Messages Do Diffuse Faster than Messengers: Reconciling Disparate Estimates of the Morphogen Bicoid Diffusion Coefficient

Abstract

The gradient of Bicoid (Bcd) is key for the establishment of the anterior-posterior axis in Drosophila embryos. The gradient properties are compatible with the SDD model in which Bcd is synthesized at the anterior pole and then diffuses into the embryo and is degraded with a characteristic time. Within this model, the Bcd diffusion coefficient is critical to set the timescale of gradient formation. This coefficient has been measured using two optical techniques, Fluorescence Recovery After Photobleaching (FRAP) and Fluorescence Correlation Spectroscopy (FCS), obtaining estimates in which the FCS value is an order of magnitude larger than the FRAP one. This discrepancy raises the following questions: which estimate is "correct''; what is the reason for the disparity; and can the SDD model explain Bcd gradient formation within the experimentally observed times? In this paper, we use a simple biophysical model in which Bcd diffuses and interacts with binding sites to show that both the FRAP and the FCS estimates may be correct and compatible with the observed timescale of gradient formation. The discrepancy arises from the fact that FCS and FRAP report on different effective (concentration dependent) diffusion coefficients, one of which describes the spreading rate of the individual Bcd molecules (the messengers) and the other one that of their concentration (the message). The latter is the one that is more relevant for the gradient establishment and is compatible with its formation within the experimentally observed times.

αTubulin 67C and Ncd Are Essential for Establishing a Cortical Microtubular Network and Formation of the Bicoid mRNA Gradient in Drosophila

“…Subsequently, other reports measured higher diffusion rates [6], [7], calculated to be high enough to explain the SDD diffusion model, and corroborated by a recent biophysical model analysis [8]. Unfortunately, as a major drawback, all the above analyses comprised measurements of diffusion during late nuclear cycles (nc) 10–14 and at the peripheral cytoplasm of the embryo.…”

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

“…This again highlights the implications that a particular choice of model has on the interpretation of the observations. We based our choice of the parameters that were not estimated in [Sigaut et al, 2014] on the fluorescence lengthscale distribution and on the time it takes for the gradient to be established. Although there are some discrepancies between the results of the simulations of figure 4 and the experimental observations (e.g.…”

“…1 in the region where FCS experiments are performed [Sigaut et al, 2014], (20)- (21) yieldα ∼ (0.1 − 0.2)s −1 . Then, through the constraint that the total concentration observed at the anterior pole imposes on θ/α (18), we derive θ.…”

“…At z = 0.75L, this time is too long (≥ 10hs) if it is assumed that D ≈ 1µ 2 m/s, the value estimated in [Gregor et al, 2007a using FRAP, and it is too short (∼ 0.5hs) if the free diffusion coefficient of Bcd estimated in [Sigaut et al, 2014], D ≈ 20µ 2 m/s, is used instead. The solution (22) also shows that the rate of production, θ o , determines the maximum value of [Bcd] but is not involved in the convergence time.…”

“…Although the FCS result apparently reconciles the observed time it takes for the gradient to be formed with the SDD model, the question arises as to what is the reason for the discrepancy between D F CS and D F RAP . In [Sigaut et al, 2014] an explanation was provided for this apparent discrepancy. Based on previous studies on the transport of substances that diffuse and react [Pando et al, 2006] and on the analysis of FCS and FRAP experiments in such a case [Sigaut et al, 2010], it was shown in [Sigaut et al, 2014] that both the FRAP and FCS estimates of the Bcd diffusion coefficient [Gregor et al, 2007a could be correct if the interaction of Bcd with immobile or slowly moving binding sites was taken into account.…”