Biochemical Thermodynamics: Principles and Applications

Thermodynamics in Biochemistry

Basic Concepts of Thermodynamics

Thermodynamics is the study of energy transformations in matter, which is fundamental to understanding biochemical processes. The following terms are essential:

• System: A defined part of the universe under study (e.g., a cell, a reaction vessel).

• Surroundings: Everything outside the system.

• Internal Energy: The sum of all potential and kinetic energy within a system.

• Enthalpy (ΔH): The change in heat content during a reaction at constant pressure.

• Entropy (ΔS): The measure of disorder or randomness in a system.

Key Points:

• The more ordered a system, the lower its entropy.

• If no work is done on the system, entropy will always increase (Second Law of Thermodynamics).

Example: In a cell, the distribution of molecules becomes more random over time, increasing entropy.

Visualizing Entropy Changes

Entropy changes can be illustrated by physical and chemical processes:

• Phase Changes: Entropy increases as substances move from solid to liquid to gas.

• Molecular Mixing: Mixing two solutions increases entropy as molecules become more randomly distributed.

Example: Adding pure water to a solution and allowing it to mix increases the entropy of the system.

Thermodynamics of Chemical Reactions

Spontaneity and Free Energy

Thermodynamics helps predict whether a reaction will occur spontaneously, but not how fast it will proceed. The key quantity is Gibbs Free Energy (G):

• Gibbs Free Energy Equation:

$G = H - TS$

• Change in Free Energy:

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

• ΔH: Change in enthalpy (heat of reaction)

• T: Temperature in Kelvin

• ΔS: Change in entropy (randomness)

Interpretation of ΔG:

• ΔG < 0: Reaction is spontaneous and exergonic

• ΔG > 0: Reaction is non-spontaneous and endergonic

• ΔG = 0: Reaction is at equilibrium

Example: Hydrolysis of ATP is spontaneous under cellular conditions (ΔG < 0).

Variation of Reaction Spontaneity

The spontaneity of a reaction depends on the signs of ΔH and ΔS:

• ΔH < 0, ΔS > 0: Spontaneous at all temperatures (exergonic).

• ΔH < 0, ΔS < 0: Spontaneous only at low temperatures.

• ΔH > 0, ΔS > 0: Spontaneous only at high temperatures.

• ΔH > 0, ΔS < 0: Non-spontaneous at all temperatures.

Additional info: These relationships are crucial for predicting the direction of biochemical reactions under varying conditions.

Equilibrium and Free Energy

Chemical Equilibrium

At equilibrium, the concentrations of reactants and products remain constant. The equilibrium constant (K) quantifies this state:

For a general reaction: $aA + bB \rightleftharpoons cC + dD$

$K = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

• Changing concentrations shifts the reaction to restore equilibrium.

• Increasing [A] drives the reaction toward more products (C and D).

Mass Action and Non-Equilibrium Systems

Biological systems rarely reach equilibrium; instead, the reaction quotient (Q) is used:

$Q = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

• K: Value at equilibrium

• Q: Value at any point (not necessarily equilibrium)

K vs Q	ΔG	Direction
Q < K	ΔG < 0	Forward (products form)
Q = K	ΔG = 0	Equilibrium
Q > K	ΔG > 0	Reverse (reactants form)

Calculating Free Energy Changes

The actual free energy change depends on concentrations:

$\Delta G = \Delta G^\circ + RT \ln Q$

• ΔG°: Standard free energy change (1 bar, 25°C, 1M solutes)

• R: Gas constant (8.314 J·mol−1·K−1)

• T: Temperature in Kelvin

Example: Calculating ΔG for ATP hydrolysis in a cell requires actual concentrations of ATP, ADP, and Pi.

Biochemical Standard State

Defining the Biochemical Standard State

Biochemical reactions often involve water and protons (H+), which are not at 1M in cells. The biochemical standard state is defined as:

• Activity of H+ is 1 at pH 7 ($[H^+] = 10^{-7}$ M)

• Activity of H2O is defined as 1

The free energy equation is adjusted for these conditions:

$\Delta G' = \Delta G^\circ' + RT \ln Q'$

Additional info: The prime (') indicates biochemical standard state, which is more relevant for living systems.

Driving Unfavorable Reactions

Strategies for Driving Non-Spontaneous Reactions

Cells must drive reactions with positive ΔG (unfavorable). Two main strategies are used:

• Manipulate Q: Keep product concentrations low or reactant concentrations high to make Q < K.

• Reaction Coupling: Couple an unfavorable reaction to a favorable one so the overall ΔG is negative.

Example: ATP hydrolysis (ΔG < 0) is coupled to endergonic processes like muscle contraction or active transport.

Reaction	ΔG° (kJ/mol)
A → B (unfavorable)	+10
C → D (favorable)	-30
Overall: A + C → B + D	-20

Additional info: Coupling is essential for processes such as metabolite transport, nerve impulse transmission, and muscle contraction.

Summary Table: Key Thermodynamic Terms

Term	Definition
ΔH (Enthalpy)	Change in heat content of a reaction
ΔS (Entropy)	Change in disorder/randomness
ΔG (Gibbs Free Energy)	Energy available to do work
K (Equilibrium Constant)	Ratio of product to reactant concentrations at equilibrium
Q (Reaction Quotient)	Ratio of product to reactant concentrations at any time

Essential Concepts to Know

• Definitions and significance of ΔH, ΔS, and ΔG

• Gibbs free energy equation and interpretation of ΔG values

• Difference between K and Q, and their use in predicting reaction direction

• Calculation of ΔG from solute concentrations

• Distinction between chemical and biochemical standard states

• Mechanisms for driving unfavorable reactions in cells