Nucleated assembly

Let us start with the nucleated assembly that is not self-catalyzed. It turns out useful to distinguish between the mean aggregation number of all the material in the solution, N, from that in which only the activated species is considered and that we denote by Na. If we define the equilibrium constant K = exp [—.%] with g as the binding free energy, and introduce the nucleation constant Ka = exp[—/3ya], then under conditions of thermodynamic equilibrium, mass action gives (Aggeli, 2001 Ciferri, 2005 Nyrkova et al., 2000 Tobolsky and Eisenberg, 1960) 

The smaller the value of the activation constant, Ka, the sharper the transition from the monomer- to the polymer-dominated regime (Douglas et al., 2008 van Jaarsveld and van der Schoot, 2007 Scott, 1965 Tobolsky and 

Eisenberg, 1960 Wheeler and Pfeuty, 1981). The distribution of the sizes of the assemblies is bimodal over the inactive and active states of the material, where the latter is an exponential function of the aggregation number. The weight distribution is also bimodal and has peaks centered at the aggregation numbers of unity and Na (Zhao and Moore, 2003). 

If Ka -C 1, we are able to define a sharp polymerization temperature Tp = Tp( j ) that is a function of the concentration o, such that 

If the nucleated assembly is self-catalyzed, then this modifies only the role of the equilibrium constant K in the non-self-catalyzed model and has to be replaced by the ratio K/Ka. This means that we again obtain for the fraction polymerized material f=KaNa/(1 + KaNa) but that the degree of polymerization averaged over the active material only now obeys (Ciferri, 2005) 

---

Fragments MFs and nucleates assembly, regulated by Ca2+ Binds actin monomers and regulates MF assembly Binds actin monomers, inhibits MF formation, regulated by selected signal transduction pathways Nucleation of actin MF assembly in cortex and initiation of MF branches... 

Brown-Augsburger, P., Tisdale, C., Broekelmann, T., Sloan, C., and Mecham, R. P. (1995). Identification of an elastin cross-linking domain that joins three peptide chains. Possible role in nucleated assembly./. Biol. Chem. 270, 17778-17783. 

Figure 2 Chemical reaction models for (a) isodesmic and (b) nucleated supramolecular assembly. 1 and K 2>1 are equilibrium constants for the elongation reactions, and Ka 1 and K a those for the conversion between assembly active and inactive forms of the monomer units. If /f aKa, then the nucleated assembly is self-catalyzed ( autosteric ) and if K a = Ka this is not so.

A tell-tale sign of nucleated assembly is the existence of a critical concentration below which assemblies do not form in measurable quantities. Another is the observation of hysteresis in assembly and disassembly experiments... 

Let the order parameter Si be associated with the fraction active material, and be defined as S =f. For the second order parameter we choose S2 = Na (Na — 1 )Ka/X as a measure of the degree of polymerization of the active material and presume that the polymerization is highly co-operative, so K.a —> 0. The macroscopic Landau free-energy density F that describes the nucleated assembly now reads... 

IfX 1, disordered (nonhelical) assemblies do not form in any appreciable quantities. For h< 0, there is a polymerization transition from monomers to helical assemblies that is of the self-catalyzed nucleation type provided flj 3> 1. In the language of the coarse-grained self-catalyzed nucleated assembly model, the transition takes place near Xp exp [f3h] and we are able to assign an activation constant Ka exp [ 3j + 311], The theory of Section 2 approximately applies. 

Viral peptides also form amyloids (Table 2). For example, a peptide derived from herpes simplex virus (HSV) glycoprotein B (gB) forms fibrils in vitro and nucleates assembly of Ap fibrils (Cribbs et al. 2000). The peptide corresponding to residues 22-42 of HSV 1 gB formed long, uniform fibrils at pH 7.4. The region investigated had significant similarity to the C-terminal region of Af) and, like Ap peptide, exhibited neuronal toxicity. This raises the possibility of a connection between viral infection and sporadic cases of Alzheimer s disease. 

---