Dynamics of the nucleated polymerization model of prion replication

Apolipoprotein C-II Amyloid Fibrils Assemble via a Reversible Pathway that Includes Fibril Breaking and Rejoining

“…These results are consistent with recent simulations for prion protein replication, which shows that the final prion protein aggregate sizes are relatively insensitive to parameters of nucleation and elongation. 36 These findings raise some important questions as to the validity of logarithmic plots of the initial monomer concentration versus the time to reach half-maximal fibril formation (t 50 ) as a means to predict the size of the nucleus. For such studies, an irreversible simple nucleation-elongation mechanism is assumed.…”

Kinetic models of guanidine hydrochloride-induced curing of the yeast [PSI+] prion

“…We assume that any polymers with length io n fragment instantaneously into i monomers. We take n ¼5 in our model (Tanaka et al, 2006), but note that other papers have suggested lower values of 2, 3 or 4 (Masel et al, 2005;Rubenstein et al, 2007). Investigation showed that taking n¼5 instead of a smaller number had no substantial impact on our model, since expected polymer lengths are typically over 80 in our simulations, much larger than n. If we let Y i denote the number of polymers of length i, then the total number of bonds in a cell is…”

Prion dynamics with size dependency–strain phenomena

“…The parameter values used in the sequel have been quoted from Rubenstein et al [31]. Unless explicitly mentioned, they are: λ = 2400 per day, γ = 4 per day, μ 0 = 0.05 per day, and β(x) = β 0 x with β 0 = 0.03 per day.…”

“…Parameters of the nucleated polymerization model for prion growth have been estimated for the 'constant parameters model' from experimental data and are available in the literature, see [15,31] and the references therein. The parameter values used in the sequel have been quoted from Rubenstein et al [31].…”

“…Polymers can lengthen by addition of PrPc monomers, and they can replicate by splitting into smaller fragments [12,15,30]. It is worth noting that this model leads to an unimodal size distribution of PrP aggregates, which seems to be quite insensitive to small variations of parameters [31]. Greer et al [16] recently improved the model and include a mean saturation effect by the whole population of polymers onto the lenghtening process (called general incidence), and polymer joining (through a Smoluchowski coagulation equation).…”