Electric field due to alternating current injected at the surface of a metal plate

Closed form analytical expressions for the electric field interior and exterior to a metal plate, due to alternating current injected at its surface, are derived. Assuming that the current is injected and extracted by wires oriented perpendicular to the surface of the plate, the problem is decomposed into two cylindrically symmetric systems in which a single current-carrying wire lies on the coordinate axis. This simplified problem is formulated in terms of a single magnetic potential and the solution obtained by use of the Hankel transform. The resulting expression for the electric field in the plate takes the form of an analytic series. In exterior regions, the electric field is expressed in terms of Hankel transforms. The result for the physical system with two current-carrying wires is obtained by superposition

Arrow of Time, Entropy, and Protein Folding: Holistic View on Biochirality

Chirality is a universal phenomenon, embracing the space–time domains of non-organic and organic nature. The biological time arrow, evident in the aging of proteins and organisms, should be linked to the prevalent biomolecular chirality. This hypothesis drives our exploration of protein aging, in relation to the biological aging of an organism. Recent advances in the chirality discrimination methods and theoretical considerations of the non-equilibrium thermodynamics clarify the fundamental issues, concerning the biphasic, alternative, and stepwise changes in the conformational entropy associated with protein folding. Living cells represent open, non-equilibrium, self-organizing, and dissipative systems. The non-equilibrium thermodynamics of cell biology are determined by utilizing the energy stored, transferred, and released, via adenosine triphosphate (ATP). At the protein level, the synthesis of a homochiral polypeptide chain of L-amino acids (L-AAs) represents the first state in the evolution of the dynamic non-equilibrium state of the system. At the next step the non-equilibrium state of a protein-centric system is supported and amended by a broad set of posttranslational modifications (PTMs). The enzymatic phosphorylation, being the most abundant and ATP-driven form of PTMs, illustrates the principal significance of the energy-coupling, in maintaining and reshaping the system. However, the physiological functions of phosphorylation are under the permanent risk of being compromised by spontaneous racemization. Therefore, the major distinct steps in protein-centric aging include the biosynthesis of a polypeptide chain, protein folding assisted by the system of PTMs, and age-dependent spontaneous protein racemization and degradation. To the best of our knowledge, we are the first to pay attention to the biphasic, alternative, and stepwise changes in the conformational entropy of protein folding. The broader view on protein folding, including the impact of spontaneous racemization, will help in the goal-oriented experimental design in the field of chiral proteomics

Band structure and thermodynamic potentials

The behavior of different thermodynamic functions of a system of delocalized electrons in a crystal is considered in the single-band strong coupling approximation depending on the degree of energy band filling and temperature. The chemical potential, grand thermodynamic potential, internal energy, free energy, entropy, and heat capacity are numerically calculated. Dependences of these quantities on the electron concentration at high temperatures are investigated. Their limited energy spectrum leads to the special features in the behavior of these quantities in comparison with the free electron gas. © 2012 Springer Science+Business Media, Inc

Chiral Interface of Amyloid Beta (Aβ): Relevance to Protein Aging, Aggregation and Neurodegeneration

Biochirality is the subject of distinct branches of science, including biophysics, biochemistry, the stereochemistry of protein folding, neuroscience, brain functional laterality and bioinformatics. At the protein level, biochirality is closely associated with various post-translational modifications (PTMs) accompanied by the non-equilibrium phase transitions (PhTs NE). PTMs NE support the dynamic balance of the prevalent chirality of enzymes and their substrates. The stereoselective nature of most biochemical reactions is evident in the enzymatic (Enz) and spontaneous (Sp) PTMs (PTMs Enz and PTMs Sp) of proteins. Protein chirality, which embraces biophysics and biochemistry, is a subject of this review. In this broad field, we focus attention to the amyloid-beta (Aβ) peptide, known for its essential cellular functions and associations with neuropathology. The widely discussed amyloid cascade hypothesis (ACH) of Alzheimer’s disease (AD) states that disease pathogenesis is initiated by the oligomerization and subsequent aggregation of the Aβ peptide into plaques. The racemization-induced aggregation of protein and RNA have been extensively studied in the search for the contribution of spontaneous stochastic stereo-specific mechanisms that are common for both kinds of biomolecules. The failure of numerous Aβ drug-targeting therapies requires the reconsolidation of the ACH with the concept of PTMs Sp. The progress in methods of chiral discrimination can help overcome previous limitations in the understanding of AD pathogenesis. The primary target of attention becomes the network of stereospecific PTMs that affect the aggregation of many pathogenic agents, including Aβ. Extensive recent experimental results describe the truncated, isomerized and racemized forms of Aβ and the interplay between enzymatic and PTMs Sp. Currently, accumulated data suggest that non-enzymatic PTMs Sp occur in parallel to an existing metabolic network of enzymatic pathways, meaning that the presence and activity of enzymes does not prevent non-enzymatic reactions from occurring. PTMs Sp impact the functions of many proteins and peptides, including Aβ. This is in logical agreement with the silently accepted racemization hypothesis of protein aggregation (RHPA). Therefore, the ACH of AD should be complemented by the concept of PTMs Sp and RHPA