Regulation of Ion Gradients across Myocardial Ischemic Border Zones: A Biophysical Modelling Analysis

The myocardial ischemic border zone is associated with the initiation and sustenance of arrhythmias. The profile of ionic concentrations across the border zone play a significant role in determining cellular electrophysiology and conductivity, yet their spatial-temporal evolution and regulation are not well understood. To investigate the changes in ion concentrations that regulate cellular electrophysiology, a mathematical model of ion movement in the intra and extracellular space in the presence of ionic, potential and material property heterogeneities was developed. The model simulates the spatial and temporal evolution of concentrations of potassium, sodium, chloride, calcium, hydrogen and bicarbonate ions and carbon dioxide across an ischemic border zone. Ischemia was simulated by sodium-potassium pump inhibition, potassium channel activation and respiratory and metabolic acidosis. The model predicted significant disparities in the width of the border zone for each ionic species, with intracellular sodium and extracellular potassium having discordant gradients, facilitating multiple gradients in cellular properties across the border zone. Extracellular potassium was found to have the largest border zone and this was attributed to the voltage dependence of the potassium channels. The model also predicted the efflux of from the ischemic region due to electrogenic drift and diffusion within the intra and extracellular space, respectively, which contributed to depletion in the ischemic region.     

Can electromagnetic radiations induce changes in the kinetics of voltage-dependent ion channels?

Ion channels are protein molecules, which can assume distinct open and closed conformational states, a phenomenon termed ion channel kinetics. The transitions from one state to another depend on the potential energy barrier that separates those two states. Therefore, it is rational to suppose that electromagnetic waves could interact with this barrier and induce changes in the rate transitions of this kinetic process. Our aim is to answer the question: can electromagnetic radiations induce changes in the kinetics of voltage-dependent ion channels? We simulated the effects of the low and high frequency electromagnetic waves on the sodium and potassium channels of the giant axon of Loligo. The key parameter measured was the fractional open time (fv), because it reflects the voltage dependence of the kinetics of channels. The electromagnetic radiations induced the following changes in the kinetics of the potassium and sodium channels: i/ low frequency waves kept the potassium channel 50% of the time open independent on the mean voltage applied through the membrane; ii/ a gradual inhibition of the inactivation on the sodium channel, when the amplitudes of the low frequency waves were increased; iii/ high frequency waves on the potassium channel, decreased both Vo (voltage in which the channel stays 50% open) and the steepness of fv (d fv/dV) as the amplitudes of the waves increased, and iv/ high frequency and low amplitude radiations on the sodium channel decreased the maximum value of fv (in relation to control), while high amplitudes increased this value. In conclusion, high and low frequency electromagnetic radiations were able to change the kinetics of the potassium and sodium channels in a squid giant axon model.     

A new double-chamber model of ion channels. Beyond the Hodgkin and Huxley model

This paper proposes a new double-chamber model (DCM) of ion channels. The model ion channel consists of a series of three pores alternating with two chambers. The chambers are net negatively charged. The chamber's electric charge originates from dissociated amino acid side chains and is pH dependent. The chamber's net negative charge is compensated by cations present inside the chamber and in a diffuse electric layer outside the chamber. The pore's permeability is constant independent of time. One pore of the sodium channel and one of the potassium channel is a voltage-sensing pore. Due to the channel's structure, ions flow through the pores and chambers in a time-dependent manner. The model reproduces experimental voltage clamp and action potential data. The current flowing through a single sodium channel is less then one femtoampere. The DCM is considerably simpler then the Hodgkin and Huxley model (HHM) used to describe the electrophysiological properties of an axon. Unlike the HHM, the DCM can explain refractoriness, anode break excitation, accommodation and the effect of pH and temperature on the channels without additional parameters. In the DCM, the axon membrane shows repetitive activity depending on the channel density, sodium to potassium channel ratio and external potassium concentration. In the DCM, the action potential starts from 'hot spot areas' of higher channel densities and a higher sodium to potassium channel ratio, and then propagates through the whole axon.     

Immobilizing the moving parts of voltage-gated ion channels

Voltage-gated ion channels have at least two classes of moving parts, voltage sensors that respond to changes in the transmembrane potential and gates that create or deny permeant ions access to the conduction pathway. To explore the coupling between voltage sensors and gates, we have systematically immobilized each using a bifunctional photoactivatable cross-linker, benzophenone-4-carboxamidocysteine methanethiosulfonate, that can be tethered to cysteines introduced into the channel protein by mutagenesis. To validate the method, we first tested it on the inactivation gate of the sodium channel. The benzophenone-labeled inactivation gate of the sodium channel can be trapped selectively either in an open or closed state by ultraviolet irradiation at either a hyperpolarized or depolarized voltage, respectively. To verify that ultraviolet light can immobilize S4 segments, we examined its relative effects on ionic and gating currents in Shaker potassium channels, labeled at residue 359 at the extracellular end of the S4 segment. As predicted by the tetrameric stoichiometry of these potassium channels, ultraviolet irradiation reduces ionic current by approximately the fourth power of the gating current reduction, suggesting little cooperativity between the movements of individual S4 segments. Photocross-linking occurs preferably at hyperpolarized voltages after labeling residue 359, suggesting that depolarization moves the benzophenone adduct out of a restricted environment. Immobilization of the S4 segment of the second domain of sodium channels prevents channels from opening. By contrast, photocross-linking the S4 segment of the fourth domain of the sodium channel has effects on both activation and inactivation. Our results indicate that specific voltage sensors of the sodium channel play unique roles in gating, and suggest that movement of one voltage sensor, the S4 segment of domain 4, is at least a two-step process, each step coupled to a different gate.     

Peripheral nerve at extreme low temperatures 2: Pharmacologic modulation of temperature effects

Changes in temperature have profound and clinically important effects on the peripheral nerve. In a previous paper, the effects of temperature on many properties of the peripheral nerve action potential (NAP) were explored including the NAP amplitude, conduction velocity and response to paired pulse stimulation. In this paper, the effects of pharmacologic manipulations on these parameters were explored in order to further understand the mechanisms of these effects.The reduction in conduction velocity with temperature was shown to be independent of the ionic composition of the perfusate and was unaffected by potassium or sodium channel blockade. This implies that the phenomenon of reduced conduction velocities at low temperature may be related to changes in the passive properties of the axon with temperature. Blockade of sodium channels and chronic membrane depolarization produced by high perfusate potassium concentrations or high dose 4-aminopyridine impair the resistance of the nerve to hypothermia and enhance the injury to the nerve produced by cycles of cooling and rewarming. This suggests the possibility that changes in the sodium inactivation channel may be responsible for the changes in the NAP amplitude with temperature and that prolonged sodium inactivation may lead more permanent changes in excitability.     

Active site conformational changes of prostasin provide a new mechanism of protease regulation by divalent cations

Prostasin or human channel‐activating protease 1 has been reported to play a critical role in the regulation of extracellular sodium ion transport via its activation of the epithelial cell sodium channel. Here, the structure of the extracellular portion of the membrane associated serine protease has been solved to high resolution in complex with a nonselective d‐FFR chloromethyl ketone inhibitor, in an apo form, in a form where the apo crystal has been soaked with the covalent inhibitor camostat and in complex with the protein inhibitor aprotinin. It was also crystallized in the presence of the divalent cation Ca⁺². Comparison of the structures with each other and with other members of the trypsin‐like serine protease family reveals unique structural features of prostasin and a large degree of conformational variation within specificity determining loops. Of particular interest is the S1 subsite loop which opens and closes in response to basic residues or divalent ions, directly binding Ca⁺² cations. This induced fit active site provides a new possible mode of regulation of trypsin‐like proteases adapted in particular to extracellular regions with variable ionic concentrations such as the outer membrane layer of the epithelial cell.     

Effects of proteolytic enzymes on ionic conductances of squid axon membranes.

The effects of proteolytic enzymes on ionic conductances of squid axon membranes have been studied by means of the voltage clamp technique. When perfused internally alpha-chymotrypsin (1 mg/ml) increased and prolonged the depolarizing after-potential. Sodium inactivation was partially inhibited causing a prolonged sodium current, and peak sodium and steady-state potassium currents were suppressed. The time for sodium current to reach its peak was not affected. Leakage conductance increased later. On the other hand, carboxypeptidases A and B, both at 1mg/ml, suppressed the sodium and potassium conductance increases with little or no change in sodium inactivation. The mechanism that controls sodium inactivation appears to be associated with the structure of membrane proteins which is modified by alpha-chymotrypsin but not by carboxypeptidases and is located in a position accessible to alpha-chymotrypsin only from inside the membrane.     

Slow Changes of Potassium Permeability in the Squid Giant Axon

A slow potassium inactivation i.e. decrease of conductance when the inside of the membrane is made more positive with respect to the outside, has been observed for the squid axon. The conductance-potential curve is sigmoid shaped, and the ratio between maximum and minimum potassium conductance is at least 3. The time constant for the change of potassium conductance with potential is independent of the concentration of potassium in the external solution, but dependent upon potential and temperature. At 9 degrees C and at the normal sea water resting potential, the time constant is 11 sec. For lower temperature or more depolarizing potentials, the time constant is greater. The inactivation can be described by modifying the Hodgkin-Huxley equation for potassium current, using one additional parameter. The modified equation is similar in form to the Hodgkin-Huxley equation for sodium current, suggesting that the mechanism for the passive transport of potassium through the axon membrane is similar to that for sodium.     

Multiple-state model of ionic channel in reproducing the time course of electrophysiological events.

BACKGROUND: The predictions of the Hodgkin-Huxley model do not accurately fit all the measurements of voltage-clamp currents, gating charge and single-channel currents. There are many quantitative differences between the predicted and measured characteristics of the sodium and potassium channels. For example, the two-state gate model has exponential onset kinetics, whereas the sodium and potassium conductances show S-shaped activation and the sodium conductance shows an exponential inactivation. In this paper we shall examine a more general channel model that can more faithfully represent the measured properties of ionic channels in the membrane of the excitable cell. METHODS: The model is based on the generalisation of the notion of a channel with a discrete set of states. Each state has state attributes such as the state conductance, state ionic current and state gating charge. These variables can have quite different waveforms in time, in contrast with a two-state gate channel model, in which all have the same waveforms. RESULTS: The kinetics of all variables are equivalent: gating and ionic currents give equivalent information about channel kinetics; both the equilibrium values of the current and the time constants are functions of membrane potential. The results are in almost perfect concordance with the experimental data regarding the characteristics of nerve impulse. CONCLUSIONS: The expected values of the gating charge and the ionic conductance are weighted sums of the state occupancy probabilities, but the weights differ: for the expected value of the gating charge the weights are the state gating charges and for the expected value of the ionic conductance the weights are the state conductances. Since these weights are different, the expected values of the gating charge and the ionic conductance will differ.     

Effects of low-amplitude pulsed magnetic fields on cellular ion transport

Pulsed magnetic fields (PMFs) are widely used to treat difficult fractures of bone and other disorders of connective tissue. It is not clear how they interact with tissue metabolism, although it has been proposed that induced currents or electric fields impinging on cell membranes may modify their ion transport function. This hypothesis was tested by treating in vitro models for ion transport processes with short-term exposure to PMFs. No change occurred in active transport of potassium or calcium in human red cells or in calcium transport through an epithelial membrane. We considered less direct action on red cell membranes, that their permeability might be modified after PMF treatment, and also that PMFs might alter the extracellular ionic activity within connective tissue by interacting with its Donnan potential. Each of these studies proved negative, and we conclude that the PMF waveforms used here do not exert a general short-term effect on cellular ion transport.     

Modification of sodium and potassium channel gating kinetics by ether and halothane

The effect of ether and halothane on the kinetics of sodium and potassium currents were investigated in the crayfish giant axon. Both general anesthetics produced a reversible, dose-dependent speeding up of sodium current inactivation at all membrane potentials, with no change in the phase of the currents. Double-pulse inactivation experiments with ether also showed faster inactivation, but the rate of recovery from inactivation at negative potentials was not affected. Ether shifted the midpoint of the steady-state fast inactivation curve in the hyperpolarizing direction and made the curve steeper. The activation of potassium currents was faster with ether present, with no change in the voltage dependence of steady-state potassium currents. Ether and halothane are known to perturb the structure of lipid bilayer membranes; the alterations in sodium and potassium channel gating kinetics are consistent with the hypothesis that the rates of the gating processes of the channels can be affected by the state of the lipids surrounding the channels, but a direct effect of ether and halothane on the protein part of the channels cannot be ruled out. Ether did not affect the capacitance of the axon membrane.     

Ionic permeability of K, Na, and Cl in potassium-depolarized nerve. Dependency on pH, cooperative effects, and action of tetrodotoxin.

The passive ionic membrane conductances (gj) and permeabilities (Pj) of K, Na, and Cl of crayfish (Procambarus clarkii) medial giant axons were determined in the potassium-depolarized axon and compared with that of the resting axon. Passive ionic conductances and permeabilities were found to be potassium dependent with a major conductance transition occurring around an external K concentration of 12-15 mM (Vm = -60 to -65 mV). The results showed that K, Na, and Cl conductances increased by 6.2, 6.9, and 27-fold, respectively, when external K was elevated from 5.4 to 40 mM. Permeability measurements indicated that K changed minimally with K depolarization while Na and Cl underwent an order increase in permeability. In the resting axon (K0 = 5.4 mM, pH = 7.0) PK = 1.33 X 10(-5), PCl = 1.99 X 10(-6), PNa = 1.92 X 10(-8) while in elevated potassium (K0 = 40 mM, pH 7.0), PK = 1.9 X 10(-5), PCl = 1.2 X 10(-5), and PNa = 2.7 X 10(-7) cm/s. When membrane potential is reduced to 40 mV by changes in internal ions, the conductance changes are initially small. This suggests that resting channel conductances depend also on ion environments seen by each membrane surface in addition to membrane potential. In elevated potassium, K, Na, and Cl conductances and permeabilities were measured from pH 3.8 to 11 in 0.2 pH increments. Here a cooperative transition in membrane conductance or permeability occurs when pH is altered through the imidazole pK (approximately pH 6.3) region. This cooperative conductance transition involves changes in Na and Cl but not K permeabilities. A Hill coefficient n of near 4 was found for the cooperative conductance transition of both the Na and Cl ionic channel which could be interpreted as resulting from 4 protein molecules forming each of the Na and Cl ionic channels. Tetrodotoxin reduces the Hill coefficient n to near 2 for the Na channel but does not affect the Cl channel. In the resting or depolarized axon, crosslinking membrane amino groups with DIDS reduces Cl and Na permeability. Following potassium depolarization, buried amino groups appear to be uncovered. The data here suggest that potassium depolarization produces a membrane conformation change in these ionic permeability regulatory components. A model is proposed where membrane protein, which forms the membrane ionic channels, is oriented with an accessible amino terminal group on the axon exterior. In this model the ionizable groups on protein and phospholipid have varied associations with the different ionic channel access sites for K, Na, and Cl, and these groups exert considerable control over ion permeation through their surface potentials.     

Electrogenic effect during active lithium transport through somatic membrane of molluscan neurons

The effect of replacement of sodium and (or) potassium by lithium on the electrogenic effect of active ion transport through the somatic membrane of isolated neurons was studied in the snailPlanorbarius corneus. Changes observed in the electrogenic effect are evidence that intracellular lithium can be actively exchanged for extracellular potassium; lithium can play the role of extracellular potassium during activation of the pump, and intracellular lithium is actively exchanged for extracellular.     

Effects of the dipolar form of phloretin on potassium conductance in squid giant axons.

The effects of phloretin on membrane ionic conductances have been studied in the giant axon of the squid, Loligo pealei. Phloretin reversibly suppresses the potassium and sodium conductances and modifies their dependence on membrane potential (Em). Its effects on the potassium conductance (GK) are much greater than on the sodium conductance; no effects on sodium inactivation are observed. Internal perfusion of phloretin produces both greater shifts in GK(Em) and greater reductions maximum GK than does external perfusion; the effect of simultaneous internal and external perfusion is little greater than that of internal perfusion alone. Lowering the internal pH, which favors the presence of the neutral species of weakly acidic phloretin (pKa 7.4), potentiates the actions of internally perfused phloretin. Other organic cations with dipole moments similar to phloretin's have little effect on either potassium or sodium conductances in squid axons. These results can be explained by either of two mechanisms; on postulates a phloretin "receptor" near the voltage sensor component of the potassium channel which is accessible to drug molecules applied at either the outer or inner membrane surface and is much more sensitive to the neutral than the negatively charged form of the drug. The other mechanism proposes that neutral phloretin molecules are dispersed in an ordered array in the membrane interior, producing a diffuse dipole field which modifies potassium channel gating. Different experimental results support these two mechanisms, and neither hypothesis can be disproven.     

Cultured Giant Fiber Lobe of Squid Expresses Three Distinct Potassium Channel Activities in Selective Combinations

Neurons from the giant fiber lobe (GFL) of squid Loligo bleekeri were dissociated and cultured. The ionic currents were recorded using whole-cell patch clamp methods. The sodium current and the noninactivating potassium current like those elicited by the giant axon were among the currents expressed in axonal bulbs and bulblike structures upon dissociation. Meanwhile axonless cell bodies did not elicit such currents. Axonless cell bodies and some bulblike structures elicited two kinds of inactivating potassium currents, the slow- and the fast-inactivating current, which differed in their inactivation kinetics and pharmacology. Within 24 hr of plating, the current composition remained the same. While the noninactivating current was not sensitive to 4-aminopyridine, the two inactivating currents were sensitive, the slow-inactivating current being more sensitive. Selective combinations of the sodium current and the three potassium currents expressed in different structures of the acutely dissociated GFL could have resulted from cellular control of synthesis and transportation of the channel proteins to the somatic and the axonal membrane. The sodium current and the noninactivating potassium current could be recorded from some axonless cell bodies maintained in culture for over three days, indicating that the separation of the giant axon from its somata could result in the transportation of the channels normally expressed on the giant axon membrane to the somatic membrane. Received: 24 October 1995/Revised: 5 March 1996     

Regulatory Evolution and Voltage-Gated Ion Channel Expression in Squid Axon: Selection-Mutation Balance and Fitness Cliffs

It has been suggested that optimization of either axonal conduction velocity or the energy efficiency of action potential conduction predominates in the selection of voltage-gated sodium conductance levels in the squid axon. A population genetics model of channel gene regulatory function was used to examine the role of these and other evolutionary forces on the selection of both sodium and potassium channel expression levels. In this model, the accumulating effects of mutations result in degradation of gene regulatory function, causing channel gene expression to fall to near-zero in the absence of positive selection. In the presence of positive selection, channel expression levels fall to the lowest values consistent with the selection criteria, thereby establishing a selection-mutation balance. Within the parameter space of sodium and potassium conductance values, the physiological performance of the squid axon model showed marked discontinuities associated with conduction failure and excitability. These discontinuities in physiological function may produce fitness cliffs. A fitness cliff associated with conduction failure, combined with the effects of phenotypic noise, can account for the selection of sodium conductance levels, without considering either conduction velocity or metabolic cost. A fitness cliff associated with a transition in axonal excitability, combined with phenotypic noise, can explain the selection of potassium channel expression levels. The results suggest that voltage-gated ion channel expression will fall to low levels, consistent with key functional constraints, even in the absence of positive selection for energy efficiency. Channel expression levels and individual variation in channel expression within the population can be explained by regulatory evolution in combination with genetic variation in regulatory function and phenotypic noise, without resorting to more complex mechanisms, such as activity-dependent homeostasis. Only a relatively small region of the large, nominally isofunctional parameter space for channel expression will normally be occupied, because of the effects of mutation.