Figure 2. TCA Cycle image from Wikipedia.
Chemical
Relationships
By looking closely at the diagram of the TCA cycle in Fig.
2, you can see that each step of the cycle can be denoted
in this way:
1.) Acetyl-CoA + oxaloacetate + water <=> CoASH + citrate
dG =-53.9 KJ/Mol (Eq. 1)
2.) Citrate <=> isocitrate
dG =+0.8 KJ/Mol (Eq. 2)
3.) Isocitrate + NAD+ <=> a-ketogluterate + NADH
+ CO2 + H+
dG =-17.5 KJ/Mol (Eq. 3)
4.) a-Ketoglutarate + CoASH + NAD+ <=> Succinyl
CoA + NADH + CO2 + H+
dG =-43.9 KJ/Mol (Eq. 4)
5.) Succynil-CoA + GDP + Pi <=> succinate + GTP + CoASH
dG = 0 KJ/Mol (Eq. 5)
6.) Succinate + FAD <=> fumerate + FADH2
dG = 0 KJ/Mol (Eq. 6)
7.) Fumerate + water <=> L-Malate
dG = 0 KJ/Mol (Eq. 7)
8.) L-Malate + NAD+ <=> oxaloacetate + NAHD +
H+
dG = 0 KJ/Mol (Eq. 8)
Data here from "Principles of biochemistry with a
human focus", by Garrett and Grisham
The components on the left side of each arrow here can be
converted to the components on the right. The reverse is
also true. The degree to which one side is preferred is
determined by the change in Gibbs Free Energy, denoted by
the dG for each reaction's equation. Equation (1) is a gateway
into the cycle in that it takes Acetyl-CoA from the output
of another pathway: Glycolysis.
Math
For each reaction above, an equation that determines the
direction the reaction will move is of this form:
Equation 9. K versus Gibbs Free Energy:
Where R is the gas constant, G
is Gibb's free energy and K is the equation for Q calculated
at equilibrium concentrations for each component. Q for
each chemical equation is defined by the following relationship:
Equation 10. Definition of Q, The reaction quotient:
Where the [ ] symbols denote that these
are the molar concentration of each component.
Equation 11. Definition of K, the reaction quotient at equilibrium:
Equation 12. Equilibrium condition:
Assembly
The basic mathematical architecture is simple enough. But
in this simulation, for each cycle of calculations, I have
one hundred and fifty three calculations. Like a loop, the
output of these calculations is fed back into the first
step, and repeated.
In assembling this loop, first we make two physical assumptions.
Assumption One: The system will move toward minimizing energy.
(That is, the system's Q will move toward its K.) This is
a valid assumption, and a fundamental one to systems. In
nature all systems that are free to, seek an equilibrium
level where all forces acting on the system are adjusted
in such a way that the total energy of the system is minimized.
Assumption Two: This system is free to minimize the energies
mentioned in assumption one. This isn't always the case
in systems. However this too is a valid assumption in this
case. The enzymes catalyze each step, and ensure this. (Link
here to Wikipedia definition of catalysis)
For each chemical equation, each step in the cycle as depicted
by the diagram, we take the
current molar concentration value of each component and
plug it into equation 9. This gives us the reaction quotient
for that reaction step
Similarly we have a K for each reaction step, which is considered
to be unchanging though it actually changes slightly. Again,
this represents the quotient that will exist once the system
reaches equilibrium, the lowest energy it can achieve.
Remember that the ratio of K and Q will equal 1 at equilibrium.
So for each step or iteration, the ratio of K and Q gives
us both the direction and amount of change in the components
of the reaction. Based on this quotient we decrease the
difference between Q and K at each iteration, moving that
equation toward equilibrium.
In Vivo Data
Here are some concentration values for
components of the TCA cycle as found in academic papers
online.
-[NAD+]: 4.900E-06 M
-[NADH]: 7.000E-08 M
Differential
binding of NAD+ and NADH allows the transcriptional
corepressor carboxyl-terminal binding protein to serve as
a metabolic sensor, Clark C. Fjeld, William T. Birdsong,
and Richard H. Goodman, PNAS, 9202–9207, August 5, 2003,
vol. 100, no. 16
-[CO2]: 1.42 mM (rest) to 2.40 mM (exercise)
-[H+]: 4.266E-08 (rest) and 7.161E-08 M (exercise)
Carbon
Dioxide Transport and Carbonic Anhydrase in Blood and Muscle,
Cornelia Geers and Gerolf Gros, Physiological Reviews, Vol.
80, No. 2, April 2000
-[GDP]: 100 uM
-[GTP]: 255 to 323 nM
-[Pi]: 7.5mM "Several millimolar", "typically around 5–10
mM"
Modulation
of IMP Dehydrogenase Activity and Guanylate Metabolism by
Tiazofurin (2-B-D-Ribofuranosylthiazole-4-carboxamide),
May S. Lui, Mary A. Faderan, Juris J. Liepnieks, Yutaka
Natsumeda, Edith Olah, Hiremagalur N. Jayaram, and George
Weber, The Journal of Biological chemistry, Vol. 259, No.
6, Issue of April 25, pp. 5078-5082, 1984
-[GTP]: 255 to 323 nM (Reference 5)
-[FAD]: 78.5 +/- 54.3 nM
Riboflavin
and riboflavin-derived cofactors in adolescent girls with
anorexia nervosa, Callinice D Capo-chichi, Jean-Louis Guéant,
Emmanuelle Lefebvre, Nabila Bennani, Elizabeth Lorentz,
Colette Vidailhet, and Michel Vidailhet, American Journal
of Clinical Nutrition, 1999;69:672–8
-[CoASH]: 4.350E-06 M (Average of values from reference
-COASH: 2.3 to 6.4 nM/g-, assumed density of water for conversion)
CoASH
and CoASSG Levels in Lungs of Hyperoxic Rats as Potential
Biomarkers of Intramitochondrial Oxidant Stresses, Donough
J. O’Donovan, Lynette K. Rogers, Donald K. Kelley, Stephen
E. Welty,Patricia L. Ramsay, and Charles V. Smith, Pediatric
Research, Vol. 51, No. 3, 2002
