What is the last heavy atom of an amino acid?
As mentioned in the comments by Roland, this term is not common and is first used by the authors of the mentioned paper (also the package mentioned by Roland in comments - STING).

From this link you can find the definition of the Last Heavy Atom which is possibly the most distal non-hydrogen (N, C, O, S) atom in the amino-acid side chain.

$$\begin{array}{|c|c|c|c|}
\hline
Ala\ :\ C_\beta &amp; Asp\ :\ O_{\delta^2}  &amp;Trp\ :\ C_{\eta^2}  &amp;Asn\ :\ N_{\delta^2} \\
\hline
Lys\ :\ N_\zeta &amp; Glu\ :\ O_{\epsilon^2}  &amp; Ser\ :\ O_\gamma  &amp; Gln\ :\ N_{\epsilon^2} \\
\hline
Cys\ :\ S_\gamma  &amp; His\ :\ N_{\epsilon^2}  &amp; Tyr\ :\ O_\eta  &amp; Val\ :\ C_{\gamma^2} \\
\hline
Gly\ :\ C_\alpha  &amp; Leu\ :\ C_{\delta^2}  &amp; Met\ :\ C_\epsilon  &amp; Ile\ :\ C_{\delta^1} \\
\hline
Arg\ :\ N_{\eta^2} &amp; Phe\ :\ C_\zeta  &amp; Pro\ :\ C_\delta  &amp; Thr\ :\ C_{\gamma^2} \\
\hline
\end{array}$$

They have mentioned in the same link that:


  If in any of the PDB files (to be analyzed by the BLUE STAR STING components) that specific atom (LHA) is missing in the record, then our algorithms will search for the next closer atom in the side chain that would be considered as the LHA.




The exact location of some of the abovementioned atoms.

Some of the locations might be confusing. So I am just indicating what these are, for a few the amino acids (especially for the branched and cyclic side chains). [Images reproduced from here.]

Arginine



The terminal nitrogens $\eta^1$ and $\eta^2$ are symmetric and the atom that is actually (stereochemically) the most distal is considered the LHA, as inferred from the protein structure. The second choice, obviously is the $\eta^1$-Nitrogen.

Aspartic acid



The two terminal oxygens ($\delta^1$ and $\delta^2$) in the ionized form are equivalent (also otherwise because of resonance). The actual distal atom would be labelled as $\delta^2$

you can extrapolate the same for Glutamic acid

Histidine



$\epsilon^2$ refers to the pyrollic nitogen. .

Leucine



The last carbons ($\delta^1$ and $\delta^2$) are equivalent and the choice is based on the actual distance. Extrapolate for valine

Phenylalanine



$\zeta$ refers to the carbon in the para-position of the benzene ring. For tyrosine the LHA is the oxygen of the para-OH in the benzene ring.

Tryptophan



Proline




For Aspargine and Glutamine the LHA is the amide nitrogen of the side chain.