In need of help with correlations

I am in need of someone's help in correlating gene expression. I'm somewhat
new to R, and can't seem to find anyone local to help me with what I think
is a simple problem.

I need to obtain pearson and spearman correlation coefficients, and
corresponding p-values for all of the genes in my dataset that correlate to
one specific gene of interest. I'm working with mouse Affymetrix Mouse 430
2.0 arrays, so I've got about 45,000 probesets (rows; with 1st column
containing identifiers) and 30 biological replicates (columns; with the top
row containing the header information).

Sean,

I'm the maintainer of the package WGCNA that does correlation network
analysis of gene expression data. I recommend you check out the
package and the tutorials at

http://www.genetics.ucla.edu/labs/horvath/CoexpressionNetwork/Rpackages/WGCNA/Tutorials/index.html

The package contains a couple useful functions for correlation
p-values. Unlike cor.test which only takes two vectors (not matrices),
you can use the function corAndPvalue to calculate Pearson
correlations and the corresponding p-values for matrices. If you
already have the correlation matrix pre-calculated AND you have no
missing data (i.e., constant number of observations), you can also use
corPvalueStudent to calculate the p-values.

We don't use Spearman correlations much (we prefer the biweight
midcorrelation, functions bicor and bicorAndPvalue, as a robust
alternative to Pearson correlation), but you can approximate the
Spearman p-values by the Student p-values (that are used for Pearson
correlations). Statisticians who read this, please don't execute me
for this suggestion :)

To use the function cor(), you need to transpose the data so that
genes are in columns and samples in rows.
Just be aware that to correlate all probe sets at a time you need a
40k+ times 40k+ matrix to hold the result. Only a large computer (at
least 32GB of memory, possibly needing 64GB) will be able to handle
such a matrix and the necessary manipulations. The WGCNA package
contains methods to construct co-expression networks on such big sets
if necessary.

HTH,

Peter