A model for the enhancement of fitness in cyanobacteria based on resonance of a circadian oscillator with the external light-dark cycle

Circadian rhythms and the HPA axis: A systems view

The circadian timing system comprises a network of time-keeping clocks distributed across a living host whose responsibility is to allocate resources and distribute functions temporally to optimize fitness. The molecular structures generating these rhythms have evolved to accommodate the rotation of the earth in an attempt to primarily match the light/dark periods during the 24-hr day. To maintain synchrony of timing across and within tissues, information from the central clock, located in the suprachiasmatic nucleus, is conveyed using systemic signals. Leading among those signals are endocrine hormones, and while the hypothalamic-pituitary-adrenal axis through the release of glucocorticoids is a major pacesetter. Interestingly, the fundamental units at the molecular and physiological scales that generate local and systemic signals share critical structural properties. These properties enable time-keeping systems to generate rhythmic signals and allow them to adopt specific properties as they interact with each other and the external environment. The purpose of this review is to provide a broad overview of these structures, discuss their functional characteristics, and describe some of their fundamental properties as these related to health and disease. This article is categorized under: Immune System Diseases > Computational Models Immune System Diseases > Biomedical Engineering.

Giving Time Purpose: The Synechococcus elongatus Clock in a Broader Network Context

Early research on the cyanobacterial clock focused on characterizing the genes needed to keep, entrain, and convey time within the cell. As the scope of assays used in molecular genetics has expanded to capture systems-level properties (e.g., RNA-seq, ChIP-seq, metabolomics, high-throughput screening of genetic variants), so has our understanding of how the clock fits within and influences a broader cellular context. Here we review the work that has established a global perspective of the clock, with a focus on (a) an emerging network-centric view of clock architecture, (b) mechanistic insights into how temporal and environmental cues are transmitted and integrated within this network,

What season suits you best? Seasonal light changes and cyanobacterial competition

Nearly all living organisms, including some bacterial species, exhibit biological processes with a period of about 24 h called circadian (from the Latin circa, about and dies, day) rhythms. These rhythms allow living organisms to anticipate the daily alternation of light and darkness. Experiments carried out in cyanobacteria have shown the adaptive value of circadian clocks. In theseexperiments, a wild type cyanobacterial strain (with a 24 h circadian rhythm) and a mutantstrain (with a longer or shorter period) grow in competition. In different experiments, the external light dark cycle was chosen to match the circadian period of the different strains, revealing that the strain whose circadian period matches the light-dark cycle has a larger fitness. As a consequence, the initial population of one strain grows while the other decays. These experiments were made under fixed light and dark intervals. In Nature, however, this relationship changes according to the season. Therefore, seasonalchanges in light could affect the results of the competition. Using a theoretical model, we analyze how modulation of light can change the survival of the different cyanobacterial strains. Our results show that there is a clear shift in the competition due to the modulation of light, which could be verified experimentally.Received: 20 Novembre 2014,  Accepted: 29 March 2015; Edited by: C. A. Condat, G. J. Sibona; DOI: http://dx.doi.org/10.4279/PIP.070005Cite as: G Cascallares, P M Gleiser, Papers in Physics 7, 070005 (2015)This paper, by G. Cascallares, P. M. Gleiser, is licensed under the Creative Commons Attribution License 3.0. 

Diversity of KaiC-based timing systems in marine Cyanobacteria

The coordination of biological activities into daily cycles provides an important advantage for the fitness of diverse organisms. Most eukaryotes possess an internal clock ticking with a periodicity of about one day to anticipate sunrise and sunset. The 24-hour period of the free-running rhythm is highly robust against many changes in the natural environment. Among prokaryotes, only Cyanobacteria are known to harbor such a circadian clock. Its core oscillator consists of just three proteins, KaiA, KaiB, and KaiC that produce 24-hour oscillations of KaiC phosphorylation, even in vitro. This unique three-protein oscillator is well documented for the freshwater cyanobacterium Synechococcus elongatus PCC 7942. Several physiological studies demonstrate a circadian clock also for other Cyanobacteria including marine species. Genes for the core clock components are present in nearly all marine cyanobacterial species, though there are large differences in the specific composition of these genes. In the first section of this review we summarize data on the model circadian clock from S. elongatus PCC 7942 and compare it to the reduced clock system of the marine cyanobacterium Prochlorococcus marinus MED4. In the second part we discuss the diversity of timing mechanisms in other marine Cyanobacteria with regard to the presence or absence of different components of the clock.

An Evolutionary Fitness Enhancement Conferred by the Circadian System in Cyanobacteria

Circadian clocks are found in a wide variety of organisms from cyanobacteria to mammals. Many believe that the circadian clock system evolved as an adaption to the daily cycles in light and temperature driven by the rotation of the earth. Studies on the cyanobacterium, Synechococcus elongatus PCC 7942, have confirmed that the circadian clock in resonance with environmental cycles confers an adaptive advantage to cyanobacterial strains with different clock properties when grown in competition under light-dark cycles. The results thus far suggest that in a cyclic environment, the cyanobacterial strains whose free running periods are closest to the environmental period are the most fit and the strains lacking a functional circadian clock are at a competitive disadvantage relative to strains with a functional clock. In contrast, the circadian system provides little or no advantage to cyanobacteria grown in competition in constant light. To explain the potential mechanism of this clock-mediated enhancement in fitness in cyanobacteria, several models have been proposed; these include the limiting resource model, the diffusible inhibitor model and the cell-to-cell communication model. None of these models have been excluded by the currently available experimental data and the mechanistic basis of clock-mediated fitness enhancement remains elusive.

Suppressed cellular oscillations in after-hours mutant mice are associated with enhanced circadian phase-resetting

Within the core molecular clock, protein phosphorylation and degradation play a vital role in determining circadian period. The 'after-hours' (Afh) mutation in mouse slows the degradation of the core clock protein Cryptochrome, lengthening the period of the molecular clock in the suprachiasmatic nuclei (SCN) and behavioural wheel-running rhythms. However, we do not yet know how the Afh mutation affects other aspects of physiology or the activity of circadian oscillators in other brain regions. Here we report that daily rhythms of metabolism and ingestive behaviours are altered in these animals, as are PERIOD2::LUCIFERASE (PER2::LUC) rhythms in mediobasal hypothalamic nuclei, which influence these behaviours. Overall there is a trend towards period lengthening and a decrease in amplitude of PER2::LUC rhythms throughout the brain. Imaging of single cells from the arcuate and dorsomedial hypothalamic nuclei revealed this reduction in tissue oscillator amplitude to be due to a decrease in the amplitude, rather than a desynchrony, of single cells. Consistent with existing models of oscillator function, this cellular phenotype was associated with a greater susceptibility to phase-shifting stimuli in vivo and in vitro, with light evoking high-amplitude Type 0 resetting in Afh mutant mice. Together, these findings reveal unexpected consequences of the Afh mutation on the amplitude and synchrony of individual cellular oscillators in the SCN.

Modeling circadian clocks: From equations to oscillations

Circadian rhythms are generated at the cellular level by a small but tightly regulated genetic network. In higher eukaryotes, interlocked transcriptional-translational feedback loops form the core of this network, which ensures the activation of the right genes (proteins) at the right time of the day. Understanding how such a complex molecular network can generate robust, self-sustained oscillations and accurately responds to signals from the environment (such as light and temperature) is greatly helped by mathematical modeling. In the present paper we review some mathematical models for circadian clocks, ranging from abstract, phenomenological models to the most detailed molecular models. We explain how the equations are derived, highlighting the challenges for the modelers, and how the models are analyzed. We show how to compute bifurcation diagrams, entrainment, and phase response curves. In the subsequent paper, we discuss, through a selection of examples, how modeling efforts have contributed to a better understanding of the dynamics of the circadian regulatory network.

Circadian clocks and phosphorylation: Insights from computational modeling

Circadian clocks are based on a molecular mechanism regulated at the transcriptional, translational and post-translational levels. Recent experimental data unravel a complex role of the phosphorylations in these clocks. In mammals, several kinases play differential roles in the regulation of circadian rhythmicity. A dysfunction in the phosphorylation of one clock protein could lead to sleep disorders such as the Familial Advanced Sleep Phase Disorder, FASPS. Moreover, several drugs are targeting kinases of the circadian clocks and can be used in cancer chronotherapy or to treat mood disorders. In Drosophila, recent experimental observations also revealed a complex role of the phosphorylations. Because of its high degree of homology with mammals, the Drosophila system is of particular interest. In the circadian clock of cyanobacteria, an atypical regulatory mechanism is based only on three clock proteins (KaiA, KaiB, KaiC) and ATP and is sufficient to produce robust temperature-compensated circadian oscillations of KaiC phosphorylation. This review will show how computational modeling has become a powerful and useful tool in investigating the regulatory mechanism of circadian clocks, but also how models can give rise to testable predictions or reveal unexpected results.

Altered oscillator function affects clock resonance and is responsible for the reduced day-length sensitivity of CKB4 overexpressing plants

Most organisms have evolved a timing mechanism or circadian clock that is able to generate 24 h rhythmic oscillations in multiple biological events. The environmental fluctuations in light and temperature synchronize the expression and activity of key oscillator components that ultimately define the period, phase and amplitude of output rhythms. In Arabidopsis, overexpression of the casein kinase 2 (CK2) regulatory subunits, CKB3 or CKB4, alters the function of the clock under free-running conditions, and results in period-shortening of genes peaking at different phase angles. Here, we examine the effects of CKB4 overexpression (CKB4-ox) on a number of clock outputs that are modulated by day length or photoperiod. We have found a phase shift in gene expression, shortening of hypocotyl elongation and earlier than wild-type initiation of flowering under short-day conditions. Our study shows that the earlier expression phases of the floral induction genes GIGANTEA, FLAVIN-BINDING KELCH REPEAT F-BOX1 and CONSTANS correlate with higher abundance of the FLOWERING LOCUS T transcript under short-day conditions. Matching the period of the external light/dark cycles relative to the endogenous short period of the CKB4-ox oscillator restores the phase of gene expression and the flowering sensitivity to day length, indicating that a clock defect is responsible for the CKB4-ox phenotypes. Our studies suggest a function for CKB4 very close to the oscillator, as expression of the core components TIMING OF CAB EXPRESSION 1 and CIRCADIAN CLOCK ASSOCIATED 1 is also altered in CKB4-ox plants. Based on our results, we propose that oscillator dysfunction is responsible for the period defect of CKB4-ox plants that leads to clock dissonance with the environment and reduced sensitivity to day length.

Excitation migration in trimeric cyanobacterial photosystem I

A structure-based description of excitation migration in multireaction center light harvesting systems is introduced. The description is an extension of the sojourn expansion, which decomposes excitation migration in terms of repeated detrapping and recapture events. The approach is applied to light harvesting in the trimeric form of cyanobacterial photosystem I (PSI). Excitation is found to be shared between PSI monomers and the chlorophylls providing the strongest respective links are identified. Excitation sharing is investigated by computing cross-monomer excitation trapping probabilities. It is seen that on the average there is a nearly 40% chance of excitation cross transfer and trapping, indicating efficient coupling between monomers. The robustness and optimality of the chlorophyll network of trimeric PSI is examined.

Uncovering the design principles of circadian clocks: Mathematical analysis of flexibility and evolutionary goals

In this paper, we present the mathematical details underlying both an approach to the flexibility of regulatory networks and an analytical characterization of evolutionary goals of circadian clock networks. A fundamental problem in cellular regulation is to understand the relation between the form of regulatory networks and their function. Circadian clocks present a particularly interesting instance of this. Recent work has shown that they have complex structures involving multiple interconnected feedback loops with both positive and negative feedback. We address the question of why they have such a complex structure and argue that it is to provide the flexibility necessary to simultaneously attain multiple key properties of circadian clocks such as robust entrainment and temperature compensation. To do this we address two fundamental problems: (A) to understand the relationships between the key evolutionary aims of the clock and (B) to ascertain how flexible the clock's structure is. To address the first problem we use infinitesimal response curves (IRCs), a tool that we believe will be of general utility in the analysis of regulatory networks. To understand the second problem we introduce the flexibility dimension d, show how to calculate it and then use it to analyse a range of models. We believe our results will generalize to a broad range of regulatory networks.

Models of cell signaling pathways

Cellular signaling circuits handle an enormous range of computations. Beyond the housekeeping, replicating and other functions of individual cells, signaling circuits must implement the immensely complex logic of development and function of multicellular organisms. Computer models are useful tools to understand this complexity. Recent studies have extended such models to include electrical, mechanical and spatial details of signaling, and to address the stochastic effects that arise when small numbers of molecules interact. Increasing numbers of models have been developed in close conjunction with experiments, and this interplay gives a deeper and more reliable insight into signaling function.

The adaptive value of circadian clocks: an experimental assessment in cyanobacteria

Circadian clocks are thought to enhance the fitness of organisms by improving their ability to adapt to extrinsic influences, specifically daily changes in environmental factors such as light, temperature, and humidity. Some investigators have proposed that circadian clocks provide an additional "intrinsic adaptive value," that is, the circadian clock that regulates the timing of internal events has evolved to be such an integral part of the temporal regulation that it is useful in all conditions, even in constant environments. There have been practically no rigorous tests of either of these propositions. Using cyanobacterial strains with different clock properties growing in competition with each other, we found that strains with a functioning biological clock defeat clock-disrupted strains in rhythmic environments. In contrast to the expectations of the "intrinsic value model," this competitive advantage disappears in constant environments. In addition, competition experiments using strains with different circadian periods showed that cyanobacterial strains compete most effectively in a rhythmic environment when the frequency of their internal biological oscillator and that of the environmental cycle are similar. Together, these studies demonstrate the adaptive value of circadian temporal programming in cyanobacteria but indicate that this adaptive value is only fulfilled in cyclic environments.

Modeling the mammalian circadian clock: sensitivity analysis and multiplicity of oscillatory mechanisms

We extend the study of a computational model recently proposed for the mammalian circadian clock (Proc. Natl Acad. Sci. USA 100 (2003) 7051). The model, based on the intertwined positive and negative regulatory loops involving the Per, Cry, Bmal1, and Clock genes, can give rise to sustained circadian oscillations in conditions of continuous darkness. These limit cycle oscillations correspond to circadian rhythms autonomously generated by suprachiasmatic nuclei and by some peripheral tissues. By using different sets of parameter values producing circadian oscillations, we compare the effect of the various parameters and show that both the occurrence and the period of the oscillations are generally most sensitive to parameters related to synthesis or degradation of Bmal1 mRNA and BMAL1 protein. The mechanism of circadian oscillations relies on the formation of an inactive complex between PER and CRY and the activators CLOCK and BMAL1 that enhance Per and Cry expression. Bifurcation diagrams and computer simulations nevertheless indicate the possible existence of a second source of oscillatory behavior. Thus, sustained oscillations might arise from the sole negative autoregulation of Bmal1 expression. This second oscillatory mechanism may not be functional in physiological conditions, and its period need not necessarily be circadian. When incorporating the light-induced expression of the Per gene, the model accounts for entrainment of the oscillations by light-dark (LD) cycles. Long-term suppression of circadian oscillations by a single light pulse can occur in the model when a stable steady state coexists with a stable limit cycle. The phase of the oscillations upon entrainment in LD critically depends on the parameters that govern the level of CRY protein. Small changes in the parameters governing CRY levels can shift the peak in Per mRNA from the L to the D phase, or can prevent entrainment. The results are discussed in relation to physiological disorders of the sleep-wake cycle linked to perturbations of the human circadian clock, such as the familial advanced sleep phase syndrome or the non-24h sleep-wake syndrome.

A Cyanobacterial Circadian Timing Mechanism

Cyanobacteria such as Synechococcus elongatus PCC 7942 exhibit 24-h rhythms of gene expression that are controlled by an endogenous circadian clock that is mechanistically distinct from those described for diverse eukaryotes. Genetic and biochemical experiments over the past decade have identified key components of the circadian oscillator, input pathways that synchronize the clock with the daily environment, and output pathways that relay temporal information to downstream genes. The mechanism of the cyanobacterial circadian clock that is emerging is based principally on the assembly and disassembly of a large complex at whose heart are the proteins KaiA, KaiB, and KaiC. Signal transduction pathways that feed into and out of the clock employ protein domains that are similar to those in two-component regulatory systems of bacteria.

Motifs, modules and games in bacteria

Global explorations of regulatory network dynamics, organization and evolution have become tractable thanks to high-throughput sequencing and molecular measurement of bacterial physiology. From these, a nascent conceptual framework is developing, that views the principles of regulation in term of motifs, modules and games. Motifs are small, repeated, and conserved biological units ranging from molecular domains to small reaction networks. They are arranged into functional modules, genetically dissectible cellular functions such as the cell cycle, or different stress responses. The dynamical functioning of modules defines the organism's strategy to survive in a game, pitting cell against cell, and cell against environment. Placing pathway structure and dynamics into an evolutionary context begins to allow discrimination between those physical and molecular features that particularize a species to its surroundings, and those that provide core physiological function. This approach promises to generate a higher level understanding of cellular design, pathway evolution and cellular bioengineering.

Computational approaches to cellular rhythms

Oscillations arise in genetic and metabolic networks as a result of various modes of cellular regulation. In view of the large number of variables involved and of the complexity of feedback processes that generate oscillations, mathematical models and numerical simulations are needed to fully grasp the molecular mechanisms and functions of biological rhythms. Models are also necessary to comprehend the transition from simple to complex oscillatory behaviour and to delineate the conditions under which they arise. Examples ranging from calcium oscillations to pulsatile intercellular communication and circadian rhythms illustrate how computational biology contributes to clarify the molecular and dynamical bases of cellular rhythms.