Showing papers by "James Sneyd published in 2017"

On the dynamical structure of calcium oscillations

Abstract: Oscillations in the concentration of free cytosolic Ca2+ are an important and ubiquitous control mechanism in many cell types. It is thus correspondingly important to understand the mechanisms that underlie the control of these oscillations and how their period is determined. We show that Class I Ca2+ oscillations (i.e., oscillations that can occur at a constant concentration of inositol trisphosphate) have a common dynamical structure, irrespective of the oscillation period. This commonality allows the construction of a simple canonical model that incorporates this underlying dynamical behavior. Predictions from the model are tested, and confirmed, in three different cell types, with oscillation periods ranging over an order of magnitude. The model also predicts that Ca2+ oscillation period can be controlled by modulation of the rate of activation by Ca2+ of the inositol trisphosphate receptor. Preliminary experimental evidence consistent with this hypothesis is presented. Our canonical model has a structure similar to, but not identical to, the classic FitzHugh-Nagumo model. The characterization of variables by speed of evolution, as either fast or slow variables, changes over the course of a typical oscillation, leading to a model without globally defined fast and slow variables.

A mathematical model of calcium dynamics in HSY cells.

Abstract: Saliva is an essential part of activities such as speaking, masticating and swallowing. Enzymes in salivary fluid protect teeth and gums from infectious diseases, and also initiate the digestion process. Intracellular calcium (Ca2+) plays a critical role in saliva secretion and regulation. Experimental measurements of Ca2+ and inositol trisphosphate (IP3) concentrations in HSY cells, a human salivary duct cell line, show that when the cells are stimulated with adenosine triphosphate (ATP) or carbachol (CCh), they exhibit coupled oscillations with Ca2+ spike peaks preceding IP3 spike peaks. Based on these data, we construct a mathematical model of coupled Ca2+ and IP3 oscillations in HSY cells and perform model simulations of three different experimental settings to forecast Ca2+ responses. The model predicts that when Ca2+ influx from the extracellular space is removed, oscillations gradually slow down until they stop. The model simulation of applying a pulse of IP3 predicts that photolysis of caged IP3 causes a transient increase in the frequency of the Ca2+ oscillations. Lastly, when Ca2+-dependent activation of PLC is inhibited, we see an increase in the oscillation frequency and a decrease in the amplitude. These model predictions are confirmed by experimental data. We conclude that, although concentrations of Ca2+ and IP3 oscillate, Ca2+ oscillations in HSY cells are the result of modulation of the IP3 receptor by intracellular Ca2+, and that the period is modulated by the accompanying IP3 oscillations.

The relative contributions of store-operated and voltage-gated Ca2+ channels to the control of Ca2+ oscillations in airway smooth muscle

Abstract: KEY POINTS Agonist-dependent oscillations in the concentration of free cytosolic calcium are a vital mechanism for the control of airway smooth muscle contraction and thus are a critical factor in airway hyper-responsiveness. Using a mathematical model, closely tied to experimental work, we show that the oscillations in membrane potential accompanying the calcium oscillations have no significant effect on the properties of the calcium oscillations. In addition, the model shows that calcium entry through store-operated calcium channels is critical for calcium oscillations, but calcium entry through voltage-gated channels has much less effect. The model predicts that voltage-gated channels are less important than store-operated channels in the control of airway smooth muscle tone. ABSTRACT Airway smooth muscle contraction is typically the key mechanism underlying airway hyper-responsiveness, and the strength of muscle contraction is determined by the frequency of oscillations of intracellular calcium (Ca2+ ) concentration. In airway smooth muscle cells, these Ca2+ oscillations are caused by cyclic Ca2+ release from the sarcoplasmic reticulum, although Ca2+ influx via plasma membrane channels is also necessary to sustain the oscillations over longer times. To assess the relative contributions of store-operated and voltage-gated Ca2+ channels to this Ca2+ influx, we generated a comprehensive mathematical model, based on experimental Ca2+ measurements in mouse precision-cut lung slices, to simulate Ca2+ oscillations and changes in membrane potential. Agonist-induced Ca2+ oscillations are accompanied by oscillations in membrane potential, although the membrane potential oscillations are too small to generate large Ca2+ currents through voltage-gated Ca2+ channels, and thus have little effect on the Ca2+ oscillations. Ca2+ entry through voltage-gated channels only becomes important when the cell is depolarized (e.g. by a high external K+ concentration). As a result, agonist-induced Ca2+ oscillations are critically dependent on Ca2+ entry through store-operated channels but do not depend strongly on Ca2+ entry though voltage-gated channels.

Computational Architecture of the Granular Layer of Cerebellum-Like Structures

Abstract: In the adaptive filter model of the cerebellum, the granular layer performs a recoding which expands incoming mossy fibre signals into a temporally diverse set of basis signals. The underlying neural mechanism is not well understood, although various mechanisms have been proposed, including delay lines, spectral timing and echo state networks. Here, we develop a computational simulation based on a network of leaky integrator neurons, and an adaptive filter performance measure, which allows candidate mechanisms to be compared. We demonstrate that increasing the circuit complexity improves adaptive filter performance, and relate this to evolutionary innovations in the cerebellum and cerebellum-like structures in sharks and electric fish. We show how recurrence enables an increase in basis signal duration, which suggest a possible explanation for the explosion in granule cell numbers in the mammalian cerebellum.

Computational modeling of epithelial fluid and ion transport in the parotid duct after transfection of human aquaporin-1.

Abstract: Following transfection of aquaporin into the parotid ducts of minipigs with salivary hypofunction, the resulting increase in salivary flow rates contradicts current understanding of ductal fluid tr...

Sequential Pattern Formation in the Cerebellar Granular Layer.

Abstract: Here, we introduce a novel mechanism for temporal recoding by the cerebellar granular layer based on three key properties: the granule cell-Golgi cell inhibitory feedback loop, bursting behaviour of granule cells and the large ratio of granule cells to Golgi cells. We propose that mutual inhibition of granule cells, mediated by Golgi cell feedback inhibition, prevents simultaneous activation. Granule cells are differentiated by firing threshold, resulting in sequential bursts of spikes. We demonstrate the plausibility of the mechanism through a computational simulation of a firing rate model, and further examine its robustness by developing a spiking model incorporating realistic postsynaptic potentials.

A mathematical model of the effects of anoctamin-1 loss on intestinal slow wave entrainment

Abstract: The interstitial cells of Cajal (ICC) generate electrophysiological events called slow waves that regulate the motility of the gastrointestinal (GI) tract. Recent studies have demonstrated that the Ca2+-activated Cl− -channel, encoded by the anoctamin1 (Ano1) protein, has a major role in regulating intestinal slow waves and motility. The main aim of this study was to develop a multi-scale mathematical model capable of simulating both normal slow wave entrainment and the effects of Ano1 knockout (KO) on the normal activity. A biophysically-based cell model was adapted to simulate the effects of Ano1 KO at the cellular level. A 10mm one-dimensional (1D) model was then developed to simulate entrained intestinal slow wave propagation. Cellular KO at levels of 100% and 20% were applied to a varying-sized middle region of the 1D model. The main finding was that the level of loss of entrainment increased as both cellular and spatial Ano1 KO levels increased, mostly manifesting as ectopic activation. In the future, this model will be extended and used in combination with Ca2+ -imaging data to quantitatively investigate the effects of Ano1 loss in ICC.