The Double Nucleation Model for Sickle Cell Haemoglobin Polymerization: Full Integration and Comparison with Experimenta
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The Double Nucleation Model for Sickle Cell Haemoglobin Polymerization: Full Integration and Comparison with Experimental Data Terkia Medkour Æ Frank Ferrone Æ Fre´de´ric Galacte´ros Æ Patrick Hannaert
Received: 19 December 2007 / Accepted: 19 December 2007 / Published online: 5 February 2008 Ó Springer Science+Business Media B.V. 2008
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 (SimulinkÒ, 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°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 (r2 lcc: + 40%), and the fraction of polymer surface available for nucleation (/), from 5e-7, (3 mM) to 13 (6 mM). Similar results are obtained at 37°C. We conclude that the physicochemical description of heterogeneous nucleation warrants refinements in order to capture the whole HbS polymerization process. T. Medkour EA 2381, Pharmacochimie Mole´culaire et Syste`mes Membranaires, Universite´ Denis Diderot, Paris 7, France F. Ferrone Department of Physics, Drexel University, Philadelphia, PA, USA F. Galacte´ros Centre de la Dre´panocytose et des Thalasse´mies, CHU Henri Mondor, Creteil, France P. Hannaert (&) Inserm E0324, CHU La Mile´trie, 2 rue de la Mile´trie, BP 577, 86000 Poitiers, France e-mail: [email protected]
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Abbreviations Co initial HbS concentration (hence it is also the total HbS concentration in the model) Cs HbS solubility, i.e. HbS concentration below which no polymerization can occur; varies with temperature, see Eaton and Hofrichter (1990) HbS Sickle cell haemoglobin, deoxygenated form (Protein Data Bank identifier: 1HBS; cf. url. http://www.rcsb.org/pdb/) hon ‘‘homogeneous nucleation’’ pathway, by which metastable HbS nuclei in solution are converted into ‘‘polymers’’, Cp hen ‘‘heterogeneous nucleation’’ pathway, by which nuclei attached to existing polymer fibers are converted into ‘‘polymers’’ ODE Ordinary differential equation td The experimental lag-time during which no polymer is detected url Uniform resource locator
1 Introduction 1.1 Sickle Cell Disease and Polymerization of Haemoglobin S Sickle cell disease is a genetic
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