As virtualsue and GrandFather have advised, a hash is the way to go. You can always recreate an array from your hash afterwards if you need to. The code below uses a form of Schwartzian Transform and works by getting the three elements from each data line then sorting the data lines in descending numerical order on the number field. Thus, for whichever protein/organism combination, the smallest will come last. Finally, the sorted line items are placed in turn into the hash, successively smaller values overwriting any previous larger "duplicates". I then rebuild an array at this point but that may not be what you actually want.

use strict;
use warnings;

my %smallest =
   map  {
            $_->[0] => {
               org => $_->[1],
               val => $_->[2] }
        }
   sort { $b->[2] <=> $a->[2] }
   map  { chomp; [ split m{\t} ] }
   <DATA>;

my @sorted = ();
foreach my $protein ( sort keys %smallest )
{
    push @sorted, [
       $protein,
       $smallest{$protein}->{org},
       $smallest{$protein}->{val} ];
}

print Data::Dumper->Dump([\@sorted], [qw{*sorted}]);

__END__
protein1    organism1    0.843534
protein2    organism2    2.45
protein3    organism3    9.5322
protein4    organism4    0.3475474
protein1    organism6    9.4534
protein2    organism7    0.43534
protein2    organism8    1.2434
protein3    organism9    0.000003
protein3    orgnanism10    1.23325
[download]

Here's the output

@sorted = (
            [
              'protein1',
              'organism1',
              '0.843534'
            ],
            [
              'protein2',
              'organism7',
              '0.43534'
            ],
            [
              'protein3',
              'organism9',
              '0.000003'
            ],
            [
              'protein4',
              'organism4',
              '0.3475474'
            ]
          );
[download]

I hope this is of use.

Cheers,

JohnGG