Physical Principles in Chemoreception by Frederik W. Wiegel

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By Frederik W. Wiegel

Is it no longer sheer foolishness to attempt to use the tools of theoretical physics to organic constructions? Physics flowered since it restricted itself to the examine of extremely simple structures; nevertheless, the essence of "living issues" turns out to need to do with the intense intricacy in their constitution. Is it a hopeless endeavour to aim to convey the 2 jointly, or should still one try out however? so much of my colleagues in theoretical physics believe one will not be waste one's time and keep on with "the reliable outdated hydrogen atom", yet a few of them suppose one may still try out anyways. This minority perspective used to be shared via Bohr within the thirties, Schrödinger within the fourties, Delbrück within the fifties and sixties, PurceIl within the seventies, and so on. the speculation of chemoreception represents just a very small a part of this gigantic medical query. Its examine was once began by means of Delbriick and others within the fifties. i used to be brought to those difficulties by means of Charles DeLisi, in the course of a trip to the nationwide Institutes of overall healthiness in the summertime of 1980. in the course of the following decade I had the excitement to collaborate with George Bell, Byron Goldstein, Alan Perelson and others on the Los Alamos nationwide Laboratory. We studied a wide selection of questions, a few of them proper to the idea of chemoreception. i'm thankful to them, either for the excitement which our joint study continuously offers to me, as weIl as for his or her friendship and hospitality.

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8) 1 for the equilibrium distribution of the ligands over the available part of space. -Jl i 1 + e 1 = N. 8), which was found previously by Ryan et a1. [10], shows a formal similarity with the Fermi-Dirac distribution. This similarity is fortuitous as the ligands can be treated as distinguishable, classical particles rather than as fermions which are indistinguishable quantum particles. (c) If the ligands are described by a local number density c(l,t), as has to be done in a diffusion-equation approach, the relation between their equilibrium density c(t,oo) and n*i is given by c(7i'oo) * n· = _1_ = a·3 a 3 g.

10) where e takes small values. Eq. 5) takes the value D 1I [c I ] = 1 + ~ c\oo, f (Vl:l d y 3 ~1. 12) which provides upper bounds on the ligand flux into the receptors. In order to derive a lower bound we note that eqs. 5) are both mathematically independent expressions for the ligand flux, given the concentration profile cet) and its gradient. We then have a whole dass of expressions by considering linear combinations of these. One that will be particularly useful is 12[c 2] = c D (~) { 2 f S o c(oo) VC 2 .

9) is essentially a form of asymptotic matching, in which the solution of the diffusion problem near to a binding site in the cell membrane is matched smoothly to the solution far away from the membrane. The reader might want to consult van Dyke [3] for the applications of this method in fluid mechanics. 2. The spherical cell In order to demonstrate how the method of the effective boundary condition works we consider a spherical cell of radius R immersed in an unbounded medium. The cell carries N receptors in its outer membrane, which are uniformly distributed, so the number of binding sites per unit surface area is 35 v=~.

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