Energy

Energy Transfer and Equilibrium in Cells

Introduction

• Overview of the topic: energy transfer and avoiding equilibrium in cellular processes.

• Learning objectives:

  • Describe how energy is stored and transferred in cells.

  • Explain how free energy is determined using concentrations of reactants and products.

  • Explain how reactions or transport can be coupled to drive non-spontaneous reactions.

Energy in Cells

• Presence of Energy: Energy is ubiquitous; everything possesses energy.

• Definition of Energy: Difficult to concretely define.

Types of Energy in Cells

1. Kinetic Energy

   • Exists in the movement and heat of particles in cells.

   • Small movements of individual gas molecules, water molecules, and macromolecules involve kinetic energy.

   • Some energy is lost as heat, maintaining temperature homeostasis.

2. Potential Energy

   • Found in chemical bonds and gradients.

   • Anabolism (building reactions): Requires energy to synthesize larger molecules from smaller ones; stored in chemical bonds.

   • Catabolism (breakdown reactions): Releases energy when larger molecules are degraded to smaller ones; energy can be harvested.

   • Chemical gradients: Potential energy is held in the difference in molecule concentration across membranes. Molecules want to move towards equilibrium, releasing energy.

Equilibrium and L'Chatelier's Principle

• L'Chatelier's Principle: Systems respond to disruptions to re-establish equilibrium.

• Cell systems, individual chemical reactions, and the body as a whole continuously strive towards equilibrium, influenced by:

  • Concentration changes.

  • Temperature changes.

  • Pressure changes.

• Example: Conversions involving glucose $(C<em>6H</em>{12}O_6)$ oxidizing into carbon dioxide and water; equilibrium favors carbon dioxide and water because they are more stable and increase entropy.

Dynamics of Molecular Interactions

• Molecules form complexes and dissociate until reaching equilibrium.

• Stability of interactions depends on the number of non-covalent bonds made.

• Equilibrium: rate of formation equals rate of dissociation; doesn't imply static state.

• A cell at equilibrium is dead; must continuously add/remove substances to prevent equilibrium.

Free Energy and Reaction Dynamics

• Free Energy (ΔG): Concept by Josiah Gibbs that relates to energy available to do work in a system.

• Factors Affecting Free Energy:

  • Enthalpy (ΔH): Heat energy exchanged.

  • Entropy (ΔS): Disorder created by a reaction.

• Disorder: Influenced by heat release and the number of molecules produced during reactions.

• Spontaneous Reactions: Conditions where ΔG < 0 (exergonic). These occur without added energy.

Energy Curves and ΔG Calculation

• Energy curve illustration:

  • Vertical axis (y): energy.

  • Downward curve from reactants to products through a transition state.

• ΔG: Reflects the energy difference between reactants and products.

  • ΔG < 0: spontaneous (products lower in energy).

  • ΔG > 0: non-spontaneous (reactants lower in energy and require added energy).

• Measuring ΔH or ΔS in a cellular environment is challenging; rely on concentrations to redefine ΔG.

Recalculating ΔG Using Concentrations

• Reformulating ΔG based on concentrations:

  • Equation: $ΔG = ΔG_{naught-prime} + RT imes ln rac{[products]}{[reactants]}$

  • Constants:

  • $R$: Gas constant.

  • $T$: Temperature in Kelvin.

  • $[products]$, $[reactants]$: Concentrations of molecules involved in the reaction.

Understanding Equilibrium in the Cell

• Calculate K (equilibrium constant) at conditions in the lab and compare it with those in the cell.

• Examine how far the system is from equilibrium through ΔG calculations using cellular concentrations and equilibrium conditions.

ΔG for Reactions and Transport

1. For Reactions:

   • $ΔG = ΔG_{naught-prime} + RT imes ln rac{[products]}{[reactants]}$

2. For Transport:

   • $ΔG = ΔG_{naught-prime} + RT imes ln rac{[concentration ext{ (destination)}}{[concentration ext{ (source)}]}$

• Concept of concentration gradients driving movements.

• Charged molecules consider membrane potential:

  • Add a term $nFz$ (where:

    • $n$: charge of the molecule,

    • $F$: Faraday constant,

    • $z$: membrane potential).

Coupling Reactions to Drive Non-Spontaneous Processes

• Exergonic and Endergonic Reactions:

  • Exergonic: $ ext{ΔG} < 0$ (favorable).

  • Endergonic: $ ext{ΔG} > 0$ (requires energy).

• Mechanism to drive non-spontaneous reactions includes coupling:

  • Combine a spontaneous reaction (ex: ATP hydrolysis) with a non-spontaneous reaction.

• For example:

  • Reaction from x to y ($ΔG = +3 ext{kcal/mol}$) coupled with ATP hydrolysis ($ΔG = -7 ext{kcal/mol}$), results in a combined ΔG of -4, making both reactions proceed.

• Practical example: converting glucose to glucose-6-phosphate involves ATP hydrolysis.

Importance of Avoiding Equilibrium

• Constant changes in molecule concentrations help maintain cellular processes.

• Removing waste and consuming food prevents reactions from reaching equilibrium.

• Understanding energy needs helps plan for daily metabolic reactions (diet considerations).