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 mixing of the biochemical species, reactions follow a fractal-like kinetics. Consequently, the conventional equations for biochemical pathways fail to describe the reactions in in vivo conditions. 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.

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 in this process. We find that, before villus emergence, tight clusters of Hh-responsive mesenchymal cells form just beneath the epithelium. Cluster formation is dynamic; clusters first form dorsally and anteriorly and spread circumferentially and posteriorly. Statistical analysis of cluster distribution reveals a patterned array; with time, new clusters form in spaces between existing clusters, promoting approximately four rounds of villus emergence by E18.5. Cells within mesenchymal clusters express Patched1 and Gli1, as well as Pdgfrα, a receptor previously shown to participate in villus development. BrdU-labeling experiments show that clusters form by migration and aggregation of Hh-responsive cells. Inhibition of Hh signaling prevents cluster formation and villus development, but does not prevent emergence of villi in areas where clusters have already formed. Conversely, increasing Hh signaling increases the size of villus clusters and results in exceptionally wide villi. We conclude that Hh signals dictate the initial aspects of the formation of each villus by controlling mesenchymal cluster aggregation and regulating cluster size.epithelial-mesenchymal cross-talk | field pattern | villus morphogenesis

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We re-visit previous analyses of the classical Michaelis-Menten substrate-enzyme reaction and, with the aid of the reverse quasi-steady-state assumption, we challenge the approximation d[C]/dt approximately 0 for the basic enzyme reaction at high enzyme concentration. For the first time, an approximate solution for the concentrations of the reactants uniformly valid in time is reported. Numerical simulations are presented to verify this solution. We show that an analytical approximation can be found for the reactants for each initial condition using the appropriate quasi-steady-state assumption. An advantage of the present formalism is that it provides a new procedure for fitting experimental data to determine reaction constants. Finally, a new necessary criterion is found that ensures the validity of the reverse quasi-steady-state assumption. This is verified numerically.