cat files in specific order based on number in filename

Use brace expansion

cat file.88_{0..100}.pdb >>bigfile.pdb

To ignoring printing the error messages for non-existent files use:

cat file.88_{0..100}.pdb >>bigfile.pdb 2>/dev/null

In the zsh shell also you have the (n) globbing qualifier to request a numerical sorting (as opposed to the default of alphabetical) for globs:

cat file.88_*.pdb(n) >>bigfile.pdb 2>/dev/null

cat $(for((i=0;i<101;i++)); do echo -n "file.88_${i}.pdb "; done)

or, regarding the comment of Jesse_b:

cat $(for((i=0;i<101;i++)); do test -f "file.88_${i}.pdb" && echo -n "file.88_${i}.pdb "; done)

In shell w/o brace expansion you can use ls + xargs:

ls -v file.88_*.pdb | xargs cat > all.pdb

ls will sort files in numeric order:

-v natural sort of (version) numbers within text.