Experimental and Mathematical Analyses Relating Circadian Period and Phase of Entrainment in Neurospora crassa

Timely symbiosis: circadian control of legume-rhizobia symbiosis

Legumes house nitrogen-fixing endosymbiotic rhizobia in specialised polyploid cells within root nodules. This results in a mutualistic relationship whereby the plant host receives fixed nitrogen from the bacteria in exchange for dicarboxylic acids. This plant-microbe interaction requires the regulation of multiple metabolic and physiological processes in both the host and symbiont in order to achieve highly efficient symbiosis. Recent studies have showed that the success of symbiosis is influenced by the circadian clock of the plant host. Medicago and soybean plants with altered clock mechanisms showed compromised nodulation and reduced plant growth. Furthermore, transcriptomic analyses revealed that multiple genes with key roles in recruitment of rhizobia to plant roots, infection and nodule development were under circadian control, suggesting that appropriate timing of expression of these genes may be important for nodulation. There is also evidence for rhythmic gene expression of key nitrogen fixation genes in the rhizobium symbiont, and temporal coordination between nitrogen fixation in the bacterial symbiont and nitrogen assimilation in the plant host may be important for successful symbiosis. Understanding of how circadian regulation impacts on nodule establishment and function will identify key plant-rhizobial connections and regulators that could be targeted to increase the efficiency of this relationship.

Targeted Disruption of the Inhibitor of DNA Binding 4 (Id4) Gene Alters Photic Entrainment of the Circadian Clock

Inhibitor of DNA binding (Id) genes comprise a family of four helix-loop-helix (HLH) transcriptional inhibitors. Our earlier studies revealed a role for ID2 within the circadian system, contributing to input, output, and core clock function through its interaction with CLOCK and BMAL1. Here, we explore the contribution of ID4 to the circadian system using a targeted disruption of the Id4 gene. Attributes of the circadian clock were assessed by monitoring the locomotor activity of Id4-/- mice, and they revealed disturbances in its operation. Id4-mutant mice expressed a shorter circadian period length, attenuated phase shifts in responses to continuous and discrete photic cues, and an advanced phase angle of entrainment under a 12:12 light:dark cycle and under short and long photoperiods. To understand the basis for these properties, suprachiasmatic nucleus (SCN) and retinal structures were examined. Anatomical analysis reveals a smaller Id4-/- SCN in the width dimension, which is a finding consistent with its smaller brain. As a result of this feature, anterograde tracing in Id4-/- mice revealed retinal afferents innovate a disproportionally larger SCN area. The Id4-/- photic entrainment responses are unlikely to be due to an impaired function of the retinal pathways since Id4-/- retinal anatomy and function tested by pupillometry were similar to wild-type mice. Furthermore, these circadian characteristics are opposite to those exhibited by the Id2-/- mouse, suggesting an opposing influence of the ID4 protein within the circadian system; or, the absence of ID4 results in changes in the expression or activity of other members of the Id gene family. Expression analysis of the Id genes within the Id4-/- SCN revealed a time-of-day specific elevated Id1. It is plausible that the increased Id1 and/or absence of ID4 result in changes in interactions with bHLH canonical clock components or with targets upstream and/or downstream of the clock, thereby resulting in abnormal properties of the circadian clock and its entrainment.

A Two-Step Model of Human Entrainment: A Quantitative Study of Circadian Period and Phase of Entrainment

One of the essential characteristics of an authentic circadian clock is that the free-running period sustains an approximately 24-hour cycle. When organisms are exposed to an external stimulus, the endogenous oscillators synchronize to the cycling environment signal in a process known as entrainment. These environmental cues perform an important role in resetting the phase and period of the circadian clock. A "generalized assumption" states that when an organism has a short period, it will experience a phase advance, while an organism with a long period experiences a phase delay. Despite widespread use, this positive relationship relating period to the phase of entrainment does not describe all known experimental data. We developed a two-step entrainment model to explain a broader range of results as well as provide more quantitative analysis. We prove existence and stability of periodic orbits and given analytical solutions of the range of entrainment, fit the phase trajectory over the entire entrainment process to data from a published study for 12 subjects in extended day cycles, i.e., longer than 24 h. Our simulations closely replicated the phase data and predicted correctly the phase of entrainment. We investigate the factors related to the rate of entrainment (ROE) and present the three-dimensional parameter spaces, illustrating the various behaviors of the phase of entrainment and ROE. Our findings can be applied to diagnostics and treatments for patients with sleep disorders caused by shift work or jet lag.

Inhibitor of DNA binding 2 (Id2) Regulates Photic Entrainment Responses in Mice: Differential Responses of the Id2-/- Mouse Circadian System Are Dependent on Circadian Phase and on Duration and Intensity of Light

ID2 is a rhythmically expressed helix-loop-helix transcriptional repressor, and its deletion results in abnormal properties of photoentrainment. By examining parametric and nonparametric models of entrainment, we have started to explore the mechanism underlying this circadian phenotype. Id2-/- mice were exposed to differing photoperiods, and the phase angle of entrainment under short days was delayed 2 h as compared with controls. When exposed to long durations of continuous light, enhanced entrainment responses were observed after a delay of the clock but not with phase advances. However, the magnitude of phase shifts was not different in Id2-/- mice tested in constant darkness using a discrete pulse of saturating light. No differences were observed in the speed of clock resetting when challenged by a series of discrete pulses interspaced by varying time intervals. A photic phase-response curve was constructed, although no genotypic differences were observed. Although phase shifts produced by discrete saturating light pulses at CT16 were similar, treatment with a subsaturating pulse revealed a ~2-fold increase in the magnitude of the Id2-/- shift. A corresponding elevation of light-induced per1 expression was observed in the Id2-/- suprachiasmatic nucleus (SCN). To test whether the phenotype is based on a sensitivity change at the level of the retina, pupil constriction responses were measured. No differences were observed in responses or in retinal histology, suggesting that the phenotype occurs downstream of the retina and retinal hypothalamic tract. To test whether the phenotype is due to a reduced amplitude of state variables of the clock, the expression of clock genes per1 and per2 was assessed in vivo and in SCN tissue explants. Amplitude, phase, and period length were normal in Id2-/- mice. These findings suggest that ID2 contributes to a photoregulatory mechanism at the level of the SCN central pacemaker through control of the photic induction of negative elements of the clock.

Circadian Clock Properties and Their Relationships as a Function of Free-Running Period in Drosophila melanogaster

The stability of circadian clock mechanisms under cyclic environments contributes to increased Darwinian fitness by accurately timing daily behavior and physiology. Earlier studies on biological clocks speculated that the timing of behavior and its accuracy are determined by the intrinsic period (τ) of the circadian clock under constant conditions, its stability, the period of the external cycle (T), and resetting of the clock by environmental time cues. However, most of these previous studies suffered from certain limitations, the major ones being a narrow range of examined τ values and a non-uniformity in the genetic background across the individuals tested. We present data that rigorously test the following hypotheses by employing Drosophila melanogaster fruit flies with τ ranging from 17 to 30 h in a uniform genetic background. We tested whether 1) precision (day-to-day stability of τ) is greater for clocks with τ close to 24 h; 2) accuracy (i.e., day-to-day stability of the phase relationship (ψ), where ψ is the duration between a phase of the rhythm and a phase of the external cycle) is greater for clocks with τ close to 24 h; 3) Ψ is delayed with an increase in τ; and 4) Ψ becomes more advanced with an increase in length of zeitgeber cycle (T). We show that precision is not always maximum for ~24-h clocks, but that accuracy is greatest when τ approximates T. Further, flies exhibit a delayed phase relationship with increasing τ and an advanced phase relationship under long T-cycles as compared with shorter T-cycles. We also describe relationships between activity and rest durations and how our observations fit predictions from models of circadian entrainment. Overall, we confirm that accuracy and phase of entrained rhythm are governed by both intrinsic clock period and the length of the external cycle; however, we find that the relationship between intrinsic period and precision does not fit previous predictions.