#!/usr/bin/perl
use strict;
use warnings;
use Data::Dumper;

my @lines;
while (<DATA>) {
    chomp;
    if (/^>/) {
        push @lines, $_;
    }
    else {
        $lines[-1] .= $_;
    }
}
print Dumper \@lines;

__DATA__
>bob
123456789012345678901234567
8901234567890123
>squeaka
TTTGGACCCACAACGTACCACAGGTAT
SAJFIJEIFIRVNUTR
>trumpet
TTTTGAGACCCCCACAAAAGGATTTTT
ANDANOTHERLINERT
>nautilus
AGTCAGTCGATCGTACGTATATAACAC
CSADJOIASJNEEESA