The above diagram is taken from a paper[ref] published in 1995 by the Hungarian biochemist Gaspar Banfalvi in which he introduced circular graphs to map energy changes in metabolic cycles – in this particular case showing the relationship between the Gibbs free energy (dotted line) and the average carbon oxidation state (solid line) of intermediates in the Krebs cycle.

This post adopts Banfalvi’s innovative approach in order to further explore the redox behavior of Krebs cycle intermediates. But before we start, a brief section on calculating average carbon oxidation states.

Calculating Average Carbon Oxidation States

The overall oxidation state of a molecule is its charge magnitude taking sign into account:
Charge magnitude = sum of carbon oxidation states + sum of oxidation states of other atoms

The sum of oxidation states of other atoms is computed by assigning a value to each of these atoms in the molecule as appropriate e.g. H = +1, O = -2, N = -3 in amino group [-NH2], P = +5 in phosphate group [-O-PO3]^2-, and summing them. Subtracting this sum from the charge magnitude gives the sum of carbon oxidation states. Dividing this by the number of carbon atoms in the molecule gives the average carbon oxidation state.

Example 1: Citrate

Charge magnitude = -3
Sum of oxidation states of other atoms Hx5, Ox7 = +5 -14 = -9
Sum of carbon oxidation states = -3 – (-9) = +6
Number of carbon atoms in molecule = 6
Average carbon oxidation state = +6/6 = +1

Example 2: Urea

Charge magnitude = 0
Sum of oxidation states of other atoms Hx4, Ox1 , Nx2 = +4 -2 -6 = -4
Sum of carbon oxidation states = 0 – (-4) = +4
Number of carbon atoms in molecule = 1
Carbon oxidation state = +4/1 = +4

Example 3: 1,3-diphosphoglycerate

Charge magnitude = -4
Sum of oxidation states of other atoms Hx4, Ox10, Px2 = +4 – 20 + 10 = -6
Sum of carbon oxidation states = -4 – (-6) = +2
Number of carbon atoms in molecule = 3
Average carbon oxidation state = +2/3

Useful links for determining oxidation states

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Carbon Oxidation States and Krebs Cycle

OK so here’s a different way of illustrating the Krebs Cycle. This diagram shows the cycle in terms of the number of carbon atoms in the input, output and cycle intermediate molecules, together with their average oxidation states. The numbers inscribed in blue show the changes in oxidation state of the intermediates taking place around the cycle.

The diagram reveals a feature that is not easily discernible in conventional depictions of Krebs Cycle – namely that the cycle intermediates undergo a progressive oxidation state reduction of -1 from oxaloacetate (C4,+1½) to succinyl-CoA (C4,+½), followed by a progressive oxidation state increase of +1 from succinyl-CoA back to oxaloacetate. Since a lower carbon oxidation state reflects more energy residing in chemical bonds, these changes indicate that cycle intermediates store energy in the first half of the cycle and liberate it in the second half.

Within this overall movement of energy lies a more detailed redox picture. Consider the steps in the first half where carbon dioxide is released. Decarboxylation of isocitrate per se (C6H5O7^3-) → [C5H5O5^3-] equates to a reduction of carbon oxidation state from +1 to +2/5 in the theoretical residue shown in [ ]. But isocitrate also undergoes oxidation, which we can notate as the theoretical residue transferring charge and a hydrogen atom to the NAD+ cofactor [C5H5O5^3-] → (C5H4O5^2-) resulting in a lesser overall reduction of carbon oxidation state from +1 to +4/5. Isocitrate thus combines both reductive and oxidative roles.

Similarly, decarboxylation of α-ketoglutarate per se (C5H4O5^2-) → [C4H4O3^2-] equates to a reduction of carbon oxidation state from +4/5 to 0 in the theoretical residue. But α-ketoglutarate also undergoes two oxidative processes, which we can notate as the theoretical residue adding an -SCoA group to the molecule and transferring charge to the NAD+* cofactor [C4H4O3SCoA^2-] → (C4H4O3S-CoA^1-) resulting in a lesser overall reduction of carbon oxidation state from +4/5 to +½. Thus α-ketoglutarate also combines both reductive and oxidative roles.

Two intermediates combine reductive and oxidative roles in the second half of the cycle. Succinyl-CoA undergoes two reductive processes: the deesterification of succinyl-CoA per se and receiving charge from a phosphate ion (C4H4O3S-CoA^1-) → [C4H4O3^2-] equates to a reduction of carbon oxidation state from +½ to +0 in the theoretical residue. Succinyl-CoA also undergoes oxidation, which we can notate as the theoretical residue receiving an oxygen atom from the same phosphate ion [C4H4O3^2-] → (C4H4O4^2-) resulting in an increase of carbon oxidation state from 0 to +½. Thus succinyl-CoA exhibits equal reductive and oxidative capacity resulting in no change in the average oxidation state of the next intermediate succinate.

Finally oxaloacetate undergoes two reductive processes: the addition of an acetyl group and receiving charge from the hydrogen of a water molecule (C4H2O5^2-) → [C6H5O6^3-] equates to a reduction of carbon oxidation state from +1½ to +2/3 in the theoretical residue. Oxaloacetate also undergoes oxidation, which we can notate as the theoretical residue receiving an oxygen atom from the same water molecule [C6H5O6^3-] → (C6H5O7^3-) resulting in a lesser overall reduction of carbon oxidation state from +1½ to +1.

*note that the hydrogen atom transferred to NADH comes from CoASH not α-ketoglutarate

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Krebs Cycle net equation restricted to cycle intermediates

There are plenty of sources out here on the web which will give you the Net Equation of Krebs Cycle showing every single substance involved, and there are lots of them. What I want to do here is write a simple net equation which shows only the inputs and outputs that are directly incorporated into or sourced from the structure of the cycle intermediate molecules themselves. The equation is a concise statement of what much of the foregoing has been trying to say – that the cycle intermediates have both oxidative and reductive roles:

Question. In overall terms two molecules of water enter the Krebs cycle, so why is there only one molecule of water shown on the input side? The answer is that while the water molecule which hydrates fumarate to malate is fully incorporated into the cycle intermediate structure, the water molecule involved in the conversion of oxaloacetate to citrate is not. Only the oxygen atom of this water molecule is incorporated into the citrate structure; one hydrogen atom is used to regenerate CoA-SH from acetyl-CoA while the other donates charge (C4^2- → C6^3-) and is oxidized to H+.

One of the two input oxygen atoms shown in the equation is now accounted for, but what about the other? The answer reveals a fascinating detail of the Krebs Cycle: it comes from the phosphate ion HPO4^2- involved in GTP/ATP formation associated with the conversion of succinyl-CoA to succinate. A PO3^1- moiety is used in the conversion of GDP to GTP while the hydrogen atom regenerates CoA-SH from succinyl-CoA, leaving a single oxygen which is incorporated into the succinate molecule together with a transfer of charge (C4^1- → C4^2-).

In summary we can say that at each turn of the Krebs Cycle, an acetyl group, a water molecule and two oxygen atoms – one from another water molecule and one from a phosphate ion – are incorporated into the structures of the cycle intermediates to facilitate the oxidative formation of carbon dioxide for release and hydrogen-reduced cofactors for onward transmission to the electron transport chain and ATP production.

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Krebs Cycle Thermodynamics

All cells that generate ATP by metabolizing acetyl-CoA to carbon dioxide make use of the Krebs cycle, which drives energy production in a way that shares characteristics with other more familiar engines operating in cycles. Like them, the Krebs cycle executes energy conversion and in so doing produces heat.

As with all energy conversion processes, metabolism is not particularly efficient and only around 40% of the available energy is converted to ATP; the rest is dissipated as heat. There are two aspects to this heat production that are worthy of note. The first is the effect that heat has on reaction kinetics; even a modest increase in temperature over that of the surroundings can speed up chemical processes significantly. Warmer organisms react faster, which is vital for survival.

The second aspect is the scale of heat release; the Gibbs free energy changes in the Krebs cycle reactions are very modest so that heat production and conduction of heat out of the cell can occur while maintaining thermal stability. Even in situations of high ATP demand, the mitochondrion won’t get fried.

 Step Reaction ΔG’° kJ/mol Keq 1 Acetyl-CoA + Oxaloacetate → Citrate -32.2 2.65 x 10^5 2 Citrate → Isocitrate 13 6.47 x 10^-3 3 Isocitrate → α-ketoglutarate -8.4 2.60 x 10^1 4 α-ketoglutarate → Succinyl-CoA -33.5 4.38 x 10^5 5 Succinyl-CoA → Succinate -2.9 3.08 6 Succinate → Fumarate 0 1 7 Fumarate → Malate -3.8 4.36 8 Malate → Oxaloacetate 29.7 9.96 x 10^-6

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The equilibrium constants of the Krebs cycle reactions exhibit a mixture of reactant-favored and product-favored processes. The second half of the cycle (Steps 5-8) is essentially reversible, with Steps 1 and 4 providing the product-favored momentum. It should be noted that Steps 3 and 4 involve the release of carbon dioxide which continuously diffuses out of the cell to neighborhoods of lower concentration, thereby lowering the reaction quotient Q and enhancing product favorability.

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Structure and Nomenclature of Krebs Cycle Intermediates

The sequence of intermediates in the Krebs cycle was worked out long ago, and part of that history is preserved in their esoteric names. For example succinic acid used to be obtained from amber by distillation, which is why it is named after the Latin word for amber – succinum. All very interesting, but it doesn’t help to visualize what the molecule looks like. A better way is to learn the carbon chain shapes of the cycle intermediates, and the scientific names that describe them. The advantage of doing this is that one reinforces the other; once you have memorized these scientific names you can draw molecules directly from them.

Try this out for yourself. You know citric acid is a C6 molecule; learn to draw it with the longest carbon chain (shown in red) around three sides of a rectangle with the three -COOH groups pointing out to one side like this. Practice drawing this until you can see it in your sleep.

Now you’ve learned it, you can name it. The longest carbon chain is C5 so the scientific name is based on pentane (C5H12). The C5 chain has -COOH groups at each end, so the core molecule is pentanedioic acid, which has a carboxyl and hydroxyl group on the third carbon atom in the chain. Adding these gives 3-carboxy-3-hydroxypentanedioic acid. That’s the scientific name for citric acid.

If you can learn this name, you can draw citric acid from memory. Awesome. And it’s an easy progression from there to learn the structure of isocitric acid

The only difference is that the hydroxyl group drops down to the second carbon atom in the C5 chain. So the scientific name simply changes to 3-carboxy-2-hydroxypentanedioic acid. The molecule has one carboxyl group on a side chain (the one shown in black) and it’s this one which is released as carbon dioxide along with a hydrogen atom to reduce NAD+, the molecule rearranging itself so that an oxo- group replaces the hydroxyl group on C2

The pentanedioic acid core molecule now has only one substituent; its scientific name is 2-oxopentanedioic acid. Once learned, it’s easy to draw this C5 molecule from memory which is more than can be said for α-ketoglutaric acid. The lower carboxyl group now departs to form carbon dioxide along with a hydrogen atom to reduce NAD+, with a Coenzyme A group taking its place. The resulting molecule is easier to visualize with its C4 chain drawn around three sides of a square like this

Don’t bother with the scientific name of this one, it’s too long. Just call it succinyl-CoA. All the remaining steps of the Krebs cycle retain the C4 chain. Following deesterification the next intermediate, succinic acid, is the simplest structure of all the Krebs cycle intermediates

The scientific name is that of the core molecule, butanedioic acid. Learn this name and you can easily draw succinic acid from memory. The next steps are the removal of two hydrogen atoms from carbon atoms 2 and 3 to form fumaric acid (not shown) followed by hydration to malic acid

whose scientific name is 2-hydroxybutanedioic acid, before a final dehydrogenation to oxaloacetic acid

whose structure is much easier to draw if you can learn its scientific name, 2-oxobutanedioic acid. Here’s a summary of the Krebs cycle intermediate names, ancient and modern:

 HISTORICAL NAME SCIENTIFIC NAME Citric acid 3-carboxy-3-hydroxypentanedioic acid Isocitric acid 3-carboxy-2-hydroxypentanedioic acid α-ketoglutaric acid 2-oxopentanedioic acid Succinyl-CoA Succinic acid butanedioic acid Fumaric acid (E)-butenedioic acid Malic acid 2-hydroxybutanedioic acid Oxaloacetic acid 2-oxobutanedioic acid

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Gaspar Banfalvi, Constructing Energy Maps of Metabolic Cycles (1995)
The pioneering paper whose graphical idea is adopted in this blogpost. Balfalvi’s paper was published in Biochemical Education, now known as Biochemistry and Molecular Biology Education.

S.V. Eswaran, A New Look at the Citric Acid Molecule (1976)
This paper tells the story of Krebs’ belief that if radiolabeled CO2 was assimilated then both the CH2COOH groups in citric acid would be labeled since citric acid is a symmetrical molecule. He was wrong and this paper explains why. It’s worth reading about what was briefly known as the “Ogston Effect”* and the influence A.G. Ogston’s thinking about substrates and planar enzyme surfaces had on the subsequent development of prochirality.

*named after Alexander George Ogston (1911-1996), a British physical chemist.

Nazaret, C et al., Mitochondrial energetic metabolism: A simplified model of TCA cycle with ATP production (2009)
If you’re into modeling the chemical kinetics of metabolic systems on the basis of the Mass Action Law, you might like this paper published in the Journal of Theoretical Biology. The authors describe their model as “very simple and reduced” but even so it’s knee-deep in differential equations. Enjoy.

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P Mander February 2020