Field-driven tracer diffusion through curved bottlenecks: fine structure of first passage events.

Using scaling arguments and extensive numerical simulations, we study the dynamics of a tracer particle in a corrugated channel represented by a periodic sequence of broad chambers and narrow funnel-like bottlenecks enclosed by a hard-wall boundary. The tracer particle is affected by an external force pointing along the channel, and performs an unbiased diffusion in the perpendicular direction. We present a detailed analysis (a) of the distribution function of the height above the funnel's boundary at which the first crossing of a given bottleneck takes place, and (b) of the distribution function of the first passage time to such an event. Our analysis reveals several new features of the dynamical behaviour that are overlooked in the studies based on the Fick-Jacobs approach. In particular, trajectories passing through a funnel concentrate predominantly on its boundary, which makes first-crossing events very sensitive to the presence of binding sites and microscopic roughness.

Self-isolation or borders closing: What prevents the spread of the epidemic better?

Pandemic propagation of COVID-19 motivated us to discuss the impact of the human network clustering on epidemic spreading. Today, there are two clustering mechanisms which prevent of uncontrolled disease propagation in a connected network: an "internal" clustering, which mimics self-isolation (SI) in local naturally arranged communities, and an "external" clustering, which looks like a sharp frontiers closing (FC) between cities and countries, and which does not care about the natural connections of network agents. SI networks are "evolutionarily grown" under the condition of maximization of small cliques in the entire network, while FC networks are instantly created. Running the standard SIR model on clustered SI and FC networks, we demonstrate that the evolutionary grown clustered network prevents the spread of an epidemic better than the instantly clustered network with similar parameters. We find that SI networks have the scale-free property for the degree distribution P(k)∼k^{η}, with a small critical exponent -2<η<-1. We argue that the scale-free behavior emerges as a result of the randomness in the initial degree distributions.

Non-backtracking walks reveal compartments in sparse chromatin interaction networks.

Chromatin communities stabilized by protein machinery play essential role in gene regulation and refine global polymeric folding of the chromatin fiber. However, treatment of these communities in the framework of the classical network theory (stochastic block model, SBM) does not take into account intrinsic linear connectivity of the chromatin loci. Here we propose the polymer block model, paving the way for community detection in polymer networks. On the basis of this new model we modify the non-backtracking flow operator and suggest the first protocol for annotation of compartmental domains in sparse single cell Hi-C matrices. In particular, we prove that our approach corresponds to the maximum entropy principle. The benchmark analyses demonstrates that the spectrum of the polymer non-backtracking operator resolves the true compartmental structure up to the theoretical detectability threshold, while all commonly used operators fail above it. We test various operators on real data and conclude that the sizes of the non-backtracking single cell domains are most close to the sizes of compartments from the population data. Moreover, the found domains clearly segregate in the gene density and correlate with the population compartmental mask, corroborating biological significance of our annotation of the chromatin compartmental domains in single cells Hi-C matrices.

Spectral peculiarity and criticality of a human connectome.

We have performed the comparative spectral analysis of structural connectomes for various organisms using open-access data. Our results indicate new peculiar features of connectomes of higher organisms. We found that the spectral density of adjacency matrices of human connectome has maximal deviation from the one of randomized network, compared to other organisms. Considering the network evolution induced by the preference of 3-cycles formation, we discovered that for macaque and human connectomes the evolution with the conservation of local clusterization is crucial, while for primitive organisms the conservation of averaged clusterization is sufficient. Investigating for the first time the level spacing distribution of the spectrum of human connectome Laplacian matrix, we explicitly demonstrate that the spectral statistics corresponds to the critical regime, which is hybrid of Wigner-Dyson and Poisson distributions. This observation provides strong support for debated statement of the brain criticality.

Many-body contacts in fractal polymer chains and fractional Brownian trajectories.

We calculate the probabilities that a trajectory of a fractional Brownian motion with arbitrary fractal dimension d_{f} visits the same spot n≥3 times, at given moments t_{1},...,t_{n}, and obtain a determinant expression for these probabilities in terms of a displacement-displacement covariance matrix. Except for the standard Brownian trajectories with d_{f}=2, the resulting many-body contact probabilities cannot be factorized into a product of single-loop contributions. Within a Gaussian network model of a self-interacting polymer chain, which we suggested recently [K. Polovnikov et al., Soft Matter 14, 6561 (2018)1744-683X10.1039/C8SM00785C], the probabilities we calculate here can be interpreted as probabilities of multibody contacts in a fractal polymer conformation with the same fractal dimension d_{f}. This Gaussian approach, which implies a mapping from fractional Brownian motion trajectories to polymer conformations, can be used as a semiquantitative model of polymer chains in topologically stabilized conformations, e.g., in melts of unconcatenated rings or in the chromatin fiber, which is the material medium containing genetic information. The model presented here can be used, therefore, as a benchmark for interpretation of the data of many-body contacts in genomes, which we expect to be available soon in, e.g., Hi-C experiments.

RESULTS OF COMPREHENSIVE RADIOLOGICAL - HYGIENIC MONITORING IN SOME SETTLEMENTS OF RADIOLOGICALLY CONTAMINATED AREAS IN RIVNE REGION IN 2017. / REZUL'TATY KOMPLEKSNOGO RADIATsIINO/GIGIIeNIChNOGO MONITORYNGU OKREMYKh NASELENYKh PUNKTIV RADIOAKTYVNO ZABRUDNENYKh TERYTORII RIVNENS'KOÏ OBLASTI U 2017 r.

OBJECTIVE: Identification of the main factors of radiation exposure formation in the residents of surveyed settle-ments of radiologically contaminated territories in Rivne region and estimation of radiation doses in population ata current stage of the accident. MATERIALS AND METHODS: Comprehensive radiological and hygienic monitoring was conducted within 7 settlementsof the Rokytnivsky district of Rivne region, namely in the Stare Selo, Vezhytsya, Perehodychi, Drozdyn', Berezove,Zabolottya, and Hrabun' villages. Assay of the incorporated 137Cs was held using a whole-body counter in residentsof the villages twice a year, i.e. in May and October. Basic foodstuffs were sampled for the assay of 90Sr and 137Cs alongwith interview of residents about the foodstuff consumption. External radiation doses were estimated. Mathe-matical, dosimetric, and radiochemical methods were applied. RESULTS AND CONCLUSIONS: The annual effective exposure doses of population in the surveyed settlements of Rivneregion in the year of study were formed at the expense of internal exposure doses ranging from 0.13 mSv · year-1 to0.32 mSv · year-1, which is below the criterion for radiologically contaminated territories. It has been establishedthat the incorporation of 137Cs by the inhabitants is a principal factor of the internal radiation dose formation. The 137Cs incorporation occurs through the consumption of such basic foodstuffs as milk and forest products, primarilymushrooms, which traditionally occupy a significant part of the diet in the Polissya area. The 137Cs content in thevast majority of milk and mushroom samples significantly exceeded the permissible levels (PL). The maximum con-tent of 137Cs in the collected milk samples was 384.7 Bq · L-1, which is 4 times higher than PL, and 36.9 kBq · kg-1 indried mushrooms being 15 times higher than PL. CONCLUSIONS: The existing radiation and ecological situation in the areas that were exposed to radioactive contam-ination as a result of the Chornobyl disaster requires the continuation of monitoring of levels of radioactive con-tamination of foodstuffs, especially collected in forests, and doses of radiation exposure of the population.

BIOLOGICAL MARKERS OF EXTERNAL AND INTERNAL EXPOSURE IN SHELTER CONSTRUCTION WORKERS: A 13-YEAR EXPERIENCE.

OBJECTIVE: The aim of this study is to investigate the cellular, molecular, genetic and non-invasive functional biomarkers of occupational irradiation in workers exposed to a combination of external gamma-radiation and incorporation of transuranium elements. RESULTS: A study was performed in 688 radiation workers of Shelter object conversion into a safe system with mean shift dose of external exposure of 26.06 mSv (range: 0.1-113.35) and risk of internal exposure with transuranium elements. Several biological parameters could serve as biomarkers of exposure at radiation doses below 100 mSv and even in 20-50 mSv interval. The parallel changes were shown in decline of brain electric activity, telomere length, differences in CCND1, CDKN1A, CDKN2A, VEGFA, TP53, DDB2 genes expression. An increase in counts of dicentrics, pair fragments and TCR-variant lymphocytes at doses over professional limits shows the need of biological dosimetry. The most sensitive markers include TCR-CD4+, γ-H2AX+ and CyclinD1+ cell counts. Implementation of flow cytometry approach for these markers enables quick obtaining of quantitative data. Confounding factors included respiratory function and smoking. The study of the radiation workers with the history of chronic exposure in radiation area during 3-5 years demonstrates changes of compensatory origin, i.e. absence of telomere shortening, increased number of NK-cells in combination with lower expression of intracellular γ-H2AX. CONCLUSION: This study confirms the presence of radiation-induced changes in gene regulation of cell proliferation, telomere function and apoptosis in radiation workers exposed to external and internal exposure at doses above professional limits and increase of compensatory changes.

Effective Hamiltonian of topologically stabilized polymer states.

Topologically stabilized polymer conformations in melts of nonconcatenated polymer rings and crumpled globules are considered to be a good candidate for the description of the spatial structure of mitotic chromosomes. Despite significant efforts, the microscopic Hamiltonian capable of describing such systems still remains unknown. We describe a polymer conformation by a Gaussian network - a system with a Hamiltonian quadratic in all coordinates - and show that by tuning interaction constants, one can obtain equilibrium conformations with any fractal dimension between 2 (an ideal polymer chain) and 3 (a crumpled globule). Monomer-to-monomer distances in topologically stabilized states, according to available numerical data, fit very well the Gaussian distribution, giving an additional argument in support of the quadratic Hamiltonian model. Mathematically, the polymer conformations are mapped onto the trajectories of a subdiffusive fractal Brownian particle. Moreover, we explicitly show that the quadratic Hamiltonian with a hierarchical set of coupling constants provides the microscopic background for the description of the path integral of the fractional Brownian motion with an algebraically decaying kernel.

Finite plateau in spectral gap of polychromatic constrained random networks.

We consider critical behavior in the ensemble of polychromatic Erdos-Rényi networks and regular random graphs, where network vertices are painted in different colors. The links can be randomly removed and added to the network subject to the condition of the vertex degree conservation. In these constrained graphs we run the Metropolis procedure, which favors the connected unicolor triads of nodes. Changing the chemical potential, µ, of such triads, for some wide region of µ, we find the formation of a finite plateau in the number of intercolor links, which exactly matches the finite plateau in the network algebraic connectivity (the value of the first nonvanishing eigenvalue of the Laplacian matrix, λ_{2}). We claim that at the plateau the spontaneously broken Z_{2} symmetry is restored by the mechanism of modes collectivization in clusters of different colors. The phenomena of a finite plateau formation holds also for polychromatic networks with M≥2 colors. The behavior of polychromatic networks is analyzed via the spectral properties of their adjacency and Laplacian matrices.

Spontaneous symmetry breaking and phase coexistence in two-color networks.

We consider an equilibrium ensemble of large Erdos-Renyi topological random networks with fixed vertex degree and two types of vertices, black and white, prepared randomly with the bond connection probability p. The network energy is a sum of all unicolor triples (either black or white), weighted with chemical potential of triples µ. Minimizing the system energy, we see for some positive µ the formation of two predominantly unicolor clusters, linked by a string of N_{bw} black-white bonds. We have demonstrated that the system exhibits critical behavior manifested in the emergence of a wide plateau on the N_{bw}(µ) curve, which is relevant to a spinodal decomposition in first-order phase transitions. In terms of a string theory, the plateau formation can be interpreted as an entanglement between baby universes in two-dimensional gravity. We conjecture that the observed classical phenomenon can be considered as a toy model for the chiral condensate formation in quantum chromodynamics.

Eigenvalue tunneling and decay of quenched random network.

We consider the canonical ensemble of N-vertex Erdos-Rényi (ER) random topological graphs with quenched vertex degree, and with fugacity µ for each closed triple of bonds. We claim complete defragmentation of large-N graphs into the collection of [p^{-1}] almost full subgraphs (cliques) above critical fugacity, µ_{c}, where p is the ER bond formation probability. Evolution of the spectral density, ρ(λ), of the adjacency matrix with increasing µ leads to the formation of a multizonal support for µ>µ_{c}. Eigenvalue tunneling from the central zone to the side one means formation of a new clique in the defragmentation process. The adjacency matrix of the network ground state has a block-diagonal form, where the number of vertices in blocks fluctuates around the mean value Np. The spectral density of the whole network in this regime has triangular shape. We interpret the phenomena from the viewpoint of the conventional random matrix model and speculate about possible physical applications.

Maintenance of radiation protection at a drawing board stage of the "Shelter" Object transformation into environmentally safe system. / ZABEZPEChENNIa RADIATsIYNOGO ZAKhYSTU NA ETAPI PROEKTUVANNIa ROBIT Z PERETVORENNIa OB'IeKTA "UKRYTTIa " V EKOLOGIChNU BEZPEChNU SYSTEMU.

Special aspects of radiation protection maintenance at a drawing board stage of the "Shelter" Object transforma tion into environmentally safe system are shaped in the article. Information is provided on the basis of analysis of design plans and specifications both with project paperwork from activities at the ShO in 2002 2015 on accordance to requirements of the Ukrainian health legislation in the field of radiation hygiene regulations. Specific features of radiation factors at the ShO were identified accounting their emergency origination. Relevancy of assessment of a range of activity types and technologies impact on radiation situation in the operation environment was reviewed and substantiated. General characteristics of radiation exposure and resulting doses in personnel under the activi ty execution are provided followed by the requirements to estimates of anticipated radiation doses. Features and peculiarities of application of the Ukrainian health legislation in a field of radiation hygienic regulations are reviewed in a view of meeting the requirements of NRBU 97, NRBU 97/D 2000, OSPU 2005, SPORO 85, SP AES 88 and other health legislative regulatory documents under conditions of work at the ShO. By the virtue of analysis of radi ation hygienic factors at the ShO the special aspects of choice of individual and collective radiological protection arrangements for personnel were identified, namely the individual protective gear and respiratory protection equip ment, shielding, decontamination, dust suppression, ventilation, sanitary pass control, sanitary barriers, scope and types of radiological control, setting the design levels of radiological environment parameters, criteria for the most safe options (technologies) of work execution.

Main internal dose forming factors for inhabitants of contaminated regions at current phase of the Chernobyl nuclear power plant accident (Kyiv region as an example). / OSNOVNI ChYNNYKY FORMUVANNIa VNUTRIShN'OGO OPROMINENNIa NASELENNIa RADIOAKTYVNO ZABRUDNENYKh TERYTORIY NA POTOChNOMU ETAPI AVARII NA ChAES (NA PRYKLADI KYIVS'KOI OBLASTI).

UNLABELLED: Objective of this work is revealing of main dose forming factors of internal doses for inhabitants of contaminated regions of Kyiv region relying on the results of integral dosimetric monitoring. MATERIALS AND METHODS: Three villages have been chosen for the investigation. They are: Raghivka, Zelena Poliana (Poliske district), Karpylivka (Ivankiv district). Twice a year, in May and in October those villages' residents were inspected for content of incorporated 137Cs. They were measured by direct method at the place of residence with the help of whole body counters (WBC). The principal food samples were collected for detection of 90Sr and 137Сs content. Those villages' inhabitants were interviewed about food consumption levels. Mathematical, dosimetric and radio chemical methods were used in this workResults and conclusions. The estimation of internal doses due to intake of 137Cs by ingestion of milk and potatoes are in the range 0.3-34% of doses estimated on the base of WBC data. The contribution to the dose of internal expo sure from intake of 137Cs with the milk consumption is no more than two times higher than the contribution of pota toes consumption in the case of equal consumption levels of these products. Contributions to the dose of internal exposure from intake of 90Sr with milk and potatoes consumptions are approximately similar. Consumption of mush rooms and other wild nature products by inhabitants from the inspected settlements is the main forming factor of internal dose due to 137Cs intake.

Islands of stability in motif distributions of random networks.

We consider random nondirected networks subject to dynamics conserving vertex degrees and study, analytically and numerically, equilibrium three-vertex motif distributions in the presence of an external field h coupled to one of the motifs. For small h, the numerics is well described by the "chemical kinetics" for the concentrations of motifs based on the law of mass action. For larger h, a transition into some trapped motif state occurs in Erdos-Rényi networks. We explain the existence of the transition by employing the notion of the entropy of the motif distribution and describe it in terms of a phenomenological Landau-type theory with a nonzero cubic term. A localization transition should always occur if the entropy function is nonconvex. We conjecture that this phenomenon is the origin of the motifs' pattern formation in real evolutionary networks.

Planar diagrams from optimization for concave potentials.

We propose a toy model of a heteropolymer chain capable of forming planar secondary structures typical for RNA molecules. In this model, the sequential intervals between neighboring monomers along a chain are considered as quenched random variables, and energies of nonlocal bonds are assumed to be concave functions of those intervals. A few factors are neglected: the contribution of loop factors to the partition function, the variation in energies of different types of complementary nucleotides, the stacking interactions, and constraints on the minimal size of loops. However, the model captures well the formation of folded structures without pseudoknots in an arbitrary sequence of nucleotides. Using the optimization procedure for a special class of concave-type potentials, borrowed from optimal transport analysis, we derive the local difference equation for the ground state free energy of the chain with the planar (RNA-like) architecture of paired links. We consider various distribution functions of intervals between neighboring monomers (truncated Gaussian and scale free) and demonstrate the existence of a topological crossover from sequential to essentially nested configurations of paired links.

Peculiarities of internal radiation doses due to ¹³7Cs and 9°Sr intake in population from Zhytomyr oblast in a late period after the Chornobyl NPP accident.

STUDY OBJECTIVE: To reveal the peculiarities of internal radiation doses in the inhabitants of Zhytomyr oblast and to provide a scientific ground for arrangements on internal irradiation dose reducing in population from contaminated regions in long-term period after the ChNPP accident. MATERIALS AND METHODS: Comprehensive radiation monitoring was carried out in 4 settlements in Narodychi region of Zhytomyr oblast. The radiochemical, dosimetric methods (instrumental and numerical) were used in the study. RESULTS AND CONCLUSIONS: Significant (2-3.5 times) seasonal increase of incorporated ¹³7Cs level was revealed through a WBC-monitoring in residents (both for adults and children) of the supervised settlements of Narodytsky region, Zhytomyr oblast. The exceeding of 1.0 mSv x year⁻¹ dose was revealed in up to 5 % of inspected persons. The maximal registered in those settlements ¹³7Cs content of 350 kBq is the source of 10 mSv x year⁻¹ annual dose. ¹³7Cs content in milk samples from those settlements didn't change much during a year. Elevation of ¹³7Cs content exceeding the permissible level of 100 Bq x litre⁻¹ was found in ~30-50 % of milk samples from Narodychi and Selets villages, whereas in Motiyky and Khrystynivka villages the ¹³7Cs content didn't exceed permissible levels. 90Sr content both in potatoes and milk samples was much under the permissible level of 20 Bq x litre⁻¹. ¹³7Cs content in potato samples was under the permissible levels. It was found out that main part of internal irradiation doses in the settlements of concern is due to consumption of locally produced victuals i.e. milk and natural/forest-originated products like berries and mushrooms.

Radiation protection and health of personnel of contracting enterprises participating in works for transformation of the object "shelter" of SSE Chornobyl NPP into an ecologically safe system.

UNLABELLED: Transformation of the object "Shelter" (OS) of SSE Chornobyl NPP into an ecologically safe system is one of the most important state programs in Ukraine. Both medical and dosimetric measures on healthcare of personnel participating in these works ranks the main place among most actual problems of contemporary clinical radiobiology, radiation hygiene, and radiation protection. The study objective was to work out and implement the medical and biophysical checking of the health status and workability both with radiation protection of personnel executing works on transformation of OS into an ecologically safe system. MATERIALS AND METHODS. The interdependent complex program of medical and biophysical (for internal and external irradiation) control of personnel executing the production tasks under conditions of ionizing radiation impact and open sources of ionizing radiation. Realization of medical examination envisages the estimation of the status of haemopoietic, immune, endocrine, respiratory systems, organ of vision, nervous system, psychics status and psychophysiological adaptation, ear, both with circulatory, digestive, urogenital, and bone-muscular system. There were 19434 cases of medical control of personnel in total. RESULTS: Results of the input medical control testify to the following: 4698 (48.90%) were admitted to work, 4909 (51.10%) were rejected. Individual annual effective doses of irradiation in the major part of cases did not exceed 12 mSv. There were 1845 cases of 239+240Pu content in excrements exceeding the level of 1.5 mBq/sample at a current biophysical control. Individual doses of internal irradiation at that did not exceed 1 mSv. CONCLUSIONS: The program of medical and biophysical service for reconstruction works on the OS proved its necessity and efficiency as its results showed that under the unique radiation-hygienical conditions not engineering challenges and technical problems but issues of how to save the health and workability of people and prevent the overdose of personnel including due to an internal irradiation are most critical.

New alphabet-dependent morphological transition in random RNA alignment.

We study the fraction f of nucleotides involved in the formation of a cactuslike secondary structure of random heteropolymer RNA-like molecules. In the low-temperature limit, we study this fraction as a function of the number c of different nucleotide species. We show, that with changing c, the secondary structures of random RNAs undergo a morphological transition: f(c)→1 for c≤c(cr) as the chain length n goes to infinity, signaling the formation of a virtually perfect gapless secondary structure; while f(c)<1 for c>c(cr), which means that a nonperfect structure with gaps is formed. The strict upper and lower bounds 2≤c(cr)≤4 are proven, and the numerical evidence for c(cr) is presented. The relevance of the transition from the evolutional point of view is discussed.

Chaotic Hamiltonian systems: survival probability.

We consider the dynamical system described by the area-preserving standard mapping. It is known for this system that P(t), the normalized number of recurrences staying in some given domain of the phase space at time t (so-called "survival probability") has the power-law asymptotics, P(t) approximately t{-nu}. We present new semiphenomenological arguments which enable us to map the dynamical system near the chaos border onto the effective "ultrametric diffusion" on the boundary of a treelike space with hierarchically organized transition rates. In the framework of our approach we have estimated the exponent nu as nu=ln 2/ln(1+r{g}) approximately 1.44, where rg=([square root] 5-1)/2 is the critical rotation number.

Unzipping of two random heteropolymers: ground-state energy and finite-size effects.

We consider a pair of random heteropolymer chains with quenched primary sequences. For this system we have analyzed the dependence of average ground state energy per monomer E on chain length n in the ensemble of chains with uniform distribution of primary sequences of monomers. Every monomer of the first (second) chain is randomly and independently chosen with the uniform probability distribution p=1/c from a set of c different types A , B , C , D ,... (A', B', C', D',...) . Monomers of the first chain could form saturating reversible bonds with monomers of the second chain. The bonds between similar monomer types (such as A-A', B-B', C-C', etc.) have the attraction energy u , while the bonds between different monomer types (such as A-B', A-D', B-D', etc.) have the attraction energy v . The main attention is paid to the computation of the normalized free energy E(n) for intermediate chain lengths n and different ratios a=v/u at sufficiently low temperatures, when the entropic contribution of the loop formation is negligible compared to direct energetic interactions between chain monomers, and when the partition function of the chains is dominated by the ground state. The performed analysis allows one to derive the force f(x) which is necessary to apply for unzipping of two random heteropolymers of equal lengths whose ends are separated by the distance x , averaged over all equally distributed primary structures at low temperatures for fixed values a and c .