Wolfram Cloud is behaving erratically for me right now so I cannot test the cloud version. There is a typo. lrn = Length[nucNamesA], nucNamesA is not defined. Here is another (I think simpler) way to create the UI for selecting nucleotides.
lrn = Length[nucNamesA]
nucNamesA
numButtons = Length@nucNames; perRow = 10; selected = {}; Dynamic@selected Grid[ Map[Button[#, selected = If[MemberQ[selected, #], DeleteCases[selected, #], Append[selected, #]], Appearance -> Dynamic@{"Palette", If[MemberQ[selected, #], "Pressed", "Normal"]}] &, Partition[nucNames, UpTo@perRow], {2}], Alignment -> {Center, Center}, Spacings -> {0, 0}]