Modelling Heterogeneous Anomalous Dynamics of Radiation-Induced Double-Strand Breaks in DNA during Non-Homologous End-Joining Pathway.

The process of end-joining during nonhomologous repair of DNA double-strand breaks (DSBs) after radiation damage is considered. Experimental evidence has revealed that the dynamics of DSB ends exhibit subdiffusive motion rather than simple diffusion with rare directional movement. Traditional models often overlook the rare long-range directed motion. To address this limitation, we present a heterogeneous anomalous diffusion model consisting of subdiffusive fractional Brownian motion interchanged with short periods of long-range movement. Our model sheds light on the underlying mechanisms of heterogeneous diffusion in DSB repair and could be used to quantify the DSB dynamics on a time scale inaccessible to single particle tracking analysis. The model predicts that the long-range movement of DSB ends is responsible for the misrepair of DSBs in the form of dicentric chromosome lesions.

Diagnostics of preeclampsia based on Congo red binding to urinary components: Rationales and limitations.

Preeclampsia is a disorder that can occur during pregnancy and is one of the leading causes of death among pregnant women. This disorder occurs after the 20th week of pregnancy and is characterized by arterial hypertension, proteinuria, fetoplacental, and multiple organ dysfunctions. Despite the long history of studying preeclampsia, its etiology and pathogenesis remain poorly understood, and therapy is symptomatic. One of the factors of the disorder is believed to be misfolded proteins that are prone to form amyloid aggregates. The CRD tests, utilizing the binding of the amyloid-specific dye Congo red to urine components, demonstrate high efficiency in diagnosing preeclampsia. However, these tests have also been found to be positive in other disorders with proteinuria, presumably associated with concomitant amyloidosis. To assess the limitations of the CRD tests, we examined urine congophilia and protein components mediating Congo red positivity in patients with proteinuria, including preeclampsia, amyloid and non-amyloid nephropathies. We stained the urine samples and calculated congophilia levels. We also assessed the contribution of large protein aggregates to congophilia values using ultracentrifugation and determined the molecular weights of congophilic urinary proteins using centrifugal concentrators. All proteinuric groups demonstrate positive results in the CRD tests and congophilia levels were more than two times higher compared with the control non-proteinuric groups (p <0.01). There was a strong correlation between urine protein excretion and congophilia in amyloid nephropathy (rs = 0.76), non-amyloid nephropathies (rs = 0.90), and preeclampsia (rs = 0.90). Removal of large aggregates from urine did not affect the congophilia levels. Separation of urine protein fractions revealed congophilic components in the range of 30-100 kDa, including monomeric serum albumin. Our results indicate limitations of CRD tests in preeclampsia diagnostics in women with renal disorders and underscore the need for further research on the mechanisms of Congo red binding with urine components.

Population heterogeneity in the fractional master equation, ensemble self-reinforcement, and strong memory effects.

We formulate a fractional master equation in continuous time with random transition probabilities across the population of random walkers such that the effective underlying random walk exhibits ensemble self-reinforcement. The population heterogeneity generates a random walk with conditional transition probabilities that increase with the number of steps taken previously (self-reinforcement). Through this, we establish the connection between random walks with a heterogeneous ensemble and those with strong memory where the transition probability depends on the entire history of steps. We find the ensemble-averaged solution of the fractional master equation through subordination involving the fractional Poisson process counting the number of steps at a given time and the underlying discrete random walk with self-reinforcement. We also find the exact solution for the variance which exhibits superdiffusion even as the fractional exponent tends to 1.

Courtship suppression in Drosophila melanogaster: The role of mating failure.

Drosophila melanogaster is a popular model organism in the study of memory due to a wide arsenal of methods used to analyze neuronal activity. The most commonly used tests in research of behavioral plasticity are shock avoidance associated with chemosensory cues and courtship suppression after mating failure. Many authors emphasize the value of courtship suppression as a model of behavior most appropriate to natural conditions. However, researchers often investigate courtship suppression using immobilized and decapitated females as targets of courtship by males, which makes the data obtained from such flies less valuable. In our study, we evaluate courtship suppression towards immature mobile non-receptive females after training with mated or immature females combined with an aversive stimulus (quinine). We have shown that the previously described mechanisms of courtship suppression, as a result of the association of the courtship object with the repellent, as well as due to increased sensitivity to the anti-aphrodisiac cVA after mating failure, are not confirmed when immature mobile females are used. We discuss the reasons for the discrepancies between our results and literature data, define the conditions to be met in the courtship suppression test if the aim is to analyze the natural forms of behavioral plasticity, and present data on the test modifications to approximate conditions to natural ones.

Ensemble heterogeneity mimics ageing for endosomal dynamics within eukaryotic cells.

Transport processes of many structures inside living cells display anomalous diffusion, such as endosomes in eukaryotic cells. They are also heterogeneous in space and time. Large ensembles of single particle trajectories allow the heterogeneities to be quantified in detail and provide insights for mathematical modelling. The development of accurate mathematical models for heterogeneous dynamics has the potential to enable the design and optimization of various technological applications, for example, the design of effective drug delivery systems. Central questions in the analysis of anomalous dynamics are ergodicity and statistical ageing which allow for selecting the proper model for the description. It is believed that non-ergodicity and ageing occur concurrently. However, we found that the anomalous dynamics of endosomes is paradoxical since it is ergodic but shows ageing. We show that this behaviour is caused by ensemble heterogeneity that, in addition to space-time heterogeneity within a single trajectory, is an inherent property of endosomal motion. Our work introduces novel approaches for the analysis and modelling of heterogeneous dynamics.

Population heterogeneity in the fractional master equation, ensemble self-reinforcement, and strong memory effects.

We formulate a fractional master equation in continuous time with random transition probabilities across the population of random walkers such that the effective underlying random walk exhibits ensemble self-reinforcement. The population heterogeneity generates a random walk with conditional transition probabilities that increase with the number of steps taken previously (self-reinforcement). Through this, we establish the connection between random walks with a heterogeneous ensemble and those with strong memory where the transition probability depends on the entire history of steps. We find the ensemble-averaged solution of the fractional master equation through subordination involving the fractional Poisson process counting the number of steps at a given time and the underlying discrete random walk with self-reinforcement. We also find the exact solution for the variance which exhibits superdiffusion even as the fractional exponent tends to 1.

Communication as the Origin of Consciousness.

Since the middle of the 20th century, more and more data have appeared on the limited role of consciousness in determining human behavior. In this opinion paper, we hypothesize that the basis of consciousness is precisely the communicative function, and discuss relations of consciousness to other cognitive processes such sensory detection, decision-making and emotions. Within the framework of the hypothesis, consciousness is considered as a highly specialized function of the brain, which ensures encoding of personal information as communication messages. On a subjective level, mental representation just means the state of information to be shared in a human group. Accordingly, consciousness affects only those components of human behavior that are associated with the transmission of messages. Sensory detection, decision-making, emotions and other processes are only projected into consciousness during the encoding of information of them. The communication hypothesis assumes that consciousness is an adaptation that increases the efficiency of a collective way of life, and the emergence of consciousness is inextricably linked with the development of language in human culture. In the future, our view of consciousness provides an opportunity for an objective analysis of subjective phenomena by means of a directed study of the formation of messages both at the level of brain processes and at the level of interactions between individuals.

Human RAD51 Protein Forms Amyloid-like Aggregates In Vitro.

RAD51 is a central protein of homologous recombination and DNA repair processes that maintains genome stability and ensures the accurate repair of double-stranded breaks (DSBs). In this work, we assessed amyloid properties of RAD51 in vitro and in the bacterial curli-dependent amyloid generator (C-DAG) system. Resistance to ionic detergents, staining with amyloid-specific dyes, polarized microscopy, transmission electron microscopy (TEM), X-ray diffraction and other methods were used to evaluate the properties and structure of RAD51 aggregates. The purified human RAD51 protein formed detergent-resistant aggregates in vitro that had an unbranched cross-ß fibrillar structure, which is typical for amyloids, and were stained with amyloid-specific dyes. Congo-red-stained RAD51 aggregates demonstrated birefringence under polarized light. RAD51 fibrils produced sharp circular X-ray reflections at 4.7 Å and 10 Å, demonstrating that they had a cross-ß structure. Cytoplasmic aggregates of RAD51 were observed in cell cultures overexpressing RAD51. We demonstrated that a key protein that maintains genome stability, RAD51, has amyloid properties in vitro and in the C-DAG system and discussed the possible biological relevance of this observation.

Noninvasive Diagnostics of Renal Amyloidosis: Current State and Perspectives.

Amyloidoses is a group of diseases characterized by the accumulation of abnormal proteins (called amyloids) in different organs and tissues. For systemic amyloidoses, the disease is related to increased levels and/or abnormal synthesis of certain proteins in the organism due to pathological processes, e.g., monoclonal gammopathy and chronic inflammation in rheumatic arthritis. Treatment of amyloidoses is focused on reducing amyloidogenic protein production and inhibition of its aggregation. Therapeutic approaches critically depend on the type of amyloidosis, which underlines the importance of early differential diagnostics. In fact, the most accurate diagnostics of amyloidosis and its type requires analysis of a biopsy specimen from the disease-affected organ. However, absence of specific symptoms of amyloidosis and the invasive nature of biomaterial sampling causes the late diagnostics of these diseases, which leads to a delayed treatment, and significantly reduces its efficacy and patient survival. The establishment of noninvasive diagnostic methods and discovery of specific amyloidosis markers are essential for disease detection and identification of its type at earlier stages, which enables timely and targeted treatment. This review focuses on current approaches to the diagnostics of amyloidoses, primarily with renal involvement, and research perspectives in order to design new specific tests for early diagnosis.

Superdiffusion in self-reinforcing run-and-tumble model with rests.

This paper introduces a run-and-tumble model with self-reinforcing directionality and rests. We derive a single governing hyperbolic partial differential equation for the probability density of random-walk position, from which we obtain the second moment in the long-time limit. We find the criteria for the transition between superdiffusion and diffusion caused by the addition of a rest state. The emergence of superdiffusion depends on both the parameter representing the strength of self-reinforcement and the ratio between mean running and resting times. The mean running time must be at least 2/3 of the mean resting time for superdiffusion to be possible. Monte Carlo simulations validate this theoretical result. This work demonstrates the possibility of extending the telegrapher's (or Cattaneo) equation by adding self-reinforcing directionality so that superdiffusion occurs even when rests are introduced.

Local Analysis of Heterogeneous Intracellular Transport: Slow and Fast Moving Endosomes.

Trajectories of endosomes inside living eukaryotic cells are highly heterogeneous in space and time and diffuse anomalously due to a combination of viscoelasticity, caging, aggregation and active transport. Some of the trajectories display switching between persistent and anti-persistent motion, while others jiggle around in one position for the whole measurement time. By splitting the ensemble of endosome trajectories into slow moving subdiffusive and fast moving superdiffusive endosomes, we analyzed them separately. The mean squared displacements and velocity auto-correlation functions confirm the effectiveness of the splitting methods. Applying the local analysis, we show that both ensembles are characterized by a spectrum of local anomalous exponents and local generalized diffusion coefficients. Slow and fast endosomes have exponential distributions of local anomalous exponents and power law distributions of generalized diffusion coefficients. This suggests that heterogeneous fractional Brownian motion is an appropriate model for both fast and slow moving endosomes. This article is part of a Special Issue entitled: "Recent Advances In Single-Particle Tracking: Experiment and Analysis" edited by Janusz Szwabinski and Aleksander Weron.

Variable-order fractional master equation and clustering of particles: non-uniform lysosome distribution.

In this paper, we formulate the space-dependent variable-order fractional master equation to model clustering of particles, organelles, inside living cells. We find its solution in the long-time limit describing non-uniform distribution due to a space-dependent fractional exponent. In the continuous space limit, the solution of this fractional master equation is found to be exactly the same as the space-dependent variable-order fractional diffusion equation. In addition, we show that the clustering of lysosomes, an essential organelle for healthy functioning of mammalian cells, exhibit space-dependent fractional exponents. Furthermore, we demonstrate that the non-uniform distribution of lysosomes in living cells is accurately described by the asymptotic solution of the space-dependent variable-order fractional master equation. Finally, Monte Carlo simulations of the fractional master equation validate our analytical solution. This article is part of the theme issue 'Transport phenomena in complex systems (part 1)'.

Development of molecular tools for diagnosis of Alzheimer's disease that are based on detection of amyloidogenic proteins.

Alzheimer's disease (AD) is the most common form of dementia that usually occurs among older people. AD results from neuronal degeneration that leads to the cognitive impairment and death. AD is incurable, typically develops over the course of many years and is accompanied by a loss of functional autonomy, making a patient completely dependent on family members and/or healthcare workers. Critical features of AD are pathological polymerization of Aß peptide and microtubule-associated protein tau, accompanied by alterations of their conformations and resulting in accumulation of cross-ß fibrils (amyloids) in human brains. AD apparently progresses asymptomatically for years or even decades before the appearance of symptoms. Therefore, development of the early AD diagnosis at a pre-symptomatic stage is essential for potential therapies. This review is focused on current and potential molecular tools (including non-invasive methods) that are based on detection of amyloidogenic proteins and can be applicable to early diagnosis of AD.Abbreviations: Aß - amyloid-ß peptide; AßO - amyloid-ß oligomers; AD - Alzheimer's disease; ADRDA - Alzheimer's Disease and Related Disorders Association; APH1 - anterior pharynx defective 1; APP - amyloid precursor protein; BACE1 - ß-site APP-cleaving enzyme 1; BBB - brain blood barrier; CJD - Creutzfeldt-Jakob disease; CRM - certified reference material; CSF - cerebrospinal fluid; ELISA - enzyme-linked immunosorbent assay; FGD - 18F-fluorodesoxyglucose (2-deoxy-2-[18F]fluoro-D-glucose); IP-MS - immunoprecipitation-mass spectrometry assay; MCI - mild cognitive impairment; MDS - multimer detection system; MRI - magnetic resonance imaging; NIA-AA - National Institute on Ageing and Alzheimer's Association; NINCDS - National Institute of Neurological and Communicative Disorders and Stroke; PEN2 - presenilin enhancer 2; PET - positron emission tomography; PiB - Pittsburgh Compound B; PiB-SUVR - PIB standardized uptake value ratio; PMCA - Protein Misfolding Cycling Amplification; PrP - Prion Protein; P-tau - hyperphosphorylated tau protein; RMP - reference measurement procedure; RT-QuIC - real-time quaking-induced conversion; SiMoA - single-molecule array; ThT - thioflavin T; TSEs - Transmissible Spongiform Encephslopathies; T-tau - total tau protein.

Self-reinforcing directionality generates truncated Lévy walks without the power-law assumption.

We introduce a persistent random walk model with finite velocity and self-reinforcing directionality, which explains how exponentially distributed runs self-organize into truncated Lévy walks observed in active intracellular transport by Chen et al. [Nature Mater., 14, 589 (2015)10.1038/nmat4239]. We derive the nonhomogeneous in space and time, hyperbolic partial differential equation for the probability density function (PDF) of particle position. This PDF exhibits a bimodal density (aggregation phenomena) in the superdiffusive regime, which is not observed in classical linear hyperbolic and Lévy walk models. We find the exact solutions for the first and second moments and criteria for the transition to superdiffusion.

Deciphering anomalous heterogeneous intracellular transport with neural networks.

Intracellular transport is predominantly heterogeneous in both time and space, exhibiting varying non-Brownian behavior. Characterization of this movement through averaging methods over an ensemble of trajectories or over the course of a single trajectory often fails to capture this heterogeneity. Here, we developed a deep learning feedforward neural network trained on fractional Brownian motion, providing a novel, accurate and efficient method for resolving heterogeneous behavior of intracellular transport in space and time. The neural network requires significantly fewer data points compared to established methods. This enables robust estimation of Hurst exponents for very short time series data, making possible direct, dynamic segmentation and analysis of experimental tracks of rapidly moving cellular structures such as endosomes and lysosomes. By using this analysis, fractional Brownian motion with a stochastic Hurst exponent was used to interpret, for the first time, anomalous intracellular dynamics, revealing unexpected differences in behavior between closely related endocytic organelles.

Insights into the non-homologous end joining pathway and double strand break end mobility provided by mechanistic in silico modelling.

After radiation exposure, one of the critical processes for cellular survival is the repair of DNA double strand breaks. The pathways involved in this response are complex in nature and involve many individual steps that act across different time scales, all of which combine to produce an overall behaviour. It is therefore experimentally challenging to unambiguously determine the mechanisms involved and how they interact whilst maintaining strict control of all confounding variables. In silico methods can provide further insight into results produced by focused experimental investigations through testing of the hypotheses generated. Such computational testing can asses competing hypotheses by investigating their effects across all time scales concurrently, highlighting areas where further experimental work can have the most significance. We describe the construction of a mechanistic model by combination of several hypothesised mechanisms reported in the literature and supported by experiment. Compatibility of these mechanisms was tested by fitting simulation to results reported in the literature. To avoid over-fitting, we used an approach of sequentially testing individual mechanisms within this pathway. We demonstrate that using this approach the model is capable of reproducing published protein kinetics and overall repair trends. This provides evidence supporting the feasibility of the proposed mechanisms and revealed how they interact to produce an overall behaviour. Furthermore, we show that the assumed motion of individual double strand break ends plays a crucial role in determining overall system behaviour.

Asymptotic Behavior of the Solution of the Space Dependent Variable Order Fractional Diffusion Equation: Ultraslow Anomalous Aggregation.

We find the asymptotic representation of the solution of the variable-order fractional diffusion equation, which remains unsolved since it was proposed by Chechkin, Gorenflo, and Sokolov [J. Phys. A, 38, L679 (2005)JPHAC50305-447010.1088/0305-4470/38/42/L03]. We identify a new advection term that causes ultraslow spatial aggregation of subdiffusive particles due to dominance over the standard advection and diffusion terms in the long-time limit. This uncovers the anomalous mechanism by which nonuniform distributions can occur. We perform Monte Carlo simulations of the underlying anomalous random walk and find excellent agreement with the asymptotic solution.

Non-Markovian intracellular transport with sub-diffusion and run-length dependent detachment rate.

Intracellular transport of organelles is fundamental to cell function and health. The mounting evidence suggests that this transport is in fact anomalous. However, the reasons for the anomaly is still under debate. We examined experimental trajectories of organelles inside a living cell and propose a mathematical model that describes the previously reported transition from sub-diffusive to super-diffusive motion. In order to explain super-diffusive behaviour at long times, we introduce non-Markovian detachment kinetics of the cargo: the rate of detachment is inversely proportional to the time since the last attachment. Recently, we observed the non-Markovian detachment rate experimentally in eukaryotic cells. Here we further discuss different scenarios of how this effective non-Markovian detachment rate could arise. The non-Markovian model is successful in simultaneously describing the time averaged variance (the time averaged mean squared displacement corrected for directed motion), the mean first passage time of trajectories and the multiple peaks observed in the distributions of cargo velocities. We argue that non-Markovian kinetics could be biologically beneficial compared to the Markovian kinetics commonly used for modelling, by increasing the average distance the cargoes travel when a microtubule is blocked by other filaments. In turn, sub-diffusion allows cargoes to reach neighbouring filaments with higher probability, which promotes active motion along the microtubules.

Emergence of Lévy walks in systems of interacting individuals.

We propose a model of superdiffusive Lévy walk as an emergent nonlinear phenomenon in systems of interacting individuals. The aim is to provide a qualitative explanation of recent experiments [G. Ariel et al., Nat. Commun. 6, 8396 (2015)2041-172310.1038/ncomms9396] revealing an intriguing behavior: swarming bacteria fundamentally change their collective motion from simple diffusion into a superdiffusive Lévy walk dynamics. We introduce microscopic mean-field kinetic equations in which we combine two key ingredients: (1) alignment interactions between individuals and (2) non-Markovian effects. Our interacting run-and-tumble model leads to the superdiffusive growth of the mean-squared displacement and the power-law distribution of run length with infinite variance. The main result is that the superdiffusive behavior emerges as a cooperative effect without using the standard assumption of the power-law distribution of run distances from the inception. At the same time, we find that the collision and repulsion interactions lead to the density-dependent exponential tempering of power-law distributions. This qualitatively explains the experimentally observed transition from superdiffusion to the diffusion of mussels as their density increases [M. de Jager et al., Proc. R. Soc. B 281, 20132605 (2014)PRLBA40962-845210.1098/rspb.2013.2605].

Anomalous Metapopulation Dynamics on Scale-Free Networks.

We model transport of individuals across a heterogeneous scale-free network where a few weakly connected nodes exhibit heavy-tailed residence times. Using the empirical law of the axiom of cumulative inertia and fractional analysis, we show that "anomalous cumulative inertia" overpowers highly connected nodes in attracting network individuals. This fundamentally challenges the classical result that individuals tend to accumulate in high-order nodes. The derived residence time distribution has a nontrivial U shape which we encounter empirically across human residence and employment times.