Method - Protein Homology Detection Through Alignment of Markov Random Fields - page 19

such PSICOV, Evfold, plmDCA [ 2 4 ] as residue co-evolution. PSICOV assumes

-

that P ð X Þ is a Gaussian distribution function and calculates the correlation between

two columns by inverse covariance matrix. By contrast, plmDCA does not assume
a Gaussian distribution and is more ef

cient and also slightly more accurate.
Generally speaking, these programs are time-consuming.
The reliability of mutual information (MI) or direct information (DI) [ 2 ] depends
on the number of non-redundant sequence homologs. When there are few sequence
homologs, the resulting MI or DI is not very accurate. Therefore, it is not enough to
only use residue co-evolution strength to estimate residue interaction strength. We
can use other contact prediction programs such as PhyCMAP [ 4 ] which integrates
both residue col-evolution information, PSI-BLAST sequence pro le and others to

predict the probability of two residues in contact. PhyCMAP works much better
than PSICOV and Evfold when proteins under study have a small number of
sequence homologs [ 4 ].
In this work, we use predicted inter-residue Euclidean distance to re

ect inter-
action strength of two residues. This is based upon an assumption that two spatially-
close residues tend to have strong interaction. We predict the inter-residue distance
using sequence information such as mutual

fl

information and its power series,

PSI-BLAST sequence pro le and other protein features. See [ 5 ] for more details.

Below we brie y describe how to predict inter-residue distance from sequence

information using probabilistic neural networks (PNN).
We discretize C a C a

fl

distance into 13 bins (3 4, 4 5, 5 6, … ,14 15,

- - - -

and >15 ). Each bin is also called a label. Given a protein and a pair of two

residues i and j, let d k denote the bin into which their distance falls, and x k denote
the protein feature vector consisting of some position-speci

Å

le
information and also mutual information between two positions. We would like to
estimate the probability of observing d k given the feature vector x k :

c sequence pro

That is, instead
of only considering the most possible distance labels assigned to each pair of nodes
(residues), we would like to estimate the probability distribution of d k : The reason is

that the predicted distance probability distribution is more informative than a single
predicted value.
Formally, let p h ð

be the probability of the distance label d k conditioned on
the feature vector x k Meanwhile,

d k j x k Þ

h is the model parameter vector. We estimate

p h ð d k j x k Þ as follows:

exp ð L h ð d k ; x k ÞÞ

p h d k j x k ð Þ¼ ð 2 : 2 Þ

Z h ð x k Þ

x ðÞ¼ P d exp

where Z h is a two-

layer neural network. Figure 2.2 shows an example of the neural network with three
and

ð L h ð d ; x k ÞÞ; is the partition function and L h ð d ; x k Þ

first and second hidden layers, respectively. Each neuron is a
sigmoid function. The function L h ð

five neurons in the

d k ; x k Þ can be calculated as,