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 P\'eclet 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 P\'eclet 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.Comment: 29 pages, 12 figure

Modeling and Simulation of Mucus Flow in Human Bronchial Epithelial Cell Cultures – Part I: Idealized Axisymmetric Swirling Flow

A multi-mode nonlinear constitutive model for mucus is constructed directly from micro- and macro-rheology experimental data on cell culture mucus, and a numerical algorithm is developed for the culture geometry and idealized cilia driving conditions. This study investigates the roles that mucus rheology, wall effects, and HBE culture geometry play in the development of flow profiles and the shape of the air-mucus interface. Simulations show that viscoelasticity captures normal stress generation in shear leading to a peak in the air-mucus interface at the middle of the culture and a depression at the walls. Linear and nonlinear viscoelastic regimes can be observed in cultures by varying the hurricane radius and mean rotational velocity. The advection-diffusion of a drug concentration dropped at the surface of the mucus flow is simulated as a function of Peclet number

Assessing Interconnections Between Wilderness and Adjacent Lands: The Grand Staircase-Escalante National Monument, Utah

Wilderness managers have traditionally managed wilderness lands based on the ecological and social content of wilderness areas. The authors propose a framework to systematically account for the biophysical, socioeconomic, and wildness characteristics of the broader landscape context. The method was applied to the proposed wilderness lands of the Grand Staircase-Escalante National Monument in southern Utah. The results illustrate patterns of interdependencies across the landscape. Spatial data demonstrate links between the integrity of proposed wilderness lands and the management of adjacent land units, and links between the economic health of local communities and the management of proposed wilderness and adjacent federal lands

Transient anomalous diffusion of tracer particles in soft matter

Synopsis This paper is motivated by experiments in which time series of tracer particles in viscoelastic liquids are recorded using advanced microscopy. The experiments seek to infer either viscoelastic properties of the sample Mason and Weitz, Phys. Rev. Lett. 74, 1250–1253 1995 or diffusive properties of the specific tracer particle in the host medium Suh et al. 2009. Our focus is the latter. Experimentalists often fit data to transient anomalous diffusion: a sub-diffusive power law scaling t , with 0 1 of mean-squared displacement MSD over a finite time interval, with longtime viscous scaling t 1 . The time scales of sub-diffusion and exponents are observed to vary with particle size, particle surface chemistry, and viscoelastic properties of the host material. Until now, explicit models for transient sub-diffusive MSD scaling behavior Doi and Edwards, The Theory of Polymer Physics Oxford University Press, New York, 1986; Kremer and Grest, J. Chem. Phys. 92, 5057–5086 1990; Rubinstein and Colby, Polymer Physics Oxford University Press, New York, 2003 are limited to precisely three exponents: monomer diffusion in Rouse chain melts t 1/2 , in Zimm chain solutions t 2/3 , and in reptating chains t 1/4 . In this paper, we present an explicit parametrized family of stochastic processes generalized Langevin equations with prescribed memory kernels and derive their closed-form solutions which 1 span the complete range of transient sub-diffusive behavior and 2 possess the flexibility to tune both the time window of sub-diffusive scaling and the power law exponent . These results establish a robust family of sub-diffusive models, for which the inverse problem of parameter inference from experimental data Fricks et al., SIAM J. Appl. Math.

Global-in-time solutions for the isothermal Matovich-Pearson equations

In this paper we study the Matovich-Pearson equations describing the process of glass fiber drawing. These equations may be viewed as a 1D-reduction of the incompressible Navier-Stokes equations including free boundary, valid for the drawing of a long and thin glass fiber. We concentrate on the isothermal case without surface tension. Then the Matovich-Pearson equations represent a nonlinearly coupled system of an elliptic equation for the axial velocity and a hyperbolic transport equation for the fluid cross-sectional area. We first prove existence of a local solution, and, after constructing appropriate barrier functions, we deduce that the fluid radius is always strictly positive and that the local solution remains in the same regularity class. To the best of our knowledge, this is the first global existence and uniqueness result for this important system of equations

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

© The Author(s), 2020. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in McLaughlin, G. A., Langdon, E. M., Crutchley, J. M., Holt, L. J., Forest, M. G., Newby, J. M., & Gladfelter, A. S. (2020). Spatial heterogeneity of the cytosol revealed by machine learning-based 3D particle tracking. Molecular Biology of the Cell, 31(14), 1498-1511, doi:10.1091/mbc.E20-03-0210.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.We would like to thank the 2016 Physiology course and Christina Termini at the Marine Biological Laboratory in Woods Hole, MA, Gregory Brittingham, and Marcus Roper for initial experiments and perspectives on pipeline. We thank David Adalsteinsson for help with DataTank software and many conversations about image analysis on large datasets. We thank Emmanual Levy (Weizmann Institute) for providing plasmids encoding synthetic phase separating peptides. This work was supported by Google Cloud, the National Science Foundation (NSF), the National Institutes of Health (NIH), and the Natural Sciences and Engineering Research Council of Canada (NSERC). ASG, EML, and GAM were supported by the NSF (RoLs: 1840273), HHMI faculty scholar award and the NIH (R01GM081506). JMN was supported by the NSERC (RGPIN-2019-06435, RGPAS-2019-00014, DGECR-2019-00321) and the NSF (DMS-171474). MGF was supported by the NSF (DMS-1816630, DMS-1664645). LJH was supported by the NIH (R01GM132447)