# 0.4 Molecular distance measures

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Given a set of structures of the same molecule, it is often necessary to decide which are more similar or less similar to each other. This module presents a few ways to approach that problem, including root mean squared distance (RMSD), least RMSD, and intramolecular distance measures.

## Topics in this module

• Comparing Molecular Conformations
• RMSD and lRMSD
• Optimal Alignment for lRMSD Using Rotation Matrices
• Optimal Alignment for lRMSD Using Quaternions
• Introduction to Quaternions
• Quaternions and Three-Dimensional Rotations
• Optimal Alignment with Quaternions
• Intramolecular Distance and Related Measures

## Comparing molecular conformations

Molecules are not rigid. On the contrary, they are highly flexible objects, capable of changing shape dramatically through the rotation of dihedral angles. We need a measure to express how much a molecule changes going from one conformation to another, or alternatively, how different two conformations are from each other. Each distinct shape of a given molecule is called a conformation . Although one could conceivably compute the volume of the intersection of thealpha shapes for two conformations (see Molecular Shapes and Surfaces for an explanation of alpha shapes) to measure the shape change, this is prohibitively computationally expensive. Simpler measures of distance between conformations have been defined, based on variables such as the Cartesian coordinates for each atom, or the bond and torsion angles within the molecule. When working with Cartesian coordinates, one can represent a molecular conformation as a vector whose components are the Cartesian coordinates of the molecule's atoms. Therefore, a conformation for a molecule with N atoms can be represented as a 3N-dimensional vector of real numbers.

## Rmsd and lrmsd

One of the most widely accepted difference measures for conformations of a molecule is least root mean square deviation (lRMSD) . To calculate the RMSD of a pair of structures (say x and y), each structure must be represented as a 3N-length (assuming N atoms) vector of coordinates. The RMSD is the square root of the average of the squared distances between corresponding atoms of x and y. It is a measure of the average atomic displacement between the two conformations:

However, when molecular conformations are sampled from molecular dynamics or other forms of sampling, it is often the case that the molecule drifts away from the origin and rotates in an arbitrary way. The lRMSD distance aims at compensating for these facts by representing the minimum RMSD over all possible relative positions and orientations of the two conformations under consideration. Calculating the lRMSD consists of first finding an optimal alignment of the two structures, and then calculating their RMSD. Note that aligning two conformations may require both a translation and rotation. In other words, before computing the RMSD distance, it is necessary to remove the translation of the centroid of both conformations and to perform an "optimal alignment" or "optimal rotation" of them, since these two factors artificially increase the RMSD distance between them.

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LITNING
scanning tunneling microscope
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what is Nano technology ?
write examples of Nano molecule?
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The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
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yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
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what school?
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biomolecules are e building blocks of every organics and inorganic materials.
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research.net
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sciencedirect big data base
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Introduction about quantum dots in nanotechnology
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absolutely yes
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fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
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what is the actual application of fullerenes nowadays?
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is Bucky paper clear?
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carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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how did you get the value of 2000N.What calculations are needed to arrive at it
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