482 research outputs found
The bend stiffness of S-DNA
We formulate and solve a two-state model for the elasticity of nicked,
double-stranded DNA that borrows features from both the Worm Like Chain and the
Bragg--Zimm model. Our model is computationally simple, and gives an excellent
fit to recent experimental data through the entire overstretching transition.
The fit gives the first value for the bending stiffness of the overstretched
state as about 10 nm*kbt, a value quite different from either B-form or
single-stranded DNA.Comment: 7 pages, 1 figur
Relationship between cellular response and behavioral variability in bacterial chemotaxis
Bacterial chemotaxis in Escherichia coli is a canonical system for the study
of signal transduction. A remarkable feature of this system is the coexistence
of precise adaptation in population with large fluctuating cellular behavior in
single cells (Korobkova et al. 2004, Nature, 428, 574). Using a stochastic
model, we found that the large behavioral variability experimentally observed
in non-stimulated cells is a direct consequence of the architecture of this
adaptive system. Reversible covalent modification cycles, in which methylation
and demethylation reactions antagonistically regulate the activity of
receptor-kinase complexes, operate outside the region of first-order kinetics.
As a result, the receptor-kinase that governs cellular behavior exhibits a
sigmoidal activation curve. This curve simultaneously amplifies the inherent
stochastic fluctuations in the system and lengthens the relaxation time in
response to stimulus. Because stochastic fluctuations cause large behavioral
variability and the relaxation time governs the average duration of runs in
response to small stimuli, cells with the greatest fluctuating behavior also
display the largest chemotactic response. Finally, Large-scale simulations of
digital bacteria suggest that the chemotaxis network is tuned to simultaneously
optimize the random spread of cells in absence of nutrients and the cellular
response to gradients of attractant.Comment: 15 pages, 4 figures, Supporting information available here
http://cluzel.uchicago.edu/data/emonet/arxiv_070531_supp.pd
Torsional Directed Walks, Entropic Elasticity, and DNA Twist Stiffness
DNA and other biopolymers differ from classical polymers due to their
torsional stiffness. This property changes the statistical character of their
conformations under tension from a classical random walk to a problem we call
the `torsional directed walk'. Motivated by a recent experiment on single
lambda-DNA molecules [Strick et al., Science 271 (1996) 1835], we formulate the
torsional directed walk problem and solve it analytically in the appropriate
force regime. Our technique affords a direct physical determination of the
microscopic twist stiffness C and twist-stretch coupling D relevant for DNA
functionality. The theory quantitatively fits existing experimental data for
relative extension as a function of overtwist over a wide range of applied
force; fitting to the experimental data yields the numerical values C=120nm and
D=50nm. Future experiments will refine these values. We also predict that the
phenomenon of reduction of effective twist stiffness by bend fluctuations
should be testable in future single-molecule experiments, and we give its
analytic form.Comment: Plain TeX, harvmac, epsf; postscript available at
http://dept.physics.upenn.edu/~nelson/index.shtm
Discrete elastic model for stretching-induced flagellar polymorphs
Force-induced reversible transformations between coiled and normal polymorphs
of bacterial flagella have been observed in recent optical-tweezer experiment.
We introduce a discrete elastic rod model with two competing helical states
governed by a fluctuating spin-like variable that represents the underlying
conformational states of flagellin monomers. Using hybrid Brownian dynamics
Monte-Carlo simulations, we show that a helix undergoes shape transitions
dominated by domain wall nucleation and motion in response to externally
applied uniaxial tension. A scaling argument for the critical force is
presented in good agreement with experimental and simulation results.
Stretching rate-dependent elasticity including a buckling instability are
found, also consistent with the experiment
Two-phase stretching of molecular chains
While stretching of most polymer chains leads to rather featureless
force-extension diagrams, some, notably DNA, exhibit non-trivial behavior with
a distinct plateau region. Here we propose a unified theory that connects
force-extension characteristics of the polymer chain with the convexity
properties of the extension energy profile of its individual monomer subunits.
Namely, if the effective monomer deformation energy as a function of its
extension has a non-convex (concave up) region, the stretched polymer chain
separates into two phases: the weakly and strongly stretched monomers.
Simplified planar and 3D polymer models are used to illustrate the basic
principles of the proposed model. Specifically, we show rigorously that when
the secondary structure of a polymer is mostly due to weak non-covalent
interactions, the stretching is two-phase, and the force-stretching diagram has
the characteristic plateau. We then use realistic coarse-grained models to
confirm the main findings and make direct connection to the microscopic
structure of the monomers. We demostrate in detail how the two-phase scenario
is realized in the \alpha-helix, and in DNA double helix. The predicted plateau
parameters are consistent with single molecules experiments. Detailed analysis
of DNA stretching demonstrates that breaking of Watson-Crick bonds is not
necessary for the existence of the plateau, although some of the bonds do break
as the double-helix extends at room temperature. The main strengths of the
proposed theory are its generality and direct microscopic connection.Comment: 16 pges, 22 figure
Inferring the effective thickness of polyelectrolytes from stretching measurements at various ionic strengths: applications to DNA and RNA
By resorting to the thick-chain model we discuss how the stretching response
of a polymer is influenced by the self-avoidance entailed by its finite
thickness. The characterization of the force versus extension curve for a thick
chain is carried out through extensive stochastic simulations. The
computational results are captured by an analytic expression that is used to
fit experimental stretching measurements carried out on DNA and single-stranded
RNA (poly-U) in various solutions. This strategy allows us to infer the
apparent diameter of two biologically-relevant polyelectrolytes, namely DNA and
poly-U, for different ionic strengths. Due to the very different degree of
flexibility of the two molecules, the results provide insight into how the
apparent diameter is influenced by the interplay between the
(solution-dependent) Debye screening length and the polymers' ``bare''
thickness. For DNA, the electrostatic contribution to the effective radius,
, is found to be about 5 times larger than the Debye screening length,
consistently with previous theoretical predictions for highly-charged stiff
rods. For the more flexible poly-U chains the electrostatic contribution to
is found to be significantly smaller than the Debye screening length.Comment: iopart, 14 pages, 13 figures, to appear in J. Phys.: Condens. Matte
Theory of High-Force DNA Stretching and Overstretching
Single molecule experiments on single- and double stranded DNA have sparked a
renewed interest in the force-extension of polymers. The extensible Freely
Jointed Chain (FJC) model is frequently invoked to explain the observed
behavior of single-stranded DNA. We demonstrate that this model does not
satisfactorily describe recent high-force stretching data. We instead propose a
model (the Discrete Persistent Chain, or ``DPC'') that borrows features from
both the FJC and the Wormlike Chain, and show that it resembles the data more
closely. We find that most of the high-force behavior previously attributed to
stretch elasticity is really a feature of the corrected entropic elasticity;
the true stretch compliance of single-stranded DNA is several times smaller
than that found by previous authors. Next we elaborate our model to allow
coexistence of two conformational states of DNA, each with its own stretch and
bend elastic constants. Our model is computationally simple, and gives an
excellent fit through the entire overstretching transition of nicked,
double-stranded DNA. The fit gives the first values for the elastic constants
of the stretched state. In particular we find the effective bend stiffness for
DNA in this state to be about 10 nm*kbt, a value quite different from either
B-form or single-stranded DNAComment: 33 pages, 11 figures. High-quality figures available upon reques
Dynamics of folding in Semiflexible filaments
We investigate the dynamics of a single semiflexible filament, under the
action of a compressing force, using numerical simulations and scaling
arguments. The force is applied along the end to end vector at one extremity of
the filament, while the other end is held fixed. We find that, unlike in
elastic rods the filament folds asymmetrically with a folding length which
depends only on the bending stiffness and the applied force. It is shown that
this behavior can be attributed to the exponentially falling tension profile in
the filament. While the folding time depends on the initial configuration, at
late time, the distance moved by the terminal point of the filament and the
length of the fold shows a power law dependence on time with an exponent 1/2.Comment: 13 pages, Late
Perturbation Theory in k-Inflation Coupled to Matter
We consider k-inflation models where the action is a non-linear function of
both the inflaton and the inflaton kinetic term. We focus on a scalar-tensor
extension of k-inflation coupled to matter for which we derive a modified
Mukhanov-Sasaki equation for the curvature perturbation. Significant
corrections to the power spectrum appear when the coupling function changes
abruptly along the inflationary trajectory. This gives rise to a modification
of Starobinsky's model of perturbation features. We analyse the way the power
spectrum is altered in the infrared when such features are present.Comment: 20 pages, 1 figur
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