4BBY1020 Chemistry for the Biosciences Lecture 11: Protein Folding

Thermodynamics of Protein Folding

• Stabilising Interactions: Folded proteins are stabilised by a mixture of non-covalent and covalent interactions, as well as entropic effects.

  • Hydrogen bonds

  • Electrostatic interactions (Charged side chains and dipole interactions)

  • London forces (dispersion interactions)

  • Hydrophobic effect

  • Disulphide bonds

• Typical Energetic Contributions (Theoretical):

Solvation Effects and Water Dynamics

• Structure and Dynamics of Water ($H_2O$):

  • Forms hydrogen bonds with itself.

  • Each molecule has two hydrogen atoms and two lone pairs: acts as two hydrogen bond donors and two acceptors.

  • Water molecules are highly dynamic, exhibiting constant rotational and translational motions and rearrangements in hydrogen bonding patterns.

• Water as a Solvent:

  • Polar substances dissolve readily due to water's polar nature and H-bonding ability.

  • Non-polar substances interrupt hydrogen bonding, leading to phase separation to reduce the water interface.

• The Hydrophobic Effect:

  • Water surrounding non-polar molecules forms an "ice-like" cage.

  • the ability to move around is severely limited for all water molecules forming this cage → significant loss of entropy

  • Effect 1 (Hydrophobic Interactions): Removing hydrophobic residues from the water-protein interface to form a hydrophobic core is entropically favourable because water has higher entropy when not forming a "cage."

  • Effect 2 (Hydrophilic Interactions): Interactions between water and hydrophilic residues (charged/polar side chains) are enthalpically favourable due to hydrogen bonding and charge interactions. Though mobility is still limited, there is a significant energy benefit of forming the interactions

• Protein Shape and Solvation:

  • A globular shape with hydrophobic residues are in the core and hydrophilic residues are on the outside is favourable

  • Hydrophobic collapse is considered a key step in folding. the globular shape of proteins is a combination of hydrophobic and hydrophilic interaction

  • Hydrophobic surfaces are frequently involved in protein-protein interactions.

• Membrane Proteins:

  • Membrane proteins need to be anchored inside the membrane but may have other protein regions sitting on the membrane

  • the difference in hydrophobicity between membrane and non-membrane must be accounted for during folding

  • Examples: E. Coli BAM complex (beta-barrel-assembly machinery, PDB id: 6LYR) and E. Coli Multidrug exporter protein.

Stability and Entropy Calculations

• Relative Contributions in Context:

  • Hydrogen bonds: While the theoretical contribution is $-3\,kcal/mol$, in an unfolded state, $N-H$ and $C=O$ groups already form H-bonds with water (weaker, but lost when folding). net contribution is only about $-1\,kcal/mol$.

  • Electrostatics: The theoretical enthalpic contribution is $-5\,kcal/mol$, when unfolded charged side chains are fully solvated in water (weakens enthalpic contribution). entropic contribution remains as the water in the solvation shell around the charge is released

• Mathematical Representation of Entropy:

  • Entropy is related to the number of states ($W$) or degrees of freedom a molecule can adopt:     $S = k_B \ln(W)$

  • Where $k_B$ is Boltzmann's constant and W is the number of states (for a molecule, W = number of different conformations). For one mole of molecules, the gas constant $R$ is used:     $S = N_A k_B \ln(W) = R \ln(W)$

  • Na is avogadro’s number and R is the gas constant

• Entropy of Folding ($\Delta S_{fold}$):     

  

  • Because there is only one native state, $W_n = 1$.

  • For a protein of 100 residues with 10 conformations each, $W_u = 10^{100}$.     $\Delta S_{fold} = R \ln(1/10^{100}) = -0.44\,kcal\,mol^{-1}\,K^{-1}$

  • At $T = 300\,K$, the free energy contribution $T\Delta S$ is approximately $-132\,kcal/mol$.

• Net Free Energy Calculation for a 100-Residue Protein:

  • Hydrophobic: 40 buried residues ($-2.4\,kcal/mol$ each) = $-96\,kcal/mol$.

  • Hydrogen bonds: 40 bonds ($-1\,kcal/mol$ each) = $-40\,kcal/mol$.

  • Electrostatic: 3 salt bridges ($-1\,kcal/mol$ each) = $-3\,kcal/mol$.

  • Dispersion: 100 interactions ($-0.03\,kcal/mol$ each) = $-3\,kcal/mol$.

  • Total Enthalpic/Hydrophobic Factors: $-142\,kcal/mol$.

  • Entropy of Folding Contribution: $132\,kcal/mol$.

  • Net $\Delta G$ for folding: $-10\,kcal/mol$.

• Marginal Stability:     $\Delta G = \Delta H - T\Delta S$

  • free energy of folding has a large entropic and enthalpic contribution

  • enthalpically: non-covalent interactions favour folding

  • entropically: the separation of hydrophobic residues and solvent is favourable but the folding is unfavourable.

  • The net free energy ($\approx -10\,kcal/mol$) indicates that proteins are only marginally stable and can be easily destabilised by mutations, or changes of the environment (pH, temperature, or salt changes).

Protein Folding Kinetics and Pathways

• Experimental Findings:

  1. Folding is spontaneous.

  2. Folding is fast (milliseconds to seconds).

  3. Folding is cooperative (not a slow step-by-step process).

  4. thermodynamics suggests a free energy for folding of around -10kcal/mol

• Levinthal’s Paradox:

  • A protein with 100 amino acids and 10 conformations per residue has $10^{100}$ total possible conformations.

  • assume each conformation can be sample via internal rotations

  • If rotations occur at $10^{13}$ per second, sampling all conformations would take $10^{87}$ seconds ($10^{80}$ years).

  • Since the universe is only $1.4 \times 10^{10}$ years old and folding takes <1\,s, random "trial and error" sampling is impossible.

  • Consequence: folding times in experiment of up to 1s: there is more folding than just the sequence-structure relationship

    • folding must be biased towards native structures

    • proteins follow some pathways rather than randomly sampling

  • the amino acid sequence encodes protein structure and the different folding pathways

• Anfinsen's Experiment (1961):

  • Studied Ribonuclease A folding in bovine pancreatic ribonuclease

  • The protein was reduced with mercaptoethanol in $8\,M$ urea to yield a randomly coiled polypeptide chain.

  • Under optimal conditions of polypeptide pH and concentration, the protein reformed disulfide bonds of the native enzyme which occurs in the presence of molecular oxygen

• Disulfide Bond Formation (Bovine Pancreatic Trypsin Inhibitor - BPTI):

  • 58-residue protein with three native disulfide bonds: 5-55, 30-51, and 14-38.

  • Experimental folding shows multiple intermediate species (e.g., 5-51, 5-55, 30-51, 5-30, etc.).

  • Folding is complex and can involve non-native intermediates.

• Folding Pathway of Lysozyme:

  • multiple intermediates and multiple pathways observed

  • alpha-helices form first.

  • beta-sheets form later.

The Role of Chaperones

• Functions:

  • Actively support protein folding directly.

  • Stabilise folding intermediates to prevent protein aggregation (e.g., Hsp33).

  • Assist in protein transport across membranes.

• GroEL/GroES Complex:

  • Dimensions: Height of 184 Å with GroES; GroEL width varies from 140 Å to 80 Å. Cavity heights and widths: 33 Å, 10 Å, 71 Å.

  • Mechanism:

    • The "Closed state" exposes hydrophobic surfaces to attract the unfolded protein.

    • The "Open state" (hydrophilic residues exposed) hides hydrophobic surfaces, allowing the protein to fold in a protected environment.

Protein Misfolding and disease

• Sickle Cell Anaemia:

  • Caused by a single mutation of Glutamate (Glu) to Valine (Val).

  • The Valine in the beta-chain fits into a hydrophobic pocket formed by Phenylalanine (Phe) and Isoleucine (Ile).

  • This causes haemoglobin molecules to link up and form long fibres that rupture red blood cells.

• Alzheimer's Disease:

  • Described by Alois Alzheimer (1906) as striking changes in neurofibrils.

  • Proteins aggregate into thick bundles or tangles of fibrils, leading to neuron disintegration.

  • Associated with Amyloid-beta 42 fibrils.

• Prion Diseases (e.g., Creutzfeld-Jacob Disease):

  • PrP protein exists in two inconvertible forms (causative agent):

    1. PrPc (Normal cellular form): Dominantly alpha-helical, susceptible to proteolysis.

    2. PrPSc (Abnormal Scrapie form): Higher beta-sheet, less a-helical content, protease-resistant, aggregates of PrPsc are insoluble.

  • The PrP^{Sc} form acts as a "seed" to aggregate normal PrP^c.

  • CryoEM structures (PDB: 6AXZ, 6UUR) show tight, regular packing of beta-sheets in a hydrophobic core.

• General Pathological Misfolding:

  • Aggregation via beta-sheet formation is common.

  • Examples including Parkinson's disease, Huntington's disease, Type II diabetes, and cataracts.