**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 and the remaining 40% of sequences have a leucine, at position *j* the distribution is 40% isoleucine, 40% histidine and 20% 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: .

Here, P_{i}x describes the probability of finding amino acid *x* at position *i*, and is defined by a function in binomial form as follows:

where N is 100, n_{x} is the percentage of sequences with residue *x* (e.g. methionine) at position *i*, and p_{x} 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 ΔG_{i}stat is computed, the conservation for position *i* in a subalignment produced after a perturbation of amino acid distribution at *j* (ΔG_{i | δj}stat) is taken. Statistical coupling energy, denoted ΔΔG_{i, j}stat, is simply the difference between these two values. That is:

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*.

Read more about this topic: Statistical Coupling Analysis

### Famous quotes containing the words definition of, energy, coupling and/or definition:

“... we all know the wag’s *definition of* a philanthropist: a man whose charity increases directly as the square of the distance.”

—George Eliot [Mary Ann (or Marian)

“The persons who constitute the natural aristocracy, are not found in the actual aristocracy, or, only on its edge; as the chemical *energy* of the spectrum is found to be greatest just outside of the spectrum.”

—Ralph Waldo Emerson (1803–1882)

“The time of the seasons and the constellations

The time of milking and the time of harvest

The time of the *coupling* of man and woman

And that of beasts. Feet rising and falling.

Eating and drinking. Dung and death.”

—T.S. (Thomas Stearns)

“According to our social pyramid, all men who feel displaced racially, culturally, and/or because of economic hardships will turn on those whom they feel they can order and humiliate, usually women, children, and animals—just as they have been ordered and humiliated by those privileged few who are in power. However, this *definition* does not explain why there are privileged men who behave this way toward women.”

—Ana Castillo (b. 1953)