330 research outputs found
Attraction of like-charged macroions in the strong-coupling limit
Like-charged macroions attract each other as a result of strong electrostatic
correlations in the presence of multivalent counterions or at low temperatures.
We investigate the effective electrostatic interaction between i) two
like-charged rods and ii) two like-charged spheres using the recently
introduced strong-coupling theory, which becomes asymptotically exact in the
limit of large coupling parameter (i.e. for large counterion valency, low
temperature, or high surface charge density on macroions). Since we deal with
curved surfaces, an additional parameter, referred to as Manning parameter, is
introduced, which measures the ratio between the radius of curvature of
macroions to the Gouy-Chapman length and controls the counterion-condensation
process that directly affects the effective interactions. For sufficiently
large Manning parameters (weakly-curved surfaces), we find a strong long-ranged
attraction between two macroions that form a closely-packed bound state with
small surface-to-surface separation of the order of the counterion diameter in
agreement with recent simulations. For small Manning parameters (highly-curved
surfaces), on the other hand, the equilibrium separation increases and the
macroions unbind from each other as the confinement volume increases to
infinity. This occurs via a continuous universal unbinding transition for two
charged rods at a threshold Manning parameter of 2/3, while the transition is
discontinuous for spheres because of a pronounced potential barrier at
intermediate distances.Comment: 16 pages, 10 figure
Quantitative prediction of multivalent ligand–receptor binding affinities for influenza, cholera, and anthrax inhibition
Multivalency achieves strong, yet reversible binding by the simultaneous formation of multiple weak bonds. It is a key interaction principle in biology and promising for the synthesis of high-affinity inhibitors of pathogens. We present a molecular model for the binding affinity of synthetic multivalent ligands onto multivalent receptors consisting of n receptor units arranged on a regular polygon. Ligands consist of a geometrically matching rigid polygonal core to which monovalent ligand units are attached via flexible linker polymers, closely mimicking existing experimental designs. The calculated binding affinities quantitatively agree with experimental studies for cholera toxin (n = 5) and anthrax receptor (n = 7) and allow to predict optimal core size and optimal linker length. Maximal binding affinity is achieved for a core that matches the receptor size and for linkers that have an equilibrium end-to-end distance that is slightly longer than the geometric separation between ligand core and receptor sites. Linkers that are longer than optimal are greatly preferable compared to shorter linkers. The angular steric restriction between ligand unit and linker polymer is shown to be a key parameter. We construct an enhancement diagram that quantifies the multivalent binding affinity compared to monovalent ligands. We conclude that multivalent ligands against influenza viral hemagglutinin (n = 3), cholera toxin (n = 5), and anthrax receptor (n = 7) can outperform monovalent ligands only for a monovalent ligand affinity that exceeds a core-size dependent threshold value. Thus, multivalent drug design needs to balance core size, linker length, as well as monovalent ligand unit affinity
Beyond Poisson-Boltzmann: Fluctuations and Correlations
We formulate the non-linear field theory for a fluctuating counter-ion
distribution in the presence of a fixed, arbitrary charge distribution. The
Poisson-Boltzmann equation is obtained as the saddle-point, and the effects of
fluctuations and correlations are included by a loop-wise expansion around this
saddle point. We show that the Poisson equation is obeyed at each order in the
loop expansion and explicitly give the expansion of the Gibbs potential up to
two loops. We then apply our formalism to the case of an impenetrable, charged
wall, and obtain the fluctuation corrections to the electrostatic potential and
counter-ion density to one-loop order without further approximations. The
relative importance of fluctuation corrections is controlled by a single
parameter, which is proportional to the cube of the counter-ion valency and to
the surface charge density. We also calculate effective interactions between
charged particles, which reflect counter-ion correlation effects.Comment: 12 pages, 8 postscript figure
Variational charge renormalization in charged systems
We apply general variational techniques to the problem of the counterion
distribution around highly charged objects where strong condensation of
counterions takes place. Within a field-theoretic formulation using a
fluctuating electrostatic potential, the concept of surface-charge
renormalization is recovered within a simple one-parameter variational
procedure. As a test, we reproduce the Poisson-Boltzmann surface potential for
a single charge planar surface both in the weak-charge and strong-charge
regime. We then apply our techniques to non-planar geometries where closed-form
solutions of the non-linear Poisson-Boltzmann equation are not available. In
the cylindrical case, the Manning charge renormalization result is obtained in
the limit of vanishing salt concentration. However, for intermediate salt
concentrations a slow crossover to the non-charge-renormalized regime (at high
salt) is found with a quasi-power-law behavior which helps to understand
conflicting experimental and theoretical results for the electrostatic
persistence length of polyelectrolytes. In the spherical geometry charge
renormalization is only found at intermediate salt concentrations
Plectoneme creation reduces the rotational friction of a polymer
The torsional dynamics of a semiflexible polymer with a contour length
larger than its persistence length L_p that is rotated at fixed frequency
omega_0 at one end is studied by scaling arguments and hydrodynamic
simulations. We find a non-equilibrium transition at a critical frequency
omega_*: In the linear regime, omega_0 < omega_*, axial spinning is the
dominant dissipation mode. In the non-linear regime, omega_0 > omega_*, the
twist-dissipation mode involves the continuous creation of plectonemes close to
the driven end and the rotational friction is substantially reduced
Anisotropic Hydrodynamic Mean-Field Theory for Semiflexible Polymers under Tension
We introduce an anisotropic mean-field approach for the dynamics of
semiflexible polymers under intermediate tension, the force range where a chain
is partially extended but not in the asymptotic regime of a nearly straight
contour. The theory is designed to exactly reproduce the lowest order
equilibrium averages of a stretched polymer, and treats the full complexity of
the problem: the resulting dynamics include the coupled effects of long-range
hydrodynamic interactions, backbone stiffness, and large-scale polymer contour
fluctuations. Validated by Brownian hydrodynamics simulations and comparison to
optical tweezer measurements on stretched DNA, the theory is highly accurate in
the intermediate tension regime over a broad dynamical range, without the need
for additional dynamic fitting parameters.Comment: 22 pages, 9 figures; revised version with additional calculations and
experimental comparison; accepted for publication in Macromolecule
Theory for RNA folding, stretching, and melting including loops and salt
Secondary structure formation of nucleic acids strongly depends on salt
concentration and temperature. We develop a theory for RNA folding that
correctly accounts for sequence effects, the entropic contributions associated
with loop formation, and salt effects. Using an iterative expression for the
partition function that neglects pseudoknots, we calculate folding free
energies and minimum free energy configurations based on the experimentally
derived base pairing free energies. The configurational entropy of loop
formation is modeled by the asymptotic expression -c ln m, where m is the
length of the loop and c the loop exponent, which is an adjustable constant.
Salt effects enter in two ways: first, we derive salt induced modifications of
the free energy parameters for describing base pairing and, second, we include
the electrostatic free energy for loop formation. Both effects are modeled on
the Debye-Hueckel level including counterion condensation. We validate our
theory for two different RNA sequences: For tRNA-phe, the resultant heat
capacity curves for thermal denaturation at various salt concentrations
accurately reproduce experimental results. For the P5ab RNA hairpin, we derive
the global phase diagram in the three-dimensional space spanned by temperature,
stretching force, and salt concentration and obtain good agreement with the
experimentally determined critical unfolding force. We show that for a proper
description of RNA melting and stretching, both salt and loop entropy effects
are needed.Comment: 12 pages, 9 figures, accepted for publication in Biophysical Journa
The mean shape of transition and first-passage paths
We calculate the mean shape of transition paths and first-passage paths based
on the one-dimensional Fokker-Planck equation in an arbitrary free energy
landscape including a general inhomogeneous diffusivity profile. The transition
path ensemble is the collection of all paths that do not revisit the start
position and that terminate when first reaching the final position .
In contrast, a first-passage path can revisit but not cross its start position
before it terminates at . Our theoretical framework employs the
forward and backward Fokker-Planck equations as well as first-passage, passage,
last-passage and transition-path time distributions, for which we derive the
defining integral equations. We show that the mean time at which the transition
path ensemble visits an intermediate position is equivalent to the mean
first-passage time of reaching the starting position from without
ever visiting . The mean shape of first-passage paths is related to the
mean shape of transition paths by a constant time shift. Since for large
barrier height the mean first-passage time scales exponentially in
while the mean transition path time scales linearly inversely in , the time
shift between first-passage and transition path shapes is substantial. We
present explicit examples of transition path shapes for linear and harmonic
potentials and illustrate our findings by trajectories generated from Brownian
dynamics simulations
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