To clarify the mechanisms underlying the pancreatic β-cell response to varying glucose concentrations ([G]), electrophysiological findings were integrated into a mathematical cell model. The Ca²⁺ dynamics of the endoplasmic reticulum (ER) were also improved. The model was validated by demonstrating quiescent potential, burst–interburst electrical events accompanied by Ca²⁺ transients, and continuous firing of action potentials over [G] ranges of 0–6, 7–18, and >19 mM, respectively. These responses to glucose were completely reversible. The action potential, input impedance, and Ca²⁺ transients were in good agreement with experimental measurements. The ionic mechanisms underlying the burst–interburst rhythm were investigated by lead potential analysis, which quantified the contributions of individual current components. This analysis demonstrated that slow potential changes during the interburst period were attributable to modifications of ion channels or transporters by intracellular ions and/or metabolites to different degrees depending on [G]. The predominant role of adenosine triphosphate–sensitive K⁺ current in switching on and off the repetitive firing of action potentials at 8 mM [G] was taken over at a higher [G] by Ca²⁺- or Na⁺-dependent currents, which were generated by the plasma membrane Ca²⁺ pump, Na⁺/K⁺ pump, Na⁺/Ca²⁺ exchanger, and TRPM channel. Accumulation and release of Ca²⁺ by the ER also had a strong influence on the slow electrical rhythm. We conclude that the present mathematical model is useful for quantifying the role of individual functional components in the whole cell responses based on experimental findings.

The question of the extent to which cytosolic Ca²⁺affects sinoatrial node pacemaker activity has been discussed for decades. We examined this issue by analyzing two mathematical pacemaker models, based on the “Ca²⁺clock” (C) and “membrane clock” (M) hypotheses, together with patch-clamp experiments in isolated guinea pig sinoatrial node cells. By applying lead potential analysis to the models, the C mechanism, which is dependent on potentiation of Na⁺/Ca²⁺exchange current via spontaneous Ca²⁺release from the sarcoplasmic reticulum (SR) during diastole, was found to overlap M mechanisms in the C model. Rapid suppression of pacemaker rhythm was observed in the C model by chelating intracellular Ca²⁺, whereas the M model was unaffected. Experimental rupturing of the perforated-patch membrane to allow rapid equilibration of the cytosol with 10 mM BAPTA pipette solution, however, failed to decrease the rate of spontaneous action potential within ∼30 s, whereas contraction ceased within ∼3 s. The spontaneous rhythm also remained intact within a few minutes when SR Ca²⁺dynamics were acutely disrupted using high doses of SR blockers. These experimental results suggested that rapid disruption of normal Ca²⁺dynamics would not markedly affect spontaneous activity. Experimental prolongation of the action potentials, as well as slowing of the Ca²⁺-mediated inactivation of the L-type Ca²⁺currents induced by BAPTA, were well explained by assuming Ca²⁺chelation, even in the proximity of the channel pore in addition to the bulk cytosol in the M model. Taken together, the experimental and model findings strongly suggest that the C mechanism explicitly described by the C model can hardly be applied to guinea pig sinoatrial node cells. The possible involvement of L-type Ca²⁺current rundown induced secondarily through inhibition of Ca²⁺/calmodulin kinase II and/or Ca²⁺-stimulated adenylyl cyclase was discussed as underlying the disruption of spontaneous activity after prolonged intracellular Ca²⁺concentration reduction for >5 min.

Positive chronotropy induced by beta1-adrenergic stimulation is achieved by multiple interactions of ion channels and transporters in sinoatrial node pacemaker cells (SANs). To investigate the ionic mechanisms, we updated our SAN model developed in 2003 and incorporated the beta1-adrenergic signaling cascade developed by Kuzumoto et al. (2007). Since the slow component of the delayed rectifier K+ current (IKs) is one of the major targets of the beta1-adrenergic cascade, we developed a guinea pig model with a large IKs. The new model provided a good representation of the experimental characteristics of SANs. A comparison of individual current during diastole recorded before and after beta1-adrenergic stimulation clearly showed the negative shift of the L-type Ca2+ current (ICaL) takeoff potential, enlargement of the sustained inward current (I st), and the hyperpolarization-activated nonselective cation current (Iha) played major roles in increasing the firing frequency. Deactivation of IKs during diastole scarcely contributed to the time-dependent decrease in membrane K+ conductance, which was the major mechanism for slow diastolic depolarization, as indicated by calculating the instantaneous equilibrium potential (lead potential). This was because the activation of IKs during the preceding action potential was negligibly small. However, IKs was important in counterbalancing the increase in ICaL and the Na+/Ca2+ exchange current (INaCa), which otherwise compromised the positive chronotropic effect by elongating the action potential duration. Enhanced Ca2+ release from the sarcoplasmic reticulum failed to induce an obvious chronotropic effect in our model.

Heart rate variability (HRV) is the heart beat-to-beat variation under control of the cardiovascular function of animals. Under stressed conditions, cardiac activity is generally regulated with an upregulated sympathetic tone and withdrawal of vagal tone; thus, HRV monitoring can be a non-invasive technique to assess stress level in animals especially related to animal welfare. Among several stress-induced factors, heat stress is one of the most serious causes of physiological damage to animals. The aim of this study was to assess the effects of heat stress on HRV in small ruminants under free-moving conditions. In three experimental periods (June, August, and October), inter-beat intervals in sheep and goats (three for each) in two consecutive days were measured. HRV parameters were calculated from the inter-beat interval data by three types of analyses: time domain, frequency domain, and non-linear analyses. The temperature–humidity index (THI) was used as an indicator of heat stress, and vectorial dynamic body acceleration (VeDBA) was calculated to quantify the physical activity of the animals tested. First, we investigated correlations of THI and VeDBA with HRV parameters; subsequently, THI was divided into five categories according to the values obtained (≤ 65, 65–70, 70–75, 75–80, and >80), and the effects of the THI categories on HRV parameters were investigated with and without correcting for the effects of physical activity based on the VeDBA. The results indicated that HRV significantly decreased with increasing THI and VeDBA. For non-linear HRV parameters that were corrected for the effects of physical activity, it was suggested that there would be a threshold of THI around 80 that strongly affected HRV; high heat stress can affect the autonomic balance of animals non-linearly by inducing the sympathetic nervous system. In conclusion, to assess psychophysiological conditions of unrestrained animals by HRV analysis, the confounding effect of physical activity on HRV should be minimized for a more precise interpretation of the results.