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Cyclic coordinate descent: A robotics algorithm for protein loop closure.

ABSTRACT: In protein structure prediction, it is often the case that a protein segment must be adjusted to connect two fixed segments. This occurs during loop structure prediction in homology modeling as well as in ab initio structure prediction. Several algorithms for this purpose are based on the inverse Jacobian of the distance constraints with respect to dihedral angle degrees of freedom. These algorithms are sometimes unstable and fail to converge. We present an algorithm developed originally for inverse kinematics applications in robotics. In robotics, an end effector in the form of a robot hand must reach for an object in space by altering adjustable joint angles and arm lengths. In loop prediction, dihedral angles must be adjusted to move the C-terminal residue of a segment to superimpose on a fixed anchor residue in the protein structure. The algorithm, referred to as cyclic coordinate descent or CCD, involves adjusting one dihedral angle at a time to minimize the sum of the squared distances between three backbone atoms of the moving C-terminal anchor and the corresponding atoms in the fixed C-terminal anchor. The result is an equation in one variable for the proposed change in each dihedral. The algorithm proceeds iteratively through all of the adjustable dihedral angles from the N-terminal to the C-terminal end of the loop. CCD is suitable as a component of loop prediction methods that generate large numbers of trial structures. It succeeds in closing loops in a large test set 99.79% of the time, and fails occasionally only for short, highly extended loops. It is very fast, closing loops of length 8 in 0.037 sec on average.

SUBMITTER: Canutescu AA

PROVIDER: S-EPMC2323867 | biostudies-literature | 2003 May

REPOSITORIES: biostudies-literature

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Cyclic coordinate descent: A robotics algorithm for protein loop closure.

Canutescu Adrian A AA Dunbrack Roland L RL

Protein science : a publication of the Protein Society 20030501 5

In protein structure prediction, it is often the case that a protein segment must be adjusted to connect two fixed segments. This occurs during loop structure prediction in homology modeling as well as in ab initio structure prediction. Several algorithms for this purpose are based on the inverse Jacobian of the distance constraints with respect to dihedral angle degrees of freedom. These algorithms are sometimes unstable and fail to converge. We present an algorithm developed originally for inv ...[more]

PMID: 12717019

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Project description:BackgroundVarious forms of the so-called loop closure problem are crucial to protein structure prediction methods. Given an N- and a C-terminal end, the problem consists of finding a suitable segment of a certain length that bridges the ends seamlessly. In homology modelling, the problem arises in predicting loop regions. In de novo protein structure prediction, the problem is encountered when implementing local moves for Markov Chain Monte Carlo simulations. Most loop closure algorithms keep the bond angles fixed or semi-fixed, and only vary the dihedral angles. This is appropriate for a full-atom protein backbone, since the bond angles can be considered as fixed, while the (phi, psi) dihedral angles are variable. However, many de novo structure prediction methods use protein models that only consist of Calpha atoms, or otherwise do not make use of all backbone atoms. These methods require a method that alters both bond and dihedral angles, since the pseudo bond angle between three consecutive Calpha atoms also varies considerably.ResultsHere we present a method that solves the loop closure problem for Calpha only protein models. We developed a variant of Cyclic Coordinate Descent (CCD), an inverse kinematics method from the field of robotics, which was recently applied to the loop closure problem. Since the method alters both bond and dihedral angles, which is equivalent to applying a full rotation matrix, we call our method Full CCD (FCDD). FCCD replaces CCD's vector-based optimization of a rotation around an axis with a singular value decomposition-based optimization of a general rotation matrix. The method is easy to implement and numerically stable.ConclusionWe tested the method's performance on sets of random protein Calpha segments between 5 and 30 amino acids long, and a number of loops of length 4, 8 and 12. FCCD is fast, has a high success rate and readily generates conformations close to those of real loops. The presence of constraints on the angles only has a small effect on the performance. A reference implementation of FCCD in Python is available as supplementary information.

Project description:BackgroundExisting feature selection methods typically do not consider prior knowledge in the form of structural relationships among features. In this study, the features are structured based on prior knowledge into groups. The problem addressed in this article is how to select one representative feature from each group such that the selected features are jointly discriminating the classes. The problem is formulated as a binary constrained optimization and the combinatorial optimization is relaxed as a convex-concave problem, which is then transformed into a sequence of convex optimization problems so that the problem can be solved by any standard optimization algorithm. Moreover, a block coordinate gradient descent optimization algorithm is proposed for high dimensional feature selection, which in our experiments was four times faster than using a standard optimization algorithm.ResultsIn order to test the effectiveness of the proposed formulation, we used microarray analysis as a case study, where genes with similar expressions or similar molecular functions were grouped together. In particular, the proposed block coordinate gradient descent feature selection method is evaluated on five benchmark microarray gene expression datasets and evidence is provided that the proposed method gives more accurate results than the state-of-the-art gene selection methods. Out of 25 experiments, the proposed method achieved the highest average AUC in 13 experiments while the other methods achieved higher average AUC in no more than 6 experiments.ConclusionA method is developed to select a feature from each group. When the features are grouped based on similarity in gene expression, we showed that the proposed algorithm is more accurate than state-of-the-art gene selection methods that are particularly developed to select highly discriminative and less redundant genes. In addition, the proposed method can exploit any grouping structure among features, while alternative methods are restricted to using similarity based grouping.

Project description:BackgroundThe combination of robotic tools with assistance technology determines a slightly explored area of applications and advantages for disability or elder people in their daily tasks. Autonomous motorized wheelchair navigation inside an environment, behaviour based control of orthopaedic arms or user's preference learning from a friendly interface are some examples of this new field. In this paper, a Simultaneous Localization and Mapping (SLAM) algorithm is implemented to allow the environmental learning by a mobile robot while its navigation is governed by electromyographic signals. The entire system is part autonomous and part user-decision dependent (semi-autonomous). The environmental learning executed by the SLAM algorithm and the low level behaviour-based reactions of the mobile robot are robotic autonomous tasks, whereas the mobile robot navigation inside an environment is commanded by a Muscle-Computer Interface (MCI).MethodsIn this paper, a sequential Extended Kalman Filter (EKF) feature-based SLAM algorithm is implemented. The features correspond to lines and corners -concave and convex- of the environment. From the SLAM architecture, a global metric map of the environment is derived. The electromyographic signals that command the robot's movements can be adapted to the patient's disabilities. For mobile robot navigation purposes, five commands were obtained from the MCI: turn to the left, turn to the right, stop, start and exit. A kinematic controller to control the mobile robot was implemented. A low level behavior strategy was also implemented to avoid robot's collisions with the environment and moving agents.ResultsThe entire system was tested in a population of seven volunteers: three elder, two below-elbow amputees and two young normally limbed patients. The experiments were performed within a closed low dynamic environment. Subjects took an average time of 35 minutes to navigate the environment and to learn how to use the MCI. The SLAM results have shown a consistent reconstruction of the environment. The obtained map was stored inside the Muscle-Computer Interface.ConclusionsThe integration of a highly demanding processing algorithm (SLAM) with a MCI and the communication between both in real time have shown to be consistent and successful. The metric map generated by the mobile robot would allow possible future autonomous navigation without direct control of the user, whose function could be relegated to choose robot destinations. Also, the mobile robot shares the same kinematic model of a motorized wheelchair. This advantage can be exploited for wheelchair autonomous navigation.

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Cyclic coordinate descent: A robotics algorithm for protein loop closure.

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Cyclic coordinate descent: A robotics algorithm for protein loop closure.

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