Growth Based Morphogenesis of Vertebrate Limb Bud

Many genes and their regulatory relationships are involved in developmental phenomena. However, by chemical information alone, we cannot fully understand changing organ morphologies through tissue growth because deformation and growth of the organ are essentially mechanical processes. Here, we develop a mathematical model to describe the change of organ morphologies through cell proliferation. Our basic idea is that the proper specification of localized volume source (e.g., cell proliferation) is able to guide organ morphogenesis, and that the specification is given by chemical gradients. We call this idea “growth-based morphogenesis.” We find that this morphogenetic mechanism works if the tissue is elastic for small deformation and plastic for large deformation. To illustrate our concept, we study the development of vertebrate limb buds, in which a limb bud protrudes from a flat lateral plate and extends distally in a self-organized manner. We show how the proportion of limb bud shape depends on different parameters and also show the conditions needed for normal morphogenesis, which can explain abnormal morphology of some mutants. We believe that the ideas shown in the present paper are useful for the morphogenesis of other organs

Properties of a "phase transition" induced by antiangiogenetic therapeutical protocols

Inhibiting angiogenesis has been found to be an interesting therapeutical strategy against cancer. In fact, the success of tumor growth is subordinated to the corresponding increase of the vascular system feeding the neoplasm. However, optimization and design of proper antiangiogenetic therapeutical strategies is still an open problem. We apply a recently developed angiogenesis model to study how variations in the relevant parameters, e.g., induced by chemicals, may cause a "phase transition" to a region in the parameter space in which angiogenesis is not succesful. To demonstrate the reliability of our approach and its usefulness, we will study some specific drugs and use our model to investigate the influence of the main variables involved in a clinical treatment: the administration time, the duration of the drug effect, and the drug dose