Table 3 Analytical expressions for various descriptors of oligomer population dynamics [114]. ρo1 and ρo2 represent the rates of oligomer formation via primary and secondary nucleation, respectively, ρ+ represents the rate for fibril elongation, ρc represents the rate of oligomer conversion, and ρe represents the combined rates of oligomer conversion and dissociation
Descriptor | Non-equilibrium oligomerisation | Quasi-equilibrium oligomerisation |
|---|---|---|
Secondary nucleation-dominated | ||
Peak time | \({\tau }_{peak}=\frac{1}{{\left({\rho }_{o2}{\rho }_{c}{\rho }_{+}\right)}^\frac{1}{3}}\) | \({\tau }_{peak}=\frac{1}{{\left({\rho }_{o2}{\rho }_{+}\right)}^\frac{1}{2}}\sqrt{\frac{{\rho }_{e}}{{\rho }_{c}}}\) |
Persistence | \({\tau }_{decay}\simeq \frac{1}{{\rho }_{c}+{\rho }_{d}}\) | \({\tau }_{decay}\simeq \frac{1}{{\left({\rho }_{o2}{\rho }_{+}\right)}^\frac{1}{2}}\sqrt{\frac{{\rho }_{e}}{{\rho }_{c}}}\) |
Productivity | \(p=\frac{{\rho }_{c}}{{\rho }_{e}}\) | \(p=\frac{{\rho }_{c}}{{\rho }_{e}}\) |
Abundance | \(\frac{{c}_{peak}}{m\left(0\right)}=\frac{{\rho }_{o2}}{{\rho }_{e}}\) | \(\frac{{c}_{peak}}{m\left(0\right)}=\frac{{\rho }_{o2}}{{\rho }_{e}}\) |
Primary nucleation-dominated | ||
Peak time | \({\tau }_{peak}\simeq \frac{1}{{\left({\rho }_{o1}{\rho }_{+}\right)}^\frac{1}{2}}\sqrt{\frac{{\rho }_{e}}{{\rho }_{c}}}\), or \(\frac{1}{\sqrt{{\rho }_{+}{k}_{-}}}\) (if fragmentation dominated) | |
Persistence | \({\tau }_{decay}\simeq \frac{1}{{\rho }_{c}+{\rho }_{d}}\) | \({\tau }_{decay}\simeq \frac{1}{{\left({\rho }_{o1}{\rho }_{+}\right)}^\frac{1}{2}}\sqrt{\frac{{\rho }_{e}}{{\rho }_{c}}}\) |
Productivity | \(p=\frac{{\rho }_{c}}{{\rho }_{e}}\) | \(p=\frac{{\rho }_{c}}{{\rho }_{e}}\) |
Abundance | \(\frac{{c}_{peak}}{m\left(0\right)}=\frac{{\rho }_{o1}}{{\rho }_{e}}\) | \(\frac{{c}_{peak}}{m\left(0\right)}=\frac{{\rho }_{o1}}{{\rho }_{e}}\) |