Reconstruction of Cell Focal Adhesions using Physical Constraints and Compressive Regularization

We develop a method to reconstruct, from measured displacements of an underlying elastic substrate, the spatially dependent forces that cells or tissues impart on it. Given newly available high-resolution images of substrate displacements, it is desirable to be able to reconstruct small-scale, compactly supported focal adhesions that are often localized and exist only within the footprint of a cell. In addition to the standard quadratic data mismatch terms that define least-squares fitting, we motivate a regularization term in the objective function that penalizes vectorial invariants of the reconstructed surface stress while preserving boundaries. We solve this inverse problem by providing a numerical method for setting up a discretized inverse problem that is solvable by standard convex optimization techniques. By minimizing the objective function subject to a number of important physically motivated constraints, we are able to efficiently reconstruct stress fields with localized structure from simulated and experimental substrate displacements. Our method incorporates the exact solution for a stress tensor accurate to first-order finite differences and motivates the use of distance-based cutoffs for data inclusion and problem sparsification.

High-Speed "4D" Computational Microscopy of Bacterial Surface Motility

Bacteria exhibit surface motility modes that play pivotal roles in early-stage biofilm community development, such as type IV pili-driven "twitching" motility and flagellum-driven "spinning" and "swarming" motility. Appendage-driven motility is controlled by molecular motors, and analysis of surface motility behavior is complicated by its inherently 3D nature, the speed of which is too fast for confocal microscopy to capture. Here, we combine electromagnetic field computation and statistical image analysis to generate 3D movies close to a surface at 5 ms time resolution using conventional inverted microscopes. We treat each bacterial cell as a spherocylindrical lens and use finite element modeling to solve Maxwell's equations and compute the diffracted light intensities associated with different angular orientations of the bacterium relative to the surface. By performing cross-correlation calculations between measured 2D microscopy images and a library of computed light intensities, we demonstrate that near-surface 3D movies of Pseudomonas aeruginosa translational and rotational motion are possible at high temporal resolution. Comparison between computational reconstructions and detailed hydrodynamic calculations reveals that P. aeruginosa act like low Reynolds number spinning tops with unstable orbits, driven by a flagellum motor with a torque output of ∼2 pN μm. Interestingly, our analysis reveals that P. aeruginosa can undergo complex flagellum-driven dynamical behavior, including precession, nutation, and an unexpected taxonomy of surface motility mechanisms, including upright-spinning bacteria that diffuse laterally across the surface, and horizontal bacteria that follow helicoidal trajectories and exhibit superdiffusive movements parallel to the surface.

Bidirectional Retroviral Integration Site PCR Methodology and Quantitative Data Analysis Workflow

Integration Site (IS) assays are a critical component of the study of retroviral integration sites and their biological significance. In recent retroviral gene therapy studies, IS assays, in combination with next-generation sequencing, have been used as a cell-tracking tool to characterize clonal stem cell populations sharing the same IS. For the accurate comparison of repopulating stem cell clones within and across different samples, the detection sensitivity, data reproducibility, and high-throughput capacity of the assay are among the most important assay qualities. This work provides a detailed protocol and data analysis workflow for bidirectional IS analysis. The bidirectional assay can simultaneously sequence both upstream and downstream vector-host junctions. Compared to conventional unidirectional IS sequencing approaches, the bidirectional approach significantly improves IS detection rates and the characterization of integration events at both ends of the target DNA. The data analysis pipeline described here accurately identifies and enumerates identical IS sequences through multiple steps of comparison that map IS sequences onto the reference genome and determine sequencing errors. Using an optimized assay procedure, we have recently published the detailed repopulation patterns of thousands of Hematopoietic Stem Cell (HSC) clones following transplant in rhesus macaques, demonstrating for the first time the precise time point of HSC repopulation and the functional heterogeneity of HSCs in the primate system. The following protocol describes the step-by-step experimental procedure and data analysis workflow that accurately identifies and quantifies identical IS sequences.

Quantifying the Sensitivity of HIV-1 Viral Entry to Receptor and Coreceptor Expression

Infection by many viruses begins with fusion of viral and cellular lipid membranes, followed by entry of viral contents into the target cell and ultimately, after many biochemical steps, integration of viral DNA into that of the host cell. The early steps of membrane fusion and viral capsid entry are mediated by adsorption to the cell surface, and receptor and coreceptor binding. HIV-1 specifically targets CD4+ helper T-cells of the human immune system and binds to the receptor CD4 and coreceptor CCR5 before fusion is initiated. Previous experiments have been performed using a cell line (293-Affinofile) in which the expressions of CD4 and CCR5 concentration were independently controlled. After exposure to HIV-1 of various strains, the resulting infectivity was measured through the fraction of infected cells. To design and evaluate the effectiveness of drug therapies that target the inhibition of the entry processes, an accurate functional relationship between the CD4/CCR5 concentrations and infectivity is desired in order to more quantitatively analyze experimental data. We propose three kinetic models describing the possible mechanistic processes involved in HIV entry and fit their predictions to infectivity measurements, contrasting and comparing different outcomes. Our approach allows interpretation of the clustering of infectivity of different strains of HIV-1 in the space of mechanistic kinetic parameters. Our model fitting also allows inference of nontrivial stoichiometries of receptor and coreceptor binding and provides a framework through which to quantitatively investigate the effectiveness of fusion inhibitors and neutralizing antibodies.

Bayesian Uncertainty Quantification for Bond Energies and Mobilities Using Path Integral Analysis

Dynamic single-molecule force spectroscopy is often used to distort bonds. The resulting responses, in the form of rupture forces, work applied, and trajectories of displacements, are used to reconstruct bond potentials. Such approaches often rely on simple parameterizations of one-dimensional bond potentials, assumptions on equilibrium starting states, and/or large amounts of trajectory data. Parametric approaches typically fail at inferring complicated bond potentials with multiple minima, while piecewise estimation may not guarantee smooth results with the appropriate behavior at large distances. Existing techniques, particularly those based on work theorems, also do not address spatial variations in the diffusivity that may arise from spatially inhomogeneous coupling to other degrees of freedom in the macromolecule. To address these challenges, we develop a comprehensive empirical Bayesian approach that incorporates data and regularization terms directly into a path integral. All experimental and statistical parameters in our method are estimated directly from the data. Upon testing our method on simulated data, our regularized approach requires less data and allows simultaneous inference of both complex bond potentials and diffusivity profiles. Crucially, we show that the accuracy of the reconstructed bond potential is sensitive to the spatially varying diffusivity and accurate reconstruction can be expected only when both are simultaneously inferred. Moreover, after providing a means for self-consistently choosing regularization parameters from data, we derive posterior probability distributions, allowing for uncertainty quantification.

A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations

We develop mathematical models describing the evolution of stochastic age-structured populations. After reviewing existing approaches, we formulate a complete kinetic framework for age-structured interacting populations undergoing birth, death and fission processes in spatially dependent environments. We define the full probability density for the population-size age chart and find results under specific conditions. Connections with more classical models are also explicitly derived. In particular, we show that factorial moments for non-interacting processes are described by a natural generalization of the McKendrick-von Foerster equation, which describes mean-field deterministic behavior. Our approach utilizes mixed-type, multidimensional probability distributions similar to those employed in the study of gas kinetics and with terms that satisfy BBGKY-like equation hierarchies.

Swarming in viscous fluids: Three-dimensional patterns in swimmer- and force-induced flows

We derive a three-dimensional theory of self-propelled particle swarming in a viscous fluid environment. Our model predicts emergent collective behavior that depends critically on fluid opacity, mechanism of self-propulsion, and type of particle-particle interaction. In "clear fluids" swimmers have full knowledge of their surroundings and can adjust their velocities with respect to the lab frame, while in "opaque fluids" they control their velocities only in relation to the local fluid flow. We also show that "social" interactions that affect only a particle's propensity to swim towards or away from neighbors induces a flow field that is qualitatively different from the long-ranged flow fields generated by direct "physical" interactions. The latter can be short-ranged but lead to much longer-ranged fluid-mediated hydrodynamic forces, effectively amplifying the range over which particles interact. These different fluid flows conspire to profoundly affect swarm morphology, kinetically stabilizing or destabilizing swarm configurations that would arise in the absence of fluid. Depending upon the overall interaction potential, the mechanism of swimming ( e.g., pushers or pullers), and the degree of fluid opaqueness, we discover a number of new collective three-dimensional patterns including flocks with prolate or oblate shapes, recirculating pelotonlike structures, and jetlike fluid flows that entrain particles mediating their escape from the center of mill-like structures. Our results reveal how the interplay among general physical elements influence fluid-mediated interactions and the self-organization, mobility, and stability of new three-dimensional swarms and suggest how they might be used to kinetically control their collective behavior.

Onset, timing, and exposure therapy of stress disorders: mechanistic insight from a mathematical model of oscillating neuroendocrine dynamics

BACKGROUND

The hypothalamic-pituitary-adrenal (HPA) axis is a neuroendocrine system that regulates numerous physiological processes. Disruptions in the activity of the HPA axis are correlated with stress-related diseases such as post-traumatic stress disorder (PTSD) and major depressive disorder. In this paper, we characterize "normal" and "diseased" states of the HPA axis as basins of attraction of a dynamical system describing the inhibition of peptide hormones such as corticotropin-releasing hormone (CRH) and adrenocorticotropic hormone (ACTH) by circulating glucocorticoids such as cortisol (CORT).

RESULTS

In addition to including key physiological features such as ultradian oscillations in cortisol levels and self-upregulation of CRH neuron activity, our model distinguishes the relatively slow process of cortisol-mediated CRH biosynthesis from rapid trans-synaptic effects that regulate the CRH secretion process. We show that the slow component of the negative feedback allows external stress-induced reversible transitions between "normal" and "diseased" states in novel intensity-, duration-, and timing-dependent ways.

CONCLUSION

Our two-step negative feedback model suggests a mechanism whereby exposure therapy of stress disorders such as PTSD may act to normalize downstream dysregulation of the HPA axis. Our analysis provides a causative rationale for improving treatments and guiding the design of new protocols.

Kinetic theory of age-structured stochastic birth-death processes

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov--Born--Green--Kirkwood--Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution.

Mechanisms of blood homeostasis: lineage tracking and a neutral model of cell populations in rhesus macaques

Background

How a potentially diverse population of hematopoietic stem cells (HSCs) differentiates and proliferates to supply more than 10¹¹ mature blood cells every day in humans remains a key biological question. We investigated this process by quantitatively analyzing the clonal structure of peripheral blood that is generated by a population of transplanted lentivirus-marked HSCs in myeloablated rhesus macaques. Each transplanted HSC generates a clonal lineage of cells in the peripheral blood that is then detected and quantified through deep sequencing of the viral vector integration sites (VIS) common within each lineage. This approach allowed us to observe, over a period of 4-12 years, hundreds of distinct clonal lineages.

Results

While the distinct clone sizes varied by three orders of magnitude, we found that collectively, they form a steady-state clone size-distribution with a distinctive shape. Steady-state solutions of our model show that the predicted clone size-distribution is sensitive to only two combinations of parameters. By fitting the measured clone size-distributions to our mechanistic model, we estimate both the effective HSC differentiation rate and the number of active HSCs.

Conclusions

Our concise mathematical model shows how slow HSC differentiation followed by fast progenitor growth can be responsible for the observed broad clone size-distribution. Although all cells are assumed to be statistically identical, analogous to a neutral theory for the different clone lineages, our mathematical approach captures the intrinsic variability in the times to HSC differentiation after transplantation.

Electronic supplementary material

The online version of this article (doi:10.1186/s12915-015-0191-8) contains supplementary material, which is available to authorized users.

Influence of the disc-fovea angle on limits of RNFL variability and glaucoma discrimination

PURPOSE

To determine factors affecting the disc-fovea angle (DFA), and to test the hypotheses that adjusting for DFA improves limits of retinal nerve fiber layer (RNFL) variability in normal subjects or enhances performance of RNFL measures for glaucoma detection.

METHODS

Disc-fovea angle was measured on scanning laser ophthalmoscope fundus images from 170 eyes (110 normal and glaucoma subjects). The DFA measurements were repeated in 24 eyes. The relationship between DFA and various anatomic variables was explored. Main outcome measures were changes in 95% RNFL prediction limits or glaucoma discrimination after adjusting for DFA. We also explored the angle between temporal raphe and horizontal meridian in 19 eyes with nasal field defects limited to one hemifield.

RESULTS

Average mean deviation and DFA were -0.1 (±1.2) dB and -6.6° (±3.4°) and -4.1 (±3.3) dB and -7.9° (±3.9°) in the control and glaucoma groups, respectively (P < 0.001 and = 0.029). The average difference between DFA repeat measurements was 2.0° (±1.8°). Predictors for DFA were female sex (P = 0.004), smaller disc area (P = 0.006), and glaucoma diagnosis (P = 0.019). The absolute change in sectoral RNFL thickness was 6.1 (±3.9) and 4.6 (±3.1) μm in control and glaucoma subjects, respectively. Retinal nerve fiber layer prediction limits improved in 5, 9, and 10 o'clock sectors (P < 0.02). Discrimination ability for the best-performing RNFL sector did not improve (P = 0.936). The average angle between temporal raphe and horizontal meridian was 0.8° (±0.8°).

CONCLUSIONS

Disc-fovea angle measurements demonstrated fair intersession repeatability. While adjusting for DFA improved RNFL prediction limits in some sectors, it did not enhance glaucoma detection.

Distinct HIV-1 entry phenotypes are associated with transmission, subtype specificity, and resistance to broadly neutralizing antibodies

BACKGROUND

The efficiency of CD4/CCR5 mediated HIV-1 entry has important implications for pathogenesis and transmission. The HIV-1 receptor affinity profiling (Affinofile) system analyzes and quantifies the infectivity of HIV-1 envelopes (Envs) across a spectrum of CD4/CCR5 expression levels and distills these data into a set of Affinofile metrics. The Affinofile system has shed light on how differential CD4/CCR5 usage efficiencies contributes to an array of Env phenotypes associated with cellular tropism, viral pathogenesis, and CCR5 inhibitor resistance. To facilitate more rapid, convenient, and robust analysis of HIV-1 entry phenotypes, we engineered a reporter Affinofile system containing a Tat- and Rev-dependent Gaussia luciferase-eGFP-Reporter (GGR) that is compatible with the use of pseudotyped or replication competent viruses with or without a virally encoded reporter gene. This GGR Affinofile system enabled a higher throughput characterization of CD4/CCR5 usage efficiencies associated with differential Env phenotypes.

RESULTS

We first validated our GGR Affinofile system on isogenic JR-CSF Env mutants that differ in their affinity for CD4 and/or CCR5. We established that their GGR Affinofile metrics reflected their differential entry phenotypes on primary PBMCs and CD4+ T-cell subsets. We then applied GGR Affinofile profiling to reveal distinct entry phenotypes associated with transmission, subtype specificity, and resistance to broadly neutralizing antibodies (BNAbs). First, we profiled a panel of reference subtype B transmitted/founder (T/F) and chronic Envs (n = 12) by analyzing the infectivity of each Env across 25 distinct combinations of CD4/CCR5 expression levels. Affinofile metrics revealed that at low CCR5 levels, our panel of subtype B T/F Envs was more dependent on high levels of CD4 for HIV-1 entry compared to chronic Envs. Next, we analyzed a reference panel of 28 acute/early subtype A-D Envs, and noted that subtype C Envs could be distinguished from the other subtypes based on their infectivity profiles and relevant Affinofile metrics. Lastly, mutations known to confer resistance to VRC01 or PG6/PG19 BNAbs, when engineered into subtypes A-D Envs, resulted in significantly decreased CD4/CCR5 usage efficiency.

CONCLUSIONS

GGR Affinofile profiling reveals pathophysiological phenotypes associated with varying HIV-1 entry efficiencies, and highlight the fitness costs associated with resistance to some broadly neutralizing antibodies.

Combinatoric analysis of heterogeneous stochastic self-assembly

We analyze a fully stochastic model of heterogeneous nucleation and self-assembly in a closed system with a fixed total particle number M, and a fixed number of seeds Ns. Each seed can bind a maximum of N particles. A discrete master equation for the probability distribution of the cluster sizes is derived and the corresponding cluster concentrations are found using kinetic Monte-Carlo simulations in terms of the density of seeds, the total mass, and the maximum cluster size. In the limit of slow detachment, we also find new analytic expressions and recursion relations for the cluster densities at intermediate times and at equilibrium. Our analytic and numerical findings are compared with those obtained from classical mass-action equations and the discrepancies between the two approaches analyzed.

Iterative graph cuts for image segmentation with a nonlinear statistical shape prior

Shape-based regularization has proven to be a useful method for delineating objects within noisy images where one has prior knowledge of the shape of the targeted object. When a collection of possible shapes is available, the specification of a shape prior using kernel density estimation is a natural technique. Unfortunately, energy functionals arising from kernel density estimation are of a form that makes them impossible to directly minimize using efficient optimization algorithms such as graph cuts. Our main contribution is to show how one may recast the energy functional into a form that is minimizable iteratively and efficiently using graph cuts.

Measurement of the optic disc vertical tilt angle with spectral-domain optical coherence tomography and influencing factors

PURPOSE

To report a novel method for measuring the vertical tilt angle of the optic nerve (ON) head and to investigate the associated factors.

DESIGN

Cross-sectional diagnostic study.

METHODS

One hundred and twelve normal, glaucomatous, and glaucoma suspect eyes (99 patients) were enrolled in this study. Subjects underwent a full eye examination, biometry, and spectral-domain optical coherence tomography (SDOCT). The vertical tilt angle was measured on high-resolution cross-sectional SDOCT images passing through the ON head and foveal centers using the inner edges of the Bruch membrane opening as the reference plane. The correlation between the vertical tilt angle with the ovality index and the potential associated factors was estimated with univariate and multivariate linear regression analyses.

RESULTS

The median (interquartile range, [IQR]) axial length and visual field mean deviation were 24.5 (23.8-25.3) mm and -0.9 (-2.76 to 0.26) dB. The median (IQR) tilt angle was 3.5 (1.2-11.2) degrees. There was a moderate correlation between the ovality index and tilt angle (Spearman ρ = 0.351; P < .001). In univariate analyses, axial length, spherical equivalent, and mean deviation were correlated with the tilt angle (P = .002, P = .011, and P = .013, respectively). Axial length, mean deviation, and their interaction showed a statistically significant correlation with the tilt angle in multivariate analyses (P = .044 for axial length, P = .039 for mean deviation, and P = .028 for their interaction).

CONCLUSIONS

We describe a new method for measuring the ON head vertical tilt angle with high-resolution SDOCT imaging. The ovality index demonstrated only a moderate correlation with the tilt angle measurements and hence is not a good proxy measure for the vertical ON head tilt angle. Axial length and visual field mean deviation are the main factors associated with the ON head vertical tilt angle. The underlying basis for the relationship of vertical tilt angle and glaucoma severity should be further explored.

First passage times in homogeneous nucleation and self-assembly

Motivated by nucleation and molecular aggregation in physical, chemical, and biological settings, we present a thorough analysis of the general problem of stochastic self-assembly of a fixed number of identical particles in a finite volume. We derive the backward Kolmogorov equation (BKE) for the cluster probability distribution. From the BKE, we study the distribution of times it takes for a single maximal cluster to be completed, starting from any initial particle configuration. In the limits of slow and fast self-assembly, we develop analytical approaches to calculate the mean cluster formation time and to estimate the first assembly time distribution. We find, both analytically and numerically, that faster detachment can lead to a shorter mean time to first completion of a maximum-sized cluster. This unexpected effect arises from a redistribution of trajectory weights such that upon increasing the detachment rate, paths that take a shorter time to complete a cluster become more likely.

Affinofile profiling: how efficiency of CD4/CCR5 usage impacts the biological and pathogenic phenotype of HIV

HIV-1 envelope (Env) uses CD4 and a coreceptor (CCR5 and/or CXCR4) for viral entry. The efficiency of receptor/coreceptor mediated entry has important implications for HIV pathogenesis and transmission. The advent of CCR5 inhibitors in clinical use also underscores the need for quantitative and predictive tools that can guide therapeutic management. Historically, measuring the efficiency of CD4/CCR5 mediated HIV entry has relied on surrogate and relatively slow throughput assays that cannot adequately capture the full spectrum of Env phenotypes. In this review, we discuss the details of the Affinofile receptor affinity profiling system that has provided a quantitative and higher throughput method to characterize viral entry efficiency as a function of CD4 and CCR5 expression levels. We will then review how the Affinofile system has been used to reveal the distinct pathophysiological properties associated with Env entry phenotypes and discuss potential shortcomings of the current system.