David M. Holloway

Spatial Bistability Generates hunchback Expression Sharpness in the Drosophila Embryo

During embryonic development, the positional information provided by concentration gradients of maternal factors directs pattern formation by providing spatially dependent cues for gene expression. In the fruit fly, Drosophila melanogaster, a classic example of this is the sharp on–off activation of the hunchback (hb) gene at midembryo, in response to local concentrations of the smooth anterior–posterior Bicoid (Bcd) gradient. The regulatory region for hb contains multiple binding sites for the Bcd protein as well as multiple binding sites for the Hb protein. Some previous studies have suggested that Bcd is sufficient for properly sharpened Hb expression, yet other evidence suggests a need for additional regulation. We experimentally quantified the dynamics of hb gene expression in flies that were wild-type, were mutant for hb self-regulation or Bcd binding, or contained an artificial promoter construct consisting of six Bcd and two Hb sites. In addition to these experiments, we developed a reaction–diffusion model of hb transcription, with Bcd cooperative binding and hb self-regulation, and used Zero Eigenvalue Analysis to look for multiple stationary states in the reaction network. Our model reproduces the hb developmental dynamics and correctly predicts the mutant patterns. Analysis of our model indicates that the Hb sharpness can be produced by spatial bistability, in which hb self-regulation produces two stable levels of expression. In the absence of self-regulation, the bistable behavior vanishes and Hb sharpness is disrupted. Bcd cooperative binding affects the position where bistability occurs but is not itself sufficient for a sharp Hb pattern. Our results show that the control of Hb sharpness and positioning, by hb self-regulation and Bcd cooperativity, respectively, are separate processes that can be altered independently. Our model, which matches the changes in Hb position and sharpness observed in different experiments, provides a theoretical framework for understanding the data and in particular indicates that spatial bistability can play a central role in threshold-dependent reading mechanisms of positional information.

Analysis of pattern precision shows that Drosophila segmentation develops substantial independence from gradients of maternal gene products

We analyze the relation between maternal gradients and segmentation in Drosophila, by quantifying spatial precision in protein patterns. Segmentation is first seen in the striped expression patterns of the pair‐rule genes, such as even‐skipped (eve). We compare positional precision between Eve and the maternal gradients of Bicoid (Bcd) and Caudal (Cad) proteins, showing that Eve position could be initially specified by the maternal protein concentrations but that these do not have the precision to specify the mature striped pattern of Eve. By using spatial trends, we avoid possible complications in measuring single boundary precision (e.g., gap gene patterns) and can follow how precision changes in time. During nuclear cleavage cycles 13 and 14, we find that Eve becomes increasingly correlated with egg length, whereas Bcd does not. This finding suggests that the change in precision is part of a separation of segmentation from an absolute spatial measure, established by the maternal gradients, to one precise in relative (percent egg length) units. Developmental Dynamics 235:2949–2960, 2006.

Complex morphogenesis of surfaces: theory and experiment on coupling of reaction–diffusion patterning to growth

Reaction-diffusion theory for pattern formation is considered in relation to processes of biological development in which there is continuous growth and shape change as each new pattern forms. This is particularly common in the plant kingdom, for both unicellular and multicellular organisms. In addition to the feedbacks in the chemical dynamics, there is then another loop linking size and shape changes with the reaction-diffusion patterning of growth controllers in the growing region. In studies by computation, the codes must incorporate, alongside the usual solvers of the partial differential dynamic equations, a versatile growth code, to express any kind of shape change. We have found that regulation of shape change in particular ways (e.g. to make narrow-angle branchings) demands new features in our chemical mechanisms. Our growth algorithm is for a surface growing tangentially, but moving outward and changing shape to accommodate the extra area. This is potentially applicable both to the tunica layer of multicellular plant meristems and to the growing tip of the cell surface, e.g. in the morphogenesis of single-celled chlorophyte algae which display branching processes: whorl formation in Acetabularia (Dasycladales) and repeated dichotomous branching in Micrasterias (Desmidiaceae). For computational studies, a hemispherical shell is a reasonable idealization of the initial shape. We describe results of two types of study: (1) Pattern formation by three reaction-diffusion models, with contrasted nonlinearities, on the hemispherical shell, particularly to find conditions for robust formation of annular pattern or pattern for dichotomous branching, both of which are common in plants. (2) Sequential dichotomous branchings in a system growing and changing in shape from the hemispherical start.

ORDER AND LOCALIZATION IN REACTION-DIFFUSION PATTERN

The present work is concerned with two aspects of pattern formation: pattern localization and degree of pattern order. In reaction-diffusion models, there are three major effects. These stem from the reaction terms, the diffusion terms and the presence or absence of precursor gradients. Global analysis of reaction terms at late stages of pattern formation is at present unavailable. Therefore, we study the effect of the diffusion terms and of precursor gradients with numerical solution in two models: the Brusselator and the Gierer-Meinhardt. Differences in response to changes in the diffusion terms and the precursor gradients are related to contrasts between the nonlinear kinetics of the two models. These models both have Hill coefficient 2; effects of higher cooperativities have recently been discussed by Hunding and Engelhardt [1].

In silico evolution of the hunchback gene indicates redundancy in cis-regulatory organization and spatial gene expression

Biological development depends on the coordinated expression of genes in time and space. Developmental genes have extensive cis-regulatory regions which control their expression. These regions are organized in a modular manner, with different modules controlling expression at different times and locations. Both how modularity evolved and what function it serves are open questions. We present a computational model for the cis-regulation of the hunchback (hb) gene in the fruit fly (Drosophila). We simulate evolution (using an evolutionary computation approach from computer science) to find the optimal cis-regulatory arrangements for fitting experimental hb expression patterns. We find that the cis-regulatory region tends to readily evolve modularity. These cis-regulatory modules (CRMs) do not tend to control single spatial domains, but show a multi-CRM/multi-domain correspondence. We find that the CRM-domain correspondence seen in Drosophila evolves with a high probability in our model, supporting the biological relevance of the approach. The partial redundancy resulting from multi-CRM control may confer some biological robustness against corruption of regulatory sequences. The technique developed on hb could readily be applied to other multi-CRM developmental genes.

Noise in the segmentation gene network of Drosophila with implications for mechanisms of body axis specification

Specification of the anteroposterior (head-to-tail) axis in the fruit fly Drosophila melanogaster is one of the best understood examples of embryonic pattern formation, at the genetic level. A network of some 14 segmentation genes controls protein expression in narrow domains which are the first manifestation of the segments of the insect body. Work in the New York lab has led to a databank of more than 3300 confocal microscope images, quantifying protein expression for the segmentation genes, over a series of times during which protein pattern is developing (http://flyex.ams.sunysb.edu/FlyEx/). Quantification of the variability in expression evident in this data (both between embryos and within single embryos) allows us to determine error propagation in segmentation signalling. The maternal signal to the egg is highly variable, with noise levels more than several times those seen for expression of downstream genes. This implies that error suppression is active in the embryonic patterning mechanism. Error suppression is not possible with the favored mechanism of local concentration gradient reading for positional specification. We discuss possible patterning mechanisms which do reliably filter input noise.

Sequential construction of a model for modular gene expression control, applied to spatial patterning of the Drosophila gene hunchback

Gene network simulations are increasingly used to quantify mutual gene regulation in biological tissues. These are generally based on linear interactions between single-entity regulatory and target genes. Biological genes, by contrast, commonly have multiple, partially independent, cis-regulatory modules (CRMs) for regulator binding, and can produce variant transcription and translation products. We present a modeling framework to address some of the gene regulatory dynamics implied by this biological complexity. Spatial patterning of the hunchback (hb) gene in Drosophila development involves control by three CRMs producing two distinct mRNA transcripts. We use this example to develop a differential equations model for transcription which takes into account the cis-regulatory architecture of the gene. Potential regulatory interactions are screened by a genetic algorithms (GAs) approach and compared to biological expression data.

In Silico Evolution of Gene Cooption in Pattern-Forming Gene Networks

Gene recruitment or cooption occurs when a gene, which may be part of an existing gene regulatory network (GRN), comes under the control of a new regulatory system. Such re-arrangement of pre-existing networks is likely more common for increasing genomic complexity than the creation of new genes. Using evolutionary computations (EC), we investigate how cooption affects the evolvability, outgrowth and robustness of GRNs. We use a data-driven model of insect segmentation, for the fruit fly Drosophila, and evaluate fitness by robustness to maternal variability—a major constraint in biological development. We compare two mechanisms of gene cooption: a simpler one with gene Introduction and Withdrawal operators; and one in which GRN elements can be altered by transposon infection. Starting from a minimal 2-gene network, insufficient for fitting the Drosophila gene expression patterns, we find a general trend of coopting available genes into the GRN, in order to better fit the data. With the transposon mechanism, we find co-evolutionary oscillations between genes and their transposons. These oscillations may offer a new technique in EC for overcoming premature convergence. Finally, we comment on how a differential equations (in contrast to Boolean) approach is necessary for addressing realistic continuous variation in biochemical parameters.

New approaches to designing genes by evolution in the computer

The field of Evolutionary Computation (EC) has been inspired by ideas from the classical theory of biological evolution, with, in particular, the components of a population from which reproductive parents are chosen, a reproductive protocol, a method for altering the genetic information of offspring, and a means for testing the fitness of offspring in order to include them in the population. In turn, impressive progress in EC – understanding the reasons for efficiencies in evolutionary searches has begun to influence scientific work in the field of molecular evolution and in the modeling of biological evolution (Stemmer, 1994a,b; van Nimwegen et al. 1997; 1999; Crutchfield & van Nimwegen, 2001). In this chapter, we will discuss how developments in EC, particularly in the area of crossover operators for Genetic Algorithms (GA), provide new understanding of evolutionary search efficiencies, and the impacts this can have for biological molecular evolution, including directed evolution in the test tube.

Shaped Singular Spectrum Analysis for Quantifying Gene Expression, with Application to the Early Drosophila Embryo

In recent years, with the development of automated microscopy technologies, the volume and complexity of image data on gene expression have increased tremendously. The only way to analyze quantitatively and comprehensively such biological data is by developing and applying new sophisticated mathematical approaches. Here, we present extensions of 2D singular spectrum analysis (2D-SSA) for application to 2D and 3D datasets of embryo images. These extensions, circular and shaped 2D-SSA, are applied to gene expression in the nuclear layer just under the surface of the Drosophila (fruit fly) embryo. We consider the commonly used cylindrical projection of the ellipsoidal Drosophila embryo. We demonstrate how circular and shaped versions of 2D-SSA help to decompose expression data into identifiable components (such as trend and noise), as well as separating signals from different genes. Detection and improvement of under- and overcorrection in multichannel imaging is addressed, as well as the extraction and analysis of 3D features in 3D gene expression patterns.