Abstract
Thermodynamics is one of the best established notions in science. Some recent work in biomolecular modeling has sacrificed its rigor in favor of trendy empirical methods. Even in cases where physicsbased energy functions are used, entropy is forgotten or left “for later versions”. This text gives an overview of the utility of a more rigorous treatment of thermodynamics at the molecular level in order to understand protein folding and receptor-ligand binding. An intuitive understanding of thermodynamics is conveyed: enthalpy is the quantity of energy, while entropy stands for its quality. Recent advances in entropy estimation from information theory and physical chemistry are outlined as they apply to biological thermodynamics. The different enthalpic, entropic, and kinetic driving forces behind protein folding and binding are detailed. Finally, some medical applications enabled by an understanding of the free energy folding funnel concept are outlined, such as HIV-1 protease folding inhibitors.
TopAn Intuitive Notion Of Entropy
Internal energy and enthalpy quantify energy. Entropy measures the quality of that energy; the lower its entropy, the more useful that energy is.
Key Terms in this Chapter
Conformer: Collection of macrostate conformations of a molecule or protein with similar energies around a major energy well. Well-known examples are the boat and chair conformers of cyclohexane and glucose.
Configurational Energy Landscape: Also known as the Potential energy surface. It is a highly dimensional surface depicting the potential energy of a molecule against each distance coordinate.
Free Energy: A criterion for stability which predicts the direction of a process connecting two states. A system will undergo a process spontaneously if it lowers its free energy. For example, a partially unfolded, denatured protein in a high free energy state will fold to its native state with lower free energy. Free energy encompasses together energetic (enthalpic) and entropic driving forces.
Folding Funnel: Also known as the free energy landscape. In its reduced 3D projection, it is a cartoon of what actually is a highly dimensional free energy surface. The folding funnel is a representation of the change in enthalpy (vertical axis) and conformational entropy (both horizontal axes) during protein folding.
Microstate: Individual, unique conformation of a molecule with a given energy. Experimentally indistinguishable from other conformations with identical energy and similar conformation.
Entropy: A counting of the states available to a system in a logarithmic scale. In thermodynamics, this is multiplied by Boltzmann’s constant k B , which is only due to our arbitrary choice for the units of temperature. Entropy in information theory and thermodynamics is equally a measure of the multiplicity of states.
Hydrophobic Effect: The tendency of large solutes to gather together when solvated in associating liquids. The hydrophobic effect causes phase separation of oil drops in water at room temperature mostly to avoid disturbing the hydrogen bonding pattern of water. The disturbance of hydrogen bonding by oil causes a lowering of entropy. Phase separation occurs to raise the water entropy and lower the total free energy of the whole solution. The hydrophobic effect is the main driving force for protein folding, causing polypeptide chains to collapse onto themselves. Generalized to associating solvents other than water, it is known as the solvophobic effect.
Configurational Entropy: It is the conformational entropy plus the entropy due spatial rearrangements. For example, water has an internal molecular conformational freedom (vibrational, rotational and translational) and can also become rearranged in several hydrogen bonding constellations, giving it configurational freedom.
Macrostate: A collection of individual conformations (microstates) with the same energy. Experimentally accessible.
Conformational Entropy: A measure of the internal freedom of a molecule, having contributions from vibrations (like stretching), rotations and translations. It is a logarithmic measure of the density of states (multiplicity) of a macrostate or conformer.