Membrane localization accelerates association under conditions relevant to cellular signaling

Abstract

Translocation of cytoplasmic molecules to the plasma membrane is commonplace in cell signaling. Membrane localization has been hypothesized to increase intermolecular association rates; however, it has also been argued that association should be faster in the cytosol because membrane diffusion is slow. Here, we directly compare an identical association reaction, the binding of complementary DNA strands, in solution and on supported membranes. The measured rate constants show that for a 10-µm-radius spherical cell, association is 22- to 33-fold faster at the membrane than in the cytoplasm. The kinetic advantage depends on cell size and is essentially negligible for typical ~1 µm prokaryotic cells. The rate enhancement is attributable to a combination of higher encounter rates in two dimensions and a higher reaction probability per encounter.

Keywords: Ras activation; bimolecular reaction; membrane-associated proteins; receptor signaling; reduction of dimensionality.

Fig. 1.

Molecular association in two-dimension (2D) vs. three-dimension (3D) in cellular signaling. (A) Simplified schematic of a RTK signaling pathway. The growth factor brings about dimerization, activation, and intracellular autophosphorylation of the RTK, which recruits cytosolic proteins to the membrane. Sos, a key GEF protein for Ras GTPase activation, is recruited to the cell membrane via the adaptor protein Grb2. Membrane-associated Sos activates Ras, which activates the MAPK cascade. (B) Schematic of association in 3D in the cytosol vs. 2D on a membrane. (C) Our approach to directly compare rates in 2D vs. 3D: a controllable DNA association reaction monitored on supported membranes, and in buffers with or without viscogens.

Fig. 2.

Association reactions in solution and on membranes. (A) Schematic view of the strand displacement reaction. (B–D) Normalized traces of fluorescence as a function of time after initiating the DNA strand-displacement reactions in (B) phosphate-buffered saline, (C) phosphate-buffered saline plus 10% (w/w) Ficoll 70, and (D) on supported membranes. In these titration experiments, the fluorescent complex (B:F) was fixed; the quencher complex (Q:A) in solution titration was {50, 25, 10, 5} and {100, 50, 25, 10} for B and C, respectively; for membrane experiments, the quencher was incubated at {1×, 0.75×, 0.5×, 0.25×} of the fluorescent complex during the coupling reaction. The fitted Qs were {36, 19, 8.1, 4.2} nM, {63, 39, 22, 12} nM, and {28, 31, 25, 9.1} molecules/µm² for B–D, respectively. Membrane data shown here have been corrected for photobleaching (SI Appendix, Fig. S5). Solid curves are fits of Eq. 3. The rate constants are averages ± SEM with n = 4. (E) Statistics from independent replicates of experiments in B–D. A second set of experiments is shown in SI Appendix, Fig. S6.

Fig. 3.

Diffusion characterization in solution and on membranes. (A) Normalized FCS autocorrelation functions of DNA F:B complexes. Diffusion coefficients were obtained from fitting a 3D Brownian model to the data, except in the case of membranes, in which a 2D Brownian model was used. Diffusion coefficients are shown as fitted values ± 95% CI fitting. (B–D) Normalized FCS autocorrelation functions for DNA F:B complexes to BSA-Alexa Flour 488 (black) in (B) buffer, (C) buffer plus 10% Ficoll 70, and (D) cytosolic Xenopus egg extracts.

Fig. 4.

Association rates in 2D vs. 3D. (A and B) Changes in association rates when the numbers of molecules are kept constant in 2D and 3D. (A) Schematic showing a signaling molecule (blue) and its targets (orange) randomly distributed in the cytoplasm (Left) or on the inner aspect of the plasma membrane (Right). (B) Inferred ratio of the total association rate in 2D divided by the total association rate in 3D (R_N) for spherical cells of various sizes. We assumed equal numbers of molecules in the cytoplasm vs. on the membrane. A value of R_N greater than 1 means that 2D association is faster than 3D association. The diagonal lines are plots of the relationship $R_N=\frac{k_{2\mathrm{D}}}{k_{3\mathrm{D}}}\frac{r}{3}$ using the value of $k_{2\mathrm{D}}$ from the supported bilayer experiment and the value of $k_{3D}$ from either the buffer minus Ficoll (purple) or buffer plus Ficoll (orange) data. The radii of one prokaryote and three eukaryotic cells that span a range of sizes are shown. (C–F) Changes in association rates while keeping the mean nearest target distance the same in 2D and 3D. (C) Schematic showing nearest target distances in 2D and 3D. (D) Probability density functions for nearest target distances in 2D (red) and 3D (blue), assuming randomly distributed, non-interacting particles. Concentration (for 3D) and surface density (for 2D) values were chosen so that the average nearest target distance would be 0.1 µm for both cases. (E) The ratio of association rates keeping the mean nearest target molecule equal in 2D and 3D, as given by $R_d\approx 0.815\frac{k_{2\mathrm{D}}}{k_{3\mathrm{D}}}{c}_2^{-1/3}$. (F) The same as E except keeping the linear density ($\lambda =c^{1/3}$ for 3D and ${\sigma }^{1/2}$ for 2D) the same for 2D and 3D.

Fig. 5.

Inverting quencher orientation affects membrane advantage. (A) Schematic view of the binding of a fluorophore-containing strand to an inverted quencher on supported membranes. When coupled to the supported membrane, the iQ:iA strand has an inverted orientation compared to the B:F and Q:A strand. This orientation was achieved by moving the thiol coupling site from the end of the A strand to the Q strand. (B and C) Titration experiments of the inverted DNA reaction in (B) buffer and (C) on membranes. The titrated iQ:iA concentration and density were {100, 50, 25, 10} nM and {1×, 0.75×, 0.5×, 0.25×} for B and C, respectively.