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Models of dispersal in biological systems
Two stochastic processes that model the major modes of dispersal that are observed in nature are introduced, and explicit expressions for the mean squared displacement and other experimentally observable quantities are derived.
The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster.
Aggregation, Blowup, and Collapse: The ABC's of Taxis in Reinforced Random Walks
The question arises as to whether aggregation is possible under suitable hypotheses on the transition rules and the production of a control species that modulates the transition rates of the myxobacteria.
Mathematical modeling of tumor-induced angiogenesis
Modifications of the ECM that Facilitate EC Migration and early events in Angiogenesis 6 3.1 Signaling From Tumor To Vessel at the Onset of Angiodynamics.
Facilitated Transport of a Dpp/Scw Heterodimer by Sog/Tsg Leads to Robust Patterning of the Drosophila Blastoderm Embryo
The BMP-binding protein Crossveinless 2 is a short-range, concentration-dependent, biphasic modulator of BMP signaling in Drosophila.
The Diffusion Limit of Transport Equations Derived from Velocity-Jump Processes
It is shown that under an appropriate scaling of space and time the asymptotic behavior of solutions of such equations can be approximated by the solution of a diffusion equation obtained via a regular perturbation expansion.
Shaping BMP morphogen gradients in the Drosophila embryo and pupal wing
Recent data suggesting that pupal wing development and early Drosophila embryo development use a related set of extracellular factors, positive feedback, and BMP heterodimer formation to achieve peak levels of signaling in spatially restricted patterns are reviewed.
From Individual to Collective Behavior in Bacterial Chemotaxis
This work derives and analyzes a macroscopic system of hyperbolic differential equations describing the motion of individuals such as bacteria from a microscopic model of the behavior of individual cells using moment closure techniques in one space dimension.
A model for individual and collective cell movement in Dictyostelium discoideum.
A biologically realistic model for motile D. discoideum cells that can generate active forces, that interact via surface molecules, and that can detect and respond to chemotactic signals is described.