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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 -
Journal of Biophotonics Feb 2018Quantitative measurements of intravascular microscopic dynamics, such as absolute blood flow velocity, shear stress and the diffusion coefficient of red blood cells...
Quantitative measurements of intravascular microscopic dynamics, such as absolute blood flow velocity, shear stress and the diffusion coefficient of red blood cells (RBCs), are fundamental in understanding the blood flow behavior within the microcirculation, and for understanding why diffuse correlation spectroscopy (DCS) measurements of blood flow are dominantly sensitive to the diffusive motion of RBCs. Dynamic light scattering-optical coherence tomography (DLS-OCT) takes the advantages of using DLS to measure particle flow and diffusion within an OCT resolution-constrained three-dimensional volume, enabling the simultaneous measurements of absolute RBC velocity and diffusion coefficient with high spatial resolution. In this work, we applied DLS-OCT to measure both RBC velocity and the shear-induced diffusion coefficient within penetrating venules of the somatosensory cortex of anesthetized mice. Blood flow laminar profile measurements indicate a blunted laminar flow profile and the degree of blunting decreases with increasing vessel diameter. The measured shear-induced diffusion coefficient was proportional to the flow shear rate with a magnitude of ~0.1 to 0.5 × 10 mm . These results provide important experimental support for the recent theoretical explanation for why DCS is dominantly sensitive to RBC diffusive motion.
Topics: Algorithms; Animals; Biomechanical Phenomena; Diffusion; Dynamic Light Scattering; Erythrocytes; Female; Mechanical Phenomena; Mice; Tomography, Optical Coherence
PubMed: 28700129
DOI: 10.1002/jbio.201700070 -
Biophysical Journal Jun 2021From nutrient uptake to chemoreception to synaptic transmission, many systems in cell biology depend on molecules diffusing and binding to membrane receptors....
From nutrient uptake to chemoreception to synaptic transmission, many systems in cell biology depend on molecules diffusing and binding to membrane receptors. Mathematical analysis of such systems often neglects the fact that receptors process molecules at finite kinetic rates. A key example is the celebrated formula of Berg and Purcell for the rate that cell surface receptors capture extracellular molecules. Indeed, this influential result is only valid if receptors transport molecules through the cell wall at a rate much faster than molecules arrive at receptors. From a mathematical perspective, ignoring receptor kinetics is convenient because it makes the diffusing molecules independent. In contrast, including receptor kinetics introduces correlations between the diffusing molecules because, for example, bound receptors may be temporarily blocked from binding additional molecules. In this work, we present a modeling framework for coupling bulk diffusion to surface receptors with finite kinetic rates. The framework uses boundary homogenization to couple the diffusion equation to nonlinear ordinary differential equations on the boundary. We use this framework to derive an explicit formula for the cellular uptake rate and show that the analysis of Berg and Purcell significantly overestimates uptake in some typical biophysical scenarios. We confirm our analysis by numerical simulations of a many-particle stochastic system.
Topics: Diffusion; Kinetics; Ligands; Models, Biological; Receptors, Cell Surface
PubMed: 33794148
DOI: 10.1016/j.bpj.2021.03.021 -
European Biophysics Journal : EBJ Jul 2020A computational methodology to simulate the diffusion of ions from point sources (e.g., ion channels) is described. The outlined approach computes the ion concentration...
A computational methodology to simulate the diffusion of ions from point sources (e.g., ion channels) is described. The outlined approach computes the ion concentration from a cluster of many ion channels at pre-specified locations as a function of time using the theory of propagation integrals. How the channels' open/closed states evolve in time does not need to be known at the start of the simulation, but can be updated on-the-fly as the simulation goes along. The technique uses analytic formulas for the solutions of the diffusion equation for three common geometries: (1) ions diffusing from a membrane (planar symmetry); (2) ions diffusing into a narrow cleft for effective two-dimensional diffusion (cylindrical symmetry); and (3) ions diffusing into open space like the cytosol (spherical symmetry). Because these formulas are exact solutions valid for arbitrarily long timesteps, no spatial or time discretizations are necessary. The only discrete locations are where the ion concentration is computed, and the only discrete timesteps are when the channels' open/closed states are updated. Beyond pure diffusion, the technique is generalized to the Excess Buffer Approximation of ion chelation to give an analytic solution of this approximation of the full reaction/diffusion system. Both the pure diffusion and the diffusion/buffering algorithms scale linearly with the number of channels and the number of ion concentration locations.
Topics: Cell Membrane; Computer Simulation; Diffusion; Ion Channels; Models, Biological
PubMed: 32488299
DOI: 10.1007/s00249-020-01438-9 -
Physical Review Letters Sep 2021Bacterial swarms display intriguing dynamical states like active turbulence. Now, using a hydrodynamic model, we show that such dense active suspensions manifest...
Bacterial swarms display intriguing dynamical states like active turbulence. Now, using a hydrodynamic model, we show that such dense active suspensions manifest superdiffusion, via Lévy walks, which masquerades as a crossover from ballistic to diffusive scaling in measurements of mean-squared displacements, and is tied to the emergence of hitherto undetected oscillatory streaks in the flow. Thus, while laying the theoretical framework of an emergent advantageous strategy in the collective behavior of microorganisms, our Letter underlines the essential differences between active and inertial turbulence.
Topics: Bacterial Physiological Phenomena; Cell Movement; Diffusion; Models, Biological; Models, Theoretical; Movement
PubMed: 34558935
DOI: 10.1103/PhysRevLett.127.118001 -
Physical Review. E May 2023Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as...
Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces. Here we use techniques from large deviation theory to study the statistics of time-integrated functionals of linear diffusions, considering three classes of functionals or observables relevant for nonequilibrium systems which involve linear or quadratic integrals of the state in time. For these, we derive exact results for the scaled cumulant generating function and the rate function, characterizing the fluctuations of observables in the long-time limit, and study in an exact way the set of paths or effective process that underlies these fluctuations. The results give a complete description of how fluctuations arise in linear diffusions in terms of effective forces that remain linear in the state or, alternatively, in terms of fluctuating densities and currents that solve Riccati-type equations. We illustrate these results using two common nonequilibrium models, namely, transverse diffusions in two dimensions involving a nonconservative rotating force, and two interacting particles in contact with heat baths at different temperatures.
Topics: Stochastic Processes; Diffusion; Time Factors
PubMed: 37328997
DOI: 10.1103/PhysRevE.107.054111 -
European Biophysics Journal : EBJ Jul 2022Diffusive behavior of human serum albumin (HSA) in the presence of Mg and Cu ions was studied by pulsed field gradient nuclear magnetic resonance (PFG NMR) and dynamic...
Diffusive behavior of human serum albumin (HSA) in the presence of Mg and Cu ions was studied by pulsed field gradient nuclear magnetic resonance (PFG NMR) and dynamic light scattering (DLS). According to NMR data yielding measurements of HSA self-diffusion coefficient, a weighted average of the protein monomers and oligomers diffusion mobility in the presence of metal ions was observed. While the short-time collective diffusion measured by DLS showed one type of diffusing species in ion-free HSA solution and two molecular forms of HSA in the presence of metal ions. The light intensity correlation function analysis showed that HSA oligomers have a limited lifetime (lower limit is about 0.4 ms) intermediate between characteristic time scales of PFG NMR and DLS experiments. For a theoretical description of concentration dependence of HSA self- and collective diffusion coefficients, the phenomenological approach based on the frictional formalism of non-equilibrium thermodynamics was used (Vink theory), allowing analysis of the solvent-solute and solute-solute interactions in protein solutions. In the presence of metal ions, a significant increase of HSA protein-protein friction coefficient was shown. Based on theoretical analysis of collective diffusion data, the positive values of second virial coefficients A for HSA monomers were obtained. The A values were found to be higher for the HSA with metal ions compared with the ion-free HSA solution. This is due to the more pronounced contribution of repulsion in protein-protein interactions of HSA monomers in the presence of Mg and Cu ions.
Topics: Diffusion; Dynamic Light Scattering; Humans; Ions; Magnetic Resonance Spectroscopy; Metals; Serum Albumin, Human; Water
PubMed: 35687130
DOI: 10.1007/s00249-022-01605-0 -
Journal of Visualized Experiments : JoVE Sep 2018Diffusive convection (DC) occurs when the vertical stratified density is controlled by two opposing scalar gradients that have distinctly different molecular...
Diffusive convection (DC) occurs when the vertical stratified density is controlled by two opposing scalar gradients that have distinctly different molecular diffusivities, and the larger- and smaller- diffusivity scalar gradients have negative and positive contributions for the density distribution, respectively. The DC occurs in many natural processes and engineering applications, for example, oceanography, astrophysics and metallurgy. In oceans, one of the most remarkable features of DC is that the vertical temperature and salinity profiles are staircase-like structure, composed of consecutive steps with thick homogeneous convecting layers and relatively thin and high-gradient interfaces. The DC staircases have been observed in many oceans, especially in the Arctic and Antarctic Oceans, and play an important role on the ocean circulation and climatic change. In the Arctic Ocean, there exist basin-wide and persistent DC staircases in the upper and deep oceans. The DC process has an important effect on diapycnal mixing in the upper ocean and may significantly influence the surface ice-melting. Compared to the limitations of field observations, laboratory experiment shows its unique advantage to effectively examine the dynamic and thermodynamic processes in DC, because the boundary conditions and the controlled parameters can be strictly adjusted. Here, a detailed protocol is described to simulate the evolution process of DC staircase structure, including its generation, development and disappearance, in a rectangular tank filled with stratified saline water. The experimental setup, evolution process, data analysis, and discussion of results are described in detail.
Topics: Antarctic Regions; Arctic Regions; Climate Change; Convection; Diffusion; Ice Cover; Oceans and Seas; Salinity; Seawater; Temperature; Water Movements
PubMed: 30247476
DOI: 10.3791/58316 -
Biophysical Journal Nov 2015The efficient treatment of many ocular diseases depends on the rapid diffusive distribution of solutes such as drugs or drug delivery vehicles through the vitreous...
The efficient treatment of many ocular diseases depends on the rapid diffusive distribution of solutes such as drugs or drug delivery vehicles through the vitreous humor. However, this multicomponent hydrogel possesses selective permeability properties, which allow for the diffusion of certain molecules and particles, whereas others are immobilized. In this study, we perform an interspecies comparison showing that the selective permeability properties of the vitreous are conserved across several mammalian species. We identify the polyanionic glycosaminoglycans hyaluronic acid and heparan sulfate as two key macromolecules that establish this selective permeability. We show that electrostatic interactions between the polyanionic macromolecules and diffusing solutes can be weakened by charge screening or enzymatic glycosaminoglycan digestion. Furthermore, molecule penetration into the vitreous is also charge-dependent and only efficient as long as the net charge of the molecule does not exceed a certain threshold.
Topics: Animals; Cattle; Diffusion; Heparitin Sulfate; Humans; Hyaluronic Acid; Permeability; Sheep; Swine; Vitreous Body
PubMed: 26588575
DOI: 10.1016/j.bpj.2015.10.002 -
Biophysical Journal Jun 2018Diffusion in cellular membranes is regulated by processes that occur over a range of spatial and temporal scales. These processes include membrane fluidity, interprotein...
Diffusion in cellular membranes is regulated by processes that occur over a range of spatial and temporal scales. These processes include membrane fluidity, interprotein and interlipid interactions, interactions with membrane microdomains, interactions with the underlying cytoskeleton, and cellular processes that result in net membrane movement. The complex, non-Brownian diffusion that results from these processes has been difficult to characterize, and moreover, the impact of factors such as membrane recycling on membrane diffusion remains largely unexplored. We have used a careful statistical analysis of single-particle tracking data of the single-pass plasma membrane protein CD93 to show that the diffusion of this protein is well described by a continuous-time random walk in parallel with an aging process mediated by membrane corrals. The overall result is an evolution in the diffusion of CD93: proteins initially diffuse freely on the cell surface but over time become increasingly trapped within diffusion-limiting membrane corrals. Stable populations of freely diffusing and corralled CD93 are maintained by an endocytic/exocytic process in which corralled CD93 is selectively endocytosed, whereas freely diffusing CD93 is replenished by exocytosis of newly synthesized and recycled CD93. This trafficking not only maintained CD93 diffusivity but also maintained the heterogeneous distribution of CD93 in the plasma membrane. These results provide insight into the nature of the biological and biophysical processes that can lead to significantly non-Brownian diffusion of membrane proteins and demonstrate that ongoing membrane recycling is critical to maintaining steady-state diffusion and distribution of proteins in the plasma membrane.
Topics: Animals; CHO Cells; Cell Membrane; Cricetulus; Diffusion; Endocytosis; Exocytosis; Membrane Glycoproteins
PubMed: 29925025
DOI: 10.1016/j.bpj.2018.04.024