arXiv subjects

M. Gregory Forest

Publications and source records attributed to M. Gregory Forest.

13 recordsLinked to original sources

arXiv2024

Flagellum Pumping Efficacy in Shear-Thinning Viscoelastic Fluids

Microorganism motility often takes place within complex, viscoelastic fluid environments, e.g., sperm in cervicovaginal mucus and bacteria in biofilms. In such complex fluids, strains and stresses generated by the microorganism are stored and relax across a spectrum of length and time scales and the complex fluid can be driven out of its linear response regime. Phenomena not possible in viscous media thereby arise from feedback between the "swimmer" and the complex fluid, making swimming efficiency co-dependent on the propulsion mechanism and fluid properties. Here we parameterize a flagellar motor and filament properties together with elastic relaxation and nonlinear shear-thinning properties of the fluid in a computational immersed boundary model. We then explore swimming efficiency over this parameter space. One exemplary insight is that motor efficiency (measured by the volumetric flow rate) can be boosted vs.\ degraded by moderate vs.\ strong shear-thinning of the viscoelastic environment.

physics.flu-dyn↗

arXiv2024

Benchmarking the Immersed Boundary Method for Viscoelastic Flows

We present and analyze a series of benchmark tests regarding the application of the immersed boundary (IB) method to viscoelastic flows through and around non-trivial, stationary geometries. The IB method is widely used for the simulation of biological fluid dynamics and other modeling scenarios where a structure is immersed in a fluid. Although the IB method has been most commonly used to model systems with viscous incompressible fluids, it also can be applied to visoelastic fluids, and has enabled the study of a wide variety of dynamical problems including the settling of vesicles and the swimming of elastic filaments in fluids modeled by the Oldroyd-B constuitive equation. However, to date, relatively little work has explored the accuracy or convergence properties of the numerical scheme. Herein, we present benchmarking results for an IB solver applied to viscoelastic flows in and around non-trivial geometries using the idealized Oldroyd-B and more realistic, polymer-entanglement-based Rolie-Poly constitutive equations. We use two-dimensional numerical test cases along with results from rheology experiments to benchmark the IB method and compare it to more complex finite element and finite volume viscoelastic flow solvers. Additionally, we analyze different choices of regularized delta function and relative Lagrangian grid spacings which allow us to identify and recommend the key choices of these numerical parameters depending on the present flow regime.

physics.flu-dyn↗

arXiv2021

Existence and stability of kayaking orbits for nematic liquid crystals in simple shear flow

We use geometric methods of equivariant dynamical systems to address a long-standing open problem in the theory of nematic liquid crystals, namely a proof of the existence and asymptotic stability of kayaking periodic orbits for which the principal axis of orientation of the molecular field (the director) rotates around the vorticity axis in response to steady shear flow. With a small parameter attached to the symmetric part of the velocity gradient, the problem can be viewed as a symmetry-breaking bifurcation from an orbit of the rotation group~$\SO(3)$ that contains both logrolling (equilibrium) and tumbling (periodic rotation of the director within the plane of shear) regimes as well as a continuum of kayaking orbits. The results turn out to require expansion to second order in the perturbation parameter.

math.DS↗

arXiv2021

Rigidity percolation in random 3D rod systems

In composite materials composed of soft polymer matrix and stiff, high-aspect-ratio particles, the composite undergoes a transition in mechanical strength when the inclusion phase surpasses a critical density. This phenomenon (rheological or mechanical percolation) is well-known to occur in many composites at a critical density that exceeds the conductivity percolation threshold. Conductivity percolation occurs as a consequence of contact percolation, which refers to the conducting particles' formation of a connected component that spans the composite. Rheological percolation, however, has evaded a complete theoretical explanation and predictive description. A natural hypothesis is that rheological percolation arises due to rigidity percolation, whereby a rigid component of inclusions spans the composite. We model composites as random isotropic dispersions of soft-core rods, and study rigidity percolation in such systems. Building on previous results for two-dimensional systems, we develop an approximate algorithm that identifies spanning rigid components through iteratively identifying and compressing provably rigid motifs -- equivalently, decomposing giant rigid components into rigid assemblies of successively smaller rigid components. We apply this algorithm to random rod systems to estimate a rigidity percolation threshold and explore its dependence on rod aspect ratio. We show that this transition point, like the contact percolation transition point, scales inversely with the average (aspect ratio-dependent) rod excluded volume. However, the scaling of the rigidity percolation threshold, unlike the contact percolation scaling, is valid for relatively low aspect ratio. Moreover, the critical rod contact number is constant for aspect ratio above some relatively low value; and lies below the prediction from Maxwell's isostatic condition.

cond-mat.soft↗

arXiv2019

Measurement Error Correction in Particle Tracking Microrheology

In diverse biological applications, particle tracking of passive microscopic species has become the experimental measurement of choice -- when either the materials are of limited volume, or so soft as to deform uncontrollably when manipulated by traditional instruments. In a wide range of particle tracking experiments, a ubiquitous finding is that the mean squared displacement (MSD) of particle positions exhibits a power-law signature, the parameters of which reveal valuable information about the viscous and elastic properties of various biomaterials. However, MSD measurements are typically contaminated by complex and interacting sources of instrumental noise. As these often affect the high-frequency bandwidth to which MSD estimates are particularly sensitive, inadequate error correction can lead to severe bias in power law estimation and thereby, the inferred viscoelastic properties. In this article, we propose a novel strategy to filter high-frequency noise from particle tracking measurements. Our filters are shown theoretically to cover a broad spectrum of high-frequency noises, and lead to a parametric estimator of MSD power-law coefficients for which an efficient computational implementation is presented. Based on numerous analyses of experimental and simulated data, results suggest our methods perform very well compared to other denoising procedures.

stat.AP↗

arXiv2019

Transient crosslinking kinetics optimize gene cluster interactions

Our understanding of how chromosomes structurally organize and dynamically interact has been revolutionized through the lens of long-chain polymer physics. Major protein contributors to chromosome structure and dynamics are condensin and cohesin that stochastically generate loops within and between chains, and entrap proximal strands of sister chromatids. In this paper, we explore the ability of transient, protein-mediated, gene-gene crosslinks to induce clusters of genes, thereby dynamic architecture, within the highly repeated ribosomal DNA that comprises the nucleolus of budding yeast. We implement three approaches: live cell microscopy; computational modeling of the full genome during G1 in budding yeast, exploring four decades of timescales for transient crosslinks between 5k bp domains in the nucleolus on Chromosome XII; and, temporal network models with automated community detection algorithms applied to the full range of 4D modeling datasets. The data analysis tools detect and track gene clusters, their size, number, persistence time, and their plasticity. Of biological significance, our analysis reveals an optimal mean crosslink lifetime that promotes pairwise and cluster gene interactions through "flexible" clustering. In this state, large gene clusters self-assemble yet frequently interact, marked by gene exchanges between clusters, which in turn maximizes global gene interactions in the nucleolus. This regime stands between two limiting cases each with far less global gene interactions: with shorter crosslink lifetimes, "rigid" clustering emerges with clusters that interact infrequently; with longer crosslink lifetimes, there is a dissolution of clusters. These observations are compared with imaging experiments on a normal yeast strain and two condensin-modified mutant cell strains, applying the same image analysis pipeline to the experimental and simulated datasets.

q-bio.GN↗

arXiv2019

Limited processivity of single motors improves overall transport flux of self-assembled motor-cargo complexes

Single kinesin molecular motors can processively move along a microtubule (MT) a few micrometers on average before dissociating. However, cellular length scales over which transport occurs are several hundred microns and more. Why seemingly unreliable motors are used to transport cellular cargo remains poorly understood. We propose a new theory for how low processivity, the average length of a single bout of directed motion, can enhance cellular transport when motors and cargoes must first diffusively self assemble into complexes. We employ stochastic modeling to determine the effect of processivity on overall cargo transport flux. We show that, under a wide range of physiologically relevant conditions, possessing "infinite" processivity does not maximize flux along MTs. Rather, we find that low processivity i.e., weak binding of motors to MTs, is optimal. These results shed light on the relationship between processivity and transport efficiency and offer a new theory for the physiological benefits of low motor processivity.

q-bio.SC↗

arXiv2018

Evidence that self-similar microrheology of highly entangled polymeric solutions scales robustly with, and is tunable by, polymer concentration

We report observations of a remarkable scaling behavior with respect to concentration in the passive microbead rheology of two highly entangled polymeric solutions, polyethylene oxide (PEO) and hyaluronic acid (HA). This behavior was reported previously [Hill et al., PLOS ONE (2014)] for human lung mucus, a complex biological hydrogel, motivating the current study for synthetic polymeric solutions PEO and HA. The strategy is to identify, and focus within, a wide range of lag times $τ$ for which passive micron diameter beads exhibit self-similar (fractional, power law) mean-squared-displacement (MSD) statistics. For lung mucus, PEO at three different molecular weights (Mw), and HA at one Mw, we find ensemble-averaged MSDs of the form ${\langle}Δr^{2}(τ){\rangle} = 4D_ατ^α$, all within a common band, [1/60 sec, 3 sec], of lag times $τ$. We employ the MSD power law parameters $(D_α,α)$ to classify each polymeric solution over a range of highly entangled concentrations. By the generalized Stokes-Einstein relation, power law MSD implies power law elastic $G'(ω)$ and viscous $G''(ω)$ moduli for frequencies $1/τ$, [0.33 sec$^{-1}$, 60 sec$^{-1}$]. A natural question surrounds the polymeric properties that dictate $D_α$ and $α$, e.g. polymer concentration c, Mw, and stiffness (persistence length). In [Hill et al., PLOS ONE (2014)], we showed the MSD exponent $α$ varies linearly, while the pre-factor $D_α$ varies exponentially, with concentration, i.e. the semi-log plot, $(log(D_α),α)(c)$ of the classifier data is collinear. Here we show the same result for three distinct Mw PEO and HA at a single Mw. Future studies are required to explore the generality of these results for polymeric solutions, and to understand this scaling behavior with polymer concentration.

cond-mat.soft↗

arXiv2018

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, comprised of over 6,000 parameters, and employed 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.

q-bio.QM↗

arXiv2017

Rigid Graph Compression: Motif-based rigidity analysis for disordered fiber networks

Using particle-scale models to accurately describe property enhancements and phase transitions in macroscopic behavior is a major engineering challenge in composite materials science. To address some of these challenges, we use the graph theoretic property of rigidity to model me- chanical reinforcement in composites with stiff rod-like particles. We develop an efficient algorithmic approach called rigid graph compression (RGC) to describe the transition from floppy to rigid in disordered fiber networks ('rod-hinge systems'), which form the reinforcing phase in many composite systems. To establish RGC on a firm theoretical foundation, we adapt rigidity matroid theory to identify primitive topological network motifs that serve as rules for composing interacting rigid par- ticles into larger rigid components. This approach is computationally efficient and stable, because RGC requires only topological information about rod interactions (encoded by a sparse unweighted network) rather than geometrical details such as rod locations or pairwise distances (as required in rigidity matroid theory). We conduct numerical experiments on simulated two-dimensional rod-hinge systems to demonstrate that RGC closely approximates the rigidity percolation threshold for such systems, through comparison with the pebble game algorithm (which is exact in two dimensions). Importantly, whereas the pebble game is derived from Laman's condition and is only valid in two dimensions, the RGC approach naturally extends to higher dimensions.

cond-mat.dis-nn↗

arXiv2016

Maximum Likelihood Estimation for Single Particle, Passive Microrheology Data with Drift

Volume limitations and low yield thresholds of biological fluids have led to widespread use of passive microparticle rheology. The mean-squared-displacement (MSD) statistics of bead position time series (bead paths) are either applied directly to determine the creep compliance [Xu et al (1998)] or transformed to determine dynamic storage and loss moduli [Mason & Weitz (1995)]. A prevalent hurdle arises when there is a non-diffusive experimental drift in the data. Commensurate with the magnitude of drift relative to diffusive mobility, quantified by a Péclet number, the MSD statistics are distorted, and thus the path data must be "corrected" for drift. The standard approach is to estimate and subtract the drift from particle paths, and then calculate MSD statistics. We present an alternative, parametric approach using maximum likelihood estimation that simultaneously fits drift and diffusive model parameters from the path data; the MSD statistics (and consequently the compliance and dynamic moduli) then follow directly from the best-fit model. We illustrate and compare both methods on simulated path data over a range of Péclet numbers, where exact answers are known. We choose fractional Brownian motion as the numerical model because it affords tunable, sub-diffusive MSD statistics consistent with typical 30 second long, experimental observations of microbeads in several biological fluids. Finally, we apply and compare both methods on data from human bronchial epithelial cell culture mucus.

cond-mat.soft↗

arXiv2015

Model comparison and assessment for single particle tracking in biological fluids

State-of-the-art techniques in passive particle-tracking microscopy provide high-resolution path trajectories of diverse foreign particles in biological fluids. For particles on the order of 1 micron diameter, these paths are generally inconsistent with simple Brownian motion. Yet, despite an abundance of data confirming these findings and their wide-ranging scientific implications, stochastic modeling of the complex particle motion has received comparatively little attention. Even among posited models, there is virtually no literature on likelihood-based inference, model comparisons, and other quantitative assessments. In this article, we develop a rigorous and computationally efficient Bayesian methodology to address this gap. We analyze two of the most prevalent candidate models for 30 second paths of 1 micron diameter tracer particles in human lung mucus: fractional Brownian motion (fBM) and a Generalized Langevin Equation (GLE) consistent with viscoelastic theory. Our model comparisons distinctly favor GLE over fBM, with the former describing the data remarkably well up to the timescales for which we have reliable information.

stat.AP↗

arXiv2013

Percolation-induced exponential scaling in the large current tails of random resistor networks

There is a renewed surge in percolation-induced transport properties of diverse nano-particle composites (cf. RSC Nanoscience & Nanotechnology Series, Paul O'Brien Editor-in-Chief). We note in particular a broad interest in nano-composites exhibiting sharp electrical property gains at and above percolation threshold, which motivated us to revisit the classical setting of percolation in random resistor networks but from a multiscale perspective. For each realization of random resistor networks above threshold, we use network graph representations and associated algorithms to identify and restrict to the percolating component, thereby preconditioning the network both in size and accuracy by filtering {\it a priori} zero current-carrying bonds. We then simulate many realizations per bond density and analyze scaling behavior of the complete current distribution supported on the percolating component. We first confirm the celebrated power-law distribution of small currents at the percolation threshold, and second we confirm results on scaling of the maximum current in the network that is associated with the backbone of the percolating cluster. These properties are then placed in context with global features of the current distribution, and in particular the dominant role of the large current tail that is most relevant for material science applications. We identify a robust, exponential large current tail that: 1. persists above threshold; 2. expands broadly over and dominates the current distribution at the expense of the vanishing power law scaling in the small current tail; and 3. by taking second moments, reproduces the experimentally observed power law scaling of bulk conductivity above threshold.

cond-mat.dis-nn↗