Spontaneously generated calcium (Ca2+) waves can trigger arrhythmias in ventricular and atrial myocytes. Yet, Ca2+ waves also serve the physiological function of mediating global Ca2+ increase and muscle contraction in atrial myocytes. We examine the factors that influence Ca2+ wave initiation by mathematical modeling and large-scale computational (supercomputer) simulations. An important finding is the existence of a strong coupling between the ryanodine receptor distribution and Ca2+ dynamics. Even modest changes in the ryanodine receptor spacing profoundly affect the probability of Ca2+ wave initiation. As a consequence of this finding, we suggest that there is information flow from the contractile system to the Ca2+ control system and this dynamical interplay could contribute to the increased incidence of arrhythmias during heart failure.

We describe a finite-element model of mast cell calcium dynamics that incorporates the endoplasmic reticulum's complex geometry. The model is built upon a three-dimensional reconstruction of the endoplasmic reticulum (ER) from an electron tomographic tilt series. Tetrahedral meshes provide volumetric representations of the ER lumen, ER membrane, cytoplasm, and plasma membrane. The reaction-diffusion model simultaneously tracks changes in cytoplasmic and ER intraluminal calcium concentrations and includes luminal and cytoplasmic protein buffers. Transport fluxes via PMCA, SERCA, ER leakage, and Type II IP3 receptors are also represented. Unique features of the model include stochastic behavior of IP3 receptor calcium channels and comparisons of channel open times when diffusely distributed or aggregated in clusters on the ER surface. Simulations show that IP3R channels in close proximity modulate activity of their neighbors through local Ca2+ feedback effects. Cytoplasmic calcium levels rise higher, and ER luminal calcium concentrations drop lower, after IP3-mediated release from receptors in the diffuse configuration. Simulation results also suggest that the buffering capacity of the ER, and not restricted diffusion, is the predominant factor influencing average luminal calcium concentrations.

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Chronic hepatitis B viral infection (HBV) afflicts around 250 million individuals globally and few options for treatment exist. Once infected, the virus entrenches itself in the liver with a notoriously resilient colonisation of viral DNA (covalently-closed circular DNA, cccDNA). The majority of infections are cleared, yet we do not understand why 5% of adult immune responses fail leading to the chronic state with its collateral morbid effects such as cirrhosis and eventual hepatic carcinoma. The liver environment exhibits particularly complex spatial structures for metabolic processing and corresponding distributions of nutrients and transporters that may influence successful HBV entrenchment. We assembled a multi-scaled mathematical model of the fundamental hepatic processing unit, the sinusoid, into a whole-liver representation to investigate the impact of this intrinsic spatial heterogeneity on the HBV dynamic. Our results suggest HBV may be exploiting spatial aspects of the liver environment. We distributed increased HBV replication rates coincident with elevated levels of nutrients in the sinusoid entry point (the periportal region) in tandem with similar distributions of hepatocyte transporters key to HBV invasion (e.g., the sodium-taurocholate cotransporting polypeptide or NTCP), or immune system activity. According to our results, such co-alignment of spatial distributions may contribute to persistence of HBV infections, depending on spatial distributions and intensity of immune response as well. Moreover, inspired by previous HBV models and experimentalist suggestions of extra-hepatic HBV replication, we tested in our model influence of HBV blood replication and observe an overall nominal effect on persistent liver infection. Regardless, we confirm prior results showing a solo cccDNA is sufficient to re-infect an entire liver, with corresponding concerns for transplantation and treatment.

Degree assortativity refers to the increased or decreased probability of connecting two neurons based on their in-or out-degrees, relative to what would be expected by chance. We investigate the effects of such assortativity in a network of theta neurons. The Ott/Antonsen ansatz is used to derive equations for the expected state of each neuron, and these equations are then coarse-grained in degree space. We generate families of effective connectivity matrices parametrised by assortativity coefficient and use SVD decompositions of these to efficiently perform numerical bifurcation analysis of the coarse-grained equations. We find that of the four possible types of degree assortativity, two have no effect on the networks' dynamics, while the other two can have a significant effect.

We construct a model of calcium waves in a three-dimensional anatomically accurate parotid acinar cell, constructed from experimental data. Gradients of inositol trisphosphate receptor (IPR) density are imposed, with the IPR density being greater closer to the lumen, which has a branched structure, and inositol trisphosphate (IP3) is produced only at the basal membrane. We show (1) that IP3 equilibrates so quickly across the cell that it can be assumed to be spatially homogeneous; (2) spatial separation of the sites of IP3 action and IP3 production does not preclude the formation of stable oscillatory Ca2+ waves. However, these waves are not waves in the mathematical sense of a traveling wave with fixed profile. They result instead from a time delay between the Ca2+ rise in the apical and basal regions; (3) the ryanodine receptors serve to reinforce the Ca2+ wave, but are not necessary for the wave to exist; (4) a spatially-independent model is not sufficient to study saliva secretion, although a one-dimensional model might be sufficient. Our results here form the first stages of the construction of a multiscale and multicellular model of saliva secretion in an entire acinus.

dynamics within pacemaker cells of the gastrointestinal (GI) tract, the interstitial cells of Cajal (ICC) (a glossary of all abbreviations can be found in Table 1). They were established as the GI pacemakers (44) long after their initial discovery in the 19th century (12), and the performance and structure of the ICC network are intimately related to proper GI motility and function. Disruption of the network can result in conditions such as constipation, gastroparesis, or achalasia (33,66). The pacemaking signals themselves in the ICC are membrane depolarizations also known as slow waves (SW) that rhythmically occur at different intrinsic frequencies depending on species and tissue type. They can range in humans from three cycles per minute (cpm) in the stomach to 8 -12 cpm in the intestine (43) (63), and these depolarizations coordinate contractions in surrounding smooth muscle tissue. The physiological location, spatial scales, and the relative paucity of experimental data of the ICC continue to challenge experimentalists and theoretical explorations. It is known, however, that unitary potentials, or spontaneous-transient depolarizations (SD), of the ICC membrane generate the SW in some way, yet the mechanisms responsible for producing SD themselves are not clearly understood. Membrane channels in the ICC such as the nonspecific cation conductance (NSCC) (63) and the Ca 2ϩ -activated chloride channels (the ANO1) (84) are likely involved in SD production, but their roles are unclear.Daniel et al. (20) showed depletions of the endoplasmic reticulum (ER) Ca 2ϩ reservoir reduce the frequency of intestinal smooth muscle contractions (19) and suggested that the pacing of ICC is related to recycling Ca 2ϩ into the ER from sequestered stores in caveolae (20). It is known that Ca 2ϩ transport via the intracellular inositol-trisphosphate (IP 3 ) receptors (IP 3 R) on the ER into the cytosol (73, 78) and mitochondria (MT) uptake of cytosolic Ca 2ϩ (38, 78) is involved in generation of SW activity. Disruption of MT sodium-calcium exchangers (NCX) reduces the frequency of the Ca 2ϩ oscillations (45), albeit modestly and eventually on a time scale of minutes; notably, the MT NCX are also essential to the function of store-operated Ca 2ϩ entry (SOCE) (52). We thus hypothesize that depletions of the ER Ca 2ϩ reservoir and subsequent activation of SOCE are fundamental to pacemaking of the ICC. The eventual depletion of ER Ca 2ϩ stores and activation of ER SOCE mechanisms, such as the stromal interaction molecules (STIM) on the ER membrane sensing intraluminal ER Ca 2ϩ and their plasma membrane (PM) complements, either the Orai or transient receptor potential channels (TRPC) (11), are essential to intracellular ICC Ca 2ϩ oscillations. These Ca 2ϩ oscillations would then, in turn, determine the electrical SW activity observed by interaction with Ca 2ϩ -sensitive ion channels. Depletions of the ER Ca 2ϩ reservoir by virtue of the ER-MT Ca 2ϩ transport dynamic in a biophysically based model are of comparable timescales to those ob...