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Somitogenesis, the sequential formation of a periodic pattern along the antero-posterior axis of vertebrate embryos, is one of the most obvious examples of the segmental patterning processes that take place during embryogenesis and also one of the major unresolved events in developmental biology. In this article, we develop a mathematical formulation of a(More)
After many years of research, somitogenesis is still one of the major unresolved problems in developmental biology. Recent experimental findings show a novel type of pattern formation in which a signal sweeps along the presomitic mesoderm and narrows simultaneously as a new somite is formed. The signal then residues in the posterior half of the new somite,(More)
Somitogenesis, the process by which a bilaterally symmetric pattern of cell aggregations is laid down in a cranio-caudal sequence in early vertebrate development, provides an excellent model study for the coupling of interactions at the molecular and cellular level. Here, we review some of the key experimental results and theoretical models related to this(More)
After many years of research, the mechanisms that generate a periodic pattern of repeated elements (somites) along the length of the embryonic body axis is still one of the major unresolved problems in developmental biology. Here we present a mathematical formulation of the cell cycle model for somitogenesis proposed in Development105 (1989), 119-130.(More)
We review recent evidence illustrating the fundamental difference between cytoplasmic and test tube biochemical kinetics and thermodynamics, and showing the breakdown of the law of mass action and power-law approximation in in vivo conditions. Simulations of biochemical reactions in non-homogeneous media show that as a result of anomalous diffusion and(More)
In the adult intestine, an organized array of finger-like projections, called villi, provide an enormous epithelial surface area for absorptive function. Villi first emerge at embryonic day (E) 14.5 from a previously flat luminal surface. Here, we analyze the cell biology of villus formation and examine the role of paracrine epithelial Hedgehog (Hh) signals(More)
Disruption of normal vertebral development results from abnormal formation and segmentation of the vertebral precursors, called somites. Somitogenesis, the sequential formation of a periodic pattern along the antero-posterior axis of vertebrate embryos, is one of the most obvious examples of the segmental patterning processes that take place during(More)
An analytic formalism developed earlier to describe the time evolution of the basic enzyme reaction is extended to fully competitive systems. Time-dependent closed form solutions are derived for the three nominal cases of competition: even, slow and fast inhibitors, allowing for the first time the complete characterization of the reactions. In agreement(More)
Radiotherapy outcomes are usually predicted using the Linear Quadratic model. However, this model does not integrate complex features of tumor growth, in particular cell cycle regulation. In this paper, we propose a multiscale model of cancer growth based on the genetic and molecular features of the evolution of colorectal cancer. The model includes key(More)
Somites are transient blocks of cells that form sequentially along the antero-posterior axis of vertebrate embryos. They give rise to the vertebrae, ribs and other associated features of the trunk. In this work we develop and analyse a mathematical formulation of a version of the Clock and Wavefront model for somite formation, where the clock controls when(More)