parse on left hand side of R assignment

I keep finding myself in a situation where I want to calculate a 
variable name and then use it on the left hand side of an assignment. 
For example

iteration <- 1
varName <- paste("run",iteration,sep="")
myList$parse(text=varName) <- aColumn

I want to take some existing variable  "aColumn" and use the name 
"varName" name for it and put it into a list "myList".  That use fails 
with this error:

Error: couldn't find function "(<-"

I've tried many variations on the theme.

If I could do this with a data frame, I would be just as happy. Right 
now I'm using a list rather than a data frame because not all columns 
are of the same length. But I can work around that.