<p>Sickle cell disease is a genetic disease caused by a point mutation, where the 6th residue of β chains of hemoglobin (Hb) is replaced by valine. In an oxygen-scarce environment, the mutated Hb, sickle Hb (HbS), forms fibrils and causes fatality by blocking blood vessels. Hb has two major quaternary structures, namely the relaxed (R) state and the tense (T) state, whereas HbS fibrillation only occurs in the T state. We use molecular dynamics simulations to calculate conformational free energy and Hb-Hb cohesive energy to explain the relationship between fibrillation and quaternary structure. We found that R and T states are convertible at body temperature for both normal Hb (HbA) and HbS. However, the R state HbA fibril can spontaneously dissociate for its positive cohesive energy, while both the R and T states of HbS fibrils have an essential cohesive energy for stablization. Simulation trajectories show that the mutated residues are critical for such a difference. Tensile simulations also suggest the same trend in terms of ultimate stress and energy dissipation. This study elucidates how the quaternary structure facilitates or inhibits Hb fibrillation from a thermodynamic perspective, providing hints for designing antisickling drugs by shaping the quaternary structure.</p>