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ELife Sep 2022Single-particle tracking (SPT) directly measures the dynamics of proteins in living cells and is a powerful tool to dissect molecular mechanisms of cellular regulation....
Single-particle tracking (SPT) directly measures the dynamics of proteins in living cells and is a powerful tool to dissect molecular mechanisms of cellular regulation. Interpretation of SPT with fast-diffusing proteins in mammalian cells, however, is complicated by technical limitations imposed by fast image acquisition. These limitations include short trajectory length due to photobleaching and shallow depth of field, high localization error due to the low photon budget imposed by short integration times, and cell-to-cell variability. To address these issues, we investigated methods inspired by Bayesian nonparametrics to infer distributions of state parameters from SPT data with short trajectories, variable localization precision, and absence of prior knowledge about the number of underlying states. We discuss the advantages and disadvantages of these approaches relative to other frameworks for SPT analysis.
Topics: Animals; Bayes Theorem; Diffusion; Mammals; Single Molecule Imaging
PubMed: 36066004
DOI: 10.7554/eLife.70169 -
PloS One 2023Magnetic reconnection is a process that can rapidly convert magnetic field energy into plasma thermal energy and kinetic energy, and it is also an important energy...
Magnetic reconnection is a process that can rapidly convert magnetic field energy into plasma thermal energy and kinetic energy, and it is also an important energy conversion mechanism in space physics, astrophysics and plasma physics. Research related to analytical solutions for time-dependent three-dimensional magnetic reconnection is extremely difficult. For decades, several mathematical descriptions have been developed regarding different reconnection mechanisms, in which the equations based on magnetohydrodynamics theory outside the reconnection diffusion region are widely accepted. However, the equation set cannot be analytically solved unless specified constraints are imposed or the equations are reduced. Based on previous analytical methods for kinematic stationary reconnection, here the analytical solutions for time-dependent kinematic three-dimensional magnetic reconnection are discussed. In contrast to the counter-rotating plasma flows that existed in steady-state reconnection, it is found that spiral plasma flows, which have never been reported before, can be generated if the magnetic field changes exponentially with time. These analyses reveal new scenarios for time-dependent kinematic three-dimensional magnetic reconnection, and the deduced analytical solutions could improve our understanding of the dynamics involved in reconnection processes, as well as the interactions between the magnetic field and plasma flows during magnetic reconnection.
Topics: Biomechanical Phenomena; Physical Phenomena; Physics; Diffusion; Magnetic Fields
PubMed: 37253032
DOI: 10.1371/journal.pone.0286138 -
Biophysical Journal Jul 2019Diffusion plays a crucial role in many biological processes including signaling, cellular organization, transport mechanisms, and more. Direct observation of molecular...
Diffusion plays a crucial role in many biological processes including signaling, cellular organization, transport mechanisms, and more. Direct observation of molecular movement by single-particle-tracking experiments has contributed to a growing body of evidence that many cellular systems do not exhibit classical Brownian motion but rather anomalous diffusion. Despite this evidence, characterization of the physical process underlying anomalous diffusion remains a challenging problem for several reasons. First, different physical processes can exist simultaneously in a system. Second, commonly used tools for distinguishing between these processes are based on asymptotic behavior, which is experimentally inaccessible in most cases. Finally, an accurate analysis of the diffusion model requires the calculation of many observables because different transport modes can result in the same diffusion power-law α, which is typically obtained from the mean-square displacements (MSDs). The outstanding challenge in the field is to develop a method to extract an accurate assessment of the diffusion process using many short trajectories with a simple scheme that is applicable at the nonexpert level. Here, we use deep learning to infer the underlying process resulting in anomalous diffusion. We implement a neural network to classify single-particle trajectories by diffusion type: Brownian motion, fractional Brownian motion and continuous time random walk. Further, we demonstrate the applicability of our network architecture for estimating the Hurst exponent for fractional Brownian motion and the diffusion coefficient for Brownian motion on both simulated and experimental data. These networks achieve greater accuracy than time-averaged MSD analysis on simulated trajectories while only requiring as few as 25 steps. When tested on experimental data, both net and ensemble MSD analysis converge to similar values; however, the net needs only half the number of trajectories required for ensemble MSD to achieve the same confidence interval. Finally, we extract diffusion parameters from multiple extremely short trajectories (10 steps) using our approach.
Topics: Computer Simulation; Deep Learning; Diffusion; Models, Biological; Single Molecule Imaging
PubMed: 31280841
DOI: 10.1016/j.bpj.2019.06.015 -
Mathematical Biosciences and... Sep 2020This paper represents a literature review on traveling waves described by delayed reactiondiffusion (RD, for short) equations. It begins with the presentation of... (Review)
Review
This paper represents a literature review on traveling waves described by delayed reactiondiffusion (RD, for short) equations. It begins with the presentation of different types of equations arising in applications. The main results on wave existence and stability are presented for the equations satisfying the monotonicity condition that provides the applicability of the maximum and comparison principles. Other methods and results are described for the case where the monotonicity condition is not satisfied. The last two sections deal with delayed RD equations in mathematical immunology and in neuroscience. Existence, stability, and dynamics of wavefronts and of periodic waves are discussed.
Topics: Biology; Diffusion; Travel
PubMed: 33378863
DOI: 10.3934/mbe.2020339 -
Methods in Enzymology 2021Biomolecular condensates are membrane-less sub-cellular compartments that perform a plethora of important functions in signaling and storage. The material properties of...
Biomolecular condensates are membrane-less sub-cellular compartments that perform a plethora of important functions in signaling and storage. The material properties of biomolecular condensates such as viscosity, surface tension, viscoelasticity, and macromolecular diffusion play important roles in regulating their biological functions. Aberrations in these properties have been implicated in various neurodegenerative disorders and certain types of cancer. Unraveling the molecular driving forces that control the fluid structure and dynamics of biomolecular condensates across different length- and time-scales necessitates the application of innovative biophysical methodologies. In this chapter, we discuss major experimental techniques that are widely used to study the material states and dynamics of biomolecular condensates as well as their practical and conceptual limitations. We end this chapter with a discussion on more advanced tools that are currently emerging to address the complex fluid dynamics of these condensates.
Topics: Diffusion; Macromolecular Substances; Viscosity
PubMed: 33453924
DOI: 10.1016/bs.mie.2020.06.009 -
Scientific Reports Nov 2022Accurate and efficient forward models of photon migration in heterogeneous geometries are important for many applications of light in medicine because many biological...
Accurate and efficient forward models of photon migration in heterogeneous geometries are important for many applications of light in medicine because many biological tissues exhibit a layered structure of independent optical properties and thickness. However, closed form analytical solutions are not readily available for layered tissue-models, and often are modeled using computationally expensive numerical techniques or theoretical approximations that limit accuracy and real-time analysis. Here, we develop an open-source accurate, efficient, and stable numerical routine to solve the diffusion equation in the steady-state and time-domain for a layered cylinder tissue model with an arbitrary number of layers and specified thickness and optical coefficients. We show that the steady-state ([Formula: see text] ms) and time-domain ([Formula: see text] ms) fluence (for an 8-layer medium) can be calculated with absolute numerical errors approaching machine precision. The numerical implementation increased computation speed by 3 to 4 orders of magnitude compared to previously reported theoretical solutions in layered media. We verify our solutions asymptotically to homogeneous tissue geometries using closed form analytical solutions to assess convergence and numerical accuracy. Approximate solutions to compute the reflected intensity are presented which can decrease the computation time by an additional 2-3 orders of magnitude. We also compare our solutions for 2, 3, and 5 layered media to gold-standard Monte Carlo simulations in layered tissue models of high interest in biomedical optics (e.g. skin/fat/muscle and brain). The presented routine could enable more robust real-time data analysis tools in heterogeneous tissues that are important in many clinical applications such as functional brain imaging and diffuse optical spectroscopy.
Topics: Scattering, Radiation; Diffusion; Photons; Monte Carlo Method; Optics and Photonics
PubMed: 36347893
DOI: 10.1038/s41598-022-22649-4 -
International Journal of Molecular... Oct 2022The mechanisms of transport of substances in the brain parenchyma have been a hot topic in scientific discussion in the past decade. This discussion was triggered by the... (Review)
Review
The mechanisms of transport of substances in the brain parenchyma have been a hot topic in scientific discussion in the past decade. This discussion was triggered by the proposed glymphatic hypothesis, which assumes a directed flow of cerebral fluid within the parenchyma, in contrast to the previous notion that diffusion is the main mechanism. However, when discussing the issue of "diffusion or non-diffusion", much less attention was given to the question that diffusion itself can have a different character. In our opinion, some of the recently published results do not fit into the traditional understanding of diffusion. In this regard, we outline the relevant new theoretical approaches on transport processes in complex random media such as concepts of diffusive diffusivity and time-dependent homogenization, which expands the understanding of the forms of transport of substances based on diffusion.
Topics: Extracellular Space; Brain; Diffusion; Biological Transport; Diffusion Magnetic Resonance Imaging
PubMed: 36293258
DOI: 10.3390/ijms232012401 -
Journal of the Royal Society, Interface Dec 2021Diffusion of water into plant materials is known to decrease their mechanical strength and stiffness but improve formability. Here, we characterize water diffusion...
Diffusion of water into plant materials is known to decrease their mechanical strength and stiffness but improve formability. Here, we characterize water diffusion through areca palm leaf-sheath-a model plant material, with hierarchical structure, used in eco-friendly foodware. The diffusion process is studied using mass gain measurements and imaging of water transport. By treating the areca sheath as homogeneous ensemble, and incorporating effects of material swelling due- to water absorption, a factor typically neglected in prior studies, the diffusion coefficient for water is estimated as (6.5 ± 2.2) × 10 mm s. It is shown that neglecting the swelling results in gross underestimation of . Microstructural effects (e.g. fibre, matrix) on the diffusion are characterized using imaging of the water transport at high resolution. The observations show that the water diffuses an order of magnitude faster in the matrix (8.63 × 10 mm s) than in the fibres (7.19 × 10 mm s). This non-uniformity is also reflected in the swelling-induced strain in the leaf, mapped by image correlation. Lastly, we vary salt concentration by controlled additions of NaCl and note a non-monotonic dependence of the diffusion on concentration. Implications of the results for improving foodware manufacturing processes and product life are discussed.
Topics: Biological Transport; Diffusion; Plant Leaves; Sodium Chloride; Water
PubMed: 34847794
DOI: 10.1098/rsif.2021.0483 -
International Journal of Molecular... May 2022F Nuclear Magnetic Resonance spin-lattice relaxation experiments have been performed for a series of ionic liquids including the same anion,...
F Nuclear Magnetic Resonance spin-lattice relaxation experiments have been performed for a series of ionic liquids including the same anion, bis(trifluoromethanesulfonyl)imide, and cations with alkyl chains of different lengths: triethylhexylammonium, triethyloctylammonium decyltriethylammonium, dodecyltriethylammonium, decyltriethylammonium, and hexadecyltriethylammonium. The experiments have been carried out in a frequency range of 10 kHz to 10 MHz versus temperature. A thorough analysis of the relaxation data has led to the determination of the cation-anion as a relative translation diffusion coefficient. The diffusion coefficients have been compared with the corresponding cation-cation and anion-anion diffusion coefficients, revealing a correlation in the relative translation movement of the anion and the triethylhexylammonium, triethyloctylammonium, decyltriethylammonium, and dodecyltriethylammonium cations, whereas the relative translation diffusion between the anion and the cations with the longer alkyl chains, decyltriethylammonium and hexadecyltriethylammonium, remains rather uncorrelated (correlated to a much lesser extent).
Topics: Anions; Cations; Diffusion; Imides; Ionic Liquids
PubMed: 35682674
DOI: 10.3390/ijms23115994 -
The Journal of Physical Chemistry. B Mar 2021Enzymatic cascade reactions, where a substrate is converted into a product in several steps, play a critical role in many biological systems. The enzymes in such...
Enzymatic cascade reactions, where a substrate is converted into a product in several steps, play a critical role in many biological systems. The enzymes in such reactions are often clustered inside intracellular compartments. To understand the effect of localization, we develop a theory for cascade reactions converting substrates into intermediates and then into products when the enzymes are localized in clusters. The theory shows that the kinetic scheme that describes the reaction with dispersed enzymes changes as a result of clustering. A new reaction channel, in which the substrate is directly converted into product, appears with a diffusion-influenced rate that is expressed in terms of enzyme catalytic efficiencies, diffusion coefficient, and cluster size. This rate is proportional to the cluster channeling probability, which is the probability that an intermediate is converted into product within the cluster in which the intermediate was formed. Simple analytic formulas allow one to quantify how enzyme clustering can affect product formation and regulate the direction of metabolic reaction flux in biological and synthetic systems. The rate of the substrate conversion decreases whereas the cluster channeling probability increases as the number of enzyme molecules in a cluster increases. The interplay between these factors leads to an optimal number of enzyme molecules that maximizes the clustering efficiency.
Topics: Catalysis; Diffusion; Kinetics
PubMed: 33596074
DOI: 10.1021/acs.jpcb.0c11155