This module explains how to model a protein as a robotic manipulator and introduces the robotic path planning problem and algorithms for solving it, including the probabilistic roadmap method. Variations of the Probabilistic Roadmap Method have been employed for problems related to protein motion.
Topics in this module
Proteins as Robotic Manipulators
Robotic Path Planning
Sampling-Based Planners for Proteins
Proteins as robotic manipulators
In the modules on
protein kinematics and
inverse kinematics , it was shown that, structurally and kinematically, proteins are very similar to a class of
robotic manipulators consisting of arms connected by revolute joints. Because of this analogy, in the late 1990s, some robotics researchers began to speculate that methods developed for use with robots might also be applicable to the study of proteins. For the remainder of this module, the analogy between robots and proteins will be explored, and then a class of robotics algorithms, called path planners, that will be adapted in a later module to use with proteins, will be introduced.
Recall that a protein is a chain of amino acid residues. Each residue contributes two rotatable dihedral angles, designated φ and ψ, to the main chain of the protein, and may additionally have a side chain with up to five rotatable dihedral angles. Under the
rigid geometry simplification, these rotatable dihedral angles are the only degrees of freedom available to the protein.
A dihedral angle
is the plane uniquely defined by the first three atoms
,
, and
. Similarly,
is the plane uniquely defined by the last three atoms
, and
, and
. The dihedral angle, θ, is defined as the smallest angle
between these two planes. You can read more about the
angle between two intersecting planes .
If we replace each bond by a rigid bar and each rotatable dihedral by a revolute joint, we can build a robotic linkage kinematically equivalent to a protein under rigid geometry.
Robotic path planning
Background
Terms from robotic path planning
Work space : The work space is the geometric space in which a robot operates. It consists of obstacles and empty space that may be occupied by the robot.
Configuration : A configuration of the robot is a full description of the robot's state, including its position, orientation, and the states of any internal degrees of freedom (such as revolute joint angles).
Collision : A configuration is said to be in collision if any part of the robot overlaps with either another part of the robot or with a work space obstacle.
Free : A configuration is said to be free if it is not in collision.
Configuration space (C-space) : The space of all configurations of the robot, annotated by whether the robot is in collision or free at each configuration.
Free space : The space of all free configurations.
Work space, two-dimensional disc robot
The work space for a simple robot. The robot is a two dimensional disc. Configurations are therefore (x,y) pairs. If the robot were not circular, an orientational degree of freedom would also need to be specified.
Configuration space, two-dimensional disc robot
The configuration space corresponding to the above work space. Each point now corresponds to a configuration of the robot, rather than a real point in space. To see how it was constructed, choose any point on the robot as a reference. Now imagine the curves swept out by that point as the robot slides along the surface of the obstacles and along the border of the work space. Every configuration closer to the obstacles than this curve is in collision, and every configuration farther than the curve is free.
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Source:
OpenStax, Geometric methods in structural computational biology. OpenStax CNX. Jun 11, 2007 Download for free at http://cnx.org/content/col10344/1.6
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