Agent-Based Simulation of the COVID-19 Epidemic in Russia

The COVID-19 pandemic has created a public health emergency in Russia and across the world. The wavelike spread of the new coronavirus infection, caused by newly emerging variants of the coronavirus, has led to a high incidence rate in all subjects of the Russian Federation. It is becoming extremely topical to get the opportunity to manage the development of the epidemic and assess the impact of certain regulatory measures on this process. This will help government agencies make informed decisions to control the burden on healthcare organizations. It is often impossible to obtain such assessments without using modern mathematical models.

[On the tactics of management and treatment of patients with congenital cerebral hernias in their localization in the maxillofacial region]

The analysis of the state of two patients with congenital cerebral hernias was carried out, which made it possible to establish differences in the effect of hernias on the state of the body. In the first case, the hernia is localized in the nasal cavity, and after its removal, the postoperative cerebrospinal fluid (CSF) leakage was stopped by a flap of the mucous membrane from the opposite side of the nasal septum. In the second case clinical analysis and computed tomography made it possible to state that the hernia was in the retromaxillary space and did not affect the patient's condition. Computed tomography shows signs of moderate blood pressure on the adjacent formations, and removal of the hernia and stopping the subsequent CSF leakage were impossible. The presented observations demonstrate an ambiguous approach to resolving the issue of surgical intervention in such cases.

Random dynamical models from time series

In this work we formulate a consistent Bayesian approach to modeling stochastic (random) dynamical systems by time series and implement it by means of artificial neural networks. The feasibility of this approach for both creating models adequately reproducing the observed stationary regime of system evolution, and predicting changes in qualitative behavior of a weakly nonautonomous stochastic system, is demonstrated on model examples. In particular, a successful prognosis of stochastic system behavior as compared to the observed one is illustrated on model examples, including discrete maps disturbed by non-Gaussian and nonuniform noise and a flow system with Langevin force.

Prognosis of qualitative system behavior by noisy, nonstationary, chaotic time series

An approach to prognosis of qualitative behavior of an unknown dynamical system (DS) from weakly nonstationary chaotic time series (TS) containing significant measurement noise is proposed. The approach is based on construction of a global time-dependent parametrized model of discrete evolution operator (EO) capable of reproducing nonstationary dynamics of a reconstructed DS. A universal model in the form of artificial neural network (ANN) with certain prior limitations is used for the approximation of the EO in the reconstructed phase space. Probabilistic prognosis of the system behavior is performed using Monte Carlo Markov chain (MCMC) analysis of the posterior Bayesian distribution of the model parameters. The classification of qualitatively different regimes is supposed to be dictated by the application, i.e., it is assumed that some classifier function is predefined that maps a point of a model parameter space to a finite set of different behavior types. The ability of the approach to provide prognosis for times comparable to the observation time interval is demonstrated. Some restrictions as well as possible advances of the proposed approach are discussed.

Using the minimum description length principle for global reconstruction of dynamic systems from noisy time series

An alternative approach to determining embedding dimension when reconstructing dynamic systems from a noisy time series is proposed. The available techniques of determining embedding dimension (the false nearest-neighbor method, calculation of the correlation integral, and others) are known [H. D. I. Abarbanel, (Springer-Verlag, New York, 1997)] to be inefficient, even at a low noise level. The proposed approach is based on constructing a global model in the form of an artificial neural network. The required amount of neurons and the embedding dimension are chosen so that the description length should be minimal. The considered approach is shown to be appreciably less sensitive to the level and origin of noise, which makes it also a useful tool for determining embedding dimension when constructing stochastic models.

Markov chain Monte Carlo method in Bayesian reconstruction of dynamical systems from noisy chaotic time series

The impossibility to use the MCMC (Markov chain Monte Carlo) methods for long noisy chaotic time series (TS) (due to high computational complexity) is a serious limitation for reconstruction of dynamical systems (DSs). In particular, it does not allow one to use the universal Bayesian approach for reconstruction of a DS in the most interesting case of the unknown evolution operator of the system. We propose a technique that makes it possible to use the MCMC methods for Bayesian reconstruction of a DS from noisy chaotic TS of arbitrary long duration.

Modified Bayesian approach for the reconstruction of dynamical systems from time series

Some recent papers were concerned with applicability of the Bayesian (statistical) approach to reconstruction of dynamic systems (DS) from experimental data. A significant merit of the approach is its universality. But, being correct in terms of meeting conditions of the underlying theorem, the Bayesian approach to reconstruction of DS is hard to realize in the most interesting case of noisy chaotic time series (TS). In this work we consider a modification of the Bayesian approach that can be used for reconstruction of DS from noisy TS. We demonstrate efficiency of the modified approach for solution of two types of problems: (1) finding values of parameters of a known DS by noisy TS; (2) classification of modes of behavior of such a DS by short TS with pronounced noise.

Investigation of nonlinear dynamical properties by the observed complex behaviour as a basis for construction of dynamical models of atmospheric photochemical systems

The importance of the investigation of nonlinear dynamical properties (NDPs) of the atmospheric photochemical systems (PCSs) was demonstrated in ref. 1 and 2 (A. M. Feigin and I. B. Konovalov, J. Geophys. Res., 1996, 101 (D20), 26038; 1. B. Konovalov, A. M. Feigin and A. Y. Mukhina, J. Geophys. Res., 1999, 104 (D3), 3669). The only known way to study NDPs of any natural dynamical system (including atmospheric PCSs) is to construct a mathematical model of the system. The key point here is adequacy of the NDPs of the constructed model to the system observed. We propose a new approach to construction of such an adequate model for systems manifesting nonstationary chaotic behaviour and describe an algorithm based exclusively on nonlinear dynamical analysis of the observed time series (TS) without invoking any a priori knowledge about the properties of the system observed. Potentialities of the algorithm are demonstrated with the aid of a computer model of the mesospheric PCS. The duration of the "observed" TS is limited so that the system demonstrates only one--chaotic--type of behaviour, without any bifurcations throughout the observed TS. The proposed algorithm enabled us to make a correct prognosis of bifurcation sequences and calculate probabilities to reveal, at the time instant of interest, predicted regimes of the system's behaviour for times much greater than the length of the initial TS.

Properties of ionic channels formed by the antibiotic syringomycin E in lipid bilayers: dependence on the electrolyte concentration in the bathing solution

Using the planar lipid bilayer technique, organization of ionic channels formed by the lipodepsipeptide antibiotic syringomycin E applied to one (cis) side of a lipid bilayer was studied. Low concentrations of NaCl (0.01-0.1 M) induced the opening and closing of two types of channels - "small" and "large". The large channels had single channel conductances approximately six times greater than those of the small channels. An increase in the NaCl concentration (0.6-1.0 M) decreased almost completely the chance to reveal the large channels. Although the syringomycin channels exhibited the anion selectivity within the entire range of NaCl concentrations in the bathing solutions (from 0.001 to 1.0 M) whereas the concentration gradients across the bilayers were 2 and 4, the transfer numbers for Cl-decreased with an increase in the mean NaCl concentration (from 0.83 for 0.005 M to 0.70 for 0.5 M). Moreover, at each mean value of NaCl concentration, all conductance levels had the same ion selectivity (identical reversal potential). These results suggest that at low NaCl concentrations the large channels are clusters of small channels which synchronously open and close, while at high electrolyte concentrations the screening of the charged groups responsible for channel interactions prevents the cluster formation. A new theoretical approach for the estimation of the channel radius and the number of elementary charges located at its inner surface (based on the experimental curve of the dependence of transfer number on the NaCl concentration) was developed. Based on this theoretical approach, the channel radius equal to 1 nm and one elementary charge located at its inner surface were obtained.

Selective modification of sterol composition of hepatomas: new opportunities for chemotherapy

The absence of feedback regulation of cholesterol biosynthesis in hepatomas suggests the possibility of substitution of cholesterol with its biosynthetic precursors (7-dehydrocholesterol or lanosterol) selectively in hepatomas without the accumulation of these precursors in liver and other normal tissues, by a combination of a high cholesterol diet and specific inhibitors of cholesterol biosynthesis (AY-9944 for accumulation of 7-dehydrocholesterol and ketoconazole for accumulation of lanosterol). We suggest: (1) using a selective accumulation of 7-dehydrocholesterol in hepatoma plasma membranes to increase the sensitivity of hepatoma cells to polyene antibiotics (amphotericin B, nystatin), because polyene antibiotics have higher affinity to 7-dehydrocholesterol compared to cholesterol; (2) using a selective accumulation of lanosterol in hepatoma cells to increase the sensitivity of hepatoma cells to different antitumor agents, because lanosterol is much less effective in supporting vital cell functions (including barrier properties of natural membranes) compared to cholesterol.

The arginine taste receptor. Physiology, biochemistry, and immunohistochemistry

The amino acid, L-arginine (L-Arg), is a potent taste stimulus for the channel catfish, Ictalurus punctatus. Receptor binding studies demonstrated a high-affinity binding of L-Arg to putative taste receptor sites. This binding could be inhibited by preincubation of the tissue in the lectins Phaseolus vulgaris agglutinin (PHA) and Ricinus communis agglutinin I (RCA I). Neurophysiological studies demonstrated that the L-Arg receptor is a stimulus-gated ion channel type receptor whose conductance was stimulated by L-Arg and inhibited by D-arginine (D-Arg). To purify the receptor we subjected CHAPS solubilized partial membrane preparation from barbel epithelium to RCA I lectin affinity chromatography. The bound proteins were eluted with D-galactose. When these proteins were reconstituted into lipid bilayers, L-Arg activated single channel currents with conductances between 45 and 85 pS. Sodium dodecylsulfate polyacrylamide gel electrophoresis (SDS-PAGE) of the eluted protein showed a distinct band at approximately 83 kDa. Polyclonal antibodies raised against this 83-kDa band in guinea pigs reacted with numerous small (approximately 1 micron) sites within the taste pore of every taste bud when applied to fixed nonpermeabilized barbels. This observation suggests that the antibodies recognize an externally-facing epitope of the putative Arg receptor. The antibodies also inhibited L-Arg-stimulated currents in reconstitution studies. Sephacryl S-300 HR chromatography of the eluant from the affinity column showed a high molecular weight peak (> 700 kDa) which was recognized by the antibodies. Reconstitution of the protein from this peak into a lipid bilayer resulted in L-Arg-stimulated channels that could be inhibited by D-Arg. This high molecular weight component may be aggregates of the arginine taste receptor.

Cluster organization of ion channels formed by the antibiotic syringomycin E in bilayer lipid membranes

The cyclic lipodepsipeptide, syringomycin E, when incorporated into planar lipid bilayer membranes, forms two types of channels (small and large) that are different in conductance by a factor of sixfold. To discriminate between a cluster organization-type channel structure and other possible different structures for the two channel types, their ionic selectivity and pore size were determined. Pore size was assessed using water-soluble polymers. Ion selectivity was found to be essentially the same for both the small and large channels. Their reversal (zero current) potentials with the sign corresponding to anionic selectivity did not differ by more than 3 mV at a twofold electrolyte gradient across the bilayer. Reduction in the single-channel conductance induced by poly(ethylene glycol)s of different molecular weights demonstrated that the aqueous pore sizes of the small and large channels did not differ by more than 2% and were close to 1 nm. Based on their virtually identical selectivity and size, we conclude that large syringomycin E channels are clusters of small ones exhibiting synchronous opening and closing.

The effect of sterols on the sensitivity of membranes to the channel-forming antifungal antibiotic, syringomycin E

The ability of three sterols of different structure to influence the interaction of syringomycin E (an antifungal antibiotic that forms voltage dependent channels in planar lipid bilayers) with a planar lipid bilayer was evaluated. The rate of increase of bilayer conductance induced by syringomycin E was about 1000-times less in bilayers containing 50 mol% of cholesterol compared to bilayers without sterols. The effect of ergosterol (the primary sterol of fungal cells) on the sensitivity of bilayers to syringomycin E was much weaker than that of cholesterol, while stigmasterol (one of the main sterols of plant cells) did not significantly influence the ability of syringomycin E to induce a conductance increase in the bilayer. None of the sterols altered the single channel conductance properties of syringomycin E. These observations suggest that cholesterol affects the sensitivity of target membranes to syringomycin E by enlarging the energy barrier for channel formation rather than participating in channel formation itself.

Properties of voltage-gated ion channels formed by syringomycin E in planar lipid bilayers

Using the planar lipid bilayer technique we demonstrate that the lipodepsipeptide antibiotic, syringomycin E, forms voltage-sensitive ion channels of weak anion selectivity. The formation of channels in bilayers made from dioleoylglycerophosphatidylserine doped with syringomycin E at one side (1-40 micrograms/ml) was greatly affected by cis-positive voltage. A change of voltage from a positive to a negative value resulted in (i) an abrupt increase in the single channel conductance (the rate of increase was voltage dependent) simultaneous with (ii) a closing of these channels and an exponential decrease in macroscopic conductance over time. The strong voltage dependence of multichannel steady state conductance, the single channel conductance, the rate of opening of channels at positive voltages and closing them at negative voltages, as well as the observed abrupt increase of single channel conductance after voltage sign reversal suggest that the change of the transmembrane field induces a significant rearrangement of syringomycin E channels, including a change in the spacing of charged groups that function as voltage sensors. The conductance induced by syringomycin E increased with the sixth power of syringomycin E concentration suggesting that at least six monomers are required for channel formation.

Capsaicin and its analogs induce ion channels in planar lipid bilayers

The irritating, pungent compound, capsaicin (10-20 microM), induces the formation of non-selective ion channels with a wide variety of conductances in protein-free lipid bilayers form from a mixture of zwitterionic phospholipids. The channel-forming activity of capsaicin and four of its analogs followed the sequence: resiniferatoxin > capsaicin = pelargonic acid vanillylamide > methylcapsaicin >> veratrylamine. The ability to form channels correlated with the biological activity of these compounds observed in other studies that measured 45Ca uptake into rat dorsal root ganglion cells. The correlation obtained suggests that an interaction with the lipid bilayer may be an important component of the biological activity of capsaicin.

The influence of sterols on the sensitivity of lipid bilayers to melittin

The sensitivity of planar lipid bilayers to the permeabalizing effect of melittin was evaluated when sterols of varying structure were incorporated into the membrane. The addition of increasing amount of cholesterol (0-50 mole %) decreased the sensitivity of membranes formed from negatively charged phospholipids to melittin but did not (in amount of up to 66 mole %) change the sensitivity of membranes formed from zwitterionic lipids. 7-Dehydrocholesterol, stigmasterol and ergosterol had the same ability as that of cholesterol to decrease the membrane sensitivity to melittin, while lanosterol had no effect on the sensitivity of membranes to melittin. The results suggest that the effect of sterols is complex and cannot be explained only by a direct interaction of melittin with cholesterol, by a decrease of membrane fluidity, or by changes in distribution of surface charge.

The properties of ion channels formed by the coumarin antibiotic, novobiocin, in lipid bilayers

The coumarin antibiotic novobiocin forms ion channels of varying conductances in lipid bilayers. The conductances (about 20, 22, 14, 7 and 2 pS for 100 mM NH4Cl, CsCl, KCl, NaCl and LiCl, respectively) and selectivities (cation transference numbers in the range of 0.97-0.98) of one type of novobiocin-induced channel are similar to those found for channels formed by gramicidin A, an antibiotic of very different structure. The conductance of novobiocin channels of this type was independent of the species of the membrane lipid. This observation suggests that novobiocin molecules directly form these channels, and that channels are not formed through defects in lipid structure. The similarity in conductance and ion selectivity between channels induced by novobiocin and those formed by gramicidin A suggests that these structurally different molecules form channels with comparable internal diameter and internal surface charge distribution. Using HPLC purification we argue that the channel-forming activity of novobiocin is related to the activity of the novobiocin molecule itself, and not to a contaminant of the commercially available novobiocin sodium salt preparation.

Enhancement of gustatory nerve fibers to NaCl and formation of ion channels by commercial novobiocin

Single fibers of the rat chorda tympani nerve were used to study the mechanism of action of the antibiotic novobiocin on salt taste transduction. In the rat, novobiocin selectively enhanced the responses of sodium-specific and amiloride-sensitive chorda tympani nerve fibers (N type) without affecting more broadly responsive cation-sensitive and amiloride-insensitive fibers (E type). In the presence of amiloride, novobiocin was ineffective at enhancing the response of N-type fibers toward sodium chloride. Novobiocin also increased the conductance of bilayers formed from neutral lipids by forming nonrectifying ion channels with low conductance (approximately 7 pS in 110 mM NaCl), long open times (several seconds and longer), and high cation selectivity. Amiloride did not alter either the conductance or kinetics of these novobiocin channels. These observations suggest that even though novobiocin is able to form cation channels in lipid bilayers, and possibly in cell membranes as well, its action on the salt-taste response is through modulation of existing amiloride-sensitive sodium channels.