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Single-molecule displacement mapping unveils nanoscale heterogeneities in intracellular diffusivity.Nature Methods May 2020Intracellular diffusion underlies vital cellular processes. However, it remains difficult to elucidate how an unbound protein diffuses inside the cell with good spatial...
Intracellular diffusion underlies vital cellular processes. However, it remains difficult to elucidate how an unbound protein diffuses inside the cell with good spatial resolution and sensitivity. Here we introduce single-molecule displacement/diffusivity mapping (SMdM), a super-resolution strategy that enables the nanoscale mapping of intracellular diffusivity through local statistics of the instantaneous displacements of freely diffusing single molecules. We thus show that the diffusion of an average-sized protein in the mammalian cytoplasm and nucleus is spatially heterogeneous at the nanoscale, and that variations in local diffusivity correlate with the ultrastructure of the actin cytoskeleton and the organization of the genome, respectively. SMdM of differently charged proteins further unveils that the possession of positive, but not negative, net charges drastically impedes diffusion, and that the rate is determined by the specific subcellular environments. We thus unveil rich heterogeneities and charge effects in intracellular diffusion at the nanoscale.
Topics: Cell Nucleus; Cells, Cultured; Cytoplasm; Diffusion; Humans; Image Interpretation, Computer-Assisted; Intracellular Space; Microscopy, Fluorescence; Models, Theoretical; Nanoparticles; Proteins; Single Molecule Imaging
PubMed: 32203387
DOI: 10.1038/s41592-020-0793-0 -
Nature Communications Oct 2018Most biochemical reactions in living cells rely on diffusive search for target molecules or regions in a heterogeneous overcrowded cytoplasmic medium. Rapid...
Most biochemical reactions in living cells rely on diffusive search for target molecules or regions in a heterogeneous overcrowded cytoplasmic medium. Rapid rearrangements of the medium constantly change the effective diffusivity felt locally by a diffusing particle and thus impact the distribution of the first-passage time to a reaction event. Here, we investigate the effect of these dynamic spatiotemporal heterogeneities onto diffusion-limited reactions. We describe a general mathematical framework to translate many results for ordinary homogeneous Brownian motion to heterogeneous diffusion. In particular, we derive the probability density of the first-passage time to a reaction event and show how the dynamic disorder broadens the distribution and increases the likelihood of both short and long trajectories to reactive targets. While the disorder slows down reaction kinetics on average, its dynamic character is beneficial for a faster search and realization of an individual reaction event triggered by a single molecule.
Topics: Diffusion; Models, Theoretical; Time Factors
PubMed: 30353010
DOI: 10.1038/s41467-018-06610-6 -
Food Science and Technology... Sep 2021The effect of microwave power levels on the drying attributes of Jaya fish () in a microwave dryer was investigated in this study. Microwave power levels of 100, 180,...
The effect of microwave power levels on the drying attributes of Jaya fish () in a microwave dryer was investigated in this study. Microwave power levels of 100, 180, 300, and 450 W were used to dry 50 g of fish samples, and the drying kinetics were evaluated. Higher microwave power levels resulted in faster drying when increased from 100 to 450 W. The moisture ratio of fish during drying was calculated, and the data obtained were applied to 5 well known thin-layer mathematical models of drying, namely Approximate diffusion, Modified Henderson and Pabis, Two-Term, Logarithmic, and Midilli model. Model constants and coefficients were calculated by nonlinear regression techniques. All the models were validated using statistical parameters namely; Coefficient of determination (R), Root Mean Square Error (RMSE), Chi-square (χ), and Standard Sum of Error (SSE). The Midilli model gave an excellent fit to the experimental data of all the models evaluated. The effective diffusivity was calculated using Fick's diffusion equation, and the value varied from 1.40 × 10 to 1.08 × 10 m/s. The activation energy and the diffusivity constant were found to be 4.656W/g and 1.22 × 10 m/s, respectively.
Topics: Desiccation; Diffusion; Kinetics; Microwaves; Models, Theoretical
PubMed: 33143468
DOI: 10.1177/1082013220969353 -
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 -
Physical Review Letters Aug 2020Diffusion-mediated surface phenomena are crucial for human life and industry, with examples ranging from oxygen capture by lung alveolar surface to heterogeneous...
Diffusion-mediated surface phenomena are crucial for human life and industry, with examples ranging from oxygen capture by lung alveolar surface to heterogeneous catalysis, gene regulation, membrane permeation, and filtration processes. Their current description via diffusion equations with mixed boundary conditions is limited to simple surface reactions with infinite or constant reactivity. In this Letter, we propose a probabilistic approach based on the concept of boundary local time to investigate the intricate dynamics of diffusing particles near a reactive surface. Reformulating surface-particle interactions in terms of stopping conditions, we obtain in a unified way major diffusion-reaction characteristics such as the propagator, the survival probability, the first-passage time distribution, and the reaction rate. This general formalism allows us to describe new surface reaction mechanisms such as for instance surface reactivity depending on the number of encounters with the diffusing particle that can model the effects of catalyst fooling or membrane degradation. The disentanglement of the geometric structure of the medium from surface reactivity opens far-reaching perspectives for modeling, optimization, and control of diffusion-mediated surface phenomena.
Topics: Cell Membrane; DNA; Diffusion; Models, Biological; Models, Chemical; Proteins; Surface Properties; Thermodynamics
PubMed: 32857533
DOI: 10.1103/PhysRevLett.125.078102 -
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 -
Bulletin of Mathematical Biology Sep 2022This paper focuses on a Gilpin-Ayala growth model with spatial diffusion and Neumann boundary condition to study single species population distribution. In our...
This paper focuses on a Gilpin-Ayala growth model with spatial diffusion and Neumann boundary condition to study single species population distribution. In our heterogeneous model, we assume that the diffusive spread of population is proportional to the gradient of population per unit resource, rather than the population density itself. We investigate global well-posedness of the mathematical model, determine conditions on harvesting rate for which non-trivial equilibrium states exist and examine their global stability. We also determine conditions on harvesting that leads to species extinction through global stability of the trivial solution. Additionally, for time periodic growth, resource, capacity and harvesting functions, we prove existence of time-periodic states with the same period. We also present numerical results on the nature of nonzero equilibrium states and their dependence on resource and capacity functions as well as on Gilpin-Ayala parameter [Formula: see text]. We conclude enhanced effects of diffusion for small [Formula: see text] which in particular disallows existence of nontrivial states even in some cases when intrinsic growth rate exceeds harvesting at some locations in space for which a logistic model allows for a nonzero equilibrium density.
Topics: Diffusion; Extinction, Biological; Mathematical Concepts; Models, Biological; Population Density
PubMed: 36107169
DOI: 10.1007/s11538-022-01074-8 -
Journal of the Royal Society, Interface Jul 2023Turing's mechanism is often invoked to explain periodic patterns in nature, although direct experimental support is scarce. Turing patterns form in reaction-diffusion...
Turing's mechanism is often invoked to explain periodic patterns in nature, although direct experimental support is scarce. Turing patterns form in reaction-diffusion systems when the activating species diffuse much slower than the inhibiting species, and the involved reactions are highly nonlinear. Such reactions can originate from cooperativity, whose physical interactions should also affect diffusion. We here take direct interactions into account and show that they strongly affect Turing patterns. We find that weak repulsion between the activator and inhibitor can substantially lower the required differential diffusivity and reaction nonlinearity. By contrast, strong interactions can induce phase separation, but the resulting length scale is still typically governed by the fundamental reaction-diffusion length scale. Taken together, our theory connects traditional Turing patterns with chemically active phase separation, thus describing a wider range of systems. Moreover, we demonstrate that even weak interactions affect patterns substantially, so they should be incorporated when modelling realistic systems.
Topics: Diffusion
PubMed: 37434500
DOI: 10.1098/rsif.2023.0244 -
The Journal of the Acoustical Society... Oct 2021While the use of diffuse surfaces is becoming increasingly common in the acoustical design of performance venues and normal rooms, there is a paucity of data on the...
While the use of diffuse surfaces is becoming increasingly common in the acoustical design of performance venues and normal rooms, there is a paucity of data on the auditory perceptual effects that characterize those finishes compared to specular ones. For instance, it is not entirely clear whether and how the aural impression is affected when first reflections are swapped from specular to diffuse. In a recent work, after revising the background knowledge on physical and perceptual effects of scattering, Visentin et al. [(2020) J. Acoust. Soc. Am. 148(1), 122-140] started a systematic analysis of how diffuse reflections influence the auditory impression by considering the simplest possible case, that is, a direct sound and one lateral reflection. The present work is a step forward in the analysis, and pairs of lateral reflections without or with a ceiling reflection are considered. By means of detailed listening tests, it is shown how diffuse reflections modulate the perception of some spatial attributes. This knowledge adds to the criteria to be employed when including diffusing surfaces in the design of first reflections in rooms.
Topics: Auditory Perception; Diffusion; Sound
PubMed: 34717493
DOI: 10.1121/10.0006744 -
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