A mathematical model of the folate cycle: new insights into folate homeostasis

A mathematical model is developed for the folate cycle based on standard biochemical kinetics. We use the model to provide new insights into several different mechanisms of folate homeostasis. The model reproduces the known pool sizes of folate substrates and the fluxes through each of the loops of the folate cycle and has the qualitative behavior observed in a variety of experimental studies. Vitamin B(12) deficiency, modeled as a reduction in the V(max) of the methionine synthase reaction, results in a secondary folate deficiency via the accumulation of folate as 5-methyltetrahydrofolate (the "methyl trap"). One form of homeostasis is revealed by the fact that a 100-fold up-regulation of thymidylate synthase and dihydrofolate reductase (known to occur at the G(1)/S transition) dramatically increases pyrimidine production without affecting the other reactions of the folate cycle. The model also predicts that an almost total inhibition of dihydrofolate reductase is required to significantly inhibit the thymidylate synthase reaction, consistent with experimental and clinical studies on the effects of methotrexate. Sensitivity to variation in enzymatic parameters tends to be local in the cycle and inversely proportional to the number of reactions that interconvert two folate substrates. Another form of homeostasis is a consequence of the nonenzymatic binding of folate substrates to folate enzymes. Without folate binding, the velocities of the reactions decrease approximately linearly as total folate is decreased. In the presence of folate binding and allosteric inhibition, the velocities show a remarkable constancy as total folate is decreased.     

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.     

A Quantitative Analysis of Growth and Size Regulation in Manduca sexta: The Physiological Basis of Variation in Size and Age at Metamorphosis

Body size and development time are important life history traits because they are often highly correlated with fitness. Although the developmental mechanisms that control growth have been well studied, the mechanisms that control how a species-characteristic body size is achieved remain poorly understood. In insects adult body size is determined by the number of larval molts, the size increment at each molt, and the mechanism that determines during which instar larval growth will stop. Adult insects do not grow, so the size at which a larva stops growing determines adult body size. Here we develop a quantitative understanding of the kinetics of growth throughout larval life of Manduca sexta, under different conditions of nutrition and temperature, and for genetic strains with different adult body sizes. We show that the generally accepted view that the size increment at each molt is constant (Dyar’s Rule) is systematically violated: there is actually a progressive increase in the size increment from instar to instar that is independent of temperature. In addition, the mass-specific growth rate declines throughout the growth phase in a temperature-dependent manner. We show that growth within an instar follows a truncated Gompertz trajectory. The critical weight, which determines when in an instar a molt will occur, and the threshold size, which determines which instar is the last, are different in genetic strains with different adult body sizes. Under nutrient and temperature stress Manduca has a variable number of larval instars and we show that this is due to the fact that more molts at smaller increments are taken before threshold size is reached. We test whether the new insight into the kinetics of growth and size determination are sufficient to explain body size and development time through a mathematical model that incorporates our quantitative findings.     

Body size determination in insects: a review and synthesis of size‐ and brain‐dependent and independent mechanisms

Body size determination requires a mechanism for sensing size and a mechanism for linking size information to the termination of growth. Although the hormonal mechanisms that terminate growth are well elucidated, the mechanisms by which a body senses its own size are only partially understood; most of this understanding has come from the study of the mechanisms that control insect moulting and metamorphosis. We first review and discuss advances in our understanding of the physiological mechanisms by which insect larvae sense their size. Second, we present new findings on how larvae in which the size‐sensing mechanism has been disrupted eventually terminate growth (in a size‐independent manner). We synthesize recent insights into the genetic and molecular mechanisms of ecdysteroid regulation in Drosophila melanogaster with developmental physiology findings in Manduca sexta, paving the way for an integrated understanding of the mechanisms of body size regulation.     

The role of developmental plasticity in evolutionary innovation

Explaining the origins of novel traits is central to evolutionary biology. Longstanding theory suggests that developmental plasticity, the ability of an individual to modify its development in response to environmental conditions, might facilitate the evolution of novel traits. Yet whether and how such developmental flexibility promotes innovations that persist over evolutionary time remains unclear. Here, we examine three distinct ways by which developmental plasticity can promote evolutionary innovation. First, we show how the process of genetic accommodation provides a feasible and possibly common avenue by which environmentally induced phenotypes can become subject to heritable modification. Second, we posit that the developmental underpinnings of plasticity increase the degrees of freedom by which environmental and genetic factors influence ontogeny, thereby diversifying targets for evolutionary processes to act on and increasing opportunities for the construction of novel, functional and potentially adaptive phenotypes. Finally, we examine the developmental genetic architectures of environment-dependent trait expression, and highlight their specific implications for the evolutionary origin of novel traits. We critically review the empirical evidence supporting each of these processes, and propose future experiments and tests that would further illuminate the interplay between environmental factors, condition-dependent development, and the initiation and elaboration of novel phenotypes.     

Supply-Side Constraints Are Insufficient to Explain the Ontogenetic Scaling of Metabolic Rate in the Tobacco Hornworm,Manduca sexta

Explanations for the hypoallometric scaling of metabolic rate through ontogeny generally fall into two categories: supply-side constraints on delivery of oxygen, or decreased mass-specific intrinsic demand for oxygen. In many animals, supply and demand increase together as the body grows, thus making it impossible to tease apart the relative contributions of changing supply and demand to the observed scaling of metabolic rate. In larval insects, the large components of the tracheal system are set in size at each molt, but then remain constant in size until the next molt. Larvae of Manduca sexta increase up to ten-fold in mass between molts, leading to increased oxygen need without a concomitant increase in supply. At the molt, the tracheal system is shed and replaced with a new, larger one. Due to this discontinuous growth of the tracheal system, insect larvae present an ideal system in which to examine the relative contributions of supply and demand of oxygen to the ontogenetic scaling of metabolic rate. We observed that the metabolic rate at the beginning of successive instars scales hypoallometrically. This decrease in specific intrinsic demand could be due to a decrease in the proportion of highly metabolically active tissues (the midgut) or to a decrease in mitochondrial activity in individual cells. We found that decreased intrinsic demand, mediated by a decrease in the proportion of highly metabolically active tissues in the fifth instar, along with a decrease in the specific mitochondrial activity, contribute to the hypoallometric scaling of metabolic rate.     

A mathematical model for the regulation of juvenile hormone titers

The titer of juvenile hormone (JH) is determined by three factors: its rate of synthesis, its rate of degradation, and the degree to which JH is protected from degradation by binding to a diversity of JH-binding proteins. All three of these factors vary throughout the life history of an insect and contribute to variation in the JH titer. The relative importance of each of these factors in determining variation in the JH titer is not known and can, presumably, differ in different life stages and different species. Here we develop a mathematical model for JH synthesis, degradation, and sequestration that allows us to describe quantitatively how each of these contribute to the titer of total JH and free JH in the hemolymph. Our model allows for a diversity of JH-binding proteins with different dissociation constants, and also for a number of different modes of degradation and inactivation. The model can be used to analyze whether data on synthesis and degradation are compatible with the observed titer data. We use the model to analyze two data sets, from Manduca and Gryllus, and show that in both cases, the known data on synthesis and degradation cannot account for the observed JH titers because the role of JH sequestration by binding proteins is greatly underestimated, and/or the in vivo rate of JH degradation is greatly overestimated. These analyses suggest that there is a critical need to develop a better understanding of the in vivo role of synthesis, sequestration and degradation in JH titer regulation.     

A mathematical model of glutathione metabolism

Background and hypothesis

Based on neurochemical and genetic evidence, we suggest that both prevention and treatment of multiple addictions, such as dependence to alcohol, nicotine and glucose, should involve a biphasic approach. Thus, acute treatment should consist of preferential blocking of postsynaptic Nucleus Accumbens (NAc) dopamine receptors (D1-D5), whereas long term activation of the mesolimbic dopaminergic system should involve activation and/or release of Dopamine (DA) at the NAc site. Failure to do so will result in abnormal mood, behavior and potential suicide ideation. Individuals possessing a paucity of serotonergic and/or dopaminergic receptors, and an increased rate of synaptic DA catabolism due to high catabolic genotype of the COMT gene, are predisposed to self-medicating any substance or behavior that will activate DA release, including alcohol, opiates, psychostimulants, nicotine, gambling, sex, and even excessive internet gaming. Acute utilization of these substances and/or stimulatory behaviors induces a feeling of well being. Unfortunately, sustained and prolonged abuse leads to a toxic" pseudo feeling" of well being resulting in tolerance and disease or discomfort. Thus, a reduced number of DA receptors, due to carrying the DRD2 A1 allelic genotype, results in excessive craving behavior; whereas a normal or sufficient amount of DA receptors results in low craving behavior. In terms of preventing substance abuse, one goal would be to induce a proliferation of DA D2 receptors in genetically prone individuals. While in vivo experiments using a typical D2 receptor agonist induce down regulation, experiments in vitro have shown that constant stimulation of the DA receptor system via a known D2 agonist results in significant proliferation of D2 receptors in spite of genetic antecedents. In essence, D2 receptor stimulation signals negative feedback mechanisms in the mesolimbic system to induce mRNA expression causing proliferation of D2 receptors.

Proposal and conclusion

The authors propose that D2 receptor stimulation can be accomplished via the use of Synapatmine?, a natural but therapeutic nutraceutical formulation that potentially induces DA release, causing the same induction of D2-directed mRNA and thus proliferation of D2 receptors in the human. This proliferation of D2 receptors in turn will induce the attenuation of craving behavior. In fact as mentioned earlier, this model has been proven in research showing DNA-directed compensatory overexpression (a form of gene therapy) of the DRD2 receptors, resulting in a significant reduction in alcohol craving behavior in alcohol preferring rodents. Utilizing natural dopaminergic repletion therapy to promote long term dopaminergic activation will ultimately lead to a common, safe and effective modality to treat Reward Deficiency Syndrome (RDS) behaviors including Substance Use Disorders (SUD), Attention Deficit Hyperactivity Disorder (ADHD), Obesity and other reward deficient aberrant behaviors. This concept is further supported by the more comprehensive understanding of the role of dopamine in the NAc as a "wanting" messenger in the meso-limbic DA system.     

Analysis of Homeostatic Mechanisms in Biochemical Networks

Cell metabolism is an extremely complicated dynamical system that maintains important cellular functions despite large changes in inputs. This “homeostasis” does not mean that the dynamical system is rigid and fixed. Typically, large changes in external variables cause large changes in some internal variables so that, through various regulatory mechanisms, certain other internal variables (concentrations or velocities) remain approximately constant over a finite range of inputs. Outside that range, the mechanisms cease to function and concentrations change rapidly with changes in inputs. In this paper we analyze four different common biochemical homeostatic mechanisms: feedforward excitation, feedback inhibition, kinetic homeostasis, and parallel inhibition. We show that all four mechanisms can occur in a single biological network, using folate and methionine metabolism as an example. Golubitsky and Stewart have proposed a method to find homeostatic nodes in networks. We show that their method works for two of these mechanisms but not the other two. We discuss the many interesting mathematical and biological questions that emerge from this analysis, and we explain why understanding homeostatic control is crucial for precision medicine.     

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.