Long-range diffusion of bound Ca²⁺: time-dependent WKBJ solutions in one- and two-dimensional imaging.
- 1Institute of Neuro- and Sensory Physiology, Georg-August-University, Göttingen, Germany.
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.
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BibTeX
@article{mironov2026longrange,
title = {{Long-range diffusion of bound Ca²⁺: time-dependent WKBJ solutions in one- and two-dimensional imaging.}},
author = {Sergej L Mironov},
journal = {Frontiers in cellular neuroscience},
year = {2026},
month = oct,
doi = {10.3389/fncel.2026.1925214},
url = {https://europepmc.org/article/MED/42898928},
note = {CC BY},
}
RIS
TY - JOUR
TI - Long-range diffusion of bound Ca²⁺: time-dependent WKBJ solutions in one- and two-dimensional imaging.
AU - Sergej L Mironov
PY - 2026
DA - 2026/10/05
JO - Frontiers in cellular neuroscience
DO - 10.3389/fncel.2026.1925214
UR - https://europepmc.org/article/MED/42898928
AB - 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.
SN - 1662-5102
ER -