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Physical Review Letters Jun 2023We introduce a simple model of diffusive jump process where a fee is charged for each jump. The nonlinear cost function is such that slow jumps incur a flat fee, while...
We introduce a simple model of diffusive jump process where a fee is charged for each jump. The nonlinear cost function is such that slow jumps incur a flat fee, while for fast jumps the cost is proportional to the velocity of the jump. The model-inspired by the way taxi meters work-exhibits a very rich behavior. The cost for trajectories of equal length and equal duration exhibits giant fluctuations at a critical value of the scaled distance traveled. Furthermore, the full distribution of the cost until the target is reached exhibits an interesting "freezing" transition in the large-deviation regime. All the analytical results are corroborated by numerical simulations. Our results also apply to elastic systems near the depinning transition, when driven by a random force.
Topics: Diffusion; Algorithms
PubMed: 37354426
DOI: 10.1103/PhysRevLett.130.237102 -
Proceedings of the National Academy of... Oct 2022Remitted waves are used for sensing and imaging in diverse diffusive media from the Earth's crust to the human brain. Separating the source and detector increases the...
Remitted waves are used for sensing and imaging in diverse diffusive media from the Earth's crust to the human brain. Separating the source and detector increases the penetration depth of light, but the signal strength decreases rapidly, leading to a poor signal-to-noise ratio. Here, we show, experimentally and numerically, that wavefront shaping a laser beam incident on a diffusive sample enables an enhancement of remission by an order of magnitude at depths of up to 10 transport mean free paths. We develop a theoretical model which predicts the maximal remission enhancement. Our analysis reveals a significant improvement in the sensitivity of remitted waves to local changes of absorption deep inside diffusive media. This work illustrates the potential of coherent wavefront control for noninvasive diffuse wave imaging applications, such as diffuse optical tomography and functional near-infrared spectroscopy.
Topics: Brain; Diffusion; Humans; Signal-To-Noise Ratio
PubMed: 36191199
DOI: 10.1073/pnas.2207089119 -
Soft Matter Jun 2020We study the dynamics of a self-propelled particle advected by a steady laminar flow. The persistent motion of the self-propelled particle is described by an active...
We study the dynamics of a self-propelled particle advected by a steady laminar flow. The persistent motion of the self-propelled particle is described by an active Ornstein-Uhlenbeck process. We focus on the diffusivity properties of the particle as a function of persistence time and free-diffusion coefficient, revealing non-monotonic behaviors, with the occurrence of a minimum and a steep growth in the regime of large persistence time. In the latter limit, we obtain an analytical prediction for the scaling of the diffusion coefficient with the parameters of the active force. Our study sheds light on the effect of a flow-field on the diffusion of active particles, such as living microorganisms and motile phytoplankton in fluids.
Topics: Computer Simulation; Diffusion; Models, Theoretical; Motion
PubMed: 32469036
DOI: 10.1039/d0sm00450b -
BMC Biology Sep 2021Knowledge on the localization and mobility of enzymes inside bacterial cells is scarce, but important for understanding spatial regulation of metabolism. The four...
BACKGROUND
Knowledge on the localization and mobility of enzymes inside bacterial cells is scarce, but important for understanding spatial regulation of metabolism. The four central enzymes (Rib enzymes) of the riboflavin (RF) biosynthesis pathway in the Gram positive model bacterium Bacillus subtilis have been studied extensively in vitro, especially the heavy RF synthase, a large protein complex with a capsid structure formed by RibH and an encapsulated RibE homotrimer, which mediates substrate-channeling. However, little is known about the behavior and mobility of these enzymes in vivo.
RESULTS
We have investigated the localization and diffusion of the Rib enzymes in the cytoplasm of B. subtilis. By characterizing the diffusion of Rib enzymes in live cells using single particle tracking (SPT) we provide evidence for confined diffusion at the cell poles and otherwise Brownian motion. A majority of RibH particles showed clear nucleoid occlusion and a high degree of confined motion, which is largely abolished after treatment with Rifampicin, revealing that confinement is dependent on active transcription. Contrarily, RibE is mostly diffusive within the cell, showing only 14% encapsulation by RibH nanocompartments. By localizing different diffusive populations within single cells, we find that fast diffusion occurs mostly across the nucleoids located in the cell centers, while the slower, confined subdiffusion occurs at the crowded cell poles.
CONCLUSIONS
Our results provide evidence for locally different motion of active enzymes within the bacterial cytoplasm, setting up metabolic compartmentalization mostly at the poles of cells.
Topics: Bacillus subtilis; Cytoplasm; Diffusion; Intracellular Space; Riboflavin
PubMed: 34474681
DOI: 10.1186/s12915-021-01083-4 -
Mathematical Biosciences Dec 2022The bulk-surface wave pinning model is a reaction-diffusion system for studying cell polarisation. It is constituted by a surface reaction-diffusion equation, coupled to...
The bulk-surface wave pinning model is a reaction-diffusion system for studying cell polarisation. It is constituted by a surface reaction-diffusion equation, coupled to a bulk diffusion equation with a non-linear boundary condition. Cell polarisation arises as the surface component develops specific patterns. Since proteins diffuse much faster in the cell interior than on the membrane, in the literature, the bulk component is often assumed to be spatially homogeneous. Therefore, the model can be reduced to a single surface equation. However, in real applications a spatially non-uniform bulk component might be an important player to take into account. In this paper, we study, through numerical computations, the role of the bulk component and, more specifically, how different bulk diffusion rates might affect the polarisation response. We find that the bulk component is indeed a key factor in determining the surface polarisation response. Moreover, for certain geometries, it is the spatial heterogeneity of the bulk component that triggers the polarisation response, which might not be possible in a reduced model. Understanding how polarisation depends on bulk diffusivity might be crucial when studying models of migrating cells, which are naturally subject to domain deformation.
Topics: Diffusion; Cell Polarity
PubMed: 36397641
DOI: 10.1016/j.mbs.2022.108925 -
The Journal of Physical Chemistry... Nov 2022Diffusion is an essential means of mass transport in porous materials such as hydrogels, which are appealing in various biomedical applications. Herein, we investigate...
Diffusion is an essential means of mass transport in porous materials such as hydrogels, which are appealing in various biomedical applications. Herein, we investigate the diffusive motion of nanoparticles (NPs) in porous hydrogels to provide a microscopic view of confined diffusion. Based on the mean square displacement from particle tracking experiments, we elucidate the anomalous diffusion dynamics of the embedded NPs and reveal the heterogeneous pore structures in hydrogels. The results demonstrate that diffusive NPs can intermittently escape from single pores through void connective pathways and exhibit non-Gaussian displacement probability distribution. We simulate this scenario using the Monte Carlo method and clarify the existence of hopping events in porous diffusion. The resultant anomalous diffusion can be fully depicted by combining the hopping mechanism and the hydrodynamic effect. Our results highlight the hopping behavior through the connective pathways and establish a hybrid model to predict NP transport in porous environments.
Topics: Porosity; Diffusion; Nanoparticles; Hydrogels; Hydrodynamics; Biocompatible Materials
PubMed: 36350083
DOI: 10.1021/acs.jpclett.2c02733 -
Journal of Contaminant Hydrology Oct 2021Diffusion coefficients for Na was measured in low-permeability samples (diameter of 3 cm and average length of 7 cm) from the deep disposal site of the Siberian...
Diffusion coefficients for Na was measured in low-permeability samples (diameter of 3 cm and average length of 7 cm) from the deep disposal site of the Siberian Chemical Combine (SCC) using the end-diffusion technique. The direction of diffusion was perpendicular to the direction of bedding. Special equipment was designed and constructed for the experiment. Two types of concentration observations were used. For non-sorbing Na, EC sensors and the length distribution of sorbed elements were used. The synthetic solution used in the experiments was a model of the low-activity contaminant of the SCC and consisted of NaNO (25 g/L) and nitrate compounds of Cs, Ni, Co, and Sr (100 mg/L each). The measured values of the effective diffusion coefficients D for Na from 1.92 × 10 to 1.70 × 10 m/s. The microstructure was studied with X-ray microtomography for the same cores. Image shooting was performed on undisturbed microsamples with a size of 0.91 mm (700 vox). Spatial correlation analysis was performed after the binarization of each obtained 3-D structure. This analysis showed that the spatial correlation scale of the indicator variogram is considerably smaller than the microsample length. Then, a numerical simulation of the Laplace equation with binary coefficients for each microsample was performed. The results were analysed in the form of a plot of the tortuosity versus the porosity. Pore-scale simulations show a nonlinear decrease in the tortuosity with decreasing porosity. Exponential values in the range between 1.8 and 2.4 were found by fitting this graph with Archie's model. Anisotropic tortuosity is also detected in the horizontal and vertical directions. The diffusion coefficients of non-sorbing Na measured in this study agree with those of the pore-scale diffusion simulation of the microtomography data.
Topics: Computer Simulation; Diffusion; Permeability; Porosity; Soil
PubMed: 34298490
DOI: 10.1016/j.jconhyd.2021.103858 -
Physical Review Letters Nov 2022We investigate the dynamics of a single chiral active particle subject to an external torque due to the presence of a gravitational field. Our computer simulations...
We investigate the dynamics of a single chiral active particle subject to an external torque due to the presence of a gravitational field. Our computer simulations reveal an arbitrarily strong increase of the long-time diffusivity of the gravitactic agent when the external torque approaches the intrinsic angular drift. We provide analytic expressions for the mean-square displacement in terms of eigenfunctions and eigenvalues of the noisy-driven-pendulum problem. The pronounced maximum in the diffusivity is then rationalized by the vanishing of the lowest eigenvalues of the Fokker-Planck equation for the angular motion as the rotational diffusion decreases and the underlying classical bifurcation is approached. A simple harmonic-oscillator picture for the barrier-dominated motion provides a quantitative description for the onset of the resonance while its range of validity is determined by the crossover to a critical-fluctuation-dominated regime.
Topics: Diffusion; Computer Simulation; Motion
PubMed: 36493425
DOI: 10.1103/PhysRevLett.129.228003 -
Biophysical Journal Oct 2022Fluorescence recovery after photobleaching (FRAP) is a widely used biological experiment to study the kinetics of molecules that react and move randomly. Since the...
Fluorescence recovery after photobleaching (FRAP) is a widely used biological experiment to study the kinetics of molecules that react and move randomly. Since the development of FRAP in the 1970s, many reaction-diffusion models have been used to interpret FRAP data. However, intracellular molecules are widely observed to move by anomalous subdiffusion instead of normal diffusion. In this article, we extend a popular reaction-diffusion model of FRAP to the case of subdiffusion modeled by a fractional diffusion equation. By analyzing this reaction-subdiffusion model, we show that FRAP data are consistent with both diffusive and subdiffusive motion in many scenarios. We illustrate this general result by fitting our model to FRAP data from glucocorticoid receptors in a cell nucleus. We further show that the assumed model of molecular motion (normal diffusion or subdiffusion) strongly impacts the biological parameter values inferred from a given experimentally observed FRAP curve. We additionally analyze our model in three simplified parameter regimes and discuss parameter identifiability for varying subdiffusion exponents.
Topics: Fluorescence Recovery After Photobleaching; Receptors, Glucocorticoid; Diffusion; Kinetics; Motion
PubMed: 36127879
DOI: 10.1016/j.bpj.2022.09.015 -
Biophysical Journal Nov 2023To characterize the mechanisms governing the diffusion of particles in biological scenarios, it is essential to accurately determine their diffusive properties. To do...
To characterize the mechanisms governing the diffusion of particles in biological scenarios, it is essential to accurately determine their diffusive properties. To do so, we propose a machine-learning method to characterize diffusion processes with time-dependent properties at the experimental time resolution. Our approach operates at the single-trajectory level predicting the properties of interest, such as the diffusion coefficient or the anomalous diffusion exponent, at every time step of the trajectory. In this way, changes in the diffusive properties occurring along the trajectory emerge naturally in the prediction and thus allow the characterization without any prior knowledge or assumption about the system. We first benchmark the method on synthetic trajectories simulated under several conditions. We show that our approach can successfully characterize both abrupt and continuous changes in the diffusion coefficient or the anomalous diffusion exponent. Finally, we leverage the method to analyze experiments of single-molecule diffusion of two membrane proteins in living cells: the pathogen-recognition receptor DC-SIGN and the integrin α5β1. The analysis allows us to characterize physical parameters and diffusive states with unprecedented accuracy, shedding new light on the underlying mechanisms.
Topics: Deep Learning; Diffusion
PubMed: 37853693
DOI: 10.1016/j.bpj.2023.10.015