2.2 Free energy, enthalpy, and entropy in biological processes

Free energy, enthalpy, and entropy in biological processes

Free energy, enthalpy, and entropy govern how energy moves through living systems. Together, they explain why some biological reactions happen on their own, why others need an energy input, and how cells maintain their remarkable organization despite the universe's tendency toward disorder.

Free energy, enthalpy, and entropy

Defining thermodynamic quantities in biological systems

Free energy ($G$) is the portion of a system's energy that can actually do useful work. In cells, free energy is stored in molecules like ATP, where the phosphoanhydride bonds between phosphate groups release significant energy upon hydrolysis (about $-30.5 \text{ kJ/mol}$ under standard conditions).

Enthalpy ($H$) represents the total heat content of a system at constant pressure. In biological reactions, enthalpy changes reflect the net energy difference between bonds broken in reactants and bonds formed in products. An exothermic reaction ($\Delta H < 0$) releases heat to the surroundings; an endothermic reaction ($\Delta H > 0$) absorbs it.

Entropy ($S$) measures the disorder or number of accessible microstates in a system. Biological systems tend to increase entropy over time as ordered structures degrade and energy disperses. However, organisms locally decrease their own entropy by consuming free energy, which is consistent with the second law of thermodynamics because the total entropy of the system plus surroundings still increases.

The second law of thermodynamics states that the total entropy of an isolated system can only increase over time. This has deep implications for biology: life can build and sustain order, but only by exporting even more disorder into the environment.

Relating thermodynamic quantities

The Gibbs free energy equation ties these three quantities together:

$\Delta G = \Delta H - T\Delta S$

• $\Delta G$ = change in free energy
• $\Delta H$ = change in enthalpy
• $T$ = absolute temperature (in Kelvin)
• $\Delta S$ = change in entropy

This equation tells you that a process is favored (spontaneous) when it either releases heat (negative $\Delta H$), increases disorder (positive $\Delta S$), or both. Temperature acts as a weight on the entropy term, so entropy-driven processes become more favorable at higher temperatures.

The standard free energy change is related to the equilibrium constant by:

$\Delta G° = -RT \ln K$

• $R$ = gas constant ($8.314 \text{ J/(mol·K)}$)
• $T$ = absolute temperature
• $K$ = equilibrium constant

A large $K$ (products favored at equilibrium) corresponds to a negative $\Delta G°$, and vice versa. This equation lets you convert between experimentally measured equilibrium data and thermodynamic quantities.

Changes in thermodynamic quantities

Calculating changes in free energy, enthalpy, and entropy

To find $\Delta G$ for a process, use the Gibbs equation: $\Delta G = \Delta H - T\Delta S$. Here's how each piece is determined:

1. Measure $\Delta H$: At constant pressure, the enthalpy change equals the heat exchanged ($q_p$). Techniques like calorimetry directly measure this. For bond-breaking and bond-forming reactions, $\Delta H$ reflects the net energy difference between old and new bonds.

2. Determine $\Delta S$: For a reversible process, entropy change is calculated as:

$\Delta S = \frac{q_{\text{rev}}}{T}$

where $q_{\text{rev}}$ is the heat exchanged reversibly and $T$ is the absolute temperature. In biological contexts, entropy changes often arise from changes in molecular order: a protein unfolding increases conformational entropy, while the release of ordered water molecules from a hydrophobic surface also increases entropy.

1. Calculate $\Delta G$: Plug $\Delta H$ and $\Delta S$ into the Gibbs equation. The sign of $\Delta G$ tells you whether the process is spontaneous under those conditions.

Standard conditions and equilibrium constants

Standard conditions for biochemistry are defined as 1 atm pressure, 298 K (25°C), and 1 M concentrations of all solutes. (Note: biochemists often use a modified standard state, $\Delta G°'$, which sets pH = 7 and water activity = 1, since these better reflect physiological conditions.)

Under standard conditions:

$\Delta G° = \Delta H° - T\Delta S°$

The link to equilibrium is:

$\Delta G° = -RT \ln K$

Keep in mind that $\Delta G°$ tells you the free energy change when all species are at standard concentrations. The actual free energy change under cellular conditions ($\Delta G$) depends on the real concentrations present, calculated using:

$\Delta G = \Delta G° + RT \ln Q$

where $Q$ is the reaction quotient (the ratio of product to reactant concentrations at that moment). This distinction matters because many reactions that appear unfavorable under standard conditions are driven forward in cells by maintaining low product concentrations.

Spontaneity of biological processes

Role of free energy in determining spontaneity

The sign of $\Delta G$ determines whether a process proceeds spontaneously:

• $\Delta G < 0$ (exergonic): The reaction releases free energy and is spontaneous. Most catabolic pathways are exergonic. For example, the complete oxidation of glucose ($C_6H_{12}O_6 + 6O_2 \rightarrow 6CO_2 + 6H_2O$) has $\Delta G°' \approx -2870 \text{ kJ/mol}$.
• $\Delta G > 0$ (endergonic): The reaction requires free energy input and is non-spontaneous on its own. Anabolic reactions like protein synthesis and DNA replication fall into this category.
• $\Delta G = 0$: The system is at equilibrium, and no net work can be extracted.

"Spontaneous" here means thermodynamically favorable. It says nothing about speed. Many spontaneous reactions are extremely slow without an enzyme to lower the activation energy.

Coupled reactions and concentration dependence

Cells drive endergonic reactions by coupling them to exergonic ones so that the combined $\Delta G$ is negative. The most common strategy is ATP hydrolysis:

Concentration also matters. As a reaction proceeds, reactant concentrations drop and product concentrations rise, which changes $\Delta G$ through the $RT \ln Q$ term. Eventually, $\Delta G$ reaches zero and the reaction hits equilibrium. Cells avoid equilibrium by continuously removing products or replenishing reactants, keeping reactions far from equilibrium where they can do useful work.

Entropy and organization of life

Maintaining organization in living systems

Living systems are strikingly ordered: proteins fold into precise shapes, lipids assemble into membranes, and chromosomes organize into compact structures. All of this represents low entropy locally. How does this square with the second law?

The key is that organisms are open systems. They exchange both matter and energy with their surroundings. When a cell builds an ordered protein, it simultaneously releases heat and produces waste products that increase the entropy of the environment by more than the entropy decreased inside the cell. The total entropy of the universe still goes up.

This maintenance of order requires a constant throughput of free energy. Heterotrophs get it from food; autotrophs capture it from sunlight. If that energy supply stops, the organism dies and its ordered structures degrade toward equilibrium, which is exactly what the second law predicts.

Cellular structures and information content

Membranes are a prime example of entropy management. By forming compartments, membranes create distinct chemical environments within the cell. Ion gradients across membranes (like the proton gradient in mitochondria) store free energy that can be harnessed for ATP synthesis. The selective permeability of membranes prevents the spontaneous mixing that would increase entropy.

Genetic information stored in DNA represents an extraordinarily low-entropy state. The specific sequence of nucleotides encodes the instructions for building and maintaining the organism. DNA replication and repair mechanisms preserve this information with remarkable fidelity (error rates on the order of $10^{-9}$ per base pair per replication in humans), but these processes themselves consume free energy. The transmission of genetic information across generations sustains biological organization over time.

Evolution and the second law of thermodynamics

Evolution by natural selection does not violate the second law. Instead, it represents a process by which populations of organisms sustain and refine their organization over long timescales. Individuals with traits better suited to capturing and using free energy from their environment tend to survive and reproduce more successfully.

Over evolutionary time, this differential reproduction leads to adaptations that improve an organism's ability to maintain low internal entropy. The energy to fuel this process ultimately comes from external sources (primarily solar radiation), and the entropy exported to the environment always exceeds the local decrease in entropy within the biosphere.