Quantum-tunneling transitions and exact statistical mechanics of bistable systems with parametrized Dikandé–Kofané double-well potentials

We consider a one-dimensional system of interacting particles (which can be atoms, molecules, ions, etc.), in which particles are subjected to a bistable potential the double-well shape of which is tunable via a shape deformability parameter. Our objective is to examine the impact of shape deformability on the order of transition in quantum tunneling in the bistable system, and on the possible existence of exact solutions to the transfer-integral operator associated with the partition function of the system. The bistable potential is represented by a class composed of three families of parametrized double-well potentials, whose minima and barrier height can be tuned distinctly. It is found that the extra degree of freedom, introduced by the shape deformability parameter, favors a first-order transition in quantum tunneling, in addition to the second-order transition predicted with the $$\phi ^4$$ ϕ 4 model. This first-order transition in quantum tunneling, which is consistent with Chudnovsky’s conjecture of the influence of the shape of the potential barrier on the order of thermally assisted transitions in bistable systems, is shown to occur at a critical value of the shape-deformability parameter which is the same for the three families of parametrized double-well potentials. Concerning the statistical mechanics of the system, the associate partition function is mapped onto a spectral problem by means of the transfer-integral formalism. The condition that the partition function can be exactly integrable, is determined by a criterion enabling exact eigenvalues and eigenfunctions for the transfer-integral operator. Analytical expressions of some of these exact eigenvalues and eigenfunctions are given, and the corresponding ground-state wavefunctions are used to compute the probability density which is relevant for calculations of thermodynamic quantities such as the correlation functions and the correlation lengths. Graphic Abstract

Capturing a crucial 'disorder-to-order transition' at the heart of the coronavirus molecular pathology – triggered by highly persistent, interchangeable salt-bridges

The COVID-19 origin debate has greatly been influenced by Genome comparison studies of late, revealing the seemingly sudden emergence of the Furin-Like Cleavage Site at the S1/S2 junction of the SARS-CoV-2 Spike (FLCS_Spike) containing its 681_PRRAR_685 motif, absent in other related respiratory viruses. Being the rate-limiting (i.e., the slowest) step, the host Furin cleavage is instrumental in the abrupt increase in transmissibility in COVID-19, compared to earlier onsets of respiratory viral diseases. In such a context, the current paper entraps a disorder-to-order transition of the FLCS_Spike (concomitant to an entropy arrest) upon binding to Furin. The interaction clearly seems to be optimized for a more efficient proteolytic cleavage in SARS-CoV-2. The study further shows the formation of dynamically interchangeable and persistent networks of salt-bridges at the Spike-Furin interface in SARS-CoV-2 involving the three arginines (R682, R683, R685) of the FLCS_Spike with several anionic residues (E230, E236, D259, D264, D306) coming from Furin, strategically distributed around its catalytic triad. Multiplicity and structural degeneracy of plausible salt-bridge network archetypes seems the other key characteristic features of the Spike-Furin binding in SARS-CoV-2 allowing the system to breathe - a trademark of protein disorder transitions. Interestingly, with respect to the homologous interaction in SARS-CoV (2002/2003) taken as a baseline, the Spike-Furin binding events generally in the coronavirus lineage seems to have a preference for ionic bond formation, even with lesser number of cationic residues at their potentially polybasic FLCS_Spike patches. The interaction energies are suggestive of a characteristic metastabilities attributed to Spike-Furin interactions generally to the coronavirus lineage - which appears to be favorable for proteolytic cleavages targeted at flexible protein loops. The current findings not only offer novel mechanistic insights into the coronavirus molecular pathology and evolution but also add substantially to the existing theories of proteolytic cleavages.