of redox reactions in the
respiratory chain and the
oxidative phosphorylation catalysed by the
ATP synthase. The movement of ions across the membrane depends on a combination of two factors: •
Diffusion force caused by a concentration gradient - all particles tend to diffuse from higher concentration to lower. •
Electrostatic force caused by
electrical potential gradient -
cations like protons H+ tend to diffuse down the electrical potential, from the positive (P) side of the membrane to the negative (N) side.
Anions diffuse spontaneously in the opposite direction. These two gradients taken together can be expressed as an
electrochemical gradient.
Lipid bilayers of
biological membranes, however, are barriers for ions. This is why energy can be stored as a combination of these two gradients across the membrane. Only special membrane proteins like
ion channels can sometimes allow ions to move across the membrane (see also:
Membrane transport). In the chemiosmotic hypothesis a transmembrane
ATP synthase is central to convert energy of spontaneous flow of protons through them into chemical energy of ATP bonds. Hence researchers created the term
proton-motive force (PMF), derived from the electrochemical gradient mentioned earlier. It can be described as the measure of the potential energy stored (
chemiosmotic potential) as a combination of proton and voltage (electrical potential) gradients across a membrane. The electrical gradient is a consequence of the charge separation across the membrane (when the protons H+ move without a
counterion, such as
chloride Cl−). In most cases the proton-motive force is generated by an electron transport chain which acts as a proton pump, using the
Gibbs free energy of
redox reactions to pump protons (hydrogen ions) out across the membrane, separating the charge across the membrane. In mitochondria, energy released by the electron transport chain is used to move protons from the mitochondrial matrix (N side) to the intermembrane space (P side). Moving the protons out of the mitochondrion creates a lower concentration of positively charged protons inside it, resulting in excess negative charge on the inside of the membrane. The electrical potential gradient is about -170 mV , negative inside (N). These gradients - charge difference and the proton concentration difference both create a combined electrochemical gradient across the membrane, often expressed as the proton-motive force (PMF). In mitochondria, the PMF is almost entirely made up of the electrical component but in chloroplasts the PMF is made up mostly of the pH gradient because the charge of protons H+ is neutralized by the movement of Cl− and other anions. In either case, the PMF needs to be greater than about 460 mV (45 kJ/mol) for the ATP synthase to be able to make ATP.
Equations The proton-motive force is derived from the
Gibbs free energy. Let N denote the inside of a cell, and P denote the outside. Then :\Delta\!G = zF \Delta\!\psi + RT \ln\frac{[\mathrm{X}^{z+}]_{\text{N}} }{[\mathrm{X}^{z+}]_{\text{P}}} where • \Delta\!G is the Gibbs free energy change per unit amount of
cations transferred from P to N; • z is the
charge number of the
cation \mathrm{X}^{z+}; • \Delta\psi is the electric potential of N relative to P; • [\mathrm{X}^{z+}]_{\text{P}} and [\mathrm{X}^{z+}]_{\text{N}} are the cation concentrations at P and N, respectively; • F is the
Faraday constant; • R is the
gas constant; and • T is the
temperature. The molar Gibbs free energy change \Delta\!G is frequently interpreted as a molar electrochemical ion potential \Delta\!\mu _{\mathrm{X}^{z+}} = \Delta\!G. For an
electrochemical proton gradient z=1 and as a consequence: :\Delta\!\mu _{\mathrm{H}^{+}} = F \Delta\!\psi + RT \ln \frac{[\mathrm{H}^+]_{\text{N}} }{[\mathrm{H}^+]_{\text{P}}} = F \Delta\!\psi - (\ln 10)RT \Delta \mathrm{pH} where :\Delta\!\mathrm{pH} = \mathrm{pH}_{\mathrm{N}} - \mathrm{pH}_{\mathrm{P}}. Mitchell defined the
proton-motive force (PMF) as :\Delta\!p = -\frac{\Delta\!\mu_{\mathrm{H^{+}}}}{F}. For example, \Delta\!\mu_{\mathrm{H}^+}=1\,\mathrm{kJ}\,\mathrm{mol}^{-1} implies \Delta\!p = 10.4\,\mathrm{mV}. At 298\,\mathrm{K} this equation takes the form: \Delta\!p = -\Delta\!\psi + \left(59.1\,\mathrm{mV}\right)\Delta\!\mathrm{pH}. Note that for spontaneous proton import from the P side (relatively more positive and acidic) to the N side (relatively more negative and alkaline), \Delta\!\mu _{\mathrm{H}^+} is negative (similar to \Delta\!G) whereas PMF is positive (similar to redox cell potential \Delta E). It is worth noting that, as with any transmembrane transport process, the PMF is directional. The sign of the transmembrane electric potential difference \Delta\!\psi is chosen to represent the change in potential energy per unit charge flowing into the cell as above. Furthermore, due to redox-driven proton pumping by coupling sites, the proton gradient is always inside-alkaline. For both of these reasons, protons flow in spontaneously, from the P side to the N side; the available free energy is used to synthesize ATP (see below). For this reason, PMF is defined for proton import, which is spontaneous. PMF for proton export, i.e., proton pumping as catalyzed by the coupling sites, is simply the negative of PMF(import). The spontaneity of proton import (from the P to the N side) is universal in all bioenergetic membranes. This fact was not recognized before the 1990s, because the chloroplast thylakoid lumen was interpreted as an interior phase, but in fact it is topologically equivalent to the exterior of the chloroplast. Azzone et al. stressed that the inside phase (N side of the membrane) is the bacterial cytoplasm, mitochondrial matrix, or chloroplast stroma; the outside (P) side is the bacterial periplasmic space, mitochondrial intermembrane space, or chloroplast lumen. Furthermore, 3D tomography of the mitochondrial inner membrane shows its extensive invaginations to be stacked, similar to thylakoid disks; hence the mitochondrial intermembrane space is topologically quite similar to the chloroplast lumen.: The energy expressed here as Gibbs free energy, electrochemical proton gradient, or proton-motive force (PMF), is a combination of two gradients across the membrane: • the concentration gradient (via \Delta\!\mathrm{pH}) and • electric potential gradient \Delta\!\psi. When a system reaches equilibrium, \Delta\!\rho = 0; nevertheless, the concentrations on either side of the membrane need not be equal. Spontaneous movement across the potential membrane is determined by both concentration and electric potential gradients. The molar Gibbs free energy \Delta\!G_{\mathrm{p}} of ATP synthesis :\mathrm{ADP}^{4-} + \mathrm{H}^{+} + \mathrm{HOPO}_3^{2-} \rightarrow \mathrm{ATP}^{4-} + \mathrm{H_2 O} is also called phosphorylation potential. The equilibrium concentration ratio [\mathrm{H}^+]/[\mathrm{ATP}] can be calculated by comparing \Delta\!p and \Delta\!G_{\mathrm{p}}, for example in case of the mammalian mitochondrion: H+ / ATP = ΔGp / (Δp / 10.4 kJ·mol−1/mV) = 40.2 kJ·mol−1 / (173.5 mV / 10.4 kJ·mol−1/mV) = 40.2 / 16.7 = 2.4. The actual ratio of the proton-binding c-subunit to the ATP-synthesizing beta-subunit copy numbers is 8/3 = 2.67, showing that under these conditions, the mitochondrion functions at 90% (2.4/2.67) efficiency. In fact, the thermodynamic efficiency is mostly lower in eukaryotic cells because ATP must be exported from the matrix to the cytoplasm, and ADP and phosphate must be imported from the cytoplasm. This "costs" one "extra" proton import per ATP, hence the actual efficiency is only 65% (= 2.4/3.67). ==In mitochondria==