Open- and closed-state fast inactivation in sodium channels: differential effects of a site-3 anemone toxin

The role of sodium channel closed-state fast inactivation in membrane excitability is not well understood. We compared open- and closed-state fast inactivation, and the gating charge immobilized during these transitions, in skeletal muscle channel hNa(V)1.4. A significant fraction of total charge movement and its immobilization occurred in the absence of channel opening. Simulated action potentials in skeletal muscle fibers were attenuated when pre-conditioned by sub-threshold depolarization. Anthopleurin A, a site-3 toxin that inhibits gating charge associated with the movement of DIVS4, was used to assess the role of this voltage sensor in closed-state fast inactivation. Anthopleurin elicited opposing effects on the gating mode, kinetics and charge immobilized during open- versus closed-state fast inactivation. This same toxin produced identical effects on recovery of channel availability and remobilization of gating charge, irrespective of route of entry into fast inactivation. Our findings suggest that depolarization promoting entry into fast inactivation from open versus closed states provides access to the IFMT receptor via different rate-limiting conformational translocations of DIVS4.     

Interactions of protons with single open L-type calcium channels. Location of protonation site and dependence of proton-induced current fluctuations on concentration and species of permeant ion

We further investigated the rapid fluctuations between two different conductance levels promoted by protons when monovalent ions carry current through single L-type Ca channels. We tested for voltage dependence of the proton-induced current fluctuations and for accessibility of the protonation site from both sides of the membrane patch. The results strongly suggest an extracellular location of the protonation site. We also studied the dependence of the kinetics of the fluctuations and of the two conductance levels on the concentration of permeant ion and on external ionic strength. We find that saturation curves of channel conductance vs. [K] are similar for the two conductance levels. This provides evidence that protonation does not appreciably change the surface potential near the entry of the permeation pathway. The proton-induced conduction change must therefore result from an indirect interaction between the protonation site and the ion-conducting pathway. Concentration of permeant ion and ionic strength also affect the kinetics of the current fluctuations, in a manner consistent with our previous hypothesis that channel occupancy destabilizes the low conductance channel conformation. We show that the absence of measurable fluctuations with Li and Ba as charge carriers can be explained by significantly higher affinities of these ions for permeation sites. Low concentrations of Li reduce the Na conductance and abbreviate the lifetimes of the low conductance level seen in the presence of Na. We use whole-cell recordings to extrapolate our findings to the physiological conditions of Ca channel permeation and conclude that in the presence of 1.8 mM Ca no proton-induced fluctuations occur between pH 7.5 and 6.5. Finally, we propose a possible physical interpretation of the formal model of the protonation cycle introduced in the companion paper.     

Electrostatic Tuning of Cellular Excitability

Voltage-gated ion channels regulate the electric activity of excitable tissues, such as the heart and brain. Therefore, treatment for conditions of disturbed excitability is often based on drugs that target ion channels. In this study of a voltage-gated K channel, we propose what we believe to be a novel pharmacological mechanism for how to regulate channel activity. Charged lipophilic substances can tune channel opening, and consequently excitability, by an electrostatic interaction with the channel's voltage sensors. The direction of the effect depends on the charge of the substance. This was shown by three compounds sharing an arachidonyl backbone but bearing different charge: arachidonic acid, methyl arachidonate, and arachidonyl amine. Computer simulations of membrane excitability showed that small changes in the voltage dependence of Na and K channels have prominent impact on excitability and the tendency for repetitive firing. For instance, a shift in the voltage dependence of a K channel with −5 or +5 mV corresponds to a threefold increase or decrease in K channel density, respectively. We suggest that electrostatic tuning of ion channel activity constitutes a novel and powerful pharmacological approach with which to affect cellular excitability.     

Structure,Function, and Modification of the Voltage Sensor in Voltage-Gated Ion Channels

Voltage-gated ion channels are crucial for both neuronal and cardiac excitability. Decades of research have begun to unravel the intriguing machinery behind voltage sensitivity. Although the details regarding the arrangement and movement in the voltage-sensor domain are still debated, consensus is slowly emerging. There are three competing conceptual models: the helical-screw, the transporter, and the paddle model. In this review we explore the structure of the activated voltage-sensor domain based on the recent X-ray structure of a chimera between Kv1.2 and Kv2.1. We also present a model for the closed state. From this we conclude that upon depolarization the voltage sensor S4 moves approximately 13 A outwards and rotates approximately 180 degrees, thus consistent with the helical-screw model. S4 also moves relative to S3b which is not consistent with the paddle model. One interesting feature of the voltage sensor is that it partially faces the lipid bilayer and therefore can interact both with the membrane itself and with physiological and pharmacological molecules reaching the channel from the membrane. This type of channel modulation is discussed together with other mechanisms for how voltage-sensitivity is modified. Small effects on voltage-sensitivity can have profound effects on excitability. Therefore, medical drugs designed to alter the voltage dependence offer an interesting way to regulate excitability.     

Beating irregularity of single pacemaker cells isolated from the rabbit sinoatrial node.

Single pacemaker heart cells discharge irregularly. Data on fluctuations in interbeat interval of single pacemaker cells isolated from the rabbit sinoatrial node are presented. The coefficient of variation of the interbeat interval is quite small, approximately 2%, even though the coefficient of variation of diastolic depolarization rate is approximately 15%. It has been hypothesized that random fluctuations in interbeat interval arise from the stochastic behavior of the membrane ionic channels. To test this hypothesis, we constructed a single channel model of a single pacemaker cell isolated from the rabbit sinoatrial node, i.e., a model into which the stochastic open-close kinetics of the individual membrane ionic channels are incorporated. Single channel conductances as well as single channel open and closed lifetimes are based on experimental data from whole cell and single channel experiments that have been published in the past decade. Fluctuations in action potential parameters of the model cell are compared with those observed experimentally. It is concluded that fluctuations in interbeat interval of single sinoatrial node pacemaker cells indeed are due to the stochastic open-close kinetics of the membrane ionic channels.     

Ca channel kinetics during the spontaneous heart beat in embryonic chick ventricle cells.

The ability of Ca ions to inhibit Ca channels presents one of the most intriguing problems in membrane biophysics. Because of this negative feedback, Ca channels can regulate the current that flows through them. The kinetics of the channels depend on voltage, and, because the voltage controls the current, a strong interaction exists between voltage dependence and Ca dependence. In addition to this interaction, the proximity of pores and the local concentration of ions also determine how effectively the Ca ions influence channel kinetics. The present article proposes a model that incorporates voltage-dependent kinetics, current-dependent kinetics, and channel clustering. We have based the model on previous voltage-clamp data and on Ca and Ba action currents measured during the action potential in beating heart cells. In general we observe that great variability exists in channel kinetics from patch to patch: Ba or Ca currents have low or high amplitudes and slow or fast kinetics during essentially the same voltage regime, either applied step-protocols or spontaneous cell action potentials. To explain this variability, we have postulated that Ca channels interact through shared ions. The model we propose expands on our previous model for Ba currents. We use the same voltage-dependent rate constants for the Ca currents that we did for the Ba currents. However, we vary the current-dependent rate constants according to the species of the conducting ion. The model reproduces the main features of our data, and we use it to predict Ca channel kinetics under physiological conditions. Preliminary reports of this work have appeared (DeFelice et al., 1991, Biophys. J. 59:551a; Risso et al., 1992, Biophys. J. 61:248a).     

Capacitance fluctuations causing channel noise reduction in stochastic Hodgkin-Huxley systems

Voltage-dependent ion channels determine the electric properties of axonal cell membranes. They not only allow the passage of ions through the cell membrane, but also contribute to an additional charging of the cell membrane resulting in the so-called capacitance loading. The switching of the channel gates between an open and a closed configuration is intrinsically related to the movement of gating charge within the cell membrane. At the beginning of an action potential, the transient gating current is opposite to the direction of the current of sodium ions through the membrane. Therefore, the excitability is expected to become reduced due to the influence of a gating current. Our stochastic Hodgkin-Huxley-like modeling takes into account both the channel noise-i.e. the fluctuations of the number of open ion channels-and the capacitance fluctuations that result from the dynamics of the gating charge. We investigate the spiking dynamics of membrane patches of a variable size and analyze the statistics of the spontaneous spiking. As a main result, we find that the gating currents yield a drastic reduction of the spontaneous spiking rate for sufficiently large ion channel clusters. Consequently, this demonstrates a prominent mechanism for channel noise reduction.     

Neuroleptics antagonize a calcium-activated potassium channel in airway smooth muscle

We examined the effect of neuroleptics on Ca-activated K channels from dog airway smooth muscle cells. Because these agents inhibit a variety of other Ca-mediated processes, it seemed possible that they might also inhibit Ca-activated K channels. In excised, inside-out patches, several neuroleptics potently and reversibly inhibited the K channel from the internal but not the external surface of the patch. Measurements of the effect on open probability and open- and closed-state durations support a simple kinetic model in which neuroleptics bind to and block the open channel. Inhibition by neuroleptics was moderately voltage dependent, with blockers less potent at hyperpolarizing voltages. The relationship between voltage and the dissociation constant for the blocker suggests that the binding site is one-third of the way across the channel's electrical field. Equilibrium dissociation constants for the drug-channel complex were: haloperidol, 1.0 +/- 0.1 microM; trifluoperazine, 1.4 +/- 0.1 microM; thioridazine, 2.4 +/- 0.1 microM; and chlorpromazine, 2.0 microM. This rank-order potency is different from their potency as calmodulin inhibitors, which suggests that neuroleptics bind to the channel rather than a calmodulin-channel complex.     

Gating kinetics of batrachotoxin-modified sodium channels in neuroblastoma cells determined from single-channel measurements

We have observed the opening and closing of single batrachotoxin (BTX)-modified sodium channels in neuroblastoma cells using the patch-clamp method. The conductance of a single BTX-modified channel is approximately 10 pS. At a given membrane potential, the channels are open longer than are normal sodium channels. As is the case for normal sodium channels, the open dwell times become longer as the membrane is depolarized. For membrane potentials more negative than about -70 mV, histograms of both open-state dwell times and closed-state dwell times could be fit by single exponentials. For more depolarized potentials, although the open-state histograms could still be fit by single exponentials, the closed-state histograms required two exponentials. This data together with macroscopic voltage clamp data on the same system could be accounted for by a three-state closed-closed-open model with transition rates between these states that are exponential functions of membrane potential. One of the implications of this model, in agreement with experiment, is that there are always some closed BTX-modified sodium channels, regardless of membrane potential.     

Dampening of Hyperexcitability in CA1 Pyramidal Neurons by Polyunsaturated Fatty Acids Acting on Voltage-Gated Ion Channels

A ketogenic diet is an alternative treatment of epilepsy in infants. The diet, rich in fat and low in carbohydrates, elevates the level of polyunsaturated fatty acids (PUFAs) in plasma. These substances have therefore been suggested to contribute to the anticonvulsive effect of the diet. PUFAs modulate the properties of a range of ion channels, including K and Na channels, and it has been hypothesized that these changes may be part of a mechanistic explanation of the ketogenic diet. Using computational modelling, we here study how experimentally observed PUFA-induced changes of ion channel activity affect neuronal excitability in CA1, in particular responses to synaptic input of high synchronicity. The PUFA effects were studied in two pathological models of cellular hyperexcitability associated with epileptogenesis. We found that experimentally derived PUFA modulation of the A-type K (K_A) channel, but not the delayed-rectifier K channel, restored healthy excitability by selectively reducing the response to inputs of high synchronicity. We also found that PUFA modulation of the transient Na channel was effective in this respect if the channel''s steady-state inactivation was selectively affected. Furthermore, PUFA-induced hyperpolarization of the resting membrane potential was an effective approach to prevent hyperexcitability. When the combined effect of PUFA on the K_A channel, the Na channel, and the resting membrane potential, was simulated, a lower concentration of PUFA was needed to restore healthy excitability. We therefore propose that one explanation of the beneficial effect of PUFAs lies in its simultaneous action on a range of ion-channel targets. Furthermore, this work suggests that a pharmacological cocktail acting on the voltage dependence of the Na-channel inactivation, the voltage dependences of K_A channels, and the resting potential can be an effective treatment of epilepsy.     

KcsA closed and open: modelling and simulation studies

Bacterial homologues of mammalian potassium channels provide structures of two states of a gated K channel. Thus, the crystal structure of KcsA represents a closed state whilst that of MthK represents an open state. Using homology modelling and molecular dynamics simulations we have built a model of the transmembrane domain of KcsA in an open state and have compared its conformational stability with that of the same domain of KcsA in a closed state. Approximate Born energy calculations of monovalent cations within the two KcsA channel states suggest that the intracellular hydrophobic gate in the closed state provides a barrier of height ~5 kT to ion permeation, whilst in the open state the barrier is absent. Simulations (10 ns duration) in an octane slab (a simple membrane mimetic) suggest that closed- and open-state models are of comparable conformational stability, both exhibiting conformational drifts of ~3.3 Å C RMSD relative to the respective starting models. Substantial conformational fluctuations are observed in the intracellular gate region during both simulations (closed state and open state). In the simulation of open-state KcsA, rapid (<5 ns) exit of all three K⁺ ions occurs through the intracellular mouth of the channel. Helix kink and swivel motion is observed at the molecular hinge formed by residue G99 of the M2 helix. This motion is more substantial for the open- than for the closed-state model of the channel.     

Superstatistics analysis of the ion current distribution function: Met3PbCl influence study

A novel analysis of ion current time series is proposed. It is shown that higher (second, third and fourth) statistical moments of the ion current probability distribution function (PDF) can yield new information about ion channel properties. The method is illustrated on a two-state model where the PDF of the compound states are given by normal distributions. The proposed method was applied to the analysis of the SV cation channels of vacuolar membrane of Beta vulgaris and the influence of trimethyllead chloride (Met₃PbCl) on the ion current probability distribution. Ion currents were measured by patch-clamp technique. It was shown that Met₃PbCl influences the variance of the open-state ion current but does not alter the PDF of the closed-state ion current. Incorporation of higher statistical moments into the standard investigation of ion channel properties is proposed.     

Dynamical characterization of inactivation path in voltage-gated Na+ ion channel by non-equilibrium response spectroscopy

Inactivation path of voltage gated sodium channel has been studied here under various voltage protocols as it is the main governing factor for the periodic occurrence and shape of the action potential. These voltage protocols actually serve as non-equilibrium response spectroscopic tools to study the ion channel in non-equilibrium environment. In contrast to a lot of effort in finding the crystal structure based molecular mechanism of closed-state(CSI) and open-state inactivation(OSI); here our approach is to understand the dynamical characterization of inactivation. The kinetic flux as well as energetic contribution of the closed and open- state inactivation path is compared here for voltage protocols, namely constant, pulsed and oscillating. The non-equilibrium thermodynamic quantities used in response to these voltage protocols serve as improved characterization tools for theoretical understanding which not only agrees with the previously known kinetic measurements but also predict the energetically optimum processes to sustain the auto-regulatory mechanism of action potential and the consequent inactivation steps needed. The time dependent voltage pattern governs the population of the conformational states which when couple with characteristic rate parameters, the CSI and OSI selectivity arise dynamically to control the inactivation path. Using constant, pulsed and continuous oscillating voltage protocols we have shown that during depolarization the OSI path is more favored path of inactivation however, in the hyper-polarized situation the CSI is favored. It is also shown that the re-factorisation of inactivated sodium channel to resting state occurs via CSI path. Here we have shown how the subtle energetic and entropic cost due to the change in the depolarization magnitude determines the optimum path of inactivation. It is shown that an efficient CSI and OSI dynamical profile in principle can characterize the open-state drug blocking phenomena.     

Domain IV voltage-sensor movement is both sufficient and rate limiting for fast inactivation in sodium channels

Voltage-gated sodium channels are critical for the generation and propagation of electrical signals in most excitable cells. Activation of Na⁺ channels initiates an action potential, and fast inactivation facilitates repolarization of the membrane by the outward K⁺ current. Fast inactivation is also the main determinant of the refractory period between successive electrical impulses. Although the voltage sensor of domain IV (DIV) has been implicated in fast inactivation, it remains unclear whether the activation of DIV alone is sufficient for fast inactivation to occur. Here, we functionally neutralize each specific voltage sensor by mutating several critical arginines in the S4 segment to glutamines. We assess the individual role of each voltage-sensing domain in the voltage dependence and kinetics of fast inactivation upon its specific inhibition. We show that movement of the DIV voltage sensor is the rate-limiting step for both development and recovery from fast inactivation. Our data suggest that activation of the DIV voltage sensor alone is sufficient for fast inactivation to occur, and that activation of DIV before channel opening is the molecular mechanism for closed-state inactivation. We propose a kinetic model of sodium channel gating that can account for our major findings over a wide voltage range by postulating that DIV movement is both necessary and sufficient for fast inactivation.     

Interactions between intrinsic membrane protein and electric field. An approach to studying nerve excitability

We have approached the problem of nerve excitability through three questions: (a) What is the diagram for a channel? That is, what conformational states can the protein assume, and what transitions between these conformations are permitted? (b) What is the channel conductance associated with each conformation the channel can assume? (c) How do the rates for conformational transition depend upon membrane potential? These three questions arise from a standard statistical mechanical treatment of a nerve membrane containing several classes of identical, independent channels. Gating of channels, in this view, is associated with conformational changes of the channel protein, and it is assumed these conformations are distinct. The precise formulation of these questions is presented in terms of the theoretical treatment, and the approaches we have taken to answer the questions are indicated. Our present results indicate: Transition rates should depend exponentially on membrane potential over a limited voltage range, but probably will show a more complex dependence for extremes of the range; channels probably can take on only two conductances, open and shut, but more complicated situations are not entirely excluded; the diagram for a channel cannot be determined from standard voltage clamp data alone, but by studying gating currents and conductance fluctuations, it should be possible to select between alternative plausible physical mechanisms.     

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.     

Lipid modulation of ion channels through specific binding sites

Ion channel conformational changes within the lipid membrane are a key requirement to control ion passage. Thus, it seems reasonable to assume that lipid composition should modulate ion channel function. There is increasing evidence that this implicates not just an indirect consequence of the lipid influence on the physical properties of the membrane, but also specific binding of selected lipids to certain protein domains. The result is that channel function and its consequences on excitability, contractility, intracellular signaling or any other process mediated by such channel proteins, could be subjected to modulation by membrane lipids. From this it follows that development, age, diet or diseases that alter lipid composition should also have an influence on those cellular properties. The wealth of data on the non-annular lipid binding sites in potassium channel from Streptomyces lividans (KcsA) makes this protein a good model to study the modulation of ion channel structure and function by lipids. The fact that this protein is able to assemble into clusters through the same non-annular sites, resulting in large changes in channel activity, makes these sites even more interesting as a potential target to develop lead compounds able to disrupt such interactions and hopefully, to modulate ion channel function. This Article is Part of a Special Issue Entitled: Membrane Structure and Function: Relevance in the Cell's Physiology, Pathology and Therapy.     

The Xenopus Oocyte Cut-open Vaseline Gap Voltage-clamp Technique With Fluorometry

The cut-open oocyte Vaseline gap (COVG) voltage clamp technique allows for analysis of electrophysiological and kinetic properties of heterologous ion channels in oocytes. Recordings from the cut-open setup are particularly useful for resolving low magnitude gating currents, rapid ionic current activation, and deactivation. The main benefits over the two-electrode voltage clamp (TEVC) technique include increased clamp speed, improved signal-to-noise ratio, and the ability to modulate the intracellular and extracellular milieu.Here, we employ the human cardiac sodium channel (hNa_V1.5), expressed in Xenopus oocytes, to demonstrate the cut-open setup and protocol as well as modifications that are required to add voltage clamp fluorometry capability.The properties of fast activating ion channels, such as hNa_V1.5, cannot be fully resolved near room temperature using TEVC, in which the entirety of the oocyte membrane is clamped, making voltage control difficult. However, in the cut-open technique, isolation of only a small portion of the cell membrane allows for the rapid clamping required to accurately record fast kinetics while preventing channel run-down associated with patch clamp techniques.In conjunction with the COVG technique, ion channel kinetics and electrophysiological properties can be further assayed by using voltage clamp fluorometry, where protein motion is tracked via cysteine conjugation of extracellularly applied fluorophores, insertion of genetically encoded fluorescent proteins, or the incorporation of unnatural amino acids into the region of interest¹. This additional data yields kinetic information about voltage-dependent conformational rearrangements of the protein via changes in the microenvironment surrounding the fluorescent molecule.     

Nonequilibrium response spectroscopy of voltage-sensitive ion channel gating.

We describe a new electrophysiological technique called nonequilibrium response spectroscopy, which involves application of rapidly fluctuating (as high as 14 kHz) large-amplitude voltage clamp waveforms to ion channels. As a consequence of the irreversible (in the sense of Carnot) exchange of energy between the fluctuating field and the channel protein, the gating response is exquisitely sensitive to features of the kinetics that are difficult or impossible to adequately resolve by means of traditional stepped potential protocols. Here we focus on the application of dichotomous (telegraph) noise voltage fluctuations, a broadband Markovian colored noise that fluctuates between two values. Because Markov kinetic models of channel gating can be embedded within higher-dimensional Markov models that take into account the effects of the voltage fluctuations, many features of the response of the channels can be calculated algebraically. This makes dichotomous noise and its generalizations uniquely suitable for model selection and kinetic analysis. Although we describe its application to macroscopic ionic current measurements, the nonequilibrium response method can also be applied to gating and single channel current recording techniques. We show how data from the human cardiac isoform (hH1a) of the Na+ channel expressed in mammalian cells can be acquired and analyzed, and how these data reveal hidden aspects of the molecular kinetics that are not revealed by conventional methods.     

Multiscale Model of Dynamic Neuromodulation Integrating Neuropeptide-Induced Signaling Pathway Activity with Membrane Electrophysiology

We developed a multiscale model to bridge neuropeptide receptor-activated signaling pathway activity with membrane electrophysiology. Typically, the neuromodulation of biochemical signaling and biophysics have been investigated separately in modeling studies. We studied the effects of Angiotensin II (AngII) on neuronal excitability changes mediated by signaling dynamics and downstream phosphorylation of ion channels. Experiments have shown that AngII binding to the AngII receptor type-1 elicits baseline-dependent regulation of cytosolic Ca²⁺ signaling. Our model simulations revealed a baseline Ca²⁺-dependent response to AngII receptor type-1 activation by AngII. Consistent with experimental observations, AngII evoked a rise in Ca²⁺ when starting at a low baseline Ca²⁺ level, and a decrease in Ca²⁺ when starting at a higher baseline. Our analysis predicted that the kinetics of Ca²⁺ transport into the endoplasmic reticulum play a critical role in shaping the Ca²⁺ response. The Ca²⁺ baseline also influenced the AngII-induced excitability changes such that lower Ca²⁺ levels were associated with a larger firing rate increase. We examined the relative contributions of signaling kinases protein kinase C and Ca²⁺/Calmodulin-dependent protein kinase II to AngII-mediated excitability changes by simulating activity blockade individually and in combination. We found that protein kinase C selectively controlled firing rate adaptation whereas Ca²⁺/Calmodulin-dependent protein kinase II induced a delayed effect on the firing rate increase. We tested whether signaling kinetics were necessary for the dynamic effects of AngII on excitability by simulating three scenarios of AngII-mediated K_DR channel phosphorylation: (1), an increased steady state; (2), a step-change increase; and (3), dynamic modulation. Our results revealed that the kinetics emerging from neuromodulatory activation of the signaling network were required to account for the dynamical changes in excitability. In summary, our integrated multiscale model provides, to our knowledge, a new approach for quantitative investigation of neuromodulatory effects on signaling and electrophysiology.