TITLE:
Modeling and Simulation of the Autocatalytic Kinetics of Haemoglobin SS Polymerization: Onset of Polymerization
AUTHORS:
Edith Egbimhanhu Alagbe, Alfred Akpoveta Susu, Adedoyin Owolabi Dosunmu
KEYWORDS:
Vaso-Occlusion, Hb SS Polymerization Kinetics, Residual and Secondary Reactions, Hydrodynamics of Blood Flow, Onset of Hb SS Polymerization
JOURNAL NAME:
Journal of Biosciences and Medicines,
Vol.4 No.3,
March
17,
2016
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.