Figure 2.

Free-energy barrier formalism for Ca²⁺ transport into mitochondria via the Ca²⁺ uniporter. (A) (I–III) Consecutive states of the Ca²⁺-bound uniporter functional unit in the process of Ca²⁺ translocation that is used to derive the dependence of the rate of Ca²⁺ transport on the electrostatic membrane potential ΔΨ. Here, α_e is the ratio of the potential difference between Ca²⁺ bound at the site of uniporter facing the external side of the IMM and Ca²⁺ in the bulk phase to the total membrane potential ΔΨ, α_x is the ratio of the potential difference between Ca²⁺ bound at the site of uniporter facing the internal side of the IMM and Ca²⁺ in the bulk phase to the total membrane potential ΔΨ, β_e is the displacement of external Ca²⁺ from the coordinate of maximum potential barrier, and β_x is the displacement of internal Ca²⁺ from the coordinate of maximum potential barrier. (B) Potential energy barrier profile along the reaction coordinate that is used to derive the dependence of the rate of Ca²⁺ transport on the electrostatic membrane potential ΔΨ. The dashed line shows the profile of the potential created by the electric field of the charged membrane. The points I, II, and III correspond to the Ca²⁺-bound uniporter states depicted in the upper panel A. The rate constants k_in and k_out are related to the changes in potential energy (Gibbs free-energy) ΔG_in and ΔG_out. Note that in the absence of electric field (ΔΨ = 0 mV), the heights of the free-energy barriers in the forward and reverse directions are equal when the dissociation constants for the binding of the external and internal Ca²⁺ to the uniporter are equal: that is, $\Delta G_{\text{in}}^0=\Delta G_{\text{out}}^0=\Delta G^0$ if and only if $K_{\text{e}}^0=K_{\text{x}}^0=K^0$.