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Journal of Biomechanics Sep 2016The cartilage endplate (CEP) is implicated as the main pathway of nutrient supply to the healthy human intervertebral disc (IVD). In this study, the diffusivities of...
The cartilage endplate (CEP) is implicated as the main pathway of nutrient supply to the healthy human intervertebral disc (IVD). In this study, the diffusivities of nutrient/metabolite solutes in healthy CEP were assessed, and further correlated with tissue biochemical composition and structure. The CEPs from non-degenerated human IVD were divided into four regions: central, lateral, anterior, and posterior. The diffusivities of glucose and lactate were measured with a custom diffusion cell apparatus under 0%, 10%, and 20% compressive strains. Biochemical assays were conducted to quantify the water and glycosaminoglycan (GAG) contents. The Safranin-O and Ehrlich׳s hematoxylin and eosin staining and scanning electron microscopy (SEM) were performed to reveal the tissue structure of the CEP. Average diffusivities of glucose and lactate in healthy CEP were 2.68±0.93×10cm/s and 4.52±1.47×10cm/s, respectively. Solute diffusivities were region-dependent (p<0.0001) with the highest values in the central region, and mechanical strains impeded solute diffusion in the CEP (p<0.0001). The solute diffusivities were significantly correlated with the tissue porosities (glucose: p<0.0001, r=0.581; lactate: p<0.0001, r=0.534). Histological and SEM studies further revealed that the collagen fibers in healthy CEP are more compacted than those in the nucleus pulposus (NP) and annulus fibrosus (AF) and show no clear orientation. Compared to human AF and NP, much smaller solute diffusivities in human CEP suggested that it acts as a gateway for solute diffusion through the disc, maintaining the balance of nutritional environment in healthy human disc under mechanical loading and preventing the progression of disc degeneration.
Topics: Cartilage; Diffusion; Female; Glucose; Glycosaminoglycans; Humans; Intervertebral Disc; Intervertebral Disc Degeneration; Lactic Acid; Male; Middle Aged; Stress, Mechanical; Water
PubMed: 27338525
DOI: 10.1016/j.jbiomech.2016.06.008 -
Proceedings of the National Academy of... Dec 2022A noisy stabilized Kuramoto-Sivashinsky equation is analyzed by stochastic decomposition. For values of the control parameter for which periodic stationary patterns...
A noisy stabilized Kuramoto-Sivashinsky equation is analyzed by stochastic decomposition. For values of the control parameter for which periodic stationary patterns exist, the dynamics can be decomposed into diffusive and transverse parts which act on a stochastic potential. The relative positions of stationary states in the stochastic global potential landscape can be obtained from the topology spanned by the low-lying eigenmodes which interconnect them. Numerical simulations confirm the predicted landscape. The transverse component also predicts a universal class of vortex-like circulations around fixed points. These drive nonlinear drifting and limit cycle motion of the underlying periodic structure in certain regions of parameter space. Our findings might be relevant in studies of other nonlinear systems such as deep learning neural networks.
Topics: Diffusion; Motion; Neural Networks, Computer
PubMed: 36459639
DOI: 10.1073/pnas.2211359119 -
Biophysical Journal Jun 2023Previous studies have documented the formation of a heterodimer between the two protein kinases PDK1 and PKCα on a lipid bilayer containing their target lipids. This...
Previous studies have documented the formation of a heterodimer between the two protein kinases PDK1 and PKCα on a lipid bilayer containing their target lipids. This work investigates the association-dissociation kinetics of this PDK1:PKCα heterodimer. The approach monitors the two-dimensional diffusion of single, membrane-associated PDK1 molecules for diffusivity changes as PKCα molecules bind and unbind. In the absence of PKCα, a membrane-associated PDK1 molecule exhibits high diffusivity (or large diffusion constant, D) because its membrane-contacting PH domain binds the target PIP lipid headgroup with little bilayer penetration, yielding minimal frictional drag against the bilayer. In contrast, membrane-associated PKCα contacts the bilayer via its C1A, C1B, and C2 domains, which each bind at least one target lipid with significant bilayer insertion, yielding a large frictional drag and low diffusivity. The present findings reveal that individual fluor-PDK1 molecules freely diffusing on the membrane surface undergo reversible switching between distinct high and low diffusivity states, corresponding to the PDK1 monomer and the PDK1:PKCα heterodimer, respectively. The observed single-molecule diffusion trajectories are converted to step length time courses, then subjected to two-state, hidden Markov modeling and dwell time analysis. The findings reveal that both the PDK1 monomer state and the PDK1:PKCα heterodimer state decay via simple exponential kinetics, yielding estimates of rate constants for state switching in both directions. Notably, the PDK1:PKCα heterodimer has been shown to competitively inhibit PDK1 phosphoactivation of AKT1, and is believed to play a tumor suppressor role by limiting excess activation of the highly oncogenic PDK1/AKT1/mTOR pathway. Thus, the present elucidation of the PDK1:PKCα association-dissociation kinetics has important biological and medical implications. More broadly, the findings illustrate the power of single-molecule diffusion measurements to reveal the kinetics of association-dissociation events in membrane signaling reactions that yield a large change in diffusive mobility.
Topics: Protein Kinase C-alpha; Lipid Bilayers; Signal Transduction; Protein Binding; Diffusion
PubMed: 36733254
DOI: 10.1016/j.bpj.2023.01.041 -
Electrophoresis Dec 2023The temperature is often a critical factor affecting the diffusion of nanoparticles in complex physiological media, but its specific effects are still to be fully...
The temperature is often a critical factor affecting the diffusion of nanoparticles in complex physiological media, but its specific effects are still to be fully understood. Here, we constructed a temperature-regulated model of semidilute polymer solution and experimentally investigated the temperature-mediated diffusion of nanoparticles using the particle tracking method. By examining the ensemble-averaged mean square displacements (MSDs), we found that the MSD grows gradually as the temperature increases while the transition time from sublinear to linear stage in MSD decreases. Meanwhile, the temperature-dependent measured diffusivity of the nanoparticles shows an exponential growth. We revealed that these temperature-mediated changes are determined by the composite effect of the macroscale property of polymer solution and the microscale dynamics of polymer chain as well as nanoparticles. Furthermore, the measured non-Gaussian displacement probability distributions were found to exhibit non-Gaussian fat tails, and the tailed distribution is enhanced as the temperature increases. The non-Gaussianity was calculated and found to vary in the same trend with the tailed distribution, suggesting the occurrence of hopping events. This temperature-mediated non-Gaussian feature validates the recent theory of thermally induced activated hopping. Our results highlight the temperature-mediated changes in diffusive transport of nanoparticles in polymer solutions and may provide the possible strategy to improve drug delivery in physiological media.
Topics: Polymers; Temperature; Diffusion; Nanoparticles; Drug Delivery Systems
PubMed: 37736676
DOI: 10.1002/elps.202300054 -
Journal of Physics. Condensed Matter :... Feb 2018Chemotaxis and auto-chemotaxis are key mechanisms in the dynamics of micro-organisms, e.g. in the acquisition of nutrients and in the communication between individuals,...
Chemotaxis and auto-chemotaxis are key mechanisms in the dynamics of micro-organisms, e.g. in the acquisition of nutrients and in the communication between individuals, influencing the collective behaviour. However, chemical signalling and the natural environment of biological swimmers are generally complex, making them hard to access analytically. We present a well-controlled, tunable artificial model to study chemotaxis and autochemotaxis in complex geometries, using microfluidic assays of self-propelling oil droplets in an aqueous surfactant solution (Herminghaus et al 2014 Soft Matter 10 7008-22; Krüger et al 2016 Phys. Rev. Lett. 117). Droplets propel via interfacial Marangoni stresses powered by micellar solubilisation. Moreover, filled micelles act as a chemical repellent by diffusive phoretic gradient forces. We have studied these chemotactic effects in a series of microfluidic geometries, as published in Jin et al (2017 Proc. Natl Acad. Sci. 114 5089-94): first, droplets are guided along the shortest path through a maze by surfactant diffusing into the maze from the exit. Second, we let auto-chemotactic droplet swimmers pass through bifurcating microfluidic channels and record anticorrelations between the branch choices of consecutive droplets. We present an analytical Langevin model matching the experimental data. In a previously unpublished experiment, pillar arrays of variable sizes and shapes provide a convex wall interacting with the swimmer and, in the case of attachment, bending its trajectory and forcing it to revert to its own trail. We observe different behaviours based on the interplay of wall curvature and negative autochemotaxis, i.e. no attachment for highly curved interfaces, stable trapping at large pillars, and a narrow transition region where negative autochemotaxis makes the swimmers detach after a single orbit.
Topics: Bacteria; Chemotaxis; Diffusion; Microfluidics; Surface-Active Agents; Water
PubMed: 29243668
DOI: 10.1088/1361-648X/aaa208 -
Journal of Fluorescence May 2022In most biological processes, diffusion plays a critical role in transferring various bio-molecules to transfer desirable locations in an effective and energy-efficient...
In most biological processes, diffusion plays a critical role in transferring various bio-molecules to transfer desirable locations in an effective and energy-efficient manner. How fast molecules are transferred is measured by diffusion coefficients. Since each bio-molecules, in particular, signaling molecules have their unique diffusion coefficients and quantifying the diffusion coefficients help us to understand various time scales of both physiological and pathological processes in biological systems. Moreover, since diffusion profiles of a diffusant vary in different micro-environments of cell membranes, accurate diffusion coefficient also can provide a good picture of membrane landscapes as well as interactions of different membrane constituents. Currently, only a few experimental methods are available to assess the diffusion coefficient of a biomolecule of interest in live cells including Fluorescence Recovery After Photobleaching (FRAP). FRAP was developed to study diffusion processes of biomolecules in the cell membranes in the 1970s. Albeit its long history, the main principle of FRAP analysis has remained unchanged since its inception: fitting FRAP data to a theoretical diffusion model for the best fitting diffusion coefficient or using the relation between the half time of recovery and ROI size. In this study, we developed a flexible yet versatile confocal FRAP data analysis framework based on linear regression analysis which allows FRAP users to determine the diffusion from either single or multiple FRAP data points without data fitting. We also validated this approach for a series of fluorescently labeled soluble and membrane-bound proteins and lipids.
Topics: Cell Membrane; Diffusion; Fluorescence Recovery After Photobleaching; Membrane Proteins; Regression Analysis
PubMed: 35254627
DOI: 10.1007/s10895-022-02926-1 -
Soft Matter Nov 2021The eukaryotic cell's cytoskeleton is a prototypical example of an active material: objects embedded within it are driven by molecular motors acting on the cytoskeleton,...
The eukaryotic cell's cytoskeleton is a prototypical example of an active material: objects embedded within it are driven by molecular motors acting on the cytoskeleton, leading to anomalous diffusive behavior. Experiments tracking the behavior of cell-attached objects have observed anomalous diffusion with a distribution of displacements that is non-Gaussian, with heavy tails. This has been attributed to "cytoquakes" or other spatially extended collective effects. We show, using simulations and analytical theory, that a simple continuum active gel model driven by fluctuating force dipoles naturally creates heavy power-law tails in cytoskeletal displacements. We predict that this power law exponent should depend on the geometry and dimensionality of where force dipoles are distributed through the cell; we find qualitatively different results for force dipoles in a 3D cytoskeleton and a quasi-two-dimensional cortex. We then discuss potential applications of this model both in cells and in synthetic active gels.
Topics: Cytoskeleton; Diffusion; Gels; Mechanical Phenomena; Microtubules
PubMed: 34651152
DOI: 10.1039/d1sm00705j -
Physical Review. E Feb 2018We study diffusion-controlled two-species annihilation with a finite number of particles. In this stochastic process, particles move diffusively, and when two particles...
We study diffusion-controlled two-species annihilation with a finite number of particles. In this stochastic process, particles move diffusively, and when two particles of opposite type come into contact, the two annihilate. We focus on the behavior in three spatial dimensions and for initial conditions where particles are confined to a compact domain. Generally, one species outnumbers the other, and we find that the difference between the number of majority and minority species, which is a conserved quantity, controls the behavior. When the number difference exceeds a critical value, the minority becomes extinct and a finite number of majority particles survive, while below this critical difference, a finite number of particles of both species survive. The critical difference Δ_{c} grows algebraically with the total initial number of particles N, and when N≫1, the critical difference scales as Δ_{c}∼N^{1/3}. Furthermore, when the initial concentrations of the two species are equal, the average number of surviving majority and minority particles, M_{+} and M_{-}, exhibit two distinct scaling behaviors, M_{+}∼N^{1/2} and M_{-}∼N^{1/6}. In contrast, when the initial populations are equal, these two quantities are comparable M_{+}∼M_{-}∼N^{1/3}.
Topics: Diffusion; Extinction, Biological; Models, Theoretical; Monte Carlo Method; Stochastic Processes; Survival Analysis
PubMed: 29548130
DOI: 10.1103/PhysRevE.97.022112 -
Biophysical Journal May 2019The trajectory of a single protein in the cytosol of a living cell contains information about its molecular interactions in its native environment. However, it has...
The trajectory of a single protein in the cytosol of a living cell contains information about its molecular interactions in its native environment. However, it has remained challenging to accurately resolve and characterize the diffusive states that can manifest in the cytosol using analytical approaches based on simplifying assumptions. Here, we show that multiple intracellular diffusive states can be successfully resolved if sufficient single-molecule trajectory information is available to generate well-sampled distributions of experimental measurements and if experimental biases are taken into account during data analysis. To address the inherent experimental biases in camera-based and MINFLUX-based single-molecule tracking, we use an empirical data analysis framework based on Monte Carlo simulations of confined Brownian motion. This framework is general and adaptable to arbitrary cell geometries and data acquisition parameters employed in two-dimensional or three-dimensional single-molecule tracking. We show that, in addition to determining the diffusion coefficients and populations of prevalent diffusive states, the timescales of diffusive state switching can be determined by stepwise increasing the time window of averaging over subsequent single-molecule displacements. Time-averaged diffusion analysis of single-molecule tracking data may thus provide quantitative insights into binding and unbinding reactions among rapidly diffusing molecules that are integral for cellular functions.
Topics: Computer Simulation; Cytoplasm; Cytosol; Diffusion; Kinetics; Monte Carlo Method; Single Molecule Imaging; Time Factors
PubMed: 31030884
DOI: 10.1016/j.bpj.2019.03.039 -
ELife Apr 2022In addition to diffusive signals, cells in tissue also communicate via long, thin cellular protrusions, such as airinemes in zebrafish. Before establishing...
In addition to diffusive signals, cells in tissue also communicate via long, thin cellular protrusions, such as airinemes in zebrafish. Before establishing communication, cellular protrusions must find their target cell. Here, we demonstrate that the shapes of airinemes in zebrafish are consistent with a finite persistent random walk model. The probability of contacting the target cell is maximized for a balance between ballistic search (straight) and diffusive search (highly curved, random). We find that the curvature of airinemes in zebrafish, extracted from live-cell microscopy, is approximately the same value as the optimum in the simple persistent random walk model. We also explore the ability of the target cell to infer direction of the airineme's source, finding that there is a theoretical trade-off between search optimality and directional information. This provides a framework to characterize the shape, and performance objectives, of non-canonical cellular protrusions in general.
Topics: Animals; Cell Surface Extensions; Diffusion; Zebrafish
PubMed: 35467525
DOI: 10.7554/eLife.75690