The power of weak, transient interactions across biology: A paradigm of emergent behavior.

A growing list of diverse biological systems and their equally diverse functionalities provides realizations of a paradigm of emergent behavior. In each of these biological systems, pervasive ensembles of weak, short-lived, spatially local interactions act autonomously to convey functionalities at larger spatial and temporal scales. In this article, a range of diverse systems and functionalities are presented in a cursory manner with literature citations for further details. Then two systems and their properties are discussed in more detail: yeast chromosome biology and human respiratory mucus.

Machine learning-guided, big data-enabled, biomarker-based systems pharmacology: modeling the stochasticity of natural history and disease progression.

The incidence of systemic and metabolic co-morbidities increases with aging. The purpose was to investigate a novel paradigm for modeling the orchestrated changes in many disease-related biomarkers that occur during aging. A hybrid strategy that integrates machine learning and stochastic modeling was evaluated for modeling the long-term dynamics of biomarker systems. Bayesian networks (BN) were used to identify quantitative systems pharmacology (QSP)-like models for the inter-dependencies for three disease-related datasets of metabolic (MB), metabolic with leptin (MB-L), and cardiovascular (CVB) biomarkers from the NHANES database. Biomarker dynamics were modeled using discrete stochastic vector autoregression (VAR) equations. BN were used to derive the topological order and connectivity of a data driven QSP model structure for inter-dependence of biomarkers across the lifespan. The strength and directionality of the connections in the QSP models were evaluated using bootstrapping. VAR models based on QSP model structures from BN were assessed for modeling biomarker system dynamics. BN-restricted VAR models of order 1 were identified as parsimonious and effective for characterizing biomarker system dynamics in the MB, MB-L and CVB datasets. Simulation of annual and triennial data for each biomarker provided good fits and predictions of the training and test datasets, respectively. The novel strategy harnesses machine learning to construct QSP model structures for inter-dependence of biomarkers. Stochastic modeling with the QSP models was effective for predicting the age-varying dynamics of disease-relevant biomarkers over the lifespan.

A new probabilistic method for quantifying n-dimensional ecological niches and niche overlap.

Considerable progress has been made in the development of statistical tools to quantify trophic relationships using stable isotope ratios, including tools that address size and overlap of isotopic niches. We build upon recent progress and propose a new probabilistic method for determining niche region and pairwise niche overlap that can be extended beyond two dimensions, provides directional estimates of niche overlap, accounts for species-specific distributions in niche space, and, unlike geometric methods, produces consistent and unique bivariate projections of multivariate data. We define the niche region (NR) as a given 95% (or user-defined a) probability region in multivariate space. Overlap is calculated as the probability that an individual from species A is found in the N(R) of species B. Uncertainty is accounted for in a Bayesian framework, and is the only aspect of the methodology that depends on sample size. Application is illustrated with three-dimensional stable isotope data, but practitioners could use any continuous indicator of ecological niche in any number of dimensions. We suggest that this represents an advance in our ability to quantify and compare ecological niches in a way that is more consistent with Hutchinson's concept of an "n-dimensional hypervolume".

Statistical Methods for Microrheology of Airway Mucus with Extreme Heterogeneity.

The mucus lining of the human airway epithelium contains two gel-forming mucins, MUC5B and MUC5AC. During progression of cystic fibrosis (CF), mucus hyper-concentrates as its mucin ratio changes, coinciding with formation of insoluble, dense mucus flakes. We explore rheological heterogeneity of this pathology with reconstituted mucus matching three stages of CF progression and particle-tracking of 200 nm and 1 micron diameter beads. We introduce statistical data analysis methods specific to low signal-to-noise data within flakes. Each bead time series is decomposed into: (i) a fractional Brownian motion (fBm) classifier of the pure time-series signal; (ii) high-frequency static and dynamic noise; and (iii) low-frequency deterministic drift. Subsequent analysis focuses on the denoised fBm classifier ensemble from each mucus sample and bead diameter. Every ensemble fails a homogeneity test, compelling clustering methods to assess levels of heterogeneity. The first binary level detects beads within vs. outside flakes. A second binary level detects within-flake bead signals that can vs. cannot be disentangled from the experimental noise floor. We show all denoised ensembles, within- and outside-flakes, fail a homogeneity test, compelling additional clustering; next, all clusters with sufficient data fail a homogeneity test. These levels of heterogeneity are consistent with outcomes from a stochastic phase-separation process, and dictate applying the generalized Stokes-Einstein relation to each bead per cluster per sample, then frequency-domain averaging to assess rheological heterogeneity. Flakes exhibit a spectrum of gel-like and sol-like domains, outside-flake solutions a spectrum of sol-like domains, painting a rheological signature of the phase-separation process underlying flake-burdened mucus.

Rigorous quantification of statistical significance of the COVID-19 lockdown effect on air quality: The case from ground-based measurements in Ontario, Canada.

Preliminary analyses of satellite measurements from around the world showed drops in nitrogen dioxide (NO2) coinciding with lockdowns due to the COVID-19 pandemic. Several studies found that these drops correlated with local decreases in transportation and/or industry. None of these studies, however, has rigorously quantified the statistical significance of these drops relative to natural meteorological variability and other factors that influence pollutant levels during similar time periods in previous years. Here, we develop a novel statistical protocol that accounts for seasonal variability, transboundary influences, and new factors such as COVID-19 restrictions in explaining trends in several pollutant levels at 16 ground-based measurement sites in Southern Ontario, Canada. We find statistically significant and temporary drops in NO2 (11 out 16 sites) and CO (all 4 sites) in April-December 2020, with pollutant levels 20% lower than in the previous three years. Fewer sites (2-3 out of 16) experienced statistically significant drops in O3 and PM2.5. The statistical significance testing framework developed here is the first of its kind applied to air quality data. It highlights the benefit of a rigorous assessment of statistical significance, should analyses of pollutant levels post COVID-19 lockdowns be used to inform policy decisions.

Predicting population level hip fracture risk: a novel hierarchical model incorporating probabilistic approaches and factor of risk principles.

Fall-related hip fractures are a major public health issue. While individual-level risk assessment tools exist, population-level predictive models could catalyze innovation in large-scale interventions. This study presents a hierarchical probabilistic model that predicts population-level hip fracture risk based on Factor of Risk (FOR) principles. Model validation demonstrated that FOR output aligned with a published dataset categorized by sex and hip fracture status. The model predicted normalized FOR for 100000 individuals simulating the Canadian older-adult population. Predicted hip fracture risk was higher for females (by an average of 38%), and increased with age (by15% per decade). Potential applications are discussed.

Diving into the consumer nutrition environment: A Bayesian spatial factor analysis of neighborhood restaurant environment.

Neighborhood restaurant environment (NRE) plays a vital role in shaping residents' eating behaviors. While NRE 'healthfulness' is a multi-facet concept, most studies evaluate it based only on restaurant type, thus largely ignoring variations of in-restaurant features. In the few studies that do account for such features, healthfulness scores are simply averaged over accessible restaurants, thereby concealing any uncertainty that attributed to neighborhoods' size or spatial correlation. To address these limitations, this paper presents a Bayesian Spatial Factor Analysis for assessing NRE healthfulness in the city of Kitchener, Canada. Several in-restaurant characteristics are included. By treating NRE healthfulness as a spatially correlated latent variable, the adopted modeling approach can: (i) identify specific indicators most relevant to NRE healthfulness, (ii) provide healthfulness estimates for neighborhoods without accessible restaurants, and (iii) readily quantify uncertainties in the healthfulness index. Implications of the analysis for intervention program development and community food planning are discussed.

Technological strategies to estimate and control diffusive passage times through the mucus barrier in mucosal drug delivery.

In mucosal drug delivery, two design goals are desirable: 1) insure drug passage through the mucosal barrier to the epithelium prior to drug removal from the respective organ via mucus clearance; and 2) design carrier particles to achieve a prescribed arrival time and drug uptake schedule at the epithelium. Both goals are achievable if one can control "one-sided" diffusive passage times of drug carrier particles: from deposition at the mucus interface, through the mucosal barrier, to the epithelium. The passage time distribution must be, with high confidence, shorter than the timescales of mucus clearance to maximize drug uptake. For 100nm and smaller drug-loaded nanoparticulates, as well as pure drug powders or drug solutions, diffusion is normal (i.e., Brownian) and rapid, easily passing through the mucosal barrier prior to clearance. Major challenges in quantitative control over mucosal drug delivery lie with larger drug-loaded nanoparticulates that are comparable to or larger than the pores within the mucus gel network, for which diffusion is not simple Brownian motion and typically much less rapid; in these scenarios, a timescale competition ensues between particle passage through the mucus barrier and mucus clearance from the organ. In the lung, as a primary example, coordinated cilia and air drag continuously transport mucus toward the trachea, where mucus and trapped cargo are swallowed into the digestive tract. Mucus clearance times in lung airways range from minutes to hours or significantly longer depending on deposition in the upper, middle, lower airways and on lung health, giving a wide time window for drug-loaded particle design to achieve controlled delivery to the epithelium. We review the physical and chemical factors (of both particles and mucus) that dictate particle diffusion in mucus, and the technological strategies (theoretical and experimental) required to achieve the design goals. First we describe an idealized scenario - a homogeneous viscous fluid of uniform depth with a particle undergoing passive normal diffusion - where the theory of Brownian motion affords the ability to rigorously specify particle size distributions to meet a prescribed, one-sided, diffusive passage time distribution. Furthermore, we describe how the theory of Brownian motion provides the scaling of one-sided diffusive passage times with respect to mucus viscosity and layer depth, and under reasonable caveats, one can also prescribe passage time scaling due to heterogeneity in viscosity and layer depth. Small-molecule drugs and muco-inert, drug-loaded carrier particles 100nm and smaller fall into this class of rigorously controllable passage times for drug delivery. Second we describe the prevalent scenarios in which drug-loaded carrier particles in mucus violate simple Brownian motion, instead exhibiting anomalous sub-diffusion, for which all theoretical control over diffusive passage times is lost, and experiments are prohibitive if not impossible to measure one-sided passage times. We then discuss strategies to overcome these roadblocks, requiring new particle-tracking experiments and emerging advances in theory and computation of anomalous, sub-diffusive processes that are necessary to predict and control one-sided particle passage times from deposition at the mucosal interface to epithelial uptake. We highlight progress to date, remaining hurdles, and prospects for achieving the two design goals for 200nm and larger, drug-loaded, non-dissolving, nanoparticulates.

Calibration of higher eigenmodes of cantilevers.

A method is presented for calibrating the higher eigenmodes (resonant modes) of atomic force microscopy cantilevers that can be performed prior to any tip-sample interaction. The method leverages recent efforts in accurately calibrating the first eigenmode by providing the higher-mode stiffness as a ratio to the first mode stiffness. A one-time calibration routine must be performed for every cantilever type to determine a power-law relationship between stiffness and frequency, which is then stored for future use on similar cantilevers. Then, future calibrations only require a measurement of the ratio of resonant frequencies and the stiffness of the first mode. This method is verified through stiffness measurements using three independent approaches: interferometric measurement, AC approach-curve calibration, and finite element analysis simulation. Power-law values for calibrating higher-mode stiffnesses are reported for several cantilever models. Once the higher-mode stiffnesses are known, the amplitude of each mode can also be calibrated from the thermal spectrum by application of the equipartition theorem.

A Multiresolution Method for Parameter Estimation of Diffusion Processes.

Diffusion process models are widely used in science, engineering and finance. Most diffusion processes are described by stochastic differential equations in continuous time. In practice, however, data is typically only observed at discrete time points. Except for a few very special cases, no analytic form exists for the likelihood of such discretely observed data. For this reason, parametric inference is often achieved by using discrete-time approximations, with accuracy controlled through the introduction of missing data. We present a new multiresolution Bayesian framework to address the inference difficulty. The methodology relies on the use of multiple approximations and extrapolation, and is significantly faster and more accurate than known strategies based on Gibbs sampling. We apply the multiresolution approach to three data-driven inference problems - one in biophysics and two in finance - one of which features a multivariate diffusion model with an entirely unobserved component.

Stochastic noise in atomic force microscopy.

Having reached the quantum and thermodynamic limits of detection, atomic force microscopy (AFM) experiments are routinely being performed at the fundamental limit of signal to noise. A critical understanding of the statistical properties of noise leads to more accurate interpretation of data, optimization of experimental protocols, advancements in instrumentation, and new measurement techniques. Furthermore, accurate simulation of cantilever dynamics requires knowledge of stochastic behavior of the system, as stochastic noise may exceed the deterministic signals of interest, and even dominate the outcome of an experiment. In this article, the power spectral density (PSD), used to quantify stationary stochastic processes, is introduced in the context of a thorough noise analysis of the light source used to detect cantilever deflections. The statistical properties of PSDs are then outlined for various stationary, nonstationary, and deterministic noise sources in the context of AFM experiments. Following these developments, a method for integrating PSDs to provide an accurate standard deviation of linear measurements is described. Lastly, a method for simulating stochastic Gaussian noise from any arbitrary power spectral density is presented. The result demonstrates that mechanical vibrations of the AFM can cause a logarithmic velocity dependence of friction and induce multiple slip events in the atomic stick-slip process, as well as predicts an artifactual temperature dependence of friction measured by AFM.