Metabolism formulas

Metabolism: pathways, photosynthesis and respiration. 8 formulas for GATE BT General Biology, each with when to use it. Each is explained in the topic notes.

All 8 Metabolism formulas

FREE ENERGY UNDER CELLULAR CONDITIONS

Δ G = Δ G^{\circ'} + R T ln Q

R = 8.315 J/(mol·K); RT ≈ 2.48 kJ/mol at 25 °C. Q is the mass-action ratio [products]/[reactants]; at equilibrium Q = K'eq and ΔG = 0.

STANDARD FREE ENERGY AND EQUILIBRIUM CONSTANT

Δ G^{\circ'} = - R T ln K_{e q}^{'}

K'eq is the equilibrium constant at pH 7. Each tenfold change in K'eq changes ΔG°' by about 5.7 kJ/mol at 25 °C (this is RT ln 10).

FREE ENERGY OF A REDOX REACTION

Δ G^{\circ'} = - n F Δ E^{\circ'}

n = electrons transferred per mole of the reaction as written, F = 96.5 kJ/(V·mol), ΔE°' = E°'(electron acceptor) minus E°'(electron donor), both at pH 7.

ADENYLATE ENERGY CHARGE

Energy charge = \frac{[ ATP ] + \frac{1}{2} [ ADP ]}{[ ATP ] + [ ADP ] + [ AMP ]}

Ranges from 0 (all AMP) to 1 (all ATP); cells usually hold it at about 0.8–0.95. ATP-generating pathways are inhibited and ATP-using pathways stimulated as it rises. Adenylate kinase (2 ADP ⇌ ATP + AMP) makes [AMP] change far more, in proportion, than [ATP], which is why AMP is a sensitive low-energy signal.

COMPLETE OXIDATION OF GLUCOSE (2.5 / 1.5 CONVENTION)

ATP per glucose = 2 + 2 (2.5 or 1.5) + 2 (2.5) + 2 + 6 (2.5) + 2 (1.5)

Terms: glycolysis ATP, cytosolic NADH (2.5 each via the malate-aspartate shuttle, 1.5 each via the glycerol-3-phosphate shuttle), PDH NADH, TCA GTP (counted as ATP), TCA NADH, TCA FADH2. Gives 32 with the malate-aspartate shuttle and 30 with the glycerol-3-phosphate shuttle.

RESPIRATORY QUOTIENT

RQ = \frac{moles of CO _{2} released}{moles of O _{2} consumed}

Carbohydrate 1.0 (C6H12O6 + 6 O2 → 6 CO2 + 6 H2O). Fat about 0.7 (palmitic acid: C16H32O2 + 23 O2 → 16 CO2 + 16 H2O, RQ = 16/23 ≈ 0.70). Protein about 0.8. Above 1 for oxygen-rich substrates such as organic acids (malate 4/3), when fat is being made from carbohydrate, or with fermentation.

COMPLETE OXIDATION OF AN EVEN-CHAIN SATURATED FATTY ACID WITH C CARBONS (C ≥ 4)

Net ATP = 4 (\frac{C}{2} - 1) + 10 \cdot \frac{C}{2} - 2 = 7 C - 6

Uses 2.5 per NADH and 1.5 per FADH2, so 4 per β-oxidation round and 10 per acetyl-CoA, and 2 spent on activation. For palmitate (C = 16): 7 rounds give 28, 8 acetyl-CoA give 80, gross 108, net 106. Stearate (C = 18) gives 120. With the older ratios (3 and 2) palmitate gives 129.

CALVIN CYCLE STOICHIOMETRY

6 C O_{2} + 18 ATP + 12 NADPH \to one hexose

Per CO2 fixed: 3 ATP and 2 NADPH. Three CO2 give one net G3P using 9 ATP and 6 NADPH.

Where this was asked: 2020 (4), 2022 (1), 2024 (2), 2025 (3), 2026 (3). See the 13 previous-year questions on Metabolism. This shows what was asked, not what will be asked.

KEEP GOING

Metabolism: the notes and 13 solved previous-year questions