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In this work, we investigated individual bacteria M. tuberculosis belonging to strains of the Beijing family with different drug sensitivity (sensitive, multi and extensive drug-resistant) by surface-enhanced Raman spectroscopy (SERS) in the fingerprint region. The latter is focused on the spectral bands, which correspond to a set of glutathione bands and DNA methylation patterns revealed due to 5-methylcytosine spectral biomarkers. It is shown that these spectral features can be correlated with drug sensitivity and DNA methylation. Thus, since this kind of diagnostics is fast and operates with individual cells, it can be considered a promising tool, which significantly shortens the time required for a strain's type identification necessary to prescribe adequate therapy., Competing Interests: The authors declare that they have no competing interests., (© 2025 Zyubin et al.)

We consider a model of population growth based on the stochastic variation of the population size-controlled duplication of bacterial cells. It is shown that the proper choice of the control function allows for reproducing a variety of regimes: a logistic growth with saturation, a hindered growth typical for persistent bacterial systems, and a linear population growth detected for some mycobacterial populations. When supplied with the rectangular function having the width equal to the generation time, this approach represents the solution generalizing Rubinow's age-maturity model reproducing systems with desynchronization and saturation. The model's plausibility is confirmed by the direct comparison with real data for the growth of M. tuberculosis populations obtained with the BACTEC MGIT system under different conditions of growth synchronization., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier Inc. All rights reserved.)

Recent studies of the spread of substances penetrating the disrupted blood-brain barrier have revealed that the spread in the parenchyma surrounding a vessel has a complex character. In particular, a flow-like motion occurred for a short time that exhibits a smooth transition to diffusional spread. To address the possible physical background of such behavior, we created a system formed by a hydrogel medium with a channel filled by a marker solution, which can serve as a physical model mimicking the process of a substance passively spreading to the brain's parenchyma when the blood-brain barrier is disrupted. The key result obtained in this work consists of the conclusion that the above-mentioned two-stage character of the spread process discovered in a previous biophysical experiment on the blood-brain opening in a living mouse may originate from the specificity of transport in porous soft matter with relaxation. We propose a mathematical model based on the extended Cattaneo equation, which reproduces our experimental data; determines the crossover time coinciding with that found in the biological system; and, therefore, provides a means of interpretation of this phenomenon.

We consider subdiffusive motion, modeled by the generalized Langevin equation in an equilibrium setting, of tracer particles in channels of indefinite length in the x direction: the channels of varying width and the channels with sinusoidally meandering midline. The subdiffusion in the x direction is not affected by constraints put by the channel. This is especially astonishing for meandering channels whose centerline might be quite long. The same behavior is seen in a holonomic model of a bead on a sinusoidal and meandering wire, where some analytic insights are possible.

A miniature postsynaptic current (mPSC) is a small, rare, and highly variable spontaneous synaptic event that is generally caused by the spontaneous release of single vesicles. The amplitude and variability of mPSCs are key measures of the postsynaptic processes and are taken as the main characteristics of an elementary unit (quantal size) in traditional quantal analysis of synaptic transmission. Due to different sources of biological and measurement noise, recordings of mPSCs exhibit high trial-to-trial heterogeneity, and experimental measurements of mPSCs are usually noisy and scarce, making their analysis demanding. Here, we present a sequential procedure for precise analysis of mPSC amplitude distributions for the range of small currents. To illustrate the developed approach, we chose previously obtained experimental data on the effect of the extracellular matrix on synaptic plasticity. The proposed statistical technique allowed us to identify previously unnoticed additional modality in the mPSC amplitude distributions, indicating the formation of new immature synapses upon ECM attenuation. We show that our approach can reliably detect multimodality in the distributions of mPSC amplitude, allowing for accurate determination of the size and variability of the quantal synaptic response. Thus, the proposed method can significantly expand the informativeness of both existing and newly obtained experimental data. We also demonstrated that mPSC amplitudes around the threshold of microcurrent excitation follow the Gumbel distribution rather than the binomial statistics traditionally used for a wide range of currents, either for a single synapse or when taking into consideration small influences of the adjacent synapses. Such behaviour is argued to originate from the theory of extreme processes. Specifically, recorded mPSCs represent instant random current fluctuations, among which there are relatively larger spikes (extreme events). They required more level of coherence that can be provided by different mechanisms of network or system level activation including neuron circuit signalling and extrasynaptic processes., (© 2023. Springer Nature Limited.)

In this work, we review some physical methods of macroscopic experiments, which have been recently argued to be promising for the acquisition of valuable characteristics of biomolecular structures and interactions. The methods we focused on are electron paramagnetic resonance spectroscopy, Raman spectroscopy, and differential scanning calorimetry. They were chosen since it can be shown that they are able to provide a mutually complementary picture of the composition of cellular envelopes (with special attention paid to mycobacteria), transitions between their molecular patterning, and the response to biologically active substances (reactive oxygen species and their antagonists-antioxidants-as considered in our case study).

The resazurin reduction test is one of the basic tests for bacterial culture viability and drug resistance endorsed by the World Health Organisation. At the same time, conventional spectrophotometric and spectrofluorimetric methods demand rather bulky and expensive equipment. This induces a challenge for developing simpler approaches to sensor systems that are portable and applicable in resource-limited settings. In this work, we address two such alternative approaches, based on the colour processing of the microbiological plate's photographic images and single-channel photometry with a recently developed portable microbiological analyser. The key results consist of establishing a sequential linear correspondence between the concentration of resorufin produced due to the reduction of resazurin by viable bacteria as determined by the UV-Vis studies, the intensity of the a* channel of the CIE L*a*b* colour space and the transmitted light intensity registered by a luxmeter under the LED illumination with a yellow colour filter. This route is illustrated with the chemical system "Hydrazine hydrate - resazurin", isolating the target colour change-inducing reaction and the test of determining the minimal inhibition concentration of the antibacterial first-line drug isoniazid acting on the culture of the H37Rv strain of M. tuberculosis .

Predicting the density of liquids at ultrahigh pressures in the case when only the data measured at ambient pressure are available is a long-standing challenge for thermodynamic research. In this work, we archived this goal for molecular liquids by applying the half-sum of the Tait equation and the Murnagnan equation in the form coordinated with Tait's at low pressure for predicting the density of molecular liquids up to the pressures more than 1 GPa with uncertainty comparable with the experimental one. It is shown that the control parameter, which is needed in addition to the initial density and the isothermal compressibility can be found using the speed of sound and the density at ambient pressure and has a clear physical interpretation in terms of the characteristic frequency of intermolecular oscillation mimicking the limiting frequency of Debye's theory of heat conductivity of solids. This fact is discussed as arguing in favour of the modern phonon theory of liquid thermodynamics and expands it range of applicability to the volumetric properties of liquids at temperatures far below the critical one. The validity of the model is illustrated with the case study of classic Bridgman's dataset as well as with some examples of ultrahigh-pressure data obtained by the diamond anvil cell and shock wave compression methods., (© 2023. The Author(s).)

In this work, we discuss an opportunity to use a set of the matrix metalloproteinases MMP-1, MMP-8, and MMP-9 and the tissue inhibitor TIMP, the concentrations of which can be easily obtained via a blood test from patients suffering from tuberculosis, as the biomarker for a fast diagnosis of the drug resistance status of Mycobacterium tuberculosis . The diagnostic approach is based on machine learning with the CatBoost system, which has been supplied with additional postprocessing. The latter refers not only to the simple probabilities of ML-predicted outcomes but also to the decision tree-like procedure, which takes into account the presence of strict zeros in the primary set of probabilities. It is demonstrated that this procedure significantly elevates the accuracy of distinguishing between sensitive, multi-, and extremely drug-resistant strains.

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.

Recent interest in the antioxidant capacity of foods and beverages is based on the established medical knowledge that antioxidants play an essential role in counteracting the damaging effects of free radicals, preventing human neurodegenerative diseases, cardiovascular disorders, and even cancer. At the same time, there is no "the method" that uniquely defines the antioxidant capacity of substances; moreover, the question of interrelation between results obtained by different experimental techniques is still open. In this work, we consider the trolox equivalent antioxidant capacity (TEAC) values obtained by electron paramagnetic resonance (EPR) spectroscopy and ultraviolet-visible (UV-vis) spectroscopy using the classic objects for such studies as an example: red, rosé, and white wine samples. Based on entirely different physical principles, these two methods give values that are not so simply interrelated; this creates a demand for machine learning as a suitable tool for revealing quantitative correspondence between them. The consideration consists of an approximate correlation-based analytical model for the key argument (i.e., TEACEPR) with subsequent adjustment by machine learning-based processing utilizing the CatBoost algorithm with the usage of auxiliary chemical data, such as the total phenolic content and color index, which cannot be accurately described by analytical expressions.

This study presents an analysis of M. tuberculosis growth data obtained using the BACTEC MGIT 960 system and respective mathematical models. The system is based on the detection of a decrease in oxygen level in the broth due to the bacterial respiration. It is shown that recordings sampled with a 1 hour rate provide an opportunity to distinguish between the oxygen consumption of growing cells and active cells division when the density of micro-organisms is sufficient to enter into the synchronized division mode. More specifically, the growth of culture is continuous only with large initial dilutions; otherwise, there are jumps between different growth stages with a time interval of 13-15 h. The combination of the oxygen-quenching kinetics for an analytic reagent and the population growth kinetics resulted in a mathematical model, which consists of mixing Verhulst's and Gompertz's models. The parameters of such mixing and switching between the models' prevalences are discussed with respect to oxygen uptake reactions reflected in the changes in the experimentally registered fluorescence level., Competing Interests: Conflict of interest: All authors declare no conflicts of interest in this paper., (© 2022 the Author(s), licensee AIMS Press.)

Dissociation of a ligand isoniazid from a protein catalase was investigated using all-atom molecular dynamics (MD) simulations. Random acceleration MD (τ-RAMD) was used, in which a random artificial force applied to the ligand facilitates its dissociation. We have suggested a novel approach to extrapolate such obtained dissociation times to the zero-force limit assuming never before attempted universal exponential dependence of the bond strength on the applied force, allowing direct comparison with experimentally measured values. We have found that our calculated dissociation time was equal to 36.1 s with statistically significant values distributed in the interval of 0.2-72.0 s, which quantitatively matches the experimental value of 50 ± 8 s despite the extrapolation over 9 orders of magnitude in time.

Molecular dynamics simulations have been performed on liquid dibromomethane at thermodynamic states corresponding to temperature in the range 268-328 K and pressure varying from 1 bar to 3000 bar. The interaction model is a simple effective two-body pair potential with atom-atom Coulomb and Lennard-Jones interactions and molecules are rigid. Thermodynamic properties have been studied, including the isobaric thermal expansion coefficient, the isothermal compressibility, the heat capacities and the speed of sound. The simulation results exhibit a crossing of the isotherms of the isobaric thermal expansion coefficient at about 800 bar in very good agreement with the prediction of an isothermal fluctuation equation of state predicting such a crossing in the pressure range 650-900 bar, though experimental results up to 1000 bar do not find any crossing.

This work shows that simple compartmental epidemiological models may not reproduce actually reported country-wide statistics since the latter reflects the cumulative amount of infected persons, which in fact is a sum of outbreaks within different patched. It the same time, the multilogistic decomposition of such epidemiological curves reveals components, which are quite close to the solutions of the SIR model in logistic approximations characterised by different sets of parameters including time shifts. This line of reasoning is confirmed by processing data for Spain and Russia in details and, additionally, is illustrated for several other countries., Competing Interests: The author declares that they have no competing interests., (© 2021 Postnikov.)

Basing on existence of the mathematically sequential reduction of the three-compartmental (Susceptible-Infected-Recovered/Removed) model to the Verhulst (logistic) equation with the parameters determined by the basic characteristic of epidemic process, this model is tested in application to the recent data on COVID-19 outbreak reported by the European Centre for Disease Prevention and Control. It is shown that such a simple model adequately reproduces the epidemic dynamics not only qualitatively but for a number of countries quantitatively with a high degree of correlation that allows to use it for predictive estimations. In addition, some features of SIR model are discussed in the context, how its parameters and conditions reflect measures attempted for the disease growth prevention that is also clearly indicated by deviations from such model solutions., Competing Interests: The author declare that he has no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2020 Elsevier Ltd. All rights reserved.)

Presented here is a comprehensive study on the antioxidant properties of various alcoholic beverages: beers, wines, tinctures, and strong spirits, including whisky, brandy, cognac, vodkas, and liquors. The Trolox equivalent antioxidant capacity (TEAC) of each of these various alcoholic beverages is determined using an electron paramagnetic resonance (EPR) method, which is based on a semiempirical correlation. Moreover, the EC 50 parameter was determined on the basis of the dependences of the TEAC values obtained by this mathematical equation. Moreover, the total phenolic content (TP) and color index, which have a direct influence on the antioxidant properties of the alcoholic beverages, were identified. The results showed that all the investigated alcoholic beverages (ABs), with the exception for vodkas, exhibit antioxidant properties. By performing a statistical analysis, it was found that the TEAC value significantly depends on the TP, production method, and raw material from which the alcohol was made. However, it is assumed that the TEAC value of alcoholic beverages is independent of the alcohol content.

In this work, we argue that the volumetric properties of liquids cannot be reproduced by a single isothermal equation of state derived by the compressibility route for the whole pressure region extended up to a GPa pressure but require the consideration of two states associated with qualitatively different molecular packing properties. This is confirmed by examples of polar and non-polar substances within the range of temperatures from 203.15 K to 491.48 K and pressures up to 1200 MPa. The proposed two states model is truly predictive for the high-pressure density and isothermal compressibility using several easily measurable physico-chemical quantities: the density, the isobaric heat capacity, and the speed of sound at atmospheric pressure only. The experimental data on the density for 15 different compressed liquids, given in the literature as a function of temperature and very high-pressures, were used for the comparison and its analysis. The relative absolute average deviation for 2138 experimental data points by a two states model is close to 0.17%.

In this work, the short-time dynamics of simple liquid is explored both analytically and numerically with the focus on the interplay between the density fluctuations in a volume surrounding a chosen particle and its random walk motion. The particles interact via the Lennard-Jones potential with parameters corresponding to liquid argon. For large times, analytical calculations based on the fluctuation theory provides an explicit expression reproducing isothermal change of the self-diffusion coefficient in liquid argon corresponding to the experimental data. These results lead to the conclusion that such behavior is based on the reduced mobility of particles reflected in their density fluctuations that can be equivalently achieved in the cases of either low temperatures and pressures (supercooling) or moderate temperatures and high pressures (overdamping).

The laser speckle contrast analysis (LASCA) is one of the most applicable tools in microcirculation studies. While the basic idea, as well as experimental setup for this method, are fairly simple, there is still the room for advancing of data processing algorithms. Specifically, the conventional realizations of LASCA method may limit the spatial and/or temporal resolution and thus fail in the detection of very small contrast objects since they based on the fixed-size rectangular sliding window function. We suggest an alternative data processing algorithm based on the usage of the Gaussian sliding filter for a sequential determination of both spatial and temporal parts of the speckle contrast. The suggested replacement of conventional box filter leads to the monotonic damping of high-frequency spectral components that results in a better elimination of ringing and aliasing effects in the spatio-temporal speckle contrast outputs. Additionally, we show that such sliding filtration increases robustness with respect to the processing of a sequence of nonstabilised images. We support this consideration with representative examples of processing both surrogate and real experimental data., (© 2019 John Wiley & Sons, Ltd.)

A correction to this article has been published and is linked from the HTML version of this paper. The error has been fixed in the paper.

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., Competing Interests: The authors declare no competing interests.

We study the influence of periodic influx on a character of glycolytic oscillations within the forced Selkov system. We demonstrate that such a simple system demonstrates a rich variety of dynamical regimes (domains of entrainment of different order (Arnold tongues), quasiperiodic oscillations, and chaos), which can be qualitatively collated with the known experimental data. We determine detailed dynamical regimes exploring the map of Lyapunov characteristic exponents obtained in numerical simulations of the Selkov system with periodic influx. In addition, a special study of the chaotic regime and the scenario of its origin in this system was evaluated and discussed.

During this work, we demonstrate, for the first time, that the volumetric properties of pure ionic liquids could be truly predicted as a function of temperature from 219 K to 473 K and pressure up to 300 MPa. This has been achieved by using only density and isothermal compressibility data at atmospheric pressure through the Fluctuation Theory-based Tait-like Equation of State (FT-EoS). The experimental density data of 80 different ionic liquids, described in the literature by several research groups as a function of temperature and pressure, was then used to provide comparisons. Excellent predictive capability of FT-EoS was observed with an overall relative absolute average deviation close to 0.14% for the 15,298 data points examined during this work.

We consider two approaches to modelling the cell metabolism of 6-mercaptopurine, one of the important chemotherapy drugs used for treating acute lymphocytic leukaemia: kinetic ordinary differential equations, and Boolean networks supplied with one controlling node, which takes continual values. We analyse their interplay with respect to taking into account ATP concentration as a key parameter of switching between different pathways. It is shown that the Boolean networks, which allow avoiding the complexity of general kinetic modelling, preserve the possibility of reproducing the principal switching mechanism., Competing Interests: The authors declare no competing interests.

We consider the Ornstein-Uhlenbeck process with a broad initial probability distribution (Lévy distribution), which exhibits so-called nonspectral modes. The relaxation rate of such modes differs from those determined from the parameters of the corresponding Fokker-Plank equation. The first nonspectral mode is shown to govern the relaxation process and allows for estimation of the initial distribution's Lévy index. A method based on continuous wavelet transformation is proposed to extract both (spectral and nonspectral) relaxation rates from a stochastic data sample.

The three-compartmental demographic model by Korotaeyv-Malkov-Khaltourina, connecting population size, economic surplus, and education level, is considered from the point of view of dynamical systems theory. It is shown that there exist two integrals of motion, which enables the system to be reduced to one nonlinear ordinary differential equation. The study of its structure provides analytical criteria for the dominance ranges of the dynamics of Malthus and Kremer. Additionally, the particular ranges of parameters enable the derived general ordinary differential equations to be reduced to the models of Gompertz and Thoularis-Wallace.

The application of the continuous wavelet transform to the study of a wide class of physical processes with oscillatory dynamics is restricted by large central frequencies owing to the admissibility condition. We propose an alternative reconstruction formula for the continuous wavelet transform, which is applicable even if the admissibility condition is violated. The case of the transform with the standard reduced Morlet wavelet, which is an important example of such analysing functions, is discussed.

The relaxation of a dissipative system to its equilibrium state often shows a multiexponential pattern with relaxation rates, which are typically considered to be independent of the initial condition. The rates follow from the spectrum of a Hermitian operator obtained by a similarity transformation of the initial Fokker-Planck operator. However, some initial conditions are mapped by this similarity transformation to functions which grow at infinity. These cannot be expanded in terms of the eigenfunctions of a Hermitian operator, and show different relaxation patterns. Considering the exactly solvable examples of Gaussian and generalized Lévy Ornstein-Uhlenbeck processes (OUPs) we show that the relaxation rates belong to the Hermitian spectrum only if the initial condition belongs to the domain of attraction of the stable distribution defining the noise. While for an ordinary OUP initial conditions leading to nonspectral relaxation can be considered exotic, for generalized OUPs driven by Lévy noise, such initial conditions are the rule.

Here we consider the spatially extended model incorporating the temperature-dependent autocatalytic coefficient into the Merkin-Needham-Scott version of the Selkov system and show that this model with temperature gradient quite reasonably explains the experimentally detected traveling glycolytic nonstationary waves, which can be attributed as kinematic ones. Additionally, we analyze the influence of possibly incorporating diffusion terms into the equations. It is shown that the value of diffusivity influences the timetable for the birth of new wave and their further evolution. This result could be used as a method for the determination of diffusivity.

We introduce the temperature-dependent autocatalytic coefficient into the Merkin-Needham-Scott version of the Selkov system and consider the resulting equations as a model for temperature-controlled, self-sustained glycolytic oscillations in a closed reactor. It has been shown that this simple model reproduces key features observed in the experiments with temperature growth: (i) exponentially decreasing period of oscillations; (ii) reversal of relative duration leading and tail fronts. The applied model also reproduces the modulations of oscillations induced by the periodic temperature change.

We consider diffusion limited aggregation of particles of two different kinds. It is assumed that a particle of one kind may adhere only to another particle of the same kind. The particles aggregate on a linear substrate which consists of periodically or randomly placed particles of different kinds. We analyze the influence of initial patterns on the structure of growing clusters. It is shown that at small distances from the substrate, the cluster structures repeat initial patterns. However, starting from a critical distance the initial periodicity is abruptly lost, and the particle distribution tends to a random one. An approach describing the evolution of the number of branches is proposed. Our calculations show that the initial pattern can be detected only at the distance which is not larger than approximately one and a half of the characteristic pattern size.

We propose the modification of the complex wavelet transform adapted for an analysis of strong nonlinear oscillations with a shape far from sinusoidal. It is based on the rotation of transform modulus obtained via usage of the Morlet wavelet in such a way that higher harmonics are merged with a main one. The method is illustrated by application to the analysis of regular and chaotic oscillations generated by the Rössler system.

We discuss the biochemical three-dimensional reaction-diffusion model, which does not provide temporal self-sustained oscillations via reaction terms. However, the self-sustained oscillations and waves could be obtained using the proper boundary conditions for systems with a finite thickness. We have carried out in our numerical simulation the results quite corresponding to the experimental ones. We discuss the range of models for which our approach is applicable.

This Brief Report presents the hierarchical reaction-diffusion partial differential equations (PDE) system, which reproduces a mean-square displacement and a density relaxation process corresponding to the anomalous diffusion on a small-world network. These results are confirmed by the comparison with the known direct numerical simulations.

It has been shown that the so-called "wavelet phase" (or "time-scale") synchronization of chaotic signals is actually synchronization of smoothed functions with reduced chaotic fluctuations. This fact is based on the representation of the wavelet transform with the Morlet wavelet as a solution of the Cauchy problem for a simple diffusion equation with initial condition in a form of harmonic function modulated by a given signal. The topological background of the resulting effect is discussed. It is argued that the wavelet phase synchronization provides information about the synchronization of an averaged motion described by bounding tori instead of the fine-level classical chaotic phase synchronization.

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.

We consider the process of an epidemic spread in a population of individuals with low mobility within the SIR scheme. In a continuum limit such propagation mechanism is described by a non-linear reaction-diffusion equation with a diffusion coefficient being the function of the densities of susceptible. The traveling wave solution of the corresponding system of partial differential equations is obtained and analyzed. We show that the model allows for description of Kendall epidemic waves, and give the dependence of the infection wave's shape on the parameters of the system. An explicit calculation is done for realistic values of parameters obtained from field epidemiological data for a phocine distemper virus infection among harbor seals in 1988.