Abstract
We report a fresh and simpler approach to the modelling of the kinetics of the polymerization of Hb SS in sickle cell patients that couples the kinetics and the hydrodynamics of blood flow in mechanistic understanding of the process. The well-known two-step autocatalytic reaction scheme was used for the polymerization reaction with the assumption of simpler first-order reaction scheme for each stage. In addition, the forces acting on a particle in motion were also introduced to account for compelling settling of the red cells that lead to vessel occlusion (vaso-occlusion). A first attempt on the prediction of vessel blockage was made using this novel model. The time for the onset of the polymerization reaction was derived from hydrodynamic considerations and kinetics while the kinetic rate constants were obtained from the autocatalytic nature of the reaction. Experimental data for model validation were obtained from recruited SS patients and in vitro data of Hofrichter. Over 100 volunteers were recruited for participation in this work but less than 40% met the inclusion criteria. Participants were of age range 13 - 43 (with a mean of 26 ± 8 years) for SCD patients and 18 - 43 (with a mean of 28 ± 7 years) for control participants. Blood indices and Transcranial Doppler (TCD) test parameters of all participants were the principal parameters used for model validation. Constant k2/k1 ratios was obtained for individual in vivo/in vitro system. This ratio is unique for any individual, independent on protein sequence and also suggests the degree of expression of the symptoms of Sickle Cell Disease (SCD) with higher values reflecting greater propensity to pain crisis. Delay time, tD, was found to have an inverse relationship with the kinetic constant for the residual reaction, k1. Therefore, long delay times calculated, offer insight on why SCD patients are not in perpetual crises because enough time is provided the cells to escape microcirculation while keeping the residual reaction at the minimum. Sensitivity analysis was carried out to obviate the limitations encountered in the course of the work. Results showed the onset of occlusion to be most sensitive to the diameter of the blood vessel.
Highlights
The sickle haemoglobin was identified as the first protein to cause disease (Pauling L, Itano HA, Singer SJ, Wells IC, 1949) [1]
Sickle cell disease is characterized by a molecular hemoglobin defect which causes the polymerization of deoxygenated hemoglobins and results in reduced erythrocyte flexibility, deformation and numerous rheological effects
For all data presented here, t1/2 = time to reach 50% conversion, min; S = slope at the point of inflection = Number of nuclei formed per time per volume, min−1∙L3; tD = delay time, min; K = k2CA0, gL−1∙min−1, k1 = rate constant for the residual reaction, min−1, k2 = rate constant for the heterogeneous polymerisation, min−1
Summary
The sickle haemoglobin was identified as the first protein to cause disease (Pauling L, Itano HA, Singer SJ, Wells IC, 1949) [1] The reason for this defect is the replacement of a negative glutamic acid (Glu) molecule with a hydrophobic valine (Val) molecule on the two beta subunit of the haemoglobin. In the case of SCD, the red blood cells have lowered deformability due to repeated sickling (polymerization) and unsickling (melting) processes and eventually become irreversibly sickled and have to be removed from circulation. This happens frequently and accounts for the anemia characteristic of the disease. Occlusion of vessels is a common phenomenon as these sickled cells co-operate to form aggregates that later block the vessels
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