Towards a Stochastic Paradigm: From Fuzzy Ensembles to Cellular Functions

Abstract

The deterministic sequence → structure → function relationship is not applicable to describe how proteins dynamically adapt to different cellular conditions. A stochastic model is required to capture functional promiscuity, redundant sequence motifs, dynamic interactions, or conformational heterogeneity, which facilitate the decision-making in regulatory processes, ranging from enzymes to membraneless cellular compartments. The fuzzy set theory offers a quantitative framework to address these problems. The fuzzy formalism allows the simultaneous involvement of proteins in multiple activities, the degree of which is given by the corresponding memberships. Adaptation is described via a fuzzy inference system, which relates heterogeneous conformational ensembles to different biological activities. Sequence redundancies (e.g., tandem motifs) can also be treated by fuzzy sets to characterize structural transitions affecting the heterogeneous interaction patterns (e.g., pathological fibrillization of stress granules). The proposed framework can provide quantitative protein models, under stochastic cellular conditions.

Altered dynamics may drift pathological fibrillization in membraneless organelles

“…A series of experimental evidence, however, support the functional importance of the network of weak polar contacts in highly dynamic systems [76,77]. The mathematical framework, based on the fuzzy set theory is applicable to capture these cooperative effects [55], which can importantly contribute to both phase transition and fibrillization.…”

“…As the application of fuzzy models is relatively new to biology [54,55], we highlight a few distinctions between the fuzzy and non-fuzzy models. In non-fuzzy models the interacting motifs are fully engaged in binding with a unique target, " # ," 2 = 1 (eq.…”

Fuzzy protein theory for disordered proteins

“…This approach can also be used to describe the regulated assembly/disassembly of membraneless organelles [44,63]. Fuzzy structure-function relationships can be integrated into a fuzzy inference system [56], which can model cellular networks with different biological outcomes, similarly to the control system of artificially intelligent devices. Overall, we do not need to abandon the classical structurefunction paradigm to understand cellular behavior, just expand it to a multi-valued formalism.…”

Moonlighting Proteins in the Fuzzy Logic of Cellular Metabolism

“…These examples help illustrate and complement the ideas in this collection of papers on the topic of “The Fuzziness in Molecular Supramolecular, and Systems Chemistry”, where Gentili presents the “Fuzziness of the Molecular World” and describes natural information systems that involve fuzzy logic in large part due to proteins having multiple features and functions that vary in a context-dependent manner [ 6 ]. In addition, the paper by Fuxreiter describes using fuzzy set theory in a quantitative framework for describing the relationships between changing protein structures, interactions, and functions under changing, and somewhat unknown or unpredictable, cellular conditions [ 7 ].…”