Shared Signature Dynamics Tempered by Local Fluctuations Enables Fold Adaptability and Specificity

Recent studies have drawn attention to the evolution of protein dynamics, in addition to sequence and structure, based on the premise structure-encodes-dynamics-encodes-function. Of interest is to understand how functional differentiation is accomplished while maintaining the fold, or how intrinsic dynamics plays out in the evolution of structural variations and functional specificity. We performed a systematic computational analysis of 26,899 proteins belonging to 116 CATH superfamilies. Characterizing cooperative mechanisms and convergent/divergent features that underlie the shared/differentiated dynamics of family members required a methodology that lends itself to efficient analyses of large ensembles of proteins. We therefore introduced, SignDy, an integrated pipeline for evaluating the signature dynamics of families based on elastic network models. Our analysis confirmed that family members share conserved, highly cooperative (global) modes of motion. Importantly, our analysis discloses a subset of motions that sharply distinguishes subfamilies, which lie in a low-to-intermediate frequency regime of the mode spectrum. This regime has maximal impact on functional differentiation of families into subfamilies, while being evolutionarily conserved among subfamily members. Notably, the high-frequency end of the spectrum also reveals evolutionary conserved features across and within subfamilies; but in sharp contrast to global motions, high-frequency modes are minimally collective. Modulation of robust/conserved global dynamics by low-to-intermediate frequency fluctuations thus emerges as a versatile mechanism ensuring the adaptability of selected folds and the specificity of their subfamilies. SignDy further allows for dynamics-based categorization as a new layer of information relevant to distinctive mechanisms of action of subfamilies, beyond sequence or structural classifications.

Structure Optimization of Takagi-Sugeno Fuzzy Models

A new approach for nonlinear system identification based on Takagi-Sugeno fuzzy models is presented. The premise structure and membership functions are optimized by the LOLIMOT (local linear model tree) algorithm, see [1]. This method is extended by a subset selection technique which automatically determines the structure of the local linear models in the rule consequents. This allows to select the significant input variables for static models and additionally the determination of the dynamic orders and dead times for dynamic models. The utilized subset selection technique is the orthogonal least-squares (OLS) algorithm. It exploits the linear regression structure of the problem and thus is very fast. The applicability of the proposed approach is illustrated by the identification of a transport delay process which has operating point dependent time constants and dead times.