Modelling the Effect of Intracellular Calcium in the Rundown of L-Type Calcium Current

Aditi Agrawal1, Michael Clerx2, Ken Wang3, Liudmila Polonchuk3, David Gavaghan1, Gary Mirams2
1University of Oxford, 2University of Nottingham, 3F. Hoffmann-La Roche Ltd.


Abstract

The L-type calcium current (ICaL) plays a critical role in contraction of the heart muscle via mechanisms such as calcium-induced-calcium-release and excitation-contraction-coupling. Patch-clamp measurements of ICaL are often attenuated with time, even more so than recordings from other ion channels, in a phenomenon called “rundown”. Rundown of ICaL is attributed to several factors including the sensitivity of L-type calcium channels (LCCs) to both voltage and calcium, loss of phosphorylating agents which facilitate the upregulation of LCCs, and activation of calcium-dependent enzymes that cause the proteolytic degradation of LCCs.

In this paper, we use a mathematical model to predict how experimental conditions affect the rundown due to calcium-dependent inactivation (CDI). We do this by first deriving an analytical solution for the diffusion of the calcium-chelating buffer ([B]) from the patch hole in the cell membrane to the entirety of the cell, showing the concentration gradient with respect to time and space. We then use this equation to determine the initial conditions of the buffer at each space point before the membrane voltage is clamped to a voltage protocol. In the next steps, we model the combined effects of 1) [Ca2+] brought into the cell by LCCs under a repeated voltage-clamp protocol and 2) Chemical reaction of [Ca2+] and [B] resulting in a concentration gradient of [Ca2+], [B], and [CaB]. The resultant model simulates ICaL along with its attenuation with time due to CDI.

We repeat these simulations for various combinations of inter-pulse durations, initial time that allows diffusion of [B] into the cell, and size of the cell. We find that CDI is minimised by allowing ample time for diffusion of buffer into the cell both between pulses and before the voltage-clamp is applied, by using fast reaction buffers, and finally by picking cells of small size.