An Open Quantum System Approach to Bicoid Gradient Dynamics

A prototypical morphogen gradient that plays a key role in the early embryonic development of fruit flies, by providing positional information to cells, is that of the transcription factor Bicoid (Bcd). Recently a one-dimensional quantum walk model has been utilised to explain its multiple dynamic modes observed through fluorescence correlation spectroscopy (FCS) studies using a closed quantum system approach. In this work we use an open quantum system approach to the dynamics of the Bcd gradient formation and show that exactly the same dynamics are obtained through this more rigorous analysis. We then use the thus obtained expression for the fast dynamic modes to explain the Bcd transcription factor search times for binding to the promoter regions along the DNA. Specifically, we find that the large values of diffusivity allowed by quantum mechanics can avoid the paradox of faster-than-diffusion association rates without any need for the transcription factor to constantly alternate between 1D and 3D diffusion-based search processes. This might help explain the fast and precise transcriptional response elicited by such factors. We conclude that, since many transcription factors share a common search strategy for target gene regulatory regions, our mechanism may have a wide range of applicability.