Optimal Decoding of Cellular Identities in a Genetic Network.

In developing organisms, spatially prescribed cell identities are thought to be determined by the expression levels of multiple genes. Quantitative tests of this idea, however, require a theoretical framework capable of exposing the rules and precision of cell specification over developmental time. We use the gap gene network in the early fly embryo as an example to show how expression levels of the four gap genes can be jointly decoded into an optimal specification of position with 1% accuracy. The decoder correctly predicts, with no free parameters, the dynamics of pair-rule expression patterns at different developmental time points and in various mutant backgrounds. Precise cellular identities are thus available at the earliest stages of development, contrasting the prevailing view of positional information being slowly refined across successive layers of the patterning network. Our results suggest that developmental enhancers closely approximate a mathematically optimal decoding strategy.

Latent space of a small genetic network: Geometry of dynamics and information.

The high-dimensional character of most biological systems presents genuine challenges for modeling and prediction. Here we propose a neural network-based approach for dimensionality reduction and analysis of biological gene expression data, using, as a case study, a well-known genetic network in the early Drosophila embryo, the gap gene patterning system. We build an autoencoder compressing the dynamics of spatial gap gene expression into a two-dimensional (2D) latent map. The resulting 2D dynamics suggests an almost linear model, with a small bare set of essential interactions. Maternally defined spatial modes control gap genes positioning, without the classically assumed intricate set of repressive gap gene interactions. This, surprisingly, predicts minimal changes of neighboring gap domains when knocking out gap genes, consistent with previous observations. Latent space geometries in maternal mutants are also consistent with the existence of such spatial modes. Finally, we show how positional information is well defined and interpretable as a polar angle in latent space. Our work illustrates how optimization of small neural networks on medium-sized biological datasets is sufficiently informative to capture essential underlying mechanisms of network function.

Trading bits in the readout from a genetic network.

In the regulation of gene expression, information of relevance to the organism is represented by the concentrations of transcription factor molecules. To extract this information the cell must effectively "measure" these concentrations, but there are physical limits to the precision of these measurements. We use the gap gene network in the early fly embryo as an example of the tradeoff between the precision of concentration measurements and the transmission of relevant information. For thresholded measurements we find that lower thresholds are more important, and fine tuning is not required for near-optimal information transmission. We then consider general sensors, constrained only by a limit on their information capacity, and find that thresholded sensors can approach true information theoretic optima. The information theoretic approach allows us to identify the optimal sensor for the entire gap gene network and to argue that the physical limitations of sensing necessitate the observed multiplicity of enhancer elements, with sensitivities to combinations rather than single transcription factors.

Scale invariance in early embryonic development.

The body plan of the fruit fly is determined by the expression of just a handful of genes. We show that the spatial patterns of expression for several of these genes scale precisely with the size of the embryo. Concretely, discrete positional markers such as the peaks in striped patterns have absolute positions along the anterior-posterior axis that are proportional to embryo length, with better than 1% accuracy. Further, the information (in bits) that graded patterns of expression provide about position can be decomposed into information about fractional or scaled position and information about absolute position or embryo length; all of the available information is about scaled position, again with ~ 1% accuracy. These observations suggest that the underlying genetic network exhibits scale invariance in a deeper mathematical sense. Taking this mathematical statement seriously requires that the network dynamics have a zero mode, which connects to many other observations on this system.

Functional and ultrastructural analysis of reafferent mechanosensation in larval zebrafish.

All animals need to differentiate between exafferent stimuli, which are caused by the environment, and reafferent stimuli, which are caused by their own movement. In the case of mechanosensation in aquatic animals, the exafferent inputs are water vibrations in the animal's proximity, which need to be distinguishable from the reafferent inputs arising from fluid drag due to locomotion. Both of these inputs are detected by the lateral line, a collection of mechanosensory organs distributed along the surface of the body. In this study, we characterize in detail how hair cells-the receptor cells of the lateral line-in zebrafish larvae discriminate between such reafferent and exafferent signals. Using dye labeling of the lateral line nerve, we visualize two parallel descending inputs that can influence lateral line sensitivity. We combine functional imaging with ultra-structural EM circuit reconstruction to show that cholinergic signals originating from the hindbrain transmit efference copies (copies of the motor command that cancel out self-generated reafferent stimulation during locomotion) and that dopaminergic signals from the hypothalamus may have a role in threshold modulation, both in response to locomotion and salient stimuli. We further gain direct mechanistic insight into the core components of this circuit by loss-of-function perturbations using targeted ablations and gene knockouts. We propose that this simple circuit is the core implementation of mechanosensory reafferent suppression in these young animals and that it might form the first instantiation of state-dependent modulation found at later stages in development.

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.

Fly wing vein patterns have spatial reproducibility of a single cell.

Developmental processes in multicellular organisms occur in fluctuating environments and are prone to noise, yet they produce complex patterns with astonishing reproducibility. We measure the left-right and inter-individual precision of bilaterally symmetric fly wings across the natural range of genetic and environmental conditions and find that wing vein patterns are specified with identical spatial precision and are reproducible to within a single-cell width. The early fly embryo operates at a similar degree of reproducibility, suggesting that the overall spatial precision of morphogenesis in Drosophila performs at the single-cell level. Could development be operating at the physical limit of what a biological system can achieve?

Maternal origins of developmental reproducibility.

Cell fate decisions during multicellular development are precisely coordinated, leading to highly reproducible macroscopic structural outcomes [1-3]. The origins of this reproducibility are found at the molecular level during the earliest stages of development when patterns of morphogen molecules emerge reproducibly [4, 5]. However, although the initial conditions for these early stages are determined by the female during oogenesis, it is unknown whether reproducibility is perpetuated from oogenesis or reacquired by the zygote. To address this issue in the early Drosophila embryo, we sought to count individual maternally deposited bicoid mRNA molecules and compare variability between embryos with previously observed fluctuations in the Bicoid protein gradient [6, 7]. Here, we develop independent methods to quantify total amounts of mRNA in individual embryos and show that mRNA counts are highly reproducible between embryos to within ~9%, matching the reproducibility of the protein gradient. Reproducibility emerges from perfectly linear feedforward processes: changing the genetic dosage in the female leads to proportional changes in both mRNA and protein numbers in the embryo. Our results indicate that the reproducibility of the morphological structures of embryos originates during oogenesis, which is when the expression of maternally provided patterning factors is precisely controlled.