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1. 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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2. 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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3. A Numerical Integrator for Kinetostatic Folding of Protein Molecules Modeled as Robots with Hyper Degrees of Freedom

   https://doi.org/10.3390/robotics13100150  

   Kacem, Amal; Zbiss, Khalil; Mohammadi, Alireza (October 2024, Robotics (Special Issue Bioinspired Robotics: Toward Softer, Smarter and Safer))

   The kinetostatic compliance method (KCM) models protein molecules as nanomechanisms consisting of numerous rigid peptide plane linkages. These linkages articulate with respect to each other through changes in the molecule dihedral angles, resulting in a kinematic mechanism with hyper degrees of freedom. Within the KCM framework, nonlinear interatomic forces drive protein folding by guiding the molecule’s dihedral angle vector towards its lowest energy state in a kinetostatic manner. This paper proposes a numerical integrator that is well suited to KCM-based protein folding and overcomes the limitations of traditional explicit Euler methods with fixed step size. Our proposed integration scheme is based on pseudo-transient continuation with an adaptive step size updating rule that can efficiently compute protein folding pathways, namely, the transient three-dimensional configurations of protein molecules during folding. Numerical simulations utilizing the KCM approach on protein backbones confirm the effectiveness of the proposed integrator. 

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

   Mohammadi, Alireza; Spong, Mark W. (June 2023, 2023 American Control Conference (ACC))

   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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5. 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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