Mathematical Model of Two Isomeric Conformations for WASP Autoinhibition

Abstract

The Wiskott-Aldrich syndrome Protein (WASP) has been implicated in many diseases including Wiskott-Aldrich Syndrome (WAS) and Buruli ulcer, but no mathematical model has been developed yet to describe the kinetics/dynamics of WASP. WASP is regulated by autoinhibition. In the autoinhibited complex, intramolecular interactions with the GTPase-binding domain (GBD) occlude residues of the C terminus that regulate the Arp2/3 actin-nucleating complex. Binding of Cdc42 to the GTPase-binding domain relieves the autoinhibitory contact between the GTPase-binding domain (GBD) and the C-terminal VCA region of WASP proteins and causes a dramatic conformational change, resulting in disruption of the hydrophobic core and release of the C terminus, enabling its interaction with the actin regulatory machinery. Here we have developed a mathematical model that quantitatively describes WASP by two isomeric conformations, an active, largely unfolded conformation that is able to stimulate the Arp2/3 complex, and an inactive, folded conformation. The model invokes an intrinsic isomeric equilibrium constant  and an affinity constant  to control intramolecular contacts between the regulatory GBD and the activity-bearing VCA domain of the protein. The formulation is concentration-dependent based on steady-state equilibrium and conservation principles. By this approach we are able to quantify the fractional response of WASP against change in concentration of ligand. The model accurately predicts WASP autinhibition. The analysis confirms that WASP needs Cdc42 as an activator for maximal activation. In the absence of a ligand, WASP is regulated by the intrinsic isomeric equilibrium constant. We also find that the stability of equilibrium of the model is affected by the Cdc42 affinity of WASP.  The results further augment the understanding on the role of WASP in polymerization of actin filament and cytoskeletal rearrangement.

Keywords: Wiskott - Aldrich Syndrome Protein, autoinhibition, isomeric, conformation, receptor, ligand, enzyme, protein, binding.