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Abstract Accurate prediction of ligand-receptor binding affinity is crucial in structure-based drug design, significantly impacting the development of effective drugs. Recent advances in machine learning (ML)–based scoring functions have improved these predictions, yet challenges remain in modeling complex molecular interactions. This study introduces the AGL-EAT-Score, a scoring function that integrates extended atom-type multiscale weighted colored subgraphs with algebraic graph theory. This approach leverages the eigenvalues and eigenvectors of graph Laplacian and adjacency matrices to capture high-level details of specific atom pairwise interactions. Evaluated against benchmark datasets such as CASF-2016, CASF-2013, and the Cathepsin S dataset, the AGL-EAT-Score demonstrates notable accuracy, outperforming existing traditional and ML-based methods. The model’s strength lies in its comprehensive similarity analysis, examining protein sequence, ligand structure, and binding site similarities, thus ensuring minimal bias and over-representation in the training sets. The use of extended atom types in graph coloring enhances the model’s capability to capture the intricacies of protein-ligand interactions. The AGL-EAT-Score marks a significant advancement in drug design, offering a tool that could potentially refine and accelerate the drug discovery process. Scientific Contribution The AGL-EAT-Score presents an algebraic graph-based framework that predicts ligand-receptor binding affinity by constructing multiscale weighted colored subgraphs from the 3D structure of protein-ligand complexes. It improves prediction accuracy by modeling interactions between extended atom types, addressing challenges like dataset bias and over-representation. Benchmark evaluations demonstrate that AGL-EAT-Score outperforms existing methods, offering a robust and systematic tool for structure-based drug design. 

This paper introduces Disturbance-Aware Redundant Control (DARC), a control framework addressing the challenge of human–robot co-transportation under disturbances. Our method integrates a disturbance-aware Model Predictive Control (MPC) framework with a proactive pose optimization mechanism. The robotic system, comprising a mobile base and a manipulator arm, compensates for uncertain human behaviors and internal actuation noise through a two-step iterative process. At each planning horizon, a candidate set of feasible joint configurations is generated using a Conditional Variational Autoencoder (CVAE). From this set, one configuration is selected by minimizing an estimated control cost computed via a disturbance-aware Discrete Algebraic Riccati Equation (DARE), which also provides the optimal control inputs for both the mobile base and the manipulator arm. We derive the disturbance-aware DARE and validate DARC with simulated experiments with a Fetch robot. Evaluations across various trajectories and disturbance levels demonstrate that our proposed DARC framework outperforms baseline algorithms that lack disturbance modeling, pose optimization, or both. 

In recent years, using orthogonal matrices has been shown to be a promising approach to improving recurrent neural networks (RNNs) with training, stability, and convergence, particularly to control gradients. While gated recurrent unit (GRU) and long short-term memory (LSTM) architectures address the vanishing gradient problem by using a variety of gates and memory cells, they are still prone to the exploding gradient problem. In this work, we analyze the gradients in GRU and propose the use of orthogonal matrices to prevent exploding gradient problems and enhance long-term memory. We study where to use orthogonal matrices and propose a Neumann series–based scaled Cayley transformation for training orthogonal matrices in GRU, which we call Neumann-Cayley orthogonal GRU (NC-GRU). We present detailed experiments of our model on several synthetic and real-world tasks, which show that NC-GRU significantly outperforms GRU and several other RNNs. 

Tropomyosin kinase receptor B (TrkB) has been explored as a therapeutic target for neurological and psychiatric disorders. However, the development of TrkB agonists was hindered by our poor understanding of the TrkB agonist binding location and affinity (both affect the regulation of disorder types). This motivated us to develop a combined computational and experimental approach to study TrkB binders. First, we developed a docking method to simulate the binding affinity of TrkB and binders identified by our magnetic drug screening platform from Gotu kola extracts. The Fred Docking scores from the docking computation showed strong agreement with the experimental results. Subsequently, using this screening platform, we identified a list of compounds from the NIH clinical collection library and applied the same docking studies. From the Fred Docking scores, we selected two compounds for TrkB activation tests. Interestingly, the ability of the compounds to increase dendritic arborization in hippocampal neurons matched well with the computational results. Finally, we performed a detailed binding analysis of the top candidates and compared them with the best-characterized TrkB agonist, 7,8-dyhydroxyflavon. The screening platform directly identifies TrkB binders, and the computational approach allows for the quick selection of top candidates with potential biological activities based on the docking scores. 

This paper presents the development of a novel control algorithm designed for tasks involving human-robot collaboration. By using an 8-DOF robotic arm, our approach aims to counteract human-induced uncertainties added to the robot's nominal trajectory. To address this challenge, we incorporate a variable within the regular Model Predictive Control (MPC) framework to account for human uncertainties, which are modeled as following a normal distribution with a non-zero mean and variance. Our solution involves formulating and solving an uncertainty-aware Discrete Algebraic Ricatti Equation (ua-DARE), which yields the optimal control law for all joints to mitigate the impact of these uncertainties. We validate our methodology through theoretical analysis, demonstrating the effectiveness of the ua-DARE in providing an optimal control strategy. Our approach is further validated through simulation experiments using a Fetch robot model, where the results highlight a significant improvement in performance over a baseline algorithm that does not consider human uncertainty while solving for optimal control law.