The cardiac muscarinic receptor (M2R) regulates heart rate, in part, by modulating the acetylcholine (ACh) activated K+ current IK, ACh through dissociation of G-proteins, that in turn activate KACh channels. Recently, M2Rs were noted to exhibit intrinsic voltage sensitivity, i. e. their affinity for ligands varies in a voltage dependent manner. The voltage sensitivity of M2R implies that the affinity for ACh (and thus the ACh effect) varies throughout the time course of a cardiac electrical cycle. The aim of this study was to investigate the contribution of M2R voltage sensitivity to the rate and shape of the human sinus node action potentials in physiological and pathophysiological conditions. We developed a Markovian model of the IK, ACh modulation by voltage and integrated it into a computational model of human sinus node. We performed simulations with the integrated model varying ACh concentration and voltage sensitivity. Low ACh exerted a larger effect on IK, ACh at hyperpolarized versus depolarized membrane voltages. This led to a slowing of the pacemaker rate due to an attenuated slope of phase 4 depolarization with only marginal effect on action potential duration and amplitude. We also simulated the theoretical effects of genetic variants that alter the voltage sensitivity of M2R. Modest negative shifts in voltage sensitivity, predicted to increase the affinity of the receptor for ACh, slowed the rate of phase 4 depolarization and slowed heart rate, while modest positive shifts increased heart rate. These simulations support our hypothesis that altered M2R voltage sensitivity contributes to disease and provide a novel mechanistic foundation to study clinical disorders such as atrial fibrillation and inappropriate sinus tachycardia.
The cardiac muscarinic receptor (M2R) plays a crucial role in regulating heart rate variability and vulnerability to atrial arrhythmia by modulating the acetylcholine (ACh) activated K+ current IK, ACh. Cardiac KACh channels are heteromultimers composed of two G-protein-coupled inward rectifier K+ channel subunits, Kir 3. 1 and Kir 3. 4 [1]. ACh activation of M2R triggers dissociation of the G beta-gamma subunits (Gβɣ) that in turn directly activate Kir 3. x subunits to conduct IK, ACh. Unexpectedly, M2Rs were discovered to possess an intrinsic ability to sense transmembrane voltage [2] and the affinity of the receptor for ligands was noted to vary in response to changes in membrane voltage [3]. In particular, the affinity of the receptor for ACh is increased at hyperpolarized membrane potentials and decreased at depolarized potentials. The changes in affinity exert a downstream effect on the KACh channel such that the channel is more active (more current) at hyperpolarized potentials and less active (less current) at depolarized potentials. The observation that M2Rs are intrinsically voltage sensitive has profound implications for cellular signaling in excitable tissues, such as heart. For example, voltage sensitive behavior provides a mechanistic explanation for a decades-old enigmatic process called IK, ACh “relaxation” gating. Relaxation gating refers to a time-dependent change in current magnitude following a depolarizing or hyperpolarizing voltage step [4] and has important consequences for shaping the cardiac action potentials (AP), especially in the sinus node. We recently proposed that relaxation gating represents a voltage dependent change in ACh affinity induced by voltage dependent conformational changes within M2R [5]. Our experimental data provide a mechanistic basis to explain the participation of IK, ACh in the modest chronotropic effects induced by resting vagal tone. As a result of conformational changes in the M2R, the affinity for ACh varies throughout the cardiac electrical cycle such that low (subsaturating) ACh concentrations preferentially activate IK, ACh during diastolic membrane voltages thereby slowing the spontaneous firing rate without appreciably altering AP duration (APD). Alterations in the voltage sensitivity of M2R could theoretically contribute to cardiovascular diseases that clinically present with apparent changes in vagal tone. For example, genetic variants in M2R that shift the receptor occupancy into the hyperpolarized state would be expected to increase the affinity of the receptor for ACh and thus activate more KACh channels at a given ACh concentration (or degree of vagal tone). Accordingly, genetic variants in M2R that shift the receptor occupancy into the hyperpolarized state might explain the clinical phenotype of vagally-mediated atrial fibrillation (AF), patients who present with bradycardia in the setting of physiological (basal) ACh concentrations. Alternatively, genetic variants in M2R that shift the receptor occupancy into the depolarized state would be expected to decrease the affinity of the receptor for ACh and thus fewer KACh channels activate at a given ACh concentration (or given degree of vagal tone). This would decrease the effects of vagal modulation of heart rate, thereby increasing basal heart rate, as observed in the syndrome of inappropriate sinus tachycardia (IST). To provide insights into the contribution of M2R voltage sensitivity to cardiac electrophysiology in physiological and pathophysiological conditions, we extended our previous Markovian model of M2R [5] to incorporate Gβɣ-mediated activation of the KACh channel and integrated the revised Markovian model into a human model of the sinus node (SN) cell model [6]. Based on experimental data from isolated human SN cells [7,8], Fabbri and colleagues recently published a comprehensive model of the human SN pacemaker cell that faithfully recapitulated the effects of autonomic modulation as well as mutations associated with SN dysfunction [6]. In the Fabbri model and its parent model [9], IK, ACh is described by a voltage- and [ACh]-dependent gate, but the intrinsic voltage sensitivity of M2R is not incorporated. Here, we introduce a model reproducing the effects of M2R voltage sensitivity on human SN cell function under physiological and pathophysiological conditions. These simulations support our hypothesis that altered M2R voltage sensitivity contributes to disease and provide a novel mechanistic foundation to study clinical disorders such as AF and IST.
For decades, the contribution of IK, ACh to the modest chronotropic effects of ‘physiological’ or low-dose ACh has been debated [10–12]. Based on the M2R voltage-dependent properties, we predict that subsaturating ACh concentrations exert a larger effect during diastolic (hyperpolarized) membrane voltages, compared to the voltages during the cardiac AP (depolarized) [3,5]; thus preferentially slowing the pacemaker rate with minimal effect on APD. To test this hypothesis, we simulated the effects of varying low, sub-saturating concentrations (e. g. , 20–100 nM) of ACh on sinus node AP properties (Fig 1). The most striking effect of increasing ACh concentration was reduced slope of phase 4 depolarization and the corresponding increase in basic cycle length (Fig 1A, Table 1, Vshift = 0), with minimal shortening of APD90 (Table 2, Vshift = 0). Thus, the basic cycle length (BCL) increased from 827 ms in the absence of ACh, to 1585 ms in the presence of 0. 1 μM ACh. The AP amplitude decreased steadily by up to 4. 7 mV at the highest tested concentration of 0. 1 μM ACh (inset of Fig 1A). Simulated open probability O and IK, ACh for different ACh concentrations are shown in Fig 1B and 1C. Taken together, these simulations indicate that subsaturating concentrations of ACh slow spontaneous excitation of the SN cell by inhibiting the rise of phase 4 depolarization, without appreciably shortening APD90 or reducing the amplitude of the AP. In our previous experimental studies using isolated feline left atrial myocytes, the voltage dependence of M2R was explored by measuring the ACh concentration-IK, ACh response relationship at hyperpolarized (-100 mV) and depolarized membrane voltages (+50 mV) [3,5]. These experiments indicated that the affinity of the receptor for ACh was greater at hyperpolarized membrane voltages, compared to depolarized voltages. We reasoned that, similar to voltage-gated ion channels, putative disease-associated mutations in M2R might alter the voltage sensitivity of the M2R, with unique consequences for sinus node AP properties and heart rate responses. We modified rate parameters (Eqs 5 and 6) to shift the receptor occupancy towards a hyperpolarized state (higher affinity) or a depolarized state (lower affinity) (S1A Fig). Thus, we simulated the effects of shifting the M2R voltage sensitivity (Fig 2, S3C Fig). S1B Fig highlights the effects of voltage shifts on the state O. Negative shifts (e. g. , Vshift of -30 mV and -150 mV), which caused a more hyperpolarized state of the receptor, increased the occupancy of the U1 and B1 states, as well as the state O. Negative voltage shifts resulted in a slight leftward shift in the concentration-response curve when the cell was held at +50 mV (Fig 3E). Likewise, positive shifts in M2R voltage sensitive parameters caused a slight rightward shift in the concentration-response curve for a holding potential of Vh = -100 mV (Fig 3A). To avoid local minima during the parameter fitting, the model was forced to favor the open state (state O equal to 1), at the maximum concentration of 10 μM ACh and to favor the closed state (O equal to 0), with no ACh present. Further, U1 was forced to be as high as possible at a holding potential of -100mV and U2 at +50 mV, in the absence of ACh. Thus, negative and positive voltage shifts did not move the steady-state concentration-response relationships outside of these ranges. Notwithstanding, the voltages experienced by the single cell model vary between -60 and +30 mV (Fig 1A), within the minimum and maximum ranges defined by the parameter fitting. We previously described the kinetics of “relaxation” gating of IK, ACh in terms of activation and deactivation of KACh channels in the setting of subsaturating ACh concentrations [5]. Activation kinetics were measured by first stepping to a depolarized voltage (+60 mV) to close a large portion of KACh channels at a physiological voltage, followed by stepping through a range of voltages to measure activation of IK, ACh. Deactivation kinetics were assessed by a pre-pulse to a hyperpolarized voltage (-100 mV) to open channels, followed by variable test voltage steps to measure the rate of KACh channel closure. Accordingly, simulated IK, ACh evoked by 0. 1 μM ACh using the activation and deactivation voltage protocols are presented in S1 Fig and the kinetic parameters are described in Table 3. The simulations recapitulate the experimental features of IK, ACh relaxation gating [5], as shown in S1 Fig. The effects of voltage shifts in M2R voltage sensitive parameters on IK, ACh relaxation gating parameters are shown in Fig 3. Next, we simulated the effects of negative and positive voltage shifts in M2R voltage-sensitive parameters on sinus node APs, together with the corresponding effects on state O and IK, ACh (Fig 4). Negative shifts (e. g. , Vshift of -10 mV and -30 mV), which would be predicted to increase ACh affinity, reduced the slope of phase 4 depolarization in a concentration-dependent manner, with minimal effects on AP amplitude or APD90 (Fig 4A versus 4D, Tables 1 and 2). The reduction in the slope of phase 4 depolarization induced by a negative Vshift was due to an increase in the open probability of KACh channels relative to the control condition, thereby increasing the magnitude of IK, ACh. These results indicate that shifts in the M2R voltage sensitivity impact the rate of spontaneous depolarization of sinus node APs. To further characterize the physiological consequences of positive and negative voltage shifts, we studied the effects of variable M2R voltage sensitivity on the ACh concentration-heart rate response relationship (Fig 5A). Our model recapitulates experimental data [12] indicating that ACh concentrations ranging from 0. 01 to 0. 1 μM induce slowing of the spontaneous activity by 10% and 45%, respectively. Hyperpolarizing shifts in the M2R voltage dependent parameters shifted the relationship toward progressive spontaneous activity slowing. By contrast, depolarizing shifts in these parameters antagonized the spontaneous activity slowing induced by ACh. Taken together, these results suggest that shifts in M2R voltage sensitive parameters exert significant physiological effects on SN firing rate and AP parameters. Next, we quantified the effects of the individual ACh-influenced cardiac currents on heart rate slowing. Fig 5B illustrates the relative contributions of ACh-sensitive currents, including our new model of IK, ACh, together with formulations of the L-type Ca2+ current (ICa, L) and the hyperpolarized-activated ‘funny current’ (If) from Fabbri et al. [6]. Inspection of the individual contributions of the ACh-sensitive currents reveals that our model of IK, ACh (incorporating the voltage-sensitivity of M2R) accounts for roughly 50% of the slowing at ~30nM and more for higher concentrations. These results highlight the important contribution of M2R voltage sensitivity to heart rate slowing induced by ACh.
There are several limitations inherent in the application of the model to describe the kinetics and behavior of IK, ACh. First, the receptor-channel model was fit and optimized to recreate the kinetics of IK, ACh occurring at a concentration of 0. 1 μM ACh. While this is within the range of measured concentrations of ACh, measurements at lower concentrations could enable a more accurate reconstruction of the behavior of IK, ACh and a direct comparison to the effect of If at such concentrations. Furthermore, we acknowledge that the description of the process of dissociation of Gβɣ from the M2R to the activation of the KACh channel is highly simplified. We used a simple channel opening description with a 2-state Markovian model neglecting different binding properties of different Kir subunits or cooperativity mechanisms in binding of Gβɣ. This simplification was necessary as parameters for more complex models are not identifiable with the existent experimental data. Also, the model is not able to reproduce the distinct characteristics of the deactivation protocol time constants. The experimental data indicate that the deactivation time constant is nearly voltage-independent (Fig 3H), the model predicts an increase with membrane depolarization. Nonetheless, because the other simulated features have a very high similarity to the measured values (Fig 3B, 3C, 3F and 3G) and the time constants are in the range of less than half the length of an action potential, we believe that any error introduced does not significantly influence our findings. Additionally, dissociation or binding of Gβɣ in our model does not account for changes in the process due to other influences or any binding to sites other than the KACh channel. The SN cell model recapitulates the experimental findings that ACh inhibits If and ICa, L, which also contribute to slowing of spontaneous pacing rate [23]. We argue that unlike IK, ACh, the M2R voltage dependent effects do not influence If and ICa, L on the time scale of the AP. If and ICa, L inhibition are mediated by inhibition of the cAMP-dependent protein kinase A cascade that functions on a much slower time scale than the APD. By contrast, our simulations demonstrate that voltage dependent conformational changes in M2R influence IK, ACh throughout the cardiac AP, modulating both firing rate and APD. Finally, because our model does not fully integrate all the components of the autonomic nervous system, it is possible that the effects of the putative genetic mutations might be mitigated by compensatory changes in the autonomous nervous system’s response to changes in heart rate. The recent observation that M2Rs are intrinsically voltage sensitive has important implications for understanding the physiology and pathophysiology of parasympathetic regulation of heart rate and APD. By optimizing and integrating a new Markovian model into a human SN model, we show that low ACh concentrations preferentially slow beating rate, without shortening APD, and thereby provide additional support that IK, ACh participates in the purely chronotropic effects of basal vagal tone. Moreover, we explore the effects of altered M2R voltage sensitivity and provide a proof-of-principle foundation that altered sensitivity could result in clinical manifestations of disease states such as vagally-mediated atrial fibrillation and syndrome of inappropriate sinus tachycardia. Given the importance of parasympathetic regulation of atrial vulnerability, M2Rs represent an important therapeutic target to control or prevent atrial arrhythmias.
We developed a Markovian model to reconstruct the behavior of KACh channels at different ACh concentrations and varying transmembrane voltages (Fig 2). The model comprises 3 sub-models: (1) A Markovian model describing the kinetics of the M2R depending on different concentrations of ACh at different voltages (M2R model), (2) a Markovian model describing the activation of the KACh channel based on dispersion of Gβɣ protein from the receptor to the channel (KACh channel model), and (3) a model of potassium current through KACh channels. The parameters of the model were determined by iterative stochastic optimization as previously described [5]. Model parameterization was implemented in Matlab R2017a (The Mathworks Inc. , Natick, MA) and the Matlab Parallel Computing Toolbox. An error function based on the root mean squared differences of the measured versus simulated features of the activation protocol, deactivation protocol, and concentration response curve from [5] was minimized. Measured features were based on whole-cell voltage-clamp experiments [5]. IK, ACh for the activation and deactivation clamp protocols was recorded in the presence of 0. 1 μM ACh. The 3 best measured currents, see S1 Fig, from [5] of each protocol were then fitted to a mono-exponential equation, averaged and then normalized to Coff at -10 mV: I (t) =C+Aexp (-tτ) (10) with the constants A and C, and the time-constant τ of activation (on) and deactivation (off). We choose this strategy, as extracting mono-exponential features and then averaging them introduces less error in the overall reconstructed behavior than averaging the signals themselves. The same fitting approach was used during the model parameterization. Concentration response curves were measured as the resulting IK, ACh at either a holding potential of -100 mV or +50 mV at different ACh concentrations (Fig 5A and 5E). The currents were then normalized to the current measured at maximal ACh concentration for each holding potential. A total of 8 simulated features fs, i, consisting of six features for the voltage clamp protocols (i. e. Con, Coff, Aon, Aoff, τon, and τoff) and two for the concentration response curves (i. e. IKACh, norm, 50mV and IKACh, norm, -100mV), were compared to their corresponding measured features fm, i (Fig 5B–5D and 5F–5H): E2=∑i=18 (||fm, i−fs, i||2||fs, i||2) 2+ (1−max (O) ) + ( (1−max50mV (U2) ) 2+ (1−max−100mV (U1) ) 2) 0μM+ ( (1−max50mV (B2) ) 2+ (1−max−100mV (B1) ) 2+ (1− (B1+B2) 2) ) 10μM (11) Other components of the cost function were used to constrain the behavior of the model at specific ACh concentration and Vm, and to ensure high open probability of the channel. Without bound ACh and Vm of +50 mV, the state U2 was forced to be maximal. Respectively, U1 was forced to be maximal without bound ACh and a transmembrane voltage of -100 mV. Equivalently, with bound ACh, state B2 and B1 were forced to be maximal at -100 mV and 50 mV, respectively. Further, the sum of B1 and B2 was forced to be maximal with bound ACh. For simulations of single cell electrophysiology, the new receptor-channel model was integrated in the publically available model of human SN cells [6]. The formulations for the effect of ACh on ICaL and If were left unaltered throughout the experiments. The model was first exported to Matlab using OpenCOR (www. opencor. ws) and then modified accordingly. Numerical integration was performed by using the integrated ode15s formulation provided by Matlab. We measured BCL to characterize the rate of spontaneous activation of the simulated SN cell at varying concentration of ACh and Vshift. The maximum conductivity gK, ACh, max was set 0. 0022 μS to reproduce previously published heart rate slowing in the presence of 0−0. 1 μM ACh [12]. Furthermore, we measured the APD at 90% repolarization (APD90) to characterize the cardiac AP. The stochastic parameterization yielded the model parameters (Table 3). In comparison to the parameterization of our previous model [5], the fit error of the features from the activation and deactivation protocols was reduced from 1. 5 to 0. 68 despite the additional error terms. Respectively the squared fit error for each feature is; Con: 0. 06, Coff: 0. 025, Aon: 0. 11, Aoff: 0. 014, ton: 0. 04, toff: 0. 18, IKACh, norm, 50mV: 0. 03, IKACh, norm, -100mV: 0. 003. The total error of the features is equal to the square root of the sum of the respective squared fit errors. The corresponding modeled and measured current traces of the voltage protocols are shown in S2 Fig.
Heart rate regulation is dependent upon a delicate interplay between parasympathetic and sympathetic nerve activity at the level of the sinus node. Acetylcholine slows the heart rate by activating the M2 muscarinic receptor (M2R) that, in turn, opens the acetylcholine-activated potassium channel (IK, ACh) to slow the firing of the sinus node. Surprisingly, the M2R is sensitive to membrane potential and undergoes conformational changes throughout the cardiac action potential that alter the affinity for acetylcholine, with secondary consequences for IK, ACh activity. Here, we investigated the contribution of M2R voltage sensitivity to the rate and shape of the human sinus node action potential in physiological and pathophysiological conditions, using a Markovian model of the IK, ACh channel integrated into a computational model of human sinus node. The computational model allowed us to assess the effects of potential genetic variants that alter specific properties of voltage sensitivity. Our results indicate that alterations in the M2R voltage sensitivity play a significant role in the physiology and pathophysiology of the human sinus node and atria. Our computational model is relevant for future studies aimed at the design and development of anti-arrhythmic agents that specifically target the unique voltage-sensitive properties of M2R.
ion channel gating
medicine and health sciences
action potentials
markov models
depolarization
membrane potential
electrophysiology
neuroscience
simulation and modeling
ion channels
mathematics
cardiology
research and analysis methods
sensory physiology
proteins
biophysics
probability theory
heart rate
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biology and life sciences
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neurophysiology
Modeling effects of voltage dependent properties of the cardiac muscarinic receptor on human sinus node function