5.2 Protein folding thermodynamics and kinetics

Protein folding is a complex dance of molecules, driven by the need to minimize energy. It's all about finding the perfect balance between enthalpy and entropy, with hydrophobic interactions leading the way. The native state is the ultimate goal, representing the most stable form.

The folding process isn't random – it follows specific pathways with key transition states. The energy landscape looks like a funnel, guiding proteins to their final form. Understanding this process helps us grasp how proteins work and why they sometimes misbehave.

Thermodynamics of Protein Folding

Gibbs Free Energy and Protein Folding

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• Protein folding is a spontaneous process driven by the minimization of Gibbs free energy (ΔG), which is determined by the balance between enthalpy (ΔH) and entropy (ΔS) according to the equation $ΔG = ΔH - TΔS$, where T is the absolute temperature
• The native state of a protein is typically the most thermodynamically stable conformation, corresponding to the global minimum of the Gibbs free energy landscape
• The stability of the native state is determined by the balance between the favorable enthalpic contributions from non-covalent interactions and the unfavorable entropic cost of reducing conformational freedom

Enthalpy and Entropy in Protein Folding

• Enthalpy (ΔH) represents the heat content of the system and is influenced by the formation of non-covalent interactions such as hydrogen bonds and van der Waals forces during protein folding
• Entropy (ΔS) is a measure of the disorder or randomness of the system, and it decreases during protein folding due to the reduction in conformational freedom of the polypeptide chain
• The hydrophobic effect is a major driving force for protein folding, as it minimizes the exposure of hydrophobic residues to the aqueous environment, leading to an increase in entropy of the surrounding water molecules (hydrophobic collapse)

Forces Driving Protein Folding

Hydrophobic Interactions

• Hydrophobic interactions are the primary driving force for protein folding, as they minimize the exposure of non-polar amino acid side chains to the aqueous environment, leading to the formation of a hydrophobic core in the native state
  • The burial of hydrophobic residues within the protein interior is entropically favorable, as it releases ordered water molecules from the hydrophobic surfaces (hydrophobic effect), increasing the overall entropy of the system
  • Examples of hydrophobic amino acids include leucine, valine, and phenylalanine

Hydrogen Bonding and Secondary Structure Formation

• Hydrogen bonds form between the backbone amide and carbonyl groups, as well as between polar side chains, stabilizing secondary structures such as α-helices and β-sheets
  • The formation of hydrogen bonds is enthalpically favorable, as it lowers the overall energy of the system
  • Hydrogen bonds also contribute to the specificity of protein folding by guiding the formation of native-like interactions
• Examples of secondary structures stabilized by hydrogen bonds include:
  • α-helices (3.6 residues per turn, stabilized by i to i+4 hydrogen bonds)
  • β-sheets (parallel or antiparallel, stabilized by inter-strand hydrogen bonds)

Van der Waals Forces and Protein Packing

• Van der Waals forces are weak, non-specific attractive interactions that arise from transient dipoles induced by fluctuations in electron density
  • Although individually weak, the cumulative effect of numerous van der Waals interactions can significantly contribute to the stability of the native state
  • Van der Waals interactions are particularly important for the close packing of amino acid side chains in the protein interior, optimizing the overall shape and compactness of the folded structure
• The interplay between hydrophobic interactions, hydrogen bonding, and van der Waals forces collectively determines the unique three-dimensional structure of a protein, with the native state representing the optimal balance of these non-covalent interactions

Kinetics of Protein Folding

Folding Pathways and Transition States

• Protein folding kinetics refers to the rate and mechanism by which a polypeptide chain adopts its native three-dimensional structure
• The folding process can be described as a series of transitions between distinct conformational states, with the native state being the most stable and populated under physiological conditions
• Folding pathways represent the sequential order of events and intermediates that a protein undergoes during the folding process, from the unfolded state to the native state
  • The folding pathway is determined by the protein's amino acid sequence and the specific non-covalent interactions that form during the folding process
  • Multiple folding pathways may exist for a given protein, with the dominant pathway being the one with the lowest energy barriers between intermediates
• Transition states are high-energy, unstable conformations that represent the main kinetic barriers along the folding pathway
  • Transition states are characterized by a significant loss of conformational entropy and the formation of a critical subset of native-like interactions
  • The structure of the transition state ensemble can be probed experimentally using protein engineering techniques such as φ-value analysis, which measures the effect of mutations on the folding rate

Folding Rates and Rate-Limiting Steps

• The rate-limiting step in protein folding is typically the formation of the transition state, and the overall folding rate is determined by the height of the energy barrier between the unfolded state and the transition state
• Protein folding rates span several orders of magnitude, from microseconds to minutes or even hours, depending on the complexity of the protein and the nature of the folding pathway
  • Small, single-domain proteins (cytochrome c) often fold rapidly in the microsecond to millisecond timescale
  • Large, multi-domain proteins (luciferase) may require minutes or hours to fold properly

Protein Folding Energy Landscape

Energy Landscape Topology

• The energy landscape of protein folding is a high-dimensional surface that represents the free energy of all possible conformations of a polypeptide chain
  • The vertical axis of the energy landscape represents the free energy, while the horizontal axes represent the conformational degrees of freedom
  • The native state occupies the global minimum of the energy landscape, representing the most thermodynamically stable conformation
• The shape of the energy landscape is often described as a funnel, with the unfolded state occupying a broad, high-energy region at the top and the native state located at the narrow, low-energy bottom
  • The funnel shape arises from the progressive formation of native-like interactions and the concomitant reduction in conformational entropy as the protein approaches the native state

Folding Mechanisms and Landscape Roughness

• The roughness of the energy landscape, characterized by the presence of local minima and energy barriers, determines the folding mechanism and the existence of intermediates
  • Smooth energy landscapes with few local minima are associated with two-state folding, where the protein directly transitions from the unfolded state to the native state without populating detectable intermediates
  • Rugged energy landscapes with numerous local minima are associated with multi-state folding, where the protein populates one or more partially folded intermediates en route to the native state
• The principle of minimal frustration suggests that evolution has optimized protein sequences to minimize the number of non-native interactions and ensure a smooth, funnel-shaped energy landscape conducive to efficient folding
• The energy landscape perspective provides a unified framework for understanding the thermodynamics and kinetics of protein folding, linking the sequence, structure, and function of proteins