scholarly journals Far from equilibrium dynamics of tracer particles embedded in a growing multicellular spheroid

2020 ◽  
Author(s):  
Himadri S. Samanta ◽  
Sumit Sinha ◽  
D. Thirumalai
Keyword(s):  
Mean Square Displacement ◽  
Radial Pressure ◽  
Multicellular Spheroid ◽  
Directed Motion ◽  
Diffusive Behavior ◽  
Tracer Particles ◽  
Proliferation And Apoptosis ◽  
Local Stresses ◽  
Long Time ◽  
Far From Equilibrium

Local stresses on the cancer cells (CCs) have been measured by embedding inert tracer particles (TPs) in a growing multicellular spheroid. The utility of the experiments requires that the TPs do not alter the CC microenvironment. We show, using theory and extensive simulations, that proliferation and apoptosis of the CCs, drive the dynamics of the TPs far from equilibrium. On times less than the CC division times, the TPs exhibit sub-diffusive behavior (the mean square displacement, with βTP < 1). Surprisingly, in the long-time limit, the motion of the TPs is hyper-diffusive ( with αTP > 2) due to persistent directed motion for a number of CC division times. In contrast, CC proliferation randomizes their motion resulting from jamming at short times to super-diffusive behavior, with αCC exceeding unity, at long times. Surprisingly, the effect of the TPs on CC dynamics and radial pressure is negligible, suggesting that the TPs are reliable reporters of the CC microenvironment.

Impact of polydispersity and confinement on diffusion in hydrodynamically interacting colloidal suspensions

2021 ◽  
Vol 925 ◽  
Author(s):  
Emma Gonzalez ◽  
Christian Aponte-Rivera ◽  
Roseanna N. Zia
Keyword(s):  
Computational Study ◽  
Mean Square Displacement ◽  
Configurational Entropy ◽  
Colloidal Suspensions ◽  
Colloidal Dispersion ◽  
Length Scale ◽  
Many Body ◽  
Stokesian Dynamics ◽  
Time Dynamics ◽  
Long Time

We present a computational study of the equilibrium dynamics of a polydisperse hard-sphere colloidal dispersion confined in a spherical cavity. We account for many-body hydrodynamic and lubrication interactions between particles and with the confining cavity utilizing our confined Stokesian dynamics model, expanded here for size polydispersity. We find that, even though the tendency of polydispersity to homogenize structure in a suspension is still present in confinement, strong correlations induced by the cavity resist homogenization. Although seemingly opposite, these two effects have a common driver, which is to maximize configurational entropy of particles in the cavity interior. These structural effects couple with the hydrodynamics to change the particle dynamics: polydispersity weakens lubrication effects near the cavity wall, allowing small (large) particles to diffuse faster (slower) than in a monodisperse suspension. As a small (large) particle gets farther from the wall, polydispersity weakens many-body hydrodynamic couplings, driving diffusivity up (down). While the local cage dynamics dominates short-time self-diffusion, long-time dynamics is also affected. In the concentrated regime, polydispersity and confinement combine to induce radial de-mixing into size-segregated populations. The cavity becomes the most influential ‘nearest neighbour’, setting the length scale of and dynamics within these radial domains. This intermediate length-scale caging makes the angular dynamics insensitive to polydispersity but leads to radial long-time mean-square displacement that changes qualitatively with volume composition. These results hold promise for explaining colloidal-scale physics implicated in the functioning of biological cells, and the engineering of non-living confined colloids where size de-mixing could be useful in the design of encapsulated micro-reactors and therapeutic vesicles.

Dynamics and Traffic for Transfecting Exogenous MicroRNA as Studied by Live-Cell Microscopy

2021 ◽  
Vol 17 (8) ◽  
pp. 1647-1653
Author(s):  
Ke Yang ◽  
Yuanyuan Wang ◽  
Bo Sun ◽  
Tian Tian ◽  
Zhu Dai ◽  
...  
Keyword(s):  
Dynamic Properties ◽  
Mean Square Displacement ◽  
Small Region ◽  
Single Particle Tracking ◽  
Live Cell ◽  
Calculation Results ◽  
Long Time ◽  
Live Cell Microscopy ◽  
Cell Microscopy

MicroRNA (miRNA) has emerged as an important gene-regulator that shows great potential in gene therapy because of its unique roles in gene-regulation. However, the knowledge on their function and transportation in vivo is still lacking, and there are limited obvious evidences to define intracellular transportation of miRNA. In this study, the dynamics of exogenous miR-21 transfected into HeLa cells was traced by live-cell microscopy. Their transportation at key time points was recorded and dynamic properties were analyzed by single particle tracking (SPT) and mean square displacement (MSD) calculation. Results showed that the exogenous miRNAs bounded to cells quickly and went through lysosome into cytosol, where they were subsequently recruited into p-body. They finally were degraded, otherwise went back to cytosol in some way. Long time observation and analysis of motion mode showed that the miRNAs were confined in a small region and their motion modes were flexible in different intracellular microenvironment after entering the cells.

scholarly journals Intermediate scattering function of an anisotropic active Brownian particle

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Christina Kurzthaler ◽  
Sebastian Leitmann ◽  
Thomas Franosch
Keyword(s):  
Brownian Particle ◽  
Rotational Diffusion ◽  
Effective Diffusion ◽  
Mean Square Displacement ◽  
Scattering Function ◽  
Directed Motion ◽  
Stochastic Motion ◽  
Length Scales ◽  
Intermediate Scattering Function ◽  
Active Brownian Particle

Abstract Various challenges are faced when animalcules such as bacteria, protozoa, algae, or sperms move autonomously in aqueous media at low Reynolds number. These active agents are subject to strong stochastic fluctuations, that compete with the directed motion. So far most studies consider the lowest order moments of the displacements only, while more general spatio-temporal information on the stochastic motion is provided in scattering experiments. Here we derive analytically exact expressions for the directly measurable intermediate scattering function for a mesoscopic model of a single, anisotropic active Brownian particle in three dimensions. The mean-square displacement and the non-Gaussian parameter of the stochastic process are obtained as derivatives of the intermediate scattering function. These display different temporal regimes dominated by effective diffusion and directed motion due to the interplay of translational and rotational diffusion which is rationalized within the theory. The most prominent feature of the intermediate scattering function is an oscillatory behavior at intermediate wavenumbers reflecting the persistent swimming motion, whereas at small length scales bare translational and at large length scales an enhanced effective diffusion emerges. We anticipate that our characterization of the motion of active agents will serve as a reference for more realistic models and experimental observations.

RANDOM WALKS ON KEBAB LATTICES: LOGARITHMIC DIFFUSION ON ORDERED STRUCTURES

1995 ◽  
Vol 09 (10) ◽  
pp. 601-606 ◽  
Author(s):  
D. CASSI ◽  
S. REGINA
Keyword(s):  
Random Walks ◽  
Linear Chain ◽  
Mean Square Displacement ◽  
Analytical Techniques ◽  
Mean Square ◽  
Ordered Structure ◽  
Ordered Structures ◽  
Asymptotic Expressions ◽  
Long Time ◽  
The Mean

Kebab lattices are ordered lattices obtained matching an infinite two-dimensional lattice to each point of a linear chain. Discrete time random walks on these structures are studied by analytical techniques. The exact asymptotic expressions of the mean square displacement and of the RW Green functions show an unexpected logarithmic behavior that is the first example of such kind of law on an ordered structure. Moreover the probability of returning to the origin shows the fastest long time decay ever found for recursive random walks.

scholarly journals Surface Waves Enhance Particle Dispersion

Fluids ◽  
2019 ◽  
Vol 4 (1) ◽  
pp. 55 ◽  
Author(s):  
Mohammad Farazmand ◽  
Themistoklis Sapsis
Keyword(s):  
Free Surface ◽  
Single Particle ◽  
Wave Motion ◽  
Quadratic Function ◽  
Particle Dispersion ◽  
Diffusive Behavior ◽  
Linear Waves ◽  
Tracer Particles ◽  
Passive Tracers

We study the horizontal dispersion of passive tracer particles on the free surface of gravity waves in deep water. For random linear waves with the JONSWAP spectrum, the Lagrangian particle trajectories are computed using an exact nonlinear model known as the John–Sclavounos equation. We show that the single-particle dispersion exhibits an unusual super-diffusive behavior. In particular, for large times t, the variance of the tracer ⟨ | X ( t ) | 2 ⟩ increases as a quadratic function of time, i.e., ⟨ | X ( t ) | 2 ⟩ ∼ t 2 . This dispersion is markedly faster than Taylor’s single-particle dispersion theory which predicts that the variance of passive tracers grows linearly with time for large t. Our results imply that the wave motion significantly enhances the dispersion of fluid particles. We show that this super-diffusive behavior is a result of the long-term correlation of the Lagrangian velocities of fluid parcels on the free surface.

Velocity and displacement correlation functions for fractional generalized Langevin equations

2012 ◽  
Vol 15 (3) ◽  
Author(s):  
Trifce Sandev ◽  
Ralf Metzler ◽  
Živorad Tomovski
Keyword(s):  
Initial Conditions ◽  
Mean Square Displacement ◽  
Langevin Equations ◽  
Average Particle ◽  
Mean Square ◽  
Relaxation Functions ◽  
Long Time ◽  
The Mean ◽  
Diffusive Processes ◽  
Frictional Memory Kernel

AbstractWe study analytically a generalized fractional Langevin equation. General formulas for calculation of variances and the mean square displacement are derived. Cases with a three parameter Mittag-Leffler frictional memory kernel are considered. Exact results in terms of the Mittag-Leffler type functions for the relaxation functions, average velocity and average particle displacement are obtained. The mean square displacement and variances are investigated analytically. Asymptotic behaviors of the particle in the short and long time limit are found. The model considered in this paper may be used for modeling anomalous diffusive processes in complex media including phenomena similar to single file diffusion or possible generalizations thereof. We show the importance of the initial conditions on the anomalous diffusive behavior of the particle.

scholarly journals Relative ordering in the radial evolution of solar wind turbulence: the S-Theorem approach

2011 ◽  
Vol 29 (12) ◽  
pp. 2317-2326 ◽  
Author(s):  
G. Consolini ◽  
P. De Michelis
Keyword(s):  
Solar Wind ◽  
Open Systems ◽  
Radial Distance ◽  
Slow Solar Wind ◽  
Time Interval ◽  
Turbulent Fluctuations ◽  
Long Time ◽  
Far From Equilibrium ◽  
Radial Evolution ◽  
Degree Of Order

Abstract. Over the past few decades scientists have shown growing interest in space plasma complexity and in understanding the turbulence in magnetospheric and interplanetary media. At the beginning of the 1980s, Yu. L. Klimontovich introduced a criterion, named S-Theorem, to evaluate the degree of order in far-from-equilibrium open systems, which applied to hydrodynamic turbulence showed that turbulence flows were more organized than laminar ones. Using the same theorem we have evaluated the variation of the degree of self-organization in both Alfvénic and non-Alfvénic turbulent fluctuations with the radial evolution during a long time interval characterized by a slow solar wind. This analysis seems to show that the radial evolution of turbulent fluctuations is accompanied by a decrease in the degree of order, suggesting that, in the case of slow solar wind, the turbulence decays with radial distance.

Intracrystalline Transport Barriers Affecting the Self-Diffusion of CH4 in Zeolites |Na12|-A and |Na12-xKx|-A

2018 ◽  
Author(s):  
Niklas Hedin ◽  
Przemyslaw Rzepka ◽  
Alma Jasso-Salcedo ◽  
Tamara L. Church ◽  
Diana Bernin
Keyword(s):  
Close Contact ◽  
Mean Square Displacement ◽  
Diffusion Time ◽  
Mean Square ◽  
Zeolite A ◽  
Self Diffusion ◽  
Transport Barriers ◽  
Long Time ◽  
The Mean ◽  
Short Time

<p>Removing carbon dioxide is important for the upgrading of biogas or natural gas into compressed or liquefied methane, and adsorption-driven separation of CO<sub>2</sub> could be further advanced by developing for example new adsorbents. Zeolite adsorbents can select CO<sub>2</sub> over CH<sub>4</sub>, and we here confirmed that the adsorption of CH<sub>4</sub> on zeolite |Na<sub>12-<i>x</i></sub>K<i><sub>x</sub></i>|-A was significantly lower for samples with a high K<sup>+</sup> content, i.e. <i>x</i> > 2. Nevertheless, these samples adsorb CH<sub>4</sub> after long equilibration times as determined with <sup>1</sup>H NMR experiments. To assess further the intracrystalline diffusion of CH<sub>4</sub> in these zeolites, pulsed-field gradient NMR experiments were performed. In large crystals of zeolites |Na<sub>12-<i>x</i></sub>K<i><sub>x</sub></i>|-A, the long-time diffusion coefficients of CH<sub>4</sub> did not vary with <i>x</i>, and the mean square displacement was about 1.5 mm irrespective of the diffusion time. Also for zeolite |Na<sub>12</sub>|-A samples of three different particle sizes (~0.44, ~2.9, ~10.6 mm), the mean-square displacement of CH<sub>4</sub> was 1.5 mm and largely independent of the diffusion time. This similarity provided further evidence for an intracrystalline diffusion restriction for CH<sub>4</sub> within the medium- and large-sized zeolite A crystals, and possibly of clustering and close contact among the small zeolite A crystals. The long-time diffusion coefficient of adsorbed CH<sub>4</sub> was (at 1 atm and 298 K) about 1 ´ 10<sup>–10</sup> m<sup>2</sup>/s irrespective of the size of the zeolite particle or the studied content of K<sup>+</sup> in zeolites |Na<sub>12-<i>x</i></sub>K<i><sub>x</sub></i>|-A and |Na<sub>12</sub>|-A. The <i>T</i><sub>1</sub><i> </i>relaxation time for adsorbed CH<sub>4</sub> on zeolites |Na<sub>12-<i>x</i></sub>K<i><sub>x</sub></i>|-A with <i>x</i> > 2 was smaller than for those with <i>x</i> < 2, indicating that the short-time diffusion of CH<sub>4</sub> was hindered.</p>

Intracrystalline Transport Barriers Affecting the Self-Diffusion of CH4 in Zeolites |Na12|-A and |Na12-xKx|-A

2018 ◽  
Author(s):  
Niklas Hedin ◽  
Przemyslaw Rzepka ◽  
Alma Jasso-Salcedo ◽  
Tamara L. Church ◽  
Diana Bernin
Keyword(s):  
Close Contact ◽  
Mean Square Displacement ◽  
Diffusion Time ◽  
Mean Square ◽  
Zeolite A ◽  
Self Diffusion ◽  
Transport Barriers ◽  
Long Time ◽  
The Mean ◽  
Short Time

<p>Removing carbon dioxide is important for the upgrading of biogas or natural gas into compressed or liquefied methane, and adsorption-driven separation of CO<sub>2</sub> could be further advanced by developing for example new adsorbents. Zeolite adsorbents can select CO<sub>2</sub> over CH<sub>4</sub>, and we here confirmed that the adsorption of CH<sub>4</sub> on zeolite |Na<sub>12-<i>x</i></sub>K<i><sub>x</sub></i>|-A was significantly lower for samples with a high K<sup>+</sup> content, i.e. <i>x</i> > 2. Nevertheless, these samples adsorb CH<sub>4</sub> after long equilibration times as determined with <sup>1</sup>H NMR experiments. To assess further the intracrystalline diffusion of CH<sub>4</sub> in these zeolites, pulsed-field gradient NMR experiments were performed. In large crystals of zeolites |Na<sub>12-<i>x</i></sub>K<i><sub>x</sub></i>|-A, the long-time diffusion coefficients of CH<sub>4</sub> did not vary with <i>x</i>, and the mean square displacement was about 1.5 mm irrespective of the diffusion time. Also for zeolite |Na<sub>12</sub>|-A samples of three different particle sizes (~0.44, ~2.9, ~10.6 mm), the mean-square displacement of CH<sub>4</sub> was 1.5 mm and largely independent of the diffusion time. This similarity provided further evidence for an intracrystalline diffusion restriction for CH<sub>4</sub> within the medium- and large-sized zeolite A crystals, and possibly of clustering and close contact among the small zeolite A crystals. The long-time diffusion coefficient of adsorbed CH<sub>4</sub> was (at 1 atm and 298 K) about 1 ´ 10<sup>–10</sup> m<sup>2</sup>/s irrespective of the size of the zeolite particle or the studied content of K<sup>+</sup> in zeolites |Na<sub>12-<i>x</i></sub>K<i><sub>x</sub></i>|-A and |Na<sub>12</sub>|-A. The <i>T</i><sub>1</sub><i> </i>relaxation time for adsorbed CH<sub>4</sub> on zeolites |Na<sub>12-<i>x</i></sub>K<i><sub>x</sub></i>|-A with <i>x</i> > 2 was smaller than for those with <i>x</i> < 2, indicating that the short-time diffusion of CH<sub>4</sub> was hindered.</p>

scholarly journals Identifying short- and long-time modes of the mean-square displacement: An improved nonlinear fitting approach

AIP Advances ◽  
2019 ◽  
Vol 9 (5) ◽  
pp. 055112
Author(s):  
M. K. Riahi ◽  
I. A. Qattan ◽  
J. Hassan ◽  
D. Homouz
Keyword(s):  
Mean Square Displacement ◽  
Mean Square ◽  
Nonlinear Fitting ◽  
Long Time ◽  
The Mean
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