Quenching of tryptophan fluorescence of firefly luciferase by substrates

The interaction of firefly luciferase with substrates (luciferin and MgATP) by steady-state and time-resolved fluorescence is studied. The efficient quenching of tryptophan fluorescence of the active enzyme takes place upon its binding with substrates. In the presence of ATP the quenching is of dynamic type and is caused by structural changes in the protein molecule upon ATP binding. A model is proposed in which the complex has smaller fluorescence quantum yield than the free enzyme because of partial quenching of tryptophan fluorescence by the new microenvironment. Quenching of tryptophan fluorescence by luciferin due to the efficient energy transfer from tryptophan to luciferin is discussed. The calculated distance between Trp-419 and luciferin for the L. mingrelica luciferase in the enzyme-substrate complex is less than 12 A.     

p-adic dynamic systems

Dynamic systems in non-Archimedean number fields (i.e., fields with non-Archimedean valuations) are studied. Results are obtained for the fields of p-adic numbers and complex p-adic numbers. Simple p-adic dynamic systems have a very rich structure—attractors, Siegel disks, cycles, and a new structure called a “fuzzy cycle”. The prime number p plays the role of a parameter of the p-adic dynamic system. Changing p radically changes the behavior of the system: attractors may become the centers of Siegel disks, and vice versa, and cycles of different lengths may appear or disappear. Alexander von Humboldt Fellowship and SFB 237 Essen-Bochum-Düsseldorf, on leave from Moscow State Institute of Electronic Engineering. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 114, No. 3, pp. 349–365, March, 1998.     

Non-Archimedean Analogues of Orthogonal and Symmetric Operators and p-adic Quantization

We study orthogonal and symmetric operators in non-Archimedean Hilbert spaces in the connection with p-adic quantization. This quantization describes measurements with finite precision. Symmetric (bounded) operators in the p-adic Hilbert spaces represent physical observables. We study spectral properties of one of the most important quantum operators, namely, the operator of the position (which is represented in the p-adic Hilbert L₂-space with respect to the p-adic Gaussian measure). Orthogonal isometric isomorphisms of p-adic Hilbert spaces preserve precisions of measurements. We study properties of orthogonal operators. It is proved that each orthogonal operator in the non-Archimedean Hilbert space is continuous. However, there exist discontinuous operators with the dense domain of definition which preserve the inner product. There also exist nonisometric orthogonal operators. We describe some classes of orthogonal isometric operators and we study some general questions of the theory of non-Archimedean Hilbert spaces (in particular, general connections between topology, norm and inner product).     

On p-adic mathematical physics

A brief review of some selected topics in p-adic mathematical physics is presented. The text was submitted by the authors in English.     

Real non-Archimedean structure of spacetime

Institute of Electronic Technology, Moscow. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 86, No. 2, pp. 177–190, February, 1991.