Download Assigning and Using Oxidation Numbers in Biochemistry Lecture

In the Classroom
Assigning and Using Oxidation Numbers in Biochemistry
Lecture Courses
Christopher J. Halkides
Department of Chemistry, University of North Carolina at Wilmington, Wilmington, NC 28403-3297;
[email protected]
The purpose of this article is to illustrate the uses of
assigning oxidation numbers to metabolic intermediates and
end products in biochemical equations. Oxidation–reduction
reactions, reactions in which electrons are transferred, comprise
a major class of biochemical processes. For example, why
anaerobic metabolism produces some products but cannot
produce others is easily understood by the need to conserve
the number of electrons. Assigning oxidation numbers is a
useful bookkeeping device to help one account for all electrons,
notwithstanding some ambiguities (1, 2). It is especially useful
to have a set of rules to deal with large biomolecules. Redox
reactions can be identified when one compares oxidation
numbers between the products and reactants. Therefore, if a
biochemical reaction involves an increase in the oxidation
numbers between substrate and product, one can infer that
the oxidized form of a redox cosubstrate or coenzyme1 must
be reduced concomitantly.
Oxidation numbers are used in many chemistry courses,
and adopting them in biochemistry courses would serve to
reinforce the concept and to integrate biochemistry more
tightly into the chemistry curriculum. Achieving the latter
goal is especially timely, now that the American Chemical
Society has decided to require biochemistry as part of the
undergraduate curriculum. Yet few biochemistry textbooks
present oxidation numbers in a formal way (3). In my experience, moreover, even the best students struggle to apply their
knowledge about oxidation and reduction to biochemistry,
if they are not provided guidance. When the instructor repeatedly assigns oxidation numbers to the carbon atoms of
metabolites over the whole course, it generates simple and
explicit definitions of the concepts of oxidation and reduction. It also impels the student to focus on only the reactive
portions of large, complicated metabolites, cosubstrates,
and coenzymes. When students identify a redox reaction by
assigning and comparing oxidation numbers, they can make
two inferences about the reaction: that the redox cosubstrate
or coenzyme is probably either NAD(P)+ or FAD on one side
of the balanced equation, and that the enzyme will probably
be named as a dehydrogenase or a reductase. These inferences
may help the student learn the reactions and names of enzymes
in pathways such as glycolysis and the TCA cycle.
Assigning Oxidation Numbers
Oxidation of carbon can be defined as the making of
bonds to more electronegative atoms (principally O and N)
or the breaking of bonds to more electropositive atoms
(usually H). Reduction can be defined as the making of bonds
to more electropositive atoms or the breaking of bonds to
more electronegative ones. We know that electrons are shared
unequally in most chemical bonds owing to electronegativity
differences between the two atoms in the bond. Therefore,
oxidation has the effect of making carbon more positively
1428
O
C
H3C
Number of Bonds to O
0 2
− Number of Bonds to H
3 1
Oxidation # of Carbon =
−3 +1
O
H
C
H3C
0 3
3 0
−3 +3
O
CH3
1
3
−2
Figure 1. Calculation of the oxidation numbers of the carbon atoms
in acetaldehyde and ethyl acetate. For each carbon the number of
bonds to hydrogen is subtracted from the number of bonds to oxygen
to obtain the oxidation number of that carbon atom. Note that two
methyl carbons in ethyl acetate do not have the same oxidation
number.
charged (decreasing its electron density), and reduction has the
effect of making carbon more negatively charged (increasing
its electron density). Oxidation numbers are assigned as if
the more electronegative atom in a bond owned the electrons
completely.
We can make a simple set of rules to write oxidation
numbers for carbon atoms, slightly modified from those presented in general and organic chemistry textbooks (4–6 ).
1. To obtain the oxidation number of a carbon atom,
subtract the number of bonds to hydrogen from the number of
bonds to oxygen. This means for example that for a carbonyl
carbon, which has a C=O double bond, you must count
both bonds. So for acetaldehyde, the carbonyl carbon atom
has an oxidation number of +1, and the methyl carbon has
an oxidation number of ᎑3 (Fig. 1). Note that two methyl
carbons in ethyl acetate do not have the same oxidation
number (Fig. 1).
2. Bonds between carbon and nitrogen are treated exactly
like bonds between carbon and oxygen because nitrogen and
oxygen are both more electronegative than carbon. In a bond
between two atoms of equal electronegativity such as two carbon atoms, the electrons are treated as being shared equally.
3. The oxidation number of a free element (O2 or H2,
for example) is zero.
4. The oxidation number of oxygen in compounds with
other elements is ᎑2 except in peroxides, where it is ᎑1, and
in compounds with fluorine.
5. The oxidation number of hydrogen is +1 in C–H
bonds, O–H bonds, or N–H bonds.
6. The algebraic sum of all of the oxidation numbers in
an ion or molecule is equal to its charge.
7. In a balanced chemical equation, the total oxidation
number is conserved (is equal between reactants and products).
If one atom decreases in oxidation number as it reacts, another
atom must increase in oxidation number. The reason for this
is that electrons are not created or destroyed in a chemical
reaction.
How can we apply oxidation numbers to biochemical
equations? Although rules 6 and 7 apply to the sum of oxida-
Journal of Chemical Education • Vol. 77 No. 11 November 2000 • JChemEd.chem.wisc.edu
In the Classroom
tion numbers of all atoms, it is usually faster to sum up the
oxidation numbers of the carbon atoms only. By assuming
that oxygen, nitrogen, and hydrogen have the same oxidation
number in reactants as they do in the products, we greatly
simplify the calculation and, in effect, give students far fewer
rules to learn. This assumption is often true; however, some
exceptions are given below.
Using Oxidation Numbers
numbers of 0, and carbon 6 has an oxidation number of ᎑1,
giving glucose a net oxidation number of 0. The methyl carbon atom of ethanol has an oxidation number of ᎑3 and the
hydroxymethyl carbon has an oxidation number of ᎑1, and
we need to take into account that there are two moles of ethanol
per mole of glucose. The four carbon atoms of the two molecules of ethanol have a total oxidation number of ᎑8.
2 × ᎑1 = ᎑ 2
2 × ᎑3 = ᎑ 6
—
᎑8
Let us first examine the oxidation of succinate to fumarate
On the other hand, glucose has an oxidation number of 0.
(Fig. 2). The oxidation number of each of the two methylene
Clearly, we have not yet balanced either carbon atoms or
carbons of succinate is ᎑2 and the oxidation number of each
oxidation numbers. There are two carbon atoms still to be
of the carboxylate carbon atoms is +3; therefore, the net
accounted for and they must each have an oxidation number
oxidation number of the four carbon atoms is +3 + (᎑2) +
of +4, to sum to +8 and balance the charge and the number
(᎑2) +3 = +2. The sum of the oxidation numbers for the four
of atoms. Therefore, we know that two molecules of CO2,
carbon atoms of fumarate is +3 + (᎑1) + (᎑1) +3 = +4. According
each of which has an oxidation number of +4, must also be
to rule 7, the sum of the oxidation numbers must be equal
produced.
between products and reactants for any chemical reaction.
Three final points about anaerobic metabolism should be
Therefore, a second molecule, a cosubstrate or coenzyme,
stated.
must oxidize succinate by two electrons producing fumarate
First, oxidation numbers can be used to decide whether
and reducing the coenzyme by two electrons. In this case the
putative products of a fermentation process are possible or
coenzyme FAD is reduced to FADH2 (see Fig. 5b for structures).
impossible from the standpoint of leading or not leading to
Let us look at the hydration of fumarate to create malate
a balanced equation. Yet oxidation numbers cannot be used
as a second example from the TCA cycle (Fig. 2). The net
to discriminate between several alternative products if all the
oxidation number of the carbon atoms of fumarate is +4 (see
above) and the net oxidation number of the carbon atoms of
malate is +3 + 0 + (᎑2) +3 = +4. Since one carbon is oxidized
and one is reduced in the hydration, no net oxidation or reO
O−
O
O−
O
O−
duction has taken place (each of the hydrogen atoms of water
C
C
C
+3
+3
+3
has an oxidation number of +1, and the oxygen atom has a
H 2O
FAD
FADH
CH
CH
HC
OH
2
−1
0
−2
2
value of ᎑2, the same values as they have in the product).
− 1 HC
−2
CH2
CH2
−2
The reaction catalyzed by glutamate synthase is a nice
illustration of a reaction that may not appear to be a redox
+3
+3
+3
C
C
C
process at first glance (Fig. 3). Suppose a student knew that
O
O−
O
O−
O
O−
glutamine plus α -ketoglutarate yields two molecules of
+4
+4
+2
glutamate but forgot that the reaction also uses NADPH, a
Fumarate
Malate
Succinate
2-electron reducing agent. Could the student determine that
Figure 2. Conversion of succinate to fumarate and then to malate.
NADPH is necessary just by knowing the structures of
The oxidation number of each carbon atom is given to the left of it,
glutamine, glutamate, and α-ketoglutarate? Yes. In α-ketoand the sum of the oxidation numbers of each compound is given
glutarate the keto carbon (*) has an oxidation number of +2,
above its name. Assigning oxidation numbers to the carbon atoms
but the corresponding α-carbon atom in the glutamate moldemonstrates that the first reaction requires the 2-electron reduction of
ecule on the right (*) has an oxidation number of 0. This
a cofactor and that the second reaction does not. The cofactor is
carbon has been reduced by two electrons. Since all of other
FAD, which is reduced to FADH2; however, assigning oxidation
carbon atoms retain the same oxidation numbers from reacnumbers cannot establish the identity of the cofactor.
tion to product, there must be a 2-electron
reducing agent in the balanced equation,
−
−
−
−
which is NADPH in this case.
O
O
O
O
O
O
O
O
Oxidation numbers are quite useful in
C
C
C
C
+3
+3
+3
+3
understanding microbial fermentation, a
HC NH3+
HC NH3+
C O
HC NH3+ +2
0
0
0
process in which an organic molecule is deCH2
CH2
CH2
CH2
−2
−2
−2
−2
graded to drive ATP synthesis without net
CH2
CH2
CH2
−2
−2
−2
−2
CH2
oxidation or reduction (7 ). It is often diffiNADPH NADP
+
cult to decide whether the products of fer+3
+3
+3
+3
C
C
C
C
H
−
−
−
mentation are in redox balance with the reO
O
O
O
O
O
O
H2N
actant by inspection because the molecules
are complex. Consider the fermentation of
Glutamine
α-Ketoglutarate
Glutamate
Glutamate
glucose to two molecules of ethanol
Figure 3. Reaction catalyzed by glutamate synthase. Glutamine donates its amide
(C6H12O6 → 2CH3–CH2OH + ?), shown
nitrogen to α-ketoglutarate making 2 molecules of glutamate. The α-keto carbon (*) is
in Figure 4a. Carbon 1 has an oxidation
reduced by 2 electrons in this process. This reduction is balanced by the oxidation
number of +1, Carbons 2–5 have oxidation
of NADPH to NADP+.
+
+
JChemEd.chem.wisc.edu • Vol. 77 No. 11 November 2000 • Journal of Chemical Education
1429
In the Classroom
alternatives lead to balanced equations. Which products are
actually formed depends of course on the enzymes present
within a particular organism. For one example, the fermentation of glucose can lead either to ethanol and carbon dioxide
or to lactate (Fig. 4). Homofermenting lactic acid bacteria
produce lactate almost exclusively, whereas heterofermenting
lactic acid bacteria produce an equimolar mixture of lactate,
ethanol, and carbon dioxide. For another example, oxidation
numbers cannot be used to show why some heterofermenting
lactic acid bacteria can produce mannitol from fructose but
not glucose (Problem 5), since both glucose and fructose have
a net oxidation number of 0. For a final example, three moles
of pyruvate can be fermented to one mole of propionate, and
to two moles each of acetate and carbon dioxide, or to three
moles each of succinate and acetate (7 ).
Second, some bacteria produce H2 in their fermentations,
or even use a small amount of oxygen (7). Although it is
relatively straightforward to assign oxidation numbers to
hydrogen and oxygen to balance the equations for these
processes, a formal treatment is outside the scope of this paper.
Third, the conversion of glucose to lactate by heavily
exercising muscle in the Cori cycle can be seen as being in
redox balance using oxidation numbers (Figure 4b).
(a)
−1
CH2OH
0
H
O
H
OH
0
OH
+4
C
−3 −1
+1
H
2 H3C CH2 OH + O
O
H
OH
0
0
H
OH
(b)
CH2OH
O
H
H
OH
OH
H
H
0
+3
2 H3 C
H
C
C
OH
H
OH
+3
O
O-
OH
Figure 4. (a) Fermentation of glucose to two molecules of ethanol
and carbon dioxide. The oxidation number is given next to each
carbon. (b) The conversion of glucose to lactate. This process is
seen both in bacteria and in heavily exercising muscle.
(a)
NADPH + H+
NADP+
Extensions to Atoms Other Than Carbon
E•FAD
With respect to oxidation–reduction processes of atoms
other than carbon, those of sulfur and oxygen are among the
most important. These processes can be analyzed quantitatively by assigning redox numbers to these heteroatoms using
the rules given above. The reduction of a disulfide bond to
two thiol groups is a 2-electron process. An example of this
is the reduction of glutathione disulfide (GCH2SSCH2G) to
two molecules of glutathione (GCH2SH), where G stands for
the cysteine-containing tripeptide glutathione (Fig. 5a). Since
carbon and sulfur have about the same values for electronegativity, each sulfur atom is assigned an oxidation number of
0 in the reactant and ᎑1 in the product.2 The reducing agent
is NADPH, and the enzyme glutathione reductase transiently
reduces the tightly bound FAD cofactor to FADH2 (Fig. 5b),
which then reduces glutathione disulfide. Reduced glutathione (GCH2SH) can in turn reduce protein disulfide bonds
to protein thiol groups, in addition to its other roles (8, 9).
The reduction of O2 to 2 molecules of H2O is a 4-electron
process. It takes only 2 electrons to reduce O2 to hydrogen
peroxide (H2O2), in which each oxygen atom has an oxidation
number of 0 in the reactant and ᎑1 in the product. It also
takes two electrons to reduce hydrogen peroxide to water. The
latter process is catalyzed by glutathione peroxidase and the
reducing equivalents are supplied by GCH2SH.
Using Oxidation Numbers in the Classroom
The instructor should make the students aware that comparing oxidation numbers between reactants and products will
determine whether a given reaction is a redox reaction and
will specify the number of electrons involved. Yet assigning
and comparing oxidation numbers cannot determine which
redox molecule is the cosubstrate or coenzyme, nor does it
guarantee that a particular organism possesses the enzyme(s)
necessary to effect a given transformation (see above and
1430
2 GCH2S-H
−1
E•FADH2
GCH2S-SCH2G
0
(b)
R
N
R
N
O
N
H
N
NH
N
O
NH
N
H
O
FAD
O
FADH2
Figure 5. (a) Reduction of glutathione disulfide to glutathione. The
FAD-containing enzyme glutathione reductase uses NADPH as the
reducing agent. The sulfur atom of glutathione is reduced. (b) Structures of FAD and FADH2.
problem 5). The instructor is more likely to teach students
to think in terms of oxidation numbers by returning to this
subject repeatedly over the course of the semester, rather than
simply discussing it once at the beginning of the semester
and hoping that students apply this analysis themselves. As
elementary as it may seem to the instructor, he or she should
point out that an enzyme catalyzing a redox process is probably
named as a reductase or a dehydrogenase. For example, consider the oxidation of carbon atom #1 in ethanol (oxidation
number ᎑1) to acetaldehyde (oxidation number +1) with the
concomitant reduction of NAD+ to NADH. The enzyme is
alcohol dehydrogenase, but the instructor might ask the students
to propose a name for this enzyme as part of a lecture. Oxidation numbers can be brought into discussions of glycolysis
(lactate dehydrogenase), the TCA cycle (to define the term
oxidative decarboxylation), fatty acid degradation (which
Journal of Chemical Education • Vol. 77 No. 11 November 2000 • JChemEd.chem.wisc.edu
In the Classroom
strongly resembles the sequence of reactions involving succinate shown in Fig. 2) and amino acid metabolism (for example,
the conversion of aspartate to homoserine). Oxidation numbers
can also be brought into discussions of the electron transport
chain (by assigning the oxidation numbers of quinones), electron shuttle systems between the mitochondria and cytoplasm
(for example, dihydroxacetone phosphate and glycerol-3phosphate) or shuttle systems between cells (as in the C-4
pathway) (8, 9).
Questions for Students
1. What are the maximum and minimum oxidation
numbers that carbon can attain? Name two molecules for
which carbon has these oxidation numbers. Answer: +4 in
CO2 or bicarbonate ion, and ᎑4 in CH4.
2. Can a mole of glucose be fermented to 2 molecules
of lactic acid (CH3–CHOH–COOH)? Answer: Yes, because
the sum of the oxidation numbers of lactic acid is 0, the same
as glucose (Fig. 4b). Homofermenting lactic acid bacteria
produce lactic acid by this route; heterofermenting lactic acid
bacteria produce one mole each of lactic acid, ethanol, and
carbon dioxide (7).
3. Can a mole of glucose be fermented to two moles of
pyruvate and no other compound? Answer: No, the process
is in carbon balance but not redox balance. Another way to
think about this question is that NADH, which is also produced
in the conversion of glucose to pyruvate, must be reoxidized
to NAD+ for anaerobic metabolism to operate. Pyruvate,
which is the product of glycolysis, can be reduced by NADH
to lactate or can be decarboxylated to ethanal and CO2 (the
ethanal is then reduced to ethanol, Fig. 4), or can suffer other
fates that depend on the organism (7).
4. Can three moles of glucose be fermented to 2 moles
of butanediol, two moles of glycerol, and four moles of CO2?
Answer: Yes, the products are in redox balance and carbon
balance, and this fermentation is seen in the Bacillus genus
(7 ). Although an undergraduate biochemistry student would
not be expected to be aware of this particular fermentation,
he or she should be able to determine its possibility.
5. Is the following fermentation possible?
3 fructose → lactate + acetate + CO2 + 2 mannitol
Answer: Yes, the sum of the oxidation numbers of the carbons
of fructose, lactate, and acetate are all 0. The sum of the oxidation numbers of mannitol, CH2OH–(CHOH)4–CH2OH,
is ᎑2; when this is multiplied by its stoichiometric coefficient
of 2 it exactly cancels the +4 oxidation number of carbon
dioxide. Some heterofermenting lactic acid bacteria can use
this fermentation when fructose, but not glucose, is the carbon
source because they possess a mannitol dehydrogenase that
accepts fructose as a substrate (7 ). Again, an undergraduate
biochemistry student would not be expected to be aware of
the existence of this enzyme; that is why the question is
framed as a hypothetical.
6. Malolactic acid fermentation reduces the acidity of
wine made from grapes, especially those grown in cool
weather, giving the wine a smoother taste (7, 10). This process
(Fig. 6) converts one molecule of malate to one molecule of
lactate and one other carbon-containing compound. What
is the other compound, and why? Answer: The other compound
O−
O
+3
C
C
0 H
−2
OH
C
O
C
0 H
CH2
+3
O−
O
+3
−3
C
OH
+
?
CH3
O−
+4
0
Lactate
Malate
Figure 6. Malolactic acid fermentation in winemaking. This process gives wine a smoother taste. Malate is converted into lactate
and one other carbon-containing compound (see problem 6). The
oxidation number of each carbon atom is given to the left of it, and
the sum of the oxidation numbers of each compound is indicated.
H2N
N
H
N
N 5-Methytetrahydrofolate
N
N
H2N
OH
CH3 NH R
*
N
H
N
N 5,N10-Methenyltetrahydrofolate
N
N
OH
HC
*
N
R
H2N
N
H
N
N 5,N10-Methylenetetrahydrofolate
N
N
OH
H2C
*
N
R
Figure 7. Three derivatives of tetrahydrofolate at three different oxidation states of carbon (see problem 7).
is CO2, having an oxidation number of +4, which brings both
carbon atoms and redox numbers into balance. NOTE: It could
be argued that a more complete answer would include a water
molecule on the reactant side and would have either CO2
and OH᎑, or (equivalently) HCO3᎑ as the other product. This
balances all atoms.
7. Assign oxidation numbers to the carbon with the asterisk for the three derivatives of tetrahydrofolate shown in
Figure 7. Which is most oxidized? Which is most reduced?
Using oxidation numbers that you assigned, write a balanced
equation for the conversion of N 5,N 10-methylenetetrahydrofolate (bottom structure) to N 5-methyltetrahydrofolate
(top structure), assuming that NAD+ is the cofactor. Give a
plausible name for the enzyme that carries out this process.
Answer: N 5-methyltetrahydrofolate (᎑2) is most reduced,
N 5,N 10-methylenetetrahydrofolate (0) is intermediate, and
N 5,N 10-methenyltetrahydrofolate (+2) is most oxidized. The
balanced equation is N 5,N 10-methylenetetrahydrofolate +
NADH → N 5-methyltetrahydrofolate + NAD+. The enzyme
is named N 5,N 10-methylenetetrahydrofolate reductase, although
it could also be plausibly named N 5-methyltetrahydrofolate
dehydrogenase.
JChemEd.chem.wisc.edu • Vol. 77 No. 11 November 2000 • Journal of Chemical Education
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In the Classroom
Acknowledgments
Literature Cited
I would like to thank my students and colleagues at the
University of North Carolina at Wilmington for many helpful suggestions.
1. Woolf, A. A. J. Chem. Educ. 1988, 65, 45–46.
2. Calzaferri, G. J. Chem. Educ. 1999, 76, 362–363.
3. Abeles, R. H.; Frey, P. A.; Jencks, W. P. Biochemistry; Jones
and Bartlett: Boston, 1992.
4. Brown, T. L.; LeMay, H. E. Jr.; Bursten, B. E. Chemistry the
Central Science; Prentice Hall: Upper Saddle River, 1997.
5. Dickerson, R. E.; Gray, H. B.; Haight, G. P. Jr. Chemical Principles; Benjamin/Cummings: Menlo Park, CA, 1979.
6. McMurry, J. Organic Chemistry; 4th ed.; Brooks/Cole: Pacific
Grove, CA, 1996.
7. Stanier, R.; Ingraham, J. L.; Wheelis, M. L.; Painter, P. R. The Microbial World; 5th ed.; Prentice-Hall: Englewood Cliffs, NJ, 1986.
8. Zubay, G. Biochemistry; 4th ed.; Wm. C. Brown: Dubuque,
IA, 1998.
9. Voet, D. G.; Voet, J. G. Biochemistry; 2nd ed.; Wiley: New
York, 1995.
10. Fox, M. A.; Whitesell, J. K. Organic Chemistry; Jones and
Bartlett: Sudbury, UK, 1997.
Notes
1. A cosubstrate is an organic molecule that is bound and released during the catalytic cycle of an enzyme. A coenzyme is an
organic molecule that remains tightly bound to an enzyme over
many catalytic cycles. Thus NAD+ and NADH are cosubstrates,
and FAD and FADH2 are coenzymes.
2. It would be convenient to treat sulfur as if it were more
electronegative than carbon to stress its similarity to oxygen (esters
versus thioesters, for example). This would lead us to assign oxidation numbers to sulfur of ᎑1 and ᎑2 in the reactant and product of
this reaction, respectively. Yet the advantage of simply using the
electronegativities as given in standard textbooks is, arguably, the
overriding principle.
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Journal of Chemical Education • Vol. 77 No. 11 November 2000 • JChemEd.chem.wisc.edu