Nucleated assembly kinetics

Although the self-assembly of polymeric structures can involve nucleation and elongation steps (See Actin Assembly Kinetics Microtubule Assembly Kinetics), one can simplify the assembly process through what is known as seeded assembly. At an initial monomer concentration [M], seeded assembly is induced by the addition of pre-assembled polymeric structures consequently the polymer number concentration must remain constant. The rate of monomer incorporation into indefinite length polymers can be written as follows ... 

ACTIN ASSEMBLY KINETICS BIOCHEMICAL SELF-ASSEMBLY BIOMINERALIZATION PRION PLAQUE FORMATION Nucleation as a highly cooperative process, MICROTUBULE ASSEMBLY KINETICS... 

Fibril formation is a nucleated process that is characterized by an initial lag phase (Devlin et al., 2006 Hortschansky et al., 2005). Nucleation is followed by a fibril growth phase known as elongation. The assembly kinetics then plateau as the majority of polypeptide is incorporated into fibrillar structures. The final portion of polypeptide incorporated into fibrils is characteristic to a particular fibril system and can vary from low conversions to greater than 99% of all protein in the sample (Gras et al., 2008). 

The kinetics of F-actin-Si assembly from G-actin and Si via nucleation of actin filaments, followed by Si binding are not observed in a low ionic strength medium. Instead, the mechanism involves condensation of high affinity (G-actin)2 S complexes rapidly preformed in solution. Assembly of F-actin-Si in the presence of Si > G-actin is a quasi-irreversible process. This mechanism is therefore different from that involving the assembly of F-actin filaments, which is characterized by the initial, energetically unfavorable formation of a small number of nuclei representing a minute fraction of the population of actin molecules, followed by endwise elongation from G-actin subunits. 

The polymer self-assembly theory of Oosawa and Kasai (1962) provides valuable insights into the nature of the nucleation process. The polymerization nucleus is considered to form by the accretion of protomers, but the process is highly cooperative and unfavorable. Indeed, this is strongly suggested by the observation that thousands of actin or tubulin protomers are found in F-actin and microtubule structures if nucleation of self-assembly were readily accomplished and highly favorable, the consequence would be that many more fibers of shorter polymer length would be observed. The Oosawa kinetic theory for nucleation permits one to obtain information about the size of the polymerization nucleus if two basic assumptions can be satisfied in the experimental system. First, the rate of nuclei formation is assumed to be proportional to the loth power of the protomer concentration with io representing the number of protomers required to create the nucleus. Second, the treat-... 

Mandelkow et alP provided direct kinetic studies of nucleation by using 1 A synchrotron radiation to obtain time-resolved scattering data during cycles of assembly and disassembly after temperature shifts between 4 and 36°C. Small-angle scattering theory requires independent scattering from all particles in the solution, and the theory relates the intensity of scattering to other parameters as follows ... 

Any highly cooperative chemical or physical process that serves to generate structures that then grow by linear accretion or elongation. Nucleation is an important phase in indefinite polymerization processes (e.g., actin filament and microtubule assembly). Nucleation is typically of a high kinetic order,... 

A surface or interface can influence the assembly of fibrils by altering both the process and kinetics of fibril nucleation or elongation. This behavior is not surprising as surface properties are known to influence the absorption, confirmation, and destabilization of globular proteins or smaller peptides (Rocha et al., 2005). Surface properties influence fibril assembly in a similar way by altering the absorption, unfolding, and aggregation of monomers. 

The existence of the phase boundary between the solid and liquid phase complicates matters, since a phase boundary is associated with an increase in free energy of the system which must be offset by the overall loss of free energy. For this reason the magnitudes of the activated barriers are dependent on the size (i.e. the surface to volume ratio of the new phase) of the supramolecular assembly (crystal nucleus). This was recognized in 1939 by Volmer in his development of the kinetic theory of nucleation from homogeneous solutions and remains our best model today (Volmer 1939). 

One of the key outcomes of this theory is the concept of critical size which must be achieved by an assembly of molecules in order to be stabilized by further growth. The higher the operating level of supersaturation the smaller is this size (typically a few tens of molecules). Now, in Fig. 2.9 the supersaturation with respect to II is simply Go - Gn and is lower than Go - Gj for structure I. However it can now be seen that if for a particular solution composition the critical size is lower for II than for I then the activation free energy for nucleation is lower and kinetics will favour form II. Ultimately form II will have to transform to form I, a process that we discuss later. Overall we can say that the probability that a particular form i will appear is given by... 

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