CS-BLAST

Alignment sensitivity is measured by correctly comparing predicted alignments of residue pairs to the total number of possible alignable pairs. This is calculated with the fraction: (pairs correctly aligned)/(pairs structurally alignable)

Alignment precision is measured by the correctness of aligned residue pairs. This is calculated with the fraction: (pairs correctly aligned)/(pairs aligned)

The graph is the benchmark Biegert and Söding used to evaluate homology detection. The benchmark compares CS-BLAST to BLAST using true positives from the same superfamily versus false positive of pairs from different folds [4]. (A GRAPH NEEDS TO GO HERE)

The other graph uses detects true positives (with a different scale than the previous graph) and false positives of PSI-BLAST and CSI-BLAST and compares the two for one to five iterations [4]. (A DIFFERENT GRAPH NEEDS TO GO HERE)

CS-BLAST offers improved sensitivity and alignment quality in sequence comparison. Sequence searches with CS-BLAST are more than twice as sensitive as BLAST [4]. It produces higher quality alignments and generates reliable E-values without a loss of speed. CS-BLAST detects 139% more homologous proteins at a cumulative error rate of 20% [2]. At a 10% error rate, 138% more homologs are detected, and for the easiest cases at a 1% error rate, CS-BLAST was still 96% more effective than BLAST [2]. Additionally, CS-BLAST in 2 iterations is more sensitive than 5 iterations of PSI-BLAST. About 15% more homologs were detected in comparison [4].

Given an observed variable ${\displaystyle x}$ and a target variable ${\displaystyle y}$, a generative model defines the probabilities ${\displaystyle P(x,y)}$ and ${\displaystyle P(y)}$ separately. In order to predict the unobserved target variable, ${\displaystyle y}$, Bayes’ theorem, ${\displaystyle P(y|x)=\left({\frac {P(x|y)P(y)}{[\textstyle \sum _{y}P(x|y)P(y)\displaystyle ]}}\right)}$

is used. A generative model, as the name suggests, allows one to generate new data points ${\displaystyle (x,y)}$. The joint distribution is described as ${\displaystyle P(x,y)=P(x|y)P(y)}$. To train a generative model, the following equation is used to maximize the joint probability ${\displaystyle \prod \left({\frac {P(x_{n},y_{n})}{trainingData(x_{n},y_{n})}}\right)}$.

The discriminative model is a logistic regression maximum entropy classifier. With the discriminative model, the goal is to predict a context specific substitution probability given a query sequence. The discriminative approach for modeling substitution probabilities,${\displaystyle P(a|C_{l})}$ where ${\displaystyle C_{l}}$ describes a sequence of amino acids around position ${\displaystyle l}$ of a sequence, is based on ${\displaystyle K}$ context states. Context states are characterized by parameters emission weight (${\displaystyle v_{k}(a)}$), bias weight (${\displaystyle \pi _{k}}$), and context weight (${\displaystyle \lambda _{k}(j,a)}$) [2]. Emission probabilities from a context state are given by the emission weights as follows for ${\displaystyle d=1}$ to ${\displaystyle 20}$: ${\displaystyle P(a|k)=\left({\frac {exp(v_{k}(a))}{\sum exp(v_{k}(a'))}}\right)}$

where ${\displaystyle P(a|k)}$ is the emission probability and is the context state. In the discriminative approach, probability for a context state ${\displaystyle k}$ given context ${\displaystyle C_{l}}$ is modeled directly by the exponential of an affine function of the context account profile where ${\displaystyle C_{l}(j,a)}$ is the context count profile with a normalization constant ${\displaystyle Z(C_{l})}$ normalizes the probability to 1. This equation is as follows where the first summation takes ${\displaystyle j=-d}$ to ${\displaystyle d}$ and the second summation takes ${\displaystyle a=1}$ to ${\displaystyle 20}$: ${\displaystyle P(k|C_{l})=\left({\frac {1}{Z(C_{l})}}exp(\pi _{k}+\pi \sum \sum \lambda _{k}(j,a)(C_{l}(j,a))\right)}$.

As with the generative model, target distribution is obtained by mixing the emission probabilities of each context state weighted by the similarity.