Model Comparison and Assessment for Single Particle Tracking in Biological Fluids

References

• Aitkin, M. (1991), “Posterior Bayes Factors,” Journal of the Royal Statistical Society, Series B, 53, 111–1426.
   Google Scholar
• Albert, J., and Chib, S. (1995), “Bayesian Residual Analysis for Binary Response Regression Models,” Biometrika, 82, 747–769.
   Web of Science ®Google Scholar
• Berger, J. O., and Pericchi, L. R. (1996), “The Intrinsic Bayes Factor for Model Selection and Prediction,” Journal of the American Statistical Association, 91, 109–122.
   Web of Science ®Google Scholar
• Box, G. E. P. (1980), “Sampling and Bayes’ Inference in Scientific Modelling and Robustness,” Journal of the Royal Statistical Society, Series A, 143, 383–430.
   Google Scholar
• Brockwell, P. J., and Davis, R. A. (2009), Time Series: Theory and Methods, New York: Springer.
   Google Scholar
• Bronstein, I., Israel, Y., Kepten, E., Mai, S., Shav-Tal, Y., Barkai, E., and Garini, Y. (2009), “Transient Anomalous Diffusion of Telomeres in the Nucleus of Mammalian Cells,” Physical Review Letters, 103, 018102.
   PubMed Web of Science ®Google Scholar
• Burov, S., Jeon, J.-H., Metzler, R., and Barkai, E. (2011), “Single Particle Tracking in Systems Showing Anomalous Diffusion: The Role of Weak Ergodicity Breaking,” Physical Chemistry Chemical Physics, 13, 1800–1812.
   PubMed Web of Science ®Google Scholar
• Carlstedt, I., Lindgren, H., and Sheehan, J. K. (1983a), “The Macromolecular Structure of Human Cervical-Mucus Glycoproteins. Studies on Fragments Obtained After Reduction of Disulphide Bridges and After Subsequent Trypsin Digestion,” Biochemical Journal, 213, 427–435.
   PubMed Web of Science ®Google Scholar
• Carlstedt, I., Lindgren, H., Sheehan, J. K., Ulmsten, U., and Wingerup, L. (1983b), “Isolation and Characterization of Human Cervical-Mucus Glycoproteins,” Biochemical Journal, 211, 13–22.
   PubMed Web of Science ®Google Scholar
• Carlstedt, I., and Sheehan, J. K. (1984), “Macromolecular Properties and Polymeric Structure of Mucus Glycoproteins,” Mucus and Mucosa, 109, 157–172.
   Google Scholar
• Carlstedt, I., Sheehan, J., Ulmsten, U., and Wingerup, L. (1982), “Isolation and Purification of the Mucin Component of Human Cervical Mucus,” in Mucus in Health and Disease-II, eds. E. Chantler, J. Elder, and M. Elstein, New York: Springer, pp. 273–275.
   Google Scholar
• Caspi, A., and Granek, R. (2000), “Enhanced Diffusion in Active Intracellular Transport,” Physical Review Letters, 85, 5655–5658.
   PubMed Web of Science ®Google Scholar
• Chen, A., McKinley, S. A., Wang, S., Shi, F., Mucha, P. J., Forest, M. G., and Lai, S. K. (2014), “Transient Antibody-Mucin Interactions Produce a Dynamic Molecular Shield Against Viral Invasion,” Biophysical Journal, 106, 2028–2036.
   PubMed Web of Science ®Google Scholar
• Cone, R. A. (2009), “Barrier Properties of Mucus,” Advanced Drug Delivery Reviews, 61, 75–85.
   PubMed Web of Science ®Google Scholar
• Dawson, M., Wirtz, D., and Hanes, J. (2003), “Enhanced Viscoelasticity of Human Cystic Fibrotic Sputum Correlates With Increasing Microheterogeneity in Particle Transport,” Journal of Biological Chemistry, 278, 50393–50401.
   PubMed Web of Science ®Google Scholar
• Didier, G., McKinley, S. A., Hill, D. B., and Fricks, J. (2012), “Statistical Challenges in Microrheology,” Journal of Time Series Analysis, 33, 724–743.
   Web of Science ®Google Scholar
• Ensign, L. M., Tang, B. C., Wang, Y.-Y., Terence, A. T., Hoen, T., Cone, R., and Hanes, J. (2012), “Mucus-Penetrating Nanoparticles for Vaginal Drug Delivery Protect Against Herpes Simplex Virus,” Science Translational Medicine, 4, 138ra79.
   PubMed Web of Science ®Google Scholar
• Ernst, D., Hellmann, M., Köhler, J., and Weiss, M. (2012), “Fractional Brownian Motion in Crowded Fluids,” Soft Matter, 8, 4886–4889.
   Web of Science ®Google Scholar
• Ferry, J. D. (1980), Viscoelastic Properties of Polymers, New York: Wiley.
   Google Scholar
• Fricks, J., Yao, L., Elston, T. C., and Forest, M. G. (2009), “Time-Domain Methods for Diffusive Transport in Soft Matter,” SIAM Journal on Applied Mathematics, 69, 1277–1308.
   PubMed Web of Science ®Google Scholar
• Gelman, A. (2013), “Two Simple Examples for Understanding Posterior p-Values Whose Distributions are Far From Uniform,” Electronic Journal of Statistics, 7, 2595–2602.
   Web of Science ®Google Scholar
• Gelman, A., Meng, X.-L., and Stern, H. (1996), “Posterior Predictive Assessment of Model Fitness via Realized Discrepancies,” Statistica Sinica, 6, 733–760.
   Web of Science ®Google Scholar
• Georgiades, P., Pudney, P. D. A., Thornton, D. J., and Waigh, T. A. (2014), “Particle Tracking Microrheology of Purified Gastrointestinal Mucins,” Biopolymers, 101, 366–377.
   PubMed Web of Science ®Google Scholar
• Golding, I., and Cox, E. (2006), “Physical Nature of Bacterial Cytoplasm,” Physical Review Letters, 96, 098102.
   PubMed Web of Science ®Google Scholar
• Green, P. J. (1995), “Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination,” Biometrika, 82, 711–732.
   Web of Science ®Google Scholar
• He, Y., Burov, S., Metzler, R., and Barkai, E. (2008), “Random Time-Scale Invariant Diffusion and Transport Coefficients,” Physical Review Letters, 101, 058101.
   PubMed Web of Science ®Google Scholar
• Hill, D. B., Vasquez, P. A., Mellnik, J., McKinley, S. A., Vose, A., Mu, F., Henderson, A. G., Donaldson, S. H., Alexis, N. E., Boucher, R. C., and Forest, M. G. (2014), “A Biophysical Basis for Mucus Solids Concentration as a Candidate Biomarker for Airways Disease,” PLoS ONE, 9, e87681.
   PubMed Web of Science ®Google Scholar
• Jeffreys, H. (1961), The Theory of Probability, New York: Oxford University Press.
   Google Scholar
• Jeon, J.-H., and Metzler, R. (2010), “Analysis of Short Subdiffusive Time Series: Scatter of the Time-Averaged Mean-Squared Displacement,” Journal of Physics A, 43, 252001.
   Google Scholar
• Jeon, J.-H., Tejedor, V., Burov, S., Barkai, E., Selhuber-Unkel, C., Berg-Sørensen, K., Oddershede, L., and Metzler, R. (2011), “In Vivo Anomalous Diffusion and Weak Ergodicity Breaking of Lipid Granules,” Physical Review Letters, 106, 048103.
   PubMed Web of Science ®Google Scholar
• Kass, R. E., and Raftery, A. E. (1995), “Bayes Factors,” Journal of the American Statistical Association, 90, 773–795.
   Web of Science ®Google Scholar
• Kim, C.-J., and Nelson, C. R. (1999), State-Space Models With Regime Switching, Cambridge, MA: MIT Press.
   Google Scholar
• Kneller, G. R. (2011), “Generalized Kubo Relations and Conditions for Anomalous Diffusion: Physical Insights From a Mathematical Theorem,” The Journal of Chemical Physics, 134, 224106.
   PubMed Web of Science ®Google Scholar
• Kou, S. C. (2008), “Stochastic Modeling in Nanoscale Biophysics: Subdiffusion Within Proteins,” The Annals of Applied Statistics, 2, 501–535.
   Web of Science ®Google Scholar
• Kou, S. C., and Xie, X. S. (2004), “Generalized Langevin Equation With Fractional Gaussian Noise: Subdiffusion Within a Single Protein Molecule,” Physical Review Letters, 93, 180603.
   PubMed Web of Science ®Google Scholar
• Kubo, R. (1966), “The Fluctuation-Dissipation Theorem,” Reports on Progress in Physics, 29, 255–284.
   Web of Science ®Google Scholar
• Lai, S. K., O’Hanlon, D. E., Harrold, S., Man, S. T., Wang, Y. Y., Cone, R., and Hanes, J. (2007), “Rapid Transport of Large Polymeric Nanoparticles in Fresh Undiluted Human Mucus,” Proceedings of the National Academy of Sciences of the United States of America, 104, 1482–1487.
   PubMed Web of Science ®Google Scholar
• Lai, S. K., Wang, Y.-Y., and Hanes, J. (2009), “Mucus-Penetrating Nanoparticles for Drug and Gene Delivery to Mucosal Tissues,” Advanced Drug Delivery Reviews, 61, 158–171.
   PubMed Web of Science ®Google Scholar
• Lartillot, N., and Philippe, H. (2006), “Computing Bayes Factors Using Thermodynamic Integration,” Systematic Biology, 55, 195–207.
   PubMed Web of Science ®Google Scholar
• Li, W. L. S., and Drummond, A. J. (2012), “Model Averaging and Bayes Factor Calculation of Relaxed Molecular Clocks in Bayesian Phylogenetics,” Molecular Biology and Evolution, 29, 751–761.
   PubMed Web of Science ®Google Scholar
• Lindley, D. V. (1957), “A Statistical Paradox,” Biometrika, 44, 187–192.
   Web of Science ®Google Scholar
• Lubelski, A., Sokolov, I. M., and Klafter, J. (2008), “Nonergodicity Mimics Inhomogeneity in Single Particle Tracking,” Physical Review Letters, 100, 250602.
   PubMed Web of Science ®Google Scholar
• Lunn, D., Barrett, J., Sweeting, M., and Thompson, S. (2013), “Fully Bayesian Hierarchical Modelling in Two Stages, With Application to Meta-Analysis,” Journal of the Royal Statistical Society, Series C, 62, 551–572.
   Google Scholar
• Mandelbrot, B. B., and Ness, J. W. V. (1968), “Fractional Brownian Motions, Fractional Noises and Applications,” SIAM Review, 10, 422–437.
   Web of Science ®Google Scholar
• Mason, T. G., and Weitz, D. A. (1995), “Optical Measurements of Frequency-Dependent Linear Viscoelastic Moduli of Complex Fluids,” Physical Review Letters, 74, 1250–1253.
   PubMed Web of Science ®Google Scholar
• McKinley, S. A., Yao, L., and Forest, M. G. (2009), “Transient Anomalous Diffusion of Tracer Particles in Soft Matter,” Journal of Rheology, 53, 1487–1506.
   Web of Science ®Google Scholar
• Mellnik, J., Vasquez, P. A., McKinley, S. A., Witten, J., Hill, D. B., and Forest, M. G. (2014), “Micro-Heterogeneity Metrics for Diffusion in Soft Matter,” Soft Matter, 10, 7781–7796.
   PubMed Web of Science ®Google Scholar
• Meng, X.-L. (1994), “Posterior Predictive p-Values,” The Annals of Statistics, 22, 1142–1160.
   Web of Science ®Google Scholar
• Meroz, Y., Sokolov, I., and Klafter, J. (2013), “Test for Determining a Subdiffusive Model in Ergodic Systems From Single Trajectories,” Physical Review Letters, 110, 090601.
   PubMed Web of Science ®Google Scholar
• Metzler, R., and Klafter, J. (2000), “The Random Walk’s Guide to Anomalous Diffusion: A Fractional Dynamics Approach,” Physics Reports, 339, 1–77.
   Web of Science ®Google Scholar
• Metzler, R., Tejedor, V., Jeon, J. H., He, Y., Deng, W. H., Burov, S., and Barkai, E. (2009), “Analysis of Single Particle Trajectories: From Normal to Anomalous Diffusion,” Acta Physica Polonica B, 40, 1315.
   Web of Science ®Google Scholar
• Monnier, N., Guo, S. M., Mori, M., He, J., Lénárt, P., and Bathe, M. (2012), “Bayesian Approach to MSD-Based Analysis of Particle Motion in Live Cells,” Biophysical Journal, 103, 616–626.
   PubMed Web of Science ®Google Scholar
• Morgado, R., Oliveira, F., Batrouni, G., and Hansen, A. (2002), “Relation Between Anomalous and Normal Diffusion in Systems With Memory,” Physical Review Letters, 89, 100601.
   PubMed Web of Science ®Google Scholar
• Olmsted, S. S., Padgett, J. L., Yudin, A. I., Whaley, K. J., Moench, T. R., and Cone, R. A. (2001), “Diffusion of Macromolecules and Virus-Like Particles in Human Cervical Mucus,” Biophysical Journal, 81, 1930–1937.
   PubMed Web of Science ®Google Scholar
• O’Malley, D., Cushman, J. H., and Johnson, G. (2011), “Scaling Laws for Fractional Brownian Motion With Power-Law Clock,” Journal of Statistical Mechanics: Theory and Experiment, 2011, L01001.
   Web of Science ®Google Scholar
• Rangarajan, G., and Ding, M. (2000), “Anomalous Diffusion and the First Passage Time Problem,” Physical Review E, 62, 120–133.
   Web of Science ®Google Scholar
• Robert, C. P., Cornuet, J. M., Marin, J. M., and Pillai, N. S. (2011), “Lack of Confidence in Approximate Bayesian Computation Model Choice,” Proceedings of the National Academy of Sciences of the United States of America, 108, 15112–15117.
   PubMed Web of Science ®Google Scholar
• Rubin, D. B. (1984), “Bayesianly Justifiable and Relevant Frequency Calculations for the Applied Statistician,” The Annals of Statistics, 12, 1151–1172.
   Web of Science ®Google Scholar
• Saltzman, W. M., Radomsky, M. L., Whaley, K. J., and Cone, R. A. (1994), “Antibody Diffusion in Human Cervical Mucus,” Biophysical Journal, 66, 508–515.
   PubMed Web of Science ®Google Scholar
• Saxton, M. (2007), “A Biological Interpretation of Transient Anomalous Subdiffusion. I. Qualitative Model,” Biophysical Journal, 92, 1178–1191.
   PubMed Web of Science ®Google Scholar
• Schuster, B. S., Ensign, L. M., Allan, D. B., Suk, J. S., and Hanes, J. (2015), “Particle Tracking in Drug and Gene Delivery Research: State-of-the-Art Applications and Methods,” Advanced Drug Delivery Reviews, 91, 70–91.
   PubMed Web of Science ®Google Scholar
• Seisenberger, G., Ried, M. U., Endress, T., Büning, H., Hallek, M., and Bräuchle, C. (2001), “Real-Time Single-Molecule Imaging of the Infection Pathway of An Adeno-Associated Virus,” Science, 294, 1929.
   PubMed Web of Science ®Google Scholar
• Soussou, J. E., Moavenzadeh, F., and Gradowczyk, M. H. (1970), “Application of Prony Series to Linear Viscoelasticity,” Transactions of the Society of Rheology, 14, 573–584.
   Google Scholar
• Suk, J. S., Lai, S. K., Boylan, N. J., Dawson, M. R., Boyle, M. P., and Hanes, J. (2011), “Rapid Transport of Muco-Inert Nanoparticles in Cystic Fibrosis Sputum Treated With N-Acetyl Cysteine,” Nanomedicine, 6, 365–375.
   PubMed Web of Science ®Google Scholar
• Suk, J. S., Suh, J., Lai, S. K., and Hanes, J. (2007), “Quantifying the Intracellular Transport of Viral and Nonviral Gene Vectors in Primary Neurons,” Experimental Biology and Medicine, 232, 461–469.
   Web of Science ®Google Scholar
• Sun, D., and Berger, J. O. (2007), “Objective Bayesian Analysis for the Multivariate Normal Model,” Bayesian Statistics, 8, 525–562.
   Google Scholar
• Thornton, D. J., and Sheehan, J. K. (2004), “From Mucins to Mucus: Toward a More Coherent Understanding of This Essential Barrier,” Proceedings of the American Thoracic Society, 1, 54–61.
   PubMedGoogle Scholar
• Tolić-Nørrelykke, I., Munteanu, E.-L., Thon, G., Oddershede, L., and Berg-Sørensen, K. (2004), “Anomalous Diffusion in Living Yeast Cells,” Physical Review Letters, 93, 078102.
   PubMed Web of Science ®Google Scholar
• Toni, T., Welch, D., Strelkowa, N., Ipsen, A., and Stumpf, M. P. H. (2009), “Approximate Bayesian Computation Scheme for Parameter Inference and Model Selection in Dynamical Systems,” Journal of the Royal Society Interface, 6, 187–202.
   PubMed Web of Science ®Google Scholar
• Valentine, M., Kaplan, P., Thota, D., Crocker, J., Gisler, T., Prud’homme, R., Beck, M., and Weitz, D. (2001), “Investigating the Microenvironments of Inhomogeneous Soft Materials With Multiple Particle Tracking,” Physical Review E, 64, 061506.
   PubMed Web of Science ®Google Scholar
• Vanpaemel, W. (2010), “Prior Sensitivity in Theory Testing: An Apologia for the Bayes Factor,” Journal of Mathematical Psychology, 54, 491–498.
   Web of Science ®Google Scholar
• Verdaasdonk, J. S., Vasquez, P. A., Barry, R. M., Barry, T., Goodwin, S., Forest, M. G., and Bloom, K. (2013), “Centromere Tethering Confines Chromosome Domains,” Molecular Cell, 52, 819–831.
   PubMed Web of Science ®Google Scholar
• Vyshemirsky, V., and Girolami, M. A. (2008), “Bayesian Ranking of Biochemical System Models,” Bioinformatics, 24, 833–839.
   PubMed Web of Science ®Google Scholar
• Wong, I., Gardel, M., Reichman, D., Weeks, E., Valentine, M., Bausch, A., and Weitz, D. (2004), “Anomalous Diffusion Probes Microstructure Dynamics of Entangled F-Actin Networks,” Physical Review Letters, 92, 178101.
   PubMed Web of Science ®Google Scholar