![Figure 3. Allosteric linkage between two gating particles. (A) L-J cooperon with native interactions between (C, O) states of the L particle (pore) and (R, A) states of the J particle (voltage sensor) indicated by gray dashed lines connecting state (q, Φ) coordinates. (B) Conductance Hill energy WH[g] versus V (solid red trace) calculated from the cooperon in A under conditions of weak coupling (W = −kTlnD = −100 meV = 2.31 kcal/mol). The negative (lower) asymptote ψL = ΔqL(V − VL) represents intrinsic pore gating consistent with the pull-open mechanism (color scheme purple, D > 1 favoring A-O state). The positive (upper) asymptote is displaced vertically by kTlnD as a result of L-J interaction in the pull-open scheme, but it could also represent intrinsic pore activation ψL′ = ΔqL(V − VL′) consistent with the push-closed mechanism (blue color scheme, D′ < 1 destabilizes R-O state). The strong coupling curve (dash-dotted red line) was obtained by increasing the magnitude of the coupling energy W from −100 to −200 meV while maintaining L′ = LD constant. The asymptotic limit of large coupling (L → 0, D → ∞) yields an obligatory scheme (dotted red line) with limiting slope Δqmax = ΔqJ + ΔqL. The mean (median) voltage of activation VM = −kTln(L′J)/Δqmax (value indicated by arrow to V axis) is independent of W under these conditions.](https://cdn.rupress.org/rup/content_public/journal/jgp/144/1/10.1085_jgp.201311130/4/jgp_201311130_fig3.jpeg?Expires=1773476293&Signature=TQqv0UsHA-ZiULB-~gfAV9M7ieawT6JkoqROW8E5Mka3qehfK5TmcuLMFG5xaE4wTFXvKj5q~zZtMC6CsW73uE1~zB3xkzq44qwDdBp5BIQzXlsND0wPbierJzc6DINtgfE1nHHAWwtQWl91Z~-20i7v6uDrxkxU9ak1twtcu0fE0ij2fO~JmXTaKIHZ30uHua2~QDaxNdrA~3CXsUvgMzMcKMc~167jovYSlhBCwZnRBLel92tmSU3XcmMqubG9BVG9xVQRhf-WCu2VGq0I2ZTYD4KjwKBQaJOipxVW3jLzF8B4A28KYRwfnGVlXA1-J9VLwAcD60IGc-fQ1D2fKw__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Allosteric linkage between two gating particles. (A) L-J cooperon with native interactions between (C, O) states of the L particle (pore) and (R, A) states of the J particle (voltage sensor) indicated by gray dashed lines connecting state (q, Φ) coordinates. (B) Conductance Hill energy WH[g] versus V (solid red trace) calculated from the cooperon in A under conditions of weak coupling (W = −kTlnD = −100 meV = 2.31 kcal/mol). The negative (lower) asymptote ψL = ΔqL(V − VL) represents intrinsic pore gating consistent with the pull-open mechanism (color scheme purple, D > 1 favoring A-O state). The positive (upper) asymptote is displaced vertically by kTlnD as a result of L-J interaction in the pull-open scheme, but it could also represent intrinsic pore activation ψL′ = ΔqL(V − VL′) consistent with the push-closed mechanism (blue color scheme, D′ < 1 destabilizes R-O state). The strong coupling curve (dash-dotted red line) was obtained by increasing the magnitude of the coupling energy W from −100 to −200 meV while maintaining L′ = LD constant. The asymptotic limit of large coupling (L → 0, D → ∞) yields an obligatory scheme (dotted red line) with limiting slope Δqmax = ΔqJ + ΔqL. The mean (median) voltage of activation VM = −kTln(L′J)/Δqmax (value indicated by arrow to V axis) is independent of W under these conditions.
