Accurate determination of the preferred aggregation number of a micelle-encapsulated membrane protein dimer

The preferred aggregation number of dodeclyphoshocholine (DPC) micelles $s_{\text{dim}}^{*}$ .encapsulating dimeric and higher order protein assemblies is difficult to determine via experimental techniques due to uncertainty in dimer geometry and heterogeneity in the conformational ensemble. Dimerization of the Amyloid Precursor Protein transmembrane domain (C99) is a particular step of importance in the production of amyloid-β protein and the amyloid cascade. Molecular dynamics simulations of the C99 dimer and other transmembrane proteins have been performed to compliment micelle-phase protein structure studies. It has often been assumed that the value of $s_{\text{dim}}^{*}$ is the same as that of the pure, empty micelle. Here, we provide a convenient method for testing that assumption, while also accounting for the finite-size effects inherent in computer simulations of micelle self-assembly. Employing large, unbiased, coarse-grained molecular dynamics simulations of DPC and C99 dimer self-assembly, we determined the radius of gyration to be 21.6 ± 2.0 Å for the micelle-encapsulated dimer, and 16.0 ± 1.0 Å for the pure DPC micelle. Using these radii of gyration, we performed all-atom simulations of DPC-encapsulated C99 dimers with preferred aggregation numbers of 100 and 54 DPC to test the effect of using an expected versus a naive estimate of aggregation number on the structure of the transmembrane protein dimer. Through atomistic simulations, we determined that the transmembrane dimeric structure displays different characteristics depending on the aggregation number of the micelle, in addition to increased water penetration and micelle defects when the aggregation number is too small.