Inferring Stochastic Rates from Heterogeneous Snapshots of Particle Positions.

Many imaging techniques for biological systems-like fixation of cells coupled with fluorescence microscopy-provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics they intend to capture. These snapshot observations contain no information about individual trajectories, but still encode information about movement and demographic dynamics, especially when combined with a well-motivated biophysical model. The relationship between spatially evolving populations and single-moment representations of their collective locations is well-established with partial differential equations (PDEs) and their inverse problems. However, experimental data is commonly a set of locations whose number is insufficient to approximate a continuous-in-space PDE solution. Here, motivated by popular subcellular imaging data of gene expression, we embrace the stochastic nature of the data and investigate the mathematical foundations of parametrically inferring demographic rates from snapshots of particles undergoing birth, diffusion, and death in a nuclear or cellular domain. Toward inference, we rigorously derive a connection between individual particle paths and their presentation as a Poisson spatial process. Using this framework, we investigate the properties of the resulting inverse problem and study factors that affect quality of inference. One pervasive feature of this experimental regime is the presence of cell-to-cell heterogeneity. Rather than being a hindrance, we show that cell-to-cell geometric heterogeneity can increase the quality of inference on dynamics for certain parameter regimes. Altogether, the results serve as a basis for more detailed investigations of subcellular spatial patterns of RNA molecules and other stochastically evolving populations that can only be observed for single instants in their time evolution.

Minimal Mechanisms of Microtubule Length Regulation in Living Cells.

The microtubule cytoskeleton is responsible for sustained, long-range intracellular transport of mRNAs, proteins, and organelles in neurons. Neuronal microtubules must be stable enough to ensure reliable transport, but they also undergo dynamic instability, as their plus and minus ends continuously switch between growth and shrinking. This process allows for continuous rebuilding of the cytoskeleton and for flexibility in injury settings. Motivated by in vivo experimental data on microtubule behavior in Drosophila neurons, we propose a mathematical model of dendritic microtubule dynamics, with a focus on understanding microtubule length, velocity, and state-duration distributions. We find that limitations on microtubule growth phases are needed for realistic dynamics, but the type of limiting mechanism leads to qualitatively different responses to plausible experimental perturbations. We therefore propose and investigate two minimally-complex length-limiting factors: limitation due to resource (tubulin) constraints and limitation due to catastrophe of large-length microtubules. We combine simulations of a detailed stochastic model with steady-state analysis of a mean-field ordinary differential equations model to map out qualitatively distinct parameter regimes. This provides a basis for predicting changes in microtubule dynamics, tubulin allocation, and the turnover rate of tubulin within microtubules in different experimental environments.

Palmitate-mediated disruption of the endoplasmic reticulum decreases intracellular vesicle motility.

Essential cellular processes such as metabolism, protein synthesis, and autophagy require the intracellular transport of membrane-bound vesicles. The importance of the cytoskeleton and associated molecular motors for transport is well documented. Recent research has suggested that the endoplasmic reticulum (ER) may also play a role in vesicle transport through a tethering of vesicles to the ER. We use single-particle tracking fluorescence microscopy and a Bayesian change-point algorithm to characterize vesicle motility in response to the disruption of the ER, actin, and microtubules. This high-throughput change-point algorithm allows us to efficiently analyze thousands of trajectory segments. We find that palmitate-mediated disruption of the ER leads to a significant decrease in vesicle motility. A comparison with the disruption of actin and microtubules shows that disruption of the ER has a significant impact on vesicle motility, greater than the disruption of actin. Vesicle motility was dependent on cellular region, with greater motility in the cell periphery than the perinuclear region, possibly due to regional differences in actin and the ER. Overall, these results suggest that the ER is an important factor in vesicle transport.

Transport of lysosomes decreases in the perinuclear region: Insights from changepoint analysis.

Lysosomes are membrane-bound organelles that serve as the endpoint for endocytosis, phagocytosis, and autophagy, degrading the molecules, pathogens, and organelles localized within them. These cellular functions require intracellular transport. We use fluorescence microscopy to characterize the motion of lysosomes as a function of intracellular region, perinuclear or periphery, and lysosome diameter. Single-particle tracking data are complemented by changepoint identification and analysis of a mathematical model for state switching. We first classify lysosomal motion as motile or stationary. We then study how lysosome location and diameter affects the proportion of time spent in each state and quantify the speed during motile periods. We find that the proportion of time spent stationary is strongly region dependent, with significantly decreased motility in the perinuclear region. Increased lysosome diameter only slightly decreases speed. Overall, these results demonstrate the importance of decomposing particle trajectories into qualitatively different behaviors before conducting population-wide statistical analysis. Our results suggest that intracellular region is an important factor to consider in studies of intracellular transport.

Leaf Economics of Early- and Late-Successional Plants.

AbstractThe leaf economics spectrum ranges from cheap, short-lived leaves to expensive, long-lived leaves. Species with low leaf mass per area (LMA) and short leaf life span tend to be fast growing and shade intolerant (early successional), whereas species with high LMA and long leaf life span tend to be slow growing and shade tolerant (late successional). However, we have limited understanding of how different leaf mass components (e.g., metabolically active photosynthetic components vs. structural toughness components) contribute to variation in LMA and other leaf economics spectrum traits. Here, we develop a model of plant community dynamics in which species differ in just two traits, photosynthetic and structural LMA components, and we identify optimal values of these traits for early- and late-successional species. Most of the predicted increase in LMA from early- to late-successional species was due to structural LMA. Photosynthetic LMA did not differ consistently between early- and late-successional species, but the photosynthetic LMA to structural LMA ratio declined from early- to late-successional species. Early-successional species had high rates of instantaneous return on leaf mass investment, whereas late-successional species had high lifetime return. Our results provide theoretical support for the primary role of structural (rather than photosynthetic) LMA variation in driving relationships among leaf economics spectrum traits.

Topological Data Analysis Approaches to Uncovering the Timing of Ring Structure Onset in Filamentous Networks.

In developmental biology as well as in other biological systems, emerging structure and organization can be captured using time-series data of protein locations. In analyzing this time-dependent data, it is a common challenge not only to determine whether topological features emerge, but also to identify the timing of their formation. For instance, in most cells, actin filaments interact with myosin motor proteins and organize into polymer networks and higher-order structures. Ring channels are examples of such structures that maintain constant diameters over time and play key roles in processes such as cell division, development, and wound healing. Given the limitations in studying interactions of actin with myosin in vivo, we generate time-series data of protein polymer interactions in cells using complex agent-based models. Since the data has a filamentous structure, we propose sampling along the actin filaments and analyzing the topological structure of the resulting point cloud at each time. Building on existing tools from persistent homology, we develop a topological data analysis (TDA) method that assesses effective ring generation in this dynamic data. This method connects topological features through time in a path that corresponds to emergence of organization in the data. In this work, we also propose methods for assessing whether the topological features of interest are significant and thus whether they contribute to the formation of an emerging hole (ring channel) in the simulated protein interactions. In particular, we use the MEDYAN simulation platform to show that this technique can distinguish between the actin cytoskeleton organization resulting from distinct motor protein binding parameters.

Renewal Reward Perspective on Linear Switching Diffusion Systems in Models of Intracellular Transport.

In many biological systems, the movement of individual agents is characterized having multiple qualitatively distinct behaviors that arise from a variety of biophysical states. For example, in cells the movement of vesicles, organelles, and other intracellular cargo is affected by their binding to and unbinding from cytoskeletal filaments such as microtubules through molecular motor proteins. A typical goal of theoretical or numerical analysis of models of such systems is to investigate effective transport properties and their dependence on model parameters. While the effective velocity of particles undergoing switching diffusion dynamics is often easily characterized in terms of the long-time fraction of time that particles spend in each state, the calculation of the effective diffusivity is more complicated because it cannot be expressed simply in terms of a statistical average of the particle transport state at one moment of time. However, it is common that these systems are regenerative, in the sense that they can be decomposed into independent cycles marked by returns to a base state. Using decompositions of this kind, we calculate effective transport properties by computing the moments of the dynamics within each cycle and then applying renewal reward theory. This method provides a useful alternative large-time analysis to direct homogenization for linear advection-reaction-diffusion partial differential equation models. Moreover, it applies to a general class of semi-Markov processes and certain stochastic differential equations that arise in models of intracellular transport. Applications of the proposed renewal reward framework are illustrated for several case studies such as mRNA transport in developing oocytes and processive cargo movement by teams of molecular motor proteins.

Antibody-Mediated Immobilization of Virions in Mucus.

Antibodies have been shown to hinder the movement of herpes simplex virus virions in cervicovaginal mucus, as well as other viruses in other mucus secretions. However, it has not been possible to directly observe the mechanisms underlying this phenomenon, so the nature of virion-antibody-mucin interactions remain poorly understood. In this work, we analyzed thousands of virion traces from single particle tracking experiments to explicate how antibodies must cooperate to immobilize virions for relatively long time periods. First, using a clustering analysis, we observed a clear separation between two classes of virion behavior: freely diffusing and immobilized. While the proportion of freely diffusing virions decreased with antibody concentration, the magnitude of their diffusivity did not, implying an all-or-nothing dichotomy in the pathwise effect of the antibodies. Proceeding under the assumption that all binding events are reversible, we used a novel switch-point detection method to conclude that there are very few, if any, state switches on the experimental timescale of 20 s. To understand this slow state switching, we analyzed a recently proposed continuous-time Markov chain model for binding kinetics and virion movement. Model analysis implied that virion immobilization requires cooperation by multiple antibodies that are simultaneously bound to the virion and mucin matrix and that there is an entanglement phenomenon that accelerates antibody-mucin binding when a virion is immobilized. In addition to developing a widely applicable framework for analyzing multistate particle behavior, this work substantially enhances our mechanistic understanding of how antibodies can reinforce a mucus barrier against passive invasive species.

ZMapp Reinforces the Airway Mucosal Barrier Against Ebola Virus.

Filoviruses, including Ebola, have the potential to be transmitted via virus-laden droplets deposited onto mucus membranes. Protecting against such emerging pathogens will require understanding how they may transmit at mucosal surfaces and developing strategies to reinforce the airway mucus barrier. Here, we prepared Ebola pseudovirus (with Zaire strain glycoproteins) and used high-resolution multiple-particle tracking to track the motions of hundreds of individual pseudoviruses in fresh and undiluted human airway mucus isolated from extubated endotracheal tubes. We found that Ebola pseudovirus readily penetrates human airway mucus. Addition of ZMapp, a cocktail of Ebola-binding immunoglobulin G antibodies, effectively reduced mobility of Ebola pseudovirus in the same mucus secretions. Topical delivery of ZMapp to the mouse airways also facilitated rapid elimination of Ebola pseudovirus. Our work demonstrates that antibodies can immobilize virions in airway mucus and reduce access to the airway epithelium, highlighting topical delivery of pathogen-specific antibodies to the lungs as a potential prophylactic or therapeutic approach against emerging viruses or biowarfare agents.

Assessing the Impact of Electrostatic Drag on Processive Molecular Motor Transport.

The bidirectional movement of intracellular cargo is usually described as a tug-of-war among opposite-directed families of molecular motors. While tug-of-war models have enjoyed some success, recent evidence suggests underlying motor interactions are more complex than previously understood. For example, these tug-of-war models fail to predict the counterintuitive phenomenon that inhibiting one family of motors can decrease the functionality of opposite-directed transport. In this paper, we use a stochastic differential equations modeling framework to explore one proposed physical mechanism, called microtubule tethering, that could play a role in this "co-dependence" among antagonistic motors. This hypothesis includes the possibility of a trade-off: weakly bound trailing molecular motors can serve as tethers for cargoes and processing motors, thereby enhancing motor-cargo run lengths along microtubules; however, this introduces a cost of processing at a lower mean velocity. By computing the small- and large-time mean-squared displacement of our theoretical model and comparing our results to experimental observations of dynein and its "helper protein" dynactin, we find some supporting evidence for microtubule tethering interactions. We extrapolate these findings to predict how dynein-dynactin might interact with the opposite-directed kinesin motors and introduce a criterion for when the trade-off is beneficial in simple systems.

Hidden semi-Markov models reveal multiphasic movement of the endangered Florida panther.

Animals must move to find food and mates, and to avoid predators; movement thus influences survival and reproduction, and ultimately determines fitness. Precise description of movement and understanding of spatial and temporal patterns as well as relationships with intrinsic and extrinsic factors is important both for theoretical and applied reasons. We applied hidden semi-Markov models (HSMM) to hourly geographic positioning system (GPS) location data to understand movement patterns of the endangered Florida panther (Puma concolor coryi) and to discern factors influencing these patterns. Three distinct movement modes were identified: (1) Resting mode, characterized by short step lengths and turning angles around 180(o); (2) Moderately active (or intermediate) mode characterized by intermediate step lengths and variable turning angles, and (3) Traveling mode, characterized by long step lengths and turning angles around 0(o). Males and females, and females with and without kittens, exhibited distinctly different movement patterns. Using the Viterbi algorithm, we show that differences in movement patterns of male and female Florida panthers were a consequence of sex-specific differences in diurnal patterns of state occupancy and sex-specific differences in state-specific movement parameters, whereas the differences between females with and without dependent kittens were caused solely by variation in state occupancy. Our study demonstrates the use of HSMM methodology to precisely describe movement and to dissect differences in movement patterns according to sex, and reproductive status.

Sensing and decision-making in random search.

Many organisms locate resources in environments in which sensory signals are rare, noisy, and lack directional information. Recent studies of search in such environments model search behavior using random walks (e.g., Lévy walks) that match empirical movement distributions. We extend this modeling approach to include searcher responses to noisy sensory data. We explore the consequences of incorporating such sensory measurements into search behavior using simulations of a visual-olfactory predator in search of prey. Our results show that including even a simple response to noisy sensory data can dominate other features of random search, resulting in lower mean search times and decreased risk of long intervals between target encounters. In particular, we show that a lack of signal is not a lack of information. Searchers that receive no signal can quickly abandon target-poor regions. On the other hand, receiving a strong signal leads a searcher to concentrate search effort near targets. These responses cause simulated searchers to exhibit an emergent area-restricted search behavior similar to that observed of many organisms in nature.

Transient antibody-mucin interactions produce a dynamic molecular shield against viral invasion.

Given the difficulty in finding a cure for HIV/AIDS, a promising prevention strategy to reduce HIV transmission is to directly block infection at the portal of entry. The recent Thai RV144 trial offered the first evidence that an antibody-based vaccine may block heterosexual HIV transmission. Unfortunately, the underlying mechanism(s) for protection remain unclear. Here we theoretically examine a hypothesis that builds on our recent laboratory observation: virus-specific antibodies (Ab) can trap individual virions in cervicovaginal mucus (CVM), thereby reducing infection in vivo. Ab are known to have a weak-previously considered inconsequential-binding affinity with the mucin fibers that constitute CVM. However, multiple Ab can bind to the same virion at the same time, which markedly increases the overall Ab-mucin binding avidity, and creates an inheritable virion-mucin affinity. Our model takes into account biologically relevant length and timescales, while incorporating known HIV-Ab affinity and the respective diffusivities of viruses and Ab in semen and CVM. The model predicts that HIV-specific Ab in CVM leads to rapid formation and persistence of an HIV concentration front near the semen/CVM interface, far from the vaginal epithelium. Such an HIV concentration front minimizes the flux of HIV virions reaching target cells, and maximizes their elimination upon drainage of genital secretions. The robustness of the result implies that even exceedingly weak Ab-mucin affinity can markedly reduce the flux of virions reaching target cells. Beyond this specific application, the model developed here is adaptable to other pathogens, mucosal barriers, and geometries, as well as kinetic and diffusional effects, providing a tool for hypothesis testing and producing quantitative insights into the dynamics of immune-mediated protection.

Sensory information and encounter rates of interacting species.

Most motile organisms use sensory cues when searching for resources, mates, or prey. The searcher measures sensory data and adjusts its search behavior based on those data. Yet, classical models of species encounter rates assume that searchers move independently of their targets. This assumption leads to the familiar mass action-like encounter rate kinetics typically used in modeling species interactions. Here we show that this common approach can mischaracterize encounter rate kinetics if searchers use sensory information to search actively for targets. We use the example of predator-prey interactions to illustrate that predators capable of long-distance directional sensing can encounter prey at a rate proportional to prey density to the [Formula: see text] power (where [Formula: see text] is the dimension of the environment) when prey density is low. Similar anomalous encounter rate functions emerge even when predators pursue prey using only noisy, directionless signals. Thus, in both the high-information extreme of long-distance directional sensing, and the low-information extreme of noisy non-directional sensing, encounter rate kinetics differ qualitatively from those derived by classic theory of species interactions. Using a standard model of predator-prey population dynamics, we show that the new encounter rate kinetics derived here can change the outcome of species interactions. Our results demonstrate how the use of sensory information can alter the rates and outcomes of physical interactions in biological systems.

Micro-heterogeneity metrics for diffusion in soft matter.

Passive particle tracking of diffusive paths in soft matter, coupled with analysis of the path data, is firmly established as a fundamental methodology for characterization of both diffusive transport properties (the focus here) and linear viscoelasticity. For either focus, particle time series are typically analyzed by ensemble averaging over paths, a perfectly natural protocol for homogeneous materials or for applications where mean properties are sufficient. Many biological materials, however, are heterogeneous over length scales above the probe diameter, and the implications of heterogeneity for biologically relevant transport properties (e.g. diffusive passage times through a complex fluid layer) motivate this paper. Our goals are three-fold: first, to detect heterogeneity as reflected by the ensemble path data; second, to further decompose the ensemble of particle paths into statistically distinct clusters; and third, to fit the path data in each cluster to a model for the underlying stochastic process. After reviewing current best practices for detection and assessment of heterogeneity in diffusive processes, we introduce our strategy toward the first two goals with methods from the statistics and machine learning literature that have not found application thus far to passive particle tracking data. We apply an analysis based solely on the path data that detects heterogeneity and yields a decomposition of particle paths into statistically distinct clusters. After these two goals are achieved, one can then pursue model-fitting. We illustrate these heterogeneity metrics on diverse datasets: for numerically generated and experimental particle paths, with tunable and unknown heterogeneity, on numerical models for simple diffusion and anomalous sub-diffusion, and experimentally on sucrose, hyaluronic acid, agarose, and human lung culture mucus solutions.

A flexible simulation platform to quantify and manage emergency department crowding.

BACKGROUND: Hospital-based Emergency Departments are struggling to provide timely care to a steadily increasing number of unscheduled ED visits. Dwindling compensation and rising ED closures dictate that meeting this challenge demands greater operational efficiency. METHODS: Using techniques from operations research theory, as well as a novel event-driven algorithm for processing priority queues, we developed a flexible simulation platform for hospital-based EDs. We tuned the parameters of the system to mimic U.S. nationally average and average academic hospital-based ED performance metrics and are able to assess a variety of patient flow outcomes including patient door-to-event times, propensity to leave without being seen, ED occupancy level, and dynamic staffing and resource use. RESULTS: The causes of ED crowding are variable and require site-specific solutions. For example, in a nationally average ED environment, provider availability is a surprising, but persistent bottleneck in patient flow. As a result, resources expended in reducing boarding times may not have the expected impact on patient throughput. On the other hand, reallocating resources into alternate care pathways can dramatically expedite care for lower acuity patients without delaying care for higher acuity patients. In an average academic ED environment, bed availability is the primary bottleneck in patient flow. Consequently, adjustments to provider scheduling have a limited effect on the timeliness of care delivery, while shorter boarding times significantly reduce crowding. An online version of the simulation platform is available at http://spark.rstudio.com/klopiano/EDsimulation/. CONCLUSION: In building this robust simulation framework, we have created a novel decision-support tool that ED and hospital managers can use to quantify the impact of proposed changes to patient flow prior to implementation.

Minimal Mechanisms of Microtubule Length Regulation in Living Cells.

The microtubule cytoskeleton is responsible for sustained, long-range intracellular transport of mRNAs, proteins, and organelles in neurons. Neuronal microtubules must be stable enough to ensure reliable transport, but they also undergo dynamic instability, as their plus and minus ends continuously switch between growth and shrinking. This process allows for continuous rebuilding of the cytoskeleton and for flexibility in injury settings. Motivated by in vivo experimental data on microtubule behavior in Drosophila neurons, we propose a mathematical model of dendritic microtubule dynamics, with a focus on understanding microtubule length, velocity, and state-duration distributions. We find that limitations on microtubule growth phases are needed for realistic dynamics, but the type of limiting mechanism leads to qualitatively different responses to plausible experimental perturbations. We therefore propose and investigate two minimally-complex length-limiting factors: limitation due to resource (tubulin) constraints and limitation due to catastrophe of large-length microtubules. We combine simulations of a detailed stochastic model with steady-state analysis of a mean-field ordinary differential equations model to map out qualitatively distinct parameter regimes. This provides a basis for predicting changes in microtubule dynamics, tubulin allocation, and the turnover rate of tubulin within microtubules in different experimental environments.

Inferring stochastic rates from heterogeneous snapshots of particle positions.

Many imaging techniques for biological systems - like fixation of cells coupled with fluorescence microscopy - provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics they intend to capture. These snapshot observations contain no information about individual trajectories, but still encode information about movement and demographic dynamics, especially when combined with a well-motivated biophysical model. The relationship between spatially evolving populations and single-moment representations of their collective locations is well-established with partial differential equations (PDEs) and their inverse problems. However, experimental data is commonly a set of locations whose number is insufficient to approximate a continuous-in-space PDE solution. Here, motivated by popular subcellular imaging data of gene expression, we embrace the stochastic nature of the data and investigate the mathematical foundations of parametrically inferring demographic rates from snapshots of particles undergoing birth, diffusion, and death in a nuclear or cellular domain. Toward inference, we rigorously derive a connection between individual particle paths and their presentation as a Poisson spatial process. Using this framework, we investigate the properties of the resulting inverse problem and study factors that affect quality of inference. One pervasive feature of this experimental regime is the presence of cell-to-cell heterogeneity. Rather than being a hindrance, we show that cell-to-cell geometric heterogeneity can increase the quality of inference on dynamics for certain parameter regimes. Altogether, the results serve as a basis for more detailed investigations of subcellular spatial patterns of RNA molecules and other stochastically evolving populations that can only be observed for single instants in their time evolution.

Asymptotic analysis of microtubule-based transport by multiple identical molecular motors.

We describe a system of stochastic differential equations (SDEs) which model the interaction between processive molecular motors, such as kinesin and dynein, and the biomolecular cargo they tow as part of microtubule-based intracellular transport. We show that the classical experimental environment fits within a parameter regime which is qualitatively distinct from conditions one expects to find in living cells. Through an asymptotic analysis of our system of SDEs, we develop a means for applying in vitro observations of the nonlinear response by motors to forces induced on the attached cargo to make analytical predictions for two parameter regimes that have thus far eluded direct experimental observation: (1) highly viscous in vivo transport and (2) dynamics when multiple identical motors are attached to the cargo and microtubule.

A change point analysis protocol for comparing intracellular transport by different molecular motor combinations.

Intracellular transport by microtubule-based molecular motors is marked by qualitatively different behaviors. It is a long-standing and still-open challenge to accurately quantify the various individual-cargo behaviors and how they are affected by the presence or absence of particular motor families. In this work we introduce a protocol for analyzing change points in cargo trajectories that can be faithfully projected along the length of a (mostly) straight microtubule. Our protocol consists of automated identification of velocity change points, estimation of velocities during the behavior segments, and extrapolation to motor-specific velocity distributions. Using simulated data we show that our method compares favorably with existing methods. We then apply the technique to data sets in which quantum dots are transported by Kinesin-1, by Dynein-Dynactin-BicD2 (DDB), and by Kinesin-1/DDB pairs. In the end, we identify pausing behavior that is consistent with some tug-of-war model predictions, but also demonstrate that the simultaneous presence of antagonistic motors can lead to long processive runs that could contribute favorably to population-wide transport.