Tuberculosis (TB) remains an important public health problem and one of the leading causes of death. Individuals with latent tuberculosis infection (LTBI) have an increased risk of developing active TB. The problem of the diagnosis of the various stages of TB and the identification of infected patients in the early stages has not yet been solved. The existing tests (the tuberculin skin test and the interferon-gamma release assay) are useful to distinguish between active and latent infections. But these tests cannot be used to predict the development of active TB in individuals with LTBI. The purpose of this review was to analyze the extant data of the interaction of M. tuberculosis with immune cells and identify molecular predictive markers and markers of the early stages of TB. An analysis of more than 90 sources from the literature allowed us to determine various subpopulations of immune cells involved in the pathogenesis of TB, namely, macrophages, dendritic cells, B lymphocytes, T helper cells, cytotoxic T lymphocytes, and NK cells. The key molecular markers of the immune response to M. tuberculosis are cytokines (IL-1β, IL-6, IL-8, IL-10, IL-12, IL-17, IL-22b, IFNɣ, TNFa, and TGFß), matrix metalloproteinases (MMP-1, MMP-3, and MMP-9), and their inhibitors (TIMP-1, TIMP-2, TIMP-3, and TIMP-4). It is supposed that these molecules could be used as biomarkers to characterize different stages of TB infection, to evaluate the effectiveness of its treatment, and as targets of pharmacotherapy.

The mechanisms of transport of substances in the brain parenchyma have been a hot topic in scientific discussion in the past decade. This discussion was triggered by the proposed glymphatic hypothesis, which assumes a directed flow of cerebral fluid within the parenchyma, in contrast to the previous notion that diffusion is the main mechanism. However, when discussing the issue of “diffusion or non-diffusion”, much less attention was given to the question that diffusion itself can have a different character. In our opinion, some of the recently published results do not fit into the traditional understanding of diffusion. In this regard, we outline the relevant new theoretical approaches on transport processes in complex random media such as concepts of diffusive diffusivity and time-dependent homogenization, which expands the understanding of the forms of transport of substances based on diffusion.

Two non-identical, frequency-different pulse-coupled oscillators with time delay have been systematically studied using four-variable model of the Belousov–Zhabotinsky (BZ) reaction at mutual inhibitory, mutual excitatory, and mixed excitatory–inhibitory types of coupling. Different resonances like 1 : 2, 2 : 3, 1 : 3, etc., as well as complex rhythms and abrupt changes between them occur depending on the coupling strengths, time delay, and frequency ratio. Analogously to in-phase and anti-phase oscillations for 1 : 1 resonance, a similar phase locking exists for 1 : 2 resonance in the case of inhibitory coupling. For excitatory coupling, a bursting regime is found. The number of spikes in a single burst can be tuned by both the frequency ratio and time delay. For excitatory–inhibitory coupling, a region where one oscillator is suppressed (OS zone) has been found. Boundary of the OS zone depends on the frequency ratio. For weakly coupled oscillators, Farey sequence has been found for excitatory–inhibitory and mutual excitatory coupling.

The dynamical reaction-diffusion Selkov system as a model describing the complex traveling wave behavior is presented. The approximate amplitude-phase solution allows us to extract the base properties of the biochemical distributed system, which determines such patterns. It is shown that this relatively simple model could describe qualitatively the main features of the glycolysis waves observed in the experiments.

The main factors of pathogenesis in the pulmonary tuberculosis are not only the bacterial virulence and sensitivity of the host immune system to the pathogen, but also the degree of destruction of the lung tissue. Such destruction processes lead to the development of caverns, in most cases requiring surgical interventions besides the drug therapy. Identification of special biochemical markers allowing to assess the necessity of surgery or therapy prolongation remains a challenge. We consider promising markers—metalloproteinases—analyzing the data obtained from patients with pulmonary tuberculosis infected by different strains of Mycobacterium tuberculosis. We argue that the presence of drug-resistant strains in lungs leading to complicated clinical prognosis could be justified not only by the difference in medians of biomarkers concentration (as determined by the Mann–Whitney test for small samples), but also by the qualitative difference in their probability distributions (as detected by the Kolmogorov–Smirnov test). Our results and the provided raw data could be used for further development of precise biochemical data-based diagnostic and prognostic tools for pulmonary tuberculosis.