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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

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
Daniel
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
Maciej
characteristics of micro business
Abigail
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
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.
Virgil
is Bucky paper clear?
CYNTHIA
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
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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