Promoter methylation in a mixed feedback loop circadian clock model

A mathematical model of melatonin synthesis and interactions with the circadian clock

A new mathematical model of melatonin synthesis in pineal cells is created and connected to a slightly modified previously created model of the circadian clock in the suprachiasmatic nucleus (SCN). The SCN influences the production of melatonin by upregulating two key enzymes in the pineal. The melatonin produced enters the blood and the cerebrospinal fluid and thus the SCN, influencing the circadian clock. We show that the model of melatonin synthesis corresponds well with extant experimental data and responds similarly to clinical experiments on bright light in the middle of the night. Melatonin is widely used to treat jet lag and sleep disorders. We show how the feedback from the pineal to the SCN causes phase resetting of the circadian clock. Melatonin doses early in the evening advance the clock and doses late at night delay the clock with a dead zone in between where the phase of the clock does not change.

A mathematical model for the role of dopamine-D2 self-regulation in the production of ultradian rhythms

Many self-motivated and goal-directed behaviours display highly flexible, approximately 4 hour ultradian (shorter than a day) oscillations. Despite lacking direct correspondence to physical cycles in the environment, these ultradian rhythms may be involved in optimizing functional interactions with the environment and reflect intrinsic neural dynamics. Current evidence supports a role of mesostriatal dopamine (DA) in the expression and propagation of ultradian rhythmicity, however, the biochemical processes underpinning these oscillations remain to be identified. Here, we use a mathematical model to investigate D2 autoreceptor-dependent DA self-regulation as the source of ultradian behavioural rhythms. DA concentration at the midbrain-striatal synapses is governed through a dual-negative feedback-loop structure, which naturally gives rise to rhythmicity. This model shows the propensity of striatal DA to produce an ultradian oscillation characterized by a flexible period that is highly sensitive to parameter variations. Circadian (approximately 24 hour) regulation consolidates the ultradian oscillations and alters their response to the phase-dependent, rapid-resetting effect of a transient excitatory stimulus. Within a circadian framework, the ultradian rhythm orchestrates behavioural activity and enhances responsiveness to an external stimulus. This suggests a role for the circadian-ultradian timekeeping hierarchy in governing organized behaviour and shaping daily experience through coordinating the motivation to engage in recurring, albeit not highly predictable events, such as social interactions.

Mathematical insights into the role of dopamine signaling in circadian entrainment

The circadian clock in the mammalian brain comprises interlocked molecular feedback loops that have downstream effects on important physiological functions such as the sleep-wake cycle and hormone regulation. Experiments have shown that the circadian clock also modulates the synthesis and breakdown of the neurotransmitter dopamine. Imbalances in dopamine are linked to a host of neurological conditions including Parkinson's disease, attention-deficit/hyperactivity disorder, and mood disorders, and these conditions are often accompanied by circadian disruptions. We have previously created a mathematical model using nonlinear ordinary differential equations to describe the influences of the circadian clock on dopamine at the molecular level. Recent experiments suggest that dopamine reciprocally influences the circadian clock. Dopamine receptor D1 (DRD1) signaling has been shown to aid in the entrainment of the clock to the 24-hour light-dark cycle, but the underlying mechanisms are not well understood. In this paper, we use our mathematical model to support the experimental hypothesis that DRD1 signaling promotes circadian entrainment by modulating the clock's response to light. We model the effects of a phase advance or delay, as well as the therapeutic potential of a REV-ERB agonist. In addition to phase shifts, we study the influences of photoperiod, or day length, in the mathematical model, connect our findings with the experimental and clinical literature, and determine the parameter that affects the critical photoperiod that signals seasonal changes to physiology.

Interplay of Cellular mRNA, miRNA and Viral miRNA during Infection of a Cell

The understanding of the kinetics of gene expression in cells infected by viruses is currently limited. As a rule, the corresponding models do not take viral microRNAs (miRNAs) into account. Such RNAs are, however, operative during the replication of some viruses, including, e.g., herpesvirus. To clarify the kinetics of this category (with emphasis on the information available for herpesvirus), I introduce a generic model describing the transient interplay of cellular mRNA, protein, miRNA and viral miRNA. In the absence of viral miRNA, the cellular miRNA is considered to suppress the populations of mRNA and protein due to association with mRNA and subsequent degradation. During infection, the viral miRNA suppresses the population of cellular miRNA and via this pathway makes the mRNA and protein populations larger. This effect becomes appreciable with the progress of intracellular viral replication. Using biologically reasonable parameters, I investigate the corresponding mean-field kinetics and show the scale of the effect of viral miRNAs on cellular miRNA and mRNA. The scale of fluctuations of the populations of these species is illustrated as well by employing Monte Carlo simulations.