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Models of dispersal in biological systems
In order to provide a general framework within which the dispersal of cells or organisms can be studied, we introduce two stochastic processes that model the major modes of dispersal that areExpand
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The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster.
Expression of the Drosophila segment polarity genes is initiated by a pre-pattern of pair-rule gene products and maintained by a network of regulatory interactions throughout several stages ofExpand
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  • Open Access
Aggregation, Blowup, and Collapse: The ABC's of Taxis in Reinforced Random Walks
In many biological systems, movement of an organism occurs in response to a diffusible or otherwise transported signal, and in its simplest form this can be modeled by diffusion equations withExpand
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  • Open Access
Mathematical modeling of tumor-induced angiogenesis
3 Early Events in Angiogenesis 6 3.1 Signaling From Tumor To Vessel at the Onset of Angiogenesis . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.1 Transforming Growth Factor Beta (TGF) . . .Expand
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The Diffusion Limit of Transport Equations Derived from Velocity-Jump Processes
In this paper we study the diffusion approximation to a transport equation that describes the motion of individuals whose velocity changes are governed by a Poisson process. We show that under anExpand
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  • Open Access
From Individual to Collective Behavior in Bacterial Chemotaxis
Bacterial chemotaxis is widely studied from both the microscopic (cell) and macroscopic (population) points of view, and here we connect these very different levels of description by deriving theExpand
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Shaping BMP morphogen gradients in the Drosophila embryo and pupal wing
In the early Drosophila embryo, BMP-type ligands act as morphogens to suppress neural induction and to specify the formation of dorsal ectoderm and amnioserosa. Likewise, during pupal wingExpand
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A model for individual and collective cell movement in Dictyostelium discoideum.
  • E. Palsson, H. Othmer
  • Medicine, Biology
  • Proceedings of the National Academy of Sciences…
  • 12 September 2000
The cellular slime mold Dictyostelium discoideum is a widely used model system for studying a variety of basic processes in development, including cell-cell signaling, signal transduction, patternExpand
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Facilitated Transport of a Dpp/Scw Heterodimer by Sog/Tsg Leads to Robust Patterning of the Drosophila Blastoderm Embryo
Patterning the dorsal surface of the Drosophila blastoderm embryo requires Decapentaplegic (Dpp) and Screw (Scw), two BMP family members. Signaling by these ligands is regulated at the extracellularExpand
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  • Open Access
A model of excitation and adaptation in bacterial chemotaxis.
Bacterial chemotaxis is widely studied because of its accessibility and because it incorporates processes that are important in a number of sensory systems: signal transduction, excitation,Expand
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  • Open Access