Modulation of serotonin transporter expression by escitalopram under inflammation.

Selective serotonin reuptake inhibitors (SSRIs) are widely used for depression based on the monoamine deficiency hypothesis. However, the clinical use of these agents is controversial, in part because of their variable clinical efficacy and in part because of their delayed onset of action. Because of the complexities involved in replicating human disease and clinical dosing in animal models, the scientific community has not reached a consensus on the reasons for these phenomena. In this work, we create a theoretical hippocampal model incorporating escitalopram's pharmacokinetics, pharmacodynamics (competitive and non-competitive inhibition, and serotonin transporter (SERT) internalization), inflammation, and receptor dynamics. With this model, we simulate chronic oral escitalopram in mice showing that days to weeks are needed for serotonin levels to reach steady-state. We show escitalopram's chemical efficacy is diminished under inflammation. Our model thus offers mechanisms for how chronic escitalopram affects brain serotonin, emphasizing the importance of optimized dose and time for future antidepressant discoveries.

Morphological Murals: The Scaling and Allometry of Butterfly Wing Patterns.

The color patterns of butterflies moths are exceptionally diverse, but are very stable within a species, so that most species can be identified on the basis of their color pattern alone. The color pattern is established in the wing imaginal disc during a prolonged period of growth and differentiation, beginning during the last larval instar and ending during the first few days of the pupal stage. During this period, a variety of diffusion and reaction-diffusion signaling mechanisms determine the positions and sizes of the various elements that make up the overall color pattern. The patterning occurs while the wing is growing from a small imaginal disc to a very large pupal wing. One would therefore expect that some or all aspects of the color pattern would be sensitive to the size of the developmental field on which pattern formation takes place. To study this possibility, we analyzed the color patterns of Junonia coenia from animals whose growth patterns were altered by periodic starvation during larval growth, which produced individuals with a large range of variation in body size and wing size. Analyses of the color patterns showed that the positions and size of the pattern elements scaled perfectly isometrically with wing size. This is a puzzling finding and suggests the operation of a homeostatic or robustness mechanism that stabilizes pattern in spite of variation in the growth rate and final size of the wing.

Homeostasis despite instability.

We have shown previously that different homeostatic mechanisms in biochemistry create input-output curves with a "chair" shape. At equilibrium, for intermediate values of a parameter (often an input), a variable, Z, changes very little (the homeostatic plateau), but for low and high values of the parameter, Z changes rapidly (escape from homeostasis). In all cases previously studied, the steady state was stable for each value of the input parameter. Here we show that, for the feedback inhibition motif, stability may be lost through a Hopf bifurcation on the homeostatic plateau and then regained by another Hopf bifurcation. If the limit cycle oscillations are relatively small in the unstable interval, then the variable Z maintains homeostasis despite the instability. We show that the existence of an input interval in which there are oscillations, the length of the interval, and the size of the oscillations depend in interesting and complicated ways on the properties of the inhibition function, f, the length of the chain, and the size of a leakage parameter.

A mathematical model for histamine synthesis, release, and control in varicosities.

BACKGROUND: Histamine (HA), a small molecule that is synthesized from the amino acid histidine, plays an important role in the immune system where it is associated with allergies, inflammation, and T-cell regulation. In the brain, histamine is stored in mast cells and other non-neuronal cells and also acts as a neurotransmitter. The histamine neuron cell bodies are in the tuberomammillary (TM) nucleus of the hypothalamus and these neurons send projections throughout the central nervous system (CNS), in particular to the cerebral cortex, amygdala, basal ganglia, hippocampus, thalamus, retina, and spinal cord. HA neurons make few synapses, but release HA from the cell bodies and from varicosities when the neurons fire. Thus the HA neural system seems to modulate and control the HA concentration in projection regions. It is known that high HA levels in the extracellular space inhibit serotonin release, so HA may play a role in the etiology of depression. RESULTS: We compare model predictions to classical physiological experiments on HA half-life, the concentration of brain HA after histidine loading, and brain HA after histidine is dramatically increased or decreased in the diet. The model predictions are also consistent with in vivo experiments in which extracellular HA is measured, using Fast Scan Cyclic Voltammetry, in the premammillary nucleus (PM) after a 2 s antidromic stimulation of the TM, both without and in the presence of the H 3 autoreceptor antagonist thioperamide. We show that the model predicts well the temporal behavior of HA in the extracellular space over 30 s in both experiments. CONCLUSIONS: Our ability to measure in vivo histamine dynamics in the extracellular space after stimulation presents a real opportunity to understand brain function and control. The observed extracellular dynamics depends on synthesis, storage, neuronal firing, release, reuptake, glial cells, and control by autoreceptors, as well as the behavioral state of the animal (for example, depression) or the presence of neuroinflammation. In this complicated situation, the mathematical model will be useful for interpreting data and conducting in silico experiments to understand causal mechanisms. And, better understanding can suggest new therapeutic drug targets.

The role of skeletal muscle in liver glutathione metabolism during acetaminophen overdose.

Marked alterations in systemic glutamate-glutamine metabolism characterize the catabolic state, in which there is an increased breakdown and decreased synthesis of skeletal muscle protein. Among these alterations are a greatly increased net release of glutamine (Gln) from skeletal muscle into blood plasma and a dramatic depletion of intramuscular Gln. Understanding the catabolic state is important because a number of pathological conditions with very different etiologies are characterized by its presence; these include major surgery, sepsis, trauma, and some cancers. Acetaminophen (APAP) overdose is also accompanied by dramatic changes in systemic glutamate-glutamine metabolism including large drops in liver glutathione (for which glutamate is a precursor) and plasma Gln. We have constructed a mathematical model of glutamate and glutamine metabolism in rat which includes liver, blood plasma and skeletal muscle. We show that for the normal rat, the model solutions fit experimental data including the diurnal variation in liver glutathione (GSH). We show that for the rat chronically dosed with dexamethasone (an artificial glucocorticoid which induces a catabolic state) the model can be used to explain empirically observed facts such as the linear decline in intramuscular Gln and the drop in plasma glutamine. We show that for the Wistar rat undergoing APAP overdose the model reproduces the experimentally observed rebound of liver GSH to normal levels by the 24-h mark. We show that this rebound is achieved in part by the action of the cystine-glutamate antiporter, an amino acid transporter not normally expressed in liver but induced under conditions of oxidative stress. Finally, we explain why supplementation with Gln, a Glu precursor, assists in the preservation of liver GSH during APAP overdose despite the fact that under normal conditions only Cys is rate-limiting for GSH formation.

Bursts and the efficacy of selective serotonin reuptake inhibitors.

We present a new hypothesis for the efficacy of selective serotonin reuptake inhibitors (SSRIs). We propose that SSRIs bring the response to the phasic firing of raphe nucleus cells back to normal, even though the average extracellular 5HT concentration remains low. We discuss burst firing in the raphe nuclei and use mathematical models to argue that tonic firing and phasic firing may be decoupled and may come from different mechanisms. We use a mathematical model for serotonin synthesis, release, and reuptake in terminals to illustrate the responses in terminal regions to bursts in a normal individual and in an individual with low vesicular serotonin. We then show that acute doses of SSRIs do not bring the response to bursts back to normal, but that chronic doses do return the response to normal. These model results need to be confirmed by new electrophysiological and pharmacological experiments.

Models of dopaminergic and serotonergic signaling.

Mathematical models of dopaminergic and serotonergic synapses have enabled the authors to study quantitative aspects of the synthesis, release and reuptake of dopamine and serotonin, to investigate the effects of autoreceptors, and to explore the influence of the neurochemistry on the firing patterns of cells known to be involved in the behavioral responses to dopaminergic and serotonergic signaling. The models consist of coupled ordinary differential equations. Parameters are determined from biochemical and physiological measurements. Three results from recent IN SILICO experiments with the dopaminergic and serotonergic synapse models are described: (1) influence of substrate inhibition on the stability of dopamine and serotonin synthesis; (2) a predicted connection between serotonin reuptake transporter (SERT) density on terminals and tonic firing rates; (3) an explanation of data from autoreceptor knock-out experiments. Mathematical models are useful for studying the biology of dopaminergic and serotonergic signaling because these systems are complex and involve interactions between neurochemistry and neurobiology.

Mathematical models of folate-mediated one-carbon metabolism.

Folate-mediated one-carbon metabolism is an unusually complex metabolic network, consisting of several interlocking cycles, and compartmentation between cytosol and mitochondria. The cycles have diverse functions, the primary being thymidylate synthesis (the rate limiting step in DNA synthesis), the initial steps in purine synthesis, glutathione synthesis, and a host of methyl transfer reactions that include DNA and histone methylation. Regulation within the network is accomplished by numerous allosteric interactions in which metabolites in one part of the network affect the activity of enzymes elsewhere in the network. Although a large body of experimental work has elucidated the details of the mechanisms in every part of the network, the multitude of complex and non-linear interactions within the network makes it difficult to deduce how the network as a whole operates. Understanding the operation of this network is further complicated by the fact that human populations maintain functional polymorphisms for several enzymes in the network, and that the network is subject to continual short and long-term fluctuations in its inputs as well as in demands on its various outputs. Understanding how such a complex system operates is possible only by means of mathematical models that take account of all the reactions and interactions. Simulations with such models can be used as an adjunct to laboratory experimentation to test ideas and alternative hypotheses and interpretations quickly and inexpensively. A number of mathematical models have been developed over the years, largely motivated by the need to understand the complex mechanisms by which anticancer drugs like methotrexate inhibit nucleotide synthesis and thus limit the ability of cells to divide. More recently, mathematical models have been used to investigate the regulatory and homeostatic mechanisms that allow the system to accommodate large fluctuations in one part of the network without affecting critical functions elsewhere in the network.

Genetic basis of adaptive evolution of a polyphenism by genetic accommodation.

Polyphenisms are evolved adaptations in which a genome produces discrete alternative phenotypes in different environments. In this study, the genetic basis of the evolution of a polyphenism by genetic accommodation was investigated. A polyphenic strain and a monophenic strain of Manduca sexta (L.) were crossed and the F(1) offspring and backcross progeny were analysed. The larval colour polyphenism was found to be regulated by one sex-linked gene of major effect and many smaller effect modifier genes. The finding shows that the mechanism of genetic accommodation relies on genetic changes that are consistent with the current view of the genetic basis of adaptive evolution.

A quantitative analysis of the mechanism that controls body size in Manduca sexta.

BACKGROUND: Body size is controlled by mechanisms that terminate growth when the individual reaches a species-specific size. In insects, it is a pulse of ecdysone at the end of larval life that causes the larva to stop feeding and growing and initiate metamorphosis. Body size is a quantitative trait, so it is important that the problem of control of body size be analyzed quantitatively. The processes that control the timing of ecdysone secretion in larvae of the moth Manduca sexta are sufficiently well understood that they can be described in a rigorous manner. RESULTS: We develop a quantitative description of the empirical data on body size determination that accurately predicts body size for diverse genetic strains. We show that body size is fully determined by three fundamental parameters: the growth rate, the critical weight (which signals the initiation of juvenile hormone breakdown), and the interval between the critical weight and the secretion of ecdysone. All three parameters are easily measured and differ between genetic strains and environmental conditions. The mathematical description we develop can be used to explain how variables such as growth rate, nutrition, and temperature affect body size. CONCLUSION: Our analysis shows that there is no single locus of control of body size, but that body size is a system property that depends on interactions among the underlying determinants of the three fundamental parameters. A deeper mechanistic understanding of body size will be obtained by research aimed at uncovering the molecular mechanisms that give these three parameters their particular quantitative values.

A perspective for understanding the modes of juvenile hormone action as a lipid signaling system.

The juvenile hormones of insects regulate an unusually large diversity of processes during postembryonic development and adult reproduction. It is a long-standing puzzle in insect developmental biology and physiology how one hormone can have such diverse effects. The search for molecular mechanisms of juvenile hormone action has been guided by classical models for hormone-receptor interaction. Yet, despite substantial effort, the search for a juvenile hormone receptor has been frustrating and has yielded limited results. We note here that a number of lipid-soluble signaling molecules in vertebrates, invertebrates and plants show curious similarities to the properties of juvenile hormones of insects. Until now, these signaling molecules have been thought of as uniquely evolved mechanisms that perform specialized regulatory functions in the taxon where they were discovered. We show that this array of lipid signaling molecules share interesting properties and suggest that they constitute a large set of signal control and transduction mechanisms that include, but range far beyond, the classical steroid hormone signaling mechanism. Juvenile hormone is the insect representative of this widespread and diverse system of lipid signaling molecules that regulate protein activity in a variety of ways. We propose a synthetic perspective for understanding juvenile hormone action in light of other lipid signaling systems and suggest that lipid activation of proteins has evolved to modulate existing signal activation and transduction mechanisms in animals and plants. Since small lipids can be inserted into many different pathways, lipid-activated proteins have evolved to play a great diversity of roles in physiology and development.

The control of body size in insects.

Control mechanisms that regulate body size and tissue size have been sought at both the cellular and organismal level. Cell-level studies have revealed much about the control of cell growth and cell division, and how these processes are regulated by nutrition. Insulin signaling is the key mediator between nutrition and the growth of internal organs, such as imaginal disks, and is required for the normal proportional growth of the body and its various parts. The insulin-related peptides of insects do not appear to control growth by themselves, but act in conjunction with other hormones and signaling molecules, such as ecdysone and IDGFs. Size regulation cannot be understood solely on the basis of the mechanisms that control cell size and cell number. Size regulation requires mechanisms that gather information on a scale appropriate to the tissue or organ being regulated. A new model mechanism, using autocrine signaling, is outlined by which tissue and organ size regulation can be achieved. Body size regulation likewise requires a mechanism that integrates information at an appropriate scale. In insects, this mechanism operates by controlling the secretion of ecdysone, which is the signal that terminates the growth phase of development. The mechanisms for size assessment and the pathways by which they trigger ecdysone secretion are diverse and can be complex. The ways in which these higher-level regulatory mechanisms interact with cell- and molecular- level mechanisms are beginning to be elucidated.

A mechanistic study of evolvability using the mitogen-activated protein kinase cascade.

Evolvability is a function of the way genetic variation interacts with the mechanisms that produce the phenotype. We explore an explicitly mechanistic way of studying the evolvability of phenotypes that are produced by a relatively simple genetic mechanism, the mitogen-activated protein kinase (MAPK) cascade. We developed a quantitative model of MAPK activation that can be used to study the effects of genetic variation on the various components of this signaling cascade. We show how some standard tools of applied mathematics, such as steady-state formulations and nondimensionalization, can be used to elucidate the relative importance of variation in each gene of this mechanism. We also give insights into non-intuitive patterns of dependence and trade-off among the genes. The mechanism produces several different phenotypes (ultrasensitivity to stimulation, switch-like behavior, amount of MAPK-PP delivered, persistence of MAPK-PP activity), each of which is sensitive to different (but partially overlapping) combinations of genes. We show that the mechanism imposes clear limitations on the evolvability of each of the different phenotypes of the pathway, even in the presence of genetic variation in the components of the mechanism. This approach to the study of evolvability is generally applicable and complements the traditional approach through statistical genetics by providing a mechanistic understanding of the genetic interactions that produce the phenotype.

The nature of robustness in development.

A trait is robust to a genetic or environmental variable if its variation is weakly correlated with variation in that variable. The source of robustness lies in the fact that the developmental processes that give rise to complex traits are nonlinear. A consequence of this nonlinearity is that not all genes are equally correlated with the trait whose ontogeny they control. Here we explore how developmental mechanisms determine and alter the correlation structure between genes and the traits that they control. A formula is developed by which the correlation of a gene or environmental variable with a trait can be calculated if the mechanism that gives rise to the trait is known. The nature of robustness and the ways in which robustness can evolve are discussed in the context of the problems that arise in the analysis of inherently nonlinear systems.

Elements of butterfly wing patterns.

The color patterns on the wings of butterflies are unique among animal color patterns in that the elements that make up the overall pattern are individuated. Unlike the spots and stripes of vertebrate color patterns, the elements of butterfly wing patterns have identities that can be traced from species to species, and typically across genera and families. Because of this identity it is possible to recognize homologies among pattern elements and to study their evolution and diversification. Individuated pattern elements evolved from non-individuated precursors by compartmentalization of the wing into areas that became developmentally autonomous with respect to color pattern formation. Developmental compartmentalization led to the evolution of serially repeated elements and the emergence of serial homology. In these compartments, serial homologues were able to acquire site-specific developmental regulation and this, in turn, allowed them to diverge morphologically. Compartmentalization of the wing also reduced the developmental correlation among pattern elements. The release from this developmental constraint, we believe, enabled the great evolutionary radiation of butterfly wing patterns. During pattern evolution, the same set of individual pattern elements is arranged in novel ways to produce species-specific patterns, including such adaptations as mimicry and camouflage.

Nonlinear developmental processes as sources of dominance.

Phenotypes are the products of developmental processes whose dynamics are controlled by genes. In many developmental processes there is a nonlinear relationship between genetic variation and phenotypic variation. These nonlinear relationships can result in the emergence of dominance among alleles that control the developmental process. We explore the properties of dominance relationships in a simple developmental system consisting of a diffusion-gradient-threshold mechanism commonly deployed in pattern formation. We show that a single nonlinear process (diffusion) within this integrated mechanism leads to the emergence of dominance in all components of the mechanism. Unlike the situation in metabolic pathways, where new mutations are most likely to be recessive, the structure of the nonlinearities in this developmental mechanism is such that in certain circumstances new mutations are equally likely to be dominant or recessive. Although the dominance we observe in this system is the result of a physiological process, we also find that dominance can evolve by microevolutionary mechanisms and thus are able to reconcile the opposing views of Fisher and Wright on dominance.

The developmental and physiological basis of body size evolution in an insect.

The evolution of body size is a dominant feature of animal evolution. However, little is known about how the underlying developmental mechanisms that determine size change as body size evolves. Here we report on a case of body size evolution in the tobacco hornworm Manduca sexta that occurred over a period of nearly 30 years. We take advantage of an extensive series of physiological studies performed in the early 1970s that established the parameters that regulate body size in this species and compare their values with those of modern individuals that are descendants of the same colony. We show that three of the five processes that determine adult body size changed during this period, while two remained constant. Changes in these three developmental processes completely account for the observed evolutionary change in body size.

Hormonal control of male horn length dimorphism in Onthophagus taurus (Coleoptera: Scarabaeidae): a second critical period of sensitivity to juvenile hormone.

Male dung beetles (Onthophagus taurus) facultatively produce a pair of horns that extend from the base of the head: males larger than a threshold body size develop long horns, whereas males that do not achieve this size develop only rudimentary horns or no horns at all. Using topical applications of methoprene, we identified a sensitive period during the feeding stage of third (final) instar larvae when application of methoprene shifted the threshold body size for horn expression. Male larvae that received methoprene at this time delayed horn production until they attained a larger threshold body size than acetone-treated control larvae. This new sensitive period occurs earlier than a sensitive period previously reported for male horn regulation, and it coincides with a morph-specific pulse of ecdysteroid secretion described for this species. It appears that male horn expression is influenced by endocrine events at two different periods of larval development. We incorporate these results into an expanded model for the endocrine regulation of male horn expression.

The role of low levels of juvenile hormone esterase in the metamorphosis of Manduca sexta.

The activity of juvenile hormone esterase (JHE) in feeding fifth instar larvae of Manduca sexta increases gradually with larval weight and rises to a peak after larvae pass the critical weight when juvenile hormone secretion ceases. Starvation of larvae of Manduca sexta (L.) that had exceeded the critical weight inhibited peak levels of JHE, but did not delay entry into the wandering stage when larvae leave the plant in search of a pupation site. This suggests that peak levels of JHE may not be essential for the normal timing of metamorphosis. Starved larvae pupated normally, indicating the peak of JHE was not necessary for a morphologically normal pupation. Treatments of larvae with the selective JHE inhibitor O-ethyl-S-phenyl phosphoramidothiolate (EPPAT) that began immediately after larvae achieved the critical weight (6.0 to 6.5 grams for our strain of Manduca) delayed entry into the wandering stage. By contrast, EPPAT treatment of larvae at weights above 8.0 g had no effect on the subsequent timing of the onset of wandering. Therefore, although the normal timing of the onset of wandering does not require peak levels of JHE, it requires low to moderate levels of JHE to be present until larvae reach a weight of about 8.0 g.