Recent advances in Graphics Processing Unit (GPU) computing have allowed for computational models of whole-brain activity at unprecedented scales. In this work, we use desktop computers to build and simulate a whole-cortex mouse brain model using Hodgkin-Huxley type models for all the most active neurons in the mouse cortex. We compare the model dynamics over different types of connectivity, ranging from uniform random to realistic connectivity derived from experimental data on cell positions and the Allen Brain Atlas. By changing the external drive and coupling strength of neurons in the network, we can produce a wide range of oscillations in the gamma through delta bands. While the global mean-field behaviors of different connectivities share some similarities, an experimentally determined hierarchical connectivity allows for complex, heterogeneous behaviors typically seen in EEG recordings that are not observed in networks with nearest neighbors or uniform coupling. Moreover, our simulations reveal a wide range of spatiotemporal patterns, such as rotational or planar traveling waves, that are observed in experiments. Different traveling waves are observed with different connectivity and coupling strengths on the same connectivity. Our simulations show that many cortical behaviors emerge at scale with the full complexity of the network structure and ionic dynamics. We also provide a computational framework to explore these cortex- wide behaviors further. ### Competing Interest Statement The authors have declared no competing interest.

While circadian disruption is recognized as a potential driver of depression, its real-world impact is poorly understood. A critical step to addressing this is the noninvasive collection of physiological time-series data outside laboratory settings in large populations. Digital tools offer promise in this endeavor. Here, using wearable data, we first quantify the degrees of circadian disruption, both between different internal rhythms and between each internal rhythm and the sleep-wake cycle. Our analysis, based on over 50,000 days of data from over 800 first-year training physicians, reveals bidirectional links between digital markers of circadian disruption and mood both before and after they began shift work, while accounting for confounders such as demographic and geographic variables. We further validate this by finding clinically relevant changes in the 9-item Patient Health Questionnaire score. Our findings validate a scalable digital measure of circadian disruption that could serve as a marker for psychiatric intervention.

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.

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.

The neurotransmitter dopamine (DA) is known to be influenced by the circadian timekeeping system in the mammalian brain. We have previously created a single-cell differential equations model to understand the mechanisms behind circadian rhythms of extracellular DA. In this paper, we investigate the dynamics in our model and study different behaviors such as entrainment to the 24-hour light-dark cycle and robust periodicity versus decoupling, quasiperiodicity, and chaos. Imbalances in DA are often accompanied by disrupted circadian rhythms, such as in Parkinson's disease, hyperactivity, and mood disorders. Our model provides new insights into the links between the circadian clock and DA. We show that the daily rhythmicity of DA can be disrupted by decoupling between interlocked loops of the clock circuitry or by quasiperiodic clock behaviors caused by misalignment with the light-dark cycle. The model can be used to further study how the circadian clock affects the dopaminergic system, and to help develop therapeutic strategies for disrupted DA rhythms.

Many enzymes in one-carbon metabolism (OCM) are up- or down-regulated by the sex hormones which vary diurnally and throughout the menstrual cycle. During pregnancy, estradiol and progesterone levels increase tremendously to modulate physiological changes in the reproductive system. In this work, we extend and improve an existing mathematical model of hepatic OCM to understand the dynamic metabolic changes that happen during the menstrual cycle and pregnancy due to estradiol variation. In particular, we add the polyamine drain on S-adenosyl methionine and the direct effects of estradiol on the enzymes cystathionine β-synthase (CBS), thymidylate synthase (TS), and dihydrofolate reductase (DHFR). We show that the homocysteine concentration varies inversely with estradiol concentration, discuss the fluctuations in 14 other one-carbon metabolites and velocities throughout the menstrual cycle, and draw comparisons with the literature. We then use the model to study the effects of vitamin B12, vitamin B6, and folate deficiencies and explain why homocysteine is not a good biomarker for vitamin deficiencies. Additionally, we compute homocysteine throughout pregnancy, and compare the results with experimental data. Our mathematical model explains how numerous homeostatic mechanisms in OCM function and provides new insights into how homocysteine and its deleterious effects are influenced by estradiol. The mathematical model can be used by others for further in silico experiments on changes in one-carbon metabolism during the menstrual cycle and pregnancy.

BACKGROUND:The superchiasmatic nucleus (SCN) serves as the primary circadian (24hr) clock in mammals and is known to control important physiological functions such as the sleep-wake cycle, hormonal rhythms, and neurotransmitter regulation. Experimental results suggest that some of these functions reciprocally influence circadian rhythms, creating a highly complex network. Among the clock's downstream products, orphan nuclear receptors REV-ERB and ROR are particularly interesting because they coordinately modulate the core clock circuitry. Recent experimental evidence shows that REV-ERB and ROR are not only crucial for lipid metabolism but are also involved in dopamine (DA) synthesis and degradation, which could have meaningful clinical implications for conditions such as Parkinson's disease and mood disorders.METHODS:We create a mathematical model consisting of differential equations that express how the circadian variables are influenced by light, how REV-ERB and ROR feedback to the clock, and how REV-ERB, ROR, and BMAL1-CLOCK affect the dopaminergic system. The structure of the model is based on the findings of experimentalists.RESULTS:We compare our model predictions to experimental data on clock components in different light-dark conditions and in the presence of genetic perturbations. Our model results are consistent with experimental results on REV-ERB and ROR and allow us to predict the circadian variations in tyrosine hydroxylase and monoamine oxidase seen in experiments. By connecting our model to an extant model of dopamine synthesis, release, and reuptake, we are able to predict circadian oscillations in extracellular DA and homovanillic acid that correspond well with experimental observations.CONCLUSIONS:The predictions of the mathematical model are consistent with a wide variety of experimental observations. Our calculations show that the mechanisms proposed by experimentalists by which REV-ERB, ROR, and BMAL1-CLOCK influence the DA system are sufficient to explain the circadian oscillations observed in dopaminergic variables. Our mathematical model can be used for further investigations of the effects of the mammalian circadian clock on the dopaminergic system. The model can also be used to predict how perturbations in the circadian clock disrupt the dopaminergic system and could potentially be used to find drug targets that ameliorate these disruptions.

Monoclonal antibodies have shown promising results as a form of cancer immunotherapy used either alone or in combination with another treatment. We model a monoclonal antibody in combination with a dendritic cell (DC) vaccine in order to study treatment optimization. Certain proteins on tumor cells allow the tumor cells to bind to specific receptors on immune cells, rendering the immune cells ineffective. Experiments using mouse models show that a combination of antibodies to these proteins with tumor suppressing drugs improves the effectiveness of cancer vaccines. We create independent models of each of the two treatments in combination with DC therapy, fit them to experimental data, and create a final, data-informed model of the combined treatment. This new model can be used to develop novel therapies involving monoclonal antibodies.