Structural Compliance Analysis and Internal Motion Properties of Proteins From a Robot Kinematics Perspective: Formulation of Basic Equations

2016 ◽  
Vol 8 (2) ◽  
Author(s):  
Keisuke Arikawa
Keyword(s):  
Kinematic Model ◽  
Structural Data ◽  
Forced Response ◽  
Internal Motion ◽  
Robot Kinematics ◽  
Dihedral Angles ◽  
Protein Model ◽  
Applied Forces ◽  
Basic Equations ◽  
Structural Compliance

From a perspective of robot kinematics, we develop a method for predicting internal motion properties and understanding the functions of proteins from their three-dimensional (3D) structural data (protein data bank (PDB) data). The key ideas are based on the structural compliance analysis of proteins. In this paper, we mainly discuss the basic equations for the analysis. First, a kinematic model of a protein is introduced. Proteins are simply modeled as serial manipulators constrained by linear springs, where the dihedral angles on the main chains correspond to the joint angles of manipulators. Then, the kinematic equations of the protein model are derived. In particular, the forced response or the deformation caused by the forces in static equilibrium forms the basis for the structural compliance analysis. In the formulations, the protein models are regarded as manipulators that control the positions in the model or the distances between them, by the dihedral angles on the main chains. Next, the structural compliance of the protein model is defined, and a method for extracting the information about the internal motion properties from the structural compliance is shown. In general, the structural compliance refers to the relationship between the applied forces and the deformation of the parts surrounded by the application points. We define it in a more general form by separating the parts whose deformations are evaluated from those where forces are applied. When decomposing motion according to the magnitude of the structural compliance, we can infer that the lower compliance motion will easily occur. Finally, we show two application examples using PDB data of lactoferrin and hemoglobin. Despite using an approximate protein model, the predicted internal motion properties agree with the measured ones.

Analyzing Internal Motion of Proteins From Viewpoint of Robot Kinematics: Formulation of Group Forced Response Method

2012 ◽  
Author(s):  
Keisuke Arikawa
Keyword(s):  
Protein Structures ◽  
Computational Cost ◽  
Three Dimensional ◽  
Structural Data ◽  
Simple Calculation ◽  
Forced Response ◽  
Internal Motion ◽  
Robot Kinematics ◽  
Internal Motions ◽  
Applied Forces

An analogous relationship exists between the kinematic structures of proteins and robotic mechanisms. Hence, using this analogy, we attempt to understand the internal motions of proteins from the perspective of robot kinematics. In this study, we propose a method called group forced response (GFR) method for predicting the internal motion of proteins on the basis of their three-dimensional structural data (PDB data). In this method, we apply forces in static equilibrium to groups of atoms (e.g., secondary structures, domains, and subunits) and not to specific atoms. Furthermore, we predict the internal motion of proteins by analyzing the relative motion caused among groups by the applied forces. First, we show a method for approximately modeling protein structures as a robotic mechanism and the basic kinematic equations of the model. Next, the GFR method is formulated (e.g., Jacobian matrix for group motions, magnitude of forces applied to groups, and decomposition of motions into modes according to structural compliances). Finally, we present example applications of the proposed method in real protein structures. Despite the approximations in the model, low computational cost, and use of simple calculation parameters, the results almost agree with measured internal motions.

Kinematic Modeling and Internal Motion Analysis of Proteins From a Robot Kinematics Viewpoint

2011 ◽  
Author(s):  
Keisuke Arikawa
Keyword(s):  
Jacobian Matrix ◽  
Robot Manipulator ◽  
Kinematic Model ◽  
Internal Motion ◽  
Robot Kinematics ◽  
Kinematic Modeling ◽  
Serial Link ◽  
Internal Motions ◽  
Basic Equations ◽  
External Forces

This paper discusses the kinematic modeling of proteins and the analysis of their internal motion from the viewpoint of robot kinematics. First, a kinematic model of a protein is introduced. This model consists of multiple serial link mechanisms and interaction lines (lines between alpha carbons). The protein model is regarded as a type of a robot manipulator that uses joint angles to control the lengths of the interaction lines, and the Jacobian matrix of the manipulator is derived. On the basis of this Jacobian matrix, the basic equations for calculating the deformation caused by external forces and evaluating the structural compliance of specified parts are derived. Finally, by combining the derived basic equations, we analyze the internal motions of lactoferrin and hemoglobin and compare the results with the reported measured characteristics of their internal motions. Despite the approximations by the model, the results obtained by the proposed method agree with the measured internal motion.

Extension of the Kinematics-Based Method for Predicting the Motion of Proteins

2014 ◽  
Author(s):  
Keisuke Arikawa
Keyword(s):  
Computational Cost ◽  
Three Dimensional ◽  
Structural Data ◽  
Data Bank ◽  
Serial Manipulators ◽  
Protein Model ◽  
The Matrix ◽  
Basic Equations ◽  
Definition Of ◽  
Structural Compliance

On the basis of an analogy between the kinematic structures of proteins and robotic mechanisms, we have so far developed methods for predicting the internal motion of proteins from three-dimensional structural data in the protein data bank (PDB). With these methods, we model proteins as serial manipulators constrained by springs, and calculate the structural compliance of the protein model. In this study, toward more practical purposes, we reformulate and extend the existing methods by broadening the definition of structural compliance and reducing the number of variables for expressing the conformation of the model. The broadening is performed by separating the parts whose deformations are evaluated from those where forces are applied. This separation allows the calculation of the effective forces causing deformation in other specified parts. We also reduce the number of conformation variables from the consideration based on the algebraic structure of the basic equations. The size of the matrix whose inverse must be calculated is thus minimized, and the computational cost is reduced. We verify the effectiveness of these extensions by analyzing the PDB data of some proteins.

Analyzing Motion Properties of Proteins Affected by Localized Structures From a Robot Kinematics Perspective

2015 ◽  
Author(s):  
Keisuke Arikawa
Keyword(s):  
Protein Data Bank ◽  
Complex Shape ◽  
Structural Data ◽  
Data Bank ◽  
Robot Kinematics ◽  
Motion Prediction ◽  
Serial Manipulators ◽  
Localized Structures ◽  
Motion Modes ◽  
Structural Compliance

On the basis of robot kinematics, we have thus far developed a method for predicting the motion of proteins from their 3D structural data given in the Protein Data Bank (PDB data). In this method, proteins are modeled as serial manipulators constrained by springs and the structural compliance properties of the models are evaluated. We focus on localized instead of whole structures of proteins. Employing the same model used in our method of motion prediction, the motion properties of the localized structures and the relation between the motion properties of localized and whole structures are analyzed. First, we present a method for graphically expressing the deformation of objects with a complex shape, such as proteins, by approximating the shape as a rectangular prism with a mesh on its surface. We then formulate a method for comparing the motion properties of localized structures cleaved from the whole structure and those remaining in it by expressing the motion of the latter using the decomposed motion modes of the former according to the structural compliance. Finally, we show a method for evaluating the effect of a localized structure on the motion properties of proteins by applying forces to localized structures. In the formulations, we demonstrate applications as illustrative examples using the PDB data of a real protein.

A Computational Framework for Predicting the Motions of a Protein System From a Robot Kinematics Viewpoint

2013 ◽  
Author(s):  
Keisuke Arikawa
Keyword(s):  
Robot Manipulator ◽  
Structural Data ◽  
Protein Molecule ◽  
Data Bank ◽  
Computational Time ◽  
Robot Kinematics ◽  
Efficient Computation ◽  
Elastic Network Model ◽  
Computational Framework ◽  
Structural Compliance

There is an analogy between the kinematic structures of proteins and robotic mechanisms. On the basis of this analogy, we have so far developed some methods for predicting the internal motions of proteins from their three-dimensional structural data in protein data bank (PDB). However, these methods are basically applicable to a single protein molecule. In this study, we extended these methods to apply them to systems that consist of multiple molecules including proteins (protein systems), and developed a computational framework for predicting the motions of the molecules. The model used in this method is a type of elastic network model. In particular, proteins are modeled as a robot manipulator constrained by the springs (the dihedral angles on the main chains correspond to the joint angles). The interactions between molecules are also modeled as springs. The basic concept for predicting the motions is based on the analysis of structural compliance. By applying statically balanced forces to the model in various directions, we extracted those motions with larger structural compliance. To reduce the computational time, we formulated the method with the prospect of efficient computation including parallel computation. In addition, we developed a preparatory computer program implementing the proposed algorithms, and analyzed some protein systems. The results showed that the proposed computational framework can efficiently analyze large protein systems.

Investigation of Algorithms for Analyzing Protein Internal Motion From Viewpoint of Robot Kinematics

2010 ◽  
Author(s):  
Keisuke Arikawa
Keyword(s):  
Main Chain ◽  
Control Strategies ◽  
Three Dimensional ◽  
Internal Motion ◽  
Robot Kinematics ◽  
Redundant Manipulators ◽  
Serial Link ◽  
Protein Model ◽  
External Forces ◽  
And Control

We investigate various algorithms for analyzing the characteristics of the internal motion of proteins based on the analogies between their kinematic structures and robotic mechanisms. First, we introduce an artificial simple protein model, planar main chain (PMC), composed of a planar serial link mechanism to investigate the algorithms. Then, we develop algorithms for analyzing the conformational fluctuations by applying the manipulability analysis of robot manipulators and control strategies for redundant manipulators. Next, we develop algorithms for analyzing the conformational deformation caused by the external forces and to evaluate the compliances of the specified parts of proteins. Finally, we show that the proposed algorithms developed by using PMC models are applicable for the three dimensional main chain structures of real proteins, and may be used to analyze their characteristics of the internal motion. We also reveal some preliminary simulation results of the analysis of a real protein.

Conditions for Rigid and Flat Foldability of Degree-n Vertices in Origami

2019 ◽  
Vol 12 (1) ◽  
Author(s):  
Luca Zimmermann ◽  
Kristina Shea ◽  
Tino Stanković
Keyword(s):  
Engineering Design ◽  
Kinematic Model ◽  
Spherical Triangle ◽  
Simple Rule ◽  
Dihedral Angles ◽  
Single Vertex ◽  
Efficient Approach ◽  
Single Degree ◽  
Revolute Joints ◽  
Intrinsic Condition

Abstract In rigid origami, the complex folding motion arises from the rotation of strictly rigid faces around crease lines that represent perfect revolute joints. The rigid folding motion of an origami crease pattern is collectively determined by the kinematics of its individual vertices. Establishing a kinematic model and determining the conditions for the rigid foldability of a single vertex is thus important to exploit rigid origami in engineering design tasks. Today, there exists neither an efficient kinematic model to determine the unknown dihedral angles nor an intrinsic condition for the rigid foldability of arbitrarily complex vertices of degree n. In this paper, we present the principle of three units (PTU) that provides an efficient approach to modeling the kinematics of single degree-n vertices. The PTU is based on the notion that the kinematics of a vertex is determined by the behavior of a single underlying spherical triangle. The condition for the existence of this triangle leads to the condition for the rigid and flat foldability of degree-n vertices. These findings are transferred from single vertices to crease patterns, resulting in a simple rule to generate kinematically determinate crease patterns that can be designed to fold rigidly. Finally, we discuss the limitations of the PTU with respect to the global rigid foldability of a crease pattern.

Deployable Prismatic Structures With Origami Patterns

2014 ◽  
Author(s):  
Sicong Liu ◽  
Weilin Lv ◽  
Yan Chen ◽  
Guoxing Lu
Keyword(s):  
Design Method ◽  
Kinematic Model ◽  
The Other ◽  
Dihedral Angles ◽  
Geometric Condition ◽  
Compatibility Conditions ◽  
Deployable Structures ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Geometric Compatibility

In order to find the general condition of the rigid origami pattern for the deployable prismatic structures, the kinematic model is proposed based on the mobile assemblies of spherical 4R linkages. The kinematic and geometric compatibility conditions of the mobile assemblies are derived. Two groups of 2n-side deployable prismatic structures are obtained. When n=2, one of them is with kite-shape intersection, while the other is with parallelgram. The variations of the unit are discussed. The straight and curvy multilayer prisms are built by changing the dihedral angles between the intersecting planes. The general design method for the 2n-side multilayer deployable prismatic structures is proposed with the geometric condition of the origami patterns. All the deployable structures constructed with this method can be deployed and folded along the central axis of the prisms with single degree of freedom, which makes the structures have wide engineering applications.

scholarly journals Modeling Parallel Robot Kinematics for 3T2R and 3T3R Tasks Using Reciprocal Sets of Euler Angles

Robotics ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 68 ◽  
Author(s):  
Moritz Schappler ◽  
Svenja Tappe ◽  
Tobias Ortmaier
Keyword(s):  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Robot Kinematics ◽  
Euler Angles ◽  
Gradient Descent Algorithm ◽  
Kinematic Models ◽  
Rotational Degrees Of Freedom ◽  
Definition Of

Industrial manipulators and parallel robots are often used for tasks, such as drilling or milling, that require three translational, but only two rotational degrees of freedom (“3T2R”). While kinematic models for specific mechanisms for these tasks exist, a general kinematic model for parallel robots is still missing. This paper presents the definition of the rotational component of kinematic constraints equations for parallel robots based on two reciprocal sets of Euler angles for the end-effector orientation and the orientation residual. The method allows completely removing the redundant coordinate in 3T2R tasks and to solve the inverse kinematics for general serial and parallel robots with the gradient descent algorithm. The functional redundancy of robots with full mobility is exploited using nullspace projection.

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