Competitive inhibitors can, paradoxically, stimulate an enzymatic reaction at low to moderate doses. Competitive inhibition of an enzyme occurs when an inhibitor binds to the enzyme's binding site and blocks the enzyme's target molecule from binding. We recently proposed a detailed but straightforward mass action model for competitive inhibition of phosphoglycerate kinase 1 (PGK1) by Terazosin (TZ). The full PGK1 model has two substrates and two products which can be bound and released in either order, known as a random bi-bi mechanism. This model, with no further modification, predicts an increased reaction rate at low or moderate TZ doses, suggesting that stimulation is an intrinsic feature of competitive inhibition in enzymes with two products. This mechanism can aid in the development of novel therapies, particularly since enzyme activators are more rare and difficult to design than inhibitors. Here we propose a three-timescale reduction of that detailed model and show that the resulting rate equation retains three essential attributes of competitive inhibitor stimulation. These attributes are the biphasic dose response, the dependence on the relative rates of product dissociation from the binary and ternary complexes, and the parameter region where stimulation is possible. The resulting rate equation is a rational function which is a Monod function of each substrate, but quadratic in the denominator as a function of inhibitor dose.

Metabolic fluxes are the rates of life-sustaining chemical reactions within a cell and metabolites are the components. Determining the changes in these fluxes is crucial to understanding diseases with metabolic causes and consequences. Kinetic flux profiling (KFP) is a method for estimating flux that utilizes data from isotope tracing experiments. In these experiments, the isotope-labeled nutrient is metabolized through a pathway and integrated into the downstream metabolite pools. Measurements of proportion labeled for each metabolite in the pathway are taken at multiple time points and used to fit an ordinary differential equations model with fluxes as parameters. We begin by generalizing the process of converting diagrams of metabolic pathways into mathematical models composed of differential equations and algebraic constraints. The scaled differential equations for proportions of unlabeled metabolite contain parameters related to the metabolic fluxes in the pathway. We investigate flux parameter identifiability given data collected only at the steady state of the differential equation. Next, we give criteria for valid parameter estimations in the case of a large separation of timescales with fast-slow analysis. Bayesian parameter estimation on simulated data from KFP experiments containing both irreversible and reversible reactions illustrates the accuracy and reliability of flux estimations. These analyses provide constraints that serve as guidelines for the design of KFP experiments to estimate metabolic fluxes.

Doberman Pinschers are known for their increased susceptibility to dilated cardiomyopathy (DCM) relative to other domestic dogs. This makes the Doberman Pinscher a key model for gene-disease investigations. We conducted a genome-wide association study (GWAS) leveraging a database of genetic profiles obtained through collaboration with the Doberman Diversity Project (DDP). We worked in parallel to increase the depth and power of the DDP database. We exchanged direct correspondences with listed breeders and owners to establish health updates for participant dogs. In total, our study included data on 216, 184 single nucleotide polymorphisms (SNPs) in 46 cases and 3226 population control Doberman Pinschers. Using a generalized linear mixed model and saddlepoint approximation to correct for unbalanced group sizes, we identified a cluster of SNPs associated with DCM on chromosome 16.

Background Nuclear‐to‐mitochondrial communication regulating gene expression and mitochondrial function is a critical process following cardiac ischemic injury. In this study, we determined that cyclin C, a component of the Mediator complex, regulates cardiac and mitochondrial function in part by modifying mitochondrial fission. We tested the hypothesis that cyclin C functions as a transcriptional cofactor in the nucleus and a signaling molecule stimulating mitochondrial fission in response to stimuli such as cardiac ischemia. Methods and Results We utilized gain‐ and loss‐of‐function mouse models in which the CCNC (cyclin C) gene was constitutively expressed (transgenic, CycC cTg) or deleted (knockout, CycC cKO) in cardiomyocytes. The knockout and transgenic mice exhibited decreased cardiac function and altered mitochondria morphology. The hearts of knockout mice had enlarged mitochondria with increased length and area, whereas mitochondria from the hearts of transgenic mice were significantly smaller, demonstrating a role for cyclin C in regulating mitochondrial dynamics in vivo. Hearts from knockout mice displayed altered gene transcription and metabolic function, suggesting that cyclin C is essential for maintaining normal cardiac function. In vitro and in vivo studies revealed that cyclin C translocates to the cytoplasm, enhancing mitochondria fission following stress. We demonstrated that cyclin C interacts with Cdk1 (cyclin‐dependent kinase 1) in vivo following ischemia/reperfusion injury and that, consequently, pretreatment with a Cdk1 inhibitor results in reduced mitochondrial fission. This finding suggests a potential therapeutic target to regulate mitochondrial dynamics in response to stress. Conclusions Our study revealed that cyclin C acts as a nuclear‐to‐mitochondrial signaling factor that regulates both cardiac hypertrophic gene expression and mitochondrial fission. This finding provides new insights into the regulation of cardiac energy metabolism following acute ischemic injury.

Ankyrin-B is a multifunctional adapter protein responsible for localization and stabilization of select ion channels, transporters, and signaling molecules in excitable cells including cardiomyocytes. Ankyrin-B dysfunction has been linked with highly penetrant sinoatrial node (SAN) dysfunction and increased susceptibility to atrial fibrillation. While previous studies have identified a role for abnormal ion homeostasis in ventricular arrhythmias, the molecular mechanisms responsible for atrial arrhythmias and SAN dysfunction in human patients with ankyrin-B syndrome are unclear. Here, we develop a computational model of ankyrin-B dysfunction in atrial and SAN cells and tissue to determine the mechanism for increased susceptibility to atrial fibrillation and SAN dysfunction in human patients with ankyrin-B syndrome. Our simulations predict that defective membrane targeting of the voltage-gated L-type Ca 2+ channel Ca v 1.3 leads to action potential shortening that reduces the critical atrial tissue mass needed to sustain reentrant activation. In parallel, increased fibrosis results in conduction slowing that further increases the susceptibility to sustained reentry in the setting of ankyrin-B dysfunction. In SAN cells, loss of Ca v 1.3 slows spontaneous pacemaking activity, whereas defects in Na + /Ca 2+ exchanger and Na + /K + ATPase increase variability in SAN cell firing. Finally, simulations of the intact SAN reveal a shift in primary pacemaker site, SAN exit block, and even SAN failure in ankyrin-B-deficient tissue. These studies identify the mechanism for increased susceptibility to atrial fibrillation and SAN dysfunction in human disease. Importantly, ankyrin-B dysfunction involves changes at both the cell and tissue levels that favor the common manifestation of atrial arrhythmias and SAN dysfunction.

In order to study how n to 1 convergence sharpens timing information, we have used a simple time-window (TW) model in which the target neuron fires the first time it has received m action potentials in the previous ε milleseconds. Although the TW is convenient for proving theorems and Monte-Carlo simulations, it is a natural question whether it represents well the physiological reality. We first present simulations that show, in the case n = 3, m = 3, that the Hodgkin-Huxley model has a very sharp time window but the leaky integrate-and-fire model (LIF) does not. Simulations also show that other non-linear models including quadratic-integrate-and-fire (QIF), the theta model, and the Fitzhugh-Nagumo model also have sharp time window behavior. We then give a complete analytical treatment of the LIF and QIF models to explain why the first does not have a sharp time window but the second does. This suggests that TW neurons may give a better approximation to physiological reality than LIF neurons.

Children at about age 18 months experience acceleration in word learning. This vocabulary explosion is a robust phenomenon, although the exact shape and timing vary from child to child. One class of explanations, which we term collectively as leveraged learning, posits that knowledge of some words helps with the learning of others. In this framework, the child initially knows no words and so learning is slow. As more words are acquired, new words become easier and thus it is the acquisition of early words that fuels the explosion in learning. In this paper we examine the role of leveraged learning in the vocabulary spurt by proposing a simple model of leveraged learning. Our results show that leverage can change both the shape and timing of the acceleration, but that it cannot create acceleration if it did not exist in the corresponding model without leveraging. This model is then applied to the Zipfian distribution of word frequencies, which confirm that leveraging does not create acceleration, but that the relationship between frequency and the difficulty of learning a word may be complex.

During the second year of life, the rate at which most children learn words accelerates dramatically, the so–called “vocabulary explosion”. Most accounts posit changes in the child or specialized learning mechanisms to account for this sudden change. However, recently McMurray (2007) demonstrated that acceleration is a mathematical consequence of parallel learning and the statistical distribution of word difficulty across the language. We generalize this model by developing a stochastic version. It demonstrates that the gradual nature of learning is critical for producing acceleration, and given sufficient gradualness, virtually any distribution of word difficulty can yield acceleration. Thus, the vocabulary explosion may be even more mathematically robust than previously thought.

In order to study how the convergence of many variable-response neurons on a single target can sharpen timing information, we investigate the limit as the number of input neurons and the number of incoming spikes required to fire the target both get large with the ratio fixed. We prove that the standard deviation of the firing time of the target cell goes to zero in this limit, and we derive the asymptotic forms of the density and the standard deviation near the limit. We use the theorems to understand the behavior of octopus cells in the mammalian cochlear nucleus.