Interpretation of concentration-dependence in aggregation kinetics.

Aggregation processes are analyzed by two kinetic models, the random polymerization model and the nucleation-dependent polymerization model. A kinetic equation for the random polymerization model can be derived analytically, revealing the relation between the initial monomer concentration ([M]0), the rate constant (k(a)), time (t), the yield of detectable aggregate ([F]), and the critical aggregation number (m). However, time-course curves for the nucleation-dependent polymerization model can be obtained by numerical calculation. It is found that lag time (t(d)) and half-time (t1/2) are proportional to [M](-1) in the random polymerization model, while t(d) and t1/2 are proportional to [M1](-s) (1 < s < n; n is nucleus size) at the lower concentration and are less dependent on [M1] at the higher concentration in the nucleation-dependent polymerization model.

[1]  A. Alexandrescu,et al.  An NMR investigation of solution aggregation reactions preceding the misassembly of acid-denatured cold shock protein A into fibrils. , 1999, Journal of molecular biology.

[2]  J. Hofrichter,et al.  Kinetics and mechanism of deoxyhemoglobin S gelation: a new approach to understanding sickle cell disease. , 1974, Proceedings of the National Academy of Sciences of the United States of America.

[3]  J. Hofrichter,et al.  Supersaturation in sickle cell hemoglobin solutions. , 1976, Proceedings of the National Academy of Sciences of the United States of America.

[4]  P. Lansbury,et al.  Seeding “one-dimensional crystallization” of amyloid: A pathogenic mechanism in Alzheimer's disease and scrapie? , 1993, Cell.

[5]  J. Hofrichter,et al.  Kinetic studies on photolysis-induced gelation of sickle cell hemoglobin suggest a new mechanism. , 1980, Biophysical journal.

[6]  J. Hofrichter,et al.  Kinetics of sickle hemoglobin polymerization. I. Studies using temperature-jump and laser photolysis techniques. , 1985, Journal of molecular biology.

[7]  L. Serpell,et al.  Alzheimer's amyloid fibrils: structure and assembly. , 2000, Biochimica et biophysica acta.

[8]  S. Leibler,et al.  Kinetics of self-assembling microtubules: an "inverse problem" in biochemistry. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[9]  Masato Kodaka,et al.  Requirements for generating sigmoidal time-course aggregation in nucleation-dependent polymerization model. , 2004, Biophysical chemistry.

[10]  A. Drake,et al.  The structure and mechanism of formation of human calcitonin fibrils. , 1993, The Journal of biological chemistry.

[11]  J. Sipe,et al.  Review: history of the amyloid fibril. , 2000, Journal of structural biology.

[12]  J. Duhamel,et al.  Concentration effect on the aggregation of a self-assembling oligopeptide. , 2003, Biophysical journal.