Distribution of values of additive functions on the sequence {p+1}

Evaluation of Conformational dynamics properties of spin-labelled proteins at different degrees of nitroxide radicals immobilization

“…The problem is simplified when two-rotator model is considered [5]. The fast reorientation of the SL (motional narrowing) results in axially-symmetric Rii (RII, R• These tensor components can be related to the components of the macromolecular diffusion tensor, Dij so that the isotropic protein diffusion coefficient, Do=(DHD~)I/2-Rj_; the SL correlation time relative to the protein, rSL --R• and the deviation amplimde of the SL within the protein binding site corresponds to the effective cone angle, 6) [4,6]. Since in the common microwave frequency X-range (-9.4 GHz) rSL << (A= --A =)-t ~.…”

“…Furthermore, it has been shown that these distances at normal conditions compared to the spectrum splitting in the case of completely immobilized spins at 77 K (2Azz) are determined by the degree of averaging of the nitroxyl radical hyperfine tensor. In the simplified semi-phenomenological approach for analyzing the immobilized motion of nitroxyl radicals suggested by Timofeev and co-workers [6][7][8]11], the overall shift 2Azz --2A ~ is expressed as:…”

“…On the other hand, in the case of spin-labelled proteins in solution, one useful simplification can be achieved considering a two-rotator modet: a fast anisotropic rotator on a slowly tumbling one [5]. According to this approach the overall spinlabel motion is attempted to be described by two dynamic parameters: the protein rotational correlation time and the independent spin label motion relative to the protein [6,7]. Therefore, the ESR spectra analysis is expected to permit quantitative discrimination between the slow macromolecular rotation (re) and the fast anisotropic spin-tabel motion restricted by the protein environment and represented by the effective ordering parameter (S).…”

Discrete uniform limit law for additive functions on shifted primes

“…The Bernoulli, geometrical, binomial, discrete uniform distributions as limit ones for ν x (f x (n) < u) were investigated in [10,11,12]. Several results (general enough) can be found in [1,4,13,14].…”