Network balance via CRY signalling controls the Arabidopsis circadian clock over ambient temperatures

Circadian clocks exhibit ‘temperature compensation’, meaning that they show only small changes in period over a broad temperature range. Several clock genes have been implicated in the temperature‐dependent control of period in Arabidopsis. We show that blue light is essential for this, suggesting that the effects of light and temperature interact or converge upon common targets in the circadian clock. Our data demonstrate that two cryptochrome photoreceptors differentially control circadian period and sustain rhythmicity across the physiological temperature range. In order to test the hypothesis that the targets of light regulation are sufficient to mediate temperature compensation, we constructed a temperature‐compensated clock model by adding passive temperature effects into only the light‐sensitive processes in the model. Remarkably, this model was not only capable of full temperature compensation and consistent with mRNA profiles across a temperature range, but also predicted the temperature‐dependent change in the level of LATE ELONGATED HYPOCOTYL, a key clock protein. Our analysis provides a systems‐level understanding of period control in the plant circadian oscillator.     

Photoperiod sensitivity of the Arabidopsis circadian clock is tissue-specific

Tissue-specific functions of the circadian clock in Arabidopsis have recently been revealed. The vasculature clock shows distinctive gene expression profiles compared to the clock in other tissues under light-dark cycles. However, it has not yet been established whether the vasculature clock also shows unique gene expression patterns that correlate with temperature cycles, another important environmental cue. Here, we detected diel phase of TIMING OF CAB EXPRESSION 1 (TOC1) expression in the vasculature and whole leaf under long-day light-dark cycles and temperature cycles. We found that the vasculature clock had advanced TOC1 phase under light-dark cycles but not under temperature cycles, suggesting that the vasculature clock has lower sensitivity against temperature signals. Furthermore, the phase advancement of TOC1 was seen only under long-day condition but not under short-day condition. These results support our previous conclusion that the circadian clock in vasculature preferentially senses photoperiodic signals.     

A spatial model of the plant circadian clock reveals design principles for coordinated timing

Individual plant cells possess a genetic network, the circadian clock, that times internal processes to the day‐night cycle. Mathematical models of the clock are typically either “whole‐plant” that ignore tissue or cell type‐specific clock behavior, or “phase‐only” that do not include molecular components. To address the complex spatial coordination observed in experiments, here we implemented a clock network model on a template of a seedling. In our model, the sensitivity to light varies across the plant, and cells communicate their timing via local or long‐distance sharing of clock components, causing their rhythms to couple. We found that both varied light sensitivity and long‐distance coupling could generate period differences between organs, while local coupling was required to generate the spatial waves of clock gene expression observed experimentally. We then examined our model under noisy light‐dark cycles and found that local coupling minimized timing errors caused by the noise while allowing each plant region to maintain a different clock phase. Thus, local sensitivity to environmental inputs combined with local coupling enables flexible yet robust circadian timing.     

Development of model based on clock gene expression of human hair follicle cells to estimate circadian time

ABSTRACT

Considering the effects of circadian misalignment on human pathophysiology and behavior, it is important to be able to detect an individual’s endogenous circadian time. We developed an endogenous Clock Estimation Model (eCEM) based on a machine learning process using the expression of 10 circadian genes. Hair follicle cells were collected from 18 healthy subjects at 08:00, 11:00, 15:00, 19:00, and 23:00 h for two consecutive days, and the expression patterns of 10 circadian genes were obtained. The eCEM was designed using the inverse form of the circadian gene rhythm function (i.e., Circadian Time = F(gene)), and the accuracy of eCEM was evaluated by leave-one-out cross-validation (LOOCV). As a result, six genes (PER1, PER3, CLOCK, CRY2, NPAS2, and NR1D2) were selected as the best model, and the error range between actual and predicted time was 3.24 h. The eCEM is simple and applicable in that a single time-point sampling of hair follicle cells at any time of the day is sufficient to estimate the endogenous circadian time.     

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.     

Rhythmic oscillations in KaiC1 phosphorylation and ATP/ADP ratio in nitrogen-fixing cyanobacterium Cyanothece sp. ATCC 51142

Cyanobacterial circadian clock composed of the Kai oscillator has been unraveled in the model strain Synechococcus elongatus PCC 7942. Recent studies with nitrogen-fixing Cyanothece sp. ATCC 51142 show rhythmic oscillations in the cellular program even in continuous light albeit with a cycle time of ~11 h. In the present study, we investigate correlation between cellular rhythms, KaiC1 phosphorylation cycle, ATP/ADP ratio, and the redox state of plastoquinone pool in Cyanothece. KaiC1 phosphorylation cycle of Cyanothece was similar to that of Synechococcus under diurnal cycles. However, under continuous light, the cycle time was shorter (11 h), in agreement with physiological and gene expression studies. Interestingly, the ATP/ADP ratio also oscillates with an 11 h period, peaking concomitantly with the respiratory burst. We propose a mathematical model with C/N ratio as a probable signal regulating the clock in continuous light and emphasize the existence of a single timing mechanism regardless of the cycle time.     

Dynamic modelling and analysis of biochemical networks: mechanism-based models and model-based experiments

Systems biology applies quantitative, mechanistic modelling to study genetic networks, signal transduction pathways and metabolic networks. Mathematical models of biochemical networks can look very different. An important reason is that the purpose and application of a model are essential for the selection of the best mathematical framework. Fundamental aspects of selecting an appropriate modelling framework and a strategy for model building are discussed. Concepts and methods from system and control theory provide a sound basis for the further development of improved and dedicated computational tools for systems biology. Identification of the network components and rate constants that are most critical to the output behaviour of the system is one of the major problems raised in systems biology. Current approaches and methods of parameter sensitivity analysis and parameter estimation are reviewed. It is shown how these methods can be applied in the design of model-based experiments which iteratively yield models that are decreasingly wrong and increasingly gain predictive power.     

Parametric sensitivity analysis and reduction of a detailed nutritional model of plant cell cultures

A kinetic model of plant nutrition described by Cloutier et al. (Cloutier et al., 2008. Biotechnol Bioeng 99:189-200) is progressively simplified so as to obtain a predictive model that describes the evolution of the biomass and the extracellular and intracellular concentrations of three determining nutrients, that is, free intracellular nitrogen, phosphate, and carbohydrate compounds. Three techniques of global sensitivity analysis are successively applied to assess the model parameter influence and potential correlation. The resulting dynamic model is able to predict plant growth for the two most encountered plant bioprocesses, namely suspension cells and hairy roots.     

Mathematical modeling reveals threshold mechanism in CD95-induced apoptosis

Mathematical modeling is required for understanding the complex behavior of large signal transduction networks. Previous attempts to model signal transduction pathways were often limited to small systems or based on qualitative data only. Here, we developed a mathematical modeling framework for understanding the complex signaling behavior of CD95(APO-1/Fas)-mediated apoptosis. Defects in the regulation of apoptosis result in serious diseases such as cancer, autoimmunity, and neurodegeneration. During the last decade many of the molecular mechanisms of apoptosis signaling have been examined and elucidated. A systemic understanding of apoptosis is, however, still missing. To address the complexity of apoptotic signaling we subdivided this system into subsystems of different information qualities. A new approach for sensitivity analysis within the mathematical model was key for the identification of critical system parameters and two essential system properties: modularity and robustness. Our model describes the regulation of apoptosis on a systems level and resolves the important question of a threshold mechanism for the regulation of apoptosis.     

胶州湾生物-物理耦合模型参数灵敏度分析

参数灵敏度分析旨在评价模型中各参数对模拟结果的影响程度,是参数优化和模型校正的基础步骤,也是认识模型行为的重要工具。所建的胶州湾生物-物理耦合模型包括浮游植物、浮游动物、营养盐、碎屑和溶解氧5类状态变量,对其涉及的50个参数进行灵敏度分析,得到3个非常灵敏性参数、2个灵敏性参数、11个比较灵敏性参数和34个不太灵敏性参数。非常灵敏及灵敏性参数包括浮游植物生长速率(μPRPC)、暗反应修正因子(FAC)、光饱和强度(α)、浮游植物死亡率(μDEPC)和水体消光系数(bla),主要影响浮游植物生长和死亡过程,反映了浮游植物在生态系统中的基础性和重要性作用。这5个参数显著地影响碳和营养盐循环,是整个胶州湾生态系统最主要的影响参数,应优先进行优化。比较灵敏性参数的影响主要表现在营养盐对浮游植物生长或死亡的限制以及温度对光饱和量的限制,浮游动物生长、牧食和死亡过程以及浮游植物生物量对牧食的限制,叶绿素a的生产,缺氧条件下沉积物释放磷以及浮游植物对磷的摄取等过程,这些参数对于各状态变量的灵敏性存在不同程度的差异,从而表征不同的特点。与不太灵敏性参数相关的过程主要为叶绿素a和碎屑消光作用,温度对浮游植物生长、浮游动物牧食、碎屑和沉积物矿化的限制,碎屑和沉积物矿化与沉降,与无机氮相关的大部分过程,溶解氧浓度变化等,这些过程除了受模型内部参数影响外,还在很大程度上受水深、海水温度和陆源污染等外部因素影响。比较灵敏及不太灵敏性参数影响模型局部过程,是模型校正的重要依据,除了非常灵敏及灵敏性参数以外,叶绿素a、浮游动物、碎屑和无机磷四种状态变量可分别根据叶绿素a最大生产系数(K CHmax)、浮游动物一级死亡率(μDEZC1)、有机碎屑矿化率(μREDC)和浮游植物磷摄取的半饱和常数(h UPPP)进行校正。与营养盐相关参数的灵敏度分析表明,胶州湾浮游植物处于磷限制,无机氮主要受陆源排污影响。因此,对无机氮的校正主要通过合理设置沿岸河流径流量或陆源污染物浓度与比例以及无机氮初始场。溶解氧对各参数均不太灵敏。     

Parameter optimization and sensitivity analysis for large kinetic models using a real-coded genetic algorithm

Dynamic modeling is a powerful tool for predicting changes in metabolic regulation. However, a large number of input parameters, including kinetic constants and initial metabolite concentrations, are required to construct a kinetic model. Therefore, it is important not only to optimize the kinetic parameters, but also to investigate the effects of their perturbations on the overall system. We investigated the efficiency of the use of a real-coded genetic algorithm (RCGA) for parameter optimization and sensitivity analysis in the case of a large kinetic model involving glycolysis and the pentose phosphate pathway in Escherichia coli K-12. Sensitivity analysis of the kinetic model using an RCGA demonstrated that the input parameter values had different effects on model outputs. The results showed highly influential parameters in the model and their allowable ranges for maintaining metabolite-level stability. Furthermore, it was revealed that changes in these influential parameters may complement one another. This study presents an efficient approach based on the use of an RCGA for optimizing and analyzing parameters in large kinetic models.     

Variable thermal sensitivity as output of a circadian clock controlling the bimodal rhythm of temperature choice in the ant Camponotus mus

Along a thermal gradient and under a LD 1212 h cycle, nurse workers of the ant Camponotus mus select for the brood two different temperatures daily: 30.8°C at the middle of the light period (circadian phase = 90°), and 27.5°C 8 h later, during the dark period (CP = 210°). Brood-carrying activity proved to be self-sustained, running its two daily bursts free with a similar period of 23.5 h, under both LL and DD. The LD alternation acted as a strong Zeitgeber. A phase-delay of the LD 1212 h cycle reset the overt rhythm at once, being both daily events locked-on to the delayed light: dark transition. However, changes in expression, non-occurrence, or even splitting of the two daily brood-carrying events during resetting depended on the phase of the delayed DL transition. By comparing the occurrence of activity with predictions based on a threshold curve of thermal sensitivity, results indicated that an immediate resetting of the involved pacemaker actually takes place. Nurse workers do not directly control the total time spent by the brood at the selected temperature. Instead, the endogenously-driven thermal sensitivity triggers their thermal-searching behavior at two critical times of the day, when environmental temperature is expected to reach its maximum and minimum.     

An analysis of the class of gene regulatory functions implied by a biochemical model

Understanding the integrated behavior of genetic regulatory networks, in which genes regulate one another's activities via RNA and protein products, is emerging as a dominant problem in systems biology. One widely studied class of models of such networks includes genes whose expression values assume Boolean values (i.e., on or off). Design decisions in the development of Boolean network models of gene regulatory systems include the topology of the network (including the distribution of input- and output-connectivity) and the class of Boolean functions used by each gene (e.g., canalizing functions, post functions, etc.). For example, evidence from simulations suggests that biologically realistic dynamics can be produced by scale-free network topologies with canalizing Boolean functions. This work seeks further insights into the design of Boolean network models through the construction and analysis of a class of models that include more concrete biochemical mechanisms than the usual abstract model, including genes and gene products, dimerization, cis-binding sites, promoters and repressors. In this model, it is assumed that the system consists of N genes, with each gene producing one protein product. Proteins may form complexes such as dimers, trimers, etc. The model also includes cis-binding sites to which proteins may bind to form activators or repressors. Binding affinities are based on structural complementarity between proteins and binding sites, with molecular binding sites modeled by bit-strings. Biochemically plausible gene expression rules are used to derive a Boolean regulatory function for each gene in the system. The result is a network model in which both topological features and Boolean functions arise as emergent properties of the interactions of components at the biochemical level. A highly biased set of Boolean functions is observed in simulations of networks of various sizes, suggesting a new characterization of the subset of Boolean functions that are likely to appear in gene regulatory networks.