  Protein aggregation in cell membrane is vital for the majority of biological
functions. Recent experimental results suggest that transmembrane domains of
proteins such as $\alpha$-helices and $\beta$-sheets have different structural
rigidities. We use molecular dynamics simulation of a coarse-grained model of
protein-embedded lipid membranes to investigate the mechanisms of protein
clustering. For a variety of protein concentrations, our simulations under
thermal equilibrium conditions reveal that the structural rigidity of
transmembrane domains dramatically affects interactions and changes the shape
of the cluster. We have observed stable large aggregates even in the absence of
hydrophobic mismatch which has been previously proposed as the mechanism of
protein aggregation. According to our results, semi-flexible proteins aggregate
to form two-dimensional clusters while rigid proteins, by contrast, form
one-dimensional string-like structures. By assuming two probable scenarios for
the formation of a two-dimensional triangular structure, we calculate the lipid
density around protein clusters and find that the difference in lipid
distribution around rigid and semiflexible proteins determines the one- or
two-dimensional nature of aggregates. It is found that lipids move faster
around semiflexible proteins than rigid ones. The aggregation mechanism
suggested in this paper can be tested by current state-of-the-art experimental
facilities.
