Protein Ligand Binding Affinity: Converting Ki to ΔG

Note: This blog post is part of a series, and we are currently working on building a web server for these calculations to enhance user convenience. Please stay tuned for updates and upcoming features.

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There are several ways to express the affinity of binding between a protein and a ligand. Among various representation methods, in this article, we will explain the "conversion formula" that translates the inhibition constant (Ki), which indicates the strength of binding, into the energy-based value ΔG. We'll also discuss essential considerations when performing these conversions and provide a Python-based conversion script for your use.

 

Understanding Protein-Ligand Binding Affinity

In the world of biochemistry, understanding how proteins interact with ligands is fundamental. The affinity of binding quantifies how tightly a ligand binds to a protein, and it can be expressed in different ways. One common measure is the inhibition constant, denoted as Ki, and another is the Gibbs free energy change, ΔG.

Conversion Formula: Ki to ΔG

The conversion between Ki and ΔG involves a mathematical formula:

ΔG = -RT * ln(Ki)

Let's break down the components of this formula:

ΔG (Gibbs Free Energy Change): ΔG represents the change in Gibbs free energy, a critical parameter in thermodynamics. It describes the maximum reversible work a system can do under constant temperature and pressure. A negative ΔG indicates a spontaneous process, while a positive value suggests a non-spontaneous one. When ΔG is zero, the reaction is at equilibrium.

Ki (Inhibition Constant): Ki is the inhibition constant, a dimensionless value that quantifies the strength of the interaction between a protein and a ligand. It reflects how effectively a ligand inhibits the activity of a protein.

R (Gas Constant): R is the universal gas constant (1.987 cal/(mol·K)) used in the formula. It relates energy to temperature and pressure.

T (Temperature): Temperature (in Kelvin) at which the reaction occurs. Remember to convert Celsius to Kelvin (add 273.15) for this formula.

ln (Natural Logarithm): The natural logarithm function, denoted as "ln," helps convert Ki (dimensionless) into energy units.

 

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Here are two crucial points to consider:

1. Unit of ΔG: Verify whether ΔG is expressed in kilojoules, joules, or calories per mole. R values differ based on these units. In many papers, ΔG is reported in kilocalories per mole (kcal/mol).

2. Ki Unit and Scale: When plugging Ki into the formula, ensure you adjust the unit if it's expressed in nM. For example, if Ki is given as 19.4, you must convert it to the appropriate unit, such as 19.4 * 1e-9 for nM.

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Considerations and Python Conversion Script

When using the conversion formula, ensure you input the temperature in Kelvin, and take note of the units to maintain consistency. For practicality, we've created a Python script that incorporates these considerations:

import math

def ki_to_dg(ki, temperature_Celsius = 25):
    # R_J = 8.314  # J/(mol·K)
    R_cal = 1.987  # cal/(mol·K)
    temperature_Kelvin = temperature_Celsius + 273.15
    Ki = ki * 1e-9
    dg = -R_cal * temperature_Kelvin * math.log(Ki)	# cal/mol
    dg_kcal_mol = dg / 1000
    return dg_kcal_mol


# Example usage:
ki = 12
temperature = 25  # Replace with your temperature in Celsius
delta_g = ki_to_dg(ki, temperature)
print(f"ΔG = {delta_g} kcal/mol")

 

This script takes your Ki value, temperature in Celsius as inputs, and calculates ΔG in kilocalories per mole. Ensure that you adjust Ki to the appropriate unit, as demonstrated in the example.

Stay tuned for our upcoming web server, which will further simplify these conversions online. In the meantime, this Python script should help streamline your work in the lab or your research projects.

 

 

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Reference

1. https://www.novoprolabs.com/tools/deltag2kd

Calculate dissociation constant from ΔG

2. https://www.chem.purdue.edu/gchelp/howtosolveit/Thermodynamics/K_from_DelG.html

Equilibrium Constant from Delta G

3. https://en.wikipedia.org/wiki/Gas_constant

Gas constant - Wikipedia

4. https://www.toppr.com/guides/chemistry-formulas/gibbs-free-energy-formula/

Gibbs Free Energy Formula : Structure, Preparations and Properties

5. https://general.chemistrysteps.com/gibbs-free-energy-and-equilibrium-constant/