Inhomogeneous Population Research Articles

Spreading processes in “post-epidemic” environments. II. Safety patterns on scale-free networks

This paper continues our previous study on spreading processes in inhomogeneous populations consisting of susceptible and immune individuals (Blavatska and Holovatch, 2021). A special role in such populations is played by “safety patterns” of susceptible nodes surrounded by the immune ones. Here, we analyze spreading on scale-free networks, where the distribution of node connectivity k obeys a power-law decay ∼k−λ. We assume, that only a fraction p of individual nodes can be affected by spreading process, while remaining 1−p are immune. We apply the synchronous cellular automaton algorithm and study the stationary states and spatial patterning in SI, SIS and SIR models in a range 2<λ<3. Two immunization scenarios, the random immunization and an intentional one, that targets the highest degrees nodes are considered. A distribution of safety patterns is obtained for the case of both scenarios. Estimates for the threshold values of the effective spreading rate βc as a function of active agents fraction p and parameter λ are obtained and efficiency of both vaccination techniques is analyzed quantitatively. The impact of the underlying network heterogeneous structure is manifest e.g. in decreasing the βc values within the random scenario as compared to corresponding values in the case of regular lattices. This result quantitatively confirms the compliance of scale-free networks for disease spreading. On contrary, the vaccination within the targeted scenario makes the complex networks much more resistant to epidemic spreading as compared with regular lattice structures.

RNA nucleotide methylation: 2021 update.

Among RNA modifications, transfer of methylgroups from the typical cofactor S-adenosyl-l-methionine by methyltransferases (MTases) to RNA is by far the most common reaction. Since our last review about a decade ago, the field has witnessed the re-emergence of mRNA methylation as an important mechanism in gene regulation. Attention has then spread to many other RNA species; all being included into the newly coined concept of the "epitranscriptome." The focus moved from prokaryotes and single cell eukaryotes as model organisms to higher eukaryotes, in particular to mammals. The perception of the field has dramatically changed over the past decade. A previous lack of phenotypes in knockouts in single cell organisms has been replaced by the apparition of MTases in numerous disease models and clinical investigations. Major driving forces of the field include methylation mapping techniques, as well as the characterization of the various MTases, termed "writers." The latter term has spilled over from DNA modification in the neighboring epigenetics field, along with the designations "readers," applied to mediators of biological effects upon specific binding to a methylated RNA. Furthermore "eraser" enzymes effect the newly discovered oxidative removal of methylgroups. A sense of reversibility and dynamics has replaced the older perception of RNA modification as a concrete-cast, irreversible part of RNA maturation. A related concept concerns incompletely methylated residues, which, through permutation of each site, lead to inhomogeneous populations of numerous modivariants. This review recapitulates the major developments of the past decade outlined above, and attempts a prediction of upcoming trends. This article is categorized under: RNA Processing > RNA Editing and Modification.

Epidemic dynamics in inhomogeneous populations and the role of superspreaders

A variant of the susceptible-infected-recovered model for an inhomogeneous population is introduced to account for the effect of variability in susceptibility and infectiousness across a population. An initial formulation of this dynamics leads to infinitely many differential equations. Our model, however, can be reduced to a single first-order one-dimensional differential equation. Using this approach, we provide quantitative solutions for different distributions. In particular, we use GPS data from $\ensuremath{\sim}{10}^{7}$ cell phones to determine an empirical distribution of the number of individual contacts and use this to infer a possible distribution of susceptibility and infectivity. We quantify the effect of superspreaders on the early growth rate ${\mathcal{R}}_{0}$ of the infection and on the final epidemic size, the total number of people who are ever infected. We discuss the features of the distribution that contribute most to the dynamics of the infection.

Distinct population code for movement kinematics and changes of ongoing movements in human subthalamic nucleus.

The subthalamic nucleus (STN) is theorized to globally suppress movement through connections with downstream basal ganglia structures. Current theories are supported by increased STN activity when subjects withhold an uninitiated action plan, but a critical test of these theories requires studying STN responses when an ongoing action is replaced with an alternative. We perform this test in subjects with Parkinson's disease using an extended reaching task where the movement trajectory changes mid-action. We show that STN activity decreases during action switches, contrary to prevalent theories. Furthermore, beta oscillations in the STN local field potential, which are associated with movement inhibition, do not show increased power or spiking entrainment during switches. We report an inhomogeneous population neural code in STN, with one sub-population encoding movement kinematics and direction and another encoding unexpected action switches. We suggest an elaborate neural code in STN that contributes to planning actions and changing the plans.

Numerical Characterization of Acoustic Cavitation Bubbles with Respect to the Bubble Size Distribution at Equilibrium

In addition to bubble number density, bubble size distribution is an important population parameter governing the activity of acoustic cavitation bubbles. In the present paper, an iterative numerical method for equilibrium size distribution is proposed and combined to a model for bubble counting, in order to approach the number density within a population of acoustic cavitation bubbles of inhomogeneous sizing, hence the sonochemical activity of the inhomogeneous population based on discretization into homogenous groups. The composition of the inhomogeneous population is analyzed based on cavitation dynamics and shape stability at 300 kHz and 0.761 W/cm2 within the ambient radii interval ranging from 1 to 5 µm. Unstable oscillation is observed starting from a radius of 2.5 µm. Results are presented in terms of number probability, number density, and volume probability within the population of acoustic cavitation bubbles. The most probable group having an equilibrium radius of 3 µm demonstrated a probability in terms of number density of 27%. In terms of contribution to the void, the sub-population of 4 µm plays a major role with a fraction of 24%. Comparisons are also performed with the homogenous population case both in terms of number density of bubbles and sonochemical production of HO•,HO2•, and H• under an oxygen atmosphere.

Spatially Inhomogeneous Populations with Seed-Banks: I. Duality, Existence and Clustering

AbstractWe consider a system of interacting Moran models with seed-banks. Individuals live in colonies and are subject to resampling and migration as long as they are active. Each colony has a seed-bank into which individuals can retreat to become dormant, suspending their resampling and migration until they become active again. The colonies are labelled by $${\mathbb {Z}}^d$$ Z d , $$d \ge 1$$ d ≥ 1 , playing the role of a geographic space. The sizes of the active and the dormant population are finite and depend on the location of the colony. Migration is driven by a random walk transition kernel. Our goal is to study the equilibrium behaviour of the system as a function of the underlying model parameters. In the present paper, under a mild condition on the sizes of the active populations, the system is well defined and has a dual. The dual consists of a system of interacting coalescing random walks in an inhomogeneous environment that switch between an active state and a dormant state. We analyse the dichotomy of coexistence (= multi-type equilibria) versus clustering (= mono-type equilibria) and show that clustering occurs if and only if two random walks in the dual starting from arbitrary states eventually coalesce with probability one. The presence of the seed-bank enhances genetic diversity. In the dual this is reflected by the presence of time lapses during which the random walks are dormant and do not move.

Single Molecule Fluorescence Energy Transfer Study of Ribosome Protein Synthesis

Single molecule fluorescence energy transfer is a method that tracks the tRNA dynamics during ribosomal protein synthesis. By tracking individual ribosomes, inhomogeneous populations are identified, which shed light on mechanisms. This method can be used to track biological conformational changes in general to reveal dynamic-function relationships in many other complexed biosystems. Single molecule methods can observe non-rate limiting steps and low-populated key intermediates, which are not accessible by conventional ensemble methods due to the average effect.

Single Molecule Fluorescence Energy Transfer Study of Ribosome Protein Synthesis.

The ribosome is a large ribonucleoprotein complex that assembles proteins processively along mRNA templates. The diameter of the ribosome is approximately 20 nm to accommodate large tRNA substrates at the A-, P- and E-sites. Consequently, the ribosome dynamics are naturally de-phased quickly. Single molecule method can detect each ribosome separately and distinguish inhomogeneous populations, which is essential to reveal the complicated mechanisms of multi-component systems. We report the details of a smFRET method based on the Nikon Ti2 inverted microscope to probe the ribosome dynamics between the ribosomal protein L27 and tRNAs. The L27 is labeled at its unique Cys 53 position and reconstituted into a ribosome that is engineered to lack L27. The tRNA is labeled at its elbow region. As the tRNA moves to different locations inside the ribosome during the elongation cycle, such as pre- and post- translocation, the FRET efficiencies and dynamics exhibit differences, which have suggested multiple subpopulations. These subpopulations are not detectable by ensemble methods. The TIRF-based smFRET microscope is built on a manual or motorized inverted microscope, with home-built laser illumination. The ribosome samples are purified by ultracentrifugation, loaded into a home-built multi-channel sample cell and then illuminated via an evanescent laser field. The reflection laser spot can be used to achieve feedback control of perfect focus. The fluorescence signals are separated by a motorized filter-turret and collected by two digital CMOS cameras. The intensities are retrieved via the NIS-Elements software.

Somatic Comorbidities and Cardiovascular Safety in Ketamine Use for Treatment-Resistant Depression.

Background and Objectives: There is evidence for ketamine efficacy in treatment-resistant depression (TRD). Several safety and tolerability concerns arise that some psychotropic agents may provide blood pressure or/and heart rate alterations. The aim of this study is to review blood pressure measurements in course of the treatment with ketamine on treatment refractory inpatients with somatic comorbidities in the course of MDD and BP. Materials and Methods: The study population of 49 patients comprised MDD and BP subjects treated with ketamine registered in the naturalistic observational protocol of treatment-resistant mood disorders (NCT04226963). Results: The conducted analysis showed that among people suffering from hypertension there is a higher increase in systolic blood pressure (RR) after infusion 2 (p = 0.004) than among people who do not suffer from hypertension. Patients with hypertension have a higher increase in diastolic RR compared to those not suffering from hypertension (p = 0,038). Among the subjects with diabetes mellitus, significant differences occurred for infusions 2 (p = 0.020), 7 (p = 0.020), and 8 (p = 0.035) for heart rate (HR), compared to subjects without diabetes mellitus. A higher increase in diastolic RR was noted in the group of subjects suffering from diabetes mellitus (p = 0.010) compared to those who did not. In the hyperlipidemic patients studied, a significantly greater decrease in HR after infusion 5 (p = 0.031) and systolic RR after infusion 4 (p = 0.036) was noted compared to nonpatients. People after a stroke had significantly higher increases in diastolic RR after infusions 4 (p = 0.021) and 6 (p = 0.001) than those who did not have a stroke. Patients suffering from epilepsy had a significantly greater decrease in systolic RR after the 8th infusion (p = 0.017) compared to those without epilepsy. Limitations: The study may be underpowered due to the small sample size. The observations apply to inhomogeneous TRD population in a single-site with no blinding and are limited to the acute administration. Conclusions: This study supports evidence for good safety and tolerability profile for short-term IV ketamine use in TRD treatment. However, risk mitigation measures are to be considered in patients with metabolic and cardiovascular comorbidities.

Spatial drivers of instability in marine size-spectrum ecosystems

Size-spectrum models are a recent class of models describing the dynamics of a whole community based on a description of individual organisms. The models are motivated by marine ecosystems where they cover the size range from multicellular plankton to the largest fish. We propose to extend the size-spectrum model with spatial components. The spatial dynamics is governed by a random motion and a directed movement in the direction of increased fitness, which we call ‘fitness-taxis’. We use the model to explore whether spatial irregularities of marine communities can occur due to the internal dynamics of predator–prey interactions and spatial movements. This corresponds to a pattern-formation analysis generalized to an entire ecosystem but is not limited to one prey and one predator population. The analyses take the form of Fourier analysis and numerical experiments. Results show that diffusion always stabilizes the equilibrium but fitness-taxis destabilizes it, leading to non-stationary spatially inhomogeneous population densities, which are travelling in size. However, there is a strong asymmetry between fitness-induced destabilizing effects and diffusion-induced stabilizing effects with the latter dominating over the former. These findings reveal that fitness taxis acts as a possible mechanism behind pattern formations in ecosystems with high diversity of organism sizes, which can drive the emergence of spatial heterogeneity even in a spatially homogeneous environment.

When the Best Pandemic Models are the Simplest.

Simple SummaryThere is a large variety of data available about the coronavirus pandemic, but we still lack data about some important factors. Who is likely to infect whom and under what conditions and how long after becoming infected? These factors are the essence of transmission dynamics. Two groups using identical complex models can be expected to make different predictions simply because they make different choices for such transmission parameters in the model. A policy setter has no way to choose between their predictions. Simple models are not good for assessing contact tracing and detecting asymptomatic carriers, and do not replace agent-based models. However, we explain how simple models can be used to answer complex questions by adding what we call satellite equations, addressing questions involving age groups, death rates, and likelihood of transmission to nursing homes and to uninfected, isolated populations. Simple models are ideal for showing policy setters who are not mathematically sophisticated the kinds of interventions that are needed to achieve public goals.As the coronavirus pandemic spreads across the globe, people are debating policies to mitigate its severity. Many complex, highly detailed models have been developed to help policy setters make better decisions. However, the basis of these models is unlikely to be understood by non-experts. We describe the advantages of simple models for COVID-19. We say a model is “simple” if its only parameter is the rate of contact between people in the population. This contact rate can vary over time, depending on choices by policy setters. Such models can be understood by a broad audience, and thus can be helpful in explaining the policy decisions to the public. They can be used to evaluate the outcomes of different policies. However, simple models have a disadvantage when dealing with inhomogeneous populations. To augment the power of a simple model to evaluate complicated situations, we add what we call “satellite” equations that do not change the original model. For example, with the help of a satellite equation, one could know what his/her chance is of remaining uninfected through the end of an epidemic. Satellite equations can model the effects of the epidemic on high-risk individuals, death rates, and nursing homes and other isolated populations. To compare simple models with complex models, we introduce our “slightly complex” Model J. We find the conclusions of simple and complex models can be quite similar. However, for each added complexity, a modeler may have to choose additional parameter values describing who will infect whom under what conditions, choices for which there is often little rationale but that can have big impacts on predictions. Our simulations suggest that the added complexity offers little predictive advantage.

Metabolic Risk Factors and Cardiovascular Safety in Ketamine Use for Treatment Resistant Depression.

IntroductionKetamine exhibits antidepressant properties in treatment-resistant depression (TRD) with some concern over its cardiovascular safety and tolerability issues. This paper reports on the cardiovascular safety in short-term intravenous ketamine treatment in TRD inpatients with major depressive disorder (MDD) and bipolar disorder (BP).Materials and MethodsThe observational study population comprises 35 MDD and 14 BP subjects treated with intravenous ketamine.ResultsBlood pressure (RR) and heart rate (HR) values returned to baseline within 1.5-hours post infusion with no sequelae for all study subjects. Six time points were analyzed for each infusion: 0’, 15’, 30’, 45’, 60’ and 90’ for RR and HR. After the infusion significant peaks in systolic (p = 0.004) and diastolic (p = 0.038) RR were seen. In concomitant medication with selective serotonin reuptake inhibitors (SSRIs), higher RR peaks (p = 0.020; p = 0.048) were seen as compared to other subjects. The decrease in HR was greater (p = 0.02) in the absence of concomitant medication with mood stabilizers as compared to subjects receiving mood stabilizing medication accompanied by the observation of a greater decrease in diastolic RR among those taking mood stabilizers (p = 0.009).LimitationsThe study may be underpowered due to the small sample size. The observations apply to an inhomogeneous TRD population in a single-site, pilot study, with no blinding and are limited to the acute administration.ConclusionThe study demonstrates good safety and tolerability profile of intravenous ketamine as add-on intervention to current psychotropic medication in TRD, regardless of the MDD or BP type of mood disorders. The abatement of elevated RR and BP scores was observed in time with no sequelae nor harm. Still, cardiovascular risks appear to be more pronounced in subjects with comorbid arterial hypertension and diabetes mellitus.

A New Approach to 3D Modeling of Inhomogeneous Populations of Viral Regulatory RNA.

Tertiary structure (3D) is the physical context of RNA regulatory activity. Retroviruses are RNA viruses that replicate through the proviral DNA intermediate transcribed by hosts. Proviral transcripts form inhomogeneous populations due to variable structural ensembles of overlapping regulatory RNA motifs in the 5′-untranslated region (UTR), which drive RNAs to be spliced or translated, and/or dimerized and packaged into virions. Genetic studies and structural techniques have provided fundamental input constraints to begin predicting HIV 3D conformations in silico. Using SimRNA and sets of experimentally-determined input constraints of HIVNL4-3 trans-activation responsive sequence (TAR) and pairings of unique-5′ (U5) with dimerization (DIS) or AUG motifs, we calculated a series of 3D models that differ in proximity of 5′-Cap and the junction of TAR and PolyA helices; configuration of primer binding site (PBS)-segment; and two host cofactors binding sites. Input constraints on U5-AUG pairings were most compatible with intramolecular folding of 5′-UTR motifs in energetic minima. Introducing theoretical constraints predicted metastable PolyA region drives orientation of 5′-Cap with TAR, U5 and PBS-segment helices. SimRNA and the workflow developed herein provides viable options to predict 3D conformations of inhomogeneous populations of large RNAs that have been intractable to conventional ensemble methods.

Defect Engineering for Quantum Grade Rare-Earth Nanocrystals.

Nanostructured systems that combine optical and spin transitions offer new functionalities for quantum technologies by providing efficient quantum light-matter interfaces. Rare-earth (RE) ion-doped nanoparticles are promising in this field as they show long-lived optical and spin quantum states. However, further development of their use in highly demanding applications, such as scalable single-ion-based quantum processors, requires controlling defects that currently limit coherence lifetimes. In this work, we show that a post-treatment process that includes multistep high-temperature annealing followed by high-power microwave oxygen plasma processing advantageously improves key properties for quantum technologies. We obtain single crystalline Eu3+:Y2O3 nanoparticles (NPs) of 100 nm diameter, presenting bulk-like inhomogeneous line widths (Γinh) and population lifetimes (T1). Furthermore, a significant coherence lifetime (T2) extension, up to a factor of 5, is successfully achieved by modifying the oxygen-related point defects in the NPs by the oxygen plasma treatment. These promising results confirm the potential of engineered RE NPs to integrate devices such as cavity-based single-photon sources, quantum memories, and processors. In addition, our strategy could be applied to a large variety of oxides to obtain outstanding crystalline quality NPs for a broad range of applications.

Asymmetry and Rippling in Mixed Surfactant Bilayers from All-Atom and Coarse-Grained Simulations: Interdigitation and Per Chain Entropy

Understanding lateral organizations of self-assembled bilayers is crucial to gain a control on functionally relevant topologies. We study self-assembled bilayers composed of a surfactant, behenyl trimethyl ammonium chloride (BTMAC), a cosurfactant, stearyl alcohol (SA), at a ratio of 2:1 in the presence of water at 283 K employing subsequent all-atom (AA) and coarse-grained (CG) molecular dynamics simulations. Differences in initial configurations lead to the formation of bilayers at ripple or square phases or interdigitated gel phases of varying trans-leaflet asymmetry. The AA ripple and gel phases are reproduced well at the CG level using bonded potentials from Boltzmann inversion of AA canonical sampling and nonbonded potentials from MARTINI. Inhomogeneous populations of disordered chains with higher per chain configurational entropy and tilt result in rippling stabilized by periodic hydrophobic energy barrier and strong interdigitation. Order parameters of the asymmetric bilayers are sufficiently coupled to the per chain entropies at both levels of resolutions to serve as a reflector of the per chain configurational entropy inaccessible by experiments. Thus, trans-bilayer asymmetry may be a controlling parameter to induce rippling in a bilayer of industrial importance. This work will be useful for future investigation on domain-associated transport and signaling in biomembranes at a low temperature.

Modeling of oil–water separation efficiency in three-phase separators: Effect of emulsion rheology and droplet size distribution

The multi-fluid Eulerian multiphase model coupled with the inhomogeneous population balance model is applied to predict the gas, oil, and water separation behavior and emulsion destabilization in a high-pressure horizontal three-phase separator. The population balance model is applied to predict the evolving droplet size distribution due to droplet coalescence in the crude oil emulsion. The effect of water fraction on the emulsion viscosity was incorporated to predict the existence of the dense packed layer or zone (DPZ) – a high water-fraction emulsion layer formed at the interface between the oil and water phases. The novel emulsion viscosity model incorporates a dependence on the local droplet size. Parameter estimation for the droplet coalescence kernel in the population balance equation is determined from experimental measurements of emulsion separation kinetics. A proportional integral derivative (PID) controller logic is used to maintain the gas/oil and oil/water interface levels by automatically adjusting the oil and water outlet pressure, respectively. The pilot separator experimental measurements include inlet and outlet flowrates and density, and electrical capacitance measurement of the vertical water concentration profile. The CFD model determines the flow patterns, phase distributions and the dispersed water droplet size distribution in the emulsion in the separator. The model results are in good agreement with the data for the separation efficiency from the water flow rate in and out of the separator, the phase distributions and the DPZ at different flow rates and water fractions. This study demonstrates the importance in multiphase separator design and troubleshooting of including the influence of water fraction on emulsion viscosity and the droplet size distribution with droplet coalescence phenomena. The methodology presented has significant advantages over previously published methods and improves on the value and potential impact toward research and industry practice.

Measurement and simulation of atomic motion in nanoscale optical trapping potentials

Atoms trapped in the evanescent field around a nanofiber experience strong coupling to the light guided in the fiber mode. However, due to the intrinsically strong positional dependence of the coupling, thermal motion of the ensemble limits the use of nanofiber trapped atoms for some quantum tasks. We investigate the thermal dynamics of such an ensemble by using short light pulses to make a spatially inhomogeneous population transfer between atomic states. As we monitor the wave packet of atoms created by this scheme, we find a damped oscillatory behavior which we attribute to sloshing and dispersion of the atoms. Oscillation frequencies range around 100 kHz, and motional dephasing between atoms happens on a timescale of 10 $\mu$s. Comparison to Monte Carlo simulations of an ensemble of 1000 classical particles yields reasonable agreement for simulated ensemble temperatures between 25 $\mu$K and 40 $\mu$K.

Circular cumulant reductions for macroscopic dynamics of Kuramoto ensemble with multiplicative intrinsic noise

We demonstrate the application of the circular cumulant approach for thermodynamically large populations of phase elements, where the Ott–Antonsen properties are violated by a multiplicative intrinsic noise. The infinite cumulant equation chain is derived for the case of a sinusoidal sensitivity of the phase to noise. For inhomogeneous populations, a Lorentzian distribution of natural frequencies is adopted. Two-cumulant model reductions, which serve as a generalization of the Ott–Antonsen ansatz, are reported. The accuracy of these model reductions and the macroscopic collective dynamics of the system are explored for the case of a Kuramoto-type global coupling. The Ott–Antonsen ansatz and the Gaussian approximation are found to be not uniformly accurate for non-high frequencies.

Average Measures of Phase and Synchrony in Inhomogeneous Populations of Circadian Oscillators

Circadian misalignment between the phase of molecular circadian oscillators and the external environment has been linked to adverse health effects, including cardiovascular disease, obesity, cancer, and psychiatric disorders. Desynchrony of the circadian clock within populations of oscillators has also been linked to these conditions. For this reason, we wish to develop a control strategy to shift molecular circadian phase while also controlling for population synchrony. Previous work has demonstrated that model predictive control can effectively solve this problem when synchrony is determined directly by measuring the phase of each cell in a homogeneous population. Such cell-specific phase measurements are rarely possible in vivo, and such homogeneity is not biologically plausible. For these reasons, we wish to design an observer that can accurately determine the mean phase of the population and derive a proxy for population synchrony. We show that a model parameterized with the average parameter set of the population can be used to sense phase from mean population expression levels, despite inaccuracies when sensing the phase of a single cell. Similarly, we are able to use the average amplitude of the population in comparison to the amplitude of the average population oscillator as a measure of synchrony within the population. Taken together, these two metrics, based on the average behavior of the cell, allow us to control the phase and synchrony of the population of cellular oscillators without measuring the phase of individual cells.

Dynamical analysis of a discrete conformable fractional order bacteria population model in a microcosm

In this paper, conformable fractional order differential equations with piecewise constant arguments are used for a modeling population density of a bacteria species in a microcosm. The discretization process of a differential equation with piecewise constant arguments gives us two dimensional discrete dynamical system in the interval t∈[nh,(n+1)h). By using the center manifold theorem and the bifurcation theory, it is shown that the discrete dynamical system undergoes flip and Neimark–Sacker bifurcation depending on the parameter r. It is observed that the model describes some biological phenomena for a bacteria population such as homogeneous bacteria distributions and inhomogeneous spatial population distributions. In addition, the effect of fractional order derivative on dynamic behavior of the system is investigated. Finally, all theoretical results are supported by numerical simulations.