Convolutional neural networks automate detection for tracking of submicron-scale particles in 2D and 3D.

Particle tracking is a powerful biophysical tool that requires conversion of large video files into position time series, i.e., traces of the species of interest for data analysis. Current tracking methods, based on a limited set of input parameters to identify bright objects, are ill-equipped to handle the spectrum of spatiotemporal heterogeneity and poor signal-to-noise ratios typically presented by submicron species in complex biological environments. Extensive user involvement is frequently necessary to optimize and execute tracking methods, which is not only inefficient but introduces user bias. To develop a fully automated tracking method, we developed a convolutional neural network for particle localization from image data, comprising over 6,000 parameters, and used machine learning techniques to train the network on a diverse portfolio of video conditions. The neural network tracker provides unprecedented automation and accuracy, with exceptionally low false positive and false negative rates on both 2D and 3D simulated videos and 2D experimental videos of difficult-to-track species.

Hydrodynamics of transient cell-cell contact: The role of membrane permeability and active protrusion length.

In many biological settings, two or more cells come into physical contact to form a cell-cell interface. In some cases, the cell-cell contact must be transient, forming on timescales of seconds. One example is offered by the T cell, an immune cell which must attach to the surface of other cells in order to decipher information about disease. The aspect ratio of these interfaces (tens of nanometers thick and tens of micrometers in diameter) puts them into the thin-layer limit, or "lubrication limit", of fluid dynamics. A key question is how the receptors and ligands on opposing cells come into contact. What are the relative roles of thermal undulations of the plasma membrane and deterministic forces from active filopodia? We use a computational fluid dynamics algorithm capable of simulating 10-nanometer-scale fluid-structure interactions with thermal fluctuations up to seconds- and microns-scales. We use this to simulate two opposing membranes, variously including thermal fluctuations, active forces, and membrane permeability. In some regimes dominated by thermal fluctuations, proximity is a rare event, which we capture by computing mean first-passage times using a Weighted Ensemble rare-event computational method. Our results demonstrate a parameter regime in which the time it takes for an active force to drive local contact actually increases if the cells are being held closer together (e.g., by nonspecific adhesion), a phenomenon we attribute to the thin-layer effect. This leads to an optimal initial cell-cell separation for fastest receptor-ligand binding, which could have relevance for the role of cellular protrusions like microvilli. We reproduce a previous experimental observation that fluctuation spatial scales are largely unaffected, but timescales are dramatically slowed, by the thin-layer effect. We also find that membrane permeability would need to be above physiological levels to abrogate the thin-layer effect.

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.

Engineering Polymer-Binding Bispecific Antibodies for Enhanced Pretargeted Delivery of Nanoparticles to Mucus-Covered Epithelium.

Mucus represents a major barrier to sustained and targeted drug delivery to mucosal epithelium. Ideal drug carriers should not only rapidly diffuse across mucus, but also bind the epithelium. Unfortunately, ligand-conjugated particles often exhibit poor penetration across mucus. In this work, we explored a two-step "pretargeting" approach through engineering a bispecific antibody that binds both cell-surface ICAM-1 and polyethylene glycol (PEG) on the surface of nanoparticles, thereby effectively decoupling cell targeting from particle design and formulation. When tested in a mucus-coated Caco-2 culture model that mimics the physiological process of mucus clearance, pretargeting increased the amount of PEGylated particles binding to cells by around 2-fold or more compared to either non-targeted or actively targeted PEGylated particles. Pretargeting also markedly enhanced particle retention in mouse intestinal tissues. Our work underscores pretargeting as a promising strategy to improve the delivery of therapeutics to mucosal surfaces.

First-Passage Time to Clear the Way for Receptor-Ligand Binding in a Crowded Environment.

Certain biological reactions, such as receptor-ligand binding at cell-cell interfaces and macromolecules binding to biopolymers, require many smaller molecules crowding a reaction site to be cleared. Examples include the T-cell interface, a key player in immunological information processing. Diffusion sets a limit for such cavitation to occur spontaneously, thereby defining a time scale below which active mechanisms must take over. We consider N independent diffusing particles in a closed domain, containing a subregion with N_{0} particles, on average. We investigate the time until the subregion is empty, allowing a subsequent reaction to proceed. The first-passage time is computed using an efficient exact simulation algorithm and an asymptotic approximation in the limit that cavitation is rare. In this limit, we find that the mean first-passage time is subexponential, T∝e^{N_{0}}/N_{0}^{2}. For the case of T-cell receptors, we find that stochastic cavitation is exceedingly slow, 10^{9} s at physiological densities; however, it can be accelerated to occur within 5 s with only a fourfold dilution.

Stochastic hybrid model of spontaneous dendritic NMDA spikes.

Following recent advances in imaging techniques and methods of dendritic stimulation, active voltage spikes have been observed in thin dendritic branches of excitatory pyramidal neurons, where the majority of synapses occur. The generation of these dendritic spikes involves both Na(+) ion channels and M-methyl-D-aspartate receptor (NMDAR) channels. During strong stimulation of a thin dendrite, the resulting high levels of glutamate, the main excitatory neurotransmitter in the central nervous system and an NMDA agonist, modify the current-voltage (I-V) characteristics of an NMDAR so that it behaves like a voltage-gated Na(+) channel. Hence, the NMDARs can fire a regenerative dendritic spike, just as Na(+) channels support the initiation of an action potential following membrane depolarization. However, the duration of the dendritic spike is of the order 100 ms rather than 1 ms, since it involves slow unbinding of glutamate from NMDARs rather than activation of hyperpolarizing K(+) channels. It has been suggested that dendritic NMDA spikes may play an important role in dendritic computations and provide a cellular substrate for short-term memory. In this paper, we consider a stochastic, conductance-based model of dendritic NMDA spikes, in which the noise originates from the stochastic opening and closing of a finite number of Na(+) and NMDA receptor ion channels. The resulting model takes the form of a stochastic hybrid system, in which membrane voltage evolves according to a piecewise deterministic dynamics that is coupled to a jump Markov process describing the opening and closing of the ion channels. We formulate the noise-induced initiation and termination of a dendritic spike in terms of a first-passage time problem, under the assumption that glutamate unbinding is negligible, which we then solve using a combination of WKB methods and singular perturbation theory. Using a stochastic phase-plane analysis we then extend our analysis to take proper account of the combined effects of glutamate unbinding and noise on the termination of a spike.

Effects of moderate noise on a limit cycle oscillator: counterrotation and bistability.

The effects of noise on the dynamics of nonlinear systems is known to lead to many counterintuitive behaviors. Using simple planar limit cycle oscillators, we show that the addition of moderate noise leads to qualitatively different dynamics. In particular, the system can appear bistable, rotate in the opposite direction of the deterministic limit cycle, or cease oscillating altogether. Utilizing standard techniques from stochastic calculus and recently developed stochastic phase reduction methods, we elucidate the mechanisms underlying the different dynamics and verify our analysis with the use of numerical simulations. Last, we show that similar bistable behavior is found when moderate noise is applied to the FitzHugh-Nagumo model, which is more commonly used in biological applications.

Metastable behavior in Markov processes with internal states.

A perturbation framework is developed to analyze metastable behavior in stochastic processes with random internal and external states. The process is assumed to be under weak noise conditions, and the case where the deterministic limit is bistable is considered. A general analytical approximation is derived for the stationary probability density and the mean switching time between metastable states, which includes the pre exponential factor. The results are illustrated with a model of gene expression that displays bistable switching. In this model, the external state represents the number of protein molecules produced by a hypothetical gene. Once produced, a protein is eventually degraded. The internal state represents the activated or unactivated state of the gene; in the activated state the gene produces protein more rapidly than the unactivated state. The gene is activated by a dimer of the protein it produces so that the activation rate depends on the current protein level. This is a well studied model, and several model reductions and diffusion approximation methods are available to analyze its behavior. However, it is unclear if these methods accurately approximate long-time metastable behavior (i.e., mean switching time between metastable states of the bistable system). Diffusion approximations are generally known to fail in this regard.

Breakdown of fast-slow analysis in an excitable system with channel noise.

We consider a stochastic version of an excitable system based on the Morris-Lecar model of a neuron, in which the noise originates from stochastic sodium and potassium ion channels opening and closing. One can analyze neural excitability in the deterministic model by using a separation of time scales involving a fast voltage variable and a slow recovery variable, which represents the fraction of open potassium channels. In the stochastic setting, spontaneous excitation is initiated by ion channel noise. If the recovery variable is constant during initiation, the spontaneous activity rate can be calculated using Kramer's rate theory. The validity of this assumption in the stochastic model is examined using a systematic perturbation analysis. We find that, in most physically relevant cases, this assumption breaks down, requiring an alternative to Kramer's theory for excitable systems with one deterministic fixed point. We also show that an exit time problem can be formulated in an excitable system by considering maximum likelihood trajectories of the stochastic process.

A computational model for the cancer field effect.

Introduction: The Cancer Field Effect describes an area of pre-cancerous cells that results from continued exposure to carcinogens. Cells in the cancer field can easily develop into cancer. Removal of the main tumor mass might leave the cancer field behind, increasing risk of recurrence. Methods: The model we propose for the cancer field effect is a hybrid cellular automaton (CA), which includes a multi-layer perceptron (MLP) to compute the effects of the carcinogens on the gene expression of the genes related to cancer development. We use carcinogen interactions that are typically associated with smoking and alcohol consumption and their effect on cancer fields of the tongue. Results: Using simulations we support the understanding that tobacco smoking is a potent carcinogen, which can be reinforced by alcohol consumption. The effect of alcohol alone is significantly less than the effect of tobacco. We further observe that pairing tumor excision with field removal delays recurrence compared to tumor excision alone. We track cell lineages and find that, in most cases, a polyclonal field develops, where the number of distinct cell lineages decreases over time as some lineages become dominant over others. Finally, we find tumor masses rarely form via monoclonal origin.

Cooperative motility, force generation and mechanosensing in a foraging non-photosynthetic diatom.

Diatoms are ancestrally photosynthetic microalgae. However, some underwent a major evolutionary transition, losing photosynthesis to become obligate heterotrophs. The molecular and physiological basis for this transition is unclear. Here, we isolate and characterize new strains of non-photosynthetic diatoms from the coastal waters of Singapore. These diatoms occupy diverse ecological niches and display glucose-mediated catabolite repression, a classical feature of bacterial and fungal heterotrophs. Live-cell imaging reveals deposition of secreted extracellular polymeric substance (EPS). Diatoms moving on pre-existing EPS trails (runners) move faster than those laying new trails (blazers). This leads to cell-to-cell coupling where runners can push blazers to make them move faster. Calibrated micropipettes measure substantial single-cell pushing forces, which are consistent with high-order myosin motor cooperativity. Collisions that impede forward motion induce reversal, revealing navigation-related force sensing. Together, these data identify aspects of metabolism and motility that are likely to promote and underpin diatom heterotrophy.

Isolating intrinsic noise sources in a stochastic genetic switch.

The stochastic mutual repressor model is analysed using perturbation methods. This simple model of a gene circuit consists of two genes and three promotor states. Either of the two protein products can dimerize, forming a repressor molecule that binds to the promotor of the other gene. When the repressor is bound to a promotor, the corresponding gene is not transcribed and no protein is produced. Either one of the promotors can be repressed at any given time or both can be unrepressed, leaving three possible promotor states. This model is analysed in its bistable regime in which the deterministic limit exhibits two stable fixed points and an unstable saddle, and the case of small noise is considered. On small timescales, the stochastic process fluctuates near one of the stable fixed points, and on large timescales, a metastable transition can occur, where fluctuations drive the system past the unstable saddle to the other stable fixed point. To explore how different intrinsic noise sources affect these transitions, fluctuations in protein production and degradation are eliminated, leaving fluctuations in the promotor state as the only source of noise in the system. The process without protein noise is then compared to the process with weak protein noise using perturbation methods and Monte Carlo simulations. It is found that some significant differences in the random process emerge when the intrinsic noise source is removed.

Effects of demographic noise on the synchronization of a metapopulation in a fluctuating environment.

We use the theory of noise-induced phase synchronization to analyze the effects of demographic noise on the synchronization of a metapopulation of predator-prey systems within a fluctuating environment (Moran effect). Treating each local predator-prey population as a stochastic urn model, we derive a Langevin equation for the stochastic dynamics of the metapopulation. Assuming each local population acts as a limit cycle oscillator in the deterministic limit, we use phase reduction and averaging methods to derive the steady-state probability density for pairwise phase differences between oscillators, which is then used to determine the degree of synchronization of the metapopulation.

Personalized Virus Load Curves for Acute Viral Infections.

We introduce an explicit function that describes virus-load curves on a patient-specific level. This function is based on simple and intuitive model parameters. It allows virus load analysis of acute viral infections without solving a full virus load dynamic model. We validate our model on data from mice influenza A, human rhinovirus data, human influenza A data, and monkey and human SARS-CoV-2 data. We find wide distributions for the model parameters, reflecting large variability in the disease outcomes between individuals. Further, we compare the virus load function to an established target model of virus dynamics, and we provide a new way to estimate the exponential growth rates of the corresponding infection phases. The virus load function, the target model, and the exponential approximations show excellent fits for the data considered. Our virus-load function offers a new way to analyze patient-specific virus load data, and it can be used as input for higher level models for the physiological effects of a virus infection, for models of tissue damage, and to estimate patient risks.

HSP70 chaperones RNA-free TDP-43 into anisotropic intranuclear liquid spherical shells.

The RNA binding protein TDP-43 forms intranuclear or cytoplasmic aggregates in age-related neurodegenerative diseases. In this study, we found that RNA binding-deficient TDP-43 (produced by neurodegeneration-causing mutations or posttranslational acetylation in its RNA recognition motifs) drove TDP-43 demixing into intranuclear liquid spherical shells with liquid cores. These droplets, which we named "anisosomes", have shells that exhibit birefringence, thus indicating liquid crystal formation. Guided by mathematical modeling, we identified the primary components of the liquid core to be HSP70 family chaperones, whose adenosine triphosphate (ATP)-dependent activity maintained the liquidity of shells and cores. In vivo proteasome inhibition within neurons, to mimic aging-related reduction of proteasome activity, induced TDP-43-containing anisosomes. These structures converted to aggregates when ATP levels were reduced. Thus, acetylation, HSP70, and proteasome activities regulate TDP-43 phase separation and conversion into a gel or solid phase.

Local synaptic signaling enhances the stochastic transport of motor-driven cargo in neurons.

The tug-of-war model of motor-driven cargo transport is formulated as an intermittent trapping process. An immobile trap, representing the cellular machinery that sequesters a motor-driven cargo for eventual use, is located somewhere within a microtubule track. A particle representing a motor-driven cargo that moves randomly with a forward bias is introduced at the beginning of the track. The particle switches randomly between a fast moving phase and a slow moving phase. When in the slow moving phase, the particle can be captured by the trap. To account for the possibility that the particle avoids the trap, an absorbing boundary is placed at the end of the track. Two local signaling mechanisms--intended to improve the chances of capturing the target--are considered by allowing the trap to affect the tug-of-war parameters within a small region around itself. The first is based on a localized adenosine triphosphate (ATP) concentration gradient surrounding a synapse, and the second is based on a concentration of tau--a microtubule-associated protein involved in Alzheimer's disease--coating the microtubule near the synapse. It is shown that both mechanisms can lead to dramatic improvements in the capture probability, with a minimal increase in the mean capture time. The analysis also shows that tau can cause a cargo to undergo random oscillations, which could explain some experimental observations.

Quasi-steady state reduction of molecular motor-based models of directed intermittent search.

We present a quasi-steady state reduction of a linear reaction-hyperbolic master equation describing the directed intermittent search for a hidden target by a motor-driven particle moving on a one-dimensional filament track. The particle is injected at one end of the track and randomly switches between stationary search phases and mobile nonsearch phases that are biased in the anterograde direction. There is a finite possibility that the particle fails to find the target due to an absorbing boundary at the other end of the track. Such a scenario is exemplified by the motor-driven transport of vesicular cargo to synaptic targets located on the axon or dendrites of a neuron. The reduced model is described by a scalar Fokker-Planck (FP) equation, which has an additional inhomogeneous decay term that takes into account absorption by the target. The FP equation is used to compute the probability of finding the hidden target (hitting probability) and the corresponding conditional mean first passage time (MFPT) in terms of the effective drift velocity V, diffusivity D, and target absorption rate λ of the random search. The quasi-steady state reduction determines V, D, and λ in terms of the various biophysical parameters of the underlying motor transport model. We first apply our analysis to a simple 3-state model and show that our quasi-steady state reduction yields results that are in excellent agreement with Monte Carlo simulations of the full system under physiologically reasonable conditions. We then consider a more complex multiple motor model of bidirectional transport, in which opposing motors compete in a "tug-of-war", and use this to explore how ATP concentration might regulate the delivery of cargo to synaptic targets.

Spatial heterogeneity of the cytosol revealed by machine learning-based 3D particle tracking.

The spatial structure and physical properties of the cytosol are not well understood. Measurements of the material state of the cytosol are challenging due to its spatial and temporal heterogeneity. Recent development of genetically encoded multimeric nanoparticles (GEMs) has opened up study of the cytosol at the length scales of multiprotein complexes (20-60 nm). We developed an image analysis pipeline for 3D imaging of GEMs in the context of large, multinucleate fungi where there is evidence of functional compartmentalization of the cytosol for both the nuclear division cycle and branching. We applied a neural network to track particles in 3D and then created quantitative visualizations of spatially varying diffusivity. Using this pipeline to analyze spatial diffusivity patterns, we found that there is substantial variability in the properties of the cytosol. We detected zones where GEMs display especially low diffusivity at hyphal tips and near some nuclei, showing that the physical state of the cytosol varies spatially within a single cell. Additionally, we observed significant cell-to-cell variability in the average diffusivity of GEMs. Thus, the physical properties of the cytosol vary substantially in time and space and can be a source of heterogeneity within individual cells and across populations.

LPS-binding IgG arrests actively motile Salmonella Typhimurium in gastrointestinal mucus.

The gastrointestinal (GI) mucosa is coated with a continuously secreted mucus layer that serves as the first line of defense against invading enteric bacteria. We have previously shown that antigen-specific immunoglobulin G (IgG) can immobilize viruses in both human airway and genital mucus secretions through multiple low-affinity bonds between the array of virion-bound IgG and mucins, thereby facilitating their rapid elimination from mucosal surfaces and preventing mucosal transmission. Nevertheless, it remains unclear whether weak IgG-mucin crosslinks could reinforce the mucus barrier against the permeation of bacteria driven by active flagella beating, or in predominantly MUC2 mucus gel. Here, we performed high-resolution multiple particle tracking to capture the real-time motion of hundreds of individual fluorescent Salmonella Typhimurium in fresh, undiluted GI mucus from Rag1-/- mice, and analyzed the motion using a hidden Markov model framework. In contrast to control IgG, the addition of anti-lipopolysaccharide IgG to GI mucus markedly reduced the progressive motility of Salmonella by lowering the swim speed and retaining individual bacteria in an undirected motion state. Effective crosslinking of Salmonella to mucins was dependent on Fc N-glycans. Our findings implicate IgG-mucin crosslinking as a broadly conserved function that reduces mucous penetration of both bacterial and viral pathogens.

Directed intermittent search for a hidden target on a dendritic tree.

Motivated by experimental observations of active (motor-driven) intracellular transport in neuronal dendrites, we analyze a stochastic model of directed intermittent search on a tree network. A particle injected from the cell body or soma into the primary branch of the dendritic tree randomly switches between a stationary search phase and a mobile nonsearch phase that is biased in the forward direction. A (synaptic) target is presented somewhere within the tree, which the particle can locate if it is within a certain range and in the searching phase. We approximate the moment generating function using Green's function methods. The moment generating function is then used to compute the hitting probability and conditional mean first passage time to the target. We show that in contrast to a previously explored finite interval case, there is a range of parameters for which a bidirectional search strategy is more efficient than a unidirectional one in finding the target.