Multiple dynamic modes of Bicoid morphogen gradient are explained by a quantum-classical model

Extracellular diffusion coupled with degradation is considered a dominant mechanism behind the establishment of morphogen gradients. However, the fundamental nature of these biophysical processes, visa viz, the Bicoid (Bcd) morphogen gradient, remains unclear. Fluorescence correlation spectroscopy has recently revealed multiple modes of Bcd transport at different spatial and temporal locations across the embryo. Here, we show that these observations are best fitted by a model fundamentally based on quantum mechanics. It is thus hypothesized that the transient quantum coherences in collaboration with unitary noise are responsible for the observed dynamics and relaxation to a non-equilibrium steady-state of the Bcd morphogen gradient. Furthermore, simulating the associated probability distribution for the model shows that the observed non-zero concentration of the Bcd molecules in the posterior-most parts of the embryo is a result of non-Gaussian distribution characteristic to quantum evolution. We conclude that with the Bcd gradient being essentially a one-dimensional problem, a simple one-dimensional model suffices for its analysis. (c) 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).