Protein interactions aided by strong protein-lipid interactions, abundant lipid recruiters, and low protein concentrations benefit most widely from membrane localization.

<p>a,b) Enhancement ratios from ODE simulation (colored lines) and theory (black solid lines in all panels). The dashed black line is the upper limit for the enhancement ratio given by K_a^eff/K_a^PP = γ. σ = 1nm. Between the limiting cases where the membrane surface area is either too large to enhance binding (V/A⟶0) or is too small to effect binding (V/A⟶∞), a broad region of enhanced binding occurs. The vertical gray line is the V/A ratio for the yeast plasma membrane (0.5μm), for reference, and most physiologic V/A values fall in the range ~0.05–20μm (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006031#pcbi.1006031.s005" target="_blank">S3 Table</a>). Within this physiologic range of V/A values is where we generally observe the largest enhancements. The cell geometry pictures provide examples of how one can produce different V/A ratios along the x-axis relative to the central sphere. A maximum enhancement for each parameter set is reached at a value of V/A where lipids still outnumber proteins (shown on upper x axis). Increasing (a) protein-lipid affinities and (b) lipid concentrations produces greater possibilities for enhancement. (c) Increases in the membrane stickiness (K_a^PM[M]_eq) produces monotonic increases in enhancement for all values of γ>1. (d) For lower expression levels relative to binding strength (K_a^PP = 10⁶M^-1), membrane localization can act as a switch to turn on assembly from <50% to >50% (shaded areas). (e) Timescales to equilibrate were calculated from simulations of both ODEs (solid lines) and reaction-diffusion (RD) (green points) (Methods). Weak lipid binding can reduce speeds (blue) relative to pure solution binding (dashed). The approximate theoretical bounds shown here for time-scales of binding either purely in solution (dashed) or on the membrane (gray) derive from the kinetics of irreversible association (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006031#pcbi.1006031.s001" target="_blank">S1 Text</a> section 4C).