Order selection for heterogeneous semiparametric hidden Markov models.

Hidden Markov models (HMMs), which can characterize dynamic heterogeneity, are valuable tools for analyzing longitudinal data. The order of HMMs (ie, the number of hidden states) is typically assumed to be known or predetermined by some model selection criterion in conventional analysis. As prior information about the order frequently lacks, pairwise comparisons under criterion-based methods become computationally expensive with the model space growing. A few studies have conducted order selection and parameter estimation simultaneously, but they only considered homogeneous parametric instances. This study proposes a Bayesian double penalization (BDP) procedure for simultaneous order selection and parameter estimation of heterogeneous semiparametric HMMs. To overcome the difficulties in updating the order, we create a brand-new Markov chain Monte Carlo algorithm coupled with an effective adjust-bound reversible jump strategy. Simulation results reveal that the proposed BDP procedure performs well in estimation and works noticeably better than the conventional criterion-based approaches. Application of the suggested method to the Alzheimer's Disease Neuroimaging Initiative research further supports its usefulness.

Dynamical heterogeneity in active glasses is inherently different from its equilibrium behavior.

Activity-driven glassy dynamics, while ubiquitous in collective cell migration, intracellular transport, dynamics in bacterial and ant colonies, etc., also extends the scope and extent of the as-yet mysterious physics of glass transition. Active glasses are hitherto assumed to be qualitatively similar to their equilibrium counterparts at an effective temperature, [Formula: see text]. Here, we combine large-scale simulations and an analytical mode-coupling theory (MCT) for such systems and show that, in fact, an active glass is inherently different from an equilibrium glass. Although the relaxation dynamics can be equilibrium-like at a [Formula: see text], effects of activity on the dynamic heterogeneity (DH), which is a hallmark of glassy dynamics, are quite nontrivial and complex. With no preexisting data, we employ four distinct methods for reliable estimates of the DH length scales. Our work shows that active glasses exhibit dramatic growth of DH and systems with similar relaxation times, and thus, [Formula: see text] can have widely varying DH. To theoretically study DH, we extend active MCT and find good qualitative agreement between the theory and simulation results. Our results pave avenues for understanding the role of DH in glassy dynamics and can have fundamental significance even in equilibrium.

Fractional Coupling of Primary and Johari-Goldstein Relaxations in a Model Polymer.

A polymer model exhibiting heterogeneous Johari−Goldstein (JG) secondary relaxation is studied by extensive molecular-dynamics simulations of states with different temperature and pressure. Time−temperature−pressure superposition of the primary (segmental) relaxation is evidenced. The time scales of the primary and the JG relaxations are found to be highly correlated according to a power law. The finding agrees with key predictions of the Coupling Model (CM) accounting for the decay in a correlation function due to the relaxation and diffusion of interacting systems. Nonetheless, the exponent of the power law, even if it is found in the range predicted by CM (0<ξ<1), deviates from the expected one. It is suggested that the deviation could depend on the particular relaxation process involved in the correlation function and the heterogeneity of the JG process.

The Lineage Differentiation and Dynamic Heterogeneity of Thymic Epithelial Cells During Thymus Organogenesis.

Although much progress has been made recently in revealing the heterogeneity of the thymic stromal components, the molecular programs of cell lineage divergency and temporal dynamics of thymic epithelial cell (TEC) development are largely elusive. Here, we constructed a single-cell transcriptional landscape of non-hematopoietic cells from mouse thymus spanning embryonic to adult stages, producing transcriptomes of 30,959 TECs. We resolved the transcriptional heterogeneity of developing TECs and highlighted the molecular nature of early TEC lineage determination and cortico-medullary thymic epithelial cell lineage divergency. We further characterized the differentiation dynamics of TECs by clarification of molecularly distinct cell states in the thymus developing trajectory. We also identified a population of Bpifa1+ Plet1+ mTECs that was preserved during thymus organogenesis and highly expressed tissue-resident adult stem cell markers. Finally, we highlighted the expression of Aire-dependent tissue-restricted antigens mainly in Aire+ Csn2+ mTECs and Spink5+ Dmkn+ mTECs in postnatal thymus. Overall, our data provided a comprehensive characterization of cell lineage differentiation, maturation, and temporal dynamics of thymic epithelial cells during thymus organogenesis.

Investigating Adult Stem Cells Through Lineage analyses.

A simple, universal and fundamental definition of adult stem cell communities is proposed. Key principles of cell lineage methods for defining adult stem cell numbers, locations and behaviors are critically evaluated, emphasizing the imperatives of capturing the full spectrum of individual stem cell behaviors, examining a variety of experimental time periods and avoiding unwarranted assumptions. The focus is first on defining fundamentals and then addresses stem cell heterogeneity, potential hierarchies and how individual cells serve the function of a stem cell community.

Elastic and Dynamic Heterogeneity in Aging Alginate Gels.

Anomalous aging in soft glassy materials has generated a great deal of interest because of some intriguing features of the underlying relaxation process, including the emergence of "ultra-long-range" dynamical correlations. An intriguing possibility is that such a huge correlation length is reflected in detectable ensemble fluctuations of the macroscopic material properties. We tackle this issue by performing replicated mechanical and dynamic light scattering (DLS) experiments on alginate gels, which recently emerged as a good model-system of anomalous aging. Here we show that some of the monitored quantities display wide variability, including large fluctuations in the stress relaxation and the occasional presence of two-step decay in the DLS decorrelation functions. By quantifying elastic fluctuation through the standard deviation of the elastic modulus and dynamic heterogeneities through the dynamic susceptibility, we find that both quantities do increase with the gel age over a comparable range. Our results suggest that large elastic fluctuations are closely related to ultra-long-range dynamical correlation, and therefore may be a general feature of anomalous aging in gels.

Molecular Dynamics Study of Lipid and Cholesterol Reorganization Due to Membrane Binding and Pore Formation by Listeriolysin O.

Pore-forming toxins are proteins expressed by bacteria to primarily cause infections in the host cell. Cholesterol-dependent cytolysins (CDCs) are a class of proteins whose pore-forming ability requires the presence of cholesterol in the membrane. Upon binding to the target cell, cholesterol-recognizing residues in the membrane binding D4 subdomain assist in stabilizing both the pre-pore and pore states which occur during protein oligomerization on the cell membrane. Super resolution-stimulated emission depletion (STED) microscopy experiments (Sarangi et al. in Langmuir, 32:9649-9657, 2016) on supported lipid bilayers have shown that listeriolysin (LLO), a CDC expressed by Listeria monocytogenes, a food-borne pathogen, induces both spatial and dynamic heterogeneity in bilayer membranes. Here, we use all-atom molecular dynamics simulations to explore molecular details of the induced membrane reorganization by considering two distinct states of the oligomerized LLO protein in a 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC): cholesterol membrane. In the membrane bound (MB) state, four D4 subunits are placed at the bilayer interface in a pre-pore configuration and the membrane-inserted (MI) state consists of a tetrameric arc-like pore configuration. By analyzing lipid-order parameters, mobilities, and diffusion coefficients, we examine the induced spatial heterogeneity that occurs in both the MB and MI states. This heterogeneity is primarily driven by the local density enhancement of cholesterol in the vicinity of the MB, D4 subunits leading to distinct differences in lipid and cholesterol mobility across the two leaflets as well as enhanced lipid mobilities in regions where cholesterol is depleted. The leaflet-induced heterogeneity is greater for the MB state when compared with the MI state and the dynamic variations are more pronounced in the extracellular leaflet when compared with the cytosolic leaflet. Our study provides molecular-level insights into the inhomogeneity and perturbation induced in bilayer membranes upon LLO binding and pore formation and is expected to represent trends across PFTs in the broad CDC subclass of proteins.

Non-Markovian Methods in Glass Transition.

A model for the heterogeneity of local dynamics in polymer and other glass-forming materials is provided here. The fundamental characteristics of the glass transition phenomenology emerge when simulating a condensed matter open cluster that has a strong interaction with its heterogeneous environment. General glass transition features, such as non-exponential structural relaxations, the slowing down of relaxation times with temperature and specific off-equilibrium glassy dynamics can be reproduced by non-Markovian dynamics simulations with the minimum computer resources. Non-Markovian models are shown to be useful tools for obtaining insights into the complex dynamics involved in the glass transition phenomenon, including whether or not there is a need for a growing correlation length or the relationship between the non-exponentiality of structural relaxations and dynamic heterogeneity.

Dynamic heterogeneity influences the leader-follower dynamics during epithelial wound closure.

Cells of epithelial tissue proliferate and pack together to attain an eventual density homeostasis. As the cell density increases, spatial distribution of velocity and force show striking similarity to the dynamic heterogeneity observed elsewhere in dense granular matter. While the physical nature of this heterogeneity is somewhat known in the epithelial cell monolayer, its biological relevance and precise connection to cell density remain elusive. Relevantly, we had demonstrated how large-scale dynamic heterogeneity in the monolayer stress field in the bulk could critically influence the emergence of leader cells at the wound margin during wound closure, but did not connect the observation to the corresponding cell density. In fact, numerous previous reports had essentially associated long-range force and velocity correlation with either cell density or dynamic heterogeneity, without any generalization. Here, we attempted to unify these two parameters under a single framework and explored their consequence on the dynamics of leader cells, which eventually affected the efficacy of collective migration and wound closure. To this end, we first quantified the dynamic heterogeneity by the peak height of four-point susceptibility. Remarkably, this quantity showed a linear relationship with cell density over many experimental samples. We then varied the heterogeneity, by changing cell density, and found this change altered the number of leader cells at the wound margin. At low heterogeneity, wound closure was slower, with decreased persistence, reduced coordination and disruptive leader-follower interactions. Finally, microscopic characterization of cell-substrate adhesions illustrated how heterogeneity influenced orientations of focal adhesions, affecting coordinated cell movements. Together, these results demonstrate the importance of dynamic heterogeneity in epithelial wound healing. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Dynamic Heterogeneity in Ring-Linear Polymer Blends.

We present results from a direct statistical analysis of long molecular dynamics (MD) trajectories for the orientational relaxation of individual ring molecules in blends with equivalent linear chains. Our analysis reveals a very broad distribution of ring relaxation times whose width increases with increasing ring/linear molecular length and increasing concentration of the blend in linear chains. Dynamic heterogeneity is also observed in the pure ring melts but to a lesser extent. The enhanced degree of dynamic heterogeneity in the blends arises from the substantial increase in the intrinsic timescales of a large subpopulation of ring molecules due to their involvement in strong threading events with a certain population of the linear chains present in the blend. Our analysis suggests that the relaxation dynamics of the rings are controlled by the different states of their threading by linear chains. Unthreaded or singly-threaded rings exhibit terminal relaxation very similar to that in their own melt, but multiply-threaded rings relax much slower due to the long lifetimes of the corresponding topological interactions. By further analyzing the MD data for ring molecule terminal relaxation in terms of the sum of simple exponential functions we have been able to quantify the characteristic relaxation times of the corresponding mechanisms contributing to ring relaxation both in their pure melts and in the blends, and their relative importance. The extra contribution due to ring-linear threadings in the blends becomes immediately apparent through such an analysis.

Effect of Initial Conformation on the Starch Biopolymer Film Formation Studied by NMR.

The formation of a rigid porous biopolymer scaffold from aqueous samples of 1% w/v (suspension) and 5% w/v (gel) corn starch was studied using optical and nuclear magnetic resonance (NMR) techniques. The drying process of these systems was observed using a single-sided NMR scanner by application of the Carr-Purcell-Meiboom-Gill pulse sequence at different layer positions. The echo decays were analyzed and spin-spin relaxation times (T2) were obtained for each layer. From the depth dependent T2 relaxation time study, it was found that the molecular mobility of water within the forming porous matrix of these two samples varied notably at different stages of film formation. At an intermediate stage, a gradual decrease in mobility of the emulsion sample towards the air-sample interface was observed, while the gel sample remained homogeneous all along the sample height. At a later stage of drying, heterogeneity in the molecular dynamics was observed in both samples showing low mobility at the bottom part of the sample. A wide-angle X-ray diffraction study confirmed that the structural heterogeneity persisted in the final film obtained from the 5% corn starch aqueous sample, whereas the film obtained from the 1% corn starch in water was structurally homogeneous.

Overhauser Dynamic Nuclear Polarization for the Study of Hydration Dynamics, Explained.

We outline the physical properties of hydration water that are captured by Overhauser Dynamic Nuclear Polarization (ODNP) relaxometry and explore the insights that ODNP yields about the water and the surface that this water is coupled to. As ODNP relies on the pairwise cross-relaxation between the electron spin of a spin probe and a proton nuclear spin of water, it captures the dynamics of single-particle diffusion of an ensemble of water molecules moving near the spin probe. ODNP principally utilizes the same physics as other nuclear magnetic resonance (NMR) relaxometry (i.e., relaxation measurement) techniques. However, in ODNP, electron paramagnetic resonance (EPR) excites the electron spins probes and their high net polarization acts as a signal amplifier. Furthermore, it renders ODNP parameters highly sensitive to water moving at rates commensurate with the EPR frequency of the spin probe (typically 10GHz). Also, ODNP selectively enhances the NMR signal contributions of water moving within close proximity to the spin label. As a result, ODNP can capture ps-ns movements of hydration waters with high sensitivity and locality, even in samples with protein concentrations as dilute as 10 µM. To date, the utility of the ODNP technique has been demonstrated for two major applications: the characterization of the spatial variation in the properties of the hydration layer of proteins or other surfaces displaying topological diversity, and the identification of structural properties emerging from highly disordered proteins and protein domains. The former has been shown to correlate well with the properties of hydration water predicted by MD simulations and has been shown capable of evaluating the hydrophilicity or hydrophobicity of a surface. The latter has been demonstrated for studies of an interhelical loop of proteorhodopsin, the partial structure of α-synuclein embedded at the lipid membrane surface, incipient structures adopted by tau proteins en route to fibrils, and the structure and hydration profile of a transmembrane peptide. This chapter focuses on offering a mechanistic understanding of the ODNP measurement and the molecular dynamics encoded in the ODNP parameters. In particular, it clarifies how the electron-nuclear dipolar coupling encodes information about the molecular dynamics in the nuclear spin self-relaxation and, more importantly, the electron-nuclear spin cross-relaxation rates. The clarification of the molecular dynamics underlying ODNP should assist in establishing a connection to theory and computer simulation that will offer far richer interpretations of ODNP results in future studies.

Origin of the emergent fragile-to-strong transition in supercooled water.

Liquids can be broadly classified into two categories, fragile and strong ones, depending on how their dynamical properties change with temperature. The dynamics of a strong liquid obey the Arrhenius law, whereas the fragile one displays a super-Arrhenius law, with a much steeper slowing down upon cooling. Recently, however, it was discovered that many materials such as water, oxides, and metals do not obey this simple classification, apparently exhibiting a fragile-to-strong transition far above [Formula: see text] Such a transition is particularly well known for water, and it is now regarded as one of water's most important anomalies. This phenomenon has been attributed to either an unusual glass transition behavior or the crossing of a Widom line emanating from a liquid-liquid critical point. Here by computer simulations of two popular water models and through analyses of experimental data, we show that the emergent fragile-to-strong transition is actually a crossover between two Arrhenius regimes with different activation energies, which can be naturally explained by a two-state description of the dynamics. Our finding provides insight into the fragile-to-strong transition observed in a wide class of materials.

Effect of external static electric fields on the dynamic heterogeneity of ionic liquids.

Ionic liquids (ILs) exhibit behavior analogous to supercooled liquids at room or even higher temperatures. ILs usually work under an externally applied static electric field (E). In this work, molecular dynamics simulations were performed with 1-ethyl-3-methyl-imidazolium tetrafluorborate ([EMI+][BF4-]) under E, with the aim of discovering the influence of E on the dynamic heterogeneity of ILs. ILs show more homogeneous dynamics with increasing E, as indicated by non-Gaussian parameters and dynamic susceptibility. The dynamic heterogeneity is greater in the E direction than that in the perpendicular directions under the same E. Despite the dynamic heterogeneity, only a small decoupling between diffusion and relaxation is observed under E.

Sex-Specific Heterogeneity in Fixed Morphological Traits Influences Individual Fitness in a Monogamous Bird Population.

Theoretical work has emphasized the important role of individual traits on population dynamics, but empirical models are often based on average or stage-dependent demographic rates. In this study on a monogamous bird, the Eurasian hoopoe (Upupa epops), we show how the interactions between male and female fixed and dynamic heterogeneity influence demographic rates and population dynamics. We built an integral projection model including individual sex, age, condition (reflecting dynamic heterogeneity), and fixed morphology (reflecting fixed heterogeneity). Fixed morphology was derived from a principal component analysis of six morphological traits. Our results revealed that reproductive success and survival were linked to fixed heterogeneity, whereas dynamic heterogeneity influenced mainly the timing of reproduction. Fixed heterogeneity had major consequences for the population growth rate, but interestingly, its effect on population dynamics differed between the sexes. Female fixed morphology was directly linked to annual reproductive success, whereas male fixed morphology also influenced annual survival, being twice higher in large than in small males. Even in a monogamous bird with shared parental care, large males can reach 10% higher fitness than females. Including the dynamics of male and female individual traits in population models refines our understanding of the individual mechanisms that influence demographic rates and population dynamics and can help in identifying differences in sex-specific strategies.

Modelling time to population extinction when individual reproduction is autocorrelated.

In nature, individual reproductive success is seldom independent from year to year, due to factors such as reproductive costs and individual heterogeneity. However, population projection models that incorporate temporal autocorrelations in individual reproduction can be difficult to parameterise, particularly when data are sparse. We therefore examine whether such models are necessary to avoid biased estimates of stochastic population growth and extinction risk, by comparing output from a matrix population model that incorporates reproductive autocorrelations to output from a standard age-structured matrix model that does not. We use a range of parameterisations, including a case study using moose data, treating probabilities of switching reproductive class as either fixed or fluctuating. Expected time to extinction from the two models is found to differ by only small amounts (under 10%) for most parameterisations, indicating that explicitly accounting for individual reproductive autocorrelations is in most cases not necessary to avoid bias in extinction estimates.

Role of Dynamic Heterogeneities in Ionic Liquids: Insights from All-Atom and Coarse-Grained Molecular Dynamics Simulation Studies.

We performed molecular dynamics simulations for the room-temperature ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate ([Bmim][PF6 ]). By employing all-atom (AA) and coarse-grained (CG) models, we compared the characteristic times of various dynamical modes, from vibration to diffusion, and the importance of dynamical heterogeneities at different levels of chemical resolution and over broad temperature ranges. It was shown that coarse graining leads to a substantial speedup in molecular dynamics, whereas it weakly affects the strength of dynamical heterogeneities. Despite the general speedup, several relationships between dynamical modes on different timescales were preserved. In particular, the heterogeneity timescales of the AA and CG models collapse onto the same curve as a function of the structural (α) relaxation time τα . Moreover, vibrational amplitudes and relaxation times τα are related at both levels of chemical resolution. We argue that the robustness of these relationships assists the development of dynamically consistent coarse-graining strategies and justifies the use of simplified models for a theoretical understanding of viscous liquids.

Ideal probe single-molecule experiments reveal the intrinsic dynamic heterogeneity of a supercooled liquid.

The concept of dynamic heterogeneity and the picture of the supercooled liquid as a mosaic of environments with distinct dynamics that interchange in time have been invoked to explain the nonexponential relaxations measured in these systems. The spatial extent and temporal persistence of these regions of distinct dynamics have remained challenging to identify. Here, single-molecule fluorescence measurements using a probe similar in size and mobility to the host o-terphenyl unambiguously reveal exponential relaxations distributed in time and space and directly demonstrate ergodicity of the system down to the glass transition temperature. In the temperature range probed, at least 200 times the structural relaxation time of the host is required to recover ensemble-averaged relaxation at every spatial region in the system.

A novel data-driven algorithm to reveal and track the ribosome heterogeneity in single molecule studies.

The unique advantage of the single molecule approach is to reveal the inhomogeneous subpopulations in an ensemble. For example, smFRET (single molecule fluorescence resonance energy transfer) can identify multiple subpopulations based on the FRET efficiency histograms. However, identifying multiple FRET states with overlapping average values remains challenging. Here, we report a new concept and method to analyze the single molecule FRET data of a ribosome system. The main results are as follows: 1. based on a hierarchic concept, multiple ribosome subpopulations are identified. 2. The subpopulations are self-identified via the cross-correlation analysis of the FRET histogram profiles. The dynamic heterogeneity is tracked after 2 min intervals on the same ribosomes individually. 3. The major ribosome subpopulations exchange with each other with a certain pattern, indicating some correlations among the motions of the tRNAs and the ribosomal components. Experiments under the conditions of 20% glycerol or 1mM viomycin supported this conclusion.

Use of posterior predictive checks as an inferential tool for investigating individual heterogeneity in animal population vital rates.

The investigation of individual heterogeneity in vital rates has recently received growing attention among population ecologists. Individual heterogeneity in wild animal populations has been accounted for and quantified by including individually varying effects in models for mark-recapture data, but the real need for underlying individual effects to account for observed levels of individual variation has recently been questioned by the work of Tuljapurkar et al. (Ecology Letters, 12, 93, 2009) on dynamic heterogeneity. Model-selection approaches based on information criteria or Bayes factors have been used to address this question. Here, we suggest that, in addition to model-selection, model-checking methods can provide additional important insights to tackle this issue, as they allow one to evaluate a model's misfit in terms of ecologically meaningful measures. Specifically, we propose the use of posterior predictive checks to explicitly assess discrepancies between a model and the data, and we explain how to incorporate model checking into the inferential process used to assess the practical implications of ignoring individual heterogeneity. Posterior predictive checking is a straightforward and flexible approach for performing model checks in a Bayesian framework that is based on comparisons of observed data to model-generated replications of the data, where parameter uncertainty is incorporated through use of the posterior distribution. If discrepancy measures are chosen carefully and are relevant to the scientific context, posterior predictive checks can provide important information allowing for more efficient model refinement. We illustrate this approach using analyses of vital rates with long-term mark-recapture data for Weddell seals and emphasize its utility for identifying shortfalls or successes of a model at representing a biological process or pattern of interest. We show how posterior predictive checks can be used to strengthen inferences in ecological studies. We demonstrate the application of this method on analyses dealing with the question of individual reproductive heterogeneity in a population of Antarctic pinnipeds.