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The internal degrees of freedom of a protein

The degrees of freedom of a system are a set of parameters that may be varied independently to define the state of the system. For example, the location of a point in the Cartesian 2D plane may be defined as a displacement along the x-axis and a displacement along the y-axis, given as a (x,y) pair. It may also be given as a rotation about the origin by θ degrees and a distance r from the origin, given as a (r,θ) pair. In either case, a point moving freely in a plane has exactly two degrees of freedom.

As mentioned before, the spatial arrangement of the atoms in a protein constitute its conformation. In the PDB coordinate file above, we can see that one obvious way to define a protein conformation is by giving x, y, and z coordinates for each atom, relative to some arbitrary origin. These are not independent degrees of freedom, however, because atoms within a molecule are not allowed to leave the vicinity of their neighboring atoms (if no chemical reaction takes place). Pairs of atoms bonded to each other, for example, are constrained to remain close, so moving one atom causes others connected to it to move in a dependent fashion. In the kinematics terminology, this means that the true, effective or independent number of degrees of freedom is much less than the input space parameters -an (x,y,z) tuple for each atom-. The remainder of this section defines a set of independent degrees of freedom that more readily model how proteins and other organic molecules can actually move.

Bonds and bond length

The atoms in proteins are connected to one another through covalent bonds. Each pair of bonded atoms has a preferred separation distance called the bond length . The bond length can vary slightly with a spring-like vibration, and is thus a degree of freedom, but realistic variations in bond length are so small that most simulations assume it is fixed for any pair of atoms. This is a very common assumption in the literature and reduces the effective degrees of freedom of a protein; the remainder of this module makes this assumption.

Although bond lengths will not be allowed to vary in this work, the presence of bonds is still important because it allows us to represent the connectivity of the protein as an undirected graph data structure, where the atoms are the nodes and the bonds between them are undirected edges. In some cases, it is helpful to artificially break any cycles in the graph, and choose an atom from the interior as an anchor atom. The graph can then be treated as a tree data structure, with the anchor atom as the root.

A protein as a graph data structure

A tree-like representation of protein connectivity, for a very small molecule. Cycles are broken by ignoring one bond in each.

Bond angles

Bond length is an independent degree of freedom given two connected atoms. A set of three atoms bonded in sequence defines another degree of freedom: the angle between the two adjacent bonds. This is, appropriately, referred to as the bond angle . The bond angle can be calculated as the angle between the two vectors corresponding to the bonds from the central atom to each of its neighbors. As a reminder, the angle between two vectors is the inverse cosine of the ratio of the dot product of the vectors to the product of their lengths. Like bond lengths, bond angles tend to be characteristic of the atom types involved, and, with few exceptions, vary little. Thus, like bond lengths, this module considers all bond angles as fixed (again, this is a common assumption).

Questions & Answers

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
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
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.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
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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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