BiologyBiochemistryUniversity
AQAAPOntarioNSWCBSEGCE O-LevelMoECAPS

Hill Equation (Fractional Saturation) Calculator

Models cooperative ligand binding (fractional saturation $\theta$).

Use the free calculatorCheck the variablesOpen the advanced solver
Open Advanced Calculator
This is the free calculator preview. Advanced walkthroughs stay in the app.
Result
Ready
Fractional Saturation

Formula first

Overview

The Hill Equation describes the fraction of a macromolecule saturated by a ligand as a function of the ligand concentration. It is primarily used to quantify cooperative binding in multi-site proteins, where the binding of one ligand influences the affinity of subsequent binding sites.

Symbols

Variables

= Fractional Saturation, [L] = Ligand Concentration, = Dissociation Constant, n = Hill Coefficient

Fractional Saturation
Variable
[L]
Ligand Concentration
Variable
Dissociation Constant
Variable
Hill Coefficient
Variable

Apply it well

When To Use

When to use: Apply this formula when analyzing sigmoidal binding curves that deviate from standard hyperbolic Michaelis-Menten kinetics. It is appropriate for systems where multiple binding sites interact, such as hemoglobin or multi-subunit enzymes, at equilibrium.

Why it matters: Quantifying cooperativity explains how biological systems achieve high sensitivity to small changes in ligand concentration. This switch-like behavior is essential for physiological processes like oxygen transport and metabolic regulation.

Avoid these traps

Common Mistakes

  • Using in different units than .
  • Convert units and scales before substituting, especially percentages, time units, or powers of ten.
  • Interpret the answer with its unit and context; a percentage, rate, ratio, and physical quantity do not mean the same thing.

One free problem

Practice Problem

The protein Myoglobin binds Oxygen with a Hill coefficient n=1.0 (non-cooperative) and = 2 mmHg. Calculate the fractional saturation θ when the partial pressure of Oxygen is 2 mmHg.

Ligand Concentration2
Dissociation Constant2
Hill Coefficient1

Solve for: theta

Hint: θ = [L]^n / (Kd + [L]^n). Since n=1, θ = [L] / (Kd + [L]).

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Lehninger Principles of Biochemistry by David L. Nelson and Michael M. Cox
  2. Biochemistry by Donald Voet, Judith G. Voet, and Charlotte W. Pratt
  3. Wikipedia: Hill equation (biochemistry)
  4. IUPAC Gold Book
  5. Lehninger Principles of Biochemistry
  6. Atkins' Physical Chemistry
  7. Lehninger Principles of Biochemistry, 7th Edition
  8. Atkins' Physical Chemistry, 11th Edition