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.