Akinori Noma

Minor contribution of cytosolic Ca2+ transients to the pacemaker rhythm in guinea pig sinoatrial node cells

The question of the extent to which cytosolic Ca(2+) affects sinoatrial node pacemaker activity has been discussed for decades. We examined this issue by analyzing two mathematical pacemaker models, based on the Ca(2+) 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(+)/Ca(2+) exchange current via spontaneous Ca(2+) 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 Ca(2+), 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 Ca(2+) dynamics were acutely disrupted using high doses of SR blockers. These experimental results suggested that rapid disruption of normal Ca(2+) dynamics would not markedly affect spontaneous activity. Experimental prolongation of the action potentials, as well as slowing of the Ca(2+)-mediated inactivation of the L-type Ca(2+) currents induced by BAPTA, were well explained by assuming Ca(2+) 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 Ca(2+) current rundown induced secondarily through inhibition of Ca(2+)/calmodulin kinase II and/or Ca(2+)-stimulated adenylyl cyclase was discussed as underlying the disruption of spontaneous activity after prolonged intracellular Ca(2+) concentration reduction for >5 min.

Time-dependent changes in membrane excitability during glucose-induced bursting activity in pancreatic β cells.

In our companion paper, the physiological functions of pancreatic β cells were analyzed with a new β-cell model by time-based integration of a set of differential equations that describe individual reaction steps or functional components based on experimental studies. In this study, we calculate steady-state solutions of these differential equations to obtain the limit cycles (LCs) as well as the equilibrium points (EPs) to make all of the time derivatives equal to zero. The sequential transitions from quiescence to burst–interburst oscillations and then to continuous firing with an increasing glucose concentration were defined objectively by the EPs or LCs for the whole set of equations. We also demonstrated that membrane excitability changed between the extremes of a single action potential mode and a stable firing mode during one cycle of bursting rhythm. Membrane excitability was determined by the EPs or LCs of the membrane subsystem, with the slow variables fixed at each time point. Details of the mode changes were expressed as functions of slowly changing variables, such as intracellular [ATP], [Ca2+], and [Na+]. In conclusion, using our model, we could suggest quantitatively the mutual interactions among multiple membrane and cytosolic factors occurring in pancreatic β cells.

A Novel Method to Quantify Contribution of Channels and Transporters to Membrane Potential Dynamics

The action potential, once triggered in ventricular or atrial myocytes, automatically proceeds on its time course or is generated spontaneously in sinoatrial node pacemaker cells. It is induced by complex interactions among such cellular components as ion channels, transporters, intracellular ion concentrations, and signaling molecules. We have developed what is, to our knowledge, a new method using a mathematical model to quantify the contribution of each cellular component to the automatic time courses of the action potential. In this method, an equilibrium value, which the membrane potential is approaching at a given moment, is calculated along the time course of the membrane potential. The calculation itself is based on the time-varying conductance and the reversal potentials of individual ion channels and electrogenic ion transporters. Since the equilibrium potential moves in advance of the membrane potential change, we refer to it as the lead potential, V(L). The contribution of an individual current was successfully quantified by comparing dV(L)/dt before and after fixing the time-dependent change of a component of interest, such as the variations in the open probability of a channel or the turnover rate of an ion transporter. In addition to the action potential, the lead-potential analysis should also be applicable in all types of membrane excitation in many different kinds of cells.

Analyzing electrical activities of pancreatic β cells using mathematical models.

Bursts of repetitive action potentials are closely related to the regulation of glucose-induced insulin secretion in pancreatic β cells. Mathematical studies with simple β-cell models have established the central principle that the burst-interburst events are generated by the interaction between fast membrane excitation and slow cytosolic components. Recently, a number of detailed models have been developed to simulate more realistic β cell activity based on expanded findings on biophysical characteristics of cellular components. However, their complex structures hinder our intuitive understanding of the underlying mechanisms, and it is becoming more difficult to dissect the role of a specific component out of the complex network. We have recently developed a new detailed model by incorporating most of ion channels and transporters recorded experimentally (the Cha-Noma model), yet the model satisfies the charge conservation law and reversible responses to physiological stimuli. Here, we review the mechanisms underlying bursting activity by applying mathematical analysis tools to representative simple and detailed models. These analyses include time-based simulation, bifurcation analysis and lead potential analysis. In addition, we introduce a new steady-state I-V (ssI-V) curve analysis. We also discuss differences in electrical signals recorded from isolated single cells or from cells maintaining electrical connections within multi-cell preparations. Towards this end, we perform simulations with our detailed pancreatic β-cell model.

EAD and DAD mechanisms analyzed by developing a new human ventricular cell model

It has long been suggested that the Ca(2+)-mechanisms are largely involved in generating the early afterdepolarization (EAD) as well as the delayed afterdepolarization (DAD). This view was examined in a quantitative manner by applying the lead potential analysis to a new human ventricular cell model. In this ventricular cell model, the tight coupled LCC-RyR model (CaRU) based on local control theory (Hinch etxa0al. 2004) and ion channel models mostly based on human electrophysiological data were included to reproduce realistic Ca(2+) dynamics as well as the membrane excitation. Simultaneously, the Ca(2+) accumulation near the Ca(2+) releasing site was incorporated as observed in real cardiac myocytes. The maximum rate of ventricular repolarization (-1.02xa0mV/ms) is due to IK1 (-0.55xa0mV/ms) and the rest is provided nearly equally by INCX (-0.20xa0mV/ms), INaL (-0.16xa0mV/ms) and INaT (-0.13xa0mV/ms). These INaL and INaT components are due to closure of the voltage gate, which remains partially open during the plateau potential. DADs could be evoked by applying high-frequency stimulations supplemented by a partial Na(+)/K(+) pump inhibition, or by a microinjection of Ca(2+). EADs was evoked by retarding the inactivation of INaL. The lead potential (VL) analysis revealed that IK1 and IKr played the primary role to reverse the AP repolarization to depolarizing limb of EAD. ICaL and INCX amplified EAD, while the remaining currents partially antagonized dVL/dt. The maximum rate of rise of EAD was attributable to the rapid activation of both ICaL (45.5%) and INCX (54.5%).

Characterization of the cardiac Na+/K+ pump by development of a comprehensive and mechanistic model

A large amount of experimental data on the characteristics of the cardiac Na(+)/K(+) pump have been accumulated, but it remains difficult to predict the quantitative contribution of the pump in an intact cell because most measurements have been made under non-physiological conditions. To extrapolate the experimental findings to intact cells, we have developed a comprehensive Na(+)/K(+) pump model based on the thermodynamic framework (Smith and Crampin, 2004) of the Post-Albers reaction cycle combined with access channel mechanisms. The new model explains a variety of experimental results for the Na(+)/K(+) pump current (I(NaK)), including the dependency on the concentrations of Na(+) and K(+), the membrane potential and the free energy of ATP hydrolysis. The model demonstrates that both the apparent affinity and the slope of the substrate-I(NaK) relationship measured experimentally are affected by the composition of ions in the extra- and intracellular solutions, indirectly through alteration in the probability distribution of individual enzyme intermediates. By considering the voltage dependence in the Na(+)- and K(+)-binding steps, the experimental voltage-I(NaK) relationship could be reconstructed with application of experimental ionic compositions in the model, and the view of voltage-dependent K(+) binding was supported. Re-evaluation of charge movements accompanying Na(+) and K(+) translocations gave a reasonable number for the site density of the Na(+)/K(+) pump on the membrane. The new model is relevant for simulation of cellular functions under various interventions, such as depression of energy metabolism.

A Model of Na+/H+ Exchanger and Its Central Role in Regulation of pH and Na+ in Cardiac Myocytes

A new kinetic model of the Na(+)/H(+) exchanger (NHE) was developed by fitting a variety of major experimental findings, such as ion-dependencies, forward/reverse mode, and the turnover rate. The role of NHE in ion homeostasis was examined by implementing the NHE model in a minimum cell model including intracellular pH buffer, Na(+)/K(+) pump, background H(+), and Na(+) fluxes. This minimum cell model was validated by reconstructing recovery of pH(i) from acidification, accompanying transient increase in [Na(+)](i) due to NHE activity. Based on this cell model, steady-state relationships among pH(i), [Na(+)](I), and [Ca(2+)](i) were quantitatively determined, and thereby the critical level of acidosis for cell survival was predicted. The acidification reported during partial blockade of the Na(+)/K(+) pump was not attributed to a dissipation of the Na(+) gradient across the membrane, but to an increase in indirect H(+) production. This NHE model, though not adapted to the dimeric behavioral aspects of NHE, can provide a strong clue to quantitative prediction of degree of acidification and accompanying disturbance of ion homeostasis under various pathophysiological conditions.

A Human Ventricular Myocyte Model with a Refined Representation of Excitation-Contraction Coupling

Cardiac Ca(2+)-induced Ca(2+) release (CICR) occurs by a regenerative activation of ryanodine receptors (RyRs) within each Ca(2+)-releasing unit, triggered by the activation of L-type Ca(2+) channels (LCCs). CICR is then terminated, most probably by depletion of Ca(2+) in the junctional sarcoplasmic reticulum (SR). Hinch etxa0al. previously developed a tightly coupled LCC-RyR mathematical model, known as the Hinch model, that enables simulations to deal with a variety of functional states of whole-cell populations of a Ca(2+)-releasing unit using a personal computer. In this study, we developed a membrane excitation-contraction model of the human ventricular myocyte, which we call the human ventricular cell (HuVEC) model. This model is a hybrid of the most recent HuVEC models and the Hinch model. We modified the Hinch model to reproduce the regenerative activation and termination of CICR. In particular, we removed the inactivated RyR state and separated the single step of RyR activation by LCCs into triggering and regenerative steps. More importantly, we included the experimental measurement of a transient rise in Ca(2+) concentrations ([Ca(2+)], 10-15 μM) during CICR in the vicinity of Ca(2+)-releasing sites, and thereby calculated the effects of the local Ca(2+) gradient on CICR as well as membrane excitation. This HuVEC model successfully reconstructed both membrane excitation and key properties of CICR. The time course of CICR evoked by an action potential was accounted for by autonomous changes in an instantaneous equilibrium open probability of couplons. This autonomous time course was driven by a core feedback loop including the pivotal local [Ca(2+)], influenced by a time-dependent decay in the SR Ca(2+) content during CICR.

Modeling analysis of inositol 1,4,5-trisphosphate receptor-mediated Ca2+ mobilization under the control of glucagon-like peptide-1 in mouse pancreatic β-cells

Glucagon-like peptide-1 (GLP-1) is an intestinally derived blood glucose-lowering hormone that potentiates glucose-stimulated insulin secretion from pancreatic β-cells. The secretagogue action of GLP-1 is explained, at least in part, by its ability to stimulate cAMP production so that cAMP may facilitate the release of Ca(2+) from inositol trisphosphate receptor (IP3R)-regulated Ca(2+) stores. However, a quantitative model has yet to be provided that explains the molecular mechanisms and dynamic processes linking GLP-1-stimulated cAMP production to Ca(2+) mobilization. Here, we performed simulation studies to investigate how GLP-1 alters the abilities of Ca(2+) and IP3 to act as coagonists at IP3R Ca(2+) release channels. A new dynamic model was constructed based on the Kaftan model, which demonstrates dual steady-state allosteric regulation of the IP3R by Ca(2+) and IP3. Data obtained from β-cells were then analyzed to understand how GLP-1 facilitates IP3R-mediated Ca(2+) mobilization when UV flash photolysis is used to uncage Ca(2+) and IP3 intracellularly. When the dynamic model for IP3R activation was incorporated into a minimal cell model, the Ca(2+) transients and oscillations induced by GLP-1 were successfully reconstructed. Simulation studies indicated that transient and oscillatory responses to GLP-1 were produced by sequential positive and negative feedback regulation due to fast activation and slow inhibition of the IP3R by Ca(2+). The slow rate of Ca(2+)-dependent inhibition was revealed to provide a remarkable contribution to the time course of the decay of cytosolic Ca(2+) transients. It also served to drive and pace Ca(2+) oscillations that are significant when evaluating how GLP-1 stimulates insulin secretion.

Mechanisms underlying the volume regulation of interstitial fluid by capillaries: a simulation study

Background Control of the extracellular fluid volume is one of the most indispensable issues for homeostasis of the internal milieu. However, complex interdependence of the pressures involved in determination of fluid exchange makes it difficult to predict a steady-state tissue volume under various physiological conditions without mathematical approaches. Methods Here, we developed a capillary model based on the Starlings principle, which allowed us to clarify the mechanisms of the interstitial-fluid volume regulation. Three well known safety factors against edema: (1) low tissue compliance in negative pressure ranges; (2) lymphatic flow driven by the tissue pressure; and (3) protein washout by the lymph, were incorporated into the model in sequence. Results An increase in blood pressure at the venous end of the capillary induced an interstitial-fluid volume increase, which, in turn, reduced negative tissue pressure to prevent edema. The lymphatic flow alleviated the edema by both carrying fluid away from the tissue and decreasing the colloidal osmotic pressure. From the model incorporating all three factors, we found that the interstitial-fluid volume changed quickly after the blood pressure change, and that the protein movement towards a certain equilibrium point followed the volume change. Conclusion Mathematical analyses revealed that the system of the capillary is stable near the equilibrium point at steady state and normal physiological capillary pressure. The time course of the tissue-volume change was determined by two kinetic mechanisms: rapid fluid exchange and slow protein fluxes.