Kinetic studies on photolysis-induced gelation of sickle cell hemoglobin suggest a new mechanism

Abstract

The kinetics of deoxyhemoglobin S gelation have been investigated using photolytic dissociation of the carbon monoxide complex to initiate the process. Measurements over a wide range of times, 10(-3)-10(4) show that both the concentration dependence of the tenth-time (i.e., the time required to complete one-tenth the reaction) and the time dependence of the process decrease as gelation speeds up. In slowly gelling samples, where single domains of polymers are formed in the small sample volumes employed with this technique (1-2 x 10(-9) cm3), there is a marked increase in the variability of the tenth-times. These results are explained by a mechanism in which gelation is initiated by homogeneous nucleation of polymers in the bulk solution phase, followed by heterogeneous nucleation on the surface of existing polymers. At the lowest concentrations, homogeneous nucleation is so improbable that stochastic behavior is observed in the small sample volumes, and heterogeneous nucleation is the dominant pathway for polymer formation, thereby accounting for the high time dependence. At the highest concentrations homogeneous nucleation becomes much more probable, and the time dependence decreases. The decrease in concentration dependence of the tenth-time with increasing concentration results from a decrease in size of both the homogeneous and heterogeneous critical nuclei. The model rationalizes the major observations on the kinetics of gelation of deoxyhemoglobin S, and is readily testable by further experiments.

Nucleated polymerization with secondary pathways. III. Equilibrium behavior and oligomer populations

“…More formally, we note that for n c = 1, Eqs. (45), (6) and (7) are exactly verified. For n c > 1, substituting M(t) = m tot − m(t), a polynomial equation of order n c + 1 is found for m(∞) which must be solved.…”

“…Eqs. (45), (6) and (7), are also to good approximation satisfied even for k n > 0 in a wide range of parameter space that is relevant to the analysis of experimental data. More formally, we note that for n c = 1, Eqs.…”

“…In order to solve for f(∞, j) we may rewrite the relation as: (9) Eqs. (45) and (6) give m(∞) and P(∞). Substituting these into the master equation and rearranging yields: (10) This difference equation admits, as can be confirmed by direct substitution, the exact solution: (11) where (a) n is the Pochhammer symbol defined as (a) n = a(a + 1) … (a + n − 1) = Γ(a + n)/ (12) where the gamma function can be used instead of the factorials to provide a straightforward continuous extension.…”

“…The polymerisation of proteins into fibrillar structures is a type of behavior characteristic of many different systems, both in the context of functional [1][2][3][4][5] and aberrant biological pathways [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] in nature. In particular, aberrant protein aggregation is observed in relation with 50 or more disorders associated with formation of amyloid fibrils [14,16,21].…”

Nucleation of amyloid fibrils

“…[9][10][11][12][13][14][16][17][18]29,30,33,36,38,44,[52][53][54]68,70) or by the temperature at a fixed protein concentration (e.g., Refs. 9,10,14,19,25,26,70,74,76).…”