Biological Systems from an Engineer’s Point of View

Mathematical modeling of the processes that pattern embryonic development (often called biological pattern formation) has a long and rich history [1,2]. These models proposed sets of hypothetical interactions, which, upon analysis, were shown to be capable of generating patterns reminiscent of those seen in the biological world, such as stripes, spots, or graded properties. Pattern formation models typically demonstrated the sufficiency of given classes of mechanisms to create patterns that mimicked a particular biological pattern or interaction. In the best cases, the models were able to make testable predictions [3], permitting them to be experimentally challenged, to be revised, and to stimulate yet more experimental tests (see review in [4]). In many other cases, however, the impact of the modeling efforts was mitigated by limitations in computer power and biochemical data. In addition, perhaps the most limiting factor was the mindset of many modelers, using Occam’s razor arguments to make the proposed models as simple as possible, which often generated intriguing patterns, but those patterns lacked the robustness exhibited by the biological system. In hindsight, one could argue that a greater attention to engineering principles would have focused attention on these shortcomings, including potential failure modes, and would have led to more complex, but more robust, models. Thus, despite a few successful cases in which modeling and experimentation worked in concert, modeling fell out of vogue as a means to motivate decisive test experiments. The recent explosion of molecular genetic, genomic, and proteomic data—as well as of quantitative imaging studies of biological tissues—has changed matters dramatically, replacing a previous dearth of molecular details with a wealth of data that are difficult to fully comprehend. This flood of new data has been accompanied by a new influx of physical scientists into biology, including engineers, physicists, and applied mathematicians [5–7]. These individuals bring with them the mindset, methodologies, and mathematical toolboxes common to their own fields, which are proving to be appropriate for analysis of biological systems. However, due to inherent complexity, biological systems seem to be like nothing previously encountered in the physical sciences. Thus, biological systems offer cutting edge problems for most scientific and engineering-related disciplines. It is therefore no wonder that there might seem to be a “bandwagon” of new biology-related research programs in departments that have traditionally focused on nonliving systems. Modeling biological interactions as dynamical systems (i.e., systems of variables changing in time) allows investigation of systems-level topics such as the robustness of patterning mechanisms, the role of feedback, and the self-regulation of size. The use of tools from engineering and applied mathematics, such as sensitivity analysis and control theory, is becoming more commonplace in biology. In addition to giving biologists some new terminology for describing their systems, such analyses are extremely useful in pointing to missing data and in testing the validity of a proposed mechanism. A paper in this issue of PLoS Biology clearly and honestly applies analytical tools to the authors’ research and obtains insights that would have been difficult if not impossible by other means [8]

Graded Dorsal and Differential Gene Regulation in the Drosophila Embryo

A gradient of Dorsal activity patterns the dorsoventral (DV) axis of the early Drosophila melanogaster embryo by controlling the expression of genes that delineate presumptive mesoderm, neuroectoderm, and dorsal ectoderm. The availability of the Drosophila melanogaster genome sequence has accelerated the study of embryonic DV patterning, enabling the use of systems-level approaches. As a result, our understanding of Dorsal-dependent gene regulation has expanded to encompass a collection of more than 50 genes and 30 cis-regulatory sequences. This information, which has been integrated into a spatiotemporal atlas of gene regulatory interactions, comprises one of the best-understood networks controlling any developmental process to date. In this article, we focus on how Dorsal controls differential gene expression and how recent studies have expanded our understanding of Drosophila embryonic development from the cis-regulatory level to that controlling morphogenesis of the embryo

Size-dependent regulation of dorsal–ventral patterning in the early Drosophila embryo

How natural variation in embryo size affects patterning of the Drosophila embryo dorsal–ventral (DV) axis is not known. Here we examined quantitatively the relationship between nuclear distribution of the Dorsal transcription factor, boundary positions for several target genes, and DV axis length. Data were obtained from embryos of a wild-type background as well as from mutant lines inbred to size select embryos of smaller or larger sizes. Our data show that the width of the nuclear Dorsal gradient correlates with DV axis length. In turn, for some genes expressed along the DV axis, the boundary positions correlate closely with nuclear Dorsal levels and with DV axis length; while the expression pattern of others is relatively constant and independent of the width of the Dorsal gradient. In particular, the patterns of snail (sna) and ventral nervous system defective (vnd) correlate with nuclear Dorsal levels and exhibit scaling to DV length; while the pattern of intermediate neuroblasts defective (ind) remains relatively constant with respect to changes in Dorsal and DV length. However, in mutants that exhibit an abnormal expansion of the Dorsal gradient which fails to scale to DV length, only sna follows the Dorsal distribution and exhibits overexpansion; in contrast, vnd and ind do not overexpand suggesting some additional mechanism acts to refine the dorsal boundaries of these two genes. Thus, our results argue against the idea that the Dorsal gradient works as a global system of relative coordinates along the DV axis and suggest that individual targets respond to changes in embryo size in a gene-specific manner

Image analysis and empirical modeling of gene and protein expression

Protein gradients and gene expression patterns are major determinants in the differentiation and fate map of the developing embryo. Here we discuss computational methods to quantitatively measure the positions of gene expression domains and the gradients of protein expression along the dorsal–ventral axis in the Drosophila embryo. Our methodology involves three layers of data. The first layer, or the primary data, consists of z-stack confocal images of embryos processed by in situ hybridization and/or antibody stainings. The secondary data are relationships between location, usually an x-axis coordinate, and fluorescent intensity of gene or protein detection. Tertiary data comprise the optimal parameters that arise from fits of the secondary data to empirical models. The tertiary data are useful to distill large datasets of imaged embryos down to a tractable number of conceptually useful parameters. This analysis allows us to detect subtle phenotypes and is adaptable to any set of genes or proteins with a canonical pattern. For example, we show how insights into the Dorsal transcription factor protein gradient and its target gene ventral-neuroblasts defective (vnd) were obtained using such quantitative approaches

Quantitative imaging of the Dorsal nuclear gradient reveals limitations to threshold-dependent patterning in Drosophila

The NF-κB-related transcription factor, Dorsal, forms a nuclear concentration gradient in the early Drosophila embryo, patterning the dorsal-ventral (DV) axis to specify mesoderm, neurogenic ectoderm, and dorsal ectoderm cell fates. The concentration of nuclear Dorsal is thought to determine these patterning events; however, the levels of nuclear Dorsal have not been quantified previously. Furthermore, existing models of Dorsal-dependent germ layer specification and patterning consider steady-state levels of Dorsal relative to target gene expression patterns, yet both Dorsal gradient formation and gene expression are dynamic. We devised a quantitative imaging method to measure the Dorsal nuclear gradient while simultaneously examining Dorsal target gene expression along the DV axis. Unlike observations from other insects such as Tribolium, we find the Dorsal gradient maintains a constant bell-shaped distribution during embryogenesis. We also find that some classical Dorsal target genes are located outside the region of graded Dorsal nuclear localization, raising the question of whether these genes are direct Dorsal targets. Additionally, we show that Dorsal levels change in time during embryogenesis such that a steady state is not reached. These results suggest that the multiple gene expression outputs observed along the DV axis do not simply reflect a steady-state Dorsal nuclear gradient. Instead, we propose that the Dorsal gradient supplies positional information throughout nuclear cycles 10-14, providing additional evidence for the idea that compensatory combinatorial interactions between Dorsal and other factors effect differential gene expression along the DV axis

Quantifying the Gurken morphogen gradient in Drosophila oogenesis

Quantitative information about the distribution of morphogens is crucial for understanding their effects on cell-fate determination, yet it is difficult to obtain through direct measurements. We have developed a parameter estimation approach for quantifying the spatial distribution of Gurken, a TGFα-like EGFR ligand that acts as a morphogen in Drosophila oogenesis. Modeling of Gurken/EGFR system shows that the shape of the Gurken gradient is controlled by a single dimensionless parameter, the Thiele modulus, which reflects the relative importance of ligand diffusion and degradation. By combining the model with genetic alterations of EGFR levels, we have estimated the value of the Thiele modulus in the wild-type egg chamber. This provides a direct characterization of the shape of the Gurken gradient and demonstrates how parameter estimation techniques can be used to quantify morphogen gradients in development

Size-dependent regulation of dorsal–ventral patterning in the early Drosophila embryo

How natural variation in embryo size affects patterning of the Drosophila embryo dorsal–ventral (DV) axis is not known. Here we examined quantitatively the relationship between nuclear distribution of the Dorsal transcription factor, boundary positions for several target genes, and DV axis length. Data were obtained from embryos of a wild-type background as well as from mutant lines inbred to size select embryos of smaller or larger sizes. Our data show that the width of the nuclear Dorsal gradient correlates with DV axis length. In turn, for some genes expressed along the DV axis, the boundary positions correlate closely with nuclear Dorsal levels and with DV axis length; while the expression pattern of others is relatively constant and independent of the width of the Dorsal gradient. In particular, the patterns of snail (sna) and ventral nervous system defective (vnd) correlate with nuclear Dorsal levels and exhibit scaling to DV length; while the pattern of intermediate neuroblasts defective (ind) remains relatively constant with respect to changes in Dorsal and DV length. However, in mutants that exhibit an abnormal expansion of the Dorsal gradient which fails to scale to DV length, only sna follows the Dorsal distribution and exhibits overexpansion; in contrast, vnd and ind do not overexpand suggesting some additional mechanism acts to refine the dorsal boundaries of these two genes. Thus, our results argue against the idea that the Dorsal gradient works as a global system of relative coordinates along the DV axis and suggest that individual targets respond to changes in embryo size in a gene-specific manner

XMM-Newton spectroscopy of an X-ray selected sample of RL AGNs

This paper presents the X-ray spectroscopy of an X-ray selected sample of 25 radio-loud (RL) AGNs extracted from the XBSS sample. The main goal is to study the origin of the X-ray spectral differences usually observed between radio-loud and radio-quiet (RQ) AGNs. To this end, a comparison sample of 53 RQ AGNs has been also extracted from the same XBSS sample and studied together with the sample of RL AGNs. We have focused the analysis on the distribution of the X-ray spectral indices of the power-law component that models the large majority of the spectra in both samples. We find that the mean X-ray energy spectral index is very similar in the 2 samples and close to alpha_X~1. However, the intrinsic distribution of the spectral indices is significantly broader in the sample of RL AGNs. In order to investigate the origin of this difference, we have divided the RL AGNs into blazars and ``non-blazars'', on the basis of the available optical and radio information. We find strong evidence that the broad distribution observed in the RL AGN sample is mainly due to the presence of the blazars. Furthermore, within the blazar class we have found a link between the X-ray spectral index and the value of the radio-to-X-ray spectral index suggesting that the observed X-ray emission is directly connected to the emission of the relativistic jet. This trend is not observed among the ``non-blazars'' RL AGNs. This favours the hypothesis that, in these latter sources, the X-ray emission is not significantly influenced by the jet emission and it has probably an origin similar to the RQ AGNs. Overall, the results presented here indicate that the observed distribution of the X-ray spectral indices in a given sample of RL AGNs is strongly dependent on the amount of relativistic beaming present in the selected sources.Comment: 18 pages, 10 figures, accepted for publication in A&

What should a quantitative model of masking look like and why would we want it?

Quantitative models of backward masking appeared almost as soon as computing technology was available to simulate them; and continued interest in masking has lead to the development of new models. Despite this long history, the impact of the models on the field has been limited because they have fundamental shortcomings. This paper discusses these shortcomings and outlines what future quantitative models should look like. It also discusses several issues about modeling and how a model could be used by researchers to better explore masking and other aspects of cognition