# Statistical coupling analysis

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**Statistical Coupling Analysis (SCA)** is a method used in [bioinformatics](/source/Bioinformatics) to study how pairs of [amino acids](/source/Amino_acids) in a protein sequence [evolve together](/source/Covariation). It analyzes a [multiple sequence alignment](/source/Multiple_sequence_alignment) (MSA), which is a display of the sequences of many related proteins arranged to highlight similarities and differences. SCA measures how much the amino acid makeup at one position in the protein changes when the amino acid makeup at another position is altered. This relationship is quantified as **statistical coupling energy**. A higher coupling energy indicates that the amino acids at both positions are more likely to have co-evolved and are therefore functionally or structurally linked. In simpler terms, it helps scientists understand which parts of a protein are working together and how they have changed over evolutionary time.[1]

## Definition of statistical coupling energy

Statistical coupling energy measures how a perturbation of amino acid distribution at one site in an MSA affects the amino acid distribution at another site. For example, consider a multiple sequence alignment with sites (or columns) *a* through *z*, where each site has some distribution of amino acids. At position *i*, 60% of the sequences have a [valine](/source/Valine) and the remaining 40% of sequences have a [leucine](/source/Leucine), at position *j* the distribution is 40% [isoleucine](/source/Isoleucine), 40% [histidine](/source/Histidine) and 20% [methionine](/source/Methionine), *k* has an average distribution (the 20 amino acids are present at roughly the same frequencies seen in all proteins), and *l* has 80% histidine, 20% valine. Since positions *i*, *j* and *l* have an amino acid distribution different from the mean distribution observed in all proteins, they are said to have some degree of **conservation**.

In statistical coupling analysis, the conservation (ΔGstat) at each site (*i*) is defined as: \Delta G_i^{stat} = \sqrt{\sum_x (\ln P_i^x)^2}.[2]

Here, Pix describes the probability of finding amino acid *x* at position *i*, and is defined by a function in [binomial form](/source/Binomial_distribution#Mean) as follows:

P_i^x = \frac{N!}{n_x!(N - n_x)!}p_x^{n_x}(1 - p_x)^{N - n_x},

where N is 100, nx is the percentage of sequences with residue *x* (e.g. methionine) at position *i*, and px corresponds to the approximate distribution of amino acid *x* in all positions among all sequenced proteins. The summation runs over all 20 amino acids. After ΔGistat is computed, the conservation for position *i* in a subalignment produced after a perturbation of amino acid distribution at *j* (ΔGi | δjstat) is taken. Statistical coupling energy, denoted ΔΔGi, jstat, is simply the difference between these two values. That is:

\Delta\Delta G_{i, j}^{stat} = \Delta G_{i | \delta j}^{stat} - \Delta G_i^{stat}, or, more commonly, \Delta\Delta G_{i, j}^{stat} = \sqrt{\sum_x (\ln P_{i|\delta j}^x - \ln P_i^x)^2}

Statistical coupling energy is often systematically calculated between a fixed, perturbated position, and all other positions in an MSA. Continuing with the example MSA from the beginning of the section, consider a perturbation at position *j* where the amino distribution changes from 40% I, 40% H, 20% M to 100% I. If, in a subsequent subalignment, this changes the distribution at *i* from 60% V, 40% L to 90% V, 10% L, but does not change the distribution at position *l*, then there would be some amount of statistical coupling energy between *i* and *j* but none between *l* and *j*.

## Applications

Ranganathan and Lockless originally developed SCA to examine thermodynamic (energetic) coupling of residue pairs in proteins.[3] Using the [PDZ domain](/source/PDZ_domain) family, they were able to identify a small network of residues that were energetically coupled to a binding site residue. The network consisted of both residues spatially close to the binding site in the tertiary fold, called contact pairs, and more distant residues that participate in longer-range energetic interactions. Later applications of SCA by the [Ranganathan group](http://ranganathanlab.org/) on the [GPCR](/source/GPCR), [serine protease](/source/Serine_protease) and [hemoglobin](/source/Hemoglobin) families also showed energetic coupling in sparse networks of residues that cooperate in [allosteric communication](/source/Allosteric_enzyme).[4]

Statistical coupling analysis has also been used as a basis for computational protein design. In 2005, Socolich et al.[5] used an SCA for the [WW domain](/source/WW_domain) to create artificial proteins with similar [thermodynamic stability](/source/Equilibrium_unfolding#Thermal_denaturation) and [structure](/source/Protein_structure) to natural WW domains. The fact that 12 out of the 43 designed proteins with the same SCA profile as natural WW domains properly folded provided strong evidence that little information—only coupling information—was required for specifying the protein fold. This support for the SCA hypothesis was made more compelling considering that a) the successfully folded proteins had only 36% average [sequence identity](/source/Sequence_alignment) to natural WW folds, and b) none of the artificial proteins designed without coupling information folded properly. An accompanying study showed that the artificial WW domains were functionally similar to natural WW domains in [ligand binding affinity and specificity](/source/Ligand_(biochemistry)#Receptor/ligand_binding_affinity).[6]

In [*de novo* protein structure prediction](/source/Protein_structure_prediction#Ab_initio_protein_modelling), it has been shown that, when combined with a simple residue-residue distance metric, SCA-based scoring can fairly accurately distinguish native from non-native protein folds.[7]

## See also

[Mutual information](/source/Mutual_information)

## External links

- [What is a WW domain?](http://www.bork.embl-heidelberg.de/Modules/ww_summary.html)
- [Ranganathan lecture on statistical coupling analysis (audio included)](https://web.archive.org/web/20120213161040/http://esmane.physics.lsa.umich.edu/wl/external/ICSB/2005/20051021-umwlap001-02-ranganathan-movies/realaudio/f001.htm)
- [Protein folding — a step closer?](http://www.pandasthumb.org/archives/2005/10/protein-folding.html) - A summary of the Ranganathan lab's SCA-based design of artificial yet functional WW domains.

## References

1. ["Supplementary Material for 'Evolutionarily conserved networks of residues mediate allosteric communication in proteins.'"](http://www.hhmi.swmed.edu/Labs/rr/SCA.html)

1. Dekker; Fodor, A; Aldrich, RW; Yellen, G et al. (2004). "A perturbation-based method for calculating explicit likelihood of evolutionary co-variance in multiple sequence alignments". *Bioinformatics*. **20** (10): 1565–1572. [doi:10.1093/bioinformatics/bth128](https://doi.org/10.1093/bioinformatics/bth128). [PMID 14962924](https://pubmed.ncbi.nlm.nih.gov/14962924)

1. Lockless SW, Ranaganathan R (1999). "Evolutionarily conserved pathways of energetic connectivity in protein families". *Science*. **286** (5438): 295–299. [doi:10.1126/science.286.5438.295](https://doi.org/10.1126/science.286.5438.295). [PMID 10514373](https://pubmed.ncbi.nlm.nih.gov/10514373)

1. Suel; Lockless, SW; Wall, MA; Ranganathan, R et al. (2003). "Evolutionarily conserved networks of residues mediate allosteric communication in proteins.". *Nature Structural Biology*. **10** (1): 59–69. [doi:10.1038/nsb881](https://doi.org/10.1038/nsb881). [PMID 12483203](https://pubmed.ncbi.nlm.nih.gov/12483203). [S2CID 67749580](https://api.semanticscholar.org/CorpusID:67749580)

1. Socolich; Lockless, SW; Russ, WP; Lee, H; Gardner, KH; Ranganathan, R et al. (2005). "Evolutionary information for specifying a protein fold". *Nature*. **437** (7058): 512–518. [Bibcode:2005Natur.437..512S](https://ui.adsabs.harvard.edu/abs/2005Natur.437..512S). [doi:10.1038/nature03991](https://doi.org/10.1038/nature03991). [PMID 16177782](https://pubmed.ncbi.nlm.nih.gov/16177782). [S2CID 4363255](https://api.semanticscholar.org/CorpusID:4363255)

1. Russ; Lowery, DM; Mishra, P; Yaffe, MB; Ranganathan, R et al. (2005). "Natural-like function in artificial WW domains". *Nature*. **437** (7058): 579–583. [Bibcode:2005Natur.437..579R](https://ui.adsabs.harvard.edu/abs/2005Natur.437..579R). [doi:10.1038/nature03990](https://doi.org/10.1038/nature03990). [PMID 16177795](https://pubmed.ncbi.nlm.nih.gov/16177795). [S2CID 4424336](https://api.semanticscholar.org/CorpusID:4424336)

1. Bartlett GJ, Taylor WR (2008). ["Using scores derived from statistical coupling analysis to distinguish correct and incorrect folds in de-novo protein structure prediction."](https://archive.today/20121217204114/http://www3.interscience.wiley.com/cgi-bin/fulltext/116842426/HTMLSTART). *Proteins*. **71** (1): 950–959. [doi:10.1002/prot.21779](https://doi.org/10.1002/prot.21779). [PMID 18004776](https://pubmed.ncbi.nlm.nih.gov/18004776). [S2CID 33836866](https://api.semanticscholar.org/CorpusID:33836866). Archived from [the original](http://www3.interscience.wiley.com/cgi-bin/fulltext/116842426/HTMLSTART) on 2012-12-17.

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Adapted from the Wikipedia article [Statistical coupling analysis](https://en.wikipedia.org/wiki/Statistical_coupling_analysis) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Statistical_coupling_analysis?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.