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Branched Pathways
Branched pathways, also known as branch points (not to be confused with the mathematical branch point), are a common pattern found in metabolism. This is where an intermediate Chemical species, species is chemically made or transformed by multiple enzymatic processes. Linear biochemical pathway, linear pathways only have one enzymatic reaction producing a species and one enzymatic reaction consuming the species. Branched pathways are present in numerous metabolic reactions, including glycolysis, the synthesis of lysine, glutamine, and penicillin, and in the production of the aromatic amino acids. In general, a single branch may have b producing branches and d consuming branches. If the intermediate at the branch point is given by s_i, then the rate of change of s_i is given by: : \sum_^b v_i-\sum_^d v_j=\frac At steady-state when ds_i/dt = 0 the consumption and production rates must be equal: : \sum_^b v_i=\sum_^d v_j Biochemical pathways can be investigated by computer si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Branch Point
In the mathematical field of complex analysis, a branch point of a multivalued function is a point such that if the function is n-valued (has n values) at that point, all of its neighborhoods contain a point that has more than n values. Multi-valued functions are rigorously studied using Riemann surfaces, and the formal definition of branch points employs this concept. Branch points fall into three broad categories: algebraic branch points, transcendental branch points, and logarithmic branch points. Algebraic branch points most commonly arise from functions in which there is an ambiguity in the extraction of a root, such as solving the equation w^2=z for w as a function of z. Here the branch point is the origin, because the analytic continuation of any solution around a closed loop containing the origin will result in a different function: there is non-trivial monodromy. Despite the algebraic branch point, the function w is well-defined as a multiple-valued function and, in an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
