Type: Package
Title: The tRNA Adaptation Index
Version: 0.2.2
Date: 2025-03-19
Description: Functions and example files to calculate the tRNA adaptation index, a measure of the level of co-adaptation between the set of tRNA genes and the codon usage bias of protein-coding genes in a given genome. The methodology is described in dos Reis, Wernisch and Savva (2003) <doi:10.1093/nar/gkg897>, and dos Reis, Savva and Wernisch (2004) <doi:10.1093/nar/gkh834>.
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
LazyData: TRUE
RoxygenNote: 7.3.2
Encoding: UTF-8
NeedsCompilation: no
Packaged: 2025-03-21 16:41:53 UTC; mario
Author: Mario dos Reis [aut, cre]
Maintainer: Mario dos Reis <mariodosreis@gmail.com>
Repository: CRAN
Date/Publication: 2025-04-16 14:50:02 UTC

E. coli K-12 codon bias and tRNA numbers

Description

A list with elements trna, a vector of length 64 of tRNA gene copy numbers in the Escherichia coli K-12 genome, w, a data frame with some codon bias statistics for 49 E. coli K-12 coding genes, and m, a 49 by 61 matrix of codon frequencies for the 49 genes in question.

Usage

ecolik12

Format

An object of class list of length 3.

Author(s)

Mario dos Reis

Examples

# 87 tRNA genes in the E. coli K-12 genome:
sum(ecolik12$trna)

# Two copies are isoacceptors for Phe, with anticodon GAA (codon TTC)
ecolik12$trna[2]

# ecolik12$w, a data frame with codon bias statistics
names(ecolik12$w)

# Effective number of codons vs. gene length (in codons)
plot(ecolik12$w$Nc, ecolik12$w$L_aa, xlab="Nc", ylab="Gene length")

Correlation between tAI and Nc adjusted

Description

Calculates the correlation between tAI and Nc (adjusted for GC content at third codon positions).

Usage

get.s(tAI, nc, gc3)

Arguments

tAI

a vector of length n with tAI values for genes

nc

a vector of length n with Nc values for genes

gc3

a vector of length n with GC content at third codon positions for genes

Value

Numeric of length one with the correlation between tAI and Nc adjusted

Author(s)

Mario dos Reis

The tRNA adaptation index

Description

Calculates the tRNA adaptation index (tAI) of dos Reis et al. (2003, 2004).

Usage

get.tai(x, w)

Arguments

x

an n by 60 matrix of codon frequencies for n open reading frames.

w

a vector of length 60 of relative adaptiveness values for codons.

Details

The tRNA adaptation index (tAI) is a measure of the level of co-adaptation between the set of tRNA genes and the codon usage bias of protein-coding genes in a given genome. STOP and methionine codons are ignored. The standard genetic code is assumed.

Value

A vector of length n of tAI values.

Author(s)

Mario dos Reis

References

dos Reis M., Wernisch L., and Savva R. (2003) Unexpected correlations between gene expression and codon usage bias from microarray data for the whole Escherichia coli K-12 genome. Nucleic Acids Res., 31: 6976–85.

dos Reis M., Savva R., and Wernisch L. (2004) Solving the riddle of codon usage preferences: a test for translational selection. Nucleic Acids Res., 32: 5036–44.

See Also

get.ws

Examples

# Calculate relative adaptiveness values (ws) for E. coli K-12
eco.ws <- get.ws(tRNA=ecolik12$trna, sking=1)

# Calculate tAI for a set of 49 E. coli K-12 coding genes
eco.tai <- get.tai(ecolik12$m[,-33], eco.ws)

# Plot tAI vs. effective number of codons (Nc)
plot(eco.tai, ecolik12$w$Nc, xlab="tAI", ylab="Nc")

Relative adaptiveness values

Description

Calculates the relative adaptiveness values of codons based on the number of tRNA genes.

Usage

get.ws(tRNA, s = NULL, sking)

Arguments

tRNA

a vector of length 64 with tRNA gene copy numbers

s

a vector of length 9 with selection penalties for codons

sking

a vector of length 1 indicating the superkingdom

Details

The relative adaptiveness values are calculated as described in dos Reis et al. (2003, 2004). If s = NULL, the s values are set to the optimised values of dos Reis et al. (2004). sking indicates the superkingdom, with 0 indicating Eukaryota, and 1 Prokaryota.

Value

A vector of length 60 of relative adaptiveness values.

Author(s)

Mario dos Reis

References

dos Reis M., Wernisch L., and Savva R. (2003) Unexpected correlations between gene expression and codon usage bias from microarray data for the whole Escherichia coli K-12 genome. Nucleic Acids Res., 31: 6976–85.

dos Reis M., Savva R., and Wernisch L. (2004) Solving the riddle of codon usage preferences: a test for translational selection. Nucleic Acids Res., 32: 5036–44.

Examples

eco.ws <- get.ws(tRNA=ecolik12$trna, sking=1)

Adjusted effective number of codons (Nc)

Description

The adjusted Nc is f(gc3s) - Nc

Usage

nc.adj(nc, gc3)

Arguments

nc

a vector of length n with the effective number of codons for genes

gc3

a vector of length n with corresponding GC composition at third codon positions

Details

The adjusted Nc is calculated as described in dos Reis et al. (2004).

Value

A vector of length n with adjusted Nc values

Author(s)

Mario dos Reis

References

dos Reis M., Savva R., and Wernisch L. (2004) Solving the riddle of codon usage preferences: a test for translational selection. Nucleic Acids Res., 32: 5036–44.

See Also

nc.f for the function used to calculate f(gc3s)

Examples


eco.ncadj <- nc.adj(ecolik12$w$Nc, ecolik12$w$GC3s)
plot(eco.ncadj ~ ecolik12$w$Nc, xlab="Nc", ylab="Nc adjusted")

Nc vs. GC3s

Description

Calculates the expected Nc value of a gene for a given GC content at the third codon positions.

Usage

nc.f(x)

Arguments

x

a vector of GC contents at third codon positions

Details

Without selection on codon bias, the expected value of Nc as a function of GC content at third positions, x, is given by

f(x) = -6 + x + 34/(x^2 + (1.025 - x)^2).

This equation follows dos Reis et al. (2004, see also Wright 1990 for the original).

Value

A vector of Nc values for the given GC contents.

Author(s)

Mario dos Reis

References

Wright F. (1990) The 'effective number of codons' used in a gene. Gene, 87: 23–9.

dos Reis M., Savva R., and Wernisch L. (2004) Solving the riddle of codon usage preferences: a test for translational selection. Nucleic Acids Res., 32: 5036–44.

Examples

curve(nc.f(x), xlab="GC3s content", ylab="Nc")
points(ecolik12$w$GC3s, ecolik12$w$Nc, pch=19)

Monte Carlo test of correlation between tAI and Nc adjusted

Description

Calculates the p-value (using a Monte Carlo or randomisation test) that the correlation (the S value) between tAI and the adjusted Nc for a set of genes is different from zero.

Usage

ts.test(m, ws, nc, gc3s, ts.obs, samp.size, n = 1000)

Arguments

m

a k by 60 matrix of codon frequencies for k genes

ws

vector of length 60 of relative adaptiveness values of codons

nc

vector of length k of Nc values for genes

gc3s

vector of length k of GC content at third codon position for genes

ts.obs

vector of length 1 with observed correlation between tAI and Nc adjusted for the k genes

samp.size

a vector of length 1 with the number of genes to be sampled from m (see details)

n

the number of permutations of ws in the randomisation test

Details

The Monte Carlo test is described in dos Reis et al. (2004). When working with complete genomes, matrix m can have a very large number of rows (large k). In this case it may be advisable to choose samp.size < k to speed up the computation.

Value

A list with elements p.value, the p-value for the test, and ts.simulated, a vector of length n with the simulated correlations between tAI and adjusted Nc.

Author(s)

Mario dos Reis

References

dos Reis M., Savva R., and Wernisch L. (2004) Solving the riddle of codon usage preferences: a test for translational selection. Nucleic Acids Res., 32: 5036–44.

Examples

eco.ws <- get.ws(tRNA=ecolik12$trna, sking=1)
eco.tai <- get.tai(ecolik12$m[,-33], eco.ws)
ts.obs <- get.s(eco.tai, ecolik12$w$Nc, ecolik12$w$GC3s)

# The S-value (dos Reis et al. 2004):
ts.obs # [1] 0.9065442

# There seems to be a high correlation between tAI and Nc adjusted for
# the 49 genes in ecolik12$m. Is the correlation statistically significant?
ts.mc <- ts.test(ecolik12$m[,-33], eco.ws, ecolik12$w$Nc, ecolik12$w$GC3s, 
                 ts.obs, samp.size=dim(ecolik12$m)[1])
# The p-value is zero:
ts.mc$p.value # [1] 0

# Histogram of simulated S-values:
hist(ts.mc$ts.simulated, n=50, xlab = "Simulated S values", 
     xlim=c(min(ts.mc$ts.simulated), ts.obs))
# Add the observed S-value as a red vertical line:
abline(v=ts.obs, col="red")