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1. Prediction of Protein Folding Pathways under Entropy-Loss Constraints using Quadratic Programming-Based Nonlinear Control

   Mohammadi, Alireza; Spong, Mark W. (May 2023, Proceedings of the American Control Conference)

   This paper investigates the problem of prediction of protein molecule folding pathways under entropy-loss constraints by formulating a control synthesis problem whose solutions are obtained by solving large-scale quadratic programming (QP) optimizations with nonlinear constraints. The utilized non-iterative and computationally efficient algorithm, which is based on solving generalized eigenvalue problems, prevents an unpredictable and potentially large number of iterations at each protein conformation for computing the folding control inputs. The synthesized control inputs remain close to the renowned kinetostatic compliance method (KCM) reference vector field while satisfying proper quadratic inequality constraints that limit the rate of molecule entropy-loss during folding. 

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2. Predicting Protein Folding Pathways with Quadratic Constraints on Rates of Entropy Change: A Nonlinear Optimization-Based Control Approach

   https://doi.org/10.1115/1.4068504  

   Mohammadi, Alireza; Spong, Mark W (April 2025, Journal of Dynamic Systems, Measurement, and Control)

   Abstract This paper addresses the problem of algorithmic prediction of protein folding pathways, namely, the transient three-dimensional conformations of protein molecules during folding, under constrained rates of entropy change. We formulate the physics-based prediction of folding pathways as a control synthesis problem, where the control inputs guide the protein folding simulations. These folding control inputs are obtained from largescale trust-region subproblems (TRS) utilizing a computationally efficient algorithm with no need for outer iterations. The proposed control synthesis approach, which leverages the solutions obtained from a special generalized eigenvalue problem, avoids potentially cumbersome and unpredictable iterative computations at each protein conformation. Moreover, the TRS-based control inputs align the closed-loop dynamics closely with the kinetostatic compliance method (KCM) reference vector field while satisfying ellipsoidal constraints on the folding control inputs. Finally, we provide conditions for existence and uniqueness of the resulting closed-loop solutions, which are the protein folding pathways under constraints on the rate of entropy change. Numerical simulations utilizing the KCM approach on protein backbones confirm the effectiveness of the proposed framework. 

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3. Chetaev Instability Framework for Kinetostatic Compliance-Based Protein Unfolding

   https://doi.org/10.1109/LCSYS.2022.3176433  

   Mohammadi, A; Spong, Mark W. (January 2022, IEEE Control Systems Letters)

   Understanding the process of protein unfolding plays a crucial role in various applications such as design of folding-based protein engines. Using the well-established kinetostatic compliance (KCM)-based method for modeling of protein conformation dynamics and a recent nonlinear control theoretic approach to KCM-based protein folding, this letter formulates protein unfolding as a destabilizing control analysis/synthesis problem. In light of this formulation, it is shown that the Chetaev instability framework can be used to investigate the KCM-based unfolding dynamics. In particular, a Chetaev function for analysis of unfolding dynamics under the effect of optical tweezers and a class of control Chetaev functions for synthesizing control inputs that elongate protein strands from their folded conformations are presented. Based on the presented control Chetaev function, an unfolding input is derived from the Artstein-Sontag universal formula and the results are compared against optical tweezer-based unfolding. 

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4. Sign Gradient Descent Algorithms for Kinetostatic Protein Folding

   https://doi.org/10.1109/MARSS58567.2023.10294128  

   Mohammadi, A; Al_Janaideh, M (October 2023, IEEE)

   This paper proposes a sign gradient descent (SGD) algorithm for predicting the three-dimensional folded protein molecule structures under the kinetostatic compliance method (KCM). In the KCM framework, which can be used to simulate the range of motion of peptide-based nanorobots/nanomachines, protein molecules are modeled as a large number of rigid nano-linkages that form a kinematic mechanism under motion constraints imposed by chemical bonds while folding under the kinetostatic effect of nonlinear interatomic force fields. In a departure from the conventional successive kinetostatic fold compliance framework, the proposed SGD-based iterative algorithm in this paper results in convergence to the local minima of the free energy of protein molecules corresponding to their final folded conformations in a faster and more robust manner. KCM-based folding dynamics simulations of the backbone chains of protein molecules demonstrate the effectiveness of the proposed algorithm. 

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5. Communication- and Control-aware Optimal Quantizer Selection for Multi-agent Control

   https://doi.org/10.1109/LCSYS.2024.3416858  

   Afshari, M; Maity, D; Tsiotras, P (June 2024, IEEE control systems letters)

   We consider a multi-agent linear quadratic optimal control problem. Due to communication constraints, the agents are required to quantize their local state measurements before communicating them to the rest of the team, thus resulting in a decentralized information structure. The optimal controllers are to be synthesized under this decentralized and quantized information structure. The agents are given a set of quantizers with varying quantization resolutions—higher resolution incurs higher communication cost and vice versa. The team must optimally select the quantizer to prioritize agents with ‘highquality’ information for optimizing the control performance under communication constraints. We show that there exist a sepatation between the optimal solution to the control problem and the choice of the optimal quantizer. We show that the optimal controllers are linear and the optimal selection of the quantizers can be determined by solving a linear program. 

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