Docking Problem Research Articles

Unified Sampling and Ranking for Protein Docking with DFMDock.

Diffusion models have shown promise in addressing the protein docking problem. Traditionally, these models are used solely for sampling docked poses, with a separate confidence model for ranking. We introduce DFMDock (Denoising Force Matching Dock), a diffusion model that unifies sampling and ranking within a single framework. DFMDock features two output heads: one for predicting forces and the other for predicting energies. The forces are trained using a denoising force matching objective, while the energy gradients are trained to align with the forces. This design enables our model to sample using the predicted forces and rank poses using the predicted energies, thereby eliminating the need for an additional confidence model. Our approach outperforms the previous diffusion model for protein docking, DiffDock-PP, with a sampling success rate of 44% compared to its 8%, and a Top- 1 ranking success rate of 16% compared to 0% on the Docking Benchmark 5.5 test set. In successful decoy cases, the DFMDock Energy forms a binding funnel similar to the physics-based Rosetta Energy, suggesting that DFMDock can capture the underlying energy landscape.

Fully Flexible Molecular Alignment Enables Accurate Ligand Structure Modeling.

Accurate protein-ligand binding poses are the prerequisites of structure-based binding affinity prediction and provide the structural basis for in-depth lead optimization in small molecule drug design. However, it is challenging to provide reasonable predictions of binding poses for different molecules due to the complexity and diversity of the chemical space of small molecules. Similarity-based molecular alignment techniques can effectively narrow the search range, as structurally similar molecules are likely to have similar binding modes, with higher similarity usually correlated to higher success rates. However, molecular similarity is not consistently high because molecules often require changes to achieve specific purposes, leading to reduced alignment precision. To address this issue, we propose a new alignment method─Z-align. This method uses topological structural information as a criterion for evaluating similarity, reducing the reliance on molecular fingerprint similarity. Our method has achieved success rates significantly higher than those of other methods at moderate levels of similarity. Additionally, our approach can comprehensively and flexibly optimize bond lengths and angles of molecules, maintaining a high accuracy even when dealing with larger molecules. Consequently, our proposed solution helps in achieving more accurate binding poses in protein-ligand docking problems, facilitating the development of small molecule drugs. Z-align is freely available as a web server at https://cloud.zelixir.com/zalign/home.

Improving the artificial bee colony algorithm with a proprietary estimation of distribution mechanism for protein–ligand docking

The protein–ligand docking problem plays an essential role in structure-based drug design. The challenge for a protein–ligand docking method is how to execute an efficient conformational search to explore a well-designed scoring function. In this study, we improved the artificial bee colony (ABC) algorithm and proposed an approach called ABC-EDM to solve the protein–ligand docking problem. ABC-EDM employs the scoring function of the classical AutoDock Vina to evaluate a solution during docking simulation. ABC-EDM adopts the search framework of the canonical ABC algorithm to execute conformational search. By further investigating the characteristics of the protein–ligand docking problem, a proprietary search mechanism inspired by estimation of distribution algorithm, i.e., estimation of distribution mechanism (EDM), is designed to enhance the performance of ABC-EDM. To verify the effectiveness of the proposed ABC-EDM, we compare it with three variants of the ABC algorithm, three evolutionary computation algorithms, and AutoDock Vina. The experimental results show that ABC-EDM can effectively solve the protein–ligand docking problem, and it can achieve a success rate 5% higher than AutoDock Vina on the GOLD dataset. This study reveals that taking advantage of problem-specific information about the protein–ligand docking problem to enhance a docking method contributes to solving this problem.

Fault-tolerant control for satellite autonomous rendezvous with quality characteristics and actuator uncertainties

An autonomous fault detection and fault-tolerant control solution combining Model Predictive Control (MPC) and Label Distributed Learning (LDL) is developed for the position tracking and attitude synchronization problems in autonomous satellite rendezvous and docking. The proposed algorithm can deal with center of mass (CM) variations and time-varying mass characteristics due to satellite fuel consumption, actuator saturation and fault, and external disturbances. Firstly, a six-degree-of-freedom (6-DOF) satellite translation-rotation coupling model was established to express the relative motion between the satellite and the target, taking the above factors into account. Subsequently, an on-board autonomous closed-loop fault-tolerant control algorithm using MPC is proposed, in which an LDL-based fault detection mechanism is embedded. The scheme specifies that propulsion faults are estimated by calculating the difference between the MPC's prediction of the satellite's future state and the measured change in the actual state. And the mapping matrix between the commanded force/torque and the actual force of the propulsion system is updated in real time to achieve autonomous fault detection and compensation on board the satellite. Among them, the LDL-based fault detection scheme is trained offline. It requires only simple matrix operations for on-orbit use, which is low-cost and suitable for resource-limited space environments. The additional creation of a time-varying disturbance observer allows the estimation and compensation of unmodelled errors and external disturbances. The stability of the proposed fault-tolerant control algorithm is rigorously demonstrated using Lyapunov analysis. Finally, numerical simulations show that the proposed method can successfully achieve autonomous satellite docking under different combinations of thruster faults.

Multiphase Autonomous Docking via Model-Based and Hierarchical Reinforcement Learning

With the rise of traffic around Earth’s orbit, spacecraft mission designs have placed an unprecedented demand on the capabilities of autonomous systems. In the early 2000s, the state-of-the-art autonomous spacecraft controllers were designed for static and uncluttered environments. A little over a decade later, the challenges facing spacecraft autonomy now include cluttered, dynamic environments with time-varying constraints, logical modes, fault tolerances, uncertain dynamics, and complex maneuvers. With this rise in complexity, many areas of research have been investigating more experimental control strategies, such as reinforcement learning (RL), as a potential solution to this problem. The research presented herein aims to expand on efforts to quantify the use of RL in autonomous rendezvous, proximity operations, and docking (ARPOD) environments, with consideration to the inherent drawbacks of the more common algorithms present in the field. We present hierarchical model-based RL as a solution to an autonomous docking problem. This algorithm can learn satellite parameters, extrapolate trajectory information, and learn uncertain dynamics via data collection. By using gradient-free model predictive control logic, the algorithm can handle nondifferentiable objectives and complex constraints. Lastly, the hierarchical structure demonstrates an ability to generate feasible trajectories in the presence of integrated third-party subcontrollers commonly found in spacecraft. This study highlights the ability of the hierarchical algorithm to combine and manipulate third-party subpolicies to achieve trajectories not previously trained on.

A dual-population multi-objective evolutionary algorithm driven by generative adversarial networks for benchmarking and protein-peptide docking

Multi-objective optimization problems (MOPs) are characterized as optimization problems in which multiple conflicting objective functions are optimized simultaneously. To solve MOPs, some algorithms used machine learning models to drive the evolutionary algorithms, leading to the design of a variety of model-based evolutionary algorithms. However, model collapse occurs during the generation of candidate solutions, which results in local optima and poor diversity in model-based evolutionary algorithms. To address this problem, we propose a dual-population multi-objective evolutionary algorithm driven by Wasserstein generative adversarial network with gradient penalty (DGMOEA), where the dual-populations coordinate and cooperate to generate high-quality solutions, thus improving the performance of the evolutionary algorithm. We compare the proposed algorithm with the 7 state-of-the-art algorithms on 20 multi-objective benchmark functions. Experimental results indicate that DGMOEA achieves significant results in solving MOPs, where the metrics IGD and HV outperform the other comparative algorithms on 15 and 18 out of 20 benchmarks, respectively. Our algorithm is evaluated on the LEADS-PEP dataset containing 53 protein-peptide complexes, and the experimental results on solving the protein-peptide docking problem indicated that DGMOEA can effectively reduce the RMSD between the generated and the original peptide's 3D poses and achieve more competitive results.

OPTIMAL DOCKING PROBLEM OF UAV AT DETECTED MOVING OBJECT

OPTIMAL DOCKING PROBLEM OF UAV AT DETECTED MOVING OBJECT

Hybrid Systems Approach to Autonomous Rendezvous and Docking of an Underactuated Satellite

This work examines the autonomous rendezvous, proximity operations, and docking (ARPOD) problem wherein a “deputy” spacecraft must maneuver and dock with a “chief” spacecraft. This problem is challenging in that the deputy is modeled to be underactuated; thrust is only allowable along a single axial direction (its local axis) and rotation is only allowed about its local axis. Furthermore, the deputy’s coupled translational and attitudinal dynamics (modeled via the Clohessy–Wiltshire equations with inputs) do not allow local controllability about the equilibrium point when linearized. To solve this underactuated ARPOD problem, we design a periodic bimodal switching control law that drives the deputy to a docking configuration with the chief. We model the system to have hybrid (i.e., continuous and discrete) dynamics and recast the docking objective as a set stabilization problem. The main result of this work is a rigorous proof that leverages properties of geometric control, Floquet theory, and homogeneity to show that the switching control law renders the objective set to be locally asymptotically stable. Numerical simulations are provided to illustrate the main result.

DockSurf: A Molecular Modeling Software for the Prediction of Protein/Surface Adhesion.

The elucidation of structural interfaces between proteins and inorganic surfaces is a crucial aspect of bionanotechnology development. Despite its significance, the interfacial structures between proteins and metallic surfaces are yet to be fully understood, and the lack of experimental investigation has impeded the development of many devices. To overcome this limitation, we suggest considering the generation of protein/surface structures as a molecular docking problem with a homogenous plan as the target. To this extent, we propose a new software, DockSurf, which aims to quickly propose reliable protein/surface structures. Our approach considers the conformational exploration with Euler's angles, which provide a cartography instead of a unique structure. Interaction energies were derived from quantum mechanics computations for a set of small molecules that describe protein atom types and implemented in a Derjaguin, Landau, Verwey, and Overbeek potential for the consideration of large systems such as proteins. The validation of DockSurf software was conducted with molecular dynamics for corona proteins with gold surfaces and provided enthusiastic results. This software is implemented in the RPBS platform to facilitate widespread access to the scientific community.

Two-Step Adaptive Control for Planar Type Docking of Autonomous Underwater Vehicle

Planar type docking enables a convenient underwater energy supply for irregularly shaped autonomous underwater vehicles (AUVs), but the corresponding control method is still challenging. Conventional control methods for torpedo-shaped AUVs are not suitable for planar type docking due to the significant differences in system structures and motion characteristics. This paper proposes a two-step adaptive control method to solve the planar type docking problem. The method makes a seamless combination of horizontal dynamic positioning and visual servo docking considering ocean current disturbance. The current disturbance is estimated and canceled in the pre-docking step using a current observer, and the positioning error is further compensated for by the vertical visual servo technique in the docking step. Reduced order dynamic models are distinctively established for different docking steps according to the motion characteristics, based on which the dynamic controllers are designed considering the model parameter uncertainties. Simulation is conducted with an initial distance of 10 m in the horizontal direction and 3 m in depth. Stable and accurate dynamic positioning under up to 0.4 m/s of current disturbances with different directions is validated. A 0.5 m lateral positioning error is successfully compensated for by the visual servo docking step. The proposed control method provides a valuable reference for similar types of docking application.

Spacecraft Rendezvous and Docking Using the Explicit Reference Governor Approach

This article investigates the autonomous spacecraft rendezvous and docking problem in the presence of space obstacle, path constraints, and thrust limitation constraint. By introducing the frame of explicit reference governor (ERG), a combination scheme of guidance and control is proposed to guarantee the system stabilization and constraints satisfaction. Specifically, an artificial potential function (APF) method is employed to guide a collision-free trajectory, and then the constraints are satisfied via limiting the states within the safe invariant set. Furthermore, a simplified method is proposed to obtain the maximum bound of the Lyapunov-based invariant sets, which ensures input bounded and collision avoidance. System convergence under the potential field is proved through the Lyapunov stability analysis. Numerical simulation results demonstrate the comprehensive validation and good performance of the proposed method.

Обзор маневров космических аппаратов на околокруговых орбитах

This paper presents comprehensive information about spacecraft (SC) maneuvers in the vicinity of a circular orbit. The implementation of SC maneuvers in the vicinity of circular orbits makes it possible to solve many research and applied problems. Typical examples are the problems of rendezvous and docking of SC moving in near-circular orbits, the implementation of a group flight of several SC in a given configuration, the deployment and maintenance of low-orbit systems to solve the problems of providing communications and remote sensing of the Earth. Practical examples of SC maneuvers are given.

High performance assembly of complex structural parts in special environments – research on space manipulator assisted module docking method

PurposeCompared with the robotic manipulation in structured environment, high performance assembly of complex parts in extreme special environment is facing great challenges because of the uncertainty in the environment, and the decline of the control accuracy of the robot and the sensor accuracy. The assembly and construction of the space station is a typical case. An important step in the construction of the space station is the module positioning and docking with the auxiliary of the space manipulator. The operation of the manipulator is faced with many problems, such as low sensing information accuracy, large end position deviation and the requirement of weak impact in the docking process. The purpose of this paper is to design a docking method at the strategy level to effectively solve the problems that may be faced in the docking process.Design/methodology/approachInspired by the research of robotic high-precision compliant assembly, this paper introduces the concept of Attractive Region in Environment (ARIE) into the space manipulator–assisted module docking. The contact configuration space of the docking mechanism and the existence of ARIE are systematically analyzed. The docking strategy based on ARIE framework is proposed, in which the impedance control is used to ensure the weak impact during the docking process.FindingsFor the androgynous peripheral spacecraft docking mechanism, a large range of attractive region exists in the high-dimensional contact configuration space. The docking strategy based on ARIE framework can be designed according to the geometric characteristics of the constraint region and the structural characteristics of the docking mechanism. The virtual models and the simulation environment are established, and the effectiveness of the proposed method is preliminarily verified.Originality/valueBased on the research results of robotic precision compliant manipulation, in this paper, the theory of ARIE is first systematically applied to the analysis of spacecraft docking problem and the design of docking scheme. The effectiveness of the proposed docking method is preliminarily verified for the requirements of large position tolerance and weak impact. The research results will provide theoretical support and technical reference for the assembly and construction of space station and other space manipulator operations.

Entropy-based lamarckian quantum-behaved particle swarm optimization for flexible ligand docking.

AutoDock is a widely used software for flexible ligand docking problems since it is open source and easy to be implemented. In this paper, a novel hybrid algorithm is proposed and applied in the docking environment of AutoDock version 4.2.6 in order to enhance the accuracy and the efficiency for dockings with flexible ligands. This search algorithm, called entropy-based Lamarckian quantum-behaved particle swarm optimization (ELQPSO), is a combination of the QPSO with an entropy-based update strategy and the Solis and Wet local search (SWLS) method. By using the PDBbind core set v.2016, the ELQPSO is compared with the Lamarckian genetic algorithm (LGA), Lamarckian particle swarm optimization (LPSO) and Lamarckian QPSO (LQPSO). The experimental results reveal that the corresponding docking program of ELQPSO, named as EQDOCK in this paper, has a competitive performance in dealing with the protein-ligand docking problems. Moreover, for the test cases with different number of torsions, the EQDOCK outperforms the other three docking programs in finding docking conformations with small root mean squared deviation (RMSD) values in most cases. In particular, it has an advantage of solving highly flexible ligand docking problems over the others.

The development of molecular docking and molecular dynamics and their application in the field of chemistry and computer simulation

With the rapid development of modern life science, computational Molecular docking has gradually become one of the core disciplines and methods of modern life science research. Computational docking studies the relationship between the structure and pharmacodynamics of biological macromolecules and the interaction between biological macromolecules and ligands. It promotes the development of protein engineering, protein design, and computer-aided drug design with powerful and various docking software in predicting the three-dimensional structure and dynamic characteristics of proteins from protein sequences. Nowadays, this computing power can be provided by the GPU through the use of a general-purpose computing model on GPUs. This article presents two approaches to parallelizing the descriptive algorithms on the GPU to solve the molecular docking problem and then evaluating them in terms of the computation time achieved. The proposed approaches are effective in accelerating molecular docking on GPUs compared to a single-core or multicore CPU. Besides introducing parallelization approaches, we propose a new descriptive algorithm based on the bee swarm algorithm to solve the molecular docking problem as an alternative to traditional descriptive algorithms such as the genetic algorithm.

Autonomous Satellite Rendezvous and Proximity Operations with Time-Constrained Sub-Optimal Model Predictive Control

This paper presents a time-constrained model predictive control strategy for the 6 degree-of-freedom (6DOF) autonomous rendezvous and docking problem between a controllable “deputy” spacecraft and an uncontrollable “chief” spacecraft. The control strategy accounts for computational time constraints due to limited onboard processing speed. The translational dynamics model is derived from the Clohessy-Wiltshire equations and the angular dynamics are modeled on gas jet actuation about the deputy's center of mass. Simulation results are shown to achieve the docking configuration under computational time constraints by limiting the number of allowed algorithm iterations when computing each input. Specifically, we show that upwards of 90% of computations can be eliminated from a model predictive control implementation without significantly harming control performance.

Safety-Critical Control for Systems With Impulsive Actuators and Dwell Time Constraints

This paper presents extensions of control barrier function (CBF) and control Lyapunov function (CLF) theory to systems wherein all actuators cause impulsive changes to the state trajectory, and can only be used again after a minimum dwell time has elapsed. These rules define a hybrid system, wherein the controller must at each control cycle choose whether to remain on the current state flow or to jump to a new trajectory. We first derive a sufficient condition to render a specified set forward invariant using extensions of CBF theory. We then derive related conditions to ensure asymptotic stability in such systems, and apply both conditions online in an optimization-based control law with aperiodic impulses. We simulate both results on a spacecraft docking problem with multiple obstacles.

Accuracy of Relative Navigation Using Time-of-Flight Cameras

Three-dimensional time-of-flight cameras are being used increasingly widely, and they have found applications in robotics for information support of motion control tasks. They are also considered promising for spacecraft control at short distances from other spacecraft. One such application is relative navigation in the problem of docking with a non-cooperative spacecraft. In this case, the values of the relative coordinates’ measurement errors that the time-of-flight camera can provide are very important. This paper proposes a method for estimating the magnitude of errors in measuring relative coordinates, which depend on the shape of the passive spacecraft, and the distance, observation angle, and parameters of the time-of-flight camera. The lower Cramer–Rao bound is used as an estimate.

Elucidating the function of hypothetical PE_PGRS45 protein of Mycobacterium tuberculosis as an oxido-reductase: a potential target for drug repurposing for the treatment of tuberculosis

Mycobacterium tuberculosis (Mtb) encodes a total of 67 PE_PGRS proteins and definite functions of many of them are still unknown. This study reports PE_PGRS45 (Rv2615c) protein from Mtb as NADPH dependent oxido-reductase having substrate specificity for fatty acyl Coenzyme A. Computational studies predicted PE_PGRS45 to be an integral membrane protein of Mtb. Expression of PE_PGRS45 in non-pathogenic Mycobacterium smegmatis, which does not possess PE_PGRS genes, confirmed its membrane localization. This protein was observed to have NADPH binding motif. Experimental validation confirmed its NADPH dependent oxido-reductase activity (Km value = 34.85 ± 9.478 μM, Vmax = 96.77 ± 7.184 nmol/min/mg of protein). Therefore, its potential to be targeted by first line anti-tubercular drug Isoniazid (INH) was investigated. INH was predicted to bind within the active site of PE_PGRS45 protein and experiments validated its inhibitory effect on the oxido-reductase activity of PE_PGRS45 with IC50/Ki values of 5.66 μM. Mtb is resistant to first line drugs including INH. Therefore, to address the problem of drug resistant TB, docking and Molecular Dynamics (MD) simulation studies between PE_PGRS45 and three drugs (Entacapone, Tolcapone and Verapamil) which are being used in Parkinson’s and hypertension treatment were performed. PE_PGRS45 bound the three drugs with similar or better affinity in comparison to INH. Additionally, INH and these drugs bound within the same active site of PE_PGRS45. This study discovered Mtb’s PE_PGRS45 protein to have an oxido-reductase activity and could be targeted by drugs that can be repurposed for TB treatment. Furthermore, in-vitro and in-vivo validation will aid in drug-resistant TB treatment. HIGHLIGHTS In-silico and in-vitro studies of hypothetical protein PE_PGRS45 (Rv2615c) of Mycobacterium tuberculosis (Mtb) reveals it to be an integral membrane protein PE_PGRS45 protein has substrate specificity for fatty acyl Coenzyme A (fatty acyl CoA) and possess NADPH dependent oxido-reductase activity Docking and simulation studies revealed that first line anti-tubercular drug Isoniazid (INH) and other drugs with anti-TB property have strong affinity for PE_PGRS45 protein Oxido-reductase activity of PE_PGRS45 protein is inhibited by INH PE_PGRS45 protein could be targeted by drugs that can be repurposed for TB treatment Communicated by Ramaswamy H. Sarma

Fast solution of three‐dimensional elliptic equations with randomly generated jumping coefficients by using tensor‐structured preconditioners

AbstractIn this paper, we propose and analyze the numerical algorithms for fast solution of periodic elliptic problems in random media in , . Both the two‐dimensional (2D) and three‐dimensional (3D) elliptic problems are considered for the jumping equation coefficients built as a checkerboard type configuration of bumps randomly distributed on a large , or lattice, respectively. The finite element method discretization procedure on a 3D uniform tensor grid is described in detail, and the Kronecker tensor product approach is proposed for fast generation of the stiffness matrix. We introduce tensor techniques for the construction of the low Kronecker rank spectrally equivalent preconditioner in a periodic setting to be used in the framework of the preconditioned conjugate gradient iteration. The discrete 3D periodic Laplacian pseudo‐inverse is first diagonalized in the Fourier basis, and then the diagonal matrix is reshaped into a fully populated third‐order tensor of size . The latter is approximated by a low‐rank canonical tensor by using the multigrid Tucker‐to‐canonical tensor transform. As an example, we apply the presented solver in numerical analysis of stochastic homogenization method where the 3D elliptic equation should be solved many hundred times, and where for every random sampling of the equation coefficient one has to construct the new stiffness matrix and the right‐hand side. The computational characteristics of the presented solver in terms of a lattice parameter and the grid‐size, , in both 2D and 3D cases are illustrated in numerical tests. Our solver can be used in various applications where the elliptic problem should be solved for a number of different coefficients for example, in many‐particle dynamics, protein docking problems or stochastic modeling.