The algebraic curves of planar polynomial differential systems with homogeneous nonlinearities

We consider planar polynomial systems of ordinary differential equations of the form x˙=x+Pn(x, y), y˙=y+Qn(x, y), where Pn(x, y), Qn(x, y) are homogeneous polynomials of degreen. We study the algebraic and non-algebraic invariant curves of these systems with emphasis on limit cycles

Kinetic Path Summation, Multi--Sheeted Extension of Master Equation, and Evaluation of Ergodicity Coefficient

We study the Master equation with time--dependent coefficients, a linear kinetic equation for the Markov chains or for the monomolecular chemical kinetics. For the solution of this equation a path summation formula is proved. This formula represents the solution as a sum of solutions for simple kinetic schemes (kinetic paths), which are available in explicit analytical form. The relaxation rate is studied and a family of estimates for the relaxation time and the ergodicity coefficient is developed. To calculate the estimates we introduce the multi--sheeted extensions of the initial kinetics. This approach allows us to exploit the internal ("micro")structure of the extended kinetics without perturbation of the base kinetics.Comment: The final journal versio

MPTP-Treated Zebrafish Recapitulate ‘Late-Stage’ Parkinson’s-like Cognitive Decline

The zebrafish is a promising model species in biomedical research, including neurotoxicology and neuroactive drug screening. 1-Methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP) evokes degeneration of dopaminergic neurons and is commonly used to model Parkinson’s disease (PD) in laboratory animals, including zebrafish. However, cognitive phenotypes in MPTP-evoked experimental PD models remain poorly understood. Here, we established an LD50 (292 mg/kg) for intraperitoneal MPTP administration in adult zebrafish, and report impaired spatial working memory (poorer spontaneous alternation in the Y-maze) in a PD model utilizing fish treated with 200 µg of this agent. In addition to conventional behavioral analyses, we also employed artificial intelligence (AI)-based approaches to independently and without bias characterize MPTP effects on zebrafish behavior during the Y-maze test. These analyses yielded a distinct cluster for 200-µg MPTP (vs. other) groups, suggesting that high-dose MPTP produced distinct, computationally detectable patterns of zebrafish swimming. Collectively, these findings support MPTP treatment in adult zebrafish as a late-stage experimental PD model with overt cognitive phenotypes. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.Funding: The experiments were implemented using the equipment and unique scientific installation “Biological collection–Genetic biomodels of neuropsychiatric disorders” (No. 493387) of the Federal State Budgetary Scientific Institution “Scientific Research Institute of Neurosciences and Medicine” theme no. AAAA-A21-121011990039-2 (2021–2025). The study partially used the facilities and equipment of the Resource Fund of Applied Genetics MIPT (support grant 075-15-2021-684)

Adapted Lethality: What We Can Learn from Guinea Pig-Adapted Ebola Virus Infection Model

Establishment of small animal models of Ebola virus (EBOV) infection is important both for the study of genetic determinants involved in the complex pathology of EBOV disease and for the preliminary screening of antivirals, production of therapeutic heterologic immunoglobulins, and experimental vaccine development. Since the wild-type EBOV is avirulent in rodents, the adaptation series of passages in these animals are required for the virulence/lethality to emerge in these models. Here, we provide an overview of our several adaptation series in guinea pigs, which resulted in the establishment of guinea pig-adapted EBOV (GPA-EBOV) variants different in their characteristics, while uniformly lethal for the infected animals, and compare the virologic, genetic, pathomorphologic, and immunologic findings with those obtained in the adaptation experiments of the other research groups