Biophysical Mechanism of Parasympathetic Excitation of Urinary Bladder Smooth Muscle Cells: a Simulation Study

A computational model of large conductance voltage and calcium activated potassium channels: implications for calcium dynamics and electrophysiology in detrusor smooth muscle cells

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.

A biophysically constrained computational model of the action potential of mouse urinary bladder smooth muscle

Urinary incontinence is associated with enhanced spontaneous phasic contractions of the detrusor smooth muscle (DSM). Although a complete understanding of the etiology of these spontaneous contractions is not yet established, it is suggested that the spontaneously evoked action potentials (sAPs) in DSM cells initiate and modulate the contractions. In order to further our understanding of the ionic mechanisms underlying sAP generation, we present here a biophysically detailed computational model of a single DSM cell. First, we constructed mathematical models for nine ion channels found in DSM cells based on published experimental data: two voltage gated Ca2+ ion channels, an hyperpolarization-activated ion channel, two voltage-gated K+ ion channels, three Ca2+-activated K+ ion channels and a non-specific background leak ion channel. The ion channels' kinetics were characterized in terms of maximal conductances and differential equations based on voltage or calcium-dependent activation and inactivation. All ion channel models were validated by comparing the simulated currents and current-voltage relations with those reported in experimental work. Incorporating these channels, our DSM model is capable of reproducing experimentally recorded spike-type sAPs of varying configurations, ranging from sAPs displaying after-hyperpolarizations to sAPs displaying after-depolarizations. The contributions of the principal ion channels to spike generation and configuration were also investigated as a means of mimicking the effects of selected pharmacological agents on DSM cell excitability. Additionally, the features of propagation of an AP along a length of electrically continuous smooth muscle tissue were investigated. To date, a biophysically detailed computational model does not exist for DSM cells. Our model, constrained heavily by physiological data, provides a powerful tool to investigate the ionic mechanisms underlying the genesis of DSM electrical activity, which can further shed light on certain aspects of urinary bladder function and dysfunction.