Supplement-2. Kinetic impact of [H+]o in H+ exporting pump with acceptor group Do
Reaction scheme, simplified from Fig. 1B.
Symbols:
S (1): So + Si;
SH (2): SoH + SiH;
DoH (3) and Do(4) as in Fig. 1B;
k1: transition probability from cytoplasmic H+ to SH, comprising several steps;
k2: transition probability from cytoplasmic SH to S; comprising several steps, e.g. initial photoisomerization (k2 = k20·light, k20: reference value) and transfer of H+ from SH to DoH;
k3: transition probability from DoH to Do, dissociation of H+ into external bulk solution;
k4: transition probability from Do to DoH, association of H+ from external bulk solution.
p1 p2, p3, p4: probabilities of indicated states to be occupied
Conditions and definitions:
p1 p2, p3, p4: probabilities of indicated states to be occupied
k3, k4 > k1, k2.
k4 = k40 [H+]o;
k40 = k4 at reference [H+]o;
K = k4/k3;
K0 = k40/k3;
p1 + p2 = 1;
p3 + p4 = 1.
Steady-state conditions:
0 = dp1/dt = -k1p1 + k2p2p4
0 = dp2/dt = k1p1 - k2p2p4;
0 = dp3/dt = k2p2p4 + k4p4 - k3p3;
0 = dp3/dt = -k2p2p4 - k4p4 + k3p3;
Turnover: I = k2p2p4.
After some algebra:
I = k1k2/(k1 + k1K + k2K);
Reciprocal:
1/I = (1+K)/k2 + K/k1.
At high pHo (K<1):
1/I = 1/k2 + K/k1,
= 1/k2 + K0[H+]o/k1;
DpHo induced change:
Parallel, straight lines with slope 1/(k20·light) and vertical displacements K0[H+]o/k1 from origin (Fig. 2B),
q.e.d.
1