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.

Dynamical questions in volume transmission.

In volume transmission (or neuromodulation) neurons do not make one-to-one connections to other neurons, but instead simply release neurotransmitter into the extracellular space from numerous varicosities. Many well-known neurotransmitters including serotonin (5HT), dopamine (DA), histamine (HA), Gamma-Aminobutyric Acid (GABA) and acetylcholine (ACh) participate in volume transmission. Typically, the cell bodies are in one volume and the axons project to a distant volume in the brain releasing the neurotransmitter there. We introduce volume transmission and describe mathematically two natural homeostatic mechanisms. In some brain regions several neurotransmitters in the extracellular space affect each other's release. We investigate the dynamics created by this comodulation in two different cases: serotonin and histamine; and the comodulation of 4 neurotransmitters in the striatum and we compare to experimental data. This kind of comodulation poses new dynamical questions as well as the question of how these biochemical networks influence the electrophysiological networks in the brain.

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.

An In Vivo Definition of Brain Histamine Dynamics Reveals Critical Neuromodulatory Roles for This Elusive Messenger.

Histamine is well known for mediating peripheral inflammation; however, this amine is also found in high concentrations in the brain where its roles are much less known. In vivo chemical dynamics are difficult to measure, thus fundamental aspects of histamine's neurochemistry remain undefined. In this work, we undertake the first in-depth characterization of real time in vivo histamine dynamics using fast electrochemical tools. We find that histamine release is sensitive to pharmacological manipulation at the level of synthesis, packaging, autoreceptors and metabolism. We find two breakthrough aspects of histamine modulation. First, differences in H3 receptor regulation between sexes show that histamine release in female mice is much more tightly regulated than in male mice under H3 or inflammatory drug challenge. We hypothesize that this finding may contribute to hormone-mediated neuroprotection mechanisms in female mice. Second, a high dose of a commonly available antihistamine, the H1 receptor inverse agonist diphenhydramine, rapidly decreases serotonin levels. This finding highlights the sheer significance of pharmaceuticals on neuromodulation. Our study opens the path to better understanding and treating histamine related disorders of the brain (such as neuroinflammation), emphasizing that sex and modulation (of serotonin) are critical factors to consider when studying/designing new histamine targeting therapeutics.

Voltammetric Approach for Characterizing the Biophysical and Chemical Functionality of Human Induced Pluripotent Stem Cell-Derived Serotonin Neurons.

Depression is quickly becoming one of the world's most pressing public health crises, and there is an urgent need for better diagnostics and therapeutics. Behavioral models in animals and humans have not adequately addressed the diagnosis and treatment of depression, and biomarkers of mental illnesses remain ill-defined. It has been very difficult to identify biomarkers of depression because of in vivo measurement challenges. While our group has made important strides in developing in vivo tools to measure such biomarkers (e.g., serotonin) in mice using voltammetry, these tools cannot be easily applied for depression diagnosis and drug screening in humans due to the inaccessibility of the human brain. In this work, we take a chemical approach, ex vivo, to introduce a human-derived system to investigate brain serotonin. We utilize human induced pluripotent stem cells differentiated into serotonin neurons and establish a new ex vivo model of real-time serotonin neurotransmission measurements. We show that evoked serotonin release responds to stimulation intensity and tryptophan preloading, and that serotonin release and reuptake kinetics resemble those found in vivo in rodents. Finally, after selective serotonin reuptake inhibitor (SSRI) exposure, we find dose-dependent internalization of the serotonin reuptake transporters (a signature of the in vivo response to SSRI). Our new human-derived chemical model has great potential to provide an ex vivo chemical platform as a translational tool for in vivo neuropsychopharmacology.

The roles of growth regulation and appendage patterning genes in the morphogenesis of treehopper pronota.

Treehoppers of the insect family Membracidae have evolved enlarged and elaborate pronotal structures, which is hypothesized to involve co-opted expression of genes that are shared with the wings. Here, we investigate the similarity between the pronotum and wings in relation to growth. Our study reveals that the ontogenetic allometry of the pronotum is similar to that of wings in Membracidae, but not the outgroup. Using transcriptomics, we identify genes related to translation and protein synthesis, which are mutually upregulated. These genes are implicated in the eIF2, eIF4/p70S6K and mTOR pathways, and have known roles in regulating cell growth and proliferation. We find that species-specific differential growth patterning of the pronotum begins as early as the third instar, which suggests that expression of appendage patterning genes occurs long before the metamorphic molt. We propose that a network related to growth and size determination is the more likely mechanism shared with wings. However, regulators upstream of the shared genes in pronotum and wings need to be elucidated to substantiate whether co-option has occurred. Finally, we believe it will be helpful to distinguish the mechanisms leading to pronotal size from those regulating pronotal shape as we make sense of this spectacular evolutionary innovation.

Spiracular fluttering decouples oxygen uptake and water loss: a stochastic PDE model of respiratory water loss in insects.

In insect respiration, oxygen from the air diffuses through a branching system of air-filled tubes to the cells of the body and carbon dioxide produced in cellular respiration diffuses out. The tracheal system has a very large surface area, so water loss is a potential threat and the question of how insects regulate oxygen uptake and water loss has been an important issue in insect physiology for the past century. The tracheal system starts at spiracles on the surface of the body that insects can open and close, and three phases are observed experimentally, open or closed for relatively long periods of time and opening and closing rapidly, which is called fluttering. In previous work we have shown that during this flutter phase, no matter how small the percentage of time that the spiracles are open, the insect can absorb almost as much oxygen as if the spiracle were always open, if the insect flutters fast enough. This left open the question of water loss during the flutter phase, which is the question addressed in this paper. We formulate a stochastic diffusion-convection model for the concentration of water vapor in the tracheae. Mathematical analysis of the model yields an explicit formula for water loss as a function of six non-dimensional parameters and we use experimental data from various insects to show that, for parameters in the physiological ranges, water loss during the flutter phase is approximately proportional to the percentage of time open. This means that the insect can solve the oxygen uptake versus water loss problem by choosing to have their spiracles open a small percentage of time during the flutter phase and fluttering rapidly.

The genetic control paradigm in biology: What we say, and what we are entitled to mean.

We comment on the article by Keith Baverstock (2021) and provide critiques of the concepts of genetic control, genetic blueprint and genetic program.

The development of shape. Modular control of growth in the lepidopteran forewing.

The mechanisms by which tissues and organs achieve their final size and shape during development are largely unknown. Although we have learned much about the mechanisms that control growth, little is known about how those play out to achieve a structure's specific final size and shape. The wings of insects are attractive systems for the study of the control of morphogenesis, because they are perfectly flat and two-dimensional, composed of two closely appressed cellular monolayers in which morphogenetic processes can be easily visualized. The wings of Lepidoptera arise from imaginal disks whose structure is always perfectly congruent with that of the adult wing, so that it is possible to fate-map corresponding positions on the larval disk to those of the adult wing. Here we show that the forewing imaginal disks of Junonia coenia are subdivided into four domains, with characteristic patterns of expression of known patterning genes Spalt (Sal), Engrailed (En), and Cubitus interruptus (Ci). We show that DNA and protein synthesis, as well as mitoses, are spatially patterned in a domain-specific way. Knockdown of Sal and En using produced domain-specific reductions in the shape of the forewing. Knockdown of signaling pathways involved in the regulation of growth likewise altered the shape of the forewing in a domain-specific way. Our results reveal a multi-level regulation of forewing shape involving hormones and growth-regulating genes.

One-carbon metabolism during the menstrual cycle and pregnancy.

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 ß-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.

Inflammation-Induced Histamine Impairs the Capacity of Escitalopram to Increase Hippocampal Extracellular Serotonin.

Commonly prescribed selective serotonin reuptake inhibitors (SSRIs) inhibit the serotonin transporter to correct a presumed deficit in extracellular serotonin signaling during depression. These agents bring clinical relief to many who take them; however, a significant and growing number of individuals are resistant to SSRIs. There is emerging evidence that inflammation plays a significant role in the clinical variability of SSRIs, though how SSRIs and inflammation intersect with synaptic serotonin modulation remains unknown. In this work, we use fast in vivo serotonin measurement tools to investigate the nexus between serotonin, inflammation, and SSRIs. Upon acute systemic lipopolysaccharide (LPS) administration in male and female mice, we find robust decreases in extracellular serotonin in the mouse hippocampus. We show that these decreased serotonin levels are supported by increased histamine activity (because of inflammation), acting on inhibitory histamine H3 heteroreceptors on serotonin terminals. Importantly, under LPS-induced histamine increase, the ability of escitalopram to augment extracellular serotonin is impaired because of an off-target action of escitalopram to inhibit histamine reuptake. Finally, we show that a functional decrease in histamine synthesis boosts the ability of escitalopram to increase extracellular serotonin levels following LPS. This work reveals a profound effect of inflammation on brain chemistry, specifically the rapidity of inflammation-induced decreased extracellular serotonin, and points the spotlight at a potentially critical player in the pathology of depression, histamine. The serotonin/histamine homeostasis thus, may be a crucial new avenue in improving serotonin-based treatments for depression.SIGNIFICANCE STATEMENT Acute LPS-induced inflammation (1) increases CNS histamine, (2) decreases CNS serotonin (via inhibitory histamine receptors), and (3) prevents a selective serotonin reuptake inhibitor (SSRI) from effectively increasing extracellular serotonin. A targeted depletion of histamine recovers SSRI-induced increases in extracellular hippocampal serotonin.

Genetic assimilation and accommodation: Models and mechanisms.

Genetic assimilation and genetic accommodation are mechanisms by which novel phenotypes are produced and become established in a population. Novel characters may be fixed and canalized so they are insensitive to environmental variation, or can be plastic and adaptively responsive to environmental variation. In this review we explore the various theories that have been proposed to explain the developmental origin and evolution of novel phenotypes and the mechanisms by which canalization and phenotypic plasticity evolve. These theories and models range from conceptual to mathematical and have taken different views of how genes and environment contribute to the development and evolution of the properties of phenotypes. We will argue that a deeper and more nuanced understanding of genetic accommodation requires a recognition that phenotypes are not static entities but are dynamic system properties with no fixed deterministic relationship between genotype and phenotype. We suggest a mechanistic systems-view of development that allows one to incorporate both genes and environment in a common model, and that enables both quantitative analysis and visualization of the evolution of canalization and phenotypic plasticity.

Autoreceptor control of serotonin dynamics.

BACKGROUND: Serotonin is a neurotransmitter that has been linked to a wide variety of behaviors including feeding and body-weight regulation, social hierarchies, aggression and suicidality, obsessive compulsive disorder, alcoholism, anxiety, and affective disorders. Full understanding involves genomics, neurochemistry, electrophysiology, and behavior. The scientific issues are daunting but important for human health because of the use of selective serotonin reuptake inhibitors and other pharmacological agents to treat disorders. This paper presents a new deterministic model of serotonin metabolism and a new systems population model that takes into account the large variation in enzyme and transporter expression levels, tryptophan input, and autoreceptor function. RESULTS: We discuss the steady state of the model and the steady state distribution of extracellular serotonin under different hypotheses on the autoreceptors and we show the effect of tryptophan input on the steady state and the effect of meals. We use the deterministic model to interpret experimental data on the responses in the hippocampus of male and female mice, and to illustrate the short-time dynamics of the autoreceptors. We show there are likely two reuptake mechanisms for serotonin and that the autoreceptors have long-lasting influence and compare our results to measurements of serotonin dynamics in the substantia nigra pars reticulata. We also show how histamine affects serotonin dynamics. We examine experimental data that show very variable response curves in populations of mice and ask how much variation in parameters in the model is necessary to produce the observed variation in the data. Finally, we show how the systems population model can potentially be used to investigate specific biological and clinical questions. CONCLUSIONS: We have shown that our new models can be used to investigate the effects of tryptophan input and meals and the behavior of experimental response curves in different brain nuclei. The systems population model incorporates individual variation and can be used to investigate clinical questions and the variation in drug efficacy. The codes for both the deterministic model and the systems population model are available from the authors and can be used by other researchers to investigate the serotonergic system.

Mechanism of threshold size assessment: Metamorphosis is triggered by the TGF-beta/Activin ligand Myoglianin.

Although the mechanisms that control growth are now well understood, the mechanism by which animals assess their body size remains one of the great puzzles in biology. The final larval instar of holometabolous insects, after which growth stops and metamorphosis begins, is specified by a threshold size. We investigated the mechanism of threshold size assessment in the tobacco hornworm, Manduca sexta. The threshold size was found to change depending on the amount of exposure to poor nutrient conditions whereas hypoxia treatment consistently led to a lower threshold size. Under these various conditions, the mass of the muscles plus integuments was correlated with the threshold size. Furthermore, the expression of myoglianin (myo) increased at the threshold size in both M. sexta and Tribolium castaneum. Knockdown of myo in T. castaneum led to larvae that underwent supernumerary larval molts and stayed in the larval stage permanently even after passing the threshold size. We propose that increasing levels of Myo produced by the growing tissues allow larvae to assess their body size and trigger metamorphosis at the threshold size.

Spiracular fluttering increases oxygen uptake.

Many insects show discontinuous respiration with three phases, open, closed, and fluttering, in which the spiracles open and close rapidly. The relative durations of the three phases and the rate of fluttering during the flutter phase vary for individual insects depending on developmental stage and activity, vary between insects of the same species, and vary even more between different species. We studied how the rate of oxygen uptake during the flutter phase depends on the rate of fluttering. Using a mathematical model of oxygen diffusion in the insect tracheal system, we derive a formula for oxygen uptake during the flutter phase and how it depends on the length of the tracheal system, percentage of time open during the flutter phase, and the flutter rate. Surprisingly, our results show that an insect can have its spiracles closed a high percentage of time during the flutter phase and yet receive almost as much oxygen as if the spiracles were always open, provided the spiracles open and close rapidly. We investigate the respiratory gain due to fluttering for four specific insects. Our formula shows that respiratory gain increases with body size and with increased rate of fluttering. Therefore, insects can regulate their rate of oxygen uptake by varying the rate of fluttering while keeping the spiracles closed during a large fraction of the time during the flutter phase. We also use a mathematical model to show that water loss is approximately proportional to the percentage of time the spiracles are open. Thus, insects can achieve both high oxygen intake and low water loss by keeping the spiracles closed most of the time and fluttering while open, thereby decoupling the challenge of preventing water loss from the challenge of obtaining adequate oxygen uptake.

Diverse nanostructures underlie thin ultra-black scales in butterflies.

Recently, it has been shown that animals such as jumping spiders, birds, and butterflies have evolved ultra-black coloration comparable to the blackest synthetic materials. Of these, certain papilionid butterflies have reflectances approaching 0.2%, resulting from a polydisperse honeycomb structure. It is unknown if other ultra-black butterflies use this mechanism. Here, we examine a phylogenetically diverse set of butterflies and demonstrate that other butterflies employ simpler nanostructures that achieve ultra-black coloration in scales thinner than synthetic alternatives. Using scanning electron microscopy, we find considerable interspecific variation in the geometry of the holes in the structures, and verify with finite-difference time-domain modeling that expanded trabeculae and ridges, found across ultra-black butterflies, reduce reflectance up to 16-fold. Our results demonstrate that butterflies produce ultra-black by creating a sparse material with high surface area to increase absorption and minimize surface reflection. We hypothesize that butterflies use ultra-black to increase the contrast of color signals.

Origin of the mechanism of phenotypic plasticity in satyrid butterfly eyespots.

Plasticity is often regarded as a derived adaptation to help organisms survive in variable but predictable environments, however, we currently lack a rigorous, mechanistic examination of how plasticity evolves in a large comparative framework. Here, we show that phenotypic plasticity in eyespot size in response to environmental temperature observed in Bicyclus anynana satyrid butterflies is a complex derived adaptation of this lineage. By reconstructing the evolution of known physiological and molecular components of eyespot size plasticity in a comparative framework, we showed that 20E titer plasticity in response to temperature is a pre-adaptation shared by all butterfly species examined, whereas expression of EcR in eyespot centers, and eyespot sensitivity to 20E, are both derived traits found only in a subset of species with eyespots.

A well-known family of butterflies have circular patterns on their wings that look like eyes. These eye-like markings help deflect predators away from the butterfly's body so they attack the outer edges of their wings. However, in certain seasons, such as the dry season in Africa, the best way for this family to survive is by not drawing any attention to their bodies. Thus, butterflies born during this season shrink the size of their eyespots so they can hide among the dry leaves. How this family of butterflies are able to change the size of these eye-like spots has only been studied in the species Bicyclus anynana. During development low temperatures, which signify the beginning of the dry season, reduce the amount of a hormone called 20E circulating in the blood of this species. This changes the behavior of hormone-sensitive cells in the eyespots making them smaller in size. But it remains unclear how B. anynana evolved this remarkable tactic and whether its relatives have similar abilities. Now, Bhardwaj et al. show that B. anynana is the only one of its relatives that can amend the size of its eyespots in response to temperature changes. In the experiments, 13 different species of butterflies, mostly from the family that has eyespots, were developed under two different temperatures. Low temperatures caused 20E hormone levels to decrease in all 13 species. However, most of these species did not develop smaller eyespots in response to this temperature change. This includes species that are known to have larger and smaller eyespots depending on the season. Like B. anynana, four of the species studied have receptors for the 20E hormone at the center of their eyespots. However, changing 20E hormone levels in these species did not reduce eyespot size. These results show that although temperature changes alter hormone levels in a number of species, only B. anynana have taken advantage of this mechanism to regulate eyespot size. In addition, Bhardwaj et al. found that this unique mechanism evolved from several genetic changes over millions of years. Other species likely use other environmental cues to trigger seasonal changes in the size of their eyespots.

Fast serotonin voltammetry as a versatile tool for mapping dynamic tissue architecture: I. Responses at carbon fibers describe local tissue physiology.

It is important to monitor serotonin neurochemistry in the context of brain disorders. Specifically, a better understanding of biophysical alterations and associated biochemical functionality within subregions of the brain will enable better of understanding of diseases such as depression. Fast voltammetric tools at carbon fiber microelectrodes provide an opportunity to make direct evoked and ambient serotonin measurements in vivo in mice. In this study, we characterize novel stimulation and measurement circuitries for serotonin analyses in brain regions relevant to psychiatric disease. Evoked and ambient serotonin in these brain areas, the CA2 region of the hippocampus and the medial prefrontal cortex, are compared to ambient and evoked serotonin in the substantia nigra pars reticulata, an area well established previously for serotonin measurements with fast voltammetry. Stimulation of a common axonal location evoked serotonin in all three brain regions. Differences are observed in the serotonin release and reuptake profiles between these three brain areas which we hypothesize to arise from tissue physiology heterogeneity around the carbon fiber microelectrodes. We validate this hypothesis mathematically and via confocal imaging. We thereby show that fast voltammetric methods can provide accurate information about local physiology and highlight implications for chemical mapping. Cover Image for this issue: doi: 10.1111/jnc.14739.

Allometry, Scaling, and Ontogeny of Form-An Introduction to the Symposium.

Until recently, the study of allometry has been mostly descriptive, and consisted of a diversity of methods for fitting regressions to bivariate or multivariate morphometric data. During the past decade, researchers have been developing methods to extract biological information from allometric data that could be used to deduce the underlying mechanisms that gave rise to the allometry. In addition, an increasing effort has gone into understanding the kinetics of growth and the regulatory mechanisms that control growth of the body and its component parts. The study of allometry and scaling has now become an exceptionally diverse field, with different investigators applying state of the art methods and concepts in evolution, developmental biology, cell biology, and genetics. Diversity has caused divergence, and we felt that although there is general agreement about the new goals for the study of allometry (understanding underlying mechanisms and how those evolve to produce different morphologies), progress is hindered by lack of coordination among the different approaches. We felt the time was right to bring these diverse practitioners together in a symposium to discuss their most recent work in the hope of forging new functional, conceptual, and collaborative connections among established and novice practitioners.