A
bstract
We derive explicit expressions for the elements of the {
β
}-expansion for the nonsinglet Adler
D
A
-function and Bjorken polarized sum rules
S
Bjp
in the N
4
LO using recent results by ...Chetyrkin for these quantities computed within extended QCD including any number of fermion representations. We discuss the properties of the {
β
}-expansion for
D
A
and
S
Bjp
at higher orders which follow from the Crewther
1
and the Broadhurst-Kataev
2
relation.
The cytoplasm and biomembranes in biological cells contain large numbers of proteins that cyclically change their shapes. They are molecular machines that can function as molecular motors or carry ...out various other tasks in the cell. Many enzymes also undergo conformational changes within their turnover cycles. We analyze the advection effects that nonthermal fluctuating hydrodynamic flows induced by active proteins have on other passive molecules in solution or membranes. We show that the diffusion constants of passive particles are enhanced substantially. Furthermore, when gradients of active proteins are present, a chemotaxis-like drift of passive particles takes place. In lipid bilayers, the effects are strongly nonlocal, so that active inclusions in the entire membrane contribute to local diffusion enhancement and the drift. All active proteins in a biological cell or in a membrane contribute to such effects and all passive particles, and the proteins themselves, will be subject to them.
Biological cells contain large numbers of active proteins that repeatedly change their conformations and need a supply of ATP or other substrates to maintain their cyclic operation. Whereas these protein machines have a variety of specific functions, acting as motors, ion pumps, or enzymes, they also induce fluctuating hydrodynamic flows in the cytoplasm. Because such fluctuating flows are nonthermal, energy can be extracted from them and work can be performed. We show that these flows can substantially enhance diffusive motions of passive particles. Furthermore, when gradients in concentrations of active proteins or substrate (ATP) are present, a chemotaxis-like drift should take place. Such nonequilibrium effects are universal: They hold for all passive particles and also for the protein machines themselves.
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