The paths of actin filaments propelled over a heavy meromyosin (HMM) surface in the in vitro motility assay (IVMA) can statistically be described by a path persistence length (LPP) and has been hypothesized to be proportional to the flexural rigidity of the filaments. Here, we have studied the LPP at high (130 mM) ionic strength along with the persistence length of actin filaments in solution (LPS) to elucidate how HMM binding affects the flexural rigidity of actin filaments. Characterization and control of material properties, such as the path persistence length, is useful in engineered devices that takes advantages of the function of the muscle contractile proteins e.g. for biocomputation. It has been suggested that myosin binding reduces Lpp for phalloidin stabilizedact in filaments. This is consistent with the results presented here where the phalloidin stabilized actin filaments rigidity is reduced to the level of phalloidin free actin filaments in the IVMA. Further, reducing the MgATP concentration in the IVMA would increase the HMM head density along the actin filament hence making the effect of myosin binding more pronounced. A reduced [MgATP] from 1 mM to 0.02-0.05 mM did indeed reduce the LPP from 10-12 mm to 6-7 mm for both phalloidin-stabilized and phalloidin free actin filaments. Additionally, we found a negative correlation between the LPS and the [HMM]/actin ratio. However, this [HMM] dependent reduction observed in LPS was too small to account for the reduction in LPP seen with reduced [MgATP] in the IVMA. Monte-Carlo simulations and theoretical analysis revealed that the large reduction in LPP is consistent with the idea that every head attachment adds an extra angular displacement.(Support from EU-FP7-FET-ABACUS grant number 613044).