114 research outputs found
Fractional diffusion modeling of ion channel gating
An anomalous diffusion model for ion channel gating is put forward. This
scheme is able to describe non-exponential, power-law like distributions of
residence time intervals in several types of ion channels. Our method presents
a generalization of the discrete diffusion model by Millhauser, Salpeter and
Oswald [Proc. Natl. Acad. Sci. USA 85, 1503 (1988)] to the case of a
continuous, anomalous slow conformational diffusion. The corresponding
generalization is derived from a continuous time random walk composed of
nearest neighbor jumps which in the scaling limit results in a fractional
diffusion equation. The studied model contains three parameters only: the mean
residence time, a characteristic time of conformational diffusion, and the
index of subdiffusion. A tractable analytical expression for the characteristic
function of the residence time distribution is obtained. In the limiting case
of normal diffusion, our prior findings [Proc. Natl. Acad. Sci. USA 99, 3552
(2002)] are reproduced. Depending on the chosen parameters, the fractional
diffusion model exhibits a very rich behavior of the residence time
distribution with different characteristic time-regimes. Moreover, the
corresponding autocorrelation function of conductance fluctuations displays
nontrivial features. Our theoretical model is in good agreement with
experimental data for large conductance potassium ion channels
Levy stable distributions via associated integral transform
We present a method of generation of exact and explicit forms of one-sided,
heavy-tailed Levy stable probability distributions g_{\alpha}(x), 0 \leq x <
\infty, 0 < \alpha < 1. We demonstrate that the knowledge of one such a
distribution g_{\alpha}(x) suffices to obtain exactly g_{\alpha^{p}}(x), p=2,
3,... Similarly, from known g_{\alpha}(x) and g_{\beta}(x), 0 < \alpha, \beta <
1, we obtain g_{\alpha \beta}(x). The method is based on the construction of
the integral operator, called Levy transform, which implements the above
operations. For \alpha rational, \alpha = l/k with l < k, we reproduce in this
manner many of the recently obtained exact results for g_{l/k}(x). This
approach can be also recast as an application of the Efros theorem for
generalized Laplace convolutions. It relies solely on efficient definite
integration.Comment: 12 pages, typos removed, references adde
Static Solitons of the Sine-Gordon Equation and Equilibrium Vortex Structure in Josephson Junctions
The problem of vortex structure in a single Josephson junction in an external
magnetic field, in the absence of transport currents, is reconsidered from a
new mathematical point of view. In particular, we derive a complete set of
exact analytical solutions representing all the stationary points (minima and
saddle-points) of the relevant Gibbs free-energy functional. The type of these
solutions is determined by explicit evaluation of the second variation of the
Gibbs free-energy functional. The stable (physical) solutions minimizing the
Gibbs free-energy functional form an infinite set and are labelled by a
topological number Nv=0,1,2,... Mathematically, they can be interpreted as
nontrivial ''vacuum'' (Nv=0) and static topological solitons (Nv=1,2,...) of
the sine-Gordon equation for the phase difference in a finite spatial interval:
solutions of this kind were not considered in previous literature. Physically,
they represent the Meissner state (Nv=0) and Josephson vortices (Nv=1,2,...).
Major properties of the new physical solutions are thoroughly discussed. An
exact, closed-form analytical expression for the Gibbs free energy is derived
and analyzed numerically. Unstable (saddle-point) solutions are also classified
and discussed.Comment: 17 pages, 4 Postscript figure
First Passage Time Distribution and Number of Returns for Ultrametric Random Walk
In this paper, we consider a homogeneous Markov process \xi(t;\omega) on an
ultrametric space Q_p, with distribution density f(x,t), x in Q_p, t in R_+,
satisfying the ultrametric diffusion equation df(x,t)/dt =-Df(x,t). We
construct and examine a random variable \tau (\omega) that has the meaning the
first passage times. Also, we obtain a formula for the mean number of returns
on the interval (0,t] and give its asymptotic estimates for large t.Comment: 20 page
Prediction of infrared light emission from pi-conjugated polymers: a diagrammatic exciton basis valence bond theory
There is currently a great need for solid state lasers that emit in the
infrared, as this is the operating wavelength regime for applications in
telecommunications. Existing --conjugated polymers all emit in the visible
or ultraviolet, and whether or not --conjugated polymers that emit in the
infrared can be designed is an interesting challenge. On the one hand, the
excited state ordering in trans-polyacetylene, the --conjugated polymer
with relatively small optical gap, is not conducive to light emission because
of electron-electron interaction effects. On the other hand, excited state
ordering opposite to that in trans-polyacetylene is usually obtained by
chemical modification that increases the effective bond-alternation, which in
turn increases the optical gap. We develop a theory of electron correlation
effects in a model -conjugated polymer that is obtained by replacing the
hydrogen atoms of trans-polyacetylene with transverse conjugated groups, and
show that the effective on-site correlation in this system is smaller than the
bare correlation in the unsubstituted system. An optical gap in the infrared as
well as excited state ordering conducive to light emission is thereby predicted
upon similar structural modifications.Comment: 15 pages, 15 figures, 1 tabl
ΠΠΈΠΊΡΠΎΠ ΠΠ ΠΈ ΠΌΠ°Π»ΡΠ΅ ΠΈΠ½ΡΠ΅ΡΡΠ΅ΡΠΈΡΡΡΡΠΈΠ΅ Π ΠΠ ΠΊΠ°ΠΊ ΠΈΠ½ΡΡΡΡΠΌΠ΅Π½ΡΡ Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½Π½ΠΎΠΉ ΡΠ΅Π³ΡΠ»ΡΡΠΈΠΈ ΠΊΠ»Π΅ΡΠΎΡΠ½ΡΡ ΠΏΡΠΎΡΠ΅ΡΡΠΎΠ² Π΄Π»Ρ ΡΠ΅ΡΠ°ΠΏΠΈΠΈ ΠΎΠ½ΠΊΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ Π·Π°Π±ΠΎΠ»Π΅Π²Π°Π½ΠΈΠΉ
MicroRNAs and small interfering RNAs (siRNAs) belong to an extensive class of small non-coding RNAsΒ and play an important role in gene expression regulation in cells. It is shown that changes in the amountΒ or activity of these molecules may lead to the development of various diseases, including cancer. ThisΒ made it possible to consider them as promising diagnostic and prognostic markers, as well as tools for theΒ directed regulation of protein synthesis in the cell and targets for therapy. This review summarizes theΒ basic knowledge about the biogenesis, distribution and the mechanisms of action of microRNA and siRNA,Β as well as currently used ways of target genes expression management with their help. Possible methodsΒ of these molecules delivery into the cell in vitro and in vivo are considered.ΠΠΈΠΊΡΠΎΠ ΠΠ ΠΈ ΠΌΠ°Π»ΡΠ΅ ΠΈΠ½ΡΠ΅ΡΡΠ΅ΡΠΈΡΡΡΡΠΈΠ΅ Π ΠΠ (ΠΌΠΈΠ ΠΠ) ΠΎΡΠ½ΠΎΡΡΡΡΡ ΠΊ ΠΎΠ±ΡΠΈΡΠ½ΠΎΠΌΡ ΠΊΠ»Π°ΡΡΡ ΠΌΠ°Π»ΡΡ
Π½Π΅ΠΊΠΎΠ΄ΠΈΡΡΡΡΠΈΡ
Π ΠΠ ΠΈ ΠΈΠ³ΡΠ°ΡΡ Π²Π°ΠΆΠ½ΡΡ ΡΠΎΠ»Ρ Π² ΡΠ΅Π³ΡΠ»ΡΡΠΈΠΈ ΡΠΊΡΠΏΡΠ΅ΡΡΠΈΠΈ Π³Π΅Π½ΠΎΠ² Π² ΠΊΠ»Π΅ΡΠΊΠ°Ρ
. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎΒ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΡ Π² ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π΅ ΠΈΠ»ΠΈ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ Π²ΠΎΠ·Π΄Π΅ΠΉΡΡΠ²ΠΈΡ ΡΡΠΈΡ
ΠΌΠΎΠ»Π΅ΠΊΡΠ» ΠΌΠΎΠ³ΡΡ ΡΠΎΠΏΡΠΎΠ²ΠΎΠΆΠ΄Π°ΡΡ ΡΠ°Π·Π²ΠΈΡΠΈΠ΅ ΡΠ°Π·Π»ΠΈΡΠ½ΡΡ
Π·Π°Π±ΠΎΠ»Π΅Π²Π°Π½ΠΈΠΉ, Π²ΠΊΠ»ΡΡΠ°Ρ ΠΎΠ½ΠΊΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΠ΅. ΠΡΠΎ ΠΏΠΎΠ·Π²ΠΎΠ»ΠΈΠ»ΠΎ ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡ ΠΈΡ
ΠΊΠ°ΠΊ ΠΏΠ΅ΡΡΠΏΠ΅ΠΊΡΠΈΠ²Π½ΡΠ΅ Π΄ΠΈΠ°Π³Π½ΠΎΡΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΈ ΠΏΡΠΎΠ³Π½ΠΎΡΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΌΠ°ΡΠΊΠ΅ΡΡ, Π° ΡΠ°ΠΊΠΆΠ΅ ΠΈΠ½ΡΡΡΡΠΌΠ΅Π½ΡΡ Π΄Π»Ρ Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½Π½ΠΎΠΉΒ ΡΠ΅Π³ΡΠ»ΡΡΠΈΠΈ ΡΠΈΠ½ΡΠ΅Π·Π° Π±Π΅Π»ΠΊΠΎΠ² Π² ΠΊΠ»Π΅ΡΠΊΠ΅ ΠΈ ΠΌΠΈΡΠ΅Π½ΠΈ Π΄Π»Ρ ΡΠ΅ΡΠ°ΠΏΠΈΠΈ. Π Π΄Π°Π½Π½ΠΎΠΌ ΠΎΠ±Π·ΠΎΡΠ΅ ΡΡΠΌΠΌΠΈΡΠΎΠ²Π°Π½Ρ ΠΎΡΠ½ΠΎΠ²Π½ΡΠ΅Β Π·Π½Π°Π½ΠΈΡ ΠΎ Π±ΠΈΠΎΠ³Π΅Π½Π΅Π·Π΅, ΡΠ°ΡΠΏΡΠΎΡΡΡΠ°Π½Π΅Π½ΠΈΠΈ ΠΈ ΠΌΠ΅Ρ
Π°Π½ΠΈΠ·ΠΌΠ°Ρ
Π²ΠΎΠ·Π΄Π΅ΠΉΡΡΠ²ΠΈΡ ΠΌΠΈΠΊΡΠΎΠ ΠΠ ΠΈ ΠΌΠΈΠ ΠΠ, Π° ΡΠ°ΠΊΠΆΠ΅ ΡΠΏΠΎΡΠΎΠ±Ρ Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½Π½ΠΎΠ³ΠΎ Π²Π»ΠΈΡΠ½ΠΈΡ Π½Π° ΡΠΊΡΠΏΡΠ΅ΡΡΠΈΡ Π³Π΅Π½ΠΎΠ² Ρ ΠΈΡ
ΠΏΠΎΠΌΠΎΡΡΡ, ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΠ΅ΠΌΡΠ΅ Π² Π½Π°ΡΡΠΎΡΡΠ΅Π΅ Π²ΡΠ΅ΠΌΡ.Β Π Π°ΡΡΠΌΠΎΡΡΠ΅Π½Ρ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΡΠ΅ Π²Π°ΡΠΈΠ°Π½ΡΡ Π΄ΠΎΡΡΠ°Π²ΠΊΠΈ ΠΌΠΎΠ»Π΅ΠΊΡΠ» Π² ΠΊΠ»Π΅ΡΠΊΡ in vitro ΠΈ in vivo
A theoretical investigation of the low lying electronic structure of poly(p-phenylene vinylene)
The two-state molecular orbital model of the one-dimensional phenyl-based
semiconductors is applied to poly(p-phenylene vinylene). The energies of the
low-lying excited states are calculated using the density matrix
renormalization group method. Calculations of both the exciton size and the
charge gap show that there are both Bu and Ag excitonic levels below the band
threshold. The energy of the 1Bu exciton extrapolates to 2.60 eV in the limit
of infinite polymers, while the energy of the 2Ag exciton extrapolates to 2.94
eV. The calculated binding energy of the 1Bu exciton is 0.9 eV for a 13
phenylene unit chain and 0.6 eV for an infinite polymer. This is expected to
decrease due to solvation effects. The lowest triplet state is calculated to be
at ca. 1.6 eV, with the triplet-triplet gap being ca. 1.6 eV. A comparison
between theory, and two-photon absorption and electroabsorption is made,
leading to a consistent picture of the essential states responsible for most of
the third-order nonlinear optical properties. An interpretation of the
experimental nonlinear optical spectroscopies suggests an energy difference of
ca. 0.4 eV between the vertical energy and ca. 0.8 eV between the relaxed
energy, of the 1Bu exciton and the band gap, respectively.Comment: LaTeX, 19 pages, 7 eps figures included using epsf. To appear in
Physical Review B, 199
Bulk and surface properties in the critical phase of the two-dimensional XY model
Monte Carlo simulations of the two-dimensional XY model are performed in a
square geometry with various boundary conditions (BC). Using conformal mappings
we deduce the exponent of the order parameter correlation
function and its surface analogue as a function of the temperature
in the critical (low-temperature) phase of the model.Comment: 26 pages, iop macro, one reference added, typos correcte
ΠΠ»Π³ΠΎΡΠΈΡΠΌ Ρ ΠΊΠ²Π°Π΄ΡΠ°ΡΠΈΡΠ½ΡΠΌ Π²ΡΠ΅ΠΌΠ΅Π½Π΅ΠΌ Π²ΡΠΏΠΎΠ»Π½Π΅Π½ΠΈΡ Π΄Π»Ρ ΡΠ³Π»Π°ΠΆΠΈΠ²Π°Π½ΠΈΡ ΠΈΠ½ΡΠ΅ΡΠ²Π°Π»ΡΠ½ΡΡ ΡΡΠ½ΠΊΡΠΈΠΉ
Magnetic critical behavior of two-dimensional random-bond Potts ferromagnets in confined geometries
We present a numerical study of 2D random-bond Potts ferromagnets. The model
is studied both below and above the critical value which discriminates
between second and first-order transitions in the pure system. Two geometries
are considered, namely cylinders and square-shaped systems, and the critical
behavior is investigated through conformal invariance techniques which were
recently shown to be valid, even in the randomness-induced second-order phase
transition regime Q>4. In the cylinder geometry, connectivity transfer matrix
calculations provide a simple test to find the range of disorder amplitudes
which is characteristic of the disordered fixed point. The scaling dimensions
then follow from the exponential decay of correlations along the strip. Monte
Carlo simulations of spin systems on the other hand are generally performed on
systems of rectangular shape on the square lattice, but the data are then
perturbed by strong surface effects. The conformal mapping of a semi-infinite
system inside a square enables us to take into account boundary effects
explicitly and leads to an accurate determination of the scaling dimensions.
The techniques are applied to different values of Q in the range 3-64.Comment: LaTeX2e file with Revtex, revised versio
- β¦