# Subfamily specific conservation profiles for proteins based on n-gram patterns

- John K Vries
^{1}Email author and - Xiong Liu
^{1}

**9**:72

**DOI: **10.1186/1471-2105-9-72

© Vries and Liu; licensee BioMed Central Ltd. 2008

**Received: **03 April 2007

**Accepted: **30 January 2008

**Published: **30 January 2008

## Abstract

### Background

A new algorithm has been developed for generating conservation profiles that reflect the evolutionary history of the subfamily associated with a query sequence. It is based on n-gram patterns (NP{*n,m*}) which are sets of *n* residues and *m* wildcards in windows of size *n+m*. The generation of conservation profiles is treated as a signal-to-noise problem where the signal is the count of n-gram patterns in target sequences that are similar to the query sequence and the noise is the count over all target sequences. The signal is differentiated from the noise by applying singular value decomposition to sets of target sequences rank ordered by similarity with respect to the query.

### Results

The new algorithm was used to construct 4,248 profiles from 120 randomly selected Pfam-A families. These were compared to profiles generated from multiple alignments using the consensus approach. The two profiles were similar whenever the subfamily associated with the query sequence was well represented in the multiple alignment. It was possible to construct subfamily specific conservation profiles using the new algorithm for subfamilies with as few as five members. The speed of the new algorithm was comparable to the multiple alignment approach.

### Conclusion

Subfamily specific conservation profiles can be generated by the new algorithm without aprioi knowledge of family relationships or domain architecture. This is useful when the subfamily contains multiple domains with different levels of representation in protein databases. It may also be applicable when the subfamily sample size is too small for the multiple alignment approach.

## Background

Protein homologs are amino acid sequences with a common evolutionary ancestor. Substitutions, insertions and deletions over the course of evolutionary time cause the patterns of residues and gaps in homologs to drift away from each other [1, 2]. Conservation profiles are a measure of the shared patterns that remain. The conserved regions revealed in profiles are useful for identifying sites that are important for structure and function [3]. Traditionally they have been constructed from multiple sequence alignments (MSA) using scoring matrices and weighted averages [4]. This approach yields a consensus profile that is a function of the sequence sample in the multiple alignment. It also requires a chain of assumptions that can be problematic. There are many ways to generate scoring matrices and these matrices vary in their sensitivity to remote homologs [5–8]. Many proteins contain multiple domains or overlapping and/or nested domains that strongly influence alignment [9]. Sequences for multiple alignments often require preprocessing to eliminate low complexity regions [10]. The protein sequence samples available for multiple alignment are frequently skewed requiring the application of weighting algorithms [11]. Finally, multiple alignment requires a parameterized gap penalty [12].

A new algorithm for generating sequence specific conservation profiles has been developed that avoids the assumptions associated with the MSA approach. It is based on n-gram patterns (NP{*n,m*}) which are sets of n residues and m wildcards in windows of size *n+m* that start with a residue.

Interest in these patterns was sparked by the success of an alignment-independent protein classification algorithm based on the distribution of NP{4,2} patterns [13]. A study was conducted comparing the classification results obtained using 4-grams in windows of 5 or 6 with published results obtained using PSI-BLAST [12]. Unpublished classification runs using windows of 7 with 3 gaps were also performed. Classification runs with 4-grams alone or with windows of 5 with 1 gap were not as effective as windows of 6 with 2 gaps. Increasing the size of the window to 7 with 3 gaps showed no further improvement in classification accuracy. It was also possible to lower the combinatoric complexity associated with NP{4,2} patterns by eliminating the wildcard in the first position without adversely affecting the results. Features of interest in NP{4,2} patterns included: (1) the inclusion of all possible n-gram combinations for 1 ≤ n ≤ 4; (2) a window wide enough to capture alpha helix and beta sheet related periodicities for 2 ≤ n ≤ 5; (3) an implied scoring matrix due to the presence of wildcards at variable positions; (4) a low probability for finding redundant n-gram patterns in the same sequence; (5) a high probability of family membership for two sequences that contain the same pair of non-overlapping NP{4,2} patterns; and (6) the existence of all theoretically possible NP{4,2} patterns in nature [13, 14]. The new algorithm generates conservation profiles by exploiting the difference in the distribution of NP{4,2} patterns between family and non-family members. Family membership is determined without apriori knowledge by analyzing the covariance of NP{4,2} pattern counts in sequence samples with progressively increasing degrees of similarity. Samples with low degrees of similarity contain mostly noise. Samples with high degrees of similarity contain mostly family members. This results in two variance patterns that can be separated using singular value decomposition (SVD). Separate reconstruction of the traces using the first and second eigenvectors provides an effective filter for detecting the weak signal generated by a small number of family members in a randomly distributed set of non-family members.

## Results

### Theoretical background

Let us define an n-gram pattern (NP{*n,m*}) in a protein sequence to be a set of *n* specific residues and *m* wildcards (gaps) in a window of size *w* where *w = n+m*. Let us represent the amino acid patterns in protein sequences as collections of overlapping n-gram patterns. If we add the constraint that an n-gram pattern must not begin with a wildcard in order to reduce the problem of combinatorics, each position in a protein sequence contains *(w-1)!/((w-1)-(n-1))!(n-1)!* unique n-gram patterns. If the sequence is also a member of a protein family that descended from a common evolutionary ancestor it will share a portion of its n-gram patterns with family members. This will lead to an n-gram pattern distribution for the family that differs from the distribution over the protein universe. Let us define the conservation profile for such a sequence as the ratio of the average n-gram pattern count at each position over its family members to the average n-gram pattern count over the protein universe. When there is apriori knowledge of family membership, determining the n-gram pattern conservation profile for a sequence is reduced to a straight-forward counting task. When family membership is not known a different approach is required.

If the n-gram patterns at each position in a query sequence are counted over the protein universe, a profile is obtained that is a mixture of signal and noise. The signal reflects the expectation for an n-gram pattern at each position given that it is a member of a protein family. The noise reflects the expectation for the same n-gram pattern over all sequences. It would be possible to obtain the conservation profile for the query sequence from the counts over the protein universe if the signal could be separated from the noise. This can be accomplished by separating the sequences in the protein universe into samples (bins) based on similarity to the query sequence. Bins with low degrees of similarity will contain mostly noise. Bins with high degrees of similarity will contain mostly signal. Since noise is randomly distributed, the covariance between signal and noise will be low. If a covariance matrix were generated from the bins, singular value decomposition [15] of the matrix should separate the variance into a set of eigenpairs reflecting mostly signal and a set of eigenpairs reflecting mostly noise. In such a case, conservation profiles could be obtained by reconstructing the samples with the eigenpairs reflecting predominantly signal.

The strength of a signal is a function of the size of its family and the degree of conservation of each n-gram pattern. For bins reconstructed from eigenpairs reflecting signal variance, the average amplitude should increase as the percentage of family members increases. The average amplitude of reconstructions from eigenpairs reflecting noise variance should go in the opposite direction. If the signal from the protein family were significantly stronger than the noise, it should appear in the first eigenpair.

*w*along the sequence one residue at a time. From a study of the statistical properties of NP{

*n,m*} patterns for 1 ≤

*n*≤ 5 and 0 ≤

*m*≤ 3 in the UniProt database [16] or the SPT data set (~2.1 M sequences), it is apparent that the useful range for

*n*and

*m*is very narrow. For all observed values of

*n*, the noise level is roughly proportional to the product of the probability of its residue elements. This implies that the noise level decreases as the value of

*n*increases. Unfortunately, raising

*n*to values higher than 4 results in NP{

*n,m*} sample sizes that are too small for statistical analysis. The value for

*m*has little effect on the noise level. Increasing the value of

*m*improves the ability to recognize patterns with gaps which is offset by an increase in combinatorial complexity. The presence of a variable gap creates an implied scoring matrix. A good compromise for the

*n*and

*m*parameters appears to be NP{4,2}. The distribution of NP{4,2} patterns is shown in Figure 1a. The plot shows that all possible NP{4,2} patterns (20^4*10), 1.6 M) occur in UniProt [16]. The sample sizes range from ~180,000 for the most common patterns to ~20 for the rarest patterns. The majority of patterns have a flat distribution with a sample size of ~4,000.

Since the strength of NP{4,2} conservation signals in a query sequence is a function of the size of the family and the degree of conservation at each position, families with more than 100 members and degrees of conservation greater than 25% have expected counts that are significantly greater than the counts expected for noise. Unfortunately, more than 2/3 of protein families have less than 100 members and degrees of conservation may be less than 25% [17]. One way to enhance the signal to noise ratio for these smaller families is to analyze shared pairs of NP{4,2} patterns. This increases the effective value of the *n* parameter to 5–8 depending on the degree of overlap. Allowing a variable gap between a pair of NP{4,2} patterns also extends the effective range of the *m* parameter. The distribution of the overlap between shared pairs of NP{4,2} patterns in the SPT data set is shown in Figure 1b. The highest probability is associated with an overlap of 5. This drops exponentially to a very small probability as the overlap approaches 0. This is demonstrated in Figure 1c which treats shared NP{4,2} pairs as events in a Poisson distribution [18]. The y-axis in this figure shows the expectation by random chance for the overlapping pairs in carbonic anhydrase (P00918) over the 2,128,677 sequences in the SPT data set for overlaps ranging from 0–5. The highest noise level (expectation by random chance) occurs when the overlap is zero which is equivalent to the NP{4,2} pattern by itself. The figure shows that the noise level drops as the effective value of the *n* parameter increases.

Let us define the offset between shared pairs of NP{4,2} patterns to be the absolute difference between the starting positions of the NP{4,2} pairs in each sequence. If the offset between shared sequences were a random event, it should reflect the distribution of the NP{4,2} pattern overlaps depicted in Figure 1b. Figure 1d which plots the offsets for NP{4,2} shared pairs from 100 randomly selected sequences from the SPT data set shows that more than 80% of the pairs have the same offset. This implies that the majority of shared NP{4,2} patterns form a fixed local alignment (NPLA). This suggests that sequence comparison based on pairs of NP{4,2} patterns with fixed offsets (NPLAs) should work better than pairs of patterns with variable offsets since NPLAs have a higher information content (higher signal to noise ratio in this context). The algorithm described in the next section generates conservation profiles for query sequences by counting the common elements in the NPLAs shared by family members. It identifies family membership by applying singular value decomposition to the covariance matrix created from samples of the protein universe with progressively increasing degrees of similarity to the query.

### The NPLA algorithm

### Computational efficiency

*n*residues) in common between all family members for 1 ≤

*n*≤ 4. It should be noted that this process was not related to NP{4,2} patterns. The objective was to lower the computational burden by eliminating up front a significant percentage of the sequences that had no chance of containing family members. The idea was to find an n-gram that was present in all family members and to eliminate processing on all sequences that did not contain that n-gram. The size of the n-gram was critical because smaller n-grams are more likely to be found in all family members, but larger n-grams were less likely to be found by random chance. The best balance was achieved with trigrams where

*n*= 3. Approximately 96% of all family members over the 8183 Pfam-A families had at least one trigram in common, while the expectation of finding a trigram match by random chance in the SPT data set was approximately 275. When

*n*was smaller than 3, the expectation of finding a match in the SPT data set by random chance was too high to be useful. When

*n*was larger than 3, the coverage for family members was too low. An inverted index was created mapping the trigrams in the SPT data set to integers representing UniProt accession numbers. A preprocessor for queries was constructed which looked up each trigram in the query sequence while incrementing the integer position of its UniProt accession number in a collection sequence. Sorting this buffer in descending order based on trigram hits and taking the first 40,000 members (top 2%) captured the majority of the family while eliminating 98% of the noise. This decreased the processing time by two orders of magnitude. Computational times of approximately 1 minute were achieved on conventional CPUs. Comparison of profiles generated with the complete and reduced SPT data set over a selection of 4,248 queries showed an average rmsd difference of less than 5%. This is illustrated for the P00918 profile in Figure 4. The example shown here is typical for all the ICPs generated from the SPT data set. The reduced SPT data was used in the studies comparing ICP conservation profiles to profiles generated from MSAs. The time complexity for the NPLA algorithm is comparable to the time complexity of the standard sequence search algorithms such as PSI-Blast. The time complexity of running PSI-BLAST on the SPT database is O(

*nl*), where

*n*is the number of sequences in the SPT database and

*l*is the length of the longest sequence [21, 22]. The time complexity of running the NPLA algorithm is O(

*n'l*), where

*n'*is the top 2% percent of the sequences in the SPT database.

### Comparison of the NPLA method and the consensus method

The NPLA algorithm generates a conservation profile that is different from the profile generated by MACP. The NPLA algorithm only sees family members that are related to the domains present in the query sequence. The MACP profile may see family members containing domains that are not part of the query sequence. This depends on the parameters used for multiple alignment. If the multiple alignment is constructed so that only the domains in the query sequence are represented in the alignment, the NPLA algorithm and the MACP algorithm should yield similar results. The NPLA algorithm yields a profile that is specific to the subfamily of the query sequence without requiring information about the domain and subdomain architecture of the family. The term ICP reflects that fact that the NPLA profile tends to be invariant with respect to sample size as long as five or more subfamily members are present.

To show the difference between the ICP profile and the MACP profile, the profiles from 120 randomly selected Pfam-A families were examined [17]. The Valdar-Thornton approach [4] was used to generate the MACPs. The mathematical basis for this method is outlined in the methods section. The test set was created from a list of Pfam-A accession numbers (8,183) that had been sorted into ascending order based on the number of members in each family's full alignment. Four samples of 30 accession numbers each were drawn from this list centered on N = 30, N = 100, N = 500 and N = 1000 where N was the number of sequences in the full alignment. The respective number of seed alignment sequences in each of the four samples were 203, 441, 1,666 and 1,938. Each family was clustered hierarchically according to the pairwise evolutionary distance between its family members using the approach outlined in the methods section. Subfamilies were simulated by generating MACPs from each cluster that contained the query sequence and a minimum of 20 members. Each MACP was compared to the corresponding ICP by advancing the traces against one another one position at a time and selecting the best rmsd fit. Prior to this step, the two traces were normalized for power so that each had an average power of 1.0 arbitrary units per position. The additional constraint that the shorter of the two sequences should have a minimum of 90% overlap was also enforced. The mathematical basis for the Valdar-Thornton approach, the details of the clustering approach and a table of the UniProt accession numbers used in this study are presented in the Methods Section.

Comparison of ICP and MACP as a function of cluster level

LEVEL | N30 | RMSD30 | N100 | RMSD100 | N500 | RMSD500 | N1000 | RMSD1000 |
---|---|---|---|---|---|---|---|---|

| 203 | 0.999 | 441 | 1.024 | 1666 | 0.954 | 1938 | 0.977 |

| 137 | 0.992 | 434 | 1.007 | 1666 | 0.944 | 1938 | 0.969 |

| 29 | 0.908 | 359 | 0.975 | 1649 | 0.933 | 1933 | 0.958 |

| 11 | 0.861 | 232 | 0.929 | 1599 | 0.928 | 1903 | 0.948 |

| 145 | 0.911 | 1523 | 0.922 | 1863 | 0.938 | ||

| 103 | 0.910 | 1373 | 0.915 | 1703 | 0.926 | ||

| 80 | 0.941 | 1100 | 0.919 | 1486 | 0.916 | ||

| 39 | 0.831 | 864 | 0.913 | 1252 | 0.901 | ||

| 19 | 0.820 | 667 | 0.898 | 1032 | 0.890 | ||

| 470 | 0.875 | 862 | 0.893 | ||||

| 346 | 0.871 | 672 | 0.878 | ||||

| 223 | 0.852 | 465 | 0.870 |

## Discussion and Conclusion

The NPLA algorithm generates conservation profiles by treating conservation as a signal-to-noise problem where the signal is the probability of shared pairs of NP{4,2} n-gram patterns between family members and the noise is the probability of those pairs by random chance. The NPLA conservation profiles are specific to the query sequence and cover all of its residues. The conservation profiles do not require multiple alignment or explicit scoring matrices and they are not influenced by multiple, overlapping or nested domains. The NPLA conservation profiles are generated from target sequence samples containing mixtures of signal (family members) and noise (non-family members). They are invariant as long as the overall count of family members is sufficient and there is a steady progression in the similarity of family members over the target samples from low to high.

Comparison of the ICP profiles generated by the NPLA algorithm with the MACP profiles generated from multiple sequence alignment over a large sample of Pfam-A families shows that the ICP trace is nearly identical to the MACP trace whenever the query sequence is well represented in the multiple alignment used for the MACP. The degree of representation can be assessed by examining the distribution of evolutionary distances over family members and comparing that with the distribution with respect to the query sequence. Query distributions with means below the means of their families tend to have good representations. The opposite is true for query distributions with means above their family means. The absolute value of the family mean is also important. If the mean is high, the family tends to have a high percentage of remote homologs. If the mean is low, the family tends to have a single dominant subfamily. When the query sequence is a good representation of the family consensus, the ICP and MACP traces are nearly identical. When the query sequence is poorly represented in the consensus, the MACP is not a good representation for the subfamily of the query. The ICP, however, remains valid as long as the criteria outlined in Figure 4 hold. These criteria are generally solid for any family with at least 30 members and they hold for some families with as few as 10 members.

In its original form, the NPLA algorithm required the query sequence to be compared with every sequence in UniProt. This was slow from a computational standpoint requiring up to 1 hour to process a single query. Since the distribution of the noise remains the same as long as the sample of noise is sufficient, a method that eliminates most noise, but does not eliminate the signal should lower the computational time without affecting the ultimate result. Such a method was developed based on an inverted index of trigrams. Detailed comparison studies showed that the noise could be reduced by 98% without changing the final result. Under these circumstances a processing time of 1 hour was reduced to 1 minute.

ICP conservation profiles can be rapidly generated for any query sequence without knowledge of domains or family relationships. The statistical validity of the traces is easy to assess. This approach provides a means for generating conservation profiles when the subfamily sample size is too small for the multiple alignment approach. Since the ICP is specific to the query sequence and it covers all the residues in the sequence, it is useful for studies that seek to correlate sequence derived features such as hydropathy or structure derived features such as normal modes (GNM) [23] with conservation. Studies are currently underway relating such features to the ICP using relative entropy measurements and Mahalanobis distances [24].

## Methods

### Database sources and histograms

The database for the studies in this paper contained data downloaded from the Pfam ftp site [25]. The data was downloaded on 02-Nov-2005. The database also contained a total of 2,345,429 entries from the UniProt database [16]. Exclusion of sequences shorter than 75 residues or longer than 1500 residues resulted in a final set of 2,128,677 sequences. This will be referred to as the SPT data set. The family memberships used in this paper were obtained from the Pfam-A.full file in the Pfam distribution. Pfam-A contained 8,183 families. This file also served as the source for the multiple alignments associated with each Pfam-A family.

The sequences in the SPT data set were parsed into a series of n-gram sets and n-gram pattern sets. N-grams are contiguous runs of n residues. N-gram patterns are contiguous runs of residues and wildcards (see below). Histograms reflecting the probability of a given n-gram were constructed for values of n ranging from 1 to 8. Similar histograms were constructed bracketing the range of n-gram patterns reported in this study.

### Consensus based conservation profiles

*Cons(i)*represents the degree of conservation at

*i*th position in a multiple alignment. It is a number that varies from a minimum of 0.0 to a maximum of 1.0. The total number of sequences in the multiple alignment is represented by

*N*.

*Mut(S*

_{ j }

*(i), S*

_{ k }

*(i))*represents the score associated with a mutation at the

*i*th position between the

*j*th and

*k*th sequences in the multiple alignment. The weights

*W*

_{ j }and

*W*

_{ k }associated with the

*j*th and

*k*th sequences are used to correct for sample skew. The mutation score

*Mut(a,b)*associated with a mutation of amino acid

*a*to amino acid

*b*is obtained from a substitution matrix using equation 2. The substitution matrix used in this study was BLOSSUM62 [2].

*m(a,b)*represents the score obtained from the substitution matrix when residue

*a*is replaced by residue

*b*while

*max(m)*and

*min(m)*represent the highest and lowest substitution scores in the matrix. This has the effect of normalizing the scores in the substitution matrix to the interval from 0.0 to 1.0. The weights used to correct for sample skew are calculated using equation 3. In this equation

*W*

_{ j }is the weight associated with the

*j*th sequence in the multiple alignment.

*N*is the total number of sequences in the multiple alignment and

*Dist(S*

_{ j },

*S*

_{ k }

*)*is the evolutionary distance between the

*j*th and the

*k*th sequences.

*Dist(S*

_{ j },

*S*

_{ k }

*)*between the

*j*th and

*k*th sequences in a multiple alignment is defined by equation 4. In this equation, sequences that are close to each

other from the evolutionary standpoint have small values for *Dist(S*_{
j
}, *S*_{
k
}*)*. The final MACP profile for each sequence was obtained by removing the non-residue positions in each sequence in the multiple alignment.

### Hierarchical clusters

Pfam-A Seed Alignment Sources used in ICP-MACP Comparison

S30 (N = 207) | S100 (N = 441) | S500 (N = 1,666) | S1000 (N = 1,931) | ||||
---|---|---|---|---|---|---|---|

PF02160 | PF07292 | PF00778 | PF03351 | PF00215 | PF01544 | PF00038 | PF00974 |

PF02262 | PF07298 | PF00812 | PF03428 | PF00251 | PF01555 | PF00079 | PF01032 |

PF02288 | PF07386 | PF01190 | PF03619 | PF00317 | PF01561 | PF00239 | PF01138 |

PF02509 | PF07413 | PF01199 | PF03663 | PF00328 | PF01638 | PF00285 | PF01423 |

PF02783 | PF07454 | PF01491 | PF03709 | PF00410 | PF01794 | PF00348 | PF01425 |

PF03068 | PF07515 | PF01500 | PF03914 | PF00464 | PF02491 | PF00437 | PF01699 |

PF03173 | PF07574 | PF01874 | PF03942 | PF00466 | PF02910 | PF00462 | PF02080 |

PF03206 | PF07775 | PF01946 | PF04221 | PF00636 | PF03062 | PF00481 | PF02811 |

PF03215 | PF07781 | PF02005 | PF04329 | PF00650 | PF03358 | PF00482 | PF02932 |

PF03409 | PF07842 | PF02076 | PF05047 | PF00781 | PF03507 | PF00498 | PF03764 |

PF03612 | PF07959 | PF02589 | PF05127 | PF00846 | PF04069 | PF00682 | PF03797 |

PF03676 | PF08001 | PF02709 | PF06761 | PF01056 | PF04607 | PF00690 | PF04539 |

PF03762 | PF08004 | PF02758 | PF07470 | PF01065 | PF05368 | PF00844 | PF07728 |

PF03829 | PF08315 | PF03140 | PF07486 | PF01409 | PF07478 | PF00899 | PF07885 |

PF03964 | PF08470 | PF03350 | PF08379 | PF01421 | PF08541 | PF00948 | PF08544 |

## Declarations

### Acknowledgements

Support by the NIH grant # 5R01LM007994-02 is gratefully acknowledged. We also thank Dr. Ivet Bahar for her helpful suggestions and thoughtful review of the manuscript.

## Authors’ Affiliations

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