Exact Green's function of the reversible diffusion-influenced reaction for an isolated pair in two dimensions.
Ontology highlight
ABSTRACT:
SUBMITTER: Prustel T
PROVIDER: S-EPMC3422329 | biostudies-other | 2012 Aug
REPOSITORIES: biostudies-other
Similar Datasets
Project description:We investigate reversible diffusion-influenced reactions of an isolated pair in two dimensions. To this end, we employ convolution relations that permit deriving the survival probability of the reversible reaction directly in terms of the survival probability of the irreversible reaction. Furthermore, we make use of the mean reaction time approximation to write the irreversible survival probability in restricted spaces as a single exponential. In this way, we obtain exact and approximative expressions in the time domain for the reversible survival probability for three different two dimensional spatial domains: The infinite plane, the annular domain, and the surface of a sphere. Our obtained results should prove useful in the context of membrane-bound reversible diffusion-influenced reactions in cell biology.
| S-EPMC3855148 | 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:Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction-diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction-diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction-diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially-confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially-confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.
| S-EPMC4583548 | 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: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:BACKGROUND: Receptors and scaffold proteins usually possess a high number of distinct binding domains inducing the formation of large multiprotein signaling complexes. Due to combinatorial reasons the number of distinguishable species grows exponentially with the number of binding domains and can easily reach several millions. Even by including only a limited number of components and binding domains the resulting models are very large and hardly manageable. A novel model reduction technique allows the significant reduction and modularization of these models. RESULTS: We introduce methods that extend and complete the already introduced approach. For instance, we provide techniques to handle the formation of multi-scaffold complexes as well as receptor dimerization. Furthermore, we discuss a new modeling approach that allows the direct generation of exactly reduced model structures. The developed methods are used to reduce a model of EGF and insulin receptor crosstalk comprising 5,182 ordinary differential equations (ODEs) to a model with 87 ODEs. CONCLUSION: The methods, presented in this contribution, significantly enhance the available methods to exactly reduce models of combinatorial reaction networks.
| S-EPMC2570670 | biostudies-literature
Project description:Bistable opsins are photopigments expressed in both invertebrates and vertebrates. These light-sensitive G-protein-coupled receptors undergo a reversible reaction upon illumination. A first photon initiates the cis to trans isomerization of the retinal chromophore-attached to the protein through a protonated Schiff base-and a series of transition states that eventually results in the formation of the thermally stable and active Meta state. Excitation by a second photon reverts this process to recover the original ground state. On the other hand, monostable opsins (e.g., bovine rhodopsin) lose their chromophore during the decay of the Meta II state (i.e., they bleach). Spectroscopic studies on the molecular details of the two-photon cycle in bistable opsins are limited. Here, we describe the successful expression and purification of recombinant rhodopsin-1 from the jumping spider Hasarius adansoni (JSR1). In its natural configuration, spectroscopic characterization of JSR1 is hampered by the similar absorption spectra in the visible spectrum of the inactive and active states. We solved this issue by separating their absorption spectra by replacing the endogenous 11-cis retinal chromophore with the blue-shifted 9-cis JSiR1. With this system, we used time-resolved ultraviolet-visible spectroscopy after pulsed laser excitation to obtain kinetic details of the rise and decay of the photocycle intermediates. We also used resonance Raman spectroscopy to elucidate structural changes of the retinal chromophore upon illumination. Our data clearly indicate that the protonated Schiff base is stable throughout the entire photoreaction. We additionally show that the accompanying conformational changes in the protein are different from those of monostable rhodopsin, as recorded by light-induced FTIR difference spectroscopy. Thus, we envisage JSR1 as becoming a model system for future studies on the reaction mechanisms of bistable opsins, e.g., by time-resolved x-ray crystallography.
| S-EPMC6451042 | biostudies-literature
Project description:The accuracy of RNA secondary structure prediction decreases with the span of a base pair, i.e., the number of nucleotides that it encloses. The dynamic programming algorithms for RNA folding can be easily specialized in order to consider only base pairs with a limited span L, reducing the memory requirements to O(nL), and further to O(n) by interleaving backtracking. However, the latter is an approximation that precludes the retrieval of the globally optimal structure. So far, the ViennaRNA package therefore does not provide a tool for computing optimal, span-restricted minimum energy structure. Here, we report on an efficient backtracking algorithm that reconstructs the globally optimal structure from the locally optimal fragments that are produced by the interleaved backtracking implemented in RNALfold. An implementation is integrated into the ViennaRNA package. The forward and the backtracking recursions of RNALfold are both easily constrained to structural components with a sufficiently negative z-scores. This provides a convenient method in order to identify hyper-stable structural elements. A screen of the C. elegans genome shows that such features are more abundant in real genomic sequences when compared to a di-nucleotide shuffled background model.
| S-EPMC7823788 | biostudies-literature
Project description:Heterogeneous catalysis is a surface phenomenon. Yet, though the catalysis itself takes place on surfaces, the reactants and products rapidly take the form of another physical state, as either a liquid or a gas. Catalytic reactions within a self-assembled monolayer are confined within two dimensions, as the molecules involved do not leave the surface. Surface-enhanced Raman spectroscopy is an ideal technique to probe these self-assembled monolayers as it gives molecular information in a measured volume limited to the surface. We show how surface-enhanced Raman spectroscopy can be used to determine the reaction kinetics of a two-dimensional reaction. As a proof of principle, we study the photocatalytic reduction of p-nitrothiophenol. A study of the reaction rate and dilution effects leads to the conclusion that a dimerization must take place as one of the reaction steps.
| S-EPMC4834625 | biostudies-literature
Project description:Coherent condensate states of particles obeying either Bose or Fermi statistics are in the focus of interest in modern physics. Here we report on condensation of collective excitations with Bose statistics, cyclotron magnetoexcitons, in a high-mobility two-dimensional electron system in a magnetic field. At low temperatures, the dense non-equilibrium ensemble of long-lived triplet magnetoexcitons exhibits both a drastic reduction in the viscosity and a steep enhancement in the response to the external electromagnetic field. The observed effects are related to formation of a super-absorbing state interacting coherently with the electromagnetic field. Simultaneously, the electrons below the Fermi level form a super-emitting state. The effects are explicable from the viewpoint of a coherent condensate phase in a non-equilibrium system of two-dimensional fermions with a fully quantized energy spectrum. The condensation occurs in the space of vectors of magnetic translations, a property providing a completely new landscape for future physical investigations.
| S-EPMC5116097 | biostudies-literature