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Biomedical subjects

Cyrill B Muratov

Publications and source records attributed to Cyrill B Muratov.

10 recordsLinked to original sources
PubMed2007

Noise can play an organizing role for the recurrent dynamics in excitable media.

We analyze patterns of recurrent activity in a prototypical model of an excitable medium in the presence of noise. Without noise, this model robustly predicts the existence of spiral waves as the only recurrent patterns in two dimensions. With small noise, however, we found that this model is also capable of generating coherent target patterns, another type of recurrent activity that is widely observed experimentally. These patterns remain essentially deterministic despite the presence of the noise, yet their existence is impossible without it. Their degree of coherence can also be made arbitrarily high for wide ranges of the parameters, which does not require fine-tuning. Our findings demonstrate the need to reexamine current modeling approaches to active biological media.

Animals↗
PubMed2006

Non-meanfield deterministic limits in chemical reaction kinetics.

A general mechanism is proposed by which small intrinsic fluctuations in a system far from equilibrium can result in nearly deterministic dynamical behaviors which are markedly distinct from those realized in the meanfield limit. The mechanism is demonstrated for the kinetic Monte Carlo version of the Schnakenberg reaction where we identified a scaling limit in which the global deterministic bifurcation picture is fundamentally altered by fluctuations. Numerical simulations of the model are found to be in quantitative agreement with theoretical predictions.

Chemical Phenomena↗
PubMed2006

Quantitative models of developmental pattern formation.

Pattern formation in developing organisms can be regulated at a variety of levels, from gene sequence to anatomy. At this level of complexity, mechanistic models of development become essential for integrating data, guiding future experiments, and predicting the effects of genetic and physical perturbations. However, the formulation and analysis of quantitative models of development are limited by high levels of uncertainty in experimental measurements, a large number of both known and unknown system components, and the multiscale nature of development. At the same time, an expanding arsenal of experimental tools can constrain models and directly test their predictions, making the modeling efforts not only necessary, but feasible. Using a number of problems in fruit fly development, we discuss how models can be used to test the feasibility of proposed patterning mechanisms and characterize their systems-level properties.

Animals↗
PubMed2005

Two distinct mechanisms of coherence in randomly perturbed dynamical systems.

We carefully examine two mechanisms--coherence resonance and self-induced stochastic resonance--by which small random perturbations of excitable systems with large time scale separation may lead to the emergence of new coherent behaviors in the form of limit cycles. We analyze what controls the degree of coherence in these two mechanisms and classify their very different properties. In particular we show that coherence resonance arises only at the onset of bifurcation and is rather insensitive against variations in the noise amplitude and the time scale separation ratio. In contrast, self-induced stochastic resonance may arise away from bifurcations and the properties of the limit cycle it induces are controlled by both the noise amplitude and the time scale separation ratio.

Journal Article↗
PubMed2004

Signal propagation and failure in discrete autocrine relays.

A mechanistic model of discrete one-dimensional arrays of autocrine cells interacting via diffusible signals is investigated. Under physiologically relevant assumptions, the model is reduced to a system of ordinary differential equations for the intracellular variables, with a particular, biophysically derived type of long-range coupling between cells. Exact discrete traveling wave and static kink solutions are obtained in the model with sharp threshold nonlinearity. It is argued that the considered mechanism may be used extensively for transmission of information in tissues during homeostasis and development.

Autocrine Communication↗
PubMed2003

Transitions in the model of epithelial patterning.

We analyze pattern formation in the model of cell communication in Drosophila egg development. The model describes the regulatory network formed by the epidermal growth factor receptor (EGFR) and its ligands. The network is activated by the oocyte-derived input that is modulated by feedback loops within the follicular epithelium. We analyze these dynamics within the framework of a recently proposed mathematical model of EGFR signaling (Shvartsman et al. [2002] Development 129:2577-2589). The emphasis is on the large-amplitude solutions of the model that can be correlated with the experimentally observed patterns of protein and gene expression. Our analysis of transitions between the major classes of patterns in the model can be used to interpret the experimentally observed phenotypic transitions in eggshell morphology in Drosophila melanogaster. The existence of complex patterns in the model can be used to account for complex eggshell morphologies in related fly species.

Animals↗
PubMed2003

Long-range signal transmission in autocrine relays.

Intracellular signaling induced by peptide growth factors can stimulate secretion of these molecules into the extracellular medium. In autocrine and paracrine networks, this can establish a positive feedback loop between ligand binding and ligand release. When coupled to intercellular communication by autocrine ligands, this positive feedback can generate constant-speed traveling waves. To demonstrate that, we propose a mechanistic model of autocrine relay systems. The model is relevant to the physiology of epithelial layers and to a number of in vitro experimental formats. Using asymptotic and numerical tools, we find that traveling waves in autocrine relays exist and have a number of unusual properties, such as an optimal ligand binding strength necessary for the maximal speed of propagation. We compare our results to recent observations of autocrine and paracrine systems and discuss the steps toward experimental tests of our predictions.

Autocrine Communication↗
PubMed2003

Discrete models of autocrine cell communication in epithelial layers.

Pattern formation in epithelial layers heavily relies on cell communication by secreted ligands. Whereas the experimentally observed signaling patterns can be visualized at single-cell resolution, a biophysical framework for their interpretation is currently lacking. To this end, we develop a family of discrete models of cell communication in epithelial layers. The models are based on the introduction of cell-to-cell coupling coefficients that characterize the spatial range of intercellular signaling by diffusing ligands. We derive the coupling coefficients as functions of geometric, cellular, and molecular parameters of the ligand transport problem. Using these coupling coefficients, we analyze a nonlinear model of positive feedback between ligand release and binding. In particular, we study criteria of existence of the patterns consisting of clusters of a few signaling cells, as well as the onset of signal propagation. We use our model to interpret recent experimental studies of the EGFR/Rhomboid/Spitz module in Drosophila development.

Animals↗
PubMed2002

Modeling and computational analysis of EGF receptor-mediated cell communication in Drosophila oogenesis.

Autocrine signaling through the Epidermal Growth Factor Receptor (EGFR) operates at various stages of development across species. A recent hypothesis suggested that a distributed network of EGFR autocrine loops was capable of spatially modulating a simple single-peaked input into a more complex two-peaked signaling pattern, specifying the formation of a pair organ in Drosophila oogenesis (two respiratory appendages on the eggshell). To test this hypothesis, we have integrated genetic and biochemical information about the EGFR network into a mechanistic model of transport and signaling. The model allows us to estimate the relative spatial ranges and time scales of the relevant feedback loops, to interpret the phenotypic transitions in eggshell morphology and to predict the effects of new genetic manipulations. We have found that the proposed mechanism with a single diffusing inhibitor is sufficient to convert a single-peaked extracellular input into a two-peaked pattern of intracellular signaling. Based on extensive computational analysis, we predict that the same mechanism is capable of generating more complex patterns. At least indirectly, this can be used to account for more complex eggshell morphologies observed in related fly species. We propose that versatility in signaling mediated by autocrine loops can be systematically explored using experiment-based mechanistic models and their analysis.

Animals↗