Frieden, B. Roy, and Robert A. Gatenby. “Cell development obeys maximum Fisher information.” Frontiers in bioscience (Elite edition) 5 (2013): 1017.
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Eukaryotic cell development has been optimized by natural selection to obey maximal intracellular flux of messenger proteins. This, in turn, implies maximum Fisher information on angular position about a target nuclear pore complex (NPR). The cell is simply modeled as spherical, with cell membrane (CM) diameter 10 μm and concentric nuclear membrane (NM) diameter 6 μm. The NM contains ≈ 3000 nuclear pore complexes (NPCs). Development requires messenger ligands to travel from the CM-NPC-DNA target binding sites. Ligands acquire negative charge by phosphorylation, passing through the cytoplasm over Newtonian trajectories toward positively charged NPCs (utilizing positive nuclear localization sequences). The CM-NPC channel obeys maximized mean protein flux F and Fisher information I at the NPC, with first-order δI = 0 and approximate 2nd-order δ2I ≈ 0 stability to environmental perturbations. Many of its predictions are confirmed, including the dominance of protein pathways of from 1–4 proteins, a 4nm size for the EGFR protein and the flux value F ≈1016 proteins/m2-s. After entering the nucleus, each protein ultimately delivers its ligand information to a DNA target site with maximum probability, i.e. maximum Kullback-Liebler entropy HKL . In a smoothness limit HKL → IDNA/2, so that the total CM-NPC-DNA channel obeys maximum Fisher I . Thus maximum information → non-equilibrium, one condition for life.