The Double Nucleation Model for Sickle Cell Haemoglobin Polymerization: Full Integration and Comparison with Experimental Data

Abstract

Sickle cell haemoglobin (HbS) polymerization reduces erythrocyte deformability, causing deleterous vaso-occlusions. The double-nucleation model states that polymers grow from HbS aggregates, the nuclei, (i) in solution (homogeneous nucleation), (ii) onto existing polymers (heterogeneous nucleation). When linearized at initial HbS concentration, this model predicts early polymerization and its characteristic delay-time (Ferrone et al. J Mol Biol 183(4):591-610, 611-631, 1985). Addressing its relevance for describing complete polymerization, we constructed the full, non-linearized model (Simulink), The MathWorks). Here, we compare the simulated outputs to experimental progress curves (n = 6-8 different [HbS], 3-6 mM range, from Ferrone's group). Within 10% from start, average root mean square (rms) deviation between simulated and experimental curves is 0.04 +/- 0.01 (25 degrees C, n = 8; mean +/- standard error). Conversely, for complete progress curves, averaged rms is 0.48 +/- 0.04. This figure is improved to 0.13 +/- 0.01 by adjusting heterogeneous pathway parameters (p < 0.01): the nucleus stability (sigma(2) micro( cc ): + 40%), and the fraction of polymer surface available for nucleation (phi), from 5e(-7), (3 mM) to 13 (6 mM). Similar results are obtained at 37 degrees C. We conclude that the physico-chemical description of heterogeneous nucleation warrants refinements in order to capture the whole HbS polymerization process.

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

“…(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. Eq.…”

“…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].…”

Dynamics of protein aggregation and oligomer formation governed by secondary nucleation

“…In this context, kinetic analysis represents a valuable tool to increase our mechanistic understanding of the aggregation process and of the resulting fibril distributions. So far, however, theoretical studies of filamentous growth kinetics have focussed on average system observables, including the total mass and number of aggregates, [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43] but the form of the full filament distribution has remained challenging a) tctm3@cam.ac.uk b) tpjk2@cam.ac.uk to obtain. In this paper, we present an analytical study of the temporal evolution of the size distribution of filamentous protein aggregates.…”

Editorial: Characterization and Analysis of Heterogeneity in Biological Systems

“…(2) focus on the origin of life and on the characteristics of heterogeneity in genetic code structure proposing an evolution model for ARN protein coding. Medkour et al (2008) investigate the role of polymers heterogeneity in haemoglobin polymerization. They propose a deterministic approach by constructing a double nucleation model where parameters are estimated from experimental data.…”