated that in many typical situations biochemical and genetic regulatory systems may utilize intrinsic noise to their advantage.

Stochastic resonance and synchronization in the crayfish caudal photoreceptor

Stochastic resonance is the process by which noise added to a weak external stimulus can enhance encoding efficiency in the sensory periphery and thence in the central nervous system. Stochastic synchronization is the process by which noisy phase synchronization of two periodic (or aperiodic) signals can occur. Together with a brief review of both concepts, we illustrate their applications to the encoding of weak external hydrodynamic signals in the mechanosensory system of the crayfish.

Identification of rhythmic subsystems in the circadian cycle of crassulacean acid metabolism under thermoperiodic perturbations

Leaves of the Crassulacean acid metabolism (CAM) plant Kalanchoë daigremontiana Hamet et Perrier de la Bâthie show overt circadian rhythms in net CO2 uptake, leaf conductance to water and intercellular CO2 concentration, which are entrained by periodic temperature cycles. To probe their sensitivity to thermoperiodic perturbations, intact leaves were exposed to continuous light intensity and temperature cycles with a period of 16 h, applying a set of different baseline temperatures and thermodriver amplitudes. All three overt rhythms were analyzed with respect to their frequency spectra and their phase relations with the thermodriver. For most stimulation protocols, stomatal conductance and net CO2 change were fully or partially entrained by the temperature pulses, while the internal CO2 concentration remained dominated by oscillations in the circadian range. Prolonged time series recorded for up to 22 d in continuous light underline the robustness of these circadian oscillations. This suggests that the overt circadian rhythm of net CO2 uptake in CAM results from the interaction of two coupled original systems: (i) an endogenous cycle of CO2 fixation in the mesophyll, showing very robust periodic activity, and (ii) stomatal movements that respond to environmental stimuli independently of rhythmic processes in the mesophyll, and thus modulate the gas exchange amplitude.

Metabolomics in systems biology

The primary aim of "omic" technologies is the nontargeted identification of all gene products (transcripts, proteins, and metabolites) present in a specific biological sample. By their nature, these technologies reveal unexpected properties of biological systems. A second and more challenging aspect of omic technologies is the refined analysis of quantitative dynamics in biological systems. For metabolomics, gas and liquid chromatography coupled to mass spectrometry are well suited for coping with high sample numbers in reliable measurement times with respect to both technical accuracy and the identification and quantitation of small-molecular-weight metabolites. This potential is a prerequisite for the analysis of dynamic systems. Thus, metabolomics is a key technology for systems biology. The aim of this review is to (a) provide an in-depth overview about metabolomic technology, (b) explore how metabolomic networks can be connected to the underlying reaction pathway structure, and (c) discuss the need to investigate integrative biochemical networks.

Dynamic interactions of cyclic AMP transients and spontaneous Ca(2+) spikes

Transient increases of intracellular Ca(2+) drive many cellular processes, ranging from membrane channel kinetics to transcriptional regulation, and links of Ca(2+) to other second messengers should activate signalling networks. However, real-time kinetic interactions have been difficult to investigate. Here we report observations of spontaneous increases in concentration of cyclic AMP (cAMP) in embryonic spinal neurons, and their dynamic interactions with Ca(2+) oscillations. Blocking the production of these cAMP transients decreases the intrinsic frequency of spontaneous Ca(2+) spikes, whereas inducing cAMP increases causes spike frequency to increase. Transients of cAMP in turn are absent when Ca(2+) spikes are blocked, and are generated only in response to specific patterns of stimulated spikes that mimic endogenous Ca(2+) kinetics. We present a mathematical model of Ca(2+)-cAMP reciprocity that generates the slow cAMP oscillations and reproduces the dynamics of Ca(2+)-cAMP interactions observed experimentally. The model predicts that this module of coupled second messengers is tuned to optimize production of cAMP transients, and that simultaneous stimulation of Ca(2+) and cAMP systems produces distinct temporal patterns of oscillations of both messengers. Our findings may prove useful in the investigation of the regulation of gene expression by second-messenger transients.

Spatiotemporal variation of metabolism in a plant circadian rhythm: the biological clock as an assembly of coupled individual oscillators

The complex dynamic properties of biological timing in organisms remain a central enigma in biology despite the increasingly precise genetic characterization of oscillating units and their components. Although attempts to obtain the time constants from oscillations of gene activity and biochemical units have led to substantial progress, we are still far from a full molecular understanding of endogenous rhythmicity and the physiological manifestations of biological clocks. Applications of nonlinear dynamics have revolutionized thinking in physics and in biomedical and life sciences research, and spatiotemporal considerations are now advancing our understanding of development and rhythmicity. Here we show that the well known circadian rhythm of a metabolic cycle in a higher plant, namely the crassulacean acid metabolism mode of photosynthesis, is expressed as dynamic patterns of independently initiated variations in photosynthetic efficiency (phi(PSII)) over a single leaf. Noninvasive highly sensitive chlorophyll fluorescence imaging reveals randomly initiated patches of varying phi(PSII) that are propagated within minutes to hours in wave fronts, forming dynamically expanding and contracting clusters and clearly dephased regions of phi(PSII). Thus, this biological clock is a spatiotemporal product of many weakly coupled individual oscillators, defined by the metabolic constraints of crassulacean acid metabolism. The oscillators operate independently in space and time as a consequence of the dynamics of metabolic pools and limitations of CO(2) diffusion between tightly packed cells.