Passage Time Analysis Research Articles

Optimized Collective Variable for Collapse Transition in Linear Hydrophobic Polymers: Importance of Hydration Water and End-to-End Distance.

Choosing an appropriate collective variable (CV) for any biomolecular process is a challenging task. Researchers are developing methods to solve this issue using a variety of methodologies, most recently using machine learning (ML) methods. In this work, we investigate the mechanism of collapse transition across various lengths of polymer systems through adaptively sampled multiple short trajectories utilizing the Time Lagged Independent Component Analysis (TICA) framework. From TICA analysis, it is revealed that the radius of gyration (Rg) and end-to-end distance serve as good order parameters (OPs) for these systems describing overall energy landscapes. Markov state model (MSM) and mean first passage time (MFPT) analysis suggest that hydration water (Nw) plays a determining role in dictating the time scale and barrier for the collapsed transition for the C40 system. P-fold analysis on identifying transition state ensembles (TSE) identified by committor analysis also strengthens the role of Nw in such a transition. TICA, MSM, and committor analyses on the collapse transition for C45 reveal similarities with C40 systems in different aspects. Furthermore, we propose a pipeline integrating XGBoost regression along with an interpretable ML model, Shapley Additive exPlanation (SHAP) to precisely elucidate the contribution of each OP locally at the TSE. Through this approach, we observe that the collapse transition is primarily driven by Nw for both polymer systems. A carefully designed protocol for the collapsed transition of C60 systems indirectly reiterates the above result. Overall, our results suggest that while the end-to-end distance should be considered for better resolution of metastable states in the landscape, Nw is the crucial coordinate to be used in enhanced sampling for the exploration of actual collapse transitions for linear hydrophobic polymer systems. The Python code for analyzing the contribution of different OPs in the TSE using an ML-aided protocol is available on GitHub (https://github.com/saikat-ai/linear_polymer_project).

First Passage Times of Long Transient Dynamics in Ecology.

Long transient dynamics in ecological models are characterized by extended periods in one state or regime before an eventual, and often abrupt, transition. One mechanism leading to long transient dynamics is the presence of ghost attractors, states where system dynamics slow down and the system lingers before eventually transitioning to the true attractor. This transition results solely from system dynamics rather than external factors. This paper investigates the dynamics of a classical herbivore-grazer model with the potential for ghost attractors or alternative stable states. We propose an intuitive threshold for first passage time analysis applicable to both bistable and ghost attractor regimes. By formulating the first passage time problem as a backward Kolmogorov equation, we examine how the mean first passage time changes as parameters are varied from the ghost attractor regime to the bistable one, through a saddle-node bifurcation. Our results reveal that the mean and variance of first passage times vary smoothly across the bifurcation threshold, eliminating the deterministic distinction between ghost attractors and bistable regimes. This work suggests that first passage time analysis can be an informative way to classify the length of a long transient. A better understanding of the duration of long transients may contribute to greater ecological understanding and more effective environmental management.

Jacobi Processes with Jumps as Neuronal Models: A First Passage Time Analysis

Jacobi Processes with Jumps as Neuronal Models: A First Passage Time Analysis

The energy landscape of Aβ42: a funnel to disorder for the monomer becomes a folding funnel for self-assembly.

The aggregation of amyloid-β (Aβ) peptides, particularly Aβ1-42, plays a key role in Alzheimer's disease pathogenesis. In this study, we investigate how dimerisation transforms the free energy surface (FES) of the Aβ1-42 monomer when it interacts with another Aβ1-42 peptide. We find that the monomer FES is a structurally inverted funnel with a disordered state at the global minimum. However, in the presence of a second Aβ1-42 peptide, the landscape becomes a folding funnel, leading to a β-hairpin state. Using first passage time analysis, we analyse the pathway for the transition from disordered to the β-hairpin state, which highlights the initial formation of a D23-K28 salt bridge as the driving force, together with hydrophobic contacts.

Noise-induced dynamics in a single species model with Allee effect driven by correlated colored noises

In this paper, a single species model with Allee effect driven by correlated colored noises is proposed and investigated. The stationary probability density of the model is obtained using the approximative Fokker–Planck equation, and its shape is discussed in detail. P-bifurcation and noise-induced bistability are explored, followed by the observation of noise-enhanced stability through mean first passage time analysis. Our findings demonstrate that: (i) noise can induce P-bifurcation, causing the structure of a stationary probability distribution to shift from unimodal to monotonic under positive correlation and switch from unimodal to bimodal under negative correlation; (ii) correlation time promotes population growth, leading to a higher probability of large population size and delaying the extinction process; (iii) noise-enhanced stability induced by multiplicative noise depends on both additive noise and correlation time, while it always exists for additive noise.

First passage time analysis of spatial mutation patterns reveals sub-clonal evolutionary dynamics in colorectal cancer.

The signature of early cancer dynamics on the spatial arrangement of tumour cells is poorly understood, and yet could encode information about how sub-clones grew within the expanding tumour. Novel methods of quantifying spatial tumour data at the cellular scale are required to link evolutionary dynamics to the resulting spatial architecture of the tumour. Here, we propose a framework using first passage times of random walks to quantify the complex spatial patterns of tumour cell population mixing. First, using a simple model of cell mixing we demonstrate how first passage time statistics can distinguish between different pattern structures. We then apply our method to simulated patterns of mutated and non-mutated tumour cell population mixing, generated using an agent-based model of expanding tumours, to explore how first passage times reflect mutant cell replicative advantage, time of emergence and strength of cell pushing. Finally, we explore applications to experimentally measured human colorectal cancer, and estimate parameters of early sub-clonal dynamics using our spatial computational model. We infer a wide range of sub-clonal dynamics, with mutant cell division rates varying between 1 and 4 times the rate of non-mutated cells across our sample set. Some mutated sub-clones emerged after as few as 100 non-mutant cell divisions, and others only after 50,000 divisions. The majority were consistent with boundary driven growth or short-range cell pushing. By analysing multiple sub-sampled regions in a small number of samples, we explore how the distribution of inferred dynamics could inform about the initial mutational event. Our results demonstrate the efficacy of first passage time analysis as a new methodology in spatial analysis of solid tumour tissue, and suggest that patterns of sub-clonal mixing can provide insights into early cancer dynamics.

Bridging the first and last passage times for Lévy models

Research in classical ruin theory has largely focused on the first passage time analysis of a surplus process below level 0. Recently, inspired by numerous applications in finance, physics, and optimization, there has been an accrued interest in the analysis of the last passage time (below level 0). In this paper, we aim to bridge the first and the last passage times and unify their analyses. For this purpose, we consider negative excursions of an underlying process in two manners, cumulative and noncumulative, and introduce two random times, denoted by sr and lr, where r can be interpreted as a measure of a decision maker’s tolerance to negative excursions. Our analysis focuses on spectrally negative Lévy processes, for which we derive the Laplace transform and some distributional quantities of these random times in terms of standard scale functions. An application to credit risk management is considered at the end.

Nucleation and growth of crystals inside polyethylene nano-droplets.

Polymer crystallization is a long-standing interesting problem both in fundamental polymer physics and in polymer manufacturing. Fundamentally, the connectivity of the macromolecules provides a unique feature for the study of nucleation and growth of crystals in contrast to the crystallization of smaller molecules. In addition, understanding the crystallization in polymers is industrially important due to the necessity of its control to achieve mechanically durable plastic materials. Molecular dynamics simulations offer a suitable way of studying this phenomenon due to their capability to probe the small time and length scales that are characteristic of nucleation. In this paper, we use a long alkane chain model to study nucleation and the growth of polyethylene crystals both within bulk and nano-droplets whose diameters range from about 6 to 11nm. It is found that the droplets approach being more spherical during the nucleation whereas they deviate from this shape during the growth regime. Strikingly, a mean first passage time analysis indicates that the nucleation rate per unit volume decreases as the droplet size is increased. Finally, visual inspection of the simulation snapshots suggests that nuclei majorly emerged from the surface of the droplets.

Smooth coarse-graining and colored noise dynamics in stochastic inflation

We consider stochastic inflation coarse-grained using a general class of exponential filters. Such a coarse-graining prescription gives rise to inflaton-Langevin equations sourced by colored noise that is correlated in e-fold time. The dynamics are studied first in slow-roll for simple potentials using first-order perturbative, semi-analytical calculations which are later compared to numerical simulations. Subsequent calculations are performed using an exponentially correlated noise which appears as a leading order correction to the full slow-roll noise correlation functions of the type 〈ξ(N)ξ(N')〉(n) ∼ (cosh[n(N-N'+1])-1. We find that the power spectrum of curvature perturbations \U0001d4ab ζ is suppressed at small e-folds, with the suppression controlled by n. Furthermore, we use the leading order, exponentially correlated noise and perform a first passage time analysis to compute the statistics of the stochastic e-fold distribution \U0001d4a9 and derive an approximate expression for the mean number of e-folds 〈\U0001d4a9〉. Comparing analytical results with numerical simulations of the inflaton dynamics, we show that the leading order noise correlation function can be used as a very good approximation of the exact noise, the latter being more difficult to simulate.

Resident and transient coyotes exhibit differential patterns of movement behavior across heterogeneous landscapes in the southeastern United States.

Coyotes (Canis latrans) are a highly adaptable canid species whose behavioral plasticity has allowed them to persist in a wide array of habitats throughout North America. As generalists, coyotes can alter movement patterns and change territorial strategies between residency (high site fidelity) and transiency (low site fidelity) to maximize fitness. Uncertainty remains about resident and transient coyote movement patterns and habitat use because research has reached conflicting conclusions regarding patterns of habitat use by both groups. We quantified effects of habitat on resident and transient coyote movement behavior using first passage time (FPT) analysis, which assesses recursive movement along an individual's movement path to delineate where they exhibit area‐restricted search (ARS) behaviors relative to habitat attributes. We quantified monthly movement rates for 171 coyotes (76 residents and 53 transients) and then used estimated FPT values in generalized linear mixed models to quantify monthly habitat use for resident and transient coyotes. Transients had greater movement rates than residents across all months except January. Resident FPT values were positively correlated with agricultural land cover during fall and winter, but negatively correlated with agriculture during spring. Resident FPT values were also negatively correlated with developed habitats during May–August, deciduous land cover during June–August, and wetlands during September–January except November. FPT values of transient coyotes were positively correlated with developed areas throughout much of the year and near wetlands during July–September. Transient FPT values were negatively correlated with agriculture during all months except June and July. High FPT values (ARS behavior) of residents and transients were generally correlated with greater densities of edge habitat. Although we observed high individual variation in space use, our study found substantive differences in habitat use between residents and transients, providing further evidence that complexity and plasticity of coyote habitat use is influenced by territorial strategy.

Environmental and Biological Factors Influencing Dispersal of Neonate Leatherback Turtles (Dermochelys coriacea) From an Endangered Costa Rican Nesting Population

Quantifying early life movements is essential to understanding migratory pathways and habitat use that can impact individuals’ success later in life. To gauge how neonatal movements set the stage for later habitat use, we tracked neonate leatherback turtles (n=94) with acoustic tags from Pacuare, Costa Rica, in 2016 and 2018. We analyzed movements using a first passage time analysis and random walk models, the results of which indicated neonates followed a fixed compass direction as they traveled away from shore and that strong currents in these areas resulted in advection. We combined the tracking data with concurrent environmental variables in a generalized additive mixed model framework. Our results showed the south-east current flow in this area has spatial and temporal structure that was not driven by the tidal current or local wind speed. Accounting for advection by the currents, in-water neonate swimming speed was significantly related to current speed, first passage time, and the year. Neonates had three main response strategies to currents above 0.5 m s-1, with most increasing their swimming speed and the rest maintaining either a constant or decreased swimming speed. Neonates were significantly larger in 2018 than in 2016 but their average swimming speed was not significantly related to body size, indicating that environmental factors were more important contributors to their dispersal. We conclude that abiotic factors, including the strength and direction of the currents, significantly affect the swimming and dispersal strategy of neonate leatherback turtles and these results can help to inform strategies for releases of neonate turtles from hatcheries, future tracking studies, and conservation efforts.

Rare events and first passage time statistics from the energy landscape.

We analyze the probability distribution of rare first passage times corresponding to transitions between product and reactant states in a kinetic transition network. The mean first passage times and the corresponding rate constants are analyzed in detail for two model landscapes and the double funnel landscape corresponding to an atomic cluster. Evaluation schemes based on eigendecomposition and kinetic path sampling, which both allow access to the first passage time distribution, are benchmarked against mean first passage times calculated using graph transformation. Numerical precision issues severely limit the useful temperature range for eigendecomposition, but kinetic path sampling is capable of extending the first passage time analysis to lower temperatures, where the kinetics of interest constitute rare events. We then investigate the influence of free energy based state regrouping schemes for the underlying network. Alternative formulations of the effective transition rates for a given regrouping are compared in detail to determine their numerical stability and capability to reproduce the true kinetics, including recent coarse-graining approaches that preserve occupancy cross correlation functions. We find that appropriate regrouping of states under the simplest local equilibrium approximation can provide reduced transition networks with useful accuracy at somewhat lower temperatures. Finally, a method is provided to systematically interpolate between the local equilibrium approximation and exact intergroup dynamics. Spectral analysis is applied to each grouping of states, employing a moment-based mode selection criterion to produce a reduced state space, which does not require any spectral gap to exist, but reduces to gap-based coarse graining as a special case. Implementations of the developed methods are freely available online.

Accelerated kinetic Monte Carlo: A case study; vacancy and dumbbell interstitial diffusion traps in concentrated solid solution alloys.

Vacancy and self-interstitial atomic diffusion coefficients in concentrated solid solution alloys can have a non-monotonic concentration dependence. Here, the kinetics of monovacancies and ⟨100⟩ dumbbell interstitials in Ni-Fe alloys are assessed using lattice kinetic Monte Carlo (kMC). The non-monotonicity is associated with superbasins, which impels using accelerated kMC methods. Detailed implementation prescriptions for first passage time analysis kMC (FPTA-kMC), mean rate method kMC (MRM-kMC), and accelerated superbasin kMC (AS-kMC) are given. The accelerated methods are benchmarked in the context of diffusion coefficient calculations. The benchmarks indicate that MRM-kMC underestimates diffusion coefficients, while AS-kMC overestimates them. In this application, MRM-kMC and AS-kMC are computationally more efficient than the more accurate FPTA-kMC. Our calculations indicate that composition dependence of migration energies is at the origin of the vacancy's non-monotonic behavior. In contrast, the difference between formation energies of Ni-Ni, Ni-Fe, and Fe-Fe dumbbell interstitials is at the origin of their non-monotonic diffusion behavior. Additionally, the migration barrier crossover composition-based on the situation where Ni or Fe atom jumps have lower energy barrier than the other one-is introduced. KMC simulations indicate that the interplay between composition dependent crossover of migration energy and geometrical site percolation explains the non-monotonic concentration-dependence of atomic diffusion coefficients.

Statistical Characteristics of the First Passage Time Analysis for the Gene Regulatory Circuit in Bacillus subtilis by Cell Mapping Method

In this paper, we will explore the stochastic exit problem for the gene regulatory circuit in B. subtilis affected by colored noise. The stochastic exit problem studies the state transition in B. subtilis (from competent state to vegetative state in this case) through three different quantities: the probability density function of the first passage time, the mean of first passage time, and the reliability function. To satisfy the Markov nature, we convert the colored noise system into the equivalent white noise system. Then, the stochastic generalized cell mapping method can be used to explore the stochastic exit problem. The results indicate that the intensity of noise and system parameters have the effect on the transition from competent to vegetative state in B. subtilis. In addition, the effectiveness of the stochastic generalized cell mapping method is verified by Monte Carlo simulation.

Determinants of Brain Rhythm Burst Statistics

Brain rhythms recorded in vivo, such as gamma oscillations, are notoriously variable both in amplitude and frequency. They are characterized by transient epochs of higher amplitude known as bursts. It has been suggested that, despite their short-life and random occurrence, bursts in gamma and other rhythms can efficiently contribute to working memory or communication tasks. Abnormalities in bursts have also been associated with e.g. motor and psychiatric disorders. It is thus crucial to understand how single cell and connectivity parameters influence burst statistics and the corresponding brain states. To address this problem, we consider a generic stochastic recurrent network of Pyramidal Interneuron Network Gamma (PING) type. Using the stochastic averaging method, we derive dynamics for the phase and envelope of the amplitude process, and find that they depend on only two meta-parameters that combine all the model parameters. This allows us to identify an optimal parameter regime of healthy variability with similar statistics to those seen in vivo; in this regime, oscillations and bursts are supported by synaptic noise. The probability density for the rhythm’s envelope as well as the mean burst duration are then derived using first passage time analysis. Our analysis enables us to link burst attributes, such as duration and frequency content, to system parameters. Our general approach can be extended to different frequency bands, network topologies and extra populations. It provides the much needed insight into the biophysical determinants of rhythm burst statistics, and into what needs to be changed to correct rhythms with pathological statistics.

Site stability and pipe diffusion of hydrogen under localised shear in aluminium

ABSTRACTThis paper studies the effect of a plastic shear on the tetrahedral vs. octahedral site stability for hydrogen, in aluminium. Based on Density Functional Theory calculations, it is shown that the tetrahedral site remains the most stable site. It transforms into the octahedral site of the local hexagonal compact structure of the intrinsic stacking fault. The imperfect stacking is slightly attractive with respect to a regular lattice site. It is also shown that the shearing process involves a significant decrease of the energetic barrier for hydrogen jumps, at half the value of the Shockley partial Burgers vector, but not in the intrinsic stacking fault. These jumps involve a displacement component perpendicular to the shearing direction which favours an enhancement of hydrogen diffusion along edge dislocation cores (pipe diffusion). The magnitude of the boost in the jump rate in the direction of the dislocation line, according to Transition State Theory and taking into account the zero point energy correction, is of the order of a factor 50, at room temperature. First Passage Time Analysis is used to evaluate the effect on diffusion which is significant, by only at the nanoscale. Indeed, the common dislocation densities are too small for these effects (trapping, or pipe diffusion) to have a signature at the macroscopic level. The observed drop of the effective diffusion coefficient could therefore be attributed to the production of debris during plastic straining, as proposed in the literature.

Movements of Australian Wood Ducks (Chenonetta jubata) in an agricultural landscape

ABSTRACTWe deployed satellite transmitters to provide the first detailed picture of the movement behaviour of Australian Wood Ducks (Chenonetta jubata) through agricultural landscapes where the availability and spatial arrangement of resources are highly predictable. We measured movement distances and home-range areas of individual Australian Wood Ducks and investigated their site fidelity by comparing the overlap of successive home-range areas on a fortnightly temporal scale. First passage time (FPT) analysis was used to determine the spatial scales at which foraging occurs within home-range areas. We found a peak of movement activity around the periods of dawn and dusk similar to many waterfowl species. The mean overlap of core home-range areas over successive 2 week periods was 89.81% (± 2.38 SD), which demonstrates strong site fidelity. Area-restricted search (ARS) occurred at the scale of individual foraging (ca.100 m), with no clear peaks at larger spatial scales. This finding implies that search effort was expended equally across the combined utilisation distribution of Australian Wood Ducks in this agricultural landscape. Our results support the conclusions of previous studies suggesting that the movement behaviour of Australian Wood Ducks is shaped strongly by the temporal and spatial predictability of their grazing areas and access to water in the form of farm dams.

The analysis of MX/M/1 queue with two-stage vacations policy

In this article, we consider a batch arrival MX/M/1 queue with two-stage vacations policy that comprises of single working vacation and multiple vacations, denoted by MX/M/1/SWV + MV. Using the matrix analytic method, we derive the probability generating function (PGF) of the stationary system size and investigate the stochastic decomposition structure of stationary system size. Further, we obtain the Laplace–Stieltjes transform (LST) of stationary sojourn time of a customer by the first passage time analysis. At last, we illustrate the effects of various parameters on the performance measures numerically and graphically by some numerical examples.

Reaction time for trimolecular reactions in compartment-based reaction-diffusion models.

Trimolecular reaction models are investigated in the compartment-based (lattice-based) framework for stochastic reaction-diffusion modeling. The formulae for the first collision time and the mean reaction time are derived for the case where three molecules are present in the solution under periodic boundary conditions. For the case of reflecting boundary conditions, similar formulae are obtained using a computer-assisted approach. The accuracy of these formulae is further verified through comparison with numerical results. The presented derivation is based on the first passage time analysis of Montroll [J. Math. Phys. 10, 753 (1969)]. Montroll's results for two-dimensional lattice-based random walks are adapted and applied to compartment-based models of trimolecular reactions, which are studied in one-dimensional or pseudo one-dimensional domains.

Bridging Dynamics of Telechelic Polymers between Solid Surfaces

We employ Brownian dynamics simulations combined with forward flux sampling and theoretical first-passage time analyses to describe the rates of transitions between loops and bridges of telechelic polymers between solid surfaces representing e.g. latex colloids in the limit that the telechelic stickers bind strongly enough to the surfaces to make free chains very rare. It is shown that the bridge formation rate can be expressed by combining times for two processes, namely, the escape of one end sticker from the narrow-but-deep association well near the colloidal surface and the longer-range motion of the chain end to the other surface inhibited by stretching free energy. We find that when using multibead chains to represent the telechelic polymers, the longer-range motion requires use of a multidimensional first passage time analysis that we borrow from the work of Likhtman and co-workers, which was originally developed to describe polymer end fluctuations in a one-dimensional reptation tube. From these i...