Self-assembly critical concentration

The value of EM for a cooperative self-assembled structure provides a measure of the monomer concentration at which trivial polymeric structures start to compete, and therefore EM represents the upper limit of the concentration range within which the cooperative structure is stable (Scheme 2). The lower limit of this range is called the critical self-assembly concentration (csac) and is determined by the stoichiometry of the assembly and the strength of the non-covalent binding interactions weaker interactions and larger numbers of components raise the csac and narrow the stability window of the assembly (8). Theoretical treatments of the thermodynamics of the self-assembly process have been reported by Hunter (8), Sanders (9), and Mandolini (10). The value of EM is lowered by enthalpic contributions associated with... 

Critical self-assembly concentration, csac = [monomer], when---------= 1... 

It may be conceivable that the structure formation of barnacle adhesive is determined by critical self-assembly concentrations of the adhesive proteins within an interfacial gap between a barnacle base and a substrate. It can further be suggested that the biopolymers form coherent gel structures, in which two transitions of critical protein concentrations determine the arrangement of adhesive globules from a dense sheet-like formation to a slightly loose sponge-like formation to a very loose branched or web-like structure. 

The expression in Eq. 24 is due to a slight revision [70] of a previous expression published by Hunter et al. as the csac (critical self-assembly concentration) [69], and is based on the approximation that the chain fraction is essentially constituted by the monomer only. 

Defining critical self-assembly concentration (csac) as the concentration at which half the porphyrin inonomers are assembled into a macrocycle, the concentration dependence of the self-assembly process was investigated. It was found that csac for the dimer is 3 x 10 mol dm , while the tetramer only assembles at much higher concentrations, csac = 3x 10 mol dm. These results were rationalized by considering the equilibria shown in Fig. 5 and the relationship between csac and the effective molarity, EM ( M=Kciosed/ Kopen)> leading to Eq. 1 ... 

Micelles the mostly spherical nanoscale aggregates formed by amphiphilic compounds above their critical micelle concentration in aqueous solution have a narrow size distribution and are dynamic, because there is a fast exchange of amphiphiles in solution and those incorporated in micelles. However, micelles are defined as self-assembled structures, since the structure is in thermodynamical equilibrium. 

Self-assembly of the precursor components in the EISA process starts after evaporation of part of the volatile solvent, which progressively enriches the solution with respect to surfactant, precursor, and water. When their concentration in the deposited him achieves a certain critical level, mesostructure formation takes place. The latter is in equilibrium with the processing atmosphere. So the relative humidity, as well as the temperature during him deposition, represent some of the most important parameters influencing the mesostructure formation. 

Figure 3. Critical concentration behavior of actin self-assembly. For the top diagram depicting the macroscopic critical concentration curve, one determines the total amount of polymerized actin by methods that measure the sum of addition and release processes occurring at both ends. Examples of such methods are sedimentation, light scattering, fluorescence assays with pyrene-labeled actin, and viscosity measurements. Forthe bottom curves, the polymerization behavior is typically determined by fluorescence assays conducted under conditions where one of the ends is blocked by the presence of molecules such as gelsolin (a barbed-end capping protein) or spectrin-band 4.1 -actin (a complex prepared from erythrocyte membranes, such that only barbed-end growth occurs). Note further that the barbed end (or (+)-end) has a lower critical concentration than the pointed end (or (-)-end). This differential stabilization requires the occurrence of ATP hydrolysis to supply the free energy that drives subunit addition to the (+)-end at the expense of the subunit loss from the (-)-end.

The threshold concentration of monomer that must be exceeded for any observable polymer formation in a self-assembling system. In the context of Oosawa s condensation-equilibrium model for protein polymerization, the cooperativity of nucleation and the intrinsic thermodynamic instability of nuclei contribute to the sudden onset of polymer formation as the monomer concentration reaches and exceeds the critical concentration. Condensation-equilibrium processes that exhibit critical concentration behavior in vitro include F-actin formation from G-actin, microtubule self-assembly from tubulin, and fibril formation from amyloid P protein. Critical concentration behavior will also occur in indefinite isodesmic polymerization reactions that involve a stable template. One example is the elongation of microtubules from centrosomes, basal bodies, or axonemes. 

Kadler K, Hojima Y, Prockop DJ (1987) Assembly of collagen fibrils de novo by cleavage of the type I pC-collagen with procollagen C-proteinase. Assay of critical concentration demonstrates that collagen self-assembly is a classical example of an entropy-driven process. J Biol Chem 262 15696-15701... 

The simplest way in which a process occurs by itself is when it is under thermodynamic control. The folding of a protein, or the self-assembly of micelles at the critical micelle concentration (cmc) are examples of spontaneous processes the latter are characterized by a negative free-energy change, as the self-orgaiuzed product has a lower energy than the single components. ... 

Figure 5.3 Self-assembly of a vesicle. Water-soluble molecules can be entrapped inside, ionic molecules on the polar head groups of the surface, amphiphatic molecules in the hydrophobic bilayer, (cac critical aggregate concentration).

Surfactants having a positive curvature, above a given concentration usually called the critical micellar concentration, cmc, self-assemble to form oil-in-water aggregates called normal micelles. The surfactant most often used is sodium dodecyl sulfate, Na(DS) or SDS. To make particles, the counterion of the surfactant is replaced by ions which participate in the chemical reaction. These are called functionalized surfactants. 

Several major barriers need to be overcome for the development of nonviral gene delivery systems into true therapeutic products for use in humans. These barriers fall into three classes manufacturing, formulation, and stability (extracellular barriers and intracellular barriers) (85). Cationic lipids and cationic polymers self-assemble with DNA to form small particles that are suitable for cellular uptake. At the therapeutic doses positively charged particles readily aggregate as their concentration increases, and are quickly precipitated above their critical flocculation concentration. 

Pronounced self-assembly of 281 and 282 in nonpolar solvents (e.g., aliphatic and aromatic hydrocarbons) takes place as a result of hydrogen bonding between amide groups to result in the formation of gels above a critical gelation concentration. 

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