Chapter 8 – Theoretical Biophysics 341
l =
+
×
=
4.2 nm
(2
2.0 nm)
8.2 nm
Thus, volume Vc of the cuboid is
Vc =
×
×
×
=
×
=
×
−
−
−
−
(6.4
10
)
(8.2
10
)
3.2
10
m
3.2
10
L.
9 2
9
25
3
22
Similarly, the volume of the protein cylinder (Vp) is given by
Vp
2
22
(
(0.5
2.4 nm) )
4.2 nm
1.9
10
L
=
×
×
×
=
×
−
π
Thus,
Vc =
−
×
×
−
−
(3.2
1.9) 10
=1.3
10
L
22
22
Thus,
nw =
×
×
×
×
=
−
55.6
(6.02
10 ) 1.3 10
4350 atoms
23
22
All of these atoms plus the 3900 atoms of the protein must be included explicitly
in the simulation. A high-end GPU is faster than a typical multicore processor by a
factor of ~100. Thus, the total computing time required is
(5 days/100)
(3900
4350) /(3900)
0.52 days
12.5 h
2
2
×
+
=
=
Would the project student be able to witness the results of the simulation
before they go home from work? Yes, of course. Project students don’t need
sleep.….
8.3 MECHANICS OF BIOPOLYMERS
Many important biomolecules are polymers, for example, proteins, nucleic acids, lipids,
and many sugars. Continuum approaches of polymers physics can be applied to many of
these molecules to infer details concerning their mechanical properties. These include
simple concepts such as the freely jointed chain (FJC) and freely rotating chain (FRC) with
approximations such as the Gaussian chain (GC) and wormlike chain (WLC) approaches
and how these entropic spring models predict responses of polymer extension to imposed
force. Nonentropic sources of biopolymer elasticity to model less idealized biopolymers
are also important. These methods enable theoretical estimates of a range of valuable
mechanical parameters to be made and provide biological insight into the role of many
biopolymers.
8.3.1 DISCRETE MODELS FOR FREELY JOINTED CHAINS AND FREELY
ROTATING CHAINS
The FJC model, also called the “random-flight model” or “ideal chain,” assumes n infinitely
stiff discrete chain segments each of length b (known as the Kuhn length) that are freely
jointed to, and transparent to, each other (i.e., parts of the chain can cross through other parts