Peter G. Finichiu Andrew M. James Lesley Larsen Robin A. J. Smith Michael P. Murphy

Peter G. Finichiu Andrew M. James Lesley Larsen Robin A. J. Smith Michael P. Murphy

Supplementary Material

Mitochondrial accumulation of a lipophilic cation conjugated to an ionisable group depends on membrane potential, pH gradient and pKa: implications for the design of mitochondrial probes and therapies

Peter G. Finichiu • Andrew M. James •Lesley Larsen•Robin A. J. Smith • Michael P. Murphy

Derivation of Equation 1

Equation 1 describes the accumulation ratio (ACR) into energised mitochondria of a lipophilic cation conjugated to a weak acid (A) or base (B) as a function of mitochondrial membrane potential (m), pH gradient (pH) and with thepKaof the weak acid or base. The assumptions made in deriving Equation 1 are that only the singly charged compounds are accumulated into mitochondria in response to them. Thus the zwitterionic form of the lipophilic cation (X), conjugated to a weak acid (AH) would not be taken up in response to mand the dicationic form of the lipophilic cation (X), conjugated to a weak base (B) would not be membrane permeant. The two relevant equilibria are:

For the weak acid () only the mono-cationic form () is affected by the m and its uptake from extra-mitochondrial phase such as the cytosol (cyt) into mitochondria (mito)is described by the Nernst equation.

(1)

This rearranges to:

(2)

The Henderson-Hasselbalchequationdescribes the ratio between protonated and dissociated fraction of the compound as a function of pH in the cytosol and mitochondrial matrix.

(3)

(4)

Substituting (2) into (4) gives:

(5)

The total concentration in each phase is:

(6) = +

(7) = +

Substitution of (3) into (6) yields

(8) = +

Substitution of (2) and (5) into (7) yields

(9) = +

The accumulation ratio (ACR) is defined by the total concentration of the compound inside the mitochondrion, i.e. , divided by the total concentration of the compound outside the mitochondrion, i.e. :

(10)

Therefore substitution of (8) and (9) into (10) yields

(11)

For the weak base () only the monocationic form () is affected by m and its uptake from the extramitochondrial phase such as the cytosol (cyt) into mitochondria (mito) is described by the Nernst equation.

(12)

This rearranges to:

(13)

The Henderson-Hasselbalchequationdescribes the ratio between protonated and dissociated fraction of the compound as a function of pH in the cytosol and mitochondrial matrix.

(14)

(15)

Substituting (13) into (15) gives:

(16)

The total concentration in each phase is:

(17) = +

(18) = +

Substitution of (14) into (17) yields

(19) = +

Substitution of (13) and (16) into (18) yields

(20) = +

The accumulation ratio (ACR) is defined by the total concentration of the compound inside the mitochondria () divided by the total concentration of the compound outside the mitochondrion ():

(21)

Therefore substitution of (19) and (20) into (21) yields

(22)

Summarising (11) and (22) the general accumulation ratio for a lipophilic cation conjugated to a weak acids or base is given byEquation 1where i is +1 for acid and -1 for base:

Equation 1

1