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Proceedings of the National Academy of... Mar 2020Protein mobility at solid-liquid interfaces can affect the performance of applications such as bioseparations and biosensors by facilitating reorganization of adsorbed...
Protein mobility at solid-liquid interfaces can affect the performance of applications such as bioseparations and biosensors by facilitating reorganization of adsorbed protein, accelerating molecular recognition, and informing the fundamentals of adsorption. In the case of ion-exchange chromatographic beads with small, tortuous pores, where the existence of surface diffusion is often not recognized, slow mass transfer can result in lower resin capacity utilization. We demonstrate that accounting for and exploiting protein surface diffusion can alleviate the mass-transfer limitations on multiple significant length scales. Although the surface diffusivity has previously been shown to correlate with ionic strength (IS) and binding affinity, we show that the dependence is solely on the binding affinity, irrespective of pH, IS, and resin ligand density. Different surface diffusivities give rise to different protein distributions within the resin, as characterized using confocal microscopy and small-angle neutron scattering (length scales of micrometer and nanometer, respectively). The binding dependence of surface diffusion inspired a protein-loading approach in which the binding affinity, and hence the surface diffusivity, is modulated by varying IS. Such gradient loading increased the protein uptake efficiency by up to 43%, corroborating the importance of protein surface diffusion in protein transport in ion-exchange chromatography.
Topics: Diffusion; Ion Exchange Resins; Models, Chemical; Proteins
PubMed: 32179691
DOI: 10.1073/pnas.1921499117 -
Physical Review Letters Jun 2023We analyze the onset of diffusive hydrodynamics in the one-dimensional hard-rod gas subject to stochastic backscattering. While this perturbation breaks integrability...
We analyze the onset of diffusive hydrodynamics in the one-dimensional hard-rod gas subject to stochastic backscattering. While this perturbation breaks integrability and leads to a crossover from ballistic to diffusive transport, it preserves infinitely many conserved quantities corresponding to even moments of the velocity distribution of the gas. In the limit of small noise, we derive the exact expressions for the diffusion and structure factor matrices, and show that they generically have off diagonal components. We find that the particle density structure factor is non-Gaussian and singular near the origin, with a return probability showing logarithmic deviations from diffusion.
Topics: Diffusion; Hydrodynamics; Probability
PubMed: 37390446
DOI: 10.1103/PhysRevLett.130.247101 -
The Journal of Chemical Physics Sep 2022We use coarse-grained simulations to explore the diffusion mechanism of nanoparticles with different sizes at various nanoparticle-polymer interactions in regular...
We use coarse-grained simulations to explore the diffusion mechanism of nanoparticles with different sizes at various nanoparticle-polymer interactions in regular cross-linked polymer networks. The long time diffusivities of nanoparticles show a non-monotonic tendency at various nanoparticle-polymer interactions due to the intermittent hopping of nanoparticles through network cells. The preferred locations of small nanoparticles switch from the cell centers to the corners of cells as they interact with the network more strongly, which results in the hopping energy barrier between different cells switching from cell center localization to adsorption on networks. Steric hindrance seriously hampers large nanoparticles from hopping to neighboring network cells, and the interactions between the nanoparticle and network enhance the network deformability and also affect the hopping of nanoparticles. The multiple constraint mechanisms result in the non-monotonic diffusivities of nanoparticles with different interactions and non-Brownian motions at different time scales. Our work illustrates the hopping mechanisms of nanoparticles in polymer networks from thermodynamic and dynamic points of view.
Topics: Adsorption; Computer Simulation; Diffusion; Nanoparticles; Polymers
PubMed: 36109225
DOI: 10.1063/5.0098947 -
Journal of the Royal Society, Interface Mar 2023How memory shapes animals' movement paths is a topic of growing interest in ecology, with connections to planning for conservation and climate change. Empirical studies...
How memory shapes animals' movement paths is a topic of growing interest in ecology, with connections to planning for conservation and climate change. Empirical studies suggest that memory has both temporal and spatial components, and can include both attractive and aversive elements. Here, we introduce reinforced diffusions (the continuous time counterpart of reinforced random walks) as a modelling framework for understanding the role that memory plays in determining animal movements. This framework includes reinforcement via functions of time before present and of distance away from a current location. Focusing on the interplay between memory and central place attraction (a component of home ranging behaviour), we explore patterns of space usage that result from the reinforced diffusion. Our efforts identify three qualitatively different behaviours: bounded wandering behaviour that does not collapse spatially, collapse to a very small area, and, most intriguingly, convergence to a cycle. Subsequent applications show how reinforced diffusion can create movement trajectories emulating the learning of movement routes by homing pigeons and consolidation of ant travel paths. The mathematically explicit manner with which assumptions about the structure of memory can be stated and subsequently explored provides linkages to biological concepts like an animal's 'immediate surroundings' and memory decay.
Topics: Animals; Ecology; Learning; Diffusion; Movement; Models, Biological
PubMed: 36987616
DOI: 10.1098/rsif.2022.0700 -
Physical Review. E Mar 2019Morphogen gradients play a vital role in developmental biology by enabling embryonic cells to infer their spatial location and determine their developmental fate...
Morphogen gradients play a vital role in developmental biology by enabling embryonic cells to infer their spatial location and determine their developmental fate accordingly. The standard mechanism for generating a morphogen gradient involves a morphogen being produced from a localized source and subsequently degrading. While this mechanism is effective over the length and time scales of tissue development, it fails over typical subcellular length scales due to the rapid dissipation of spatial asymmetries. In a recent theoretical work, we found an alternative mechanism for generating concentration gradients of diffusing molecules, in which the molecules switch between spatially constant diffusivities at switching rates that depend on the spatial location of a molecule. Independently, an experimental and computational study later found that Caenorhabditis elegans zygotes rely on this mechanism for cell polarization. In this paper, we extend our analysis of switching diffusivities to determine its role in protein concentration gradient formation. In particular, we determine how switching diffusivities modifies the standard theory and show how space-dependent switching diffusivities can yield a gradient in the absence of a localized source. Our mathematical analysis yields explicit formulas for the intracellular concentration gradient which closely match the results of previous experiments and numerical simulations.
Topics: Animals; Caenorhabditis elegans; Chemotaxis; Computer Simulation; Diffusion; Drosophila; Intracellular Space; Models, Biological; Morphogenesis; Protein Conformation; Proteins
PubMed: 30999457
DOI: 10.1103/PhysRevE.99.032409 -
Physical Review Letters Feb 2022The diffusive epidemic process is a paradigmatic example of an absorbing state phase transition in which healthy and infected individuals spread with different diffusion...
The diffusive epidemic process is a paradigmatic example of an absorbing state phase transition in which healthy and infected individuals spread with different diffusion constants. Using stochastic activity spreading simulations in combination with finite-size scaling analyses we reveal two qualitatively different processes that characterize the critical dynamics: subdiffusive propagation of infection clusters and diffusive fluctuations in the healthy population. This suggests the presence of a strong-coupling regime and sheds new light on a long-standing debate about the theoretical classification of the system.
Topics: Diffusion; Epidemics; Humans; Phase Transition
PubMed: 35244441
DOI: 10.1103/PhysRevLett.128.078302 -
IEEE Transactions on Visualization and... 2007This paper proposes an image-based painterly rendering algorithm for automatically synthesizing an image with color ink diffusion. We suggest a mathematical model with a...
This paper proposes an image-based painterly rendering algorithm for automatically synthesizing an image with color ink diffusion. We suggest a mathematical model with a physical base to simulate the phenomenon of color colloidal ink diffusing into absorbent paper. Our algorithm contains three main parts: a feature extraction phase, a Kubelka-Munk (KM) color mixing phase, and a color ink diffusion synthesis phase. In the feature extraction phase, the information of the reference image is simplified by luminance division and color segmentation. In the color mixing phase, the KM theory is employed to approximate the result when one pigment is painted upon another pigment layer. Then, in the color ink diffusion synthesis phase, the physically-based model that we propose is employed to simulate the result of color ink diffusion in absorbent paper using a texture synthesis technique. Our image-based ink diffusing rendering (IBCIDR) algorithm eliminates the drawback of conventional Chinese ink simulations, which are limited to the black ink domain, and our approach demonstrates that, without using any strokes, a color image can be automatically converted to the diffused ink style with a visually pleasing appearance.
Topics: Algorithms; Color; Coloring Agents; Computer Graphics; Computer Simulation; Diffusion; Image Interpretation, Computer-Assisted; Ink; Models, Chemical; Paintings; Paper; User-Computer Interface
PubMed: 17218741
DOI: 10.1109/TVCG.2007.41 -
Journal of Biomechanical Engineering Jul 2023The cartilage endplates (CEPs) on the superior and inferior surfaces of the intervertebral disk (IVD), are the primary nutrient transport pathways between the disk and...
The cartilage endplates (CEPs) on the superior and inferior surfaces of the intervertebral disk (IVD), are the primary nutrient transport pathways between the disk and the vertebral body. Passive diffusion is responsible for transporting small nutrient and metabolite molecules through the avascular CEPs. The baseline solute diffusivities in healthy CEPs have been previously studied, however alterations in CEP diffusion associated with IVD degeneration remain unclear. This study aimed to quantitatively compare the solute diffusion in healthy and degenerated human CEPs using a fluorescence recovery after photobleaching (FRAP) approach. Seven healthy CEPs and 22 degenerated CEPs were collected from five fresh-frozen human cadaveric spines and 17 patients undergoing spine fusion surgery, respectively. The sodium fluorescein diffusivities in CEP radial and vertical directions were measured using the FRAP method. The CEP calcification level was evaluated by measuring the average X-ray attenuation. No difference was found in solute diffusivities between radial and axial directions in healthy and degenerated CEPs. Compared to healthy CEPs, the average solute diffusivity was 44% lower in degenerated CEPs (Healthy: 29.07 μm2/s (CI: 23.96-33.62 μm2/s); degenerated: 16.32 μm2/s (CI: 13.84-18.84 μm2/s), p < 0.001). The average solute diffusivity had an inverse relationship with the degree of CEP calcification as determined by the normalized X-ray attenuation values (ß = -22.19, R2 = 0.633; p < 0.001). This study suggests that solute diffusion through the disk and vertebral body interface is significantly hindered by CEP calcification, providing clues to help further understand the mechanism of IVD degeneration.
Topics: Humans; Cartilage; Intervertebral Disc; Intervertebral Disc Degeneration; Biological Transport; Diffusion; Calcinosis
PubMed: 36752723
DOI: 10.1115/1.4056871 -
The Journal of Physical Chemistry. B May 2021Consider a particle whose drift velocity fluctuates due to transitions among discrete states or due to diffusion in a confined moving fluid. At long times, the dynamics...
Consider a particle whose drift velocity fluctuates due to transitions among discrete states or due to diffusion in a confined moving fluid. At long times, the dynamics of the particle in the direction of transport can be described in terms of the average drift velocity and an effective diffusivity. For both types of fluctuations, we show that the effective diffusivity is the sum of the average intrinsic diffusivity and the time integral of the velocity correlation function of the deviation of the fluctuating velocity from its mean value. For nearest-neighbor interstate transitions and for one-dimensional diffusion in a perpendicular direction, the time integral can be found in closed form. Our analytical expressions for the effective diffusivity recover the classic results for Taylor dispersion in the laminar flow of viscous fluid and for cargo transport along microtubules by molecular motors.
Topics: Diffusion; Microtubules; Viscosity
PubMed: 33881851
DOI: 10.1021/acs.jpcb.1c01856 -
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