272 factor, Bicoid acts within the nuclei. Thus, for its biological function the nuclear, as opposed to the cytoplasmic, concentrations are of crucial importance. If the degradation of Bicoid mainly occurs in the nuclei, then the scaling of the gradient could be explained because the length scale of the Bicoid gradient would depend on the nuclear density. These ideas led to an increased interest in the precise measurement of Bicoid’s diffusion, decay and nuclear shuttling rates in living embryos. The production of transgenic flies expressing fully functional GFP-tagged Bicoid protein partially allowed such measurements and produced two surprising results (Gregor et al. 2007). Firstly, during development, the nuclear concentration of Bicoid at a given position remains constant within a 10% margin, despite increasing nuclear densities (the number of nuclei increases 16-fold). This observation is in direct conflict with the explanation for scaling of the gradient in different flies because scaling requires that the gradient changes concomitantly with changing nuclear densities. In addition, nuclear stability by itself is not easy to explain given a steady state model of the gradient. Gregor et al. (2007) concluded: ‘…, rather than passively sampling a large excess of molecules in the cytoplasm, the nuclei must perturb the gradient significantly’. Several models were developed to address this question. One of them assumes that the gradient is not in a steady state, but that the total amount of Bicoid protein increases, and this increase balances the increase in nuclear volume so that the local nuclear concentrations remain constant (Coppey et al. 2007). The second surprising finding concerned the measured diffusion constant of Bicoid, which was an order of magnitude too low to account for the length scale of the gradient (Gregor et al. 2007). Even assuming non- stationary models the measured rate of Bicoid diffusion cannot explain the shape of the gradient (Grimm et al. 2010). To tackle this problem, mathematical models were developed that paid more attention to the actual cellular complexity of the early Drosophila embryo. A coarse- grained model for the syncytial blastoderm was derived which combined cytoplasmic diffusion and nucleocytoplas- mic shuttling of Bicoid (Sample and Shvartsman 2010; Kavousanakis et al. 2010). The model uses a homogenisa- tion approach that is applied in physics and engineering for the description of heterogeneous materials. If materials are structured at two clearly distinct length scales, the structure at the larger length scale might result from the repetition of a small-scale unit with internal structural complexity (the reference cell). In the case of the syncytial blastoderm, the reference cell was assumed to be a nucleus with its surrounding cytoplasm. The homogenisation approach allowed the definition of an effective (large scale) diffusiv- ity for Bicoid as a function of the geometry of the nucleus Dev Genes Evol (2011) 221:255–279 together with the surrounding cytoplasmic island, the diffusivity in the cytoplasm and nucleocytoplasmic shut- tling (Kavousanakis et al. 2010). However, these highly sophisticated approaches still did not lead to an explanation for gradient formation despite Bicoid’s low diffusivity, or to an understanding of nuclear stability and scaling. In particular, the last point remained disconcerting since the explanations invoked for each phenomenon required conflicting assumptions. Additional experimentation was required. In a recent paper, altered Bicoid proteins were analysed that had an impaired ability for nuclear transport or were lacking nuclear transport altogether (Grimm and Wieschaus 2010). Surprisingly, these Bicoid versions produced gradients indistinguishable from that of the wild-type protein. This is a striking observation since wild-type Bicoid concen- trations show huge local fluctuations depending on the nuclear cycle. Thus, one would assume intuitively that these local changes have an effect on the overall gradient. These new findings also rule out explanations for scaling that invoke nuclear density. According to a recent sugges- tion, scaling might result from the positive correlation between the amount of bicoid mRNA and egg size (Cheung et al. 2011). Finally, the new findings re-open the whole discussion on the mechanisms of gradient formation. No doubt, we are currently unable to provide a mechanistic explanation of one of the simplest patterning problems in biology, the formation of the exponentially decaying gradient of a single protein species emanating from a local source. This problem seems to be much simpler than that of self-organised patterning which motivated Turing or Gierer and Meinhardt; it is also much simpler than BMP gradient formation or the gap gene network, the two situations exemplified above. However, it touches on one key feature of development: the capability to produce the same pattern at different length scales. It was precisely this feature, in some of its extreme realisations, that Driesch believed could not be explained by physics and chemistry and for which he developed his harmonious equipotential system reflecting a type of lawfulness only found in organisms. As we do not want to take refuge in vitalistic tenets, the question arises of where we could obtain additional physicochemical explanations to explain Bicoid gradient formation. The problem here is not the lack of potential candidates, but rather the multitude of options. (1) Bicoid translation might not exclusively occur at the anterior pole and Bicoid’s rate of translation might not be constant over time as assumed in most models (Surdej and Jacobs-Lorena 1998; He et al. 2011). Indeed, bicoid mRNA is not tightly localised to the anterior cortex, but forms a steep gradient (Spirov et al. 2009; St Johnston et al. 1989; Weil et al. 2008; Little et al. 2011). Thus, Bicoid might emerge from a graded source. This might certainly help to explain the