15. Thermodynamics of Life
Reading time: ~45 minutes | Key topics: Gibbs free energy, ATP hydrolysis, coupled reactions, redox biochemistry, NAD⁺/FAD electron carriers
Free Energy and Spontaneity
The central criterion for predicting whether a biochemical process will occur spontaneously is the Gibbs free energy change ($\Delta G$). This thermodynamic quantity combines enthalpy (heat content) and entropy (disorder) into a single value that determines the direction of a reaction at constant temperature and pressure — the conditions prevailing in living cells.
where $\Delta H$ is the change in enthalpy (kJ/mol), $T$ is the absolute temperature (K), and $\Delta S$ is the change in entropy (kJ/mol·K). The sign of $\Delta G$ determines whether a process can proceed without an input of energy:
- $\Delta G < 0$ — Exergonic: The reaction is spontaneous (thermodynamically favorable). Energy is released.
- $\Delta G > 0$ — Endergonic: The reaction is non-spontaneous. Energy input is required to drive the reaction forward.
- $\Delta G = 0$ — Equilibrium: The system is at equilibrium; no net reaction occurs in either direction.
It is critical to understand that $\Delta G$ says nothing about the rate of a reaction — only whether it is energetically feasible. A reaction with a large negative $\Delta G$ may still proceed imperceptibly slowly without an enzyme catalyst. Thermodynamics determines if; kinetics determines how fast.
Standard Free Energy
To compare reactions on equal footing, biochemists define a biochemical standard state denoted by the prime symbol (′). The biochemical standard conditions are: pH 7.0, temperature 25°C (298.15 K), 1 M concentration of all solutes, and water at 55.5 M (its effective concentration in dilute aqueous solution).
The standard free energy change $\Delta G^{\circ'}$ is related to the equilibrium constant $K'_{eq}$ by:
where $R = 8.314 \text{ J/(mol·K)}$ is the gas constant and $T$ is the absolute temperature. The actual free energy change under cellular conditions depends on the concentrations of reactants and products through the mass action ratio $Q$:
Critical Distinction
$\Delta G^{\circ'}$ tells us the direction of a reaction under standard conditions (all concentrations at 1 M, pH 7). But in living cells, concentrations are far from standard. It is $\Delta G$ — the actual free energy change computed with cellular concentrations — that determines whether a reaction will proceed. A reaction with a positive $\Delta G^{\circ'}$ can still be driven forward in vivo if $Q$ is kept sufficiently small by rapid removal of products.
ATP: The Energy Currency
Adenosine triphosphate (ATP) is the universal energy currency of all living cells. It consists of the purine base adenine, the five-carbon sugar ribose, and a chain of three phosphoryl groups connected by phosphoanhydride bonds. The hydrolysis of ATP to ADP and inorganic phosphate is the primary reaction that drives thermodynamically unfavorable processes in biology.
Several factors contribute to the large negative $\Delta G^{\circ'}$ of ATP hydrolysis:
- Electrostatic repulsion relief: At physiological pH, ATP carries approximately 4 negative charges. Hydrolysis separates these repelling charges.
- Resonance stabilization: The products (ADP and P$_i$) each have greater resonance stabilization than ATP because the phosphoanhydride bond constrains electron delocalization.
- Hydration of products: ADP and P$_i$ are more effectively solvated by water than ATP, contributing favorably to the free energy change.
Under typical intracellular conditions ([ATP] $\approx$ 3 mM, [ADP] $\approx$ 0.8 mM, [P$_i$] $\approx$ 4 mM), the actual $\Delta G$ of ATP hydrolysis is approximately −50 to −54 kJ/mol, significantly more negative than the standard value because cells maintain ATP concentrations far above equilibrium.
ATP occupies an intermediate position in the thermodynamic scale of phosphorylated compounds. Compounds with a more negative $\Delta G^{\circ'}$ of hydrolysis can transfer their phosphoryl group to ADP to regenerate ATP, while ATP can phosphorylate compounds with a less negative $\Delta G^{\circ'}$:
| Compound | $\Delta G^{\circ'}$ (kJ/mol) | Role |
|---|---|---|
| Phosphoenolpyruvate (PEP) | −61.9 | Phosphoryl donor to ADP |
| 1,3-Bisphosphoglycerate | −49.4 | Phosphoryl donor to ADP |
| Creatine phosphate | −43.1 | ATP buffer in muscle |
| ATP (to ADP + P$_i$) | −30.5 | Universal energy currency |
| Glucose-6-phosphate | −13.8 | Phosphoryl acceptor from ATP |
| Glycerol-3-phosphate | −9.2 | Phosphoryl acceptor from ATP |
Coupled Reactions
Many biosynthetic reactions are thermodynamically unfavorable ($\Delta G^{\circ'} > 0$). Cells drive these reactions forward by coupling them to the highly exergonic hydrolysis of ATP. The fundamental principle is that when two reactions are coupled (occur together via a shared intermediate), their free energy changes are additive.
Consider the synthesis of glutamine from glutamate and ammonia. The uncoupled reaction is endergonic:
When coupled to ATP hydrolysis through a phosphorylated intermediate (glutamyl phosphate), the overall reaction becomes exergonic:
The overall $\Delta G^{\circ'}$ is simply the sum: $+14.2 + (-30.5) = -16.3$ kJ/mol. The reaction is now thermodynamically favorable because the free energy released by ATP hydrolysis more than compensates for the energy required for glutamine synthesis.
The Coupling Principle
Coupling does not violate thermodynamics — it simply means the enzyme catalyzes a combined reaction whose overall $\Delta G$ is the sum of the individual free energy changes. In practice, the two reactions share a common intermediate (such as a phosphorylated enzyme or substrate), ensuring they are mechanistically linked. The endergonic reaction cannot proceed alone; it is pulled forward by the exergonic partner.
Redox Reactions in Biochemistry
Oxidation-reduction (redox) reactions are the fundamental energy-transducing reactions in metabolism. Electrons flow from donors (reduced molecules such as NADH) to acceptors (oxidized molecules such as O$_2$), and the free energy released is harnessed to do work — primarily the synthesis of ATP.
Each redox couple has a standard reduction potential $E^{\circ'}$ measured in volts at pH 7. A more negative $E^{\circ'}$ indicates a stronger tendency to donate electrons (better reducing agent), while a more positive $E^{\circ'}$ indicates a stronger tendency to accept electrons (better oxidizing agent). Electrons flow spontaneously from more negative to more positive $E^{\circ'}$.
The Nernst equation relates the actual reduction potential to concentrations:
where $n$ is the number of electrons transferred and $F = 96,485$ C/mol is the Faraday constant. The relationship between the free energy change and the redox potential difference is:
A positive $\Delta E^{\circ'}$ (electrons flowing from negative to positive potential) yields a negative $\Delta G^{\circ'}$ (spontaneous reaction). Important biological redox couples include:
| Half-Reaction (Reduction) | $E^{\circ'}$ (V) |
|---|---|
| $\text{NAD}^+ + \text{H}^+ + 2e^- \rightarrow \text{NADH}$ | −0.320 |
| $\text{FAD} + 2\text{H}^+ + 2e^- \rightarrow \text{FADH}_2$ | −0.219 |
| $\text{Ubiquinone} + 2\text{H}^+ + 2e^- \rightarrow \text{Ubiquinol}$ | +0.045 |
| $\text{Cytochrome } c \text{ (Fe}^{3+}\text{)} + e^- \rightarrow \text{Cyt } c \text{ (Fe}^{2+}\text{)}$ | +0.254 |
| $\frac{1}{2}\text{O}_2 + 2\text{H}^+ + 2e^- \rightarrow \text{H}_2\text{O}$ | +0.816 |
The overall transfer of electrons from NADH to O$_2$ spans a potential difference of $\Delta E^{\circ'} = 0.816 - (-0.320) = 1.136$ V, corresponding to $\Delta G^{\circ'} = -2 \times 96.485 \times 1.136 = -219.2$ kJ/mol. This enormous free energy release is what ultimately powers oxidative phosphorylation and the synthesis of the majority of cellular ATP.
NAD⁺ and FAD as Electron Carriers
The coenzymes NAD⁺ (nicotinamide adenine dinucleotide) and FAD (flavin adenine dinucleotide) are the principal soluble electron carriers in metabolism. They accept electrons from substrates during catabolic oxidation reactions and deliver them to the electron transport chain in the mitochondrial inner membrane.
NAD⁺/NADH
The nicotinamide ring of NAD⁺ accepts a hydride ion (one hydrogen atom plus one electron, equivalent to 2e⁻ + H⁺) from the substrate. The other hydrogen atom from the substrate is released as H⁺ into solution:
The closely related coenzyme NADP⁺ differs only by an additional phosphoryl group on the 2′-hydroxyl of adenosine. Despite this small structural difference, cells strictly partition their roles: NAD⁺ functions primarily in catabolism (carries electrons to the ETC), while NADP⁺ supplies reducing power for anabolic biosynthetic reactions (fatty acid synthesis, steroid synthesis, etc.).
FAD/FADH$_2$
FAD accepts two electrons and two protons (2e⁻ + 2H⁺) to form FADH$_2$. Unlike NAD⁺, FAD can accept electrons one at a time, passing through a semiquinone (FADH·) intermediate. This makes FAD well-suited for reactions involving radical intermediates.
FAD is typically tightly bound (or covalently attached) to its enzyme as a prosthetic group, forming a class of enzymes called flavoproteins. Important examples include succinate dehydrogenase (Complex II) and acyl-CoA dehydrogenase in fatty acid oxidation.
Coenzyme Q (Ubiquinone)
Coenzyme Q is a lipid-soluble mobile electron carrier that operates within the hydrophobic interior of the inner mitochondrial membrane. Its long isoprenoid tail anchors it in the lipid bilayer. Like FAD, it can accept electrons one or two at a time, forming the semiquinone radical (Q·⁻) or the fully reduced ubiquinol (QH$_2$). Coenzyme Q collects electrons from both Complex I (NADH dehydrogenase) and Complex II (succinate dehydrogenase) and delivers them to Complex III (cytochrome bc$_1$).
Python: Free Energy Diagram
Run this Python code to visualize two key concepts in bioenergetics: (1) how coupling an endergonic reaction to ATP hydrolysis makes it exergonic, and (2) the phosphoryl transfer potential of biologically important compounds, showing why ATP occupies a central intermediate position on the thermodynamic scale. The code also computes in vivo $\Delta G$ for ATP hydrolysis and the free energy available from NADH oxidation.
Bioenergetics: Free Energy Diagrams & Calculations
PythonCoupled reaction diagrams, phosphoryl transfer potentials, and redox calculations
Click Run to execute the Python code
Code will be executed with Python 3 on the server
Key Concepts
1. The Gibbs free energy change ($\Delta G = \Delta H - T\Delta S$) determines whether a reaction is spontaneous. Exergonic reactions ($\Delta G < 0$) proceed spontaneously; endergonic reactions ($\Delta G > 0$) require energy input.
2. The standard free energy $\Delta G^{\circ'} = -RT\ln K'_{eq}$ applies under biochemical standard conditions (pH 7, 25°C, 1 M). The actual cellular $\Delta G$ depends on real concentrations: $\Delta G = \Delta G^{\circ'} + RT\ln Q$.
3. ATP hydrolysis ($\Delta G^{\circ'} = -30.5$ kJ/mol; in vivo $\approx -50$ to $-54$ kJ/mol) is highly exergonic due to electrostatic repulsion relief, resonance stabilization, and enhanced hydration of products.
4. Endergonic reactions are driven by coupling to ATP hydrolysis through shared intermediates. The $\Delta G$ values of coupled reactions are additive.
5. Redox reactions are governed by reduction potentials: $\Delta G^{\circ'} = -nF\Delta E^{\circ'}$. Electrons flow spontaneously from more negative to more positive $E^{\circ'}$.
6. NAD⁺ and FAD are the principal electron carriers in catabolism. NAD⁺ accepts a hydride (2e⁻ + H⁺); FAD accepts 2e⁻ + 2H⁺. NADPH serves anabolic pathways. Coenzyme Q is the lipid-soluble mobile carrier in the membrane.
7. The transfer of electrons from NADH to O$_2$ ($\Delta E^{\circ'} = 1.136$ V) releases $\Delta G^{\circ'} = -219$ kJ/mol, the thermodynamic driving force behind oxidative phosphorylation and the production of most cellular ATP.