Konstantin B. Blyuss

Introduction: Streptomyces species are renowned for producing bioactive natural products, particularly those that induce plant resistance against pathogens and nematodes. This study aimed to investigate the ability of metabolic bioproducts from Streptomyces netropsis IMV Ac-5025, Streptomyces violaceus IMV Ac-5027, and Streptomyces avermitilis IMV Ac-5015 to affect RNAi-mediated resistance in tomato plants against the root-knot nematode. Methods: Spectrodensitometric Thin-Layer Chromatography (TLC), High-Performance Liquid Chromatography (HPLC), and Gas Chromatography (GC) were used to identify natural products of streptomycetes. The resistance of tomato plants to Meloidogyne incognita was evaluated through artificial nematode inoculation coupled with phenological viability assessment. The extent of si/miRNA-driven gene silencing was determined via dot blot hybridization and inhibition of protein synthesis in a wheat germ cell-free translation system. Results: Soil-derived Streptomyces strains were shown to produce diverse bioactive compounds, including antibiotics, lipids, phytohormones, and sterols, and novel bioproducts were developed based on their secondary metabolites (Phytovit, Violar, Averkom, and Averkom nova). Incorporation of these bioproducts into the nutrient medium significantly improved shoot regeneration rates in isolated plant explants. Dot blot hybridization and translational inhibition assays in a wheat germ cell-free system confirmed their phytoprotective effect via the RNA interference mechanism. In vitro cultivation of tomato plants supplemented with biotreatment resulted in a marked enhancement of resistance to M. incognita . Discussion: The secondary metabolic complexes produced by Streptomyces strains promote plant growth and development while enhancing immunity and supporting the efficient operation of signaling networks involved in cellular responses to nematodes. Their activity is mediated through elicitor signals that trigger the de novo synthesis of plant si/miRNAs, which confer protection against M. incognita . These findings highlight the potential of these metabolites to advance eco-friendly strategies for controlling root-knot nematodes and to develop resistant plant lines. Conclusion: Soil-streptomycete metabolites could be utilized in RNA interference to enhance tomato resistance to root-knot nematodes via de novo synthesis of protective small interfering and microRNAs, supporting agrobiological applications.

Plant viral infections are primarily propagated by adult insect vectors, which generally require a maturation period of approximately ten to twelve days. Following ingestion of the virus from an infected host plant, these vectors become capable of transmitting the pathogen to susceptible plants. In this study, a stage-structured mathematical model was formulated and analyzed to characterize the transmission dynamics of plant viral diseases mediated by adult insect vectors. Particular emphasis was placed on assessing how the maturation period of vectors influences the progression of infection transmission. To establish the mathematical validity of the model, it was shown to possess non-negative and bounded solutions, which confirms its well-posedness. We identified all steady states and studied their stability. The results show how infection rate, maturation rate, and maturation time can cause stability changes in steady states. Numerical stability and simulations were presented to analyze the behaviors of the system in different dynamical regimes. The stabilizing effect of the maturation period can help develop control methods for the management of plant viral diseases.

RNA viruses are known for their fascinating evolutionary dynamics, characterised by high mutation rates, fast replication, and ability to form quasispecies - clouds of genetically related mutants. Fast replication in RNA viruses is achieved by a very fast but error-prone RNA-dependent RNA polymerase (RdRP). High mutation rates are a double-edged sword: they provide RNA viruses with a mechanism of fast adaptation to a changing environment or host immune system, but at the same time they pose risk to virus survivability in terms of virus mutating beyond its error threshold. Coronaviruses, being a subset of RNA viruses, are unique in having a special enzyme, exoribonuclease (ExoN), responsible for proofreading and correcting errors induced by the RdRP. In this paper we consider replication dynamics of coronaviruses with account for mutations that can be neutral, deleterious or lethal, as well as ExoN. Special attention is paid to different virus replication modes that are known to be crucial for controlling the dynamics of virus populations. We analyse extinction, mutant-only and quasispecies steady states, and study their stability in terms of different parameters, identifying regimes of error catastrophe and lethal mutagenesis. With coronaviruses being responsible for some of the largest pandemics in the last twenty years, we also model the effects of antiviral treatment with various replication inhibitors and mutagenic drugs.

In this paper we present a new method for deriving Itô stochastic delay differential equations (SDDEs) from delayed chemical master equations (DCMEs). Considering alternative formulations of SDDEs that can be derived from the same DCME, we prove that they are equivalent both in distribution, and in sample paths they produce. This allows us to formulate an algorithmic approach to deriving equivalent Itô SDDEs with a smaller number of noise variables, which increases the computational speed of simulating stochastic delayed systems. The new method is illustrated on a simple model of two interacting species, and it shows excellent agreement with the results of direct stochastic simulations, while also demonstrating a much superior speed of performance.

In this paper, we analyse a recently proposed predator-prey model with ratio dependence and Holling type III functional response, with particular emphasis on the dynamics close to extinction. By using Briot-Bouquet transformation we transform the model into a system, where the extinction steady state is represented by up to three distinct steady states, whose existence is determined by the values of appropriate Lambert W functions. We investigate how stability of extinction and coexistence steady states is affected by the rate of predation, predator fecundity, and the parameter characterising the strength of functional response. The results suggest that the extinction steady state can be stable for sufficiently high predation rate and for sufficiently small predator fecundity. Moreover, in certain parameter regimes, a stable extinction steady state can coexist with a stable prey-only equilibrium or with a stable coexistence equilibrium, and it is rather the initial conditions that determine whether prey and predator populations will be maintained at some steady level, or both of them will become extinct. Another possibility is for coexistence steady state to be unstable, in which case sustained periodic oscillations around it are observed. Numerical simulations are performed to illustrate the behaviour for all dynamical regimes, and in each case a corresponding phase plane of the transformed system is presented to show a correspondence with stable and unstable extinction steady state.

In this paper, we derive and analyze a mathematical model of a sexual response. As a starting point, we discuss two studies that proposed a connection between a sexual response cycle and a cusp catastrophe and explain why that connection is incorrect but suggests an analogy with excitable systems. This then serves as a basis for derivation of a phenomenological mathematical model of a sexual response, in which the variables represent levels of physiological and psychological arousal. Bifurcation analysis is performed to identify stability properties of the model’s steady state, and numerical simulations are performed to illustrate different types of behavior that can be observed in the model. Solutions corresponding to the dynamics associated with the Masters–Johnson sexual response cycle are represented by “canard”-like trajectories that follow an unstable slow manifold before making a large excursion in the phase space. We also consider a stochastic version of the model, for which spectrum, variance, and coherence of stochastic oscillations around a deterministically stable steady state are found analytically, and confidence regions are computed. Large deviation theory is used to explore the possibility of stochastic escape from the neighborhood of the deterministically stable steady state, and the methods of an action plot and quasi-potential are employed to compute most probable escape paths. We discuss implications of the results for facilitating better quantitative understanding of the dynamics of a human sexual response and for improving clinical practice.

In this paper, we model dynamics of pediatric vaccination as an imitation game, in which the rate of switching of vaccination strategies is proportional to perceived payoff gain that consists of the difference between perceived risk of infection and perceived risk of vaccine side effects. To account for the fact that vaccine side effects may affect people’s perceptions of vaccine safety for some period of time, we use a delay distribution to represent how memory of past side effects influences current perception of risk. We find disease-free, pure vaccinator, and endemic equilibria and obtain conditions for their stability in terms of system parameters and characteristics of a delay distribution. Numerical bifurcation analysis illustrates how stability of the endemic steady state varies with the imitation rate and the mean time delay, and this shows that it is not just the mean duration of memory of past side effects, but also the actual distribution that determines whether disease will be maintained in the population at some steady level, or if sustained periodic oscillations around this steady state will be observed. Numerical simulations illustrate a comparison of the dynamics for different mean delays and different distributions, and they show that even when periodic solutions are observed, there are differences in their amplitude and period for different distributions. We also investigate the effect of constant public health information campaigns on vaccination dynamics. The analysis suggests that the introduction of such campaigns acts as a stabilizing factor for endemic equilibrium, allowing it to remain stable for larger values of mean time delays.