Dynamics of proteins aggregation. I. Universal scaling in unbounded media

It is well understood that in some cases proteins do not fold correctly and, depending on their environment, even properly-folded proteins change their conformation spontaneously, taking on a misfolded state that leads to protein aggregation and formation of large aggregates. An important factor that contributes to the aggregation is the interactions between the misfolded proteins. Depending on the aggregation environment, the aggregates may take on various shapes forming larger structures, such as protein plaques that are often toxic. Their deposition in tissues is a major contributing factor to many neuro-degenerative diseases, such as Alzheimer's, Parkinson's, amyotrophic lateral sclerosis, and prion. This paper represents the first part in a series devoted to molecular simulation of protein aggregation. We use the PRIME, a meso-scale model of proteins, together with extensive discontinuous molecular dynamics simulation to study the aggregation process in an unbounded fluid system, as the first step toward MD simulation of the same phenomenon in crowded cellular environments. Various properties of the aggregates have been computed, including dynamic evolution of aggregate-size distribution, mean aggregate size, number of peptides that contribute to the formation of β sheets, number of various types of hydrogen bonds formed in the system, radius of gyration of the aggregates, and the aggregates' diffusivity. We show that many of such quantities follow dynamic scaling, similar to those for aggregation of colloidal clusters. In particular, at long times the mean aggregate size S(t) grows with time as, S(t) ∼ t^z, where z is the dynamic exponent. To our knowledge, this is the first time that the qualitative similarity between aggregation of proteins and colloidal aggregates has been pointed out.