61 research outputs found
Global cross-over dynamics of single semiflexible polymers
We present a mean-field dynamical theory for single semiflexible polymers
which can precisely capture, without fitting parameters, recent fluorescence
correlation spectroscopy results on single monomer kinetics of DNA strands in
solution. Our approach works globally, covering three decades of strand length
and five decades of time: it includes the complex cross-overs occurring between
stiffness-dominated and flexible bending modes, along with larger-scale
rotational and center-of-mass motion. The accuracy of the theory stems in part
from long-range hydrodynamic coupling between the monomers, which makes a
mean-field description more realistic. Its validity extends even to short,
stiff fragments, where we also test the theory through Brownian hydrodynamics
simulations.Comment: 6 pages, 5 figures; updated with minor changes to reflect published
versio
Critical Percolation Phase and Thermal BKT Transition in a Scale-Free Network with Short-Range and Long-Range Random Bonds
Percolation in a scale-free hierarchical network is solved exactly by
renormalization-group theory, in terms of the different probabilities of
short-range and long-range bonds. A phase of critical percolation, with
algebraic (Berezinskii-Kosterlitz-Thouless) geometric order, occurs in the
phase diagram, in addition to the ordinary (compact) percolating phase and the
non-percolating phase. It is found that no connection exists between, on the
one hand, the onset of this geometric BKT behavior and, on the other hand, the
onsets of the highly clustered small-world character of the network and of the
thermal BKT transition of the Ising model on this network. Nevertheless, both
geometric and thermal BKT behaviors have inverted characters, occurring where
disorder is expected, namely at low bond probability and high temperature,
respectively. This may be a general property of long-range networks.Comment: Added explanations and data. Published version. 4pages, 4 figure
DNA-Protein Binding Rates: Bending Fluctuation and Hydrodynamic Coupling Effects
We investigate diffusion-limited reactions between a diffusing particle and a
target site on a semiflexible polymer, a key factor determining the kinetics of
DNA-protein binding and polymerization of cytoskeletal filaments. Our theory
focuses on two competing effects: polymer shape fluctuations, which speed up
association, and the hydrodynamic coupling between the diffusing particle and
the chain, which slows down association. Polymer bending fluctuations are
described using a mean field dynamical theory, while the hydrodynamic coupling
between polymer and particle is incorporated through a simple heuristic
approximation. Both of these we validate through comparison with Brownian
dynamics simulations. Neither of the effects has been fully considered before
in the biophysical context, and we show they are necessary to form accurate
estimates of reaction processes. The association rate depends on the stiffness
of the polymer and the particle size, exhibiting a maximum for intermediate
persistence length and a minimum for intermediate particle radius. In the
parameter range relevant to DNA-protein binding, the rate increase is up to
100% compared to the Smoluchowski result for simple center-of-mass motion. The
quantitative predictions made by the theory can be tested experimentally.Comment: 21 pages, 11 figures, 1 tabl
d=3 Anisotropic and d=2 tJ Models: Phase Diagrams, Thermodynamic Properties, and Chemical Potential Shift
The anisotropic d=3 tJ model is studied by renormalization-group theory,
yielding the evolution of the system as interplane coupling is varied from the
isotropic three-dimensional to quasi-two-dimensional regimes.
Finite-temperature phase diagrams, chemical potential shifts, and in-plane and
interplane kinetic energies and antiferromagnetic correlations are calculated
for the entire range of electron densities. We find that the novel tau phase,
seen in earlier studies of the isotropic d=3 tJ model, and potentially
corresponding to the superconducting phase in high-T_c materials, persists even
for strong anisotropy. While the tau phase appears at low temperatures at
30-35% hole doping away from =1, at smaller hole dopings we see a complex
lamellar structure of antiferromagnetic and disordered regions, with a
suppressed chemical potential shift, a possible marker of incommensurate
ordering in the form of microscopic stripes. An investigation of the
renormalization-group flows for the isotropic two-dimensional tJ model also
shows a pre-signature of the tau phase, which appears with finite transition
temperatures upon addition of the smallest interplane coupling.Comment: 13 pages, 7 figures; replaced with published versio
Excitation Spectrum Gap and Spin-Wave Stiffness of XXZ Heisenberg Chains: Global Renormalization-Group Calculation
The anisotropic XXZ spin-1/2 Heisenberg chain is studied using
renormalization-group theory. The specific heats and nearest-neighbor spin-spin
correlations are calculated thoughout the entire temperature and anisotropy
ranges in both ferromagnetic and antiferromagnetic regions, obtaining a global
description and quantitative results. We obtain, for all anisotropies, the
antiferromagnetic spin-liquid spin-wave velocity and the Isinglike
ferromagnetic excitation spectrum gap, exhibiting the spin-wave to spinon
crossover. A number of characteristics of purely quantum nature are found: The
in-plane interaction s_i^x s_j^x + s_i^y s_j^y induces an antiferromagnetic
correlation in the out-of-plane s_i^z component, at higher temperatures in the
antiferromagnetic XXZ chain, dominantly at low temperatures in the
ferromagnetic XXZ chain, and, in-between, at all temperatures in the XY chain.
We find that the converse effect also occurs in the antiferromagnetic XXZ
chain: an antiferromagnetic s_i^z s_j^z interaction induces a correlation in
the s_i^xy component. As another purely quantum effect, (i) in the
antiferromagnet, the value of the specific heat peak is insensitive to
anisotropy and the temperature of the specific heat peak decreases from the
isotropic (Heisenberg) with introduction of either type (Ising or XY)
anisotropy; (ii) in complete contrast, in the ferromagnet, the value and
temperature of the specific heat peak increase with either type of anisotropy.Comment: New results added to text and figures. 12 pages, 18 figures, 3
tables. Published versio
Deconvolution of dynamic mechanical networks
Time-resolved single-molecule biophysical experiments yield data that contain
a wealth of dynamic information, in addition to the equilibrium distributions
derived from histograms of the time series. In typical force spectroscopic
setups the molecule is connected via linkers to a read-out device, forming a
mechanically coupled dynamic network. Deconvolution of equilibrium
distributions, filtering out the influence of the linkers, is a straightforward
and common practice. We have developed an analogous dynamic deconvolution
theory for the more challenging task of extracting kinetic properties of
individual components in networks of arbitrary complexity and topology. Our
method determines the intrinsic linear response functions of a given molecule
in the network, describing the power spectrum of conformational fluctuations.
The practicality of our approach is demonstrated for the particular case of a
protein linked via DNA handles to two optically trapped beads at constant
stretching force, which we mimic through Brownian dynamics simulations. Each
well in the protein free energy landscape (corresponding to folded, unfolded,
or possibly intermediate states) will have its own characteristic equilibrium
fluctuations. The associated linear response function is rich in physical
content, since it depends both on the shape of the well and its diffusivity---a
measure of the internal friction arising from such processes like the transient
breaking and reformation of bonds in the protein structure. Starting from the
autocorrelation functions of the equilibrium bead fluctuations measured in this
force clamp setup, we show how an experimentalist can accurately extract the
state-dependent protein diffusivity using a straightforward two-step procedure.Comment: 9 pages, 3 figures + supplementary material 14 pages, 4 figure
Transition from fractal to non-fractal scalings in growing scale-free networks
Real networks can be classified into two categories: fractal networks and
non-fractal networks. Here we introduce a unifying model for the two types of
networks. Our model network is governed by a parameter . We obtain the
topological properties of the network including the degree distribution,
average path length, diameter, fractal dimensions, and betweenness centrality
distribution, which are controlled by parameter . Interestingly, we show
that by adjusting , the networks undergo a transition from fractal to
non-fractal scalings, and exhibit a crossover from `large' to small worlds at
the same time. Our research may shed some light on understanding the evolution
and relationships of fractal and non-fractal networks.Comment: 7 pages, 3 figures, definitive version accepted for publication in
EPJ
Shortcuts in Stochastic Systems and Control of Biophysical Processes
The biochemical reaction networks that regulate living systems are all stochastic to varying degrees. The resulting randomness affects biological outcomes at multiple scales, from the functional states of single proteins in a cell to the evolutionary trajectory of whole populations. Controlling how the distribution of these outcomes changes over time-via external interventions like time-varying concentrations of chemical species-is a complex challenge. In this work, we show how counterdiabatic (CD) driving, first developed to control quantum systems, provides a versatile tool for steering biological processes. We develop a practical graph-theoretic framework for CD driving in discrete-state continuous-time Markov networks. Though CD driving is limited to target trajectories that are instantaneous stationary states, we show how to generalize the approach to allow for nonstationary targets and local control-where only a subset of system states is targeted. The latter is particularly useful for biological implementations where there may be only a small number of available external control knobs, insufficient for global control. We derive simple graphical criteria for when local versus global control is possible. Finally, we illustrate the formalism with global control of a genetic regulatory switch and local control in chaperone-assisted protein folding. The derived control protocols in the chaperone system closely resemble natural control strategies seen in experimental measurements of heat shock response in yeast and E. coli
Multicritical Points of Potts Spin Glasses on the Triangular Lattice
We predict the locations of several multicritical points of the Potts spin
glass model on the triangular lattice. In particular, continuous multicritical
lines, which consist of multicritical points, are obtained for two types of
two-state Potts (i.e., Ising) spin glasses with two- and three-body
interactions on the triangular lattice. These results provide us with numerous
examples to further verify the validity of the conjecture, which has succeeded
in deriving highly precise locations of multicritical points for several spin
glass models. The technique, called the direct triangular duality, a variant of
the ordinary duality transformation, directly relates the triangular lattice
with its dual triangular lattice in conjunction with the replica method.Comment: 18 pages, 2, figure
- …