The aspherity of random walks

Rudnick, Joseph; Gaspari, George

doi:10.1088/0305-4470/19/4/004

Cited by 373 publications

(314 citation statements)

References 3 publications

Supporting

Mentioning

305

Contrasting

Unclassified

Order By: Relevance

“…We also observed that cell tracks atop both of the flat substrates (gold-coated and TCPS) had asphericities much larger than that expected for a two-dimensional random walk (0.57) [59]. This is not surprising, as we know from the MSD data that our cell tracks are much more directed or ballistic than that for a random walk.…”

supporting

confidence: 59%

Automated, contour-based tracking and analysis of cell behaviour over long time scales in environments of varying complexity and cell density

Baker

Brasch

Manning

et al. 2014

J. R. Soc. Interface.

View full text Add to dashboard Cite

ResearchCite this article: Baker RM, Brasch ME, Manning ML, Henderson JH. 2014 Automated, contour-based tracking and analysis of cell behaviour over long time scales in environments of varying complexity and cell density. J. R. Soc. Understanding single and collective cell motility in model environments is foundational to many current research efforts in biology and bioengineering. To elucidate subtle differences in cell behaviour despite cell-to-cell variability, we introduce an algorithm for tracking large numbers of cells for long time periods and present a set of physics-based metrics that quantify differences in cell trajectories. Our algorithm, termed automated contour-based tracking for in vitro environments (ACTIVE), was designed for adherent cell populations subject to nuclear staining or transfection. ACTIVE is distinct from existing tracking software because it accommodates both variability in image intensity and multi-cell interactions, such as divisions and occlusions. When applied to low-contrast images from live-cell experiments, ACTIVE reduced error in analysing cell occlusion events by as much as 43% compared with a benchmark-tracking program while simultaneously tracking cell divisions and resulting daughter-daughter cell relationships. The large dataset generated by ACTIVE allowed us to develop metrics that capture subtle differences between cell trajectories on different substrates. We present cell motility data for thousands of cells studied at varying densities on shape-memory-polymer--based nanotopographies and identify several quantitative differences, including an unanticipated difference between two 'control' substrates. We expect that ACTIVE will be immediately useful to researchers who require accurate, long-time-scale motility data for many cells.

show abstract

supporting

confidence: 59%

Automated, contour-based tracking and analysis of cell behaviour over long time scales in environments of varying complexity and cell density

Baker

Brasch

Manning

et al. 2014

J. R. Soc. Interface.

View full text Add to dashboard Cite

show abstract

“…However, by exploiting the spatial distribution of the fluorescent intensity of the trace of each polymer that describes the local segment density (such as shown in Fig. 2 A), we also characterized the shape anisotropy of flexible polymers by using the two specific orthogonal components of the radius of gyration taken along its principal axes of inertia (5,15). We obtained an ensembleaveraged aspect ratio ϽrϾ Ϸ 2.5 similar to that obtained by using a best-fit ellipse that encompasses all the segments of the polymer.…”

Section: Resultsmentioning

confidence: 99%

“…The lack of direct conformational information has so far prevented a direct test of Kuhn's prediction (6), which is supported by computer simulations (11)(12)(13)(14)(15)(16) and analytical calculations (5). Bulk measurements such as light scattering and rheology (17,18) are inappropriate to probe the behavior of individual polymers in solution.…”

mentioning

confidence: 99%

Shape anisotropy of a single random-walk polymer

Haber

Ruiz

Wirtz

2000

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

Random walks have been used to describe a wide variety of systems ranging from cell colonies to polymers. Sixty-five years ago, Kuhn [Kuhn, W. (1934) Kolloid-Z. 68, 2-11] made the prediction, backed later by computer simulations, that the overall shape of a random-walk polymer is aspherical, yet no experimental work has directly tested Kuhn's general idea and subsequent computer simulations. By using fluorescence microscopy, we monitored the conformation of individual, long, random-walk polymers (fluorescently labeled DNA molecules) at equilibrium. We found that a polymer most frequently adopts highly extended, nonfractal structures with a strongly anisotropic shape. The ensemble-average ratio of the lengths of the long and short axes of the best-fit ellipse of the polymer was much larger than unity. R andom walks have been extensively used to describe a multitude of phenomena, ranging from cell migration within connective tissues, to Markov processes in DNA sequences, to time series in the stock market, to diffusion in gas, liquids, and solids (1-5). Sixty-five years ago, Kuhn (6) predicted that the shape of a random-walk polymer is not spherically symmetric, i.e., a regular random walk has an overall shape which is anisotropic. The intuitive idea of a spherical shape is based on a flexible polymer (or a random walk) having an isotropic end-to-end vector distribution and on the implicit rotational averaging typically done in polymer theories and experiments (7-10), yet the shape of individual polymers has not been probed directly (5, 9).The lack of direct conformational information has so far prevented a direct test of Kuhn's prediction (6), which is supported by computer simulations (11-16) and analytical calculations (5). Bulk measurements such as light scattering and rheology (17, 18) are inappropriate to probe the behavior of individual polymers in solution. These bulk experimental methods average the orientation, shape, and dynamics of a large ensemble of molecules simultaneously. Here, by monitoring the conformation, orientation, and dynamics of individual flexible polymers in dilute solutions, we directly measure the distributions of conformational parameters. We therefore test Kuhn's central prediction directly. Materials and MethodsLight microscopy (Nikon) equipped with a ϫ100, n.a. 1.30, oil-immersion lens was used to monitor the conformation of individual, fluorescently labeled DNA molecules at equilibrium. We used monodisperse Coliphage T2-phage DNA (T2-DNA) molecules (19) suspended at a concentration Ϸ20 ng͞ml (much smaller than the overlap concentration Ϸ0.13 mg͞ml) in Tris⅐EDTA buffer and an oxygen-scavenging system to reduce photobleaching (20)(21)(22). DNA molecules were stained with an intercalating dye (YOYO-1, Molecular Probes), which we verified did not affect the overall shape distribution of DNA. T2-DNA is a highly flexible polymer with a contour length of L Ϸ 56 m and a persistence length of l p Ϸ 52 nm. Hence, this polymer is a linear sequence of Ϸ1,075 (ϭ L͞l P Ͼ Ͼ 1) statistical segme...

show abstract

“…This approach, which we refer to as Slow Quenching (SQ), reversed the direction of the annealing process, at a rate of dλ /dt The structural analysis was performed using the inbuilt GROMACS packages g_sas, g_gyrate, g_dist and g_rdf. The shape of the nanoparticle was characterized in terms of an asphericity order parameter, A 3 , 48,49 derived from the moment of inertia tensor which was accumulated during the simulation,…”

Section: Core-annealing Proceduresmentioning

confidence: 99%

Self-Assembly of Calcium Carbonate Nanoparticles in Water and Hydrophobic Solvents

et al. 2014

View full text Add to dashboard Cite

The self-assembly of Ca 2+ and CO 2− 3 ions into nanoparticles in water and hydrophobic solvents is investigated using Molecular Dynamics (MD) computer simulation. A new three-stage particle assembly procedure is used which relaxes the structure of the nanoparticle towards a lower energy state. In hydrophobic solvent the bare particle is essentially spherical whereas in water it is ellipsoidally shaped. With surfactant stabilizer the nanoparticles typically exhibit non-spherical cores in model hydrophobic solvents. Binary surfactant systems exhibit synergistic effects were for example a salicylate-sulfonate combination forms a cage which promotes a compact core. Synergistic effects on the shape of the particle were also observed in a hydrophobic solvent for surfactant-stabilized systems with trace water as a third component.The simulations show that rather than being a rigid structure the carbonate core shape and stabilizing shell coverage is sensitive to solvent, surfactant and small polar molecules which act as co-surfactants.

show abstract

The aspherity of random walks

Cited by 373 publications

References 3 publications

Automated, contour-based tracking and analysis of cell behaviour over long time scales in environments of varying complexity and cell density

Automated, contour-based tracking and analysis of cell behaviour over long time scales in environments of varying complexity and cell density

Shape anisotropy of a single random-walk polymer

Self-Assembly of Calcium Carbonate Nanoparticles in Water and Hydrophobic Solvents

Contact Info

Product

Resources

About