No abstract

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.

No abstract

Dynamical regimes of two pulse coupled non-identical Belousov-Zhabotinsky oscillators have been studied experimentally as well as theoretically with the aid of ordinary differential equations and phase response curves both for pure inhibitory and pure excitatory coupling. Time delay τ between a spike in one oscillator and perturbing pulse in the other oscillator plays a significant role for the phase relations of synchronous regimes of the 1:1 and 1:2 resonances. Birhythmicity between anti-phase and in-phase oscillations for inhibitory pulse coupling as well as between 1:2 and 1:1 resonances for excitatory pulse coupling have also been found. Depending on the ratio of native periods of oscillations T2/T1, coupling strength, and time delay τ, such resonances as 1:1 (with different phase locking), 2:3, 1:2, 2:5, 1:3, 1:4, as well as complex oscillations and oscillatory death are observed.

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 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.

The drug resistance of Mycobacterium tuberculosis (MbT) remains a serious challenge to global public health as extensively drug resistant tuberculosis usually leads to a lethal outcome. In the case of diseases with resistant strains, it is extremely important to identify a specific strain as soon as possible in order to start an adequate therapy. One such diagnostic method could be the Raman spectroscopy method. We investigated M. tuberculosis strains of the Beijing family deactivated by heating, with different drug sensitivity: sensitive, multi- and extensively drug resistant. Samples, obtained from patient specimens were investigated by Raman spectrometry with the He–Ne (632.8 nm) laser excitation source. As a result, a set of optimal experimental parameters for strain discrimination were determined based on the cell-wall spectral differences. These differences distinguish between drug-sensitive and drug-resistant strains as well as between strains isolated from material samples taken from patients suffering from pulmonary and extra-pulmonary forms of tuberculosis. We suggest that the obtained results allow the usage of the Raman spectroscopy as a fast diagnostic tool for determining various strains in clinical medical practice.

In this work, we explore epidemiological dynamics by the example of tuberculosis in Russian Federation. It has been shown that the epidemiological dynamics correlates linearly with the virulence of Mycobacterium tuberculosis during the period 1987–2012. To construct an appropriate model, we have analysed (using LogLet decomposition method) epidemiological World Health Organization (WHO) data (period 1980–2014) and obtained, as result of their integration, a curve approximated by a bi-logistic function. This fact allows a subdivision of the whole population into parts, each of them satisfies the Verhulst-like models with different constant virulences introduced into each subsystem separately. Such a subdivision could be interconnected with the heterogeneous structure of mycobacterial population that has a high ability of adaptation to the host and strong mutability.