Julien O. Dubuis

Accurate measurements of dynamics and reproducibility in small genetic networks

Quantification of gene expression has become a central tool for understanding genetic networks. In many systems, the only viable way to measure protein levels is by immunofluorescence, which is notorious for its limited accuracy. Using the early Drosophila embryo as an example, we show that careful identification and control of experimental error allows for highly accurate gene expression measurements. We generated antibodies in different host species, allowing for simultaneous staining of four Drosophila gap genes in individual embryos. Careful error analysis of hundreds of expression profiles reveals that less than ∼20% of the observed embryo‐to‐embryo fluctuations stem from experimental error. These measurements make it possible to extract not only very accurate mean gene expression profiles but also their naturally occurring fluctuations of biological origin and corresponding cross‐correlations. We use this analysis to extract gap gene profile dynamics with ∼1 min accuracy. The combination of these new measurements and analysis techniques reveals a twofold increase in profile reproducibility owing to a collective network dynamics that relays positional accuracy from the maternal gradients to the pair‐rule genes.

Positional information, in bits

Significance In a developing embryo, individual cells need to “know” where they are to do the right thing. How much do they know, and where is this knowledge written down? Here, we show that these questions can be made mathematically precise. In the fruit fly embryo, information about position is thought to be encoded by the concentration of particular protein molecules, and we measure this information, in bits. Just four different kinds of molecules are almost enough to specify the identity of every cell along the long axis of the embryo, and we argue that the way in which this information is distributed reflects an optimization principle, maximizing the information available from a limited number of molecules. Cells in a developing embryo have no direct way of “measuring” their physical position. Through a variety of processes, however, the expression levels of multiple genes come to be correlated with position, and these expression levels thus form a code for “positional information.” We show how to measure this information, in bits, using the gap genes in the Drosophila embryo as an example. Individual genes carry nearly two bits of information, twice as much as would be expected if the expression patterns consisted only of on/off domains separated by sharp boundaries. Taken together, four gap genes carry enough information to define a cell’s location with an error bar of along the anterior/posterior axis of the embryo. This precision is nearly enough for each cell to have a unique identity, which is the maximum information the system can use, and is nearly constant along the length of the embryo. We argue that this constancy is a signature of optimality in the transmission of information from primary morphogen inputs to the output of the gap gene network.

Morphogenesis at criticality

Significance Biological networks are described by many parameters, and the behavior of a network is qualitatively different (monostable, bistable, oscillating, etc.) in different parts of parameter space. Critical points and surfaces are the borders between such qualitatively different regimes, as with phase transitions in equilibrium thermodynamics. We argue that, as expected from the thermodynamic case, genetic regulatory networks should exhibit behaviors near criticality that are independent of most molecular details. Analyzing recent experiments on the gap gene network in the early Drosophila embryo, we find that these signatures of criticality can be seen, quantitatively. This raises the question of why evolution has tuned this network to such a special point in its parameter space. Spatial patterns in the early fruit fly embryo emerge from a network of interactions among transcription factors, the gap genes, driven by maternal inputs. Such networks can exhibit many qualitatively different behaviors, separated by critical surfaces. At criticality, we should observe strong correlations in the fluctuations of different genes around their mean expression levels, a slowing of the dynamics along some but not all directions in the space of possible expression levels, correlations of expression fluctuations over long distances in the embryo, and departures from a Gaussian distribution of these fluctuations. Analysis of recent experiments on the gap gene network shows that all these signatures are observed, and that the different signatures are related in ways predicted by theory. Although there might be other explanations for these individual phenomena, the confluence of evidence suggests that this genetic network is tuned to criticality.

The Syncytial Drosophila Embryo as a Mechanically Excitable Medium

Mitosis in the early syncytial Drosophila embryo is highly correlated in space and time, as manifested in mitotic wavefronts that propagate across the embryo. In this paper we investigate the idea that the embryo can be considered a mechanically-excitable medium, and that mitotic wavefronts can be understood as nonlinear wavefronts that propagate through this medium. We study the wavefronts via both image analysis of confocal microscopy videos and theoretical models. We find that the mitotic waves travel across the embryo at a well-defined speed that decreases with replication cycle. We find two markers of the wavefront in each cycle, corresponding to the onsets of metaphase and anaphase. Each of these onsets is followed by displacements of the nuclei that obey the same wavefront pattern. To understand the mitotic wavefronts theoretically we analyze wavefront propagation in excitable media. We study two classes of models, one with biochemical signaling and one with mechanical signaling. We find that the dependence of wavefront speed on cycle number is most naturally explained by mechanical signaling, and that the entire process suggests a scenario in which biochemical and mechanical signaling are coupled.

Positional Information, Positional Error, and Readout Precision in Morphogenesis: A Mathematical Framework

The concept of positional information is central to our understanding of how cells determine their location in a multicellular structure and thereby their developmental fates. Nevertheless, positional information has neither been defined mathematically nor quantified in a principled way. Here we provide an information-theoretic definition in the context of developmental gene expression patterns and examine the features of expression patterns that affect positional information quantitatively. We connect positional information with the concept of positional error and develop tools to directly measure information and error from experimental data. We illustrate our framework for the case of gap gene expression patterns in the early Drosophila embryo and show how information that is distributed among only four genes is sufficient to determine developmental fates with nearly single-cell resolution. Our approach can be generalized to a variety of different model systems; procedures and examples are discussed in detail.

Quantifying the Bicoid morphogen gradient in living fly embryos.

In multicellular organisms, patterns of gene expression are established in response to gradients of signaling molecules. During fly development in early Drosophila embryos, the Bicoid (Bcd) morphogen gradient is established within the first hour after fertilization. Bcd acts as a transcription factor, initiating the expression of a cascade of genes that determine the segmentation pattern of the embryo, which serves as a blueprint for the future adult organism. A robust understanding of the mechanisms that govern this segmentation cascade is still lacking, and a new generation of quantitative measurements of the spatiotemporal concentration dynamics of the individual players in this cascade is necessary for further progress. Here we describe a series of methods that represent the beginning of the use of Bcd as a quantification example. We describe the generation of a transgenic fly line expressing a Bcd-enhanced green fluorescent protein fusion protein. Using two-photon microscopy, we analyze the Bcd concentration dynamics and measure absolute Bcd expression levels in living fly embryos. These experiments have proven to be fruitful, generating new insights into the mechanisms that lead to the establishment and readout of the Bcd gradient. Generalization of these methods to other genes in the Drosophila segmentation cascade is straightforward and should further our understanding of the early patterning processes and the architecture of the underlying genetic network structure.