Reversible diffusion-influenced reactions of an isolated pair on some two dimensional surfaces.
Ontology highlight
ABSTRACT:
SUBMITTER: Prustel T
PROVIDER: S-EPMC3855148 | biostudies-other | 2013 Nov
REPOSITORIES: biostudies-other
Similar Datasets
Project description:We derive an exact Green's function of the diffusion equation for a pair of disk-shaped interacting particles in two dimensions subject to a backreaction boundary condition. Furthermore, we use the obtained function to calculate exact expressions for the survival probability and the time-dependent rate coefficient for the initially unbound pair and the survival probability of the bound state. The derived expressions will be of particular utility for the description of reversible membrane-bound reactions in cell biology.
| S-EPMC3422329 | biostudies-other
Project description:We investigate the reversible diffusion-influenced reaction of an isolated pair in the presence of a non-Markovian generalization of the backreaction boundary condition in two space dimensions. Following earlier work by Agmon and Weiss, we consider residence time probability densities that decay slower than an exponential and that are characterized by a single parameter 0 < σ ≤ 1. We calculate an exact expression for a Green's function of the two-dimensional diffusion equation subject to a non-Markovian backreaction boundary condition that is valid for arbitrary σ and for all times. We use the obtained expression to derive the survival probability for the initially unbound pair and we calculate an exact expression for the probability S(t[line]*) that the initially bound particle is unbound. Finally, we obtain an approximate solution for long times. In particular, we show that the ultimate fate of the bound state is complete dissociation, as in the Markovian case. However, the limiting value is approached quite differently: Instead of a ~t(-1) decay, we obtain 1 - S(t[line]*) ~ t(-σ)ln t. The derived expressions should be relevant for a better understanding of reversible membrane-bound reactions in cell biology.
| S-EPMC3612112 | biostudies-other
Project description:In a living cell, the movement of biomolecules is highly regulated by the cellular organization into subcompartments that impose barriers to diffusion, can locally break the spatial isotropy, and ultimately guide these molecules to their targets. Despite the pivotal role of these processes, experimental tools to fully probe the complex connectivity (and accessibility) of the cell interior with adequate spatiotemporal resolution are still lacking. Here, we show how the heterogeneity of molecular dynamics and the location of barriers to molecular motion can be mapped in live cells by exploiting a two-dimensional (2D) extension of the pair correlation function (pCF) analysis. Starting from a time series of images collected for the same field of view, the resulting 2D pCF is calculated in the proximity of each point for each time delay and allows us to probe the spatial distribution of the molecules that started from a given pixel. This 2D pCF yields an accurate description of the preferential diffusive routes. Furthermore, we combine this analysis with the image-derived mean-square displacement approach and gain information on the average nanoscopic molecular displacements in different directions. Through these quantities, we build a fluorescence-fluctuation-based diffusion tensor that contains information on speed and directionality of the local dynamical processes. Contrary to classical fluorescence correlation spectroscopy and related methods, this combined approach can distinguish between isotropic and anisotropic local diffusion. We argue that the measurement of this iMSD tensor will contribute to advance our understanding of the role played by the intracellular environment in the regulation of molecular diffusion at the nanoscale.
| S-EPMC5002073 | biostudies-literature
Project description:Two-dimensional layered perovskites are attracting increasing attention as more robust analogues to the conventional three-dimensional metal-halide perovskites for both light harvesting and light emitting applications. However, the impact of the reduced dimensionality on the optoelectronic properties remains unclear, particularly regarding the spatial dynamics of the excitonic excited state within the two-dimensional plane. Here, we present direct measurements of exciton transport in single-crystalline layered perovskites. Using transient photoluminescence microscopy, we show that excitons undergo an initial fast diffusion through the crystalline plane, followed by a slower subdiffusive regime as excitons get trapped. Interestingly, the early intrinsic diffusivity depends sensitively on the choice of organic spacer. A clear correlation between lattice stiffness and diffusivity is found, suggesting exciton-phonon interactions to be dominant in the spatial dynamics of the excitons in perovskites, consistent with the formation of exciton-polarons. Our findings provide a clear design strategy to optimize exciton transport in these systems.
| S-EPMC7184754 | biostudies-literature
Project description:Synaptic transmission between neurons is governed by a cascade of stochastic calcium ion reaction-diffusion events within nerve terminals leading to vesicular release of neurotransmitter. Since experimental measurements of such systems are challenging due to their nanometer and sub-millisecond scale, numerical simulations remain the principal tool for studying calcium-dependent neurotransmitter release driven by electrical impulses, despite the limitations of time-consuming calculations. In this paper, we develop an analytical solution to rapidly explore dynamical stochastic reaction-diffusion problems based on first-passage times. This is the first analytical model that accounts simultaneously for relevant statistical features of calcium ion diffusion, buffering, and its binding/unbinding reaction with a calcium sensor for synaptic vesicle fusion. In particular, unbinding kinetics are shown to have a major impact on submillisecond sensor occupancy probability and therefore cannot be neglected. Using Monte Carlo simulations we validated our analytical solution for instantaneous calcium influx and that through voltage-gated calcium channels. We present a fast and rigorous analytical tool that permits a systematic exploration of the influence of various biophysical parameters on molecular interactions within cells, and which can serve as a building block for more general cell signaling simulators.
| S-EPMC7940439 | biostudies-literature
Project description:Determining atomic-level characteristics of molecules on two-dimensional surfaces is one of the fundamental challenges in chemistry. High-resolution nuclear magnetic resonance (NMR) could deliver rich structural information, but its application to two-dimensional materials has been prevented by intrinsically low sensitivity. Here we obtain high-resolution one- and two-dimensional 31P NMR spectra from as little as 160 picomoles of oligonucleotide functionalities deposited onto silicate glass and sapphire wafers. This is enabled by a factor >105 improvement in sensitivity compared to typical NMR approaches from combining dynamic nuclear polarization methods, multiple-echo acquisition, and optimized sample formulation. We demonstrate that, with this ultrahigh NMR sensitivity, 31P NMR can be used to observe DNA bound to miRNA, to sense conformational changes due to ion binding, and to follow photochemical degradation reactions.
| S-EPMC6439530 | biostudies-literature
Project description:Two-dimensional (2D) crystal growth over substrate features is fundamentally guided by the Gauss-Bonnet theorem, which mandates that rigid, planar crystals cannot conform to surfaces with nonzero Gaussian curvature. Here, we reveal how topographic curvature of lithographically designed substrate features govern the strain and growth dynamics of triangular WS2 monolayer single crystals. Single crystals grow conformally without strain over deep trenches and other features with zero Gaussian curvature; however, features with nonzero Gaussian curvature can easily impart sufficient strain to initiate grain boundaries and fractured growth in different directions. Within a strain-tolerant regime, however, triangular single crystals can accommodate considerable (<1.1%) localized strain exerted by surface features that shift the bandgap up to 150 meV. Within this regime, the crystal growth accelerates in specific directions, which we describe using a growth model. These results present a previously unexplored strategy to strain-engineer the growth directions and optoelectronic properties of 2D crystals.
| S-EPMC6544449 | biostudies-literature
Project description:The adhesion of two-dimensional (2D) materials onto other surfaces is usually considered a solid-solid mechanical contact. Here, we conduct both atomistic simulations and theoretical modeling to show that there in fact exists an energy conversion between heat and mechanical work in the attachment/detachment of two-dimensional materials on/off solid surfaces, indicating two-dimensional materials adhesion is a gas-like adsorption rather than a pure solid-solid mechanical adhesion. We reveal that the underlying mechanism of this intriguing gas-like adhesion is the configurational entropy difference between the freestanding and adhered states of the two-dimensional materials. Both the theoretical modeling and atomistic simulations predict that the adhesion induced entropy difference increases with increasing adhesion energy and decreasing equilibrium binding distance. Our findings provide a fundamental understanding of the adhesion of two-dimensional materials, which is important for designing two-dimensional materials based devices and may have general implications for nanoscale efficient actuators.
| S-EPMC5427824 | biostudies-literature
Project description:The ability to pattern functional moieties with well-defined architectures is highly important in material science, nanotechnology and bioengineering. Although two-dimensional surfaces can serve as attractive platforms, direct patterning them in solution with regular arrays remains a major challenge. Here we develop a versatile route to pattern two-dimensional free-standing surfaces in a controlled manner assisted by monomicelle close-packing assembly of block copolymers, which is unambiguously revealed by direct visual observation. This strategy allows for bottom-up patterning of polypyrrole and polyaniline with adjustable mesopores on various functional free-standing surfaces, including two-dimensional graphene, molybdenum sulfide, titania nanosheets and even on one-dimensional carbon nanotubes. As exemplified by graphene oxide-based mesoporous polypyrrole nanosheets, the unique sandwich structure with adjustable pore sizes (5-20 nm) and thickness (35-45 nm) as well as enlarged specific surface area (85 m(2) g(-1)) provides excellent specific capacitance and rate performance for supercapacitors. Therefore, this approach will shed light on developing solution-based soft patterning of given interfaces towards bespoke functions.
| S-EPMC4660032 | biostudies-literature
Project description:Traditional histology is the gold standard for tissue studies, but it is intrinsically reliant on two-dimensional (2D) images. Study of volumetric tissue samples such as whole hearts produces a stack of misaligned and distorted 2D images that need to be reconstructed to recover a congruent volume with the original sample's shape. In this paper, we develop a mathematical framework called Transformation Diffusion (TD) for stack alignment refinement as a solution to the heat diffusion equation. This general framework does not require contour segmentation, is independent of the registration method used, and is trivially parallelizable. After the first stack sweep, we also replace registration operations by operations in the space of transformations, several orders of magnitude faster and less memory-consuming. Implementing TD with operations in the space of transformations produces our Transformation Diffusion Reconstruction (TDR) algorithm, applicable to general transformations that are closed under inversion and composition. In particular, we provide formulas for translation and affine transformations. We also propose an Approximated TDR (ATDR) algorithm that extends the same principles to tensor-product B-spline transformations. Using TDR and ATDR, we reconstruct a full mouse heart at pixel size 0.92µm×0.92µm, cut 10µm thick, spaced 20µm (84G). Our algorithms employ only local information from transformations between neighboring slices, but the TD framework allows theoretical analysis of the refinement as applying a global Gaussian low-pass filter to the unknown stack misalignments. We also show that reconstruction without an external reference produces large shape artifacts in a cardiac specimen while still optimizing slice-to-slice alignment. To overcome this problem, we use a pre-cutting blockface imaging process previously developed by our group that takes advantage of Brewster's angle and a polarizer to capture the outline of only the topmost layer of wax in the block containing embedded tissue for histological sectioning.
| S-EPMC5408912 | biostudies-literature