Quantifying Asymmetry of Multimeric Proteins.

A large number of proteins assemble as homooligomers. These homooligomers accomplish their function either symmetrically or asymmetrically. If asymmetry is prevalent in a structure ensemble, the asymmetric motion will occur in any of the subunits. Many computational analysis tools implicitly use ensemble averages to determine protein motions, e.g., principle component analysis. Therefore, taken together, this approach results in a loss of the asymmetric signal and a false symmetric output, rendering it impossible to analyze asymmetric motions with available tools. A first step toward understanding asymmetric systems is the quantification of asymmetry. Only a few tools exist to calculate asymmetry quantitatively, such as the continuous symmetry measure (CSM). In this study, we present an extension of CSM delivering additional information about the subunit contributions to the overall asymmetry. Furthermore, we introduce an algorithm termed the functional asymmetry measure (FAME). FAME is based on an algorithm that predicts functionally relevant motions of a protein (PLS-FMA) and thus allows calculating asymmetry in relation to protein function. To validate our developed algorithm, we applied it to two different potassium channels, TREK-2 and KcsA, as well as to the unfolding mechanism of the carrier protein Transthyretin. For both potassium channel systems, an artificial asymmetric motion was introduced to benchmark the algorithm in addition to demonstrate the interpretation potential of the results. Therefore, the degree of overall as well as subunit based asymmetry for KcsA was quantified using CSM as the provided extension requires more than two subunits. The functional modes of asymmetric TREK-2 motions were recovered and their asymmetry was quantified using FAME as a dimeric protein is the simplest application. FAME was further used to study the asymmetry of the unfolding pathway of Transthyretin. We show the ability of both algorithms to correctly predict asymmetry. The tools are available online and can be applied to most homooligomeric systems.