What is the redox potential of a cell?
Redox potentials are used to infer the direction and free energy cost of
reactions involving electron transfer, one of the most ubiquitous and
important types of biochemical reactions. Such reduction-oxidation
reactions are characterized by a free energy change that shares some
conceptual features with that used to describe pKa in acid-base reactions
where proton transfer is involved rather than electron transfer. In this
vignette, we discuss how the redox potential can be used as a measure of
the driving force for a given oxidation-reduction reaction of interest. By
way of contrast, unlike the pH, there is no sense in which one can assign
a single redox potential to an entire cell.
The redox potential, or more accurately the reduction potential, of a
compound refers to its tendency to acquire electrons and thereby to be
reduced. Some readers might remember the mnemonic “OILRIG” which
reminds us that “oxidation is loss, reduction is gain”.
Consider a
reaction that involves an electron transfer: Aox + ne- ↔ Ared where n
electrons are taken up by the oxidized form (Aox) to give the reduced
form (Ared) of compound A. The redox potential difference ΔE between
the electron donor and acceptor is related to the associated free energy
change ΔG of the reaction via ΔG=nFΔE where n is the number of
electrons transferred and F is Faraday’s constant (96,485J/mol/V or
≈100kJ/mol/V). By inspecting tabulated values of these potentials, it is
possible to develop an intuition for the tendency for electron transfer
and hence, of the direction of the reaction.
Though ATP is often claimed to be the energy currency of the cell, in fact,
for the energetic balance of the cell the carriers of reducing power are
themselves no less important. The most important example of these
carriers is the molecule NADH in its several forms. We can use the redox
potential to connect these two molecular protagonists, and estimate an
upper bound on the number of ATP molecules that can be produced from
the oxidation of NADH (produced for example in the TCA cycle). NADH
has a redox potential of E = -0.32V and it is oxidized by oxygen with a
redox potential of E = +0.82V. The maximal associated free energy that
can be extracted is thus
ΔG = nFΔE = 2*100 (kJ/mol/V)*(0.82-(-0.32))(V) = 228kJ/mol,
where n=2 and F≈100kJ/mol/V. As ATP hydrolysis has a free energy
change of ≈50kJ/mole under physiological conditions we find that 228
kJ/Mol can suffice to produce a maximum of 228/50≈4.5 ATPs. In the
cell, oxidation of NADH proceeds through several steps in respiration
and results in the transfer of 10 protons across the membrane against
the electro-chemical potential. These proton transfers correspond to yet
another way of capturing biochemical energy. This energy is then used
by the ATPase to produce 2-3 ATPs. We thus find that about half of the
energy that was released in the transfer of electrons from NADH to
oxygen is conserved in ATP. Ensuring that the reaction proceeds in a
directional manner to produce ATP rather than consume it requires that
some of the energy will be “wasted” as the system must be out of
equilibrium.
Why should one discuss redox potentials and not free energies? The
usefulness of redox potentials lies in the ability to assemble
combinations of different donors and acceptors to assess the
thermodynamic feasibility and energy gain of every considered reaction.
If you have k possible electron transfer compounds, the ~k 2 possible
reactions can be predicted based on only the k redox potentials. The
units themselves owe their origins to the ability in this field of
electrochemistry to measure in the lab the voltage difference, i.e. the
potential measured in volts, across two chambers that contain different
electron carriers.
Just as we speak of the pH of a solution, at first guess, we might imagine
that it would be possible to speak of an apparently analogous redox
potential of the cell. Knowing the concentration of the reduced and
oxidized forms of a given reaction pair defines their pool redox potential
via the relation
E=E0+RT/nF*ln([Ared]/[Aox]).
This equation (a so-called Nernst equation) provides the value of the
redox potential under concentration conditions typical of the cell as
opposed to the artificial standard state conditions. As an example,
consider the donation of an electron to NADH resulting in the oxidized
form NAD+. In the mitochondrial matrix a ratio of 10-fold more of the
oxidized form is reported (BNID 100779). In this case, we find the factor
RT/nF*ln([Ared]/[Aox]) is ≈30mV and thus the redox potential changes
from -0.32V to -0.29V. To make sure the direction of effect we got is
sensible we notice that with an overabundance of the oxidized form the
tendency to be oxidized by oxygen is somewhat lower as seen by the fact
that the redox potential is now closer than before to that of the
oxygen/water electron exchanging pair (+0.82V). The cell is full of
molecules that are partners in oxidation-reduction reactions. Each such
pair forms a separate “redox pair” which will reach a concentration ratio
dictated by its own specific redox potential. If the whole cell was in
equilibrium, the concentrations of every pair would reach a ratio that
will cause every pair to have the same redox potential. To understand
this, notice that if they don’t have the same redox potential then there
will be a net reaction that will proceed, thus changing their respective
concentrations. Only when the concentrations change to give equal redox
potential will equilibrium be achieved.
The cell though is not at equilibrium and weak coupling between
different redox pairs leads to the establishment of different redox states
of pairs coexisting in the cell. If the fluxes of production and utilization of
the reduced and oxidized forms of a redox pair, A red and Aox and another
Bred and Box, are much larger than their interconversion flux, Ared+Box<->Aox+Bred they can have very different redox potentials. As a result it is
ill defined to ask about the overall redox potential of the cell as it will be
different for different components within the cell. By way of contrast, the
pH of the cell is much better defined since water serves as the universal
medium that couples the different acid-base reactions and equilibrates
what is known as the chemical potential of all species.
For a given redox pair in a given cell compartment the ratio of the two
compounds prescribes the redox potential in a well defined manner.
Compounds that exchange electrons quickly will be in relative
equilibrium and thus share the same redox potential. To see how these
ideas play out, it is thus most useful to consider a redox pair that
partakes in many key cellular reactions and, as a result, is tightly related
to the redox state of many compounds. Glutathione in the cytoplasm is
such a compound as it takes part in the reduction and oxidation of the
highly prevalent thiol bonds (those containing sulfur) in cystine amino
acids of many proteins. Glutathione is a tripeptide (composed of 3 amino
acids), the central one a cystine which can be in a reduced (GSH) or
oxidized form where it forms a dimer with a cystine from another
glutathione molecule (GSSG). The half reaction for glutathione is GSSG +
2e- + 2H+ <-> 2*GSH. The other half reaction is often a sulfur bond that is
“opened up” in a receptive protein thus being kept in the reduced form
owing to the constant action of glutathione. Glutathione is also a
dominant player in neutralizing reactive compounds that have a high
tendency to snatch electrons and thus oxidize other molecules. Such
compounds are made under oxidative stress as for example when the
capacity of the electron transfer reactions of respiration or
photosynthesis is reached. Collectively called ROS (reactive oxygen
species) they can create havoc in the cell and are implicated in many
processes of aging. The dual role of glutathione in keeping proteins
folded properly and limiting ROS as well as its relatively high
concentration and electron transfer reactivity make it the prime proxy
for the redox state of the cell. The concentration of glutathione in the cell
is ≈10mM (Rabinowitch BNID), making it the second most abundant
metabolite (after glutamate) ensuring that it plays a dominant role in
redox control. We point out that in other functions in the cells there are
other dominant electron pairs, in biosynthetic, anabolic reactions
NADP+/NADPH and in breakdown, catabolic reactions it is NAD+/NADH.
A number of measurements have been performed on the redox state of
the glutathione pool in different cells and under varying conditions
which allows us to probe the redox state of this pair in quantitative
detail. In budding yeast it is reported to have a redox potential of 290mV (BNID 103543) and for a mammalian cell a range between 170mV to -260mV based on the cell type, prevailing pH and whether it is
proliferating, confluent or apoptotic (BNID 101823). Given that the
standard redox potential of glutathione is -170mV, what then is the ratio
of reduced to oxidized glutathione? Using the Nernst equation (or
equivalently, from the Boltzmann distribution), a ten-fold change in the
product/reactant ratio corresponds to an increase of ≈60kJ/mole in free
energy. For each of the 2 electrons in the GSH/GSSG reaction this is equal
to 30mV. As a result the range reported of between 0 to 120 mV
variation from the standard conditions reflects a ratio of between 1:1 of
the reduced to oxidized forms (for -170mV, apoptotic cells) to 1:10,000
more of the reduced form (≈ -290mV for yeast cells).
One confusing aspect of redox reactions is that the transfer is sometimes
of electrons as in the reactions carried out by cytochromes in electron
transfer chains, and in other cases it is a combination of electrons and
protons as in the cofactor NAD+/NADH where two electrons and one
proton (H+) are transferred and finally reactions where the same number
of electrons and protons is transferred where one most naturally would
discuss transfer of hydrogens. This is for example the case for the overall
reaction of glucose oxidation where oxygen is reduced to water. Two
hydrogens have thus been transferred, so should one discuss electrons
transfer, hydrogens or protons? The definition of the redox potential
(given above) focuses only on the electron "state". What about the
protons and what happens to these when one encounters a chain of
electron transfer reactions where some intermediate compounds contain
the hydrogen protons and some do not? The explanation resides in the
surrounding water and their pH. The reaction occurs at a given pH, and
the reacting compounds are in equilibrium with this pH and thus giving
off or receiving a proton has no effect on the energetics. The aqueous
medium serves as a pool where protons can be "parked" (Ref: Steven
Rose, The chemistry of life) when the transfer reaction is solely of
electrons. These parked electrons can be borrowed back at subsequent
stages as occurs in the final stage of oxidative respiration where
cytochrome oxidase takes protons from the medium. Because one
assumes that water is ubiquitous one does not need to account for
protons except for knowing the prevailing pH which depicts the
tendency to give or receive protons. This is the reason why we discuss
electron donors and acceptors rather than hydrogen donor and
acceptors.