Regulation of biochemical reaction rates by flexible tethers

Daniel Reeves, Keith Cheveralls, and Jane Kondev

Phys. Rev. E 84, 021914 – Published 10 August 2011

Abstract

We explore how ligand-receptor binding kinetics can be controlled by tethering the receptor to the end of a flexible polymer. The tether confines the diffusive motion of the receptor thus influencing the rate at which it captures ligands that are free in solution. We compute steady-state collision rates between ligand and receptor for this “tethered-capture” mechanism using a combination of analytic and numerical techniques. In doing so, we uncover a dimensionless control parameter, the “opacity,” that determines under what conditions and to what extent a tether regulates the ligand-receptor collision rate. We compute the opacity for a number of different tethering scenarios that appear in biology and use these results to predict the affect of changing the length and flexibility of the tether on the rate at which ligands are captured from solution.

Received 2 June 2011

DOI:https://doi.org/10.1103/PhysRevE.84.021914

Authors & Affiliations

Daniel Reeves, Keith Cheveralls, and Jane Kondev^*

Department of Physics, Brandeis University, Waltham, Massachusetts 02454, USA

^*kondev@brandeis.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 84, Iss. 2 — August 2011

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Structural model of the actin binding protein formin. (b) Cartoon of formin-assisted actin polymerization. Diffusing actin monomers (pointed shapes) preferentially bind to the barbed end of the growing filament. The barbed end is capped by the FH2 domains of a formin protein dimer, from which extend tentacle-like FH1 domains that are decorated with actin binding sites. Having captured the actin monomers, the flexible tethers deliver them directly to the growing end. The tether domain unbinds from the actin, and the actin filament is elongated by one monomer length.Reuse & Permissions
Figure 2
Schematic of two models for tethered capture. (a) Explicit modeling of the tether as an anchored bead-and-spring polymer that undergoes Rouse dynamics, the terminal node of which is the receptor. (b) While the ligand is allowed to diffuse freely everywhere, the receptor is confined within a spherical potential. The potential effectively distributes the receptor's concentration throughout the sphere.Reuse & Permissions
Figure 3
Calculated apparent second-order rate constant $k_{cap}$ as a function of the characteristic size of the tether $R_{ee}$ . The rate constant is computed for the three models discussed in the text assuming model parameters $D_{l, r} = 1 μ m^{2} / s$ , $k_{mix} = 0.1 μ m^{3} / s$ , and $C_{0} = 10^{4} μ m^{- 3}$ : the harmonic potential model with coupling given in Eq. (2) ( $dots$ ), the uncoupled approximation of Eq. (2) (squares), and the spherical hard-wall potential model given in Eq. (7) (lines). Each line corresponds to a sphere of size $R = φ R_{ee}$ , for which we use three values to illustrate the sensitivity to the choice of $φ$ . A spherical hard wall offers a good approximation to the decoupled harmonic potential when $φ = 1.3$ . Our theory predicts that for values of $R_{ee}^{2} < D_{r} / C_{0} k_{mix},$ the weakly interacting condition is satisfied and the decoupling approximation should be valid. That inequality is satisfied for $R_{ee} < 32 μ m$ , and the vertical dotted line is placed at 0.2 of that limiting value.Reuse & Permissions
Figure 4
Comparison of simulation to analytic approximations for two parameter sets. Simulation data (black lines), WF approximation results (broken lines), and effective potential results (gray line) are plotted as a function of tether length, which is expressed in number of beads $N$ . The WF results have been normalized to agree with $k_{S}$ at $N = 1$ . The root-mean-squared bond length is $b = 2$ , and the ligand diffusion constant is $D_{l} = 0.005$ in simulation units. The vertical lines indicate the tether lengths at which the control parameter $σ^{2} = 10$ .Reuse & Permissions
Figure 5
Diffusion of a polymer tether. Simulations of a polymer model (gray line) are used to compute the mean-square displacement of the terminal monomer, plotted in units of $b^{2}$ vs Monte Carlo steps. These data are compared to analytic results (black line) based on the Rouse model of polymer dynamics [Eq. (D34)]. The comparison serves as a check on the validity of the simulations and as a way of estimating the diffusion constant of the simulated polymer. We show results for two polymer lengths calculated using a Kuhn length of $b = 6.3$ trial steps. The resulting diffusion constant is $D_{r} = 0.0138$ in units of $b^{2} / mcs$ .Reuse & Permissions

Physical Review E

covering statistical, nonlinear, biological, and soft matter physics