Looping over lines with Python

So I have a file that contains this:

SequenceName 4.6e-38 810..924
 SequenceName_810..924 VAWNCRQNVFWAPLFQGPYTPARYYYAPEEPKHYQEMKQCFSQTYHGMSFCDGCQIGMCH
 SequenceName 1.6e-38 887..992
 SequenceName_887..992 PLFQGPYTPARYYYAPEEPKHYQEMKQCFSQTYHGMSFCDGCQIGMCH
 

I want my program to read only the lines that contain these protein sequences. Up until now I got this, which skips the first line and read the second one:

handle = open(filename, "r")
 handle.readline()
 linearr = handle.readline().split()
 handle.close()
 
 filenamealpha = filename + ".txt"
 handle = open(filenamealpha, "w")
 handle.write(">%s\n%s\n" % (linearr[0], linearr[1]))
 handle.close()
 

But it only processes the first sequence and I need it to process every line that contains a sequence, so I need a loop, how can I do it?
The part that saves to a txt file is really important too so I need to find a way in which I can combine these two objectives.
My output with the above code is:

SequenceName_810..924
 VAWNCRQNVFWAPLFQGPYTPARYYYAPEEPKHYQEMKQCFSQTYHGMSFCDGCQIGMCH
 

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