Computer simulation of synchronization of Na/K pump molecules

The behavior of Na/K pump currents when exposed to an oscillating electric field is studied by computer simulation. The pump current from a single pump molecule was sketched based on previous experimental results. The oscillating electric field is designed as a symmetric, dichotomous waveform varying the membrane potential from −30 to −150 mV around the membrane resting potential of −90 mV. Based on experimental results from skeletal muscle fibers, the energy needed to overcome the electrochemical potentials for the Na and K-transports are calculated in response to the field’s two half-cycles. We found that a specially designed oscillating electric field can eventually synchronize the pump molecules so that all the individual pumps run at the same pumping rate and phase as the field oscillation. They extrude Na ions during the positive half-cycle and pump in K ions during the negative half-cycle. The field can force the two ion-transports into the corresponding half-cycles, respectively, but cannot determine their detailed positions. In other words, the oscillating electric field can synchronize pumps in terms of their pumping loops but not at a specific step in the loop. These results are consistent with our experimental results in measurement of the pump currents.     

Extracellular pH modulates kinetics of the Na(+),K(+)-ATPase

To investigate effects of pH on the Na(+),K(+)-ATPase, we used the Xenopus oocytes to measure transient charge movements in the absence of extracellular K(+), and steady-state currents mediated by the pump as well as ATPase activity. The activity of purified Na(+), K(+)-ATPase strongly depends on pH, which has been attributed to protonation of intracellular sites. The steady-state current reflects pump activity, the transient charge movement voltage-dependent interaction of external Na(+) ions with the pump molecule and/or conformational changes during Na(+)/Na(+) exchange. The steady-state current exhibits a characteristic voltage dependence with maximum at about 0 mV at low external K(+) (< or =2 mM) and with 50 Na(+). This dependency is not significantly affected by changes in external pH in the range from pH 9 to pH 6. Only below pH 6, the voltage dependence of pump current becomes less steep, and may be attributed to a pH-dependent inhibition of the forward pump cycle by external Na(+). External stimulation of the pump by K(+) in the absence of Na(+) can be described by a voltage-dependent K(m) value with an apparent valency z(K). At higher external pH the z(K) value is reduced. The transient current signal in the absence of external K(+) can be described by the sum of three exponentials with voltage-dependent time constants of about 50 ms, 700 micros and less than 100 micros during pulses to 0 mV. The charge distribution was calculated by integration of the transient current signals. The slowest component and the associated charge distributions do not significantly depend on external pH changes. The intermediate component of the transients is represented by a voltage-dependent rate constant which shows a minimum at about -120 mV and increases with decreasing pH. Nevertheless, the contribution to the charge movement is not altered by pH changes due to a simultaneous increase of the amplitude of this component. We conclude that reduction of external pH counteracts external K(+) and Na(+) binding.     

The sodium pump modulates the influence of I(Na) on [Ca2+]i transients in mouse ventricular myocytes

To investigate whether activity of the sarcolemmal Na pump modulates the influence of sodium current on excitation-contraction (E-C) coupling, we measured [Ca(2+)](i) transients (fluo-3) in single voltage-clamped mouse ventricular myocytes ([Na+](pip) = 15 or 0 mM) when the Na pump was activated (4.4 mM K(+)(o)) and during abrupt inhibition of the pump by exposure to 0 K with a rapid solution-switcher device. After induction of steady state [Ca2+](i) transients by conditioning voltage pulses (0.25 Hz), inhibition of the Na pump for 1.5 s immediately before and continuing during a voltage pulse (200 ms, -80 to 0 mV) caused a significant increase (15 +/- 2%; n = 16; p < 0.01) in peak systolic [Ca2+](i) when [Na+](pip) was 15 mM. In the absence of sodium current (I(Na), which was blocked by 60 microM tetrodotoxin (TTX)), inhibition of the Na pump immediately before and during a voltage pulse did not result in an increase in peak systolic [Ca2+](i). Abrupt blockade of I(Na) during a single test pulse with TTX caused a slight decrease in peak [Ca2+](i), whether the pump was active (9%) or inhibited (10%). With the reverse-mode Na/Ca exchange inhibited by KB-R 7943, inhibition of the Na pump failed to increase the magnitude of the peak systolic [Ca2+](i) (4 +/- 1%; p = NS) when [Na+](pip) was 15 mM. When [Na+](pip) was 0 mM, the amplitude of the peak systolic [Ca2+](i) was not altered by abrupt inhibition of the Na pump immediately before and during a voltage pulse. These findings in adult mouse ventricular myocytes indicate the Na pump can modulate the influence of I(Na) on E-C coupling in a single beat and provide additional evidence for the existence of Na fuzzy space, where [Na+] can significantly modulate Ca2+ influx via reverse Na/Ca exchange.     

The effects of sodium pump activity on the slow inward current in sheep cardiac Purkinje fibres

The effects of Na pump activity on the slow inward current, Isi, magnitude and twitch tension were investigated in sheep cardiac Purkinje fibres. A two-microelectrode voltage-clamp method was used, tension being measured simultaneously. Na pump activity was lowered either by reducing the extracellular K concentration, [K]O, or by applying the cardiotonic steroid strophanthidin. Reduction of [K]O from 4 to 0 mM leads to time-dependent increases in Isi magnitude and twitch tension. The increases of Isi and tension could be reversed by adding Tl, Rb, Cs or NH4 ions to the K-free superfusate. The actions of these ions are attributed to the known ability of these cations to activate the external site of the Na pump. This conclusion is supported by the observation that such activator cations do not reverse the increases in Isi and tension produced by strophanthidin. We conclude that the effects of low [K]O on Isi are mediated by Na pump inhibition. Similarly the Na pump inhibition produced by strophanthidin increases Isi and tension, although, in this case, other mechanisms may also contribute. Measurements of the activity of the electrogenic Na pump show that elevated intracellular Na ion concentration secondary to Na pump inhibition and not the instantaneous Na pump turnover rate mediates the increase in Isi magnitude.     

Ionic permeation and blockade in Ca2+-activated K+ channels of bovine chromaffin cells

Single channel currents through Ca2+-activated K+ channels of bovine chromaffin cells were measured to determine the effects of small ions on permeation through the channel. The channel selects strongly for K+ over Na+ and Cs+, and Rb+ carries a smaller current through the channel than K+. Tetraethylammonium ion (TEA+) blocks channel currents when applied to either side of the membrane; it is effective at lower concentrations when applied externally. Millimolar concentrations of internal Na+ reduce the average current through the channel and produce large fluctuations (flicker) in the open channel currents. This flickery block is analyzed by a new method, amplitude distribution analysis, which can measure block and unblock rates in the microsecond time range even though individual blocking events are not time-resolved by the recording system. The analysis shows that the rate of block by Na+ is very voltage dependent, but the unblock rate is voltage independent. These results can be explained easily by supposing that current flow through the channel is diffusion limited, a hypothesis consistent with the large magnitude of the single channel current.     

Steady-state current-voltage relationship of the Na/K pump in guinea pig ventricular myocytes

Whole-cell currents were recorded in guinea pig ventricular myocytes at approximately 36 degrees C before, during, and after exposure to maximally effective concentrations of strophanthidin, a cardiotonic steroid and specific inhibitor of the Na/K pump. Wide-tipped pipettes, in combination with a device for exchanging the solution inside the pipette, afforded reasonable control of the ionic composition of the intracellular solution and of the membrane potential. Internal and external solutions were designed to minimize channel currents and Na/Ca exchange current while sustaining vigorous forward Na/K transport, monitored as strophanthidin-sensitive current. 100-ms voltage pulses from the -40 mV holding potential were used to determine steady-state levels of membrane current between -140 and +60 mV. Control experiments demonstrated that if the Na/K pump cycle were first arrested, e.g., by withdrawal of external K, or of both internal and external Na, then neither strophanthidin nor its vehicle, dimethylsulfoxide, had any discernible effect on steady-state membrane current. Further controls showed that, with the Na/K pump inhibited by strophanthidin, membrane current was insensitive to changes of external [K] between 5.4 and 0 mM and was little altered by changing the pipette [Na] from 0 to 50 mM. Strophanthidin-sensitive current therefore closely approximated Na/K pump current, and was virtually free of contamination by current components altered by the changes in extracellular [K] and intracellular [Na] expected to accompany pump inhibition. The steady-state Na/K pump current-voltage (I-V) relationship, with the pump strongly activated by 5.4 mM external K and 50 mM internal Na (and 10 mM ATP), was sigmoid in shape with a steep positive slope between about 0 and -100 mV, a less steep slope at more negative potentials, and an extremely shallow slope at positive potentials; no region of negative slope was found. That shape of I-V relationship can be generated by a two-state cycle with one pair of voltage-sensitive rate constants and one pair of voltage-insensitive rate constants: such a two-state scheme is a valid steady-state representation of a multi-state cycle that includes only a single voltage-sensitive step.     

Two modes of gating during late Na+ channel currents in frog sartorius muscle

Na+ currents were measured during 0.4-s depolarizing pulses using the cell-attached variation of the patch-clamp technique. Patches on Cs-dialyzed segments of sartorius muscle of Rana pipiens contained an estimated 25-500 Na+ channels. Three distinct types of current were observed after the pulse onset: a large initial surge of inward current that decayed within 10 ms (early currents), a steady "drizzle" of isolated, brief, inward unitary currents (background currents), and occasional "cloudbursts" of tens to hundreds of sequential unitary inward currents (bursts). Average late currents (background plus bursts) were 0.12% of peak early current amplitude at -20 mV. 85% of the late currents were carried by bursting channels. The unit current amplitude was the same for all three types of current, with a conductance of 10.5 pS and a reversal potential of +74 mV. The magnitudes of the three current components were correlated from patch to patch, and all were eliminated by slow inactivation. We conclude that all three components were due to Na+ channel activity. The mean open time of the background currents was approximately 0.25 ms, and the channels averaged 1.2 openings for each event. Neither the open time nor the number of openings of background currents was strongly sensitive to membrane potential. We estimated that background openings occurred at a rate of 0.25 Hz for each channel. Bursts occurred once each 2,000 pulses for each channel (assuming identical channels). The open time during bursts increased with depolarization to 1-2 ms at -20 mV, whereas the closed time decreased to less than 20 ms. The fractional open time during bursts was fitted with m infinity 3 using standard Na+ channel models. We conclude that background currents are caused by a return of normal Na+ channels from inactivation, while bursts are instances where the channel's inactivation gate spontaneously loses its function for prolonged periods.     

The two C-terminal tyrosines stabilize occluded Na/K pump conformations containing Na or K ions

Interactions of the three transported Na ions with the Na/K pump remain incompletely understood. Na/K pump crystal structures show that the extended C terminus of the Na,K–adenosine triphosphatase (ATPase) α subunit directly contacts transmembrane helices. Deletion of the last five residues (KETYY in almost all Na/K pumps) markedly lowered the apparent affinity for Na activation of pump phosphorylation from ATP, a reflection of cytoplasmic Na affinity for forming the occluded E1P(Na3) conformation. ATPase assays further suggested that C-terminal truncations also interfere with low affinity Na interactions, which are attributable to extracellular effects. Because extracellular Na ions traverse part of the membrane’s electric field to reach their binding sites in the Na/K pump, their movements generate currents that can be monitored with high resolution. We report here electrical measurements to examine how Na/K pump interactions with extracellular Na ions are influenced by C-terminal truncations. We deleted the last two (YY) or five (KESYY) residues in Xenopus laevis α1 Na/K pumps made ouabain resistant by either of two kinds of point mutations and measured their currents as 10-mM ouabain–sensitive currents in Xenopus oocytes after silencing endogenous Xenopus Na/K pumps with 1 µM ouabain. We found the low affinity inhibitory influence of extracellular Na on outward Na/K pump current at negative voltages to be impaired in all of the C-terminally truncated pumps. Correspondingly, voltage jump–induced transient charge movements that reflect pump interactions with extracellular Na ions were strongly shifted to more negative potentials; this signals a several-fold reduction of the apparent affinity for extracellular Na in the truncated pumps. Parallel lowering of Na affinity on both sides of the membrane argues that the C-terminal contacts provide important stabilization of the occluded E1P(Na3) conformation, regardless of the route of Na ion entry into the binding pocket. Gating measurements of palytoxin-opened Na/K pump channels additionally imply that the C-terminal contacts also help stabilize pump conformations with occluded K ions.     

Rate of opening of a population of Na channels in frog skeletal muscle fibers

Linear Systems convolution analysis of muscle sodium currents was used to predict the opening rate of sodium channels as a function of time during voltage clamp pulses. If open sodium channel lifetimes are exponentially distributed, the channel opening rate corresponding to a sodium current obtained at any particular voltage, can be analytically obtained using a simple equation, given single channel information about the mean open-channel lifetime and current.Predictions of channel opening rate during voltage clamp pulses show that sodium channel inactivation arises coincident with a decline in channel opening rate.Sodium currents pharmacologically modified with Chloramine-T treatment so that they do not inactivate, show a predicted sustained channel opening rate.Large depolarizing voltage clamp pulses produce channel opening rate functions that resemble gating currents.The predicted channel opening rate functions are best described by kinetic models for Na channels which confer most of the charge movement to transitions between closed states.Comparisons of channel opening rate functions with gating currents suggests that there may be subtypes of Na channel with some contributing more charge movement per channel opening than others.Na channels open on average, only once during the transient period of Na activation and inactivation.After transiently opening during the activation period and then closing by entering the inactivated state, Na channels reopen if the voltage pulse is long enough and contribute to steady-state currents.The convolution model overestimates the opening rate of channels contributing to the steady-state currents that remain after the transient early Na current has subsided.     

Voltage dependence of Na/K pump current inXenopus oocytes

Summary Stage V and VI (Dumont, J.N., 1972.J. Morphol. 136:153–180) oocytes ofXenopus laevis were treated with collagenase to remove follicular cells and were placed in K-free solution for 2 to 4 days to elevate internal [Na]. Na/K pump activity was studied by restoring the eggs to normal 3mm K Barth's solution and measuring membrane current-voltage (I–V) relationships before and after the addition of 10 m dihydroouabain (DHO) using a two-microelectrode voltage clamp. Two pulse protocols were used to measure membraneI–V relationships, both allowing membrane currents to be determined twice at each of a series of membrane potentials: (i) a down-up-down sequence of 5 mV, 1-sec stair steps and (ii) a similar sequence of 1-sec voltage pulses but with consecutive pulses separated by 4-sec recovery periods at the holding potential (–40 mV). The resulting membraneI–V relationships determined both before and during exposure to DHO showed significant hysteresis between the first and second current measurements at each voltage. DHO difference curves also usually showed hysteresis indicating that DHO caused a change in a component of current that varied with time. Since, by definition, the steady-state Na/K pumpI–V relationship must be free of hysteresis, the presence of hysteresis in DHO differenceI–V curves can be used as a criterion for excluding such data from consideration as a valid measure of the Na/K pumpI–V relationship. DHO differenceI–V relationships that did not show hysteresis were sigmoid functions of membrane potential when measured in normal (90mm) external Na solution. The Na/K pump current magnitude saturated near 0 mV at a value of 1.0–1.5 A cm^–2, without evidence of negative slope conductance for potentials up to +55 mV. The Na/K pump current magnitude in Na-free external solution was approximately voltage independent. Since these forward-going Na/K pumpI–V relationships do not show a region of negative slope over the voltage range –110 to +55 mV, it is not necessary to postulate the existence of more than one voltage-dependent step in the reaction cycle of the forward-going Na/K pump.     

Review. Peering into an ATPase ion pump with single-channel recordings

In principle, an ion channel needs no more than a single gate, but a pump requires at least two gates that open and close alternately to allow ion access from only one side of the membrane at a time. In the Na+,K+-ATPase pump, this alternating gating effects outward transport of three Na+ ions and inward transport of two K+ ions, for each ATP hydrolysed, up to a hundred times per second, generating a measurable current if assayed in millions of pumps. Under these assay conditions, voltage jumps elicit brief charge movements, consistent with displacement of ions along the ion pathway while one gate is open but the other closed. Binding of the marine toxin, palytoxin, to the Na+,K+-ATPase uncouples the two gates, so that although each gate still responds to its physiological ligand they are no longer constrained to open and close alternately, and the Na+,K+-ATPase is transformed into a gated cation channel. Millions of Na+ or K+ ions per second flow through such an open pump-channel, permitting assay of single molecules and allowing unprecedented access to the ion transport pathway through the Na+,K+-ATPase. Use of variously charged small hydrophilic thiol-specific reagents to probe cysteine targets introduced throughout the pump's transmembrane segments allows mapping and characterization of the route traversed by transported ions.     

Slow currents through single sodium channels of the adult rat heart

The currents through single Na+ channels from the sarcolemma of ventricular cells dissociated from adult rat hearts were studied using the patch-clamp technique. All patches had several Na+ channels; most had 5-10, while some had up to 50 channels. At 10 degrees C, the conductance of the channel was 9.8 pS. The mean current for sets of many identical pulses inactivated exponentially with a time constant of 1.7 +/- 0.6 ms at -40 mV. Careful examination of the mean currents revealed a small, slow component of inactivation at pulse potentials ranging from -60 to -30 mV. The time constant of the slow component was between 8 and 14 ms. The channels that caused the slow component had the same conductance and reversal potential as the fast Na+ currents and were blocked by tetrodotoxin. The slow currents appear to have been caused by repeated openings of one or more channels. The holding potential influenced the frequency with which such channel reopening occurred. The slow component was prominent during pulses from a holding potential of -100 mV, while it was very small during pulses from -140 mV. Ultraslow currents through the Na+ channel were observed occasionally in patches that had large numbers of channels. They consisted of bursts of 10 or more sequential openings of a single channel and lasted for up to 150 ms. We conclude that the single channel data cannot be explained by standard models, even those that have two inactivated states or two open states of the channel. Our results suggest that Na+ channels can function in several different "modes," each with a different inactivation rate.     

Use-dependent block of sodium channels in frog myelinated nerve by tetrodotoxin and saxitoxin at negative holding potentials

Na+ currents were measured in myelinated frog nerve fibres in the presence of nanomolar concentrations of tetrodotoxin (TTX) or saxitoxin (STX) in the extracellular solution. The Na+ currents declined during a train of depolarizing pulses if the fibre was held at hyperpolarizing potentials between the pulses. At a pulse frequency of 0.8 Hz, the peak Na+ currents were reduced to 70 or 60% of the initial value in 9.3 nM TTX and 3.5 nM STX solutions, respectively. A decline of Na+ currents was also observed in two-pulse experiments. The peak Na+ current during a second test pulse did not depend on the duration (0.2 to 12 ms) of the first pulse. It decreased with increasing interval between the pulses, reached a minimum and increased again. The results are interpreted with a use-dependent blockage of Na+ channels by TTX or STX at negative holding potentials. The effects were described quantitatively, assuming a fast affinity increase of toxin receptors at Na+ channels triggered by Na+ activation followed by slow toxin binding to channels and relaxation of the receptor affinity.     

Na/K pump current in aggregates of cultured chick cardiac myocytes

Spontaneously beating aggregates of cultured embryonic chick cardiac myocytes, maintained at 37 degrees C, were voltage clamped using a single microelectrode switching clamp to measure the current generated by the Na/K pump (Ip). In resting, steady-state preparations an ouabain-sensitive current of 0.46 +/- 0.03 microA/cm2 (n = 22) was identified. This current was not affected by 1 mM Ba, which was used to reduce inward rectifier current (IK1) and linearize the current-voltage relationship. When K-free solution was used to block Ip, subsequent addition of Ko reactivated the Na/K pump, generating an outward reactivation current that was also ouabain sensitive. The reactivation current magnitude was a saturating function of Ko with a Hill coefficient of 1.7 and K0.5 of 1.9 mM in the presence of 144 mM Nao. The reactivation current was increased in magnitude when Nai was increased by lengthening the period of time that the preparation was exposed to K-free solution prior to reactivation. When Nai was raised by 3 microM monensin, steady-state Ip was increased more than threefold above the resting value to 1.74 +/- 0.09 microA/cm2 (n = 11). From these measurements and other published data we calculate that in a resting myocyte: (a) the steady-state Ip should hyperpolarize the membrane by 6.5 mV, (b) the turnover rate of the Na/K pump is 29 s-1, and (c) the Na influx is 14.3 pmol/cm2.s. We conclude that in cultured embryonic chick cardiac myocytes, the Na/K pump generates a measurable current which, under certain conditions, can be isolated from other membrane currents and has properties similar to those reported for adult cardiac cells.     

Altered ion channel conductance and ionic selectivity induced by large imposed membrane potential pulse.

The effects of large magnitude transmembrane potential pulses on voltage-gated Na and K channel behavior in frog skeletal muscle membrane were studied using a modified double vaseline-gap voltage clamp. The effects of electroconformational damage to ionic channels were separated from damage to lipid bilayer (electroporation). A 4 ms transmembrane potential pulse of -600 mV resulted in a reduction of both Na and K channel conductivities. The supraphysiologic pulses also reduced ionic selectivity of the K channels against Na+ ions, resulting in a depolarization of the membrane resting potential. However, TTX and TEA binding effects were unaltered. The kinetics of spontaneous reversal of the electroconformational damage of channel proteins was found to be dependent on the magnitude of imposed membrane potential pulse. These results suggest that muscle and nerve dysfunction after electrical shock may be in part caused by electroconformational damage to voltage-gated ion channels.     

Androgen modulates the kinetics of the delayed rectifying K+ current in the electric organ of a weakly electric fish

Weakly electric fish such as Sternopygus macrurus utilize a unique signal production system, the electric organ (EO), to navigate within their environment and to communicate with conspecifics. The electric organ discharge (EOD) generated by the Sternopygus electric organ is quasi-sinusoidal and sexually dimorphic; sexually mature males produce long duration EOD pulses at low frequencies, whereas mature females produce short duration EOD pulses at high frequencies. EOD frequency is set by a medullary pacemaker nucleus, while EOD pulse duration is determined by the kinetics of Na+ and K+ currents in the electric organ. The inactivation of the Na+ current and the activation of the delayed rectifying K+ current of the electric organ covary with EOD frequency such that the kinetics of both currents are faster in fish with high (female) EOD frequency than those with low (male) EOD frequencies. Dihydrotestosterone (DHT) implants masculinize the EOD centrally by decreasing frequency at the pacemaker nucleus (PMN). DHT also acts at the electric organ, broadening the EO pulse, which is at least partly due to a slowing of the inactivation kinetics of the Na+ current. Here, we show that chronic DHT treatment also slows the activation and deactivation kinetics of the electric organ's delayed rectifying K+ current. Thus, androgens coregulate the time-varying kinetics of two distinct ion currents in the EO to shape a sexually dimorphic communication signal.     

Properties of "creep currents" in single frog atrial cells

Changes in membrane current in response to an elevation of [Na]i were studied in enzymatically dispersed frog atrial cells. Na loading by either intracellular dialysis or exposure to the Na ionophore monensin produces changes in membrane current that resemble the "creep currents" originally observed in cardiac Purkinje fibers during exposure to low-K solutions. Na loading induces a transient outward current during depolarizing voltage-clamp pulses, followed by an inward current in response to repolarization back to the holding potential. In contrast to cardiac Purkinje fibers, Na loading of frog atrial cells induces creep currents without accompanying transient inward currents. Creep currents induced by Na loading are insensitive to K channel antagonists like Cs and 4-aminopyridine; they are not influenced by doses of Ca channel antagonists that abolish iCa, but are sensitive to changes in [Ca]o or [Na]o. A comparison of the time course of development of inward creep currents are not tail currents associated with iCa. Inward creep currents can also be induced by experimental interventions that increase the iCa amplitude. Exposure to isoproterenol enhances the iCa amplitude and induces inward creep currents; both can be attenuated by Ca channel antagonists. Both inward and outward creep currents are blocked by low doses of La, independently of La's ability to block iCa. It is concluded that (a) creep currents are not mediated by voltage-gated Na, Ca, or K channels or by an electrogenic Na,K pump; (b) inward creep currents induced either by Na loading or in response to an increase in the amplitude of iCa are triggered by an elevation of [Ca]i; and (c) creep currents may be generated by either an electrogenic Na/Ca exchange mechanism or by a nonselective cation channel activated by [Ca]i.     

A model study of the contribution of active Na-K transport to membrane repolarization in cardiac cells

A biochemical model of active Na-K transport in cardiac cells was studied in conjunction with a representation of the passive membrane currents and ion concentration changes. The active transport model is based on the thermodynamic and kinetic properties of a six-step reaction scheme for the Na,K-ATPase. It has a fixed Na:K stoechiometry of 3:2, and its activation is governed by three parameters: membrane potential intracellular Na+ concentration, and interstitial K+ concentration. The Na-K pump current is directly proportional to the density of Na,K-ATPase molecules. The passive membrane currents and ion concentration changes involve only Na+ and K+ ions, and no attempt was made to provide a precise representation of Ca2+ currents or Ca2+ concentration changes. The surface-to-volume ratio of the interstitial compartment is 55 times larger than that of the intracellular compartment. The flux balance conditions are such that the original equilibrium concentration values are re-established at each stimulation cycle. The underlying assumptions of the model were checked against experimental measurements on Na-K pump activity in a variety of preparations. In addition, the qualitative validation of the model was carried out by comparing its behavior following sudden frequency shifts to corresponding experimental observations. The overall behavior of the model is quite satisfactory and it is used to provide the following indications: (1) when the intracellular and interstitial volumes are relatively large, the ion concentration transients are small and the pumping rate depends essentially on average concentration levels. (2) An increase in internal Na+ concentration potentiates the response of the Na-K pump to rapid membrane depolarizations. (3) When the internal Na+ concentration is large enough, the Na-K pump current transient plays an important role in shaping the plateau and repolarization phase of the action potential. (4) A rapid increase in external K+ concentration during voltage clamp in multicellular preparations could saturate the Na-K pump response and lead to a fairly linear dependence of the pump activity on the internal Na+ concentration.     

Entrainment of Na/K pumps by a synchronization modulation electric field

We studied entrainment of the catalytic cycle of the Na/K pumps by an imposed external AC electric field. Our results show that a well designed dichotomous oscillating electric field with a frequency close to the pumps’ natural turnover rate can synchronize the pump molecules. Characteristics of the synchronized pumps include: (1) outward pump currents responding to Na-extrusion and inward pump currents responding to K-pumping in are separated; (2) magnitude of the outward pump currents can be up to three times higher than that of the randomly paced pump currents; (3) magnitude ratio of the outward over inward pump currents reveals the 3:2 stoichiometry of the pumps. We, further, gradually increased the field oscillating frequency in a stepwise pattern and kept pump synchronization in each step. We found that the pumps’ turnover rate could be modulated up as the field frequency increased. Consequently, the pump currents significantly increased by many fold. In summary, these results show that the catalytic cycle of Na/K pumps can be synchronized and modulated by a well designed oscillating electric field resulting in activation of the pump functions.     

Irreversible block of cardiac mutant Na+ channels by batrachotoxin

Batrachotoxin (BTX) not only keeps the voltage-gated Na(+) channel open persistently but also reduces its single-channel conductance. Although a BTX receptor has been delimited within the inner cavity of Na(+) channels, how Na(+) ions flow through the BTX-bound permeation pathway remains unclear. In this report we tested a hypothesis that Na(+) ions traverse a narrow gap between bound BTX and residue N927 at D2S6 of cardiac hNa(v)1.5 Na(+) channels. We found that BTX at 5 microM indeed elicited a strong block of hNa(v)1.5-N927K currents (approximately 70%) after 1000 repetitive pulses (+50 mV/20 ms at 2 Hz) without any effects on Na(+) channel gating. Once occurred, this unique use-dependent block of hNa(v)1.5-N927K Na(+) channels recovered little at holding potential (-140 mV), demonstrating that BTX block is irreversible under our experimental conditions. Such an irreversible effect likewise developed in fast inactivation-deficient hNa(v)1.5-N927K Na(+) channels albeit with a faster on-rate; approximately 90% of peak Na(+) currents were abolished by BTX after 200 repetitive pulses (+50 mV/20 ms). This use-dependent block of fast inactivation-deficient hNa(v)1.5-N927K Na(+) channels by BTX was duration dependent. The longer the pulse duration the larger the block developed. Among N927K/W/R/H/D/S/Q/G/E substitutions in fast inactivation-deficient hNa(v)1.5 Na(+) channels, only N927K/R Na(+) currents were highly sensitive to BTX block. We conclude that (a) BTX binds within the inner cavity and partly occludes the permeation pathway and (b) residue hNa(v)1.5-N927 is critical for ion permeation between bound BTX and D2S6, probably because the side-chain of N927 helps coordinate permeating Na(+) ions.