Download Двумерное случайное блуждание и критические явления в ДНК

G. N. Hayrapetyan1, E. Sh. Mamasakhlisov1, V. F. Morozov1,
Vl. V. Papoyan1,2, S. S. Pogosyan2, V. B. Priezzhev2
1
Department of Physics, Yerevan State University, Yerevan, Armenia
2 Bogolubov Laboratory of Theoretical Physics, JINR, Dubna, Russia
coil
region
helical
region
hydrogen
bond
helix-coil transition in a double-stranded
homopolynucleotide
(melting phenomenon)
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Poland-Sheraga type model
Ising-like sequence of base pairs
Peyrard-Bishop type model
molecular dynamics
renormalization group
“minimal” model
3D
3D
3.
For
convenience
we consider
random
the endchains
of vector
on
1.
A molecule
of DNA
considered
as walk
a
twoofrandom
which
2. Thereafter,
we
watch isthe
vectors that
connects
the end of one
of
quadratic
lattice.
In
term
of
random
walks
the
return
to
the
origin
begin
from the
sametopoint.
Complementary
pairs of nitrogen
bases
the random
chains
the end
of another. Projecting
that's vectors
will
correspond
to binding
between
complementary
pairbinding
of nitrogen
are
to create
hydrogen
bonds,
andtotoaxis
each
onto able
the planes
which
are perpendicular
of moleculewill
of
bases.
correspond
an intersection
of two random
DNA, we obtain
a two dimensional
randomchains.
walk.
2D
generating function for the first return
where fm is the probability of the first
return on the m-th step.
generating function for the any return
where pm is the probability of any
return on the m-th step.
generating function for the any return
to the origin on the quadratic lattice
statistical weight of contact with origin
 k<1 (U>0) repulsion of particle at origin
 k>1 (U<0) attraction of particle at origin
k>1 (U<0)
The internal energy per step, in units T
k<1 (U>0)
E=0
“Minimal” model
statistical weight of contact with origin
δS(m) = -c log m
c=1
kc =1
k > 1 ( T < Tc )
U<0
Tc
k < 1 ( T > Tc )
Density of the free energy
k > 1 ( T < Tc )
T  Tc
T  Tc- 0
infinite order phase transition
“loop factor” c = 1
Helicity degree & correlation function
L=N/2
T  Tc- 0
ξ   (T  Tc- 0)