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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.

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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