Chitaranjan Mahapatra

A mathematical model of the calcium transient in urinary bladder smooth muscle cells

An increase in cytoplasmic calcium (Ca²⁺) concentration ([Ca²⁺]_i) is a prerequisite for the contraction of detrusor smooth muscle (DSM) cells . The increase in [Ca²⁺]_i is accomplished by Ca²⁺ entry mainly via voltage dependent L-type Ca²⁺ channel and Ca²⁺ release from intracellular stores. We report here a simulation of the processes that regulate intracellular Ca²⁺ and their dependence on Ca²⁺ concentration. Based on experimentally recorded data, mathematical equations for Ca²⁺ current (generated mainly by L-type Ca²⁺ channel) are developed along with representation of Ca²⁺ATPase pump currents. The plasma membrane Ca²⁺ATPase (PMCA) pump and sarco/endoplasmic reticulum Ca²⁺ATPase (SERCA) pump are responsible for lowering [Ca²⁺]_i which leads to relaxation of smooth muscle. Our model simulates Ca²⁺ current, action potential and the Ca²⁺ transient response so as to reasonably mimic the experimental recordings. In novel findings, currents produced by PMCA and SERCA along with their amplitude and waveform pattern under voltage clamp condition have been predicted for DSM cells. The model has further been used to produce the Ca²⁺ transient which results because of L-type Ca²⁺ channel, Ca²⁺ release from intracellular store, PMCA, SERCA and presence of buffer in the cytoplasm. To explore the model further, Ca²⁺ transient decay rate in control condition is compared to the decay rate reached when PMCA and SERCA are inhibited. We conclude that this model can be used to describe the Ca²⁺ transient response produced by the DSM cell in response to depolarization of cell membrane.

MP42-01 QUANTITATIVE STUDY OF INWARD RECTIFYING ION CHANNEL IN DETRUSOR INSTABILITY

INTRODUCTION AND OBJECTIVES: Detrusor instability is characterized by sudden involuntary contraction of the detrusor smooth muscle (DSM) cells. In various smooth muscle cells, inward rectifying channel Ih has been playing an important role in regulating resting membrane potential (RMP) and basal tone. Therefore, a detailed biophysical study of Ih channel is essential to investigate DSM cell0s excitability towards detrusor instability. This current study aims to model Ih channel in DSM cells to analyze its0 modulating effects in internal spontaneous myogenic electrical activities. METHODS: The DSM cell membrane is represented as a parallel resistor-capacitor circuit consisting of a membrane capacitance Cm and a variable Ih ion channel conductance gh. The voltage-gated Ca2+ and K+ channels, Ca2+ activated K+ channels and leakage currents are incorporated from a published model to generate electrical activities. In this model, Hodgkin-Huxley formalism is adapted for Ih ionic currents with parameters from literature. RESULTS: The RMP is set at -50 mV to mimic the experimental value in mouse DSM cell. The maximum conductance of Ih channel is set at 0.0002 mho/cm to generate the action potential (AP) shown in figure (Blue line) by inducing synaptic input to mimic effects of purinergic neurotransmitter. By reducing the maximum conductance to 0.00016 mho/cm, DSM cell couldn0t generate any AP (black line in figure) as the cell is unable to open transient Ca channels. However, higher activation time constant causes the AP (red line) with the higher peak and slower after hyperpolarization compared to control AP (blue line). The AP (red line) is generated early due to faster activation and early crossing of the threshold value. CONCLUSIONS: The reduction of Ih channel conductance and activation time constant result hyperpolarization, slower afterhyperpolarization and a consequent reduction in DSM cell0s excitability. Presently, researchers are focusing much effort on developing novel compounds acting through different ways to minimize the severe side effects of anticholinergic agents like trospium chloride and oxybutynin. As the Ih channel blockers hyperpolarize the DSM cell, the pharmacological targeting of these channels may play a dominant role for treatment of detrusor instability.

Computational study of inward rectifying ion channel in urinary bladder over activity: student research abstract

Overactive bladder (OAB) is a social hygienic problem, which is characterized by sudden involuntary contraction of the detrusor smooth muscle (DSM) cells. From several experimental studies, it is found that DSM cells from various species including human generate spontaneous action potentials (sAPs) [1, 2], an important concept to initiate spontaneous phasic contraction activity. A primary physiological understanding for unstable urinary bladder contraction is hyperexcitability due to changes in intrinsic ionic mechanisms of DSM cells. A transient rise in cytoplasmic calcium [Ca2+]i is an important reason behind this cellular contraction event. The Ca2+ influx via L-type calcium (Ca2+) channel is essential for the rising phase of the DSM action potential (AP), whereas various potassium (K+) channels mediate the repolarization and after hyperpolarization (AHP) period of the AP, respectively [2,8]. In various smooth muscle cells, inward rectifying channel (Ih) has been playing an important role in regulating resting membrane potential (RMP) and basal tone. By using the whole cell voltage clamp method, Ih channel currents have been recorded in smooth muscle cells from various animals. The modulating role of Ih channel is also well documented in other excitatory cells like neuronal and cardiac tissues. Therefore, a detailed biophysical study of Ih channel is essential to investigate DSM cells excitability towards bladder overactivity.

Simulation study of transient receptor potential current in urinary bladder over activity: student research abstract

Overactive bladder (OAB) syndrome is a social condition, which is identified by the sudden urge to urinate due to spontaneous contraction of the detrusor smooth muscle (DSM) in the urinary bladder. Intracellular electrical activities such as spontaneous depolarization and spontaneous action potentials (sAP)s are recorded in DSM strips of mouse, rat, pig, guinea pig and humans although the number of strips showing activity and the frequency varies considerably between the species [1]. The sAPs are the important concepts to trigger the spontaneous phasic contraction in DSM strips. A primary physiological understanding for the generation of sAP is the hyper-excitability due to the interplay of various active ion channels in DSM cells. The transient rise of intracellular calcium [Ca2+]i due to influx of extracellular calcium via the opening of the L-type calcium (Ca2+) channel is essential for the generation of DSM contraction. The rising phase of the DSM action potential (AP) is regulated by various calcium (Ca2+) channels, whereas several potassium (K+) channels regulate the repolarization and after hyperpolarization (AHP) phases respectively [1]. Recently, a new type Ca2+-activated non-selective cation channels known as Transient receptor potential melastatin-4 (TRPM4) channels have been identified in the guinea pig, rodents and human as the regulator of DSM cell excitability [4]. TRPM4 channel is a sub-family of the transient receptor potential (TRP) channel family and it mediates Na+ ion selectively. Figure 1 illustrates the postulated role of the TRPM4 channel in DSM contraction. According to the postulated mechanism, the activation of the TRPM4 channels is accomplished via the release of Ca2+- from the sarcoplasmic reticulum and it initiates a positive feedback loop to maximize the DSM contractility by providing the Na+-depolarizing conductance. It causes membrane depolarization, AP generation, influx of Ca2+ and contraction in DSM cells after opening the voltage dependent calcium channel (VDCC). Therefore, quantitative analysis of the TRPM4 channel is essential to investigate its effect in altering excitability of DSM cell, which can shed light towards bladder overactivity.

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.

Simulation of In Vitro-Like Electrical Activities in Urinary Bladder Smooth Muscle Cells

Urinary bladder smooth muscle (UBSM) generates spontaneous electrical activities due to stochastic nature of purinergic neurotransmitter release from the parasympathetic nerve. The stochastic nature of the purinergic neurotransmitter release was represented by a simplified ‘point-conductance’ model to mimic in vitro-like electrical activities in UBSM cell. The point-conductance was represented by the independent synaptic conductance described by the stochastic random-walk processes and injected into a single-compartment model of mouse UBSM cell. This model successfully evoked irregular spontaneous depolarizations (SDs) and spontaneous action potential (sAP) as the properties of in vitro-like electrical activities in UBSM cells. The model mimics the T- and L-type Ca2+ ion channel blocker by setting their respective conductance to zero. We also found that the point-conductance model modulates the sAP properties by adding background activity.

Computational simulation of spike patterns in STN neuron using Izhikevich model

Parkinsons disease (PD) is one amongst the most common movement malfunction caused by neurodegeneration in basal ganglia. Several research groups have been proposed different model mechanisms to explain the pathophysiology of this disorder. It has been observed that Deep brain stimulation (DBS) at the subthalamic nucleus (STN) neuron site improves the PD as a new, effective and efficient treatment method. The firing properties of STN neurons in terms of single-spike or the burst modes modulate pathophysiological conditions in PD. It is essential to study the electrical firing properties of STN neuron to understand the PD symptoms in a better way. Nowadays, Computational models are the most effective techniques in investigating complex biological processes. Here, we have simulated different firing patterns in STN neuron using the popular Izhikevich model. By tuning some parameters in our model, we can alter the firing patterns from single mode to burst mode in single STN cell. In future, this simple firing rate model can be coupled to other neuronal models in basal ganglia to investigate movement disorders.