Mr. Residue’s Neighborhood: Using Correlated Mutations,

Mutual Information Statistics, and

Neural Networks in Residue-Residue Contact

Predictions

George Shackelford

Goal:Protein Structure Prediction

If nothing else, we could help the crystallographers.

Structure Prediction Methods

1D Methods Secondary Structure Prediction Hydrophobicity

3D Methods Structure-Structure Alignment Undertaker

What about 2D?

Residue-Residue Contacts

Given a protein sequence we say that two residues, indexed as i and j, are in \underline{contact} if the distance between their respective C_{β} atoms is less than 8 Å.

Nothing to do with Van der Waals distance This definition is arbitrary! They help with the tertiary structure We define \underline{separation} as |i − j|

How do we find these contacts?

Correlated Mutations

When a residue in a protein structure mutates, there is a possibility that an nearby residue will mutate.

salt bridges other sidechain-sidechain interactions functional regions possible size fittings

How can we detect these correlated mutations?

Using Mutual Information

Given residue indices, i and j, and the pair of columns, columns_{i,j}, under i and j we define the mutual information, MI, as

MI(i, j) = ∑_{(k,l) ∈ columns_{i,j}} p(k, l) log_{2} \frac{p(k, l)}{p(k) p(l)}

where p(k,l) is the joint probability of the corresponding residues k and l from the two columns and p(k),p(l) are the marginal probabilities. When the columns are independent MI is 0. When the columns are perfectly conserved, this value is also 0.High values of MI indicate a correlation.

University of California, Santa Cruz – p.5/18

Using Mutual Information

Problems: Likely to over-estimate when sample is small Having many recently evolved sequences can skew MI

Small Sample Correction

We hold the marginal probabilities fixed, and randomly re-arrange the joint probabilities, re-calculating the MI each time. Then we plot these values as a histogram, and fit a Gamma distribution to it. Using this distribution and the orginal MI, we can calculate an e-value.

Thinning

we thin the set of sequences in the alignment by removing those that have less than a specified percent of identity with at least one other sequence in the set. The we re-calcuate the MI and e-values using the thinned set.

Scoring Methods

S(i, j) represents our prediction of a contact between i and j and given some threshold, t: Accuracy

\frac{∑_{S(i,j)<t} Contact(i, j)}{|S(i, j) < t|}

Enrichment

\frac{∑S(i,j)<t \frac{Contact(i,j)}{P (|i−j|)}}{|S(i, j) < t|}

Results of Corrections

University of California, Santa Cruz – p.10/18

Results of Thinning

University of California, Santa Cruz – p.11/18

Neural Network

University of California, Santa Cruz – p.12/18

Inputs: Alphabets

University of California, Santa Cruz – p.13/18

Inputs: Distributions

University of California, Santa Cruz – p.14/18

Inputs: Neighboring Residues

University of California, Santa Cruz – p.15/18

Results

University of California, Santa Cruz – p.16/18

Conclusions

University of California, Santa Cruz – p.17/18

Future Work

University of California, Santa Cruz – p.18/18