L5: Protein Folding Landscapes, Kinetics, And Misfolding

Q = fraction of protein folding

horizontal = entropy - number of possible states

slopes - steeper towards N - incentivises proetin to ‘leave’ kinetic traps/transition states

Why do Statistical Distributions Matter in Folding?

• Proteins fold stochastically due to molecular fluctuations.

  • always fluctuation in the system

  • cooperativity

• Different distributions describe different aspects of folding dynamics.

  • local minima/transition state

  • free energies

  • end to end distance

Binomial Distribution - probability of protein being in folded/unfolded state @ equilibrium

Poisson Distribution - rare folding/unfolding events over time, single-molecule kinetics

Gaussian Distribution - distribution of native-state fluctuations and energy variations

Exponential Distribution - waiting times between folding transitions in an energy landscape

Energy Landscapes

• probability distributions of folding pathways

• diffusion folllows statistical laws

  • Random walk models - protein confformational exploration

  • Biased random walk - energy-driven folding

    • enthalpic contribution

    • folded vs unfolded - thermodynamic

• Mean Squared Displacement

  • efficiency of exploration

    • kinetics

    • ‘useless’ pathways/entropic conformations

    • slope of t vs MSD - lower slope = higher efficiency

Levinthal’s Paradox

100 residue polypeptide; 2 different ɸ and Ψ bond angles; each angle can be in one of 3 stable conformations.

Total conformations - 3²⁰⁰

If the protein tried each conformation in 1 femtosecond (10⁻¹⁵ sec), it would take longer than the age of the universe to find its native structure.

But in reality, proteins fold within milliseconds to minutes!

This paradox suggests that protein folding must be guided rather than purely random.

SOLVED - Anfinsen’s experiment (RNAase)

• Folding is not random but hierarchical.

• Early-stage interactions limit the search space.

• Folding energy barriers control rate-limiting steps.

How does nature solve the paradox?

physical and energetic constraints

• Energy Landscapes Guide Folding

  • biased energy funnel

  • reduce explorable conformations

  • restrict movements to lower-energy regions

• Directed Search via Local Interactions

  • Secondary structures (α-helices, β-sheets) - form early, limit search space

  • Hydrophobic collapse - reduces conformational freedom

  • local native-like interactions

• Parallel pathways

  • different parts may fold independently before assembling

  • flexibility

• Molecular Chaperones

  • Hsp70, GroEL, Hsp90

  • help prevent kinetic traps

  • stabilise partially folded states

  • create an isolated environment, preventing aggregation

x axis - kinetics

y axis - thermodynamics

Kinetics of Protein Folding & Transitions State Theory

Biochemistry - how far and how fast?

Why study kinetics? Folding time varies from microseconds to minutes, depending on solution conditions

What determines folding speed? Number of residues, number of intermediate conformations, Energy barriers and transition states, Chaperones and cellular crowding effects

Two-State vs. Multi-State Folding

ambient temperature + energetically favourable

larger energy difference = slower folding rate

how far? how stable will the resulting strcuture be?

Deep local minima → Kinetic traps → Misfolding risks.

Anfinsen’s experiment

trace amount of beta-mercaptoethanol - dissolves incorrect S-S bonds