Stanislav Y. Shvartsman

Computational modeling of the EGF-receptor system: a paradigm for systems biology

Computational models have rarely been used as tools by biologists but, when models provide experimentally testable predictions, they can be extremely useful. The epidermal growth factor receptor (EGFR) is probably the best-understood receptor system, and computational models have played a significant part in its elucidation. For many years, models have been used to analyze EGFR dynamics and to interpret mutational studies, and are now being used to understand processes including signal transduction, autocrine loops and developmental patterning. The success of EGFR modeling can be a guide to combining models and experiments productively to understand complex biological processes as integrated systems.

Argos inhibits epidermal growth factor receptor signalling by ligand sequestration.

The epidermal growth factor receptor (EGFR) has critical functions in development and in many human cancers. During development, the spatial extent of EGFR signalling is regulated by feedback loops comprising both well-understood activators and less well-characterized inhibitors. In Drosophila melanogaster the secreted protein Argos functions as the only known extracellular inhibitor of EGFR, with clearly identified roles in multiple stages of development. Argos is only expressed when the Drosophila EGFR (DER) is activated at high levels, and downregulates further DER signalling. Although there is ample genetic evidence that Argos inhibits DER activation, the biochemical mechanism has not been established. Here we show that Argos inhibits DER signalling without interacting directly with the receptor, but instead by sequestering the DER-activating ligand Spitz. Argos binds tightly to the EGF motif of Spitz and forms a 1:1 (Spitz:Argos) complex that does not bind DER in vitro or at the cell surface. Our results provide an insight into the mechanism of Argos function, and suggest new strategies for EGFR inhibitor design.

Spatial Range of Autocrine Signaling: Modeling and Computational Analysis

Autocrine loops formed by growth factors and their receptors have been identified in a large number of developmental, physiological, and pathological contexts. In general, the spatially distributed and recursive nature of autocrine signaling systems makes their experimental analysis, and often even their detection, very difficult. Here, we combine Brownian motion theory, Monte Carlo simulations, and reaction-diffusion models to analyze the spatial operation of autocrine loops. Within this modeling framework, the ability of autocrine cells to recapture the endogenous ligand and the distances traveled by autocrine ligands are explicitly related to ligand diffusion coefficients, density of surface receptors, ligand secretion rate, and rate constants of ligand binding and endocytic internalization. Applying our models to study autocrine loops in the epidermal growth factor receptor system, we find that autocrine loops can be highly localized--even at the level of a single cell. We demonstrate how the variations in molecular and cellular parameters may tune the spatial range of autocrine signals over several orders of magnitude: from microns to millimeters. We argue that this versatile regulation of the spatial range of autocrine signaling enables autocrine cells to perceive a broad spectrum of environmental information.

Dynamics of the Dorsal morphogen gradient

The dorsoventral (DV) patterning of the Drosophila embryo depends on the nuclear localization gradient of Dorsal (Dl), a protein related to the mammalian NF-κB transcription factors. Current understanding of how the Dl gradient works has been derived from studies of its transcriptional interpretation, but the gradient itself has not been quantified. In particular, it is not known whether the Dl gradient is stable or dynamic during the DV patterning of the embryo. To address this question, we developed a mathematical model of the Dl gradient and constrained its parameters by experimental data. Based on our computational analysis, we predict that the Dl gradient is dynamic and, to a first approximation, can be described as a concentration profile with increasing amplitude and constant shape. These time-dependent properties of the Dl gradient are different from those of the Bicoid and MAPK phosphorylation gradients, which pattern the anterior and terminal regions of the embryo. Specifically, the gradient of the nuclear levels of Bicoid is stable, whereas the pattern of MAPK phosphorylation changes in both shape and amplitude. We attribute these striking differences in the dynamics of maternal morphogen gradients to the differences in the initial conditions and chemistries of the anterior, DV, and terminal systems.

Order reduction for nonlinear dynamic models of distributed reacting systems

Abstract Detailed first-principles models of transport and reaction (based on partial differential equations) lead, after discretization, to dynamical systems of very high order. Systematic methodologies for model order reduction are vital in exploiting such fundamental models in the analysis, design and real-time control of distributed reacting systems. We briefly review some approaches to model order reduction we have successfully used in recent years, and illustrate their capabilities through (a) the design of an observer and stabilizing controller of a reaction-diffusion problem and (b) two-dimensional simulations of the transient behavior of a horizontal MOVPE reactor.

Drosophila eggshell is patterned by sequential action of feedforward and feedback loops.

During Drosophila oogenesis, patterning activities of the EGFR and Dpp pathways specify several subpopulations of the follicle cells that give rise to dorsal eggshell structures. The roof of dorsal eggshell appendages is formed by the follicle cells that express Broad (Br), a zinc-finger transcription factor regulated by both pathways. EGFR induces Br in the dorsal follicle cells. This inductive signal is overridden in the dorsal midline cells, which are exposed to high levels of EGFR activation, and in the anterior cells, by Dpp signaling. We show that the resulting changes in the Br pattern affect the expression of Dpp receptor thickveins (tkv), which is essential for Dpp signaling. By controlling tkv, Br controls Dpp signaling in late stages of oogenesis and, as a result, regulates its own repression in a negative-feedback loop. We synthesize these observations into a model, whereby the dynamics of Br expression are driven by the sequential action of feedforward and feedback loops. The feedforward loop controls the spatial pattern of Br expression, while the feedback loop modulates this pattern in time. This mechanism demonstrates how complex patterns of gene expression can emerge from simple inputs, through the interaction of regulatory network motifs.

MAPK substrate competition integrates patterning signals in the Drosophila embryo.

Terminal regions of the Drosophila embryo are patterned by the localized activation of the mitogen-activated protein kinase (MAPK) pathway. This depends on the MAPK-mediated downregulation of Capicua (Cic), a repressor of the terminal gap genes. We establish that downregulation of Cic is antagonized by the anterior patterning morphogen Bicoid (Bcd). We demonstrate that this effect does not depend on transcriptional activity of Bcd and provide evidence suggesting that Bcd, a direct substrate of MAPK, decreases the availability of MAPK for its other substrates, such as Cic. Based on the quantitative analysis of MAPK signaling in multiple mutants, we propose that MAPK substrate competition coordinates the actions of the anterior and terminal patterning systems. In addition, we identify Hunchback as a novel target of MAPK phosphorylation that can account for the previously described genetic interaction between the posterior and terminal systems. Thus, a common enzyme-substrate competition mechanism can integrate the actions of the anterior, posterior, and terminal patterning signals. Substrate competition can be a general signal integration strategy in networks where enzymes, such as MAPK, interact with their multiple regulators and targets.

A Combinatorial Code for Pattern Formation in Drosophila Oogenesis

Two-dimensional patterning of the follicular epithelium in Drosophila oogenesis is required for the formation of three-dimensional eggshell structures. Our analysis of a large number of published gene expression patterns in the follicle cells suggests that they follow a simple combinatorial code based on six spatial building blocks and the operations of union, difference, intersection, and addition. The building blocks are related to the distribution of inductive signals, provided by the highly conserved epidermal growth factor receptor and bone morphogenetic protein signaling pathways. We demonstrate the validity of the code by testing it against a set of patterns obtained in a large-scale transcriptional profiling experiment. Using the proposed code, we distinguish 36 distinct patterns for 81 genes expressed in the follicular epithelium and characterize their joint dynamics over four stages of oogenesis. The proposed combinatorial framework allows systematic analysis of the diversity and dynamics of two-dimensional transcriptional patterns and guides future studies of gene regulation.

Boundary homogenization for trapping by patchy surfaces

We analyze trapping of diffusing particles by nonoverlapping partially absorbing disks randomly located on a reflecting surface, the problem that arises in many branches of chemical and biological physics. We approach the problem by replacing the heterogeneous boundary condition on the patchy surface by the homogenized partially absorbing boundary condition, which is uniform over the surface. The latter can be used to analyze any problem (internal and external, steady state, and time dependent) in which diffusing particles are trapped by the surface. Our main result is an expression for the effective trapping rate of the homogenized boundary as a function of the fraction of the surface covered by the disks, the disk radius and trapping efficiency, and the particle diffusion constant. We demonstrate excellent accuracy of this expression by testing it against the results of Brownian dynamics simulations. (c) 2004 American Institute of Physics.

Nuclear Trapping Shapes the Terminal Gradient in the Drosophila Embryo

Patterning of the terminal regions of the Drosophila embryo relies on the gradient of phosphorylated ERK/MAPK (dpERK), which is controlled by the localized activation of the Torso receptor tyrosine kinase [1-4]. This model is supported by a large amount of data, but the gradient itself has never been quantified. We present the first measurements of the dpERK gradient and establish a new intracellular layer of its regulation. Based on the quantitative analysis of the spatial pattern of dpERK in mutants with different levels of Torso as well as the dynamics of the wild-type dpERK pattern, we propose that the terminal-patterning gradient is controlled by a cascade of diffusion-trapping modules. A ligand-trapping mechanism establishes a sharply localized pattern of the Torso receptor occupancy on the surface of the embryo. Inside the syncytial embryo, nuclei play the role of traps that localize diffusible dpERK. We argue that the length scale of the terminal-patterning gradient is determined mainly by the intracellular module.