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Abstract Proteins' flexibility is a feature in communicating changes in cell signaling instigated by binding with secondary messengers, such as calcium ions, associated with the coordination of muscle contraction, neurotransmitter release, and gene expression. When binding with the disordered parts of a protein, calcium ions must balance their charge states with the shape of calcium‐binding proteins and their versatile pool of partners depending on the circumstances they transmit. Accurately determining the ionic charges of those ions is essential for understanding their role in such processes. However, it is unclear whether the limited experimental data available can be effectively used to train models to accurately predict the charges of calcium‐binding protein variants. Here, we developed a chemistry‐informed, machine‐learning algorithm that implements a game theoretic approach to explain the output of a machine‐learning model without the prerequisite of an excessively large database for high‐performance prediction of atomic charges. We used the ab initio electronic structure data representing calcium ions and the structures of the disordered segments of calcium‐binding peptides with surrounding water molecules to train several explainable models. Network theory was used to extract the topological features of atomic interactions in the structurally complex data dictated by the coordination chemistry of a calcium ion, a potent indicator of its charge state in protein. Our design created a computational tool of Ca^XML, which provided a framework of explainable machine learning model to annotate ionic charges of calcium ions in calcium‐binding proteins in response to the chemical changes in an environment. Our framework will provide new insights into protein design for engineering functionality based on the limited size of scientific data in a genome space. 

Cofilin, a key actin-binding protein, orchestrates the dynamics of the actomyosin network through its actin-severing activity and by promoting the recycling of actin monomers. Recent experiments suggest that cofilin forms functionally distinct oligomers via thiol post-translational modifications (PTMs) that promote actin nucleation and assembly. Despite these advances, the structural conformations of cofilin oligomers that modulate actin activity remain elusive because there are combinatorial ways to oxidize thiols in cysteines to form disulfide bonds rapidly. This study employs molecular dynamics simulations to investigate human cofilin 1 as a case study for exploring cofilin dimers via disulfide bond formation. Utilizing a biasing scheme in simulations, we focus on analyzing dimer conformations conducive to disulfide bond formation. Additionally, we explore potential PTMs arising from the examined conformational ensemble. Using the free energy profiling, our simulations unveil a range of probable cofilin dimer structures not represented in current Protein Data Bank entries. These candidate dimers are characterized by their distinct population distributions and relative free energies. Of particular note is a dimer featuring an interface between cysteines 139 and 147 residues, which demonstrates stable free energy characteristics and intriguingly symmetrical geometry. In contrast, the experimentally proposed dimer structure exhibits a less stable free energy profile. We also evaluate frustration quantification based on the energy landscape theory in the protein−protein interactions at the dimer interfaces. Notably, the 39−39 dimer configuration emerges as a promising candidate for forming cofilin tetramers, as substantiated by frustration analysis. Additionally, docking simulations with actin filaments further evaluate the stability of these cofilin dimer-actin complexes. Our findings thus offer a computational framework for understanding the role of thiol PTM of cofilin proteins in regulating oligomerization, and the subsequent cofilin-mediated actin dynamics in the actomyosin network. 

Actin networks are essential for living cells to move, reproduce, and sense their environments. The dynamic and rheological behavior of actin networks is modulated by actin-binding proteins such as α-actinin, Arp2/3, and myosin. There is experimental evidence that actin-binding proteins modulate the cooperation of myosin motors by connecting the actin network. In this work, we present an analytical mean field model, using the Flory-Stockmayer theory of gelation, to understand how different actin-binding proteins change the connectivity of the actin filaments as the networks are formed. We follow the kinetics of the networks and estimate the concentrations of actin-binding proteins that are needed to reach connectivity percolation as well as to reach rigidity percolation. We find that Arp2/3 increases the actomyosin connectivity in the network in a non-monotonic way. We also describe how changing the connectivity of actomyosin networks modulates the ability of motors to exert forces, leading to three possible phases of the networks with distinctive dynamical characteristics: a sol phase, a gel phase, and an active phase. Thus, changes in the concentration and activity of actin-binding proteins in cells lead to a phase transition of the actin network, allowing the cells to perform active contraction and change their rheological properties.