Measuring Transmembrane Helix Interaction Strengths in Lipid Bilayers Using Steric Trapping

Abstract

We have developed a method to measure strong transmembrane (TM) helix interaction affinities in lipid bilayers that are difficult to measure by traditional dilution methods. The method, called steric trapping, couples dissociation of biotinylated TM helices to a competitive binding by monovalent streptavidin (mSA), so that dissociation is driven by the affinity of mSA for biotin and mSA concentration. By adjusting the binding affinity of mSA through mutation, the method can obtain dissociation constants of TM helix dimers (K _d,dimer) over a range of six orders of magnitudes. The K _d,dimer limit of measurable target interaction is extended 3–4 orders of magnitude lower than possible by dilution methods. Thus, steric trapping opens up new opportunities to study the folding and assembly of α-helical membrane proteins in lipid bilayer environments. Here we provide detailed methods for applying steric trapping to a TM helix dimer.

Appendix: Derivation of the Equation for the Second mSA Binding Coupled to the Dissociation of the TM Helix Dimer

Equation 4 was derived as follows according to the reaction scheme,

$$ {P}_{2}\rightleftarrows 2P\rightleftarrows 2P\text{}·\text{}\text{mSA}$$

$$ {K}_{\text{d},\text{dimer}}=\frac{{\left[P\right]}^{2}}{\left[{P}_{2}\right]},\left[{P}_{2}\right]=\frac{{\left[P\right]}^{2}}{{K}_{\text{d},\text{dimer}}}$$

(7)

$$ {K}_{\text{d},\text{biotin}}=\frac{\left[P\right]\left[\text{mSA}\right]}{\left[P\cdot \text{mSA}\right]}, \left[P\cdot \text{mSA}\right]=\frac{\left[P\right]\left[\text{mSA}\right]}{{K}_{\text{d},\text{biotin}}}$$

(8)

$$ \begin{array}{l}{\theta}_{\text{bound}}=\frac{\left[P\cdot \text{mSA}\right]}{{\left[P\right]}_{o}}=\frac{\left[P\cdot \text{mSA}\right]}{2\left[{P}_{2}\right]+\left[P\right]+\left[P\cdot \text{mSA}\right]}=\frac{\frac{\left[P\right]\left[\text{mSA}\right]}{{K}_{\text{d},\text{biotin}}}}{2\frac{{\left[P\right]}^{2}}{{K}_{\text{d},\text{dimer}}}+\left[P\right]+\frac{\left[P\right]\left[\text{mSA}\right]}{{K}_{\text{d},\text{biotin}}}}\\ \text{}\text{}\left(7\right)\wedge \left(8\right)=\frac{1}{1+\frac{{K}_{\text{d},\text{biotin}}}{\left[\text{mSA}\right]}+2\frac{{K}_{\text{d},\text{biotin}}}{{K}_{\text{d},\text{dimer}}}\frac{\left[P\right]}{\left[\text{mSA}\right]}}\end{array}$$

By using Eq. 8

$$ \left[ P \right]=\frac{{{K_{\mathrm{d},\mathrm{biotin}}}\left[ {P\cdot \mathrm{mSA}} \right]}}{{\left[ {\mathrm{mSA}} \right]}}=\frac{{{K_{\mathrm{d},\mathrm{biotin}}}\left( {{{{\left[ P \right]}}_o}\cdot {\theta_{\mathrm{bound}}}} \right)}}{{\left[ {\mathrm{mSA}} \right]}} $$

$${\theta}_{\text{bound}}=\frac{1}{1+\frac{{K}_{\text{d},\text{biotin}}}{\left[\text{mSA}\right]}+2\frac{{K}_{\text{d},\text{biotin}}{}^{2}\left({\left[P\right]}_{o}\cdot {\theta}_{\text{bound}}\right)}{{K}_{\text{d},\text{dimer}}{\left[\text{mSA}\right]}^{2}}},$$

which gives

$$2\frac{{K}_{\text{d},\text{biotin}}{}^{2}}{{K}_{\text{d},\text{dimer}}}\frac{{\left[P\right]}_{o}}{{\left[\text{mSA}\right]}^{2}}{\theta}_{\text{bound}}{}^{2}+\left(1+\frac{{K}_{\text{d},\text{biotin}}}{\left[\text{mSA}\right]}\right){\theta}_{\text{bound}}-1=0$$

Then,

$${\theta}_{\text{bound}}=\frac{-\left(1+\frac{{K}_{\text{d},\text{biotin}}}{\left[\text{mSA}\right]}\right)+{\left({\left(1+\frac{{K}_{\text{d},\text{biotin}}}{\left[\text{mSA}\right]}\right)}^{2}+8{P}_{o}\frac{{K}_{\text{d},\text{biotin}}{}^{2}}{{K}_{\text{d},\text{dimer}}}\frac{1}{{\left[\text{mSA}\right]}^{2}}\right)}^{1/2}}{4{P}_{o}\frac{{K}_{\text{d},\text{biotin}}{}^{2}}{{K}_{\text{d},\text{dimer}}}\frac{1}{{\left[\text{mSA}\right]}^{2}}}$$

[P]: SN-BAP-GpATM monomer concentration; [P ₂]: SN-BAP-GpATM dimer concentration; [P] _o : Total SN-BAP-GpATM concentration; [mSA]: Total mSA concentration; K _d,biotin: Dissociation constant for intrinsic biotin-binding affinity of mSA; K _d,dimer: Dissociation constant for GpATM dimers.