Principles of bioenergetics

Bioenergetics concerns the flow and transformation of energy in biochemical systems.

Thermodynamics underpins this study, describing how enthalpy ($H$), entropy ($S$), and free energy ($G$) interact to determine whether and how a reaction proceeds.

Free energy, equilibrium, and $K_{eq}$

Free energy ($G$) measures the amount of energy available in a system to do work. For a reaction, the change in free energy ($ 94 G$) is given by:

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

where $\Delta H$ is the enthalpy change, $T$ is the absolute temperature (in Kelvin), and $\Delta S$ is the entropy change.

• A negative $\Delta G$ indicates a spontaneous (thermodynamically favorable) reaction under the given conditions, whereas a positive $\Delta G$ indicates a nonspontaneous reaction under those conditions. Spontaneity is a thermodynamic property and does not describe reaction speed, which is a kinetic property.
• The equilibrium constant ($K_{eq}$) reflects the ratio of products to reactants at equilibrium. Under standard conditions, the relationship between $K_{eq}$ and $\Delta G^{\circ }$ is:

$$\Delta G^{\circ }=-RT\ln K_{eq}$$

Concentration and Le Ch 2btelier’s Principle
Changing reactant or product concentrations can push a reaction in one direction or the other. According to Le Ch 2btelier’s Principle, a system shifts to counteract an imposed change and move back toward equilibrium.

Endothermic and exothermic reactions

Enthalpy ($H$) represents the heat content of a reaction. By convention,

• Endothermic processes absorb heat ($\Delta H>0$).
• Exothermic processes release heat ($\Delta H<0$).

Standard heats of reaction ($\Delta H_{rxn}$) or formation ($\Delta H_f$) describe enthalpy changes under standard conditions (1 bar pressure, specified temperature).

$\Delta H$ is the change in heat content during a reaction. A positive value means heat is absorbed, and a negative value means heat is released.

The standard heat of reaction ($\Delta H_{rxn}$) measures this enthalpy change for a specific chemical reaction under standard conditions.

Similarly, the standard heat of formation ($\Delta H_f$) quantifies the enthalpy change when a compound is formed from its elements in their most stable forms.

These elements are in their standard state (the lowest-energy configuration found naturally). For example, oxygen exists as $O_2$ (a diatomic gas) and carbon as solid graphite.

In a formation reaction, a substance is generated from its elements in their standard states (e.g., diatomic $O_2$, graphite carbon).

Enthalpy is typically measured in joules ($J$) or, more commonly in chemistry, joules per mole ($J/mol$).

Hess’ Law allows enthalpy changes to be summed:

$$\Delta H_{rxn}=\Sigma \Delta H_f(\text{products})-\Sigma \Delta H_f(\text{reactants})$$

Spontaneous reactions and standard free energy change

Spontaneous reactions occur without the need for continuous external energy input. Thermodynamically, spontaneity is indicated by a negative change in free energy ($\Delta G$).

A negative $\Delta G$ means a reaction is thermodynamically favorable, but the rate at which it proceeds depends on kinetic factors. As a result, even spontaneous reactions can be slow.

The relationship between heat exchange and spontaneity can be subtle:

• An exothermic reaction ($\Delta H<0$) might not be spontaneous if it is accompanied by a significant decrease in entropy ($\Delta S$).
• An endothermic reaction ($\Delta H>0$) can be spontaneous if it involves a large increase in entropy.

Phosphoryl group transfers and ATP

In biological systems, energy transfer is often driven by the hydrolysis of ATP, a reaction with a very negative $\Delta G$ ($\Delta G\ll 0$). The energy released can be coupled to processes such as phosphoryl group transfers.

ATP hydrolyzes into ADP in the following reaction:

$$ATP+H_{2}O\to ADP+Pi+\text{free energy}$$

Biological oxidation-reduction
Cellular energy production relies on oxidation-reduction (redox) reactions, which involve the transfer of electrons through half-reactions. These redox processes are mediated by soluble electron carriers and enzymes like flavoproteins, which facilitate electron flow and play critical roles in the cell’s bioenergetic pathways.