Powers Evan T, Powers David L
Department of Chemistry, The Scripps Research Institute, La Jolla, California 92037, USA.
Biophys J. 2006 Jul 1;91(1):122-32. doi: 10.1529/biophysj.105.073767. Epub 2006 Apr 7.
The formation of amyloid and other types of protein fibrils is thought to proceed by a nucleated polymerization mechanism. One of the most important features commonly associated with nucleated polymerizations is a strong dependence of the rate on the concentration. However, the dependence of fibril formation rates on concentration can weaken and nearly disappear as the concentration increases. Using numerical solutions to the rate equations for nucleated polymerization and analytical solutions to some limiting cases, we examine this phenomenon and show that it is caused by the concentration approaching and then exceeding the equilibrium constant for dissociation of monomers from species smaller than the nucleus, a quantity we have named the "supercritical concentration". When the concentration exceeds the supercritical concentration, the monomer, not the nucleus, is the highest-energy species on the fibril formation pathway, and the fibril formation reaction behaves initially like an irreversible polymerization. We also derive a relation that can be used in a straightforward method for determining the nucleus size and the supercritical concentration from experimental measurements of fibril formation rates.
淀粉样蛋白和其他类型蛋白质纤维的形成被认为是通过成核聚合机制进行的。通常与成核聚合相关的最重要特征之一是速率对浓度的强烈依赖性。然而，随着浓度增加，纤维形成速率对浓度的依赖性会减弱并几乎消失。通过对成核聚合速率方程的数值解以及一些极限情况的解析解，我们研究了这一现象，并表明它是由浓度接近然后超过单体从小于核的物种解离的平衡常数引起的，我们将这个量称为“超临界浓度”。当浓度超过超临界浓度时，在纤维形成途径上，单体而非核是能量最高的物种，并且纤维形成反应最初表现得像不可逆聚合。我们还推导了一个关系式，可用于一种直接的方法，从纤维形成速率的实验测量中确定核的大小和超临界浓度。
