Isodesmic polymerizations

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. 

Any polymerization reaction in which the product of each elongation step can itself also undergo further polymerization. When the same types of bonds and/or conformational states that are present in the reactant(s) are generated within product(s) during elongation, the process is referred to as isodesmic polymerization. Such is the case for the indefinite polymerization of actin, tubulin, hemoglobin S, and tobacco mosaic virus coat protein. See Nudeation Protein Polymerization Actin Assembly Kinetics Microtubule Assembly Kinetics Microtubule Assembly Kinetics... 

If h > 0, then helical assemblies do not form. There is an isodesmic polymerization from monomers to "disordered" supramolecular polymers that takes place around X l. The theory of Section 1 applies and the equivalent equilibrium constant obeys K = exp [. jy. Its value can be probed by means of radiation scattering, fluorescence decay, and UV absorption spectroscopy (Brunsveld et al., 2001 Jonkheijm et al., 2006). 

Figure 10 Assembly diagram of compound 1 of Figure 6 in the solvent n-butanol (adapted from van Gestel, 2004a Weiss and Terech, 2005). Symbols represent results from UV-vis absorption, UV, fluorescence decay, FD, and circular dichroim spectroscopy, CD, and the drawn line the theoretical fits to the data. There are three types of transition I, isodesmic polymerization II, helical transition of long supramolecular polymers and III, nucleated helical assembly of the monomer units.

Scheme 1 Chain—chain equiiibria for an isodesmic polymerization.

The Noncooperative Model, (a = 7 = 1, c= 0). This model applies to assembhes that involve only intemiolecular interactions without any allosteric effect. The occupation of the various binding sites of the receptor is dictated only by statistics. This model is the reference for spotting the presence of allosteric effects in real systems. It also applies to the formation of a given ohgomer in isodesmic polymerizations. This process is exemplified by a monomer A—B that undergoes a reversible polymerization in which all of the stepwise association constants are identical and equal to K. The formation constant of each oligomer (A—B), is given by Eq. [51] in which a = y = 1, c = 0, = 1 and f) = 1 -... 

In isodesmic polymerizations, the individual monomers associate with an association constant that is independent of the polymer size. This is comparable to the simplest description of a step-growth polycondensation given by Flory s principle of equal reactivity [10]. The mechanism gives rise to a PDI of 2 in the high-concentration regime. 

Isodesmic polymerization is conceptually the most simple type of suprcunolecular polymerization. Through the cotrrse of an isodesmic supramolecular polymerization, a linear decrease in the Gibbs free energy of the polymerization is observed as a funaion of monomer conversion to polymer (p) from zero to one (p = 0 —> 1). This verifies that the affinity of a monomer to the growing polymer chain is irrespective of the length of that polymer chain. The absence of a critical concentration or... 

As a result of the difference in growth mechanism when compared with the isodesmic polymerization, these two supramolecular polymerizations differ in various characteristic features. Growth in ring-chain polymerizations leads to increases in DP and DPn and is largely dependent on both association constants for the polymerization and the overall monomer concentration. A plot of DP versus concentration identifies that as the value of fCintra increases relative to the fCinter at a fixed value for fCinter/ the conversion of rings to linear chains at the critical concentration becomes much sharper and DP increases more abruptly after this point. However, at high overall concentrations... 

C Ateff), the DP is essentially independent of Kintra- This contrasts with isodesmic polymerization, where DP rises gradually with increasing concentration. In addition, at high overall concentrations (C Meff), the isodesmic and ring-chain polymerization mechanisms are indistinguishable. 

Figures (a) Plots of DPn and DPw as functions of KCq for isodesmic polymerization without byproduct. (From D. Zhao and J.S, Moore. Org. Biomol. Chem. 2003. Copyright 2003 RCS.) (b) Theoretical relationship between the association constant Kan6 DP according to the multistage open association model. (From L. Brunsveld, B.J.B. Folmer, E.W. Meijer, and R.R Sijbesma. Chem. Rev. 101 4071, 2001. Copyright 2001 ACS.)...

Protein fibrillization can occur via two polymerization mechanisms. Isodesmic polymerization as observed with tubulin for example, occurs via... 

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