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Random Walks on Graphs: An Overview
Random Walks on Graphs: An Overview

... Random walks and Markov chains • A Markov chain describes a stochastic process over a set of states according to a transition probability matrix • Markov chains are memoryless • Random walks correspond to Markov chains: • The set of states is the set of nodes in the graph • The elements of the tran ...
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... reaction set supporting E. coli growth on a glucose substrate. A detailed description of the employed modeling procedure is provided in the Appendix. A constrained amount of glucose (<10 mmol/gDW‚h), along with unconstrained uptake routes for inorganic phosphate, oxygen, sulfate, and ammonia are ena ...
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Gene regulatory network



A gene regulatory network or genetic regulatory network (GRN) is a collection of regulators thatinteract with each other and with other substances in the cell to govern the gene expression levels of mRNA and proteins.The regulator can be DNA, RNA, protein and their complex. The interaction can be direct or indirect (through their transcribed RNA or translated protein).In general, each mRNA molecule goes on to make a specific protein (or set of proteins). In some cases this protein will be structural, and will accumulate at the cell membrane or within the cell to give it particular structural properties. In other cases the protein will be an enzyme, i.e., a micro-machine that catalyses a certain reaction, such as the breakdown of a food source or toxin. Some proteins though serve only to activate other genes, and these are the transcription factors that are the main players in regulatory networks or cascades. By binding to the promoter region at the start of other genes they turn them on, initiating the production of another protein, and so on. Some transcription factors are inhibitory.In single-celled organisms, regulatory networks respond to the external environment, optimising the cell at a given time for survival in this environment. Thus a yeast cell, finding itself in a sugar solution, will turn on genes to make enzymes that process the sugar to alcohol. This process, which we associate with wine-making, is how the yeast cell makes its living, gaining energy to multiply, which under normal circumstances would enhance its survival prospects.In multicellular animals the same principle has been put in the service of gene cascades that control body-shape. Each time a cell divides, two cells result which, although they contain the same genome in full, can differ in which genes are turned on and making proteins. Sometimes a 'self-sustaining feedback loop' ensures that a cell maintains its identity and passes it on. Less understood is the mechanism of epigenetics by which chromatin modification may provide cellular memory by blocking or allowing transcription. A major feature of multicellular animals is the use of morphogen gradients, which in effect provide a positioning system that tells a cell where in the body it is, and hence what sort of cell to become. A gene that is turned on in one cell may make a product that leaves the cell and diffuses through adjacent cells, entering them and turning on genes only when it is present above a certain threshold level. These cells are thus induced into a new fate, and may even generate other morphogens that signal back to the original cell. Over longer distances morphogens may use the active process of signal transduction. Such signalling controls embryogenesis, the building of a body plan from scratch through a series of sequential steps. They also control and maintain adult bodies through feedback processes, and the loss of such feedback because of a mutation can be responsible for the cell proliferation that is seen in cancer. In parallel with this process of building structure, the gene cascade turns on genes that make structural proteins that give each cell the physical properties it needs.It has been suggested that, because biological molecular interactions are intrinsically stochastic, gene networks are the result of cellular processes and not their cause (i.e. cellular Darwinism). However, recent experimental evidence has favored the attractor view of cell fates.
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