Journal of Computational Neuroscience (2019) 46:233–256 https://doi.org/10.1007/s10827-019-00713-9 A computational model of large conductance voltage and calcium activated potassium channels: implications for calcium dynamics and electrophysiology in detrusor smooth muscle cells Suranjana Gupta1 · Rohit Manchanda1 Received: 11 September 2018 / Revised: 14 February 2019 / Accepted: 19 February 2019 / Published online: 25 April 2019 © Springer Science+Business Media, LLC, part of Springer Nature 2019 Abstract The large conductance voltage and calcium activated potassium (BK) channels play a crucial role in regulating the excitability of detrusor smooth muscle, which lines the wall of the urinary bladder. These channels have been widely characterized in terms of their molecular structure, pharmacology and electrophysiology. They control the repolarising and hyperpolarising phases of the action potential, thereby regulating the firing frequency and contraction profiles of the smooth muscle. Several groups have reported varied profiles of BK currents and I-V curves under similar experimental conditions. However, no single computational model has been able to reconcile these apparent discrepancies. In view of the channels’ physiological importance, it is imperative to understand their mechanistic underpinnings so that a realistic model can be created. This paper presents a computational model of the BK channel, based on the Hodgkin-Huxley formalism, constructed by utilising three activation processes — membrane potential, calcium inflow from voltage-gated calcium channels on the membrane and calcium released from the ryanodine receptors present on the sarcoplasmic reticulum. In our model, we attribute the discrepant profiles to the underlying cytosolic calcium received by the channel during its activation. The model enables us to make heuristic predictions regarding the nature of the sub-membrane calcium dynamics underlying the BK channel’s activation. We have employed the model to reproduce various physiological characteristics of the channel and found the simulated responses to be in accordance with the experimental findings. Additionally, we have used the model to investigate the role of this channel in electrophysiological signals, such as the action potential and spontaneous transient hyperpolarisations. Furthermore, the clinical effects of BK channel openers, mallotoxin and NS19504, were simulated for the detrusor smooth muscle cells. Our findings support the proposed application of these drugs for amelioration of the condition of overactive bladder. We thus propose a physiologically realistic BK channel model which can be integrated with other biophysical mechanisms such as ion channels, pumps and exchangers to further elucidate its micro-domain interaction with the intracellular calcium environment. Keywords BK channel · N-shaped I-V curve · Calcium sparks · Action potential · Spontaneous transient hyperpolarisations · Spontaneous transient outward currents · Mallotoxin / Rottlerin · NS19504 Action Editor: Upinder Singh Bhalla 1 Introduction Rohit Manchanda The large conductance voltage and calcium activated [email protected] potassium (BK) or Maxi-K channels play a dominant Suranjana Gupta role in governing the excitability of the detrusor smooth [email protected] muscle (DSM) cells. They modulate the repolarisation and hyperpolarisation phases of the action potential (AP, or spike), in turn controlling the contractile activity of the 1 Computational NeuroPhysiology Lab, Department of Biosciences and Bioengineering, IIT Bombay, DSM tissue (Heppner and Bonev 1997; Vergara et al. Powai, Mumbai- 400076, India 1998; Hashitani and Brading 2003; Hashitani et al. 2004; 234 J Comput Neurosci (2019) 46:233–256 Hayase et al. 2009;Petkov2012, 2014). Modulating these from DSM cells of the same species have shown such channels via drugs may hold promise as a viable option variability. For example, Hirano et al. (1998) and Herrera to treat urinary bladder pathologies that might arise from et al. (2001) recorded BK currents from DSM cells of its channelopathies (Turner and Brading 1997; Brading guinea-pig, with the former reporting a current with an 2006). Studies have shown how alterations in any specific inactivating profile, and the latter reporting a current with a ion channel have affected network functions (Steephen partially inactivating profile. Similarly, Hristov et al. (2011) and Manchanda 2009; Mandge and Manchanda 2018). reported inactivating and non-inactivating current profiles Similarly, mutations in a single BK channel can have for BK currents recorded from human DSM cells. A similar profound consequences in an individual cell, which can inconsistency exists in the case of the BK channel I-V curves alter the frequency of signals in a smooth muscle (SM) (Klockner¨ and Isenberg 1985; Meredith et al. 2004 ). How- syncytium, thereby affecting the behaviour of the muscle. ever, although varying current and I-V profiles have been re- Thus, comprehensive insights into the channel’s biophysical ported, it is as yet unclear as to why these differences arise. functioning are required such that its influence on the The dual activation of BK channels by membrane voltage electrical and contractile activity of the detrusor can be and intracellular calcium (ζ) is a complex phenomenon as modulated in a targeted manner. these activation modalities are interdependent on each other. Amongst all known channels, the BK channel has They act synergistically on the channel to activate it (Salkoff the highest single channel conductance (100 − 300 pS) et al. 2006; Gupta and Manchanda 2018). In an experimental (Kaczorowski and Garcia 1999;Magleby2003; Ghatta setup, it is feasible to regulate the membrane potential, such et al. 2006;Petkov2012, 2014). BK channels are activated as in voltage clamp studies, but not the intracellular calcium 2+ by intracellular calcium concentration ([Ca ]i ζ = concentration. It is, therefore, experimentally challenging to 1 − 10 μM) and membrane voltage (Hristov et al. 2011; decode the interdependencies of the underlying intracellular Petkov 2012; Engbers et al. 2013;Kyleetal.2013;Petkov calcium concentration on the one hand and membrane 2014). The channels receive the activating calcium from two potential on the other. different sources (i) ryanodine receptors (RyRs), located We felt that a computational model of the BK channel on the sarcoplasmic reticulum (SR) membrane and (ii) might help shed light on the aforementioned questions, voltage-dependent calcium channels (VDCCs), present on since investigations can be carried out in the computational the plasma membrane (Herrera and Nelson 2002). In order domain that may not be amenable to experimental to activate, BK channels require high localised (micro- exploration. There are several models of BK channels domain) intracellular calcium concentration in the range available, of which only a few are smooth muscle specific 4 − 30 μM (Cheng and Lederer 2008). Calcium sparks are (Tong et al. 2011; Korogod et al. 2014; Gupta and the submembrane calcium release events mediated by RyRs, Manchanda 2014; Kochenov et al. 2015; Mahapatra et al. that locally increase the intracellular calcium concentration 2018a, b). BK channels have been primarily modelled using to ∼ 10 − 100 μM. Hence, sparks are primarily responsible two techniques, i.e., Markov modelling (Moczydlowski and for the channel’s initial activation (Parajuli et al. 2015). Latorre 1983; Cox et al. 1997;Cox2014; Mahapatra et al. Calcium influx through the membrane calcium channels 2018b) and the Hodgkin-Huxley formalism (Jaffe et al. sustains the activation of the BK channel (Hollywood et al. 2011; Tong et al. 2011; Engbers et al. 2013; Korogod 2000; Herrera and Nelson 2002; Petkov and Nelson 2005; et al. 2014; Gupta and Manchanda 2014; Kochenov et al. Petkov 2012). In all, therefore, BK channels are activated 2015; Mahapatra et al. 2018a). Models based on the by three modalities — membrane voltage, calcium influx Markov modelling technique employ several transitional through the membrane and calcium release from the SR. states to describe BK channel activity. Geng and Magleby Several groups have recorded BK currents under voltage (2015) and Rothberg and Magleby (2000) predicted a clamp conditions. The studies done so far reported BK channel model with 50 states to completely describe currents with varied temporal characteristics, namely, non- the functioning of the channel. Such models are detailed inactivating (Hristov et al. 2011), partially inactivating but computationally highly intensive and time-consuming, (Hirano et al. 1998) and completely inactivating (Herrera rendering them unsuitable for large-scale simulations, such et al. 2001) current profiles. Similarly, I-V curves with two as an integration into a smooth muscle syncytium model distinct shapes for the same presumptive channel have been (Appukuttan et al. 2015). The smooth muscle specific reported, one presenting a profile similar to non-inactivating models based on the Hodgkin-Huxley formalism are voltage-gated potassium channels (Meredith et al. 2004, computationally less intensive, but fail to reproduce the Mahapatra et al. 2018a, b) and the other presenting an ‘N- varied current and I-V profiles reported for this channel shaped’ I-V curve (Meech and Standen 1975;Klockner¨ and because the models focus on currents derived from the Isenberg 1985). This discrepancy cannot be attributed to individual molecular subunits and not on the channel’s