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Handbook of Biological Physics
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The article was published on 1996-01-01 and is currently open access. It has received 1088 citations till now.read more
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Journal ArticleDOI
Homogenization and concentrated capacity for the heat equation with non{linear variational data in reticular almost disconnected structures and applications to visual transduction
Abstract: Out of a right, circular cylinder Ωe of height H and cross-section a disc of radius R+σe one removes a stack of n≈H/e parallel, equi-spaced cylinders C
j
, j=1,2,...,n, each of radius R and height νe. Here σ, ν are fixed positive numbers and e is a positive parameter to be allowed to go to zero. The union of the C
j
almost fills Ωe in the sense that any two contiguous cylinders C
j
are at a mutual distance of the order of e and that the outer shell, i.e., the gap S
e=Ωe-Ω
o
has thickness of the order of e (Ω
o
is obtained from Ωe by formally setting e=0). The cylinder Ωe from which the C
j
are removed, is an almost disconnected structure, it is denoted by Ωe, and it arises in the mathematical theory of phototransduction. For each e>0 we consider the heat equation in the almost disconnected structure Ωe, for the unknown function u
e, with variational boundary data on the faces of the removed cylinders C
j
. The limit of this family of problems as e→0 is computed by concentrating heat capacity and diffusivity on the outer shell, and by homogenizing the u
e within the limiting cylinder Ω
o
. It is shown that the limiting problem consists of an interior diffusion in Ω
o
and a boundary diffusion on the lateral boundary S of Ω
o
. The interior diffusion is governed by the 2-dimensional heat equation in Ω
o
, for an interior limiting function u. The boundary diffusion is governed by the Laplace–Beltrami heat equation on S, for a boundary limiting function u
S
. Moreover the exterior flux of the interior limit u provides the source term for the boundary diffusion on S. Finally the interior limit u, computed on S in the sense of the traces, coincides with the boundary limit u
S
. As a consequence of the geometry of Ωe, local arguments do not suffice to prove convergence in Ω
o
, and also we have to take into account the behavior of the solution in S
e. A key, novel idea consists in extending equi-bounded and equi-Holder continuous functions in e-dependent domains, into equi-bounded and equi-Holder continuous functions in the whole ℝ
N
, by means of the Kirzbraun–Pucci extension technique. The biological origin of this problem is traced, and its application to signal transduction in the retina rod cells of vertebrates is discussed.
Journal ArticleDOI
Stereoselectivity of the membrane potential-generating citrate and malate transporters of lactic acid bacteria.
Michael Bandell,Juke S. Lolkema +1 more
TL;DR: The affinity of the S-enantiomers of citrate was at least 1 order of magnitude higher than for lactate and other substrates with uncharged R groups, indicating a specific interaction between the second carboxylate group and the protein that is responsible for high-affinity binding.
Journal ArticleDOI
Regulation of Potassium-Dependent Kdp-ATPase Expression in the Nitrogen-Fixing Cyanobacterium Anabaena torulosa
TL;DR: The KdpB polypeptides in the cyanobacterium Anabaena torulosa were shown to be two membrane-bound proteins, expressed strictly under K(+) deficiency and repressed or degraded upon readdition of K(+).
Journal ArticleDOI
Towards performance control on the Grid.
TL;DR: The design and implementation of a prototype performance control system (PerCo), which is capable of monitoring the progress of simulations and redeploying them so as to optimize performance is described and it is shown that PerCo is able to reduce overall execution time.