skip to main content

Title: Short-time diffusive fluxes over membrane receptors yields the direction of a signalling source

An essential ability of many cell types is to detect stimuli in the form of shallow chemical gradients. Such cues may indicate the direction that new growth should occur, or the location of a mate. Amplification of these faint signals is due to intra-cellular mechanisms, while the cue itself is generated by the noisy arrival of signalling molecules to surface bound membrane receptors. We employ a new hybrid numerical-asymptotic technique coupling matched asymptotic analysis and numerical inverse Laplace transform to rapidly and accurately solve the parabolic exterior problem describing the dynamic diffusive fluxes to receptors. We observe that equilibration occurs on long timescales, potentially limiting the usefulness of steady-state quantities for localization at practical biological timescales. We demonstrate that directional information is encoded primarily in early arrivals to the receptors, while equilibrium quantities inform on source distance. We develop a new homogenization result showing that complex receptor configurations can be replaced by a uniform effective condition. In the extreme scenario where the cell adopts the angular direction of the first impact, we show this estimate to be surprisingly accurate.

more » « less
Award ID(s):
Author(s) / Creator(s):
; ;
Publisher / Repository:
The royal society
Date Published:
Journal Name:
Royal Society Open Science
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    A prototype of cross-membrane signal transduction is that extracellular binding of cell surface receptors to their ligands induces intracellular signalling cascades. However, much less is known about the process in the opposite direction, called inside-out signalling. Recent studies show that it plays a more important role in regulating the functions of many cell surface receptors than we used to think. In particular, in cadherin-mediated cell adhesion, recent experiments indicate that intracellular binding of the scaffold protein p120-catenin (p120ctn) can promote extracellular clustering of cadherin and alter its adhesive function. The underlying mechanism, however, is not well understood. To explore possible mechanisms, we designed a new multiscale simulation procedure. Using all-atom molecular dynamics simulations, we found that the conformational dynamics of the cadherin extracellular region can be altered by the intracellular binding of p120ctn. More intriguingly, by integrating all-atom simulation results into coarse-grained random sampling, we showed that the altered conformational dynamics of cadherin caused by the binding of p120ctn can increase the probability of lateral interactions between cadherins on the cell surface. These results suggest that p120ctn could allosterically regulate the cis-dimerization of cadherin through two mechanisms. First, p120ctn controls the extracellular conformational dynamics of cadherin. Second, p120ctn oligomerization can further promote cadherin clustering. Therefore, our study provides a mechanistic foundation for the inside-out signalling in cadherin-mediated cell adhesion, while the computational framework can be generally applied to other cross-membrane signal transduction systems.

    more » « less
  2. null (Ed.)
    This paper presents a novel approach for pointing direction control of a rigid body with a body-fixed sensor, in the presence of control constraints and pointing direction constraints. This scheme relies on the use of artificial potentials where an attractive artificial potential is placed at the desired pointing direction and a repulsive artificial potential is used to avoid an undesirable pointing direction. The proposed control law ensures almost global asymptotic convergence of the rigid body to its desired pointing direction, while satisfying the control input constraints and avoiding the undesirable pointing direction. These theoretical results are followed by numerical simulation results that provide an illustration of the scheme for a realistic spacecraft pointing control scenario. 
    more » « less
  3. Frog virus 3 (FV3) is the type species of the genus Ranavirus (family Iridoviridae). FV3 and FV3-like viruses are globally distributed infectious agents with the capacity to replicate in three vertebrate classes (teleosts, amphibians, and reptiles). At the cellular level, FV3 and FV3-like viruses can infect cells from virtually all vertebrate classes. To date, the cellular receptors that are involved in the FV3 entry process are unknown. Class A scavenger receptors (SR-As) are a family of evolutionarily conserved cell-surface receptors that bind a wide range of chemically distinct polyanionic ligands and can function as cellular receptors for other DNA viruses, including vaccinia virus and herpes simplex virus. The present study aimed to determine whether SR-As are involved in FV3 cellular entry. By using well-defined SR-A competitive and non-competitive ligand-blocking assays and absolute qPCR, we demonstrated that the SR-A competitive ligands drastically reduced the quantities of cell-associated viral loads in frog cells. Moreover, inducing the expression of a human SR-AI in an SR-A null cell line significantly increased FV3–cell association. Together, our results indicate that SR-As are utilized by FV3 during the cellular entry process. 
    more » « less
  4. Abstract

    AnLMNcoordinate system for magnetic reconnection events is sometimes determined by definingNas the direction of the gradient across the current sheet andLas the direction of maximum variance of the magnetic field. The third direction,M, is often assumed to be the direction of zero gradient, and thus the orientation of the X line. But when there is a guide field, the X line direction may have a significant component in the L direction defined in this way. For a 2D description, a coordinate system describing such an event would preferably be defined using a different coordinate directionM′ oriented along the X line. Here we use a 3D particle‐in‐cell simulation to show that the X line is oriented approximately along the direction bisecting the asymptotic magnetic field directions on the two sides of the current sheet. We describe two possible ways to determine the orientation of the X line from spacecraft data, one using the minimum gradient direction from Minimum Directional Derivative analysis at distances of the order of the current sheet thickness from the X line, and another using the bisection direction based on the asymptotic magnetic fields outside the current sheet. We discuss conditions for validity of these estimates, and we illustrate these conditions using several Magnetospheric Multiscale (MMS) events. We also show that intersection of a flux rope due to secondary reconnection with the primary X line can destroy invariance along the X line and negate the validity of a two‐dimensional description.

    more » « less
  5. Non-asymptotic analysis of quasi-Newton methods have gained traction recently. In particular, several works have established a non-asymptotic superlinear rate of O((1/sqrt{t})^t) for the (classic) BFGS method by exploiting the fact that its error of Newton direction approximation approaches zero. Moreover, a greedy variant of BFGS was recently proposed which accelerates its convergence by directly approximating the Hessian, instead of the Newton direction, and achieves a fast local quadratic convergence rate. Alas, the local quadratic convergence of Greedy-BFGS requires way more updates compared to the number of iterations that BFGS requires for a local superlinear rate. This is due to the fact that in Greedy-BFGS the Hessian is directly approximated and the Newton direction approximation may not be as accurate as the one for BFGS. In this paper, we close this gap and present a novel BFGS method that has the best of both worlds in that it leverages the approximation ideas of both BFGS and GreedyBFGS to properly approximate the Newton direction and the Hessian matrix simultaneously. Our theoretical results show that our method outperforms both BFGS and Greedy-BFGS in terms of convergence rate, while it reaches its quadratic convergence rate with fewer steps compared to Greedy-BFGS. Numerical experiments on various datasets also confirm our theoretical findings. 
    more » « less