Synergistic inhibition of the maximum conductance of Kv1.5 channels by extracellular K+ reduction and acidification

Voltage-gated potassium (Kv) channels exist in the membranes of all living cells. Of the functional classes of Kv channels, the Kv1 channels are the largest and the best studies and are known to play essential roles in excitable cell function, providing an essential counterpoin to the various inward currents that trigger excitability. The serum potassium concentration [K _o ⁺ ] is tightly regulated in mammals and disturbances can cause significant functional alterations in the electrical behavior of excitable tissues in the nervous system and the heart. At least some of these changes may be mediated by Kv channels that are regulated by changes in the extracellular K⁺ concentration. As well as changes in serum [K _o ⁺ ], tissue acification is a frequent pathological condition known to inhibit Shaker and Kv1 voltage-gated potassium channels. In recent studies, it has become recognized that the acidification-induced inhibition of some Kv1 channels is K _o ⁺ -dependent, and the suggestion has been made that pH and K _o ⁺ may regulate the channels via a common mechanism. Here we discuss P/C type inactivation as the common pathway by which some Kv channels become unavailable at acid pH and lowered K _o ⁺ . It is suggested that binding of protons to a regulatory site in the outer pore mouth of some Kv channels favors transitions to the inactivated state, whereas K⁺ ions exert countereffects. We suggest that modulation of the number of excitable voltage-gated K⁺ channels in the open vs inactivated states of the channels by physiological H⁺ and K⁺ concentrations represents an important pathway to control Kv channel function in health and disease.     

Dynamic modification of dendritic cable properties and synaptic transmission by voltage-gated potassium channels

Computer simulations of a dendrite possessing voltage-sensitive potassium conductances were used to determine the effects of these conductances on synaptic transmission and on the propagation of synaptic signals within the dendritic tree. Potassium conductances had two principal effects on voltage transients generated by current injections or synaptic conductances. Locally (near the source of the transient), voltage-gated potassium channels produced a potassium shunt current that reduced the amplitude of voltage transients generated by depolarizing currents. This shunt current increased as the amplitude of the depolarizing transient increased and so acted to prevent large synaptic transients from reaching levels that would saturate due to a reduction in driving force. In the presence of rapidly activating potassium currents, excitatory synapses produced larger synaptic currents that were more linearly related to synaptic conductance, but these produced smaller voltage transients. The maximum amplitudes of the voltage transients were limited by the voltage sensitivity of the K⁺ conductance and the rate at which it could activate. Sufficiently rapid synaptic currents could outrun the K⁺ conductance and thus achieve high local peak amplitudes. These effects of K⁺ conductances were unrelated to whether they were located on dendrites or not, being related only to their proximity to the source of synaptic current. The second class of effects of K⁺ conductances depended on their alteration of the electrotonic structure of the postsynaptic cell and so were observed only when they were located on postsynaptic dendrites. Voltage-gated K⁺ conductances produced voltage-dependent electrotonic expansion of depolarized dendrites, which had the effect of isolating synaptic inputs on depolarized dendrites from events on the rest of the neuron. Thus, synapses on the same dendrite interacted destructively to a degree much greater than that expected from the classical driving force nonlinearity. Synapses located proximally to a depolarized dendritic region were less effected than those located distally, and the range of the nonlinear interaction between synapses was dependent on the kinetics of activation and deactivation of the conductance. When present in conjunction with rapidly activating dendritic sodium conductance, the potassium conductance sharpened the requirement for spatial and temporal coincidence to produce synaptic boosting by inward currents, and suppressed out-of-synchrony synaptic inputs.     

Potassium channel inhibition reduces cell proliferation in the GH3 pituitary cell line

Potassium (K⁺) conductances are known to be involved in cell proliferation of a number of nonexcitable cell types. The nature of the mechanism by which K⁺ channel inhibition reduces cell proliferation has remained elusive despite intensive search. We investigated whether such a phenomenon could be demonstrated in excitable cells, using the GH3 pituitary cell line as a cell model. Our aims were: (1) to study the effect of K⁺ channel inhibition on the proliferation of GH3 cells; and (2) to investigate the putative intracellular signals involved in this inhibition. Tetraethylammonium chloride (TEA), a blocker of the calcium (Ca²⁺)-dependent K⁺ conductances of GH3, was found to reversibly inhibit cell proliferation, as measured by ³H-thymidine incorporation. Cell cycle block specifically occurred at the G1/S phase of the cell cycle. This inhibition of proliferation was observed for 1–4 mM TEA, which suppressed most of the Ca²⁺-activated K⁺ current and part of the inward rectifying K⁺ current, as shown by electrophysiological experiments. Increasing extracellular K⁺ concentrations with KCl also inhibited cell proliferation in a dose-dependent manner. Both TEA and KCl depolarized the cells and increased intracellular Ca²⁺ levels ([Ca²⁺]i), showing that, in this type of excitable cell, inhibition of cell proliferation can be associated with elevated Ca²⁺ levels. Ca²⁺ and membrane resting potential (MRP) were considered as possible messengers of this inhibition. Our results suggest that cell cycle arrest of GH3 cells by K⁺ channel block probably involves an additional pathway, distinct from those of Ca²⁺ and MRP. J. Cell. Physiol. 177:402–410, 1998. © 1998 Wiley-Liss, Inc.     

Contributions of HERG current to repolarization of the human ventricular action potential

Action potential repolarization in the mammalian heart is governed by interactions of a number of time- and voltage-dependent channel-mediated currents, as well as contributions from the Na⁺/Ca²⁺ exchanger and the Na⁺/K⁺ pump. Recent work has shown that one of the K⁺ currents (HERG) which contributes to repolarization in mammalian ventricle is a locus at which a number of point mutations can have significant functional consequences. In addition, the remarkable sensitivity of this K⁺ channel isoform to inhibition by a variety of pharmacological agents and clinical drugs has resulted in HERG being a major focus for Safety Pharmacology requirements.For these reasons we and others have attempted to define the functional role for HERG-mediated K⁺ currents in repolarization of the action potential in the human ventricle. Here, we describe and evaluate changes in the formulations for two K⁺ currents, I_K1 and HERG (or I_K,r), within the framework of ten Tusscher model of the human ventricular action potential. In this computational study, new mathematical formulations for the two nonlinear K⁺ conductances, I_K1 and HERG, have been developed based upon experimental data obtained from electrophysiological studies of excised human ventricular tissue and/or myocytes. The resulting mathematical model provides much improved simulations of the relative sizes and time courses of the K⁺ currents which modulate repolarization. Our new formulation represents an important first step in defining the mechanism(s) of repolarization of the membrane action potential in the human ventricle. Our overall goal is to understand the genesis of the T-wave of the human electrocardiogram.     

Systematic characterization of the ionic basis of rabbit cellular electrophysiology using two ventricular models

Several mathematical models of rabbit ventricular action potential (AP) have been proposed to investigate mechanisms of arrhythmias and excitation-contraction coupling. Our study aims at systematically characterizing how ionic current properties modulate the main cellular biomarkers of arrhythmic risk using two widely-used rabbit ventricular models, and comparing simulation results using the two models with experimental data available for rabbit. A sensitivity analysis of AP properties, Ca²⁺ and Na⁺ dynamics, and their rate dependence to variations (±15% and ±30%) in the main transmembrane current conductances and kinetics was performed using the Shannon et al. (2004) and the [Mahajan et?al., 2008a] and [Mahajan et?al., 2008b] AP rabbit models. The effects of severe transmembrane current blocks (up to 100%) on steady-state AP and calcium transients, and AP duration (APD) restitution curves were also simulated using both models. Our simulations show that, in both virtual rabbit cardiomyocytes, APD is significantly modified by most repolarization currents, AP triangulation is regulated mostly by the inward rectifier K⁺ current (I_K1) whereas APD rate adaptation as well as [Na⁺]_i rate dependence is influenced by the Na⁺/K⁺ pump current (I_NaK). In addition, steady-state [Ca²⁺]_i levels, APD restitution properties and [Ca²⁺]_i rate dependence are strongly dependent on I_NaK, the L-Type Ca²⁺ current (I_CaL) and the Na⁺/Ca²⁺ exchanger current (I_NaCa), although the relative role of these currents is markedly model dependent. Furthermore, our results show that simulations using both models agree with many experimentally-reported electrophysiological characteristics. However, our study shows that the Shannon et al. model mimics rabbit electrophysiology more accurately at normal pacing rates, whereas Mahajan et al. model behaves more appropriately at faster rates. Our results reinforce the usefulness of sensitivity analysis for further understanding of cellular electrophysiology and validation of cardiac AP models.     

Structural stability,alternate descriptions and information

The inactivation properties of a model of the nerve membrane are examined. The inactivation kinetics are closely first order and may be characterized by Hodgkin-Huxley (H-H) parameters h_∞ and τ_h which depend on potential in agreement with experiments. Some differences from the H-H equations are identified. The forms predicted for τ_h variation with hyper-polarization and change of external [K⁺] agree with available data. While the inactivation time delay predicted by the model is too small to be detected experimentally, there are grounds for expecting that it may be larger in other tissues, as observed in Myxicola giant axons. The variation of the delay with test potential is predicted to be exponential. Although the model is coupled in the sense defined by Hoyt, it gives rise to an inactivation shift of negligible magnitude. However, introducing a simple variability in one physical parameter leads to the observed form of both the peak transient current voltage relation and the inactivation shift. Inactivation shift thus does not unambiguously indicate coupling; that it results from parametric heterogeneity may be a better hypothesis, and is readily testable. The inactivation shift dependence on current ratio, from experimental data, can be used to correct for the effects of parametric heterogeneity and obtain the value of a previously predicted fundamental parameter of excitable membranes. It is suggested that the effects of parametric heterogeneity must be considered in interpreting experiments and designing models for excitable systems.     

Period doubling of calcium spike firing in a model of a Purkinje cell dendrite

Recordings from cerebellar Purkinje cell dendrites have revealed that in response to sustained current injection, the cell firing pattern can move from tonic firing of Ca²⁺ spikes to doublet firing and even to quadruplet firing or more complex firing. These firing patterns are not modified substantially if Na⁺ currents are blocked. We show that the experimental results can be viewed as a slow transition of the neuronal dynamics through a period-doubling bifurcation. To further support this conclusion and to understand the underlying mechanism that leads to doublet firing, we develop and study a simple, one-compartment model of Purkinje cell dendrite. The neuron can also exhibit quadruplet and chaotic firing patterns that are similar to the firing patterns that some of the Purkinje cells exhibit experimentally. The effects of parameters such as temperature, applied current, and potassium reversal potential in the model resemble their effects in experiments. The model dynamics involve three time scales. Ca²⁺- dependent K⁺ currents, with intermediate time scales, are responsible for the appearance of doublet firing, whereas a very slow hyperpolarizing current transfers the neuron from tonic to doublet firing. We use the fast-slow analysis to separate the effects of the three time scales. Fast-slow analysis of the neuronal dynamics, with the activation variable of the very slow, hyperpolarizing current considered as a parameter, reveals that the transitions occurs via a cascade of period-doubling bifurcations of the fast and intermediate subsystem as this slow variable increases. We carry out another analysis, with the Ca²⁺ concentration considered as a parameter, to investigate the conditions for the generation of doublet firing in systems with one effective variable with intermediate time scale, in which the rest state of the fast subsystem is terminated by a saddle-node bifurcation. We find that the scenario of period doubling in these systems can occur only if (1) the time scale of the intermediate variable (here, the decay rate of the calcium concentration) is slow enough in comparison with the interspike interval of the tonic firing at the transition but is not too slow and (2) there is a bistability of the fast subsystem of the spike-generating variables.     

Seizure-like afterdischarges simulated in a model neuron

To explore non-synaptic mechanisms in paroxysmal discharges, we used a computer model of a simplified hippocampal pyramidal cell, surrounded by interstitial space and a “glial-endothelial” buffer system. Ion channels for Na⁺, K⁺, Ca²⁺ and Cl⁻ _, ion antiport 3Na/Ca, and “active” ion pumps were represented in the neuron membrane. The glia had “leak” conductances and an ion pump. Fluxes, concentration changes and cell swelling were computed. The neuron was stimulated by injecting current. Afterdischarge (AD) followed stimulation if depolarization due to rising interstitial K⁺ concentration ([K⁺]_o) activated persistent Na⁺ current (I _Na,P). AD was either simple or self-regenerating; either regular (tonic) or burst-type (clonic); and always self-limiting. Self-regenerating AD required sufficient I _Na,P to ensure re-excitation. Burst firing depended on activation of dendritic Ca²⁺ currents and Ca-dependent K⁺ current. Varying glial buffer function influenced [K⁺]_o accumulation and afterdischarge duration. Variations in Na⁺ and K⁺ currents influenced the threshold and the duration of AD. The data show that high [K⁺]_o and intrinsic membrane currents can produce the feedback of self-regenerating afterdischarges without synaptic input. The simulated discharge resembles neuron behavior during paroxysmal firing in living brain tissue. Action Editor: David Terman     

A unified model for two modes of bursting in GnRH neurons

Gonadotropin-releasing hormone (GnRH) neurons exhibit at least two intrinsic modes of action potential burst firing, referred to as parabolic and irregular bursting. Parabolic bursting is characterized by a slow wave in membrane potential that can underlie periodic clusters of action potentials with increased interspike interval at the beginning and at the end of each cluster. Irregular bursting is characterized by clusters of action potentials that are separated by varying durations of interburst intervals and a relatively stable baseline potential. Based on recent studies of isolated ionic currents, a stochastic Hodgkin-Huxley (HH)-like model for the GnRH neuron is developed to reproduce each mode of burst firing with an appropriate set of conductances. Model outcomes for bursting are in agreement with the experimental recordings in terms of interburst interval, interspike interval, active phase duration, and other quantitative properties specific to each mode of bursting. The model also shows similar outcomes in membrane potential to those seen experimentally when tetrodotoxin (TTX) is used to block action potentials during bursting, and when estradiol transitions cells exhibiting slow oscillations to irregular bursting mode in vitro. Based on the parameter values used to reproduce each mode of bursting, the model suggests that GnRH neurons can switch between the two through changes in the maximum conductance of certain ionic currents, notably the slow inward Ca²⁺ current I _s, and the Ca²⁺ -activated K⁺ current I _KCa. Bifurcation analysis of the model shows that both modes of bursting are similar from a dynamical systems perspective despite differences in burst characteristics.     

Voltage-dependent ionic conductances in the human malignant astrocytoma cell line U87-MG

Although the human malignant astrocytoma cell line U87-MG has been used in numerous studies, few findings are available on the properties of its membrane ion conductances. Characterization of the ion channels expressed in these cells will make it possible to study membrane ion conductance changes when a receptor is activated by its ligand. This will help to elucidate the functional properties of these receptors and their signal-transduction pathways in pathophysiological events. This work studied the voltage-dependent ionic conductances of U87-MG cells using the Whole-Cell Recording patch-clamp technique. Six types of voltage-dependent ionic currents were identified: (i) a TEA-, 4-AP- and CTX-sensitive Ca²⁺-dependent K⁺ current, (ii) a transient K⁺ current inhibited by 4-AP, (iii) an inwardly rectifying K⁺ current blocked by Ba²⁺ and 4-AP, (iv) a DIDS- and SITS-sensitive Cl^? current, (v) a TTX-sensitive Na⁺ conductance and (vi) a L-type Ca²⁺ conductance activated by BayK-8644 and inhibited by Ni and the L-type Ca²⁺ channel inhibitor, nifedipine. In addition, electrical depolarizations elicited inward currents due to voltage-independent, Ca²⁺-dependent K⁺ influx against the electrochemical gradient, probably via an ouabain-sensitive Na⁺-K⁺ pump.     

Depression of presynaptic excitation by the activation of vanilloid receptor 1 in the rat spinal dorsal horn revealed by optical imaging

Hypoxia alters neuronal function and can lead to neuronal injury or death especially in the central nervous system. But little is known about the effects of hypoxia in neurones of the peripheral nervous system (PNS), which survive longer hypoxic periods. Additionally, people have experienced unpleasant sensations during ischemia which are dedicated to changes in conduction properties or changes in excitability in the PNS. However, the underlying ionic conductances in dorsal root ganglion (DRG) neurones have not been investigated in detail. Therefore we investigated the influence of moderate hypoxia (27.0 ± 1.5 mmHg) on action potentials, excitability and ionic conductances of small neurones in a slice preparation of DRGs of young rats. The neurones responded within a few minutes non-uniformly to moderate hypoxia: changes of excitability could be assigned to decreased outward currents in most of the neurones (77%) whereas a smaller group (23%) displayed increased outward currents in Ringer solution. We were able to attribute most of the reduction in outward-current to a voltage-gated K⁺ current which activated at potentials positive to -50 mV and was sensitive to 50 nM α-dendrotoxin (DTX). Other toxins that inhibit subtypes of voltage gated K⁺ channels, such as margatoxin (MgTX), dendrotoxin-K (DTX-K), r-tityustoxin Kα (TsTX-K) and r-agitoxin (AgTX-2) failed to prevent the hypoxia induced reduction. Therefore we could not assign the hypoxia sensitive K⁺ current to one homomeric K_V channel type in sensory neurones. Functionally this K⁺ current blockade might underlie the increased action potential (AP) duration in these neurones. Altogether these results, might explain the functional impairment of peripheral neurones under moderate hypoxia.     

Diversity and modulation of ionic conductances in leech neurons

A complete understanding of animal behavior at the cellular level requires detailed information on the intrinsic biophysical properties of neurons, muscles, and the synaptic connections they make. In the past 10 to 15 years, electrophysiological studies of leech neurons have revealed a diverse array of voltage-gated ionic conductances distinguished by their pharmacological sensitivity to classic ion channel blockers. Voltage-clamp studies have provided new information about the kinetics and voltage-dependence of Na⁺ conductances, several K⁺ currents, including I_A, I_K and I_K(Ca.)' and high- and low-voltage-gated Ca²⁺ conductances. These studies showed that the action potentials of most leech neurons result from the usual sequence of permeability changes to Na⁺, K⁺, and Ca²⁺ ions. They also added insight as to the role played by particular combinations of conductances in providing individual neurons with electrical properties appropriate for the particular information they encode. Evidence is accumulating on the modulatory actions of endogenous neurotransmitters such as FMRFamide, serotonin, and octopamine on motor behaviors in the animal. Parallel studies suggest that changes in behavior can be explained, at least in part, by the alteration of firing patterns of selected neurons and muscles resulting form modulation of multiple ion conductances. This makes the leech exceptionally attractive for neuroethological studies because it is one of the simplest organisms in which the methods of psychology and neurobiology can be combined. Information gathered from this animal will therefore increase our understanding regarding general principles underlying the cellular basis of behavior. © 1995 John Wiley & Sons, Inc.     

Simulation of developmental changes in action potentials with ventricular cell models

During cardiomyocyte development, early embryonic ventricular cells show spontaneous activity that disappears at a later stage. Dramatic changes in action potential are mediated by developmental changes in individual ionic currents. Hence, reconstruction of the individual ionic currents into an integrated mathematical model would lead to a better understanding of cardiomyocyte development. To simulate the action potential of the rodent ventricular cell at three representative developmental stages, quantitative changes in the ionic currents, pumps, exchangers, and sarcoplasmic reticulum (SR) Ca²⁺ kinetics were represented as relative activities, which were multiplied by conductance or conversion factors for individual ionic systems. The simulated action potential of the early embryonic ventricular cell model exhibited spontaneous activity, which ceased in the simulated action potential of the late embryonic and neonatal ventricular cell models. The simulations with our models were able to reproduce action potentials that were consistent with the reported characteristics of the cells in vitro. The action potential of rodent ventricular cells at different developmental stages can be reproduced with common sets of mathematical equations by multiplying conductance or conversion factors for ionic currents, pumps, exchangers, and SR Ca²⁺ kinetics by relative activities.     

Potassium currents in cultured rabbit retinal pigment epithelial cells

Membrane potential and ionic currents were studied in cultured rabbit retinal pigment epithelial (RPE) cells using whole-cell patch clamp and perforated-patch recording techniques. RPE cells exhibited both outward and inward voltage-dependent currents and had a mean membrane capacitance of 26±12 pF (sd, n=92). The resting membrane potential averaged ?31±15 mV (n=37), but it was as high as ?60 mV in some cells. When K⁺ was the principal cation in the recording electrode, depolarization-activated outward currents were apparent in 91% of cells studied. Tail current analysis revealed that the outward currents were primarily K⁺ selective. The most frequently observed outward K⁺ current was a voltage- and time-dependent outward current (I _K) which resembled the delayed rectifier K⁺ current described in other cells. I _K was blocked by tetraethylammonium ions (TEA) and barium (Ba²⁺) and reduced by 4-aminopyridine (4-AP). In a few cells (3–4%), depolarization to ?50 mV or more negative potentials evoked an outwardly rectifying K⁺ current (I _Kt) which showed more rapid inactivation at depolarized potentials. Inwardly rectifying K⁺ current (I _KI) was also present in 41% of cells. I _KI was blocked by extracellular Ba²⁺ or Cs⁺ and exhibited time-dependent decay, due to Na⁺ blockade, at negative potentials. We conclude that cultured rabbit RPE cells exhibit at least three voltage-dependent K⁺ currents. The K⁺ conductances reported here may provide conductive pathways important in maintaining ion and fluid homeostasis in the subretinal space.     

A mutation that increases a novel calcium-activated potassium conductance ofParamecium tetraurelia

Summary Under two-electrode voltage clamp, a mutant ofP. tetraurelia, restless (rst/rst), showed a large increase in induced current and an outward tail current when compared to the wildtype cell for hyperpolarizing voltage steps. An increase in the induced and tail currents is also observed for depolarizing voltage steps. The larger current during voltage steps and tail in the mutant were eliminated by the use of CsCl-filled electrodes and tetraethylammonium ion (TEA⁺) in the bath solution, characterizing the lesion as affecting a K⁺ conductance. Ionophoretic injection of ethylene glycol bis-(beta-aminoethyl ether) n,n,n,n-tetraacetic acid (EGTA) to buffer internal Ca²⁺ concentration reduced the increased K⁺ current and tail of therestless cell, indicating Ca²⁺ activation of the K⁺ current. Time course and amplitude of remaining currents after blockage of K⁺ conductances with Cs⁺ and TEA⁺ were similar in wild-type andrestless cells suggesting norestless defect in entry of calcium. The Ca²⁺-activated sodium current was similar in the mutant to that in wild type arguing against a defect in calcium regulation activating the K⁺ channel in therestless cell. We conclude that therestless mutation alters a Ca²⁺-activated potassium conductance other than the one previously described. The multiplicity of Ca²⁺-activated potassium conductances inParamecium is discussed.     

Computer simulations of neuron-glia interactions mediated by ion flux

Extracellular potassium concentration, [K⁺]_o, and intracellular calcium, [Ca²⁺]_i, rise during neuron excitation, seizures and spreading depression. Astrocytes probably restrain the rise of K⁺ in a way that is only partly understood. To examine the effect of glial K⁺ uptake, we used a model neuron equipped with Na⁺, K⁺, Ca²⁺ and Cl⁻ conductances, ion pumps and ion exchangers, surrounded by interstitial space and glia. The glial membrane was either “passive”, incorporating only leak channels and an ion exchange pump, or it had rectifying K⁺ channels. We computed ion fluxes, concentration changes and osmotic volume changes. Increase of [K⁺]_o stimulated the glial uptake by the glial 3Na/2K ion pump. The [K⁺]_o flux through glial leak and rectifier channels was outward as long as the driving potential was outwardly directed, but it turned inward when rising [K⁺]_o/[K⁺]_i ratio reversed the driving potential. Adjustments of glial membrane parameters influenced the neuronal firing patterns, the length of paroxysmal afterdischarge and the ignition point of spreading depression. We conclude that voltage gated K⁺ currents can boost the effectiveness of the glial “potassium buffer” and that this buffer function is important even at moderate or low levels of excitation, but especially so in pathological states.     

Low dose of dopamine may stimulate prolactin secretion by increasing fast potassium currents

Dopamine (DA) released from the hypothalamus tonically inhibits pituitary lactotrophs. DA (at micromolar concentration) opens potassium channels, hyperpolarizing the lactotrophs and thus preventing the calcium influx that triggers prolactin hormone release. Surprisingly, at concentrations ∼1000 lower, DA can stimulate prolactin secretion. Here, we investigated whether an increase in a K⁺ current could mediate this stimulatory effect. We considered the fast K⁺ currents flowing through large-conductance BK channels and through A-type channels. We developed a minimal lactotroph model to investigate the effects of these two currents. Both I _BK and I _A could transform the electrical pattern of activity from spiking to bursting, but through distinct mechanisms. I _BK always increased the intracellular Ca²⁺ concentration, while I _A could either increase or decrease it. Thus, the stimulatory effects of DA could be mediated by a fast K⁺ conductance which converts tonically spiking cells to bursters. In addition, the study illustrates that a heterogeneous distribution of fast K⁺ conductances could cause heterogeneous lactotroph firing patterns. Action Editor: Christiane Linster     

Regression Analysis for Constraining Free Parameters in Electrophysiological Models of Cardiac Cells

A major challenge in computational biology is constraining free parameters in mathematical models. Adjusting a parameter to make a given model output more realistic sometimes has unexpected and undesirable effects on other model behaviors. Here, we extend a regression-based method for parameter sensitivity analysis and show that a straightforward procedure can uniquely define most ionic conductances in a well-known model of the human ventricular myocyte. The model''s parameter sensitivity was analyzed by randomizing ionic conductances, running repeated simulations to measure physiological outputs, then collecting the randomized parameters and simulation results as “input” and “output” matrices, respectively. Multivariable regression derived a matrix whose elements indicate how changes in conductances influence model outputs. We show here that if the number of linearly-independent outputs equals the number of inputs, the regression matrix can be inverted. This is significant, because it implies that the inverted matrix can specify the ionic conductances that are required to generate a particular combination of model outputs. Applying this idea to the myocyte model tested, we found that most ionic conductances could be specified with precision (R² > 0.77 for 12 out of 16 parameters). We also applied this method to a test case of changes in electrophysiology caused by heart failure and found that changes in most parameters could be well predicted. We complemented our findings using a Bayesian approach to demonstrate that model parameters cannot be specified using limited outputs, but they can be successfully constrained if multiple outputs are considered. Our results place on a solid mathematical footing the intuition-based procedure simultaneously matching a model''s output to several data sets. More generally, this method shows promise as a tool to define model parameters, in electrophysiology and in other biological fields.     

Effects of Na+ on the Predominant K+ Channel in the Tonoplast of Chara: Decrease of Conductance by Blocks in 100 Nanosecond Range and Induction of Oligo- or Poly-subconductance Gating Modes

We present three mechanisms by which Na⁺ inhibits the open channel currents of the predominant K⁺ channel in the tonoplast of Chara corallina: (i) Fast block, i.e., short (100 ns range) interruptions of the open channel current which are determined by open channel noise analysis, (ii): Oligo-subconductance mode, i.e., a gating mode which occurs preferentially in the presence of Na⁺; this mode comprises a discrete number (here 3) of open states with smaller conductances than normal, and (iii): Polysubconductance mode, i.e., a gating mode with a nondiscrete, large number (>30) of states with smaller conductances than the main open channel conductance. This novel mode has also been observed only in the presence of Na⁺. Received: 16 November 1999/Revised: 8 February 2000