Theory and experiment reveal unexpected calcium profiles in one-dimensional systems

TL;DR

This study combines theory and experiments to uncover unexpected calcium concentration profiles in one-dimensional systems, revealing non-linear behaviors and pattern formations influenced by buffer saturation and mobility.

Contribution

The paper provides new explicit solutions for stationary calcium profiles near channels, highlighting non-linear effects and pattern transitions in one-dimensional models.

Findings

Small calcium influx leads to quasi-exponential gradients.

Large influx causes buffer saturation and periodic calcium patterns.

Oscillatory calcium patterns observed at high fluxes.

Abstract

Calcium is an ubiquitous second messenger that triggers a plethora of key physiological responses. The events are initiated in micro- or nano-sized compartments and determined by the complex interactions with calcium-binding proteins and mechanisms of calcium clearance. Local calcium increases in the vicinity of single channels represent an essentially non-linear reaction-diffusion problem that have been analysed previously using various linearized approximations. I revisited the problem of stationary patterns that can be generated by the point calcium source in the presence of buffer and obtained new explicit solutions. Main results of the analysis of the calcium buffering are supplemented with pertinent derivations and discussion of respective mathematical problems in Appendices. I show that for small calcium influx the calcium gradients around established around channel lumen have quasi-exponential form. For bigger fluxes, when the buffer is saturated, the model predicts periodic patterns. The transition between the two regimes depend on the capacity of buffer and its mobility. Theoretical predictions were examined using a model one-dimensional system. For sufficiently big fluxes the oscillatory calcium patterns were observed. Theoretical and experimental results are discussed in terms of their possible physiological implications.