Work

Long-range diffusion of bound Ca2+: time-dependent WKBJ solutions in one- and two-dimensional imaging

Year: 2026

Type: article

Abstract: Introduction: Reaction-diffusion (RD) systems play a fundamental role in numerous biochemical and biophysical processes. Here, we present a novel analytical framework for solving RD equations by applying the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) formalism to Ca²⁺ buffering. Previous models have primarily focused on stationary Ca²⁺ nanodomains while neglecting diffusion and saturation of intracellular Ca²⁺ buffers and sensors. Results: We derive analytical solutions using WKBJ ansatz and demonstrate that sustained Ca²⁺ source produces continuously expanding distributions of free Ca²⁺, whereas the concentration of Ca²⁺-bound buffers develops at much slower timescale. These predictions are supported experimentally by measurements of one-dimensional fluorescence profiles produced by single-channel activity and two-dimensional profiles generated by whole-cell Ca²⁺ currents. Discussion: The analytical framework developed here extends Michaelis-Menten-type kinetics to reaction-diffusion systems and may therefore be broadly applicable to biochemical and biophysical processes in which diffusion cannot be neglected.

Source: Frontiers in Cellular Neuroscience

DOI: 10.3389/fncel.2026.1925214

Author: Sergej L. Mironov

Institution: University of Göttingen

Language: English

Topic: Ion channel regulation and function

Subfield: Molecular Biology

Field: Biochemistry, Genetics and Molecular Biology

Domain: Life Sciences

Open Access status: gold

Estimated APC paid: $3,801

Funder: Deutsche Forschungsgemeinschaft