Regulation of type 1 inositol 1,4,5-trisphosphate-gated calcium channels by InsP3 and calcium: Simulation of single channel kinetics based on ligand binding and electrophysiological analysis.

Cytosolic calcium acts as both a coagonist and an inhibitor of the type 1 inositol 1,4,5-trisphosphate (InsP3)-gated Ca channel, resulting in a bell-shaped Ca dependence of channel activity (Bezprozvanny, I., J. Watras, and B.E. Ehrlich. 1991. Nature. 351:751-754; Finch, E.A., T.J. Turner, and S.M. Goldin. 1991. Science. 252: 443-446; Iino, M. 1990. J. Gen. Physiol. 95:1103-1122). The ability of Ca to inhibit channel activity, however, varies dramatically depending on InsP3 concentration (Combettes, L., Z. Hannaert-Merah, J.F. Coquil, C. Rousseau, M. Claret, S. Swillens, and P. Champeil. 1994. J. Biol. Chem. 269:17561-17571; Kaftan, E.J., B.E. Ehrlich, and J. Watras. 1997. J. Gen. Physiol. 110:529-538). In the present report, we have extended the characterization of the effect of cytosolic Ca on both InsP3 binding and InsP3-gated channel kinetics, and incorporated these data into a mathematical model capable of simulating channel kinetics. We found that cytosolic Ca increased the Kd of InsP3 binding approximately 3.5-fold, but did not influence the maximal number of binding sites. The ability of Ca to decrease InsP3 binding is consistent with the rightward shift in the bell-shaped Ca dependence of InsP3-gated Ca channel activity. High InsP3 concentrations are able to overcome the Ca-dependent inhibition of channel activity, apparently due to a low affinity InsP3 binding site (Kaftan, E.J., B.E. Ehrlich, and J. Watras. 1997. J. Gen. Physiol. 110:529-538). Constants from binding analyses and channel activity determinations were used to develop a mathematical model that fits the complex Ca-dependent regulation of the type 1 InsP3-gated Ca channel. This model accurately simulated both steady state data (channel open probability and InsP3 binding) and kinetic data (channel activity and open time distributions), and yielded testable predictions with regard to the regulation of this intracellular Ca channel. Information gained from these analyses, and our current molecular model of this Ca channel, will be important for understanding the basis and regulation of intracellular Ca waves and oscillations in intact cells.     

The epithelial Na(+) channel (ENaC) is related to the hypertonicity-induced Na(+) conductance in rat hepatocytes

The epithelial Na(+) channel (ENaC) is composed of the subunits alpha, beta, and gamma [Canessa et al., Nature 367 (1994) 463-467] and typically exhibits a high affinity to amiloride [Canessa et al., Nature 361 (1993) 467-470]. When expressed in Xenopus oocytes, conflicting results were reported concerning the osmo-sensitivity of the channel [Ji et al., Am. J. Physiol. 275 (1998) C1182-C1190; Hawayda and Subramanyam, J. Gen. Physiol. 112 (1998) 97-111; Rossier, J. Gen. Physiol. 112 (1998) 95-96]. Rat hepatocytes were the first system in which amiloride-sensitive sodium currents in response to hypertonic stress were reported [Wehner et al., J. Gen. Physiol. 105 (1995) 507-535; Wehner et al., Physiologist 40 (1997) A-4]. Moreover, all three ENaC subunits are expressed in these cells [B?hmer et al., Cell. Physiol. Biochem. 10 (2000) 187-194]. Here, we injected specific antisense oligonucleotides directed against alpha-rENaC into single rat hepatocytes in confluent primary culture and found an inhibition of hypertonicity-induced Na(+) currents by 70%. This is the first direct evidence for a role of the ENaC in cell volume regulation.     

Role of K(ATP)(+) channels and adenosine in the control of coronary blood flow during exercise.

The present study was designed to examine the role of ATP-sensitive potassium (K(ATP)(+)) channels during exercise and to test the hypothesis that adenosine increases to compensate for the loss of K(ATP)(+) channel function and adenosine inhibition produced by glibenclamide. Graded treadmill exercise was used to increase myocardial O(2) consumption in dogs before and during K(ATP)(+) channel blockade with glibenclamide (1 mg/kg iv), which also blocks adenosine mediated coronary vasodilation. Cardiac interstitial adenosine concentration was estimated from arterial and coronary venous values by using a previously tested mathematical model (Kroll K and Stepp DW. Am J Physiol Heart Circ Physiol 270: H1469-H1483, 1996). Coronary venous O(2) tension was used as an index of the balance between O(2) delivery and myocardial O(2) consumption. During control exercise, myocardial O(2) consumption increased approximately 4-fold, and coronary venous O(2) tension fell from 19 to 14 Torr. After K(ATP)(+) channel blockade, coronary venous O(2) tension was decreased below control vehicle values at rest and during exercise. However, during exercise with glibenclamide, the slope of the line of coronary venous O(2) tension vs. myocardial O(2) consumption was the same as during control exercise. Estimated interstitial adenosine concentration with glibenclamide was not different from control vehicle and was well below the level necessary to overcome the 10-fold shift in the adenosine dose-response curve due to glibenclamide. In conclusion, K(ATP)(+) channel blockade decreases the balance between resting coronary O(2) delivery and myocardial O(2) consumption, but K(ATP)(+) channels are not required for the increase in coronary blood flow during exercise. Furthermore, interstitial adenosine concentration does not increase to compensate for the loss of K(ATP)(+) channel function.     

Comparison of the effects of internal TEA+ and Cs+ on potassium current in squid giant axons.

Internal tetraethylammonium (TEA) and cesium ions block outward potassium current in nerve membrane in a voltage-dependent manner. Blockade with Cs+ occurs virtually instantaneously after membrane depolarization, whereas blockade with TEA+ occurs after a delay. The latter result suggested to Armstrong (1966, J. Gen. Physiol., 50:279-293; 1969, J. Gen. Physiol., 54:553-575) that potassium channels must open before TEA+ blockade can occur, which is in contrast to Cs+ blockade, which appears to be independent of channel gating. The results in this study concerning the effect of TEA+ on inward (tail) current argue against the Armstrong model. Specifically, TEA+ (partially) blocks inward current without altering the tail current time constant. This result indicates that TEA+ can occupy its binding site within the channel whether or not the channel gates are open. This alternative hypothesis can describe both the steady-state and time-dependent components of TEA+ blockade.     

Single voltage-dependent chloride-selective channels of large conductance in cultured rat muscle

Single-channel currents of an anion-selective channel in the plasma membrane of cultured rat muscle cells (myotubes) were recorded with the patch-clamp technique (Hamill, O.P., A. Marty, E. Neher, B. Sakmann, and F.J. Sigworth, 1981. Pfluegers Arch. Eur. J. Physiol., 391:85-100). The channel is selective for Cl- over cations, and has an unusually large single-channel conductance of approximately 430 pS in symmetrical 143 mM KCl. The channel is often active at 0 mV, opening and closing spontaneously. When active, steps from 0 mV to either negative or positive membrane potentials close the channel to an apparent inactivated state. The mean effective time that a channel is open before it inactivates is approximately 1.19 s for steps to -30 mV and 0.48 s for steps to +30 mV. Returning the membrane potential to 0 mV results in recovery from inactivation. Calcium ions are not required for channel activity.     

Simulation study of a gramicidin/lipid bilayer system in excess water and lipid. II. Rates and mechanisms of water transport

A gramicidin channel in a fluid phase DMPC bilayer with excess lipid and water has been simulated. By use of the formal correspondence between diffusion and random walk, a permeability for water through the channel was calculated, and was found to agree closely with the experimental results of Rosenberg and Finkelstein (Rosenberg, P.A., and A. Finkelstein. 1978. J. Gen. Physiol. 72:327-340; 341-350) for permeation of water through gramicidin in a phospholipid membrane. By using fluctuation analysis, components of resistance to permeation were computed for movement through the channel interior, for the transition step at the channel mouth where the water molecule solvation environment changes, and for the process of diffusion up to the channel mouth. The majority of the resistance to permeation appears to occur in the transition step at the channel mouth. A significant amount is also due to structurally based free energy barriers within the channel. Only small amounts are due to local friction within the channel or to diffusive resistance for approaching the channel mouth.     

Trapping of an open-channel blocker at the frog neuromuscular acetylcholine channel.

At the ganglionic nicotinic acetylcholine channel (Gurney, A. M., and H. P. Rang, 1984, Br. J. Pharmacol., 82:623-642) and on some cholinergic neuromuscular synapses of Crustacea (Lingle, C., 1983a, J. Physiol. (Lond.), 339:395-417; Lingle, C., 1983b, J. Physiol. (Lond.), 339:419-437), some agents that block cholinergic currents by an open-channel block mechanism appear to become trapped within the channel when it subsequently closes. It is unknown whether trapping of some open-channel blockers might also occur at the neuromuscular nicotinic acetylcholine channel. Here we show that the long-lived cholinergic blocking action of chlorisondamine, a ganglionic nicotinic blocker, can in part be most simply explained by an open-channel block mechanism followed by a subsequent trapping of the blocking molecule within the closed ion channel. Unique structural characteristics of the chlorisondamine molecule place several provocative constraints on the mechanism by which trapping may be occurring.     

Shaking stack model of ion conduction through the Ca(2+)-activated K+ channel.

Motivated by the results of Neyton and Miller (1988. J. Gen. Physiol. 92:549-586), suggesting that the Ca(2+)-activated K+ channel has four high affinity ion binding sites, we propose a physically attractive variant of the single-vacancy conduction mechanism for this channel. Simple analytical expressions for conductance, current, flux ratio exponent, and reversal potential under bi-ionic conditions are found. A set of conductance data are analyzed to determine a realistic range of parameter values. Using these, we find qualitative agreement with a variety of experimental results previously reported in the literature. The exquisite selectivity of the Ca(2+)-activated K+ channel may be explained as a consequence of the concerted motion of the "stack" in the proposed mechanism.     

High-pH form of bovine rhodopsin.

Since the 1930s, the spectrum of vertebrate rhodopsin has been considered to be independent of pH (Lythgoe, R.J. 1937. J. Physiol. 89:331-358; Wald, G. 1938. J. Gen. Physiol. 21:795-832). Here I report that the spectrum of bovine rhodopsin is pH dependent. At pHs greater than 9.0, there is a shift to shorter wavelengths of its 500-nm absorption band. This shift is accounted for by the existence of a high pH form of bovine rhodopsin, with absorption maximum at 494 nm and a slightly lower extinction coefficient. The high-pH form results from the low-pH form by the deprotonation of a single group with a pK of approximately 10.2 for rhodopsin in rod disk membranes in 4.0 M KCl. The shift is observed for sheep and chicken rhodopsins, but not for frog, toad, and octopus rhodopsins. This indicates a specific amino acid difference between these rhodopsins that is potentially relevant for the mechanism of color regulation.     

Multi-ion occupancy alters gating in high-conductance, Ca(2+)-activated K+ channels

In this study, single-channel recordings of high-conductance Ca(2+)-activated K+ channels from rat skeletal muscle inserted into planar lipid bilayer were used to analyze the effects of two ionic blockers, Ba2+ and Na+, on the channel's gating reactions. The gating equilibrium of the Ba(2+)-blocked channel was investigated through the kinetics of the discrete blockade induced by Ba2+ ions. Gating properties of Na(+)-blocked channels could be directly characterized due to the very high rates of Na+ blocking/unblocking reactions. While in the presence of K+ (5 mM) in the external solution Ba2+ is known to stabilize the open state of the blocked channel (Miller, C., R. Latorre, and I. Reisin. 1987. J. Gen. Physiol. 90:427-449), we show that the divalent blocker stabilizes the closed-blocked state if permeant ions are removed from the external solution (K+ less than 10 microM). Ionic substitutions in the outer solution induce changes in the gating equilibrium of the Ba(2+)-blocked channel that are tightly correlated to the inhibition of Ba2+ dissociation by external monovalent cations. In permeant ion-free external solutions, blockade of the channel by internal Na+ induces a shift (around 15 mV) in the open probability--voltage curve toward more depolarized potentials, indicating that Na+ induces a stabilization of the closed-blocked state, as does Ba2+ under the same conditions. A kinetic analysis of the Na(+)-blocked channel indicates that the closed-blocked state is favored mainly by a decrease in opening rate. Addition of 1 mM external K+ completely inhibits the shift in the activation curve without affecting the Na(+)-induced reduction in the apparent single-channel amplitude. The results suggest that in the absence of external permeant ions internal blockers regulate the permeant ion occupancy of a site near the outer end of the channel. Occupancy of this site appears to modulate gating primarily by speeding the rate of channel opening.     

Reversal of the gating polarity of gap junctions by negative charge substitutions in the N-terminus of connexin 32

Intercellular channels formed by connexins (gap junctions) are sensitive to the application of transjunctional voltage (V(j)), to which they gate by the separate actions of their serially arranged hemichannels (Harris, A. L., D. C. Spray, and M. V. L. Bennett. 1981. J. Gen. Physiol. 77:95-117). Single channel studies of both intercellular and conductive hemichannels have demonstrated the existence of two separate gating mechanisms, termed "V(j)-gating" and "loop gating" (Trexler, E. B., M. V. L. Bennett, T. A. Bargiello, and V. K. Verselis. 1996. Proc. Natl. Acad. Sci. U.S.A. 93:5836-5841). In Cx32 hemichannels, V(j)-gating occurs at negative V(j) (Oh, S., J. B. Rubin, M. V. L. Bennett, V. K. Verselis, and T. A. Bargiello. 1999. J. Gen. Physiol. 114:339-364; Oh, S., C. K. Abrams, V. K. Verselis, and T. A. Bargiello. 2000. J. Gen. Physiol. 116:13-31). A negative charge substitution at the second amino acid position in the N-terminus reverses the polarity of V(j)-gating of Cx32 hemichannels (Verselis, V. K., C. S. Ginter, and T. A. Bargiello. 1994. Nature. 368:348-351;. J. Gen. Physiol. 116:13-31). We report that placement of a negative charge at the 5th, 8th, 9th, or 10th position can reverse the polarity of Cx32 hemichannel V(j)-gating. We conclude that the 1st through 10th amino acid residues lie within the transjunctional electric field and within the channel pore, as in this position they could sense changes in V(j) and be largely insensitive to changes in absolute membrane potential (V(m)). Conductive hemichannels formed by Cx32*Cx43E1 containing a negatively charged residue at either the 8th or 10th position display bi-polar V(j)-gating; that is, the open probability of hemichannels formed by these connexins is reduced at both positive and negative potentials and is maximal at intermediate voltages. In contrast, Cx32*Cx43E1 hemichannels with negative charges at either the 2nd or 5th positions are uni-polar, closing only at positive V(j). The simplest interpretation of these data is that the Cx32 hemichannel can adopt at least two different open conformations. The 1st-5th residues are located within the electric field in all open channel conformations, while the 8th and 10th residues lie within the electric field in one conformation and outside the electric field in the other conformation.     

The interaction of a neutral ryanoid with the ryanodine receptor channel provides insights into the mechanisms by which ryanoid binding is modulated by voltage

In an earlier investigation, we demonstrated that the likelihood of interaction of a positively charged ryanoid, 21-amino-9alpha-hydroxyryanodine, with the sarcoplasmic reticulum Ca(2+)-release channel (ryanodine receptor, RyR) is dependent on holding potential (Tanna, B., W. Welch, L. Ruest, J.L. Sutko, and A. J. Williams. 1998. J. Gen. Physiol. 112:55-69) and suggested that voltage dependence could result from either the translocation of the charged ligand to a site within the voltage drop across the channel or a voltage-driven alteration in receptor affinity. We now report experiments that allow us to assess the validity of these alternate mechanisms. Ryanodol is a neutral ryanoid that binds to RyR and induces modification of channel function. By determining the influence of transmembrane potential on the probability of channel modification by ryanodol and the rate constants of ryanodol association and dissociation, we demonstrate that the influence of voltage is qualitatively the same for both the neutral and positively charged ryanoids. These experiments establish that most, if not all, of the modification of ryanoid interaction with RyR by transmembrane holding potential results from a voltage-driven alteration in receptor affinity.     

The mechanism of rectification of iK1 in canine Purkinje myocytes.

We have characterized the inward rectifying background potassium current, iK1, of canine cardiac Purkinje myocytes in terms of its reversal potential, voltage activation curve, and "steady-state" current-voltage relation. The latter parameter was defined from the difference current between holding currents in the presence and absence of 20 mM cesium. Our data suggest that iK1 rectification does not arise exclusively from voltage-dependent gating or exclusively from voltage-dependent blockade by internal magnesium ions. The voltage activation curve constructed from tail currents fit to a Boltzmann two-state model predicts less outward current than is actually observed. The magnesium-dependent rectification due to channel blockade is too fast to account for the time-dependent gating of iK1 that gives rise to the tail currents. We propose a new model of rectification that assumes that magnesium blockade of the channel occurs simultaneously with voltage-dependent gating. The new model incorporates the kinetic schema elaborated by Matsuda, H. (1988. J. Physiol. 397:237-258) to explain the appearance of subconducting states of the iK1 channel in the presence of blocking ions. That schema suggested that iK1 channels were composed of three parallel pores, each of which could be blocked independently. In our model we considered the consequences of partial blockade of the channel. If the channels are partially blocked at potentials where normally they are mostly gated closed, and if the partially blocked channels cannot close, then blockade will have the paradoxical result of enhancing the current carried by iK1.     

Permeation through an open channel: Poisson-Nernst-Planck theory of a synthetic ionic channel.

The synthetic channel [acetyl-(LeuSerSerLeuLeuSerLeu)3-CONH2]6 (pore diameter approximately 8 A, length approximately 30 A) is a bundle of six alpha-helices with blocked termini. This simple channel has complex properties, which are difficult to explain, even qualitatively, by traditional theories: its single-channel currents rectify in symmetrical solutions and its selectivity (defined by reversal potential) is a sensitive function of bathing solution. These complex properties can be fit quantitatively if the channel has fixed charge at its ends, forming a kind of macrodipole, bracketing a central charged region, and the shielding of the fixed charges is described by the Poisson-Nernst-Planck (PNP) equations. PNP fits current voltage relations measured in 15 solutions with an r.m.s. error of 3.6% using four adjustable parameters: the diffusion coefficients in the channel's pore DK = 2.1 x 10(-6) and DCl = 2.6 x 10(-7) cm2/s; and the fixed charge at the ends of the channel of +/- 0.12e (with unequal densities 0.71 M = 0.021e/A on the N-side and -1.9 M = -0.058e/A on the C-side). The fixed charge in the central region is 0.31e (with density P2 = 0.47 M = 0.014e/A). In contrast to traditional theories, PNP computes the electric field in the open channel from all of the charges in the system, by a rapid and accurate numerical procedure. In essence, PNP is a theory of the shielding of fixed (i.e., permanent) charge of the channel by mobile charge and by the ionic atmosphere in and near the channel's pore. The theory fits a wide range of data because the ionic contents and potential profile in the channel change significantly with experimental conditions, as they must, if the channel simultaneously satisfies the Poisson and Nernst-Planck equations and boundary conditions. Qualitatively speaking, the theory shows that small changes in the ionic atmosphere of the channel (i.e., shielding) make big changes in the potential profile and even bigger changes in flux, because potential is a sensitive function of charge and shielding, and flux is an exponential function of potential.     

Gating properties conferred on BK channels by the beta3b auxiliary subunit in the absence of its NH(2)- and COOH termini

Both beta1 and beta2 auxiliary subunits of the BK-type K(+) channel family profoundly regulate the apparent Ca(2)+ sensitivity of BK-type Ca(2)+-activated K(+) channels. Each produces a pronounced leftward shift in the voltage of half-activation (V(0.5)) at a given Ca(2)+ concentration, particularly at Ca(2)+ above 1 microM. In contrast, the rapidly inactivating beta3b auxiliary produces a leftward shift in activation at Ca(2)+ below 1 microM. In the companion work (Lingle, C.J., X.-H. Zeng, J.-P. Ding, and X.-M. Xia. 2001. J. Gen. Physiol. 117:583-605, this issue), we have shown that some of the apparent beta3b-mediated shift in activation at low Ca(2)+ arises from rapid unblocking of inactivated channels, unlike the actions of the beta1 and beta2 subunits. Here, we compare effects of the beta3b subunit that arise from inactivation, per se, versus those that may arise from other functional effects of the subunit. In particular, we examine gating properties of the beta3b subunit and compare it to beta3b constructs lacking either the NH(2)- or COOH terminus or both. The results demonstrate that, although the NH(2) terminus appears to be the primary determinant of the beta3b-mediated shift in V(0.5) at low Ca(2)+, removal of the NH(2) terminus reveals two other interesting aspects of the action of the beta3b subunit. First, the conductance-voltage curves for activation of channels containing the beta3b subunit are best described by a double Boltzmann shape, which is proposed to arise from two independent voltage-dependent activation steps. Second, the presence of the beta3b subunit results in channels that exhibit an anomalous instantaneous outward current rectification that is correlated with a voltage dependence in the time-averaged single-channel current. The two effects appear to be unrelated, but indicative of the variety of ways that interactions between beta and alpha subunits can affect BK channel function. The COOH terminus of the beta3b subunit produces no discernible functional effects.     

Autophagy: The missing link between non-enzymatically glycated proteins inducing apoptosis and premature senescence of endothelial cells?

In a series of studies into the fate of endothelial cells exposed to non-enzymatically glycated collagen I, a model of cytotoxic molecules relevant to diabetic vasculopathy, we demonstrate that cells either undergo apoptosis or become prematurely senescent despite relatively spared telomeres and telomerase activity. Our most recent work shows that long-lived advanced glycation end product (AGE)-modified proteins induce 1) lysosomal permeabilization leading to the inefficiency of autophagy due to the reduced digestion (early) and non-fusion (later) of lysosomes with phagosomes—a frustrated autophagy; and 2) accumulation of lipid mediators, such as ceramide and sphingosine-1-phosphate, known to be involved in autophagic cell death. Under the experimental conditions described here, the seesaw relations between premature senescence and apoptosis are integrated by autophagy, which plays a novel function of a cellular switch between states of premature senescence and apoptosis.

Addendum to: Patschan SA, Chen J, Polotskaia A, Mendelev N, Cheng J, Patschan D, Goligorsky MS. Lipid mediators of autophagy in stress-induced premature senescence of endothelial cells. Am J Physiol Heart Circ Physiol 2008; In press.

and

Patschan S, Chen J, Gealekman O, Krupincza K, Wang M, Shu L, Shayman JA, Goligorsky MS. Mapping mechanisms and charting the time course of premature cell senescence and apoptosis: lysosomal dysfunction and ganglioside accumulation in endothelial cells. Am J Physiol Renal Physiol 2008; 294:F100-9.     

A mathematical model of cardiocyte Ca(2+) dynamics with a novel representation of sarcoplasmic reticular Ca(2+) control

Cardiac contraction and relaxation dynamics result from a set of simultaneously interacting Ca(2+) regulatory mechanisms. In this study, cardiocyte Ca(2+) dynamics were modeled using a set of six differential equations that were based on theories, equations, and parameters described in previous studies. Among the unique features of the model was the inclusion of bidirectional modulatory interplay between the sarcoplasmic reticular Ca(2+) release channel (SRRC) and calsequestrin (CSQ) in the SR lumen, where CSQ acted as a dynamic rather than simple Ca(2+) buffer, and acted as a Ca(2+) sensor in the SR lumen as well. The inclusion of this control mechanism was central in overcoming a number of assumptions that would otherwise have to be made about SRRC kinetics, SR Ca(2+) release rates, and SR Ca(2+) release termination when the SR lumen is assumed to act as a simple, buffered Ca(2+) sink. The model was sufficient to reproduce a graded Ca(2+)-induced Ca(2+) release (CICR) response, CICR with high gain, and a system with reasonable stability. As constructed, the model successfully replicated the results of several previously published experiments that dealt with the Ca(2+) dependence of the SRRC (, J. Gen. Physiol. 85:247-289), the refractoriness of the SRRC (, Am. J. Physiol. 270:C148-C159), the SR Ca(2+) load dependence of SR Ca(2+) release (, Am. J. Physiol. 268:C1313-C1329;, J. Biol. Chem. 267:20850-20856), SR Ca(2+) leak (, J. Physiol. (Lond.). 474:463-471;, Biophys. J. 68:2015-2022), SR Ca(2+) load regulation by leak and uptake (, J. Gen. Physiol. 111:491-504), the effect of Ca(2+) trigger duration on SR Ca(2+) release (, Am. J. Physiol. 258:C944-C954), the apparent relationship that exists between sarcoplasmic and sarcoplasmic reticular calcium concentrations (, Biophys. J. 73:1524-1531), and a variety of contraction frequency-dependent alterations in sarcoplasmic [Ca(2+)] dynamics that are normally observed in the laboratory, including rest potentiation, a negative frequency-[Ca(2+)] relationship, and extrasystolic potentiation. Furthermore, under the condition of a simulated Ca(2+) overload, an alternans-like state was produced. In summary, the current model of cardiocyte Ca(2+) dynamics provides an integrated theoretical framework of fundamental cellular Ca(2+) regulatory processes that is sufficient to predict a broad array of observable experimental outcomes.     

Axonal excitability revisited

The original papers of Hodgkin and Huxley (J. Physiol. 116 (1952a) 449, J. Physiol. 116 (1952b) 473, J. Physiol. 116 (1952c) 497, J. Physiol. 117 (1952d) 500) have provided a benchmark in our understanding of cellular excitability. Not surprisingly, their model of the membrane action potential (AP) requires revisions even for the squid giant axon, the preparation for which it was originally formulated. The mechanisms they proposed for the voltage-gated potassium and sodium ion currents, IK, and INa, respectively, have been superceded by more recent formulations that more accurately describe voltage-clamp measurements of these components. Moreover, the current-voltage relation for IK has a non-linear dependence upon driving force that is well described by the Goldman-Hodgkin-Katz (GHK) relation, rather than the linear dependence on driving force found by Hodgkin and Huxley. Furthermore, accumulation of potassium ions in the extracellular space adjacent to the axolemma appears to be significant even during a single AP. This paper describes the influence of these various modifications in their model on the mathematically reconstructed AP. The GHK and K+ accumulation results alter the shape of the AP, whereas the modifications in IK and INa gating have surprisingly little effect. Perhaps the most significant change in their model concerns the amplitude of INa, which they appear to have overestimated by a factor of two. This modification together with the GHK and the K+ accumulation results largely remove the discrepancies between membrane excitability of the squid giant axon and the Hodgkin and Huxley (J. Physiol. 117 (1952d) 500) model previously described (Clay, J. Neurophysiol. 80 (1998) 903).