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Biophysical Journal Feb 2021Diffusion is a fundamental mechanism for protein distribution in cell membranes. These membranes often exhibit complex shapes, which range from shallow domes to...
Diffusion is a fundamental mechanism for protein distribution in cell membranes. These membranes often exhibit complex shapes, which range from shallow domes to elongated tubular or pearl-like structures. Shape complexity of the membrane influences the diffusive spreading of proteins and molecules. Despite the importance membrane geometry plays in these diffusive processes, it is challenging to establish the dependence between diffusion and membrane morphology. We solve the diffusion equation numerically on various static curved shapes representative for experimentally observed membrane shapes. Our results show that membrane necks become diffusion barriers. We determine the diffusive half-time, i.e., the time that is required to reduce the amount of protein in the budded region by one half, and find a quadratic relation between the diffusive half-time and the averaged mean curvature of the membrane shape, which we rationalize by a scaling law. Our findings thus help estimate the characteristic diffusive timescale based on the simple measure of membrane mean curvature.
Topics: Cell Membrane; Diffusion; Membranes; Proteins
PubMed: 33359464
DOI: 10.1016/j.bpj.2020.12.014 -
The Journal of Chemical Physics Aug 2023Most biological processes in living cells rely on interactions between proteins. Live-cell compatible approaches that can quantify to what extent a given protein... (Review)
Review
Most biological processes in living cells rely on interactions between proteins. Live-cell compatible approaches that can quantify to what extent a given protein participates in homo- and hetero-oligomeric complexes of different size and subunit composition are therefore critical to advance our understanding of how cellular physiology is governed by these molecular interactions. Biomolecular complex formation changes the diffusion coefficient of constituent proteins, and these changes can be measured using fluorescence microscopy-based approaches, such as single-molecule tracking, fluorescence correlation spectroscopy, and fluorescence recovery after photobleaching. In this review, we focus on the use of single-molecule tracking to identify, resolve, and quantify the presence of freely-diffusing proteins and protein complexes in living cells. We compare and contrast different data analysis methods that are currently employed in the field and discuss experimental designs that can aid the interpretation of the obtained results. Comparisons of diffusion rates for different proteins and protein complexes in intracellular aqueous environments reported in the recent literature reveal a clear and systematic deviation from the Stokes-Einstein diffusion theory. While a complete and quantitative theoretical explanation of why such deviations manifest is missing, the available data suggest the possibility of weighing freely-diffusing proteins and protein complexes in living cells by measuring their diffusion coefficients. Mapping individual diffusive states to protein complexes of defined molecular weight, subunit stoichiometry, and structure promises to provide key new insights into how protein-protein interactions regulate protein conformational, translational, and rotational dynamics, and ultimately protein function.
Topics: Single Molecule Imaging; Diffusion; Microscopy, Fluorescence; Photobleaching; Protein Conformation
PubMed: 37589409
DOI: 10.1063/5.0155638 -
Proceedings of the National Academy of... Nov 2021Do some types of information spread faster, broader, or further than others? To understand how information diffusions differ, scholars compare structural properties of...
Do some types of information spread faster, broader, or further than others? To understand how information diffusions differ, scholars compare structural properties of the paths taken by content as it spreads through a network, studying so-called cascades. Commonly studied cascade properties include the reach, depth, breadth, and speed of propagation. Drawing conclusions from statistical differences in these properties can be challenging, as many properties are dependent. In this work, we demonstrate the essentiality of controlling for cascade sizes when studying structural differences between collections of cascades. We first revisit two datasets from notable recent studies of online diffusion that reported content-specific differences in cascade topology: an exhaustive corpus of Twitter cascades for verified true- or false-news content by Vosoughi et al. [S. Vosoughi, D. Roy, S. Aral. 359, 1146-1151 (2018)] and a comparison of Twitter cascades of videos, pictures, news, and petitions by Goel et al. [S. Goel, A. Anderson, J. Hofman, D. J. Watts. 62, 180-196 (2016)]. Using methods that control for joint cascade statistics, we find that for false- and true-news cascades, the reported structural differences can almost entirely be explained by false-news cascades being larger. For videos, images, news, and petitions, structural differences persist when controlling for size. Studying classical models of diffusion, we then give conditions under which differences in structural properties under different models do or do not reduce to differences in size. Our findings are consistent with the mechanisms underlying true- and false-news diffusion being quite similar, differing primarily in the basic infectiousness of their spreading process.
Topics: Communication; Diffusion; Humans; Information Dissemination; Social Media
PubMed: 34750252
DOI: 10.1073/pnas.2100786118 -
Analytical Chemistry Apr 2020Measuring the translational diffusion of proteins under physiological conditions can be very informative, especially when multiple diffusing species can be...
Measuring the translational diffusion of proteins under physiological conditions can be very informative, especially when multiple diffusing species can be distinguished. Diffusion NMR or diffusion-ordered spectroscopy (DOSY) is widely used to study molecular diffusion, where protons are used as probes, which can be further edited by the proton-attached heteronuclei to provide additional resolution. For example, the combination of the backbone amide protons (H) to measure diffusion with the well-resolved H/N correlations has afforded high-resolution DOSY experiments. However, significant amide-water proton exchange at physiological temperature and pH can affect the accuracy of diffusion data or cause complete loss of DOSY signals. Although aliphatic protons do not exchange with water protons, and thus are potential probes to measure diffusion rates, H/C correlations are often in spectral overlap or masked by the water signal, which hampers the use of these correlations. In this report, a method was developed that separates the nuclei used for diffusion (α protons, H) and those used for detection (H/N and C'/N correlations). This approach enables high-resolution diffusion measurements of polypeptides in a mixture of biomolecules, thereby providing a powerful tool to investigate coexisting species under physiologically relevant conditions.
Topics: Diffusion; Nuclear Magnetic Resonance, Biomolecular; Proteins
PubMed: 32163276
DOI: 10.1021/acs.analchem.9b05453 -
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 -
International Journal of Molecular... Jul 2023Intracellular environment includes proteins, sugars, and nucleic acids interacting in restricted media. In the cytoplasm, the excluded volume effect takes up to 40% of...
Intracellular environment includes proteins, sugars, and nucleic acids interacting in restricted media. In the cytoplasm, the excluded volume effect takes up to 40% of the volume available for occupation by macromolecules. In this work, we tested several approaches modeling crowded solutions for protein diffusion. We experimentally showed how the protein diffusion deviates from conventional Brownian motion in artificial conditions modeling the alteration of medium viscosity and rigid spatial obstacles. The studied tracer proteins were globular bovine serum albumin and intrinsically disordered α-casein. Using the pulsed field gradient NMR, we investigated the translational diffusion of protein probes of different structures in homogeneous (glycerol) and heterogeneous (PEG 300/PEG 6000/PEG 40,000) solutions as a function of crowder concentration. Our results showed fundamentally different effects of homogeneous and heterogeneous crowded environments on protein self-diffusion. In addition, the applied "tracer on lattice" model showed that smaller crowding obstacles (PEG 300 and PEG 6000) create a dense net of restrictions noticeably hindering diffusing protein probes, whereas the large-sized PEG 40,000 creates a "less restricted" environment for the diffusive motion of protein molecules.
Topics: Caseins; Serum Albumin, Bovine; Motion; Diffusion
PubMed: 37446325
DOI: 10.3390/ijms241311148 -
European Biophysics Journal : EBJ Apr 2018Lateral movement of a molecule in a biomembrane containing small compartments (0.23-μm diameter) and large ones (0.75 μm) is analyzed using a fractal description of...
Lateral movement of a molecule in a biomembrane containing small compartments (0.23-μm diameter) and large ones (0.75 μm) is analyzed using a fractal description of its walk. The early time dependence of the mean square displacement varies from linear due to the contribution of ballistic motion. In small compartments, walking molecules do not have sufficient time or space to develop an asymptotic relation and the diffusion coefficient deduced from the experimental records is lower than that measured without restrictions. The model makes it possible to deduce the molecule step parameters, namely the step length and time, from data concerning confined and unrestricted diffusion coefficients. This is also possible using experimental results for sub-diffusive transport. The transition from normal to anomalous diffusion does not affect the molecule step parameters. The experimental literature data on molecular trajectories recorded at a high time resolution appear to confirm the modeled value of the mean free path length of DOPE for Brownian and anomalous diffusion. Although the step length and time give the proper values of diffusion coefficient, the DOPE speed calculated as their quotient is several orders of magnitude lower than the thermal speed. This is interpreted as a result of intermolecular interactions, as confirmed by lateral diffusion of other molecules in different membranes. The molecule step parameters are then utilized to analyze the problem of multiple visits in small compartments. The modeling of the diffusion exponent results in a smooth transition to normal diffusion on entering a large compartment, as observed in experiments.
Topics: Cell Membrane; Diffusion; Fractals; Models, Biological; Movement
PubMed: 29094176
DOI: 10.1007/s00249-017-1264-0 -
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 -
The Journal of Chemical Physics Jan 2023We develop a multiscale simulation model for diffusion of solutes through porous triblock copolymer membranes. The approach combines two techniques: self-consistent...
We develop a multiscale simulation model for diffusion of solutes through porous triblock copolymer membranes. The approach combines two techniques: self-consistent field theory (SCFT) to predict the structure of the self-assembled, solvated membrane and on-lattice kinetic Monte Carlo (kMC) simulations to model diffusion of solutes. Solvation is simulated in SCFT by constraining the glassy membrane matrix while relaxing the brush-like membrane pore coating against the solvent. The kMC simulations capture the resulting solute spatial distribution and concentration-dependent local diffusivity in the polymer-coated pores; we parameterize the latter using particle-based simulations. We apply our approach to simulate solute diffusion through nonequilibrium morphologies of a model triblock copolymer, and we correlate diffusivity with structural descriptors of the morphologies. We also compare the model's predictions to alternative approaches based on simple lattice random walks and find our multiscale model to be more robust and systematic to parameterize. Our multiscale modeling approach is general and can be readily extended in the future to other chemistries, morphologies, and models for the local solute diffusivity and interactions with the membrane.
Topics: Polymers; Solutions; Solvents; Diffusion; Computer Simulation
PubMed: 36641407
DOI: 10.1063/5.0127570 -
Journal of Biological Physics Sep 2023We present an analysis of an epidemic spreading process on an Apollonian network that can describe an epidemic spreading in a non-sedentary population. We studied the...
We present an analysis of an epidemic spreading process on an Apollonian network that can describe an epidemic spreading in a non-sedentary population. We studied the modified diffusive epidemic process using the Monte Carlo method by computational analysis. Our model may be helpful for modeling systems closer to reality consisting of two classes of individuals: susceptible (A) and infected (B). The individuals can diffuse in a network according to constant diffusion rates [Formula: see text] and [Formula: see text], for the classes A and B, respectively, and obeying three diffusive regimes, i.e., [Formula: see text], [Formula: see text], and [Formula: see text]. Into the same site i, the reaction occurs according to the dynamical rule based on Gillespie's algorithm. Finite-size scaling analysis has shown that our model exhibits continuous phase transition to an absorbing state with a set of critical exponents given by [Formula: see text], [Formula: see text], and [Formula: see text] familiar to every investigated regime. In summary, the continuous phase transition, characterized by this set of critical exponents, does not have the same exponents of the mean-field universality class in both regular lattices and complex networks.
Topics: Humans; Computer Simulation; Algorithms; Epidemics; Models, Biological; Diffusion
PubMed: 37118345
DOI: 10.1007/s10867-023-09634-2