scholarly journals Speed limits of protein assembly with reversible membrane localization

2021 ◽  
Author(s):  
Bhavya Mishra ◽  
Margaret E. Johnson
Keyword(s):  
Complex Formation ◽  
Self Assembly ◽  
Membrane Lipids ◽  
First Passage Time ◽  
Relative Concentration ◽  
Three Dimensional ◽  
Reaction Network ◽  
Reaction Diffusion ◽  
Passage Time ◽  
Membrane Localization

AbstractSelf-assembly is often studied in a three-dimensional (3D) solution, but a significant fraction of binding events involve proteins that can reversibly bind and diffuse along a two-dimensional (2D) surface. In a recent study, we quantified how proteins can exploit the reduced dimension of the membrane to trigger complex formation. Here, we derive a single expression for the characteristic timescale of this multi-step assembly process, where the change in dimensionality renders rates and concentrations effectively time-dependent. We find that proteins can accelerate complex formation due to an increase in relative concentration, driving more frequent collisions which often wins out over slow-downs due to diffusion. Our model contains two protein populations that associate with one another and use a distinct site to bind membrane lipids, creating a complex reaction network. However, by identifying two major rate-limiting pathways to reach an equilibrium steady-state, we derive an accurate approximation for the mean first passage time when lipids are in abundant supply. Our theory highlights how the ‘sticking rate’, or effective adsorption coefficient of the membrane is central in controlling timescales. We also derive a corrected localization rate to quantify how the geometry of the system and diffusion can reduce rates of localization. We validate and test our results using kinetic and reaction-diffusion simulations. Our results establish how the speed of key assembly steps can shift by orders-of-magnitude when membrane localization is possible, which is critical to understanding mechanisms used in cells.

scholarly journals An exact and efficient first passage time algorithm for reaction–diffusion processes on a 2D-lattice

2014 ◽  
Vol 256 ◽  
pp. 183-197 ◽  
Author(s):  
Andri Bezzola ◽  
Benjamin B. Bales ◽  
Richard C. Alkire ◽  
Linda R. Petzold
Keyword(s):  
Diffusion Processes ◽  
First Passage Time ◽  
Reaction Diffusion ◽  
Time Algorithm ◽  
Passage Time ◽  
First Passage

A random walk on small spheres method for solving transient anisotropic diffusion problems

2019 ◽  
Vol 25 (3) ◽  
pp. 271-282
Author(s):  
Irina Shalimova ◽  
Karl K. Sabelfeld
Keyword(s):  
Random Walk ◽  
Anisotropic Diffusion ◽  
First Passage Time ◽  
Three Dimensional ◽  
Passage Time ◽  
Exit Point ◽  
Stochastic Algorithm ◽  
Probability Densities ◽  
Spatially Varying ◽  
Diffusion Problems

Abstract A meshless stochastic algorithm for solving anisotropic transient diffusion problems based on an extension of the classical Random Walk on Spheres method is developed. Direct generalization of the Random Walk on Spheres method to anisotropic diffusion equations is not possible, therefore, we have derived approximations of the probability densities for the first passage time and the exit point on a small sphere. The method can be conveniently applied to solve diffusion problems with spatially varying diffusion coefficients and is simply implemented for complicated three-dimensional domains. Particle tracking algorithm is highly efficient for calculation of fluxes to boundaries. We present some simulation results in the case of cathodoluminescence and electron beam induced current in the vicinity of a dislocation in a semiconductor material.

Random walk on rectangles and parallelepipeds algorithm for solving transient anisotropic drift-diffusion-reaction problems

2019 ◽  
Vol 25 (2) ◽  
pp. 131-146 ◽  
Author(s):  
Karl K. Sabelfeld
Keyword(s):  
Random Walk ◽  
First Passage Time ◽  
Three Dimensional ◽  
Passage Time ◽  
Diffusion Reaction ◽  
Exit Point ◽  
Drift Diffusion ◽  
Continuity Equations ◽  
Reaction Equations ◽  
Reaction Problem

Abstract In this paper a random walk on arbitrary rectangles (2D) and parallelepipeds (3D) algorithm is developed for solving transient anisotropic drift-diffusion-reaction equations. The method is meshless, both in space and time. The approach is based on a rigorous representation of the first passage time and exit point distributions for arbitrary rectangles and parallelepipeds. The probabilistic representation is then transformed to a form convenient for stochastic simulation. The method can be used to calculate fluxes to any desired part of the boundary, from arbitrary sources. A global version of the method we call here as a stochastic expansion from cell to cell (SECC) algorithm for calculating the whole solution field is suggested. Application of this method to solve a system of transport equations for electrons and holes in a semicoductor is discussed. This system consists of the continuity equations for particle densities and a Poisson equation for electrostatic potential. To validate the method we have derived a series of exact solutions of the drift-diffusion-reaction problem in a three-dimensional layer presented in the last section in details.

Stochastic simulation of fluctuation-induced reaction-diffusion kinetics governed by Smoluchowski equations

2015 ◽  
Vol 21 (1) ◽  
Author(s):  
Karl K. Sabelfeld ◽  
Alexander I. Levykin ◽  
Anastasiya E. Kireeva
Keyword(s):  
First Passage Time ◽  
Reaction Diffusion ◽  
Passage Time ◽  
Initial Distribution ◽  
Stochastic Algorithm ◽  
Diffusion Kinetics ◽  
Reaction Conditions ◽  
Segregation Effect ◽  
Smoluchowski Equations ◽  
Induced Reaction

AbstractA stochastic algorithm for simulation of fluctuation-induced reaction-diffusion kinetics is presented and further developed following our previous study [J. Math. Chem. (2015), DOI 10.1007/s10910-014-0446-6] where this method was used to describe the annihilation of spatially separate electrons and holes in a disordered semiconductor. This model is based on the spatially inhomogeneous, nonlinear Smoluchowski equations with random initial distribution density. Here we focus on the spatial distribution of the reactants, and study the segregation effect which we have found under certain reaction conditions. In addition, to extend simulations on large samples we implemented the method in the cellular-automata framework interpreted as a stochastic interacting particles system in discrete but randomly progressed time instances. We have suggested a first passage time technique to characterize the clustering of electrons and holes, which seems to be quite convenient and informative instrument also in more general processes when there is a need to analyze the segregation phenomena.

scholarly journals Characterizing Transport between the Surface Mixed Layer and the Ocean Interior with a Forward and Adjoint Global Ocean Transport Model

2005 ◽  
Vol 35 (4) ◽  
pp. 545-564 ◽  
Author(s):  
François Primeau
Keyword(s):  
Time Distribution ◽  
First Passage Time ◽  
Three Dimensional ◽  
Passage Time ◽  
Distribution Functions ◽  
Global Ocean ◽  
Surface Mixed Layer ◽  
Fluid Element ◽  
Transport Operator ◽  
Last Passage Time

Abstract The theory of first-passage time distribution functions and its extension to last-passage time distribution functions are applied to the problem of tracking the movement of water masses to and from the surface mixed layer in a global ocean general circulation model. The first-passage time distribution function is used to determine in a probabilistic sense when and where a fluid element will make its first contact with the surface as a function of its position in the ocean interior. The last-passage time distribution is used to determine when and where a fluid element made its last contact with the surface. A computationally efficient method is presented for recursively computing the first few moments of the first- and last-passage time distributions by directly inverting the forward and adjoint transport operator. This approach allows integrated transport information to be obtained directly from the differential form of the transport operator without the need to perform lengthy multitracer time integration of the transport equations. The method, which relies on the stationarity of the transport operator, is applied to the time-averaged transport operator obtained from a three-dimensional global ocean simulation performed with an OGCM. With this approach, the author (i) computes surface maps showing the fraction of the total ocean volume per unit area that ventilates at each point on the surface of the ocean, (ii) partitions interior water masses based on their formation region at the surface, and (iii) computes the three-dimensional spatial distribution of the mean and standard deviation of the age distribution of water.

DECAY OF METASTABLE STATES IN SPATIALLY EXTENDED REACTION-DIFFUSION SYSTEMS: ITS DEPENDENCE ON PARTIALLY REFLECTING BOUNDARY CONDITIONS

1996 ◽  
Vol 10 (11) ◽  
pp. 1273-1283 ◽  
Author(s):  
G. IZÚS ◽  
H.S. WIO ◽  
J. REYES DE RUEDA ◽  
O. RAMÍREZ ◽  
R. DEZA
Keyword(s):  
Boundary Conditions ◽  
First Passage Time ◽  
Piecewise Linear ◽  
Reaction Diffusion ◽  
Passage Time ◽  
Metastable States ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Spatially Extended ◽  
Linear Version

We study a piecewise linear version of a one-component, two-dimensional reaction-diffusion bistable model with partially reflecting boundary conditions, with the aim of analyzing the decay of metastable states in spatially extended systems. We have studied the dependence of systems’ Lyapunov functional in terms of a control parameter: the reflectivity at the boundary. Through the knowledge of this functional, we have computed the mean first-passage time for the decay of metastable nonhomogeneous stationary states, providing in this way dynamical information on the changes of the relative stability between attractors.

scholarly journals Kinetics of self-assembly of inclusions due to lipid membrane thickness interactions

2020 ◽  
Author(s):  
Xinyu Liao ◽  
Prashant K. Purohit
Keyword(s):  
Self Assembly ◽  
Time Scale ◽  
Lipid Membranes ◽  
Lipid Membrane ◽  
First Passage Time ◽  
Langevin Dynamics ◽  
Passage Time ◽  
Membrane Thickness ◽  
Kinetics Of ◽  
Two Inclusions

AbstractSelf-assembly of proteins on lipid membranes underlies many important processes in cell biology, such as, exo- and endo-cytosis, assembly of viruses, etc. An attractive force that can cause self-assembly is mediated by membrane thickness interactions between proteins. The free energy profile associated with this attractive force is a result of the overlap of thickness deformation fields around the proteins. The thickness deformation field around proteins of various shapes can be calculated from the solution of a boundary value problem and is relatively well understood. Yet, the time scales over which self-assembly occurs has not been explored. In this paper we compute this time scale as a function of the initial distance between two inclusions by viewing their coalescence as a first passage time problem. The first passage time is computed using both Langevin dynamics and a partial differential equation, and both methods are found to be in excellent agreement. Inclusions of three different shapes are studied and it is found that for two inclusions separated by about hundred nanometers the time to coalescence is hundreds of milliseconds irrespective of shape. Our Langevin dynamics simulation of self-assembly required an efficient computation of the interaction energy of inclusions which was accomplished using a finite difference technique. The interaction energy profiles obtained using this numerical technique were in excellent agreement with those from a previously proposed semi-analytical method based on Fourier-Bessel series. The computational strategies described in this paper could potentially lead to efficient methods to explore the kinetics of self-assembly of proteins on lipid membranes.Author summarySelf-assembly of proteins on lipid membranes occurs during exo- and endo-cytosis and also when viruses exit an infected cell. The forces mediating self-assembly of inclusions on membranes have therefore been of long standing interest. However, the kinetics of self-assembly has received much less attention. As a first step in discerning the kinetics, we examine the time to coalescence of two inclusions on a membrane as a function of the distance separating them. We use both Langevin dynamics simulations and a partial differential equation to compute this time scale. We predict that the time to coalescence is on the scale of hundreds of milliseconds for two inclusions separated by about hundred nanometers. The deformation moduli of the lipid membrane and the membrane tension can affect this time scale.

Spherical First Passage Time: A tool to investigate area-restricted search in three-dimensional movements

2010 ◽  
Vol 221 (13-14) ◽  
pp. 1665-1673 ◽  
Author(s):  
Frédéric Bailleul ◽  
Véronique Lesage ◽  
Mike O. Hammill
Keyword(s):  
First Passage Time ◽  
Three Dimensional ◽  
Passage Time ◽  
First Passage

In vitro and in vivo polysaccharides assembly: ultrastructural and cytochemical study of growing plant cell wall components.

1978 ◽  
Vol 36 (2) ◽  
pp. 434-435
Author(s):  
D. Reis ◽  
B. Vian ◽  
J. C. Roland
Keyword(s):  
Cell Wall ◽  
Self Assembly ◽  
Plant Cell Wall ◽  
Higher Plants ◽  
Three Dimensional ◽  
Cytochemical Study ◽  
Wall Components

Wall morphogenesis in higher plants is a problem still open to controversy. Until now the possibility of a transmembrane control and the involvement of microtubules were mostly envisaged. Self-assembly processes have been observed in the case of walls of Chlamydomonas and bacteria. Spontaneous gelling interactions between xanthan and galactomannan from Ceratonia have been analyzed very recently. The present work provides indications that some processes of spontaneous aggregation could occur in higher plants during the formation and expansion of cell wall.Observations were performed on hypocotyl of mung bean (Phaseolus aureus) for which growth characteristics and wall composition have been previously defined.In situ, the walls of actively growing cells (primary walls) show an ordered three-dimensional organization (fig. 1). The wall is typically polylamellate with multifibrillar layers alternately transverse and longitudinal. Between these layers intermediate strata exist in which the orientation of microfibrils progressively rotates. Thus a progressive change in the morphogenetic activity occurs.

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