Chemistry-informed Machine Learning Explains Calcium-binding Proteins’ Fuzzy Shape for Communicating Changes in Atomic States of Calcium Ions

Aug 4, 2026

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Proteins’ fuzziness functions as a signaling code, relaying calcium-ion (Ca2+) dependent changes that regulate muscle contraction, neurotransmitter release, and gene expression. When calcium binds disordered protein regions, the ion must reconcile its charge state with protein conformations and partners, yet limited experimental data makes accurate prediction of charge states for protein variants challenging. A chemistry-informed machine-learning method is proposed using ab initio electronic structure data and graph-topological features to produce explainable models and annotate atomic Ca2+ charges from scarce data.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages34

Reading Time1 h 26 min

AccessFree to download

Introduction

Role of protein fuzziness and Ca2+ signaling

Challenges in ab initio atomic charge prediction

Need for explainable machine learning with limited data

Chemistry-informed Machine Learning Explains Calcium-binding Proteins’ Fuzzy Shape for Communicating Changes in the Atomic States of Calcium Ions Pengzhi Zhang, 1,* Jules Nde,2,* Yossi Eliaz,3,4 Nathaniel Jennings,3 Piotr Cieplak,5 Margaret. S. Cheung2,6 1. Center for Bioinformatics and Computational Biology, Houston Methodist Research Institute, Houston, TX, USA 2. Department of Physics, University of Washington, Seattle, WA, USA 3. Department of Physics, University of Houston, Houston, TX, USA 4. Computer Science Department, HIT Holon Institute of Technology, Holon, Israel 5. Sanford Burnham Prebys Medical Discovery Institute, La Jolla, CA, USA 6. Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, WA, USA * These authors contributed equally Keywords: ion charge state, calcium-binding protein, EF-hand motif, graph theory, machine learning explanation, many-body interactions, calmodulin Abstract Proteins' fuzziness are features for 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. 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, but it is unclear whether the limited experimental data available can be 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 highperformance 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. With our designs, we provided a framework of explainable machine learning model to annotate atomic charges of calcium ions in calcium-binding proteins with domain knowledge in response to the chemical changes in an environment based on the limited size of scientific data in a genome space. I. Introduction Proteins’ fuzzy structures are features for communicating in biological processes, 1-3 instigated by secondary messengers such as calcium ions (Ca2+) . The binding of Ca2+ almost always induces local or global conformational changes to the protein due to the alteration of its atomic charge or electrostatic interaction. These conformational changes and the dynamics of calcium-binding proteins are intimately linked to the function of a calcium-binding protein, indicating that the surrounding environments influence its structural dynamics, thereby impacting the accessibility of its several calcium-binding loops.2,4,5 The versatility of calcium-binding proteins, often characterized by disordered domains, underscores the need of unraveling the causal relationship in determining the atomic charge states of Ca2+ and the corresponding protein configurations. Ab initio calculations have been employed for this purpose, showing that the determination of the atomic charge of Ca2+ requires information on its coordination geometry in the binding motif of a calcium-binding protein.6 However, this approach is not only labor intensive due to in part the complexity of the protein environment involving water molecules, but also computationally expensive, making it infeasible to explore a broad configurational space of calcium-binding proteins in a changing environ

FAQs

Why are fuzzy protein structures important for calcium signaling?

Fuzzy structures help communicate Ca2+-driven changes in cell signaling pathways. They enable coordination between calcium binding, conformational dynamics, and downstream biological functions like contraction, neurotransmitter release, and gene expression.

What problem does the study address regarding calcium-binding protein variants?

It addresses the uncertainty of whether limited experimental data can train models to accurately predict the charge states of Ca2+ in calcium-binding protein variants.

How does the proposed chemistry-informed machine learning approach improve prediction and explainability?

It combines ab initio electronic structure and disordered peptide segment structures with surrounding water to train explainable models. Graph/network theory extracts topological features of atomic interactions that indicate Ca2+ charge state.

Aug 4, 2026

Upload by Riley