In the end of 1980s, studies of the distribution and transcriptional effects of the Bicoid (Bcd) protein in the Drosophila
embryo provided the first molecularly-defined experimental example of a morphogen gradient [2
]. Bcd is a homeodomain transcription factor, which is translated from maternally deposited mRNA at the anterior of the embryo and patterns the AP embryonic axis by controlling the expression of multiple zygotic genes. Based on the quantitative analysis of the antibody stainings of fixed embryos, the spatial distribution of Bcd appears to be an exponential function of the AP distance [5
]. For more than two decades, this observation has been interpreted within the framework of the classical localized production, diffusion, and uniform degradation model [6
]. According to this model, degradation ensures the stability of the Bcd concentration profile, which would otherwise continue to spread throughout the embryo.
Last year, using the GFP-tagged Bcd constructs and two-photon confocal microscopy, Gregor et al. measured the Bcd gradient in live embryos () [9
]. This study provided the first information about the concentration of Bcd at the expression thresholds of its target genes and revealed a novel feature of the gradient dynamics. Specifically, it was shown that the gradient of the nuclear levels of Bcd disappears with every nuclear division and is then rapidly re-established by rapid nucleocytoplasmic shuttling of Bcd. Remarkably, both the spatial profile of nuclear Bcd along the AP axis and the levels of Bcd in individual nuclei were found to be invariant with respect to nuclear divisions (). Since Bcd is a transcription factor that must access its nuclear targets, it is not surprising that it shuttles in an out of the nuclei. It is also not surprising that the nuclear levels of Bcd are strongly affected by the dissolution and reformation of the nuclear envelope. At the same time it is not at all clear how these processes would affect the levels of Bcd at different nuclear cycles and the entire gradient.
Figure 2 (A) Two phases of nuclear divisions in the biophysical model for the formation of the Bcd gradient. The first 9 divisions occur in three-dimensions; subsequent divisions happen with nuclei arranged as a two-dimensional layer under the plasma membrane. (more ...)
As a step towards answering this question, we formulated and analyzed a model that explicitly accounts for the dynamics of the nuclear density and the nucleocytoplasmic shuttling of Bcd () [10
]. Since the time scale of Bcd degradation is unknown, we asked whether a gradient, which appears stable on the timescale of experimental observations, could be established without degradation at all. In our model Bcd is a stable molecule that rapidly equilibrates between the mobile (cytoplasmic) and trapped (nuclear) states, and nuclei act as reversible traps that slow down the Bcd diffusion. The model splits the entire process into two temporal phases: During the first phase, with low nuclear density, syncytial divisions proceed in three dimensions (nuclear cycles 1 through 9). In the next phase, nuclei are distributed in a two-dimensional layer under the plasma membrane, and the nuclear density is high ().
Using our model and the previously measured durations of the different phases of syncytial nuclear divisions [11
], we were able to show that dynamics of the gradient is controlled by only two dimensionless parameters [10
]. The first parameter, which characterizes the distance to which Bcd diffuses during the first phase of the gradient formation, depends on the diffusivity of the free Bcd molecule, the size of the embryo, and the duration of the first phase in the model. The second dimensionless parameter, which characterizes the equilibrium between nuclear and cytoplasmic Bcd at the beginning of the second phase, depends on the rate constants of the nuclear import and export of Bcd, and on the nuclear density at the beginning of 10th
Analysis of the gradient dynamics requires a specific assumption about the time-dependence of the rate of the nuclear trapping of Bcd. We assumed that this rate is proportional to the number of nuclei per unit volume; therefore it is doubled after every nuclear division [10
]. Under this assumption, we identified a relatively wide domain of the model parameters that is consistent with the experimentally determined length scale of the Bcd gradient and its temporal accuracy [6
]. Based on this, we believe that the mechanism of diffusion and reversible trapping of a stable protein is a viable alternative to the commonly used diffusion and degradation model. In the future, the validity of this new mechanism must be tested by direct in vivo
measurements of the lifetime of Bcd.
Our analysis suggests that i) the Bcd gradient is formed, essentially completely, by passive diffusion before nuclei migrate to the periphery of the embryo and ii) that subsequent nuclear divisions do not affect the gradient. Thus, within the framework of our model, nuclei act as inert sensors of Bcd and do not contribute significantly to the formation of the AP patterning gradient. As we discuss below, recent experiments suggest that nuclei play a very different role in shaping the signal that patterns the embryonic termini.