Table 1 Nomenclature and abbreviations

Posterior cumulative distribution function for the values of the property Ω at position i, given the previously known group of n amino acids present in the multiple alignment at such position

Cumulative distribution function of the absolute difference between the variances of any two properties Ω1 and Ω2 for a random combination of n amino acids

Cumulative distribution function for a random combination of n amino acids and a given property Ω

Null hypothesis in the hypothesis test for differences

Alternative hypothesis in the hypothesis test for differences

Position number in the multiple alignment

Invariable determinant position

Amino acid numbering sub-index

Total number of physicochemical properties considered in the MOSST analysis

Number of possible pairwise combinations (subsets having two elements) of properties

Number of amino acids in a multiple alignment position (without taking gaps into account)

Total number of positions in the multiple alignment

Normal distribution function with unknown parameters μ(mean) and σ (variance)

Number of amino acids in position i of the multiple alignment (without taking gaps into account)

Non-synonymous single nucleotide polymorphism

= 1 - p _{i,(Ω1,Ω2), n}

Level of significance of the null hypothesis H ₀ for the difference of the variances of the properties Ω1 and Ω2 at position i of a multiple alignment containing n amino acids

= 1 - p _{i,(Ωr,Ωs),n}

Level of significance of the null hypothesis H ₀ for the difference of the variances of the properties Ωr and Ωs at position i of a multiple alignment containing n amino acids

Value of the m^th level of significance, obtained from the set of M levels of significance of the differences between variances for all the possible pairwise combinations of properties, sorted in ascending order, for a given position i of a multiple alignment

Probability of getting a certain value or less for the absolute difference Δσ _(Ω1,Ω2) between the variances of any two properties Ω1 and Ω2

Posterior probability distribution function for the values of the property Ω at position i, given the previously known group of n amino acids present in the multiple alignment at such position

Global probability of the null hypothesis being true considering all the properties together at position i , i.e. probability of all the variances being equal at position i of a multiple alignment

Probability of getting a certain value or less for the absolute difference Δσ _(Ω1,Ω2) between the variances of any two properties Ω1 and Ω2 at position i of a multiple alignment containing n amino acids

Probability of getting a certain value or less for the absolute difference Δσ _(Ωr,Ωs) between the variances of any two properties Ωr and Ωs at position i of a multiple alignment containing n amino acids

Cumulative probability of getting a certain value or less for the variance (σ_i,Ω,n) for a given property Ω in position i of a multiple alignment containing n amino acids

Discrete probability mass function for a random combination of n amino acids and any given property Ω

Cumulative probability of getting a certain value or less for the variance for a given property Ω

Global probability for the occurrence of the amino acid j considering all properties together at position i in the multiple alignment, i.e. probability of the amino acid j satisfying all the physicochemical requirements at position i

Probability of the amino acid j (any of the 20 natural amino acids) to be present at position i (containing n amino acids in the multiple alignment analyzed) in a new protein not included in the multiple alignment, according to property Ω or Ω _r

Property numbering sub-index

Variable determinant position

Variable irrelevant position

Unknown quantity or variable

Measure, value or score of the physicochemical property Ω or Ω _r for the amino acid j at position i of a multiple alignment

Measure, value or score of the physicochemical property Ω for the amino acid j

Absolute difference between the variances of any two properties Ω1 and Ω2

Absolute difference between the variances of any two properties Ω1 and Ω2 at position i of a multiple alignment containing n amino acids

Absolute difference between the variances of any two properties Ωr and Ωs at position i of a multiple alignment containing n amino acids

Mean (of a normal distribution)

Arithmetical average of the physicochemical property Ω in position i of the multiple alignment containing a number of n amino acids

Arithmetical average of the physicochemical property Ω

Variance (of a normal distribution)

Sample variance estimator (standard deviation) of the physicochemical property Ω in position i of the multiple alignment containing a number of n amino acids

Sample variance estimator (standard deviation) of the physicochemical property Ω

Test statistic for the (n +1)^th amino acid at position i of a multiple alignment containing n amino acids

Generic physicochemical property

Physicochemical properties 1, 2 and 3

Physicochemical properties r and s