Linear free energy relationships in enzyme binding interactions studied by protein engineering

Area of Science:

• Biochemistry
• Enzyme kinetics
• Physical chemistry

Background:

• Linear free energy relationships (LFERs) have been observed in enzyme mutants, linking activation and binding energies.
• A recent proposal suggested LFERs with hydrogen bonding groups are restricted to specific Brønsted beta values (0, 1, infinity).
• This restriction was based on the non-linear energy-distance relationship of hydrogen bonds and a flawed premise about LFER requirements.

Purpose of the Study:

• To challenge the proposed limitations on LFERs with fractional Brønsted beta values.
• To demonstrate how LFERs can arise in binding interactions using a simple model.
• To reconcile theoretical models with experimental evidence regarding LFERs in enzymes.

Main Methods:

• Development of a simple theoretical model to explain LFERs in binding interactions.
• Analysis of the conditions under which LFERs can yield fractional Brønsted beta values.
• Comparison of model predictions with existing experimental data on enzyme catalysis.

Main Results:

• The study shows that LFERs can indeed arise in binding interactions, leading to fractional Brønsted beta values.
• The reasoning against fractional beta values based on hydrogen bond non-linearity is shown to be flawed.
• A key finding is that LFERs occur when interactions contribute proportionally to transition state and product binding energies relative to the ground state.

Conclusions:

• LFERs are not restricted to integer Brønsted beta values and can occur with fractional values, consistent with experimental findings.
• The non-linear nature of hydrogen bond energy with distance does not preclude LFERs with fractional beta.
• The established condition for LFERs involves proportional contributions of interactions to binding energies across different states.