The terminal regions of the fruit fly embryo are patterned by the gradient ERK/MAPK signaling, which depends on the localized activation of the Torso receptor tyrosine kinase (RTK) and controls the expression of at least two genes with distinct expression thresholds [1
]. Torso is activated by a locally processed ligand and is required both for signal transduction and for restricting the extracellular ligand diffusion [2
]. Genetic experiments established that the pattern of Torso activation is spatially restricted, but the extent of this restriction remained unclear. The pattern of Torso occupancy and activation could be smoothly varying along the surface of the embryo and then simply mapped onto the intracellular gradient of MAPK activation [5
]. Alternatively, the pattern of Torso occupancy could be strongly localized at the poles of the embryo, and the smooth dpERK gradient would have to be established by the intracellular diffusion and reaction processes [2
]. To investigate the mechanisms that establish positional information in the terminal system, we developed assays for quantifying the dpERK gradients in space and time () and across multiple genetic backgrounds ().
Quantifying the dpERK Gradients in Syncytial Drosophila Embryos
The dpERK Gradients in Embryos with Different Levels of Receptor Expression
To test whether the spatial pattern of Torso occupancy is smoothly varying or strongly localized, we analyzed the dpERK patterns in embryos with altered levels of Torso expression. If the pattern of Torso occupancy is long ranged [2
], it should become steeper upon increase in the level of the Torso expression and more shallow in embryos with lowered level of Torso. If, on the other hand, the pattern of Torso occupancy is already strongly localized and is a simple image of the spatial profile of ligand release, it should be insensitive to the level of cell-surface receptors. A similar approach was used to explore patterning gradients in other ligand-receptor systems [7
We found that the dpERK gradients in embryos with one functional copy of Torso and those with two extra copies of Torso (four copies in total) are essentially indistinguishable from the wild-type dpERK pattern [11
] (). This result, based on the direct quantitative and statistical analysis of the dpERK gradients, is consistent with the results of the previous experiments that demonstrated that the transcriptional targets of Torso and terminal structures are unaffected by changes in the level of receptor expression [3
]. This strongly supports the hypothesis that the terminal system operates in a regime where the Torso receptors are in excess and the ligand molecules are trapped close to the point of their release, as suggested in [3
]. Given the smoothly varying pattern of dpERK, this implies that positional information in the terminal system is determined mainly inside
the embryo. In this sense, the terminal gradient is different from the one that patterns the dorsoventral axis of the embryo, which is controlled by the extracellular reaction-diffusion processes [13
Here we identify the nuclear trapping of dpERK as a mechanism responsible for the intracellular spatial processing of the terminal signal. This conclusion is based on the analysis of the dynamics of the wild-type dpERK gradient (). We found that between nuclear cycles 10 and 14, the dpERK levels are amplified at the termini and attenuated in the subterminal regions of the embryo (). As shown in the Supplemental Data
(available online), the observed dynamics of the dpERK gradient is consistent with a model where dpERK is a diffusible molecule, which is trapped and dephosphorylated by the nuclei (). A uniform increase in the nuclear density would increase the trapping of the dpERK molecules at the poles and prevent their diffusion to the middle of the embryo (). This is consistent with biochemical and imaging data showing that dpERK rapidly translocates to the nucleus, which can also serve as a compartment of dpERK dephosphorylation [14
]. In addition, our model makes a testable prediction about the dynamics of the nucleocytoplasmic (N/C) ratio of phosphorylated MAPK.
Dynamics of the Wild-Type dpERK Gradients
Spatial Regulation of the dpERK Gradient by Syncytial Nuclei
Let the concentrations of cytoplasmic and nuclear dpERK at a point x
in the embryo be denoted by Cc
) and Cn
), respectively. With the system at steady state, as suggested by the low variability of the dpERK gradients at any given nuclear density ( and Figure S10
), the rate of nuclear import of dpERK is balanced by the rates of its nuclear export and dephosphorylation. Modeling these processes as first-order reactions with the rate constants k+
(nuclear import), k−
(nuclear export), and kn
(dephosphorylation in the nucleus), we arrive at the following expression for the nucleocytoplasmic (N/C) ratio of the dpERK:
The rate constants k− and kn reflect the properties of a single nucleus and a single dpERK molecule; therefore, we assume that they do not depend on the number of nuclei in the system. On the other hand, the trapping rate constant k+, which depends both on the nuclear import rate constant and nuclear density, will increase with every nuclear division. As a consequence, the N/C ratio should be an increasing function of the nuclear density. Because the right side of the equation above does not depend on x, the N/C ratio should be constant throughout the embryo.
We tested this prediction by quantifying the nuclear and cytoplasmic levels of dpERK in cycle 13 and 14 embryos (). Plotting the nuclear and cytoplasmic profiles against each other gives a clear linear relationship, as predicted by the simple formula above (). Furthermore, the nucleocytoplasmic ratio clearly increases between these two nuclear cycles (see Supplemental Data and Figure S6
): the N/C ratio is ~1.4 and ~2 at nuclear cycles 13 and 14, respectively. These measurements show that the nuclear trapping rate is indeed an increasing function of the nuclear density, as predicted by the model.
The observed N/C ratios show that a significant fraction of total dpERK nuclear. As a consequence, defects in the nuclear density should generate clear defects in the gradient. This can be tested in mutants with “holes” in the nuclear density in blastoderm embryos. For example, in shakleton
) embryos, the migration of nuclei to the poles is delayed and a number of embryos exhibit major disruptions in nuclear density [17
]. As predicted by the model, shkl
embryos show striking disruptions in the dpERK gradient (). The quantified posterior gradient of this particular mutant embryo shows a clear local correlation with the nuclear distribution, emphasizing the role of the nuclei at this stage (). In early embryos, the gradient is more extended, presumably reflecting the lack of the nuclei at the poles (Figure S12
). We found similar defects in the giant nuclei
) mutant embryos, which show a different type of defect in nuclear organization (see Figure S13
]. These results support the model in which the syncytial nuclei play an important role in shaping the dpERK gradient.
To summarize, we propose that the dpERK gradient is controlled by a cascade of at least two diffusion-trapping modules. In the extracellular compartment, a ligand-trapping mechanism, identified in previous studies, establishes a sharp gradient of Torso receptor occupancy [2
]. A similar mechanism regulates the dpERK gradient inside the embryo, where syncytial nuclei act as traps that localize diffusible dpERK. At this time, we cannot rule out that the observed sharpening of the dpERK gradient can be modulated also by changes in the spatial distribution of the Torso ligand, but currently there are no data in support of this mode of regulation.
The dynamics of the dpERK gradient is qualitatively different from that of the Bicoid gradient, which remains stable during the last five nuclear divisions [19
]. We have recently proposed that a stable gradient of Bicoid can be established in the absence of Bicoid degradation, because of the reversible trapping of Bicoid by an exponentially increasing number of nuclei [20
]. We attribute the differences between the dynamics of the Bicoid and dpERK gradients to two effects. The first effect is due to the differences in the “chemistries” of the two systems: the morphogen in the terminal system is degraded (MAPK is dephosphorylated), whereas the anterior morphogen is stable (we propose that Bicoid is not degraded on time scale of the gradient formation). The second effect is due to the differences in the initial conditions: by the 10th nuclear division, which is the starting point of the activation of the terminal system, Bicoid gradient is essentially fully established. Thus, a common biophysical framework can describe the Bicoid and dpERK gradients. It remains to be determined whether the nuclear export affects the length scale of the Dorsal gradient, which patterns the dorsoventral axis of the embryo [21