Santiago Schnell

..This behaviour is not easily explained by the existing theoretical models. We present a new model for somitogenesis that can account for this behaviour and is consistent with previous experimental observations...

..Finally, a new necessary criterion is found that ensures the validity of the reverse quasi-steady-state assumption. This is verified numerically...

..The validity of the quasi-steady-state approximation on which the present framework is based is also revised...

..It is based on a new theoretical formalism in terms of concentrations that dismisses the requirement of estimating initial velocities. Expressions for the time evolution of the concentrations of all the reactants are also given...

..We also postulate a model to account for the recently observed spatio-temporal dynamics at the molecular level...

..A phase-plane analysis allows the derivation of a new condition for its validity that is directly linked to the reaction efficiency, and contrary to widely established knowledge, is independent of the initial enzyme concentration...

..We present a modification to fractal-like kinetics following the Zipf-Mandelbrot distribution which will enable the modelling and analysis of biochemical reactions occurring in crowded intracellular environments...

..We conclude with a brief discussion of the state of modeling in the field and current challenges which need to be overcome in order to further our understanding in this area...

..We outline mathematical models to describe each patterning mechanism, present the results of numerical simulations and discuss the validity of each model in relation to our example patterning processes...

..We can also show that a simplification of the model provides a mechanism for predicting the anomalies resulting from perturbation of the wavefront...

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..We then describe recent efforts to include the fluctuation effects caused by the structural organisation of the cytoplasm and the limited diffusion of molecules due to macromolecular crowding...

..The analysis also provides a greater understanding of the signalling process controlling somite formation and allows us to understand which parameters influence somite length...

..We also show that the model can mimic the anomalies formed when progression of the wavefront is disturbed and make some experimental predictions that can be used to test the hypotheses underlying the model...

..Since different models of determination yield the same, experimentally-observed, distribution of adhesion and repulsion molecules, the patterning is independent of the details of this mechanism...

..We discuss the consequence of this result for the determination of reaction parameters in enzyme catalyzed reactions...

..In this short review, we present two quantitative frameworks that address the morphogenesis from segment to somite and discuss recent data of segmentation and epithelialization...

..We propose a simple chemotactic mechanism that together with heightened adhesion can account for the morphological changes in the time allotted for somite formation...

..We demonstrate that our new methodology reconstructs the chemical reaction steps and connectivity of the glycolytic pathway of Lactococcus lactis from time course experimental data...

..We employ this methodology to estimate the inactivation constant for the arsenate reductase catalyzed production of arsenite with appreciable enzyme inactivation...

..Predicted interactions are in agreement with gene knock-out studies available in the literature...

..Also, our results provide an explanation for experimental observations and suggest a new experimental protocol that could reveal information on the mechanism of digestion...

..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...