I am interested in matching RNA motifs (Position Weight Matrices) to cDNA sequences but am confused on the correct order of operations.

I am using the R package Biostrings which only takes DNA sequences. I downloaded cDNA sequences from Ensembl. As i understand it the cDNA sequence is the 1st strand cDNA (ie: equivalent to the template strand of the genomic DNA and a reverse complement of the mRNA sequence)

If my understanding is correct, since the RNA sequence is the reverse complement of the cDNA sequence then i should complement my RNA motifs into DNA (A -> T, C -> G, G -> C, U -> A) then reverse them ( reverse the column ordering of the PWM).

Which should mean my RNA_motif has been converted into a cDNA_motif which i can simply match against the cDNA sequence?

R code example:

    ## RNA motif "CCAU" and cDNA sequence "ATGG"
motif = matrix(c(0,1,0,0,0,1,0,0,1,0,0,0,0,0,0,1), nrow = 4)
rownames(motif) = c("A","C","G","U")
motif
# [,1] [,2] [,3] [,4]
# A    0    0    1    0
# C    1    1    0    0
# G    0    0    0    0
# U    0    0    0    1

# complement then reverse to get cDNA
rownames(motif) = c("T","G","C","A")
motif = motif[ ,ncol(motif):1]
## reorder rows for consistency
motif = motif[sort(rownames(motif)), ]
motif
# [,1] [,2] [,3] [,4]
# A    1    0    0    0
# C    0    0    0    0
# G    0    0    1    1
# T    0    1    0    0

Biostrings::countPWM(motif, "ATGG")
#[1] 1