The effect of reactions on the formation and readout of the gradient of Bicoid

Abstract

Abstract. During early development, the establishment of gradients of transcriptional factors determines the patterning of cell fates. The case of Bicoid (Bcd) in Drosophila melanogaster embryos is well documented and studied. There are still controversies as to whether SDD models in which Bcd is Synthesized at one end, then Diffuses and is Degraded can explain the gradient formation within the timescale observed experimentally. The Bcd gradient is observed in embryos that express a Bicoid-eGFP fusion protein (Bcd-GFP) which cannot differentiate if Bcd is freely diffusing or bound to immobile sites. In this work we analyze an SDID model that includes the Interaction of Bcd with binding sites. Using previously determined biophysical parameters we find that this model can explain the gradient formation within the experimentally observed time. Analyzing the differences between the free and bound Bcd distributions we observe that the latter spans over a longer lengthscale. We conclude that deriving the lengthscale from the distribution of Bcd-GFP can lead to an overestimation of the gradient lengthscale and of the degree of cooperativity that explains the distribution of the protein Hunchback whose production is regulated by Bcd.

Quantification of fluctuations from fluorescence correlation spectroscopy experiments in reaction-diffusion systems

“…The results of the theory presented in this paper also apply to FCS experiments performed in systems with other types of fluorescent species, e.g., those done in Drosophila melanogaster embryos expressing the fluorescent protein, Bcd-EGFP [38]. The interpretation of the timescales drawn from these experiments [9,39] in terms of an underlying reaction-diffusion system under the fast reaction approximation gave estimates of various biophysical parameters [10] that 052407-11 proved to be consistent with other observations [35,40]. The agreement held even if the relative weights of the experimental ACF components differed from the theoretical ones [36].…”

Anomalous Diffusion with an Irreversible Linear Reaction and Sorption-Desorption Process

“…It is worth mentioning that results obtained from (3) were used to investigate biological systems [27,28]. In particular, they have been applied to analyze experimental results of fluorescence recovery after photobleaching (FRAP) in biological systems [29], which is an experimental method widely used to explore binding interactions in cells in vitro and in vivo [30].…”

Multiple Dynamic Modes of the Bcd Gradient are Explained by Quantum Mechanics

“…In the steady-state regime, dP n (t)/dt = 0, and these differential equations simplify into a system of algebraic equations that can be solved analytically [16]. Further extensions accounting for both intrinsic noise [17][18][19][20][21] and diffusion [22][23][24][25][26][27][28][29] build upon Crick's work. Regardless of the specific model details, all of these models share the common diffusion-degradation paradigm of Crick's model in which the time evolution of the concentration fields, or probability densities, for the system is given by a deterministic reaction-diffusion equation or a coarse-grained approach based on above master equation.…”