In Alzheimer's disease (AD), many experimental and computational studies support the amyloid pore hypothesis of the Aβ42 peptide. We recently designed a β-barrel tetramer in a membrane-mimicking environment consistent with some low-resolution experimental data. In this earlier study, by using extensive replica exchange molecular dynamics simulations, we found that the wild-type (WT) Aβ42 peptides have a high propensity to form β-barrels, while the WT Aβ40 peptides do not. In this work, we have investigated the effect of mutations D23N and A2T on the Aβ42 barrel tetramer by using the same enhanced conformational sampling technique. It is known that the D23N mutation leads to early onset AD, while the A2T mutation protects from AD. This computational study in a dipalmitoylphosphatidylcholine (DPPC) lipid bilayer membrane shows that the WT sequence and its A2T variant have similar β-barrel populations and the three-dimensional model is slightly destabilized for D23N compared to its WT sequence. These extensive modeling calculations indicate that the lower and higher induced toxicity of these two mutations in AD cannot be correlated to their β-barrel tetramer stabilities in a DPPC lipid bilayer membrane.