GRAVY Score and Kyte-Doolittle Hydrophobicity

GRAVY (grand average of hydropathy) is the mean Kyte-Doolittle hydropathy value across every residue in a sequence: sum each residue’s value and divide by sequence length. A positive score means a more hydrophobic sequence on average; a negative score means a more hydrophilic one. This post explains where that scale comes from and how GRAVY compares to three other sequence-level calculators.

The Kyte-Doolittle scale

In 1982, Kyte and Doolittle published a hydropathy value for each of the 20 standard amino acids, derived from a combination of water-vapor transfer free energies and side chain burial preferences observed in known protein structures. Positive values mark more hydrophobic residues (isoleucine at 4.5, valine at 4.2), and negative values mark more hydrophilic ones (arginine at -4.5, lysine at -3.9). This is the same scale used throughout this site’s amino acid reference data.

What is the GRAVY score formula?

GRAVY = sum(Kyte-Doolittle value for each residue) / number of residues

That is the entire calculation: look up each residue’s hydropathy value, sum them, and divide by the sequence length. The GRAVY / hydrophobicity calculator runs exactly this. A positive GRAVY score indicates a sequence that is, on average, more hydrophobic; a negative score indicates one that is more hydrophilic. It says nothing about where along the sequence the hydrophobic residues sit, only the average.

A cruder but more direct read: fraction of residues by class

GRAVY averages a continuous scale, which means a few strongly hydrophobic residues can be offset by a few strongly hydrophilic ones and still land near zero. A more direct question is simply what fraction of the sequence falls into each class of side chain. This site’s amino acid reference data classifies every residue as nonpolar, polar, acidic, basic or aromatic (aromatic residues are also nonpolar but tracked separately since they matter for other calculations).

The hydrophobic residue fraction calculator reports the percentage of nonpolar and aromatic residues, and the polar residue fraction calculator reports the percentage of polar residues. Neither one weights by how hydrophobic or hydrophilic a residue is, only whether it belongs to that class, so they answer a coarser but easier to interpret question than GRAVY does.

Aliphatic index: a narrower hydrophobicity-adjacent number

The aliphatic index, from Ikai (1980), is not the same measurement as GRAVY, even though both relate to hydrophobicity. It only looks at four residues (alanine, valine, isoleucine, leucine) and weights them by the relative volume their aliphatic side chains occupy:

aliphatic index = %Ala + 2.9 x %Val + 3.9 x (%Ile + %Leu)

The coefficients 2.9 and 3.9 come directly from Ikai’s published relative volumes for valine and for isoleucine/leucine respectively. The aliphatic index calculator applies this formula to a sequence’s residue percentages. It is traditionally used as a rough thermostability proxy rather than a general hydrophobicity summary, and it ignores every residue outside that set of four entirely.

Boman index: interaction potential, not hydrophobicity itself

The Boman index, from Boman (2003), sums a different quantity: the mean free energy of transfer for each residue’s side chain, built on Guy’s water to octanol transfer values from 1985. It is framed as a potential protein interaction index, a proxy for how readily a peptide might bind other proteins, and it is calculated as a mean rather than a weighted percentage sum:

Boman index = mean(transfer free energy value for each residue)

The Boman index calculator computes this mean directly from the same per-residue reference values used throughout this site. It correlates with hydrophobicity in a general sense (residues with large hydrophobic transfer penalties tend to also score high on Kyte-Doolittle) but is measuring a distinct published quantity, not a restatement of GRAVY.

Reading these together

None of these four numbers, GRAVY, hydrophobic and polar fraction, aliphatic index, and Boman index, is a substitute for the others. Each is a named, citable summary of a sequence’s composition, built from a specific published scale, and each answers a slightly different question about the same set of residues. Comparing more than one gives a fuller picture than any single number alone.

In short, GRAVY equals the sum of each residue’s Kyte-Doolittle hydropathy value divided by sequence length, the single average that aliphatic index and Boman index each measure differently.

Primary scientific literature and citations

Kyte, J., & Doolittle, R. F. (1982). A simple method for displaying the hydropathic character of a protein. Journal of Molecular Biology, 157(1), 105-132. PubMed PMID: 7108955. DOI: 10.1016/0022-2836(82)90515-0. The original publication defining hydropathy indices for the 20 common amino acids and formulating the Grand Average of Hydropathy (GRAVY).
Ikai, A. (1980). Thermostability and aliphatic index of globular proteins. Journal of Biochemistry, 88(6), 1895-1898. PubMed PMID: 7462208. Formulated the aliphatic index equation based on the relative volume of alanine, valine, isoleucine, and leucine side chains.
Boman, H. G. (2003). Antibacterial peptides: basic facts and emerging concepts. Journal of Internal Medicine, 254(3), 197-215. PubMed PMID: 12930229. Defined the protein-binding index (Boman index) derived from amino acid transfer free energies.
Guy, H. R. (1985). Calculating and displaying the hydrophobicity of amino acid sequences. Biophysical Journal, 47(1), 61-70. PubMed PMID: 3978203. Established the transfer free energy scales from water to octanol that calibrate peptide-protein interaction indices.