Supplementary material
Derivation of Eqn 1 as done by Yin et al. (2004)
There are various mechanisms by which chloroplasts may remove the disparity
between the requirements for ATP and NADPH (Fig. S1). From the reduced
plastoquinone, a fraction (fQ) of e- follows the Q-cycle, and a fraction (1-fQ) is
transferred directly to plastocyanin. From reduced ferredoxin, a fraction (fcyc) of efollows the cyclic mode, a fraction (fpseudo) follows the pseudocyclic mode, and the
remaining fraction, (1-fcyc-fpseudo), are the linear e- transport to NADP+.
Let J2 be the rate of e- transport through PSII, and J1 be the rate of e- transport
through PSI. The rate of cyclic e- transport, Jcyc, is f cyc J 1 . The balance of inflow and
outflow of e-, both at plastoquinone and at PSI, means that:
J 2  f cyc J 1  J Q  J cyt  J 1
(S1)
where JQ is the rate of e- following the Q-cycle and Jcyt is the rate of those going
directly to the cytochrome complex and plastocyanin. Rewriting Eqn S1 gives
J 1  J 2 /(1  f cyc )
(S2)
The rate of e- transport being cyclic around PSI, Jcyc, is
J cyc  f cyc J 1  f cyc J 2 /(1  f cyc )
(S3)
Assuming that the Q-cycle, once engaged, is impartial for electrons of the whole chain
and of the cyclic flow, the value for JQ and Jcyt can be expressed by
J Q  f Q ( J 2  J cyc )  f Q J 2 /(1  f cyc )
(S4a)
J cyt  (1  f Q )( J 2  J cyc )  (1  f Q ) J 2 /(1  f cyc )
(S4b)
The rate of e- transport being pseudocyclic, Jpseudo, is
J pseudo  f pseudo J 1  f pseudo J 2 /(1  f cyc )
(S5)
The amount of linear e- transport (Jlinear) going to the end acceptor NADP+ is
1
J linear  (1  f cyc  f pseudo ) J 1  (1  f cyc  f pseudo ) J 2 /(1  f cyc )
(S6)
Therefore, the amount of NADPH production (Jnadph) is
J nadph  J linear / 2  (1  f cyc  f pseudo ) J 2 /[ 2(1  f cyc )]
(S7)
Let h denote the required number of H+ to produce 1 ATP. The expression for ATP
production (Jatp) can be derived from the number of H+ produced along various epathways (Fig. S1):
J atp  J 2 / h  J cyt / h  2 J Q / h
(S8a)
Substituting Eqns S4a and S4b into Eqn S8a and further simplifying gives:
J atp  [( 2  f Q  f cyc ) /(1  f cyc )] J 2 / h
(S8b)
This gives rise to Eqn 1 in the main text.
H2O
1 H+
1 H+
PS II
J2
Plastoquinone
Jcyt
JQ
2 H+
Cytochrome b6f
Plastocyanin
1/2 NADPH
Jcyc
PS I
J1
Ferredoxin
JNADP+
Jpseudo
NADP+
e.g. O2
Figure S1 Simple scheme for various pathways of electron transport in the light reaction of
photosynthesis. Thin arrows indicate electron transport. Thick curved arrows show the number of
protons or NADPH produced per electron transported. The rates of electron transport (J1, J2, Jcyc, Jcyt,
JNADP+, Jpseudo, JQ) are described in the texts of this supplementary material.
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