arXiv subjects

Theo Odijk

Publications and source records attributed to Theo Odijk.

15 recordsLinked to original sources

arXiv2020

Mean-field theory of the Interaction of the Magnesium Ion with Biopolymers: The Case of Lysozyme

A statistical theory is presented of the magnesium ion interacting with lysozyme under conditions where the latter is positively charged. Temporarily assuming magnesium is not noncovalently bound to the protein, I solve the nonlinear Poisson-Boltzmann equation accurately and uniformly in a perturbative fashion. The resulting expression for the effective charge, which is larger than nominal owing to overshooting, is subtle and cannot be asymptotically expanded at high ionic strengths that are practical. An adhesive potential taken from earlier work together with the assumption of possibly bound magnesium is then fitted to be in accord with measurements of the second virial coefficient by Tessier et al. The resulting numbers of bound magnesium ions as a function of MgBr2 concentration are entirely reasonable compared with densitometry measurements.

cond-mat.soft↗

arXiv2019

Long-range Correlations in a Data Sequence Extracted Via Polymeric Compaction

A numerical method is proposed to remove the quenched randomness from a data sequence of numbers. A polymer chain of beads is introduced with both a hard core interaction and an appropriate energy associated with the data sequence. The quenched randomness is hypothesized to collapse the chain to a spherical globule. Long-range informational correlations then show up in deviations from the spherical shape. The resulting coefficients within an expansion in terms of spherical harmonics go beyond the usual concept of algorithmic information or Kolmogorov complexity.

cond-mat.soft↗

arXiv2018

A Quantitative Information Measure applied to Texture Perception Attributes during Mastication

We have calculated a quantitative measure of information of experimentally determined temporal dominance of sensations (TDS) frequencies of texture attributes, for a set of diverse samples throughout the mastication cycle. The samples were emulsion filled gels, two-layered emulsion filled gels, and sausages. For the majority of the samples we find one master curve, where swallowing takes place after the information increases from its minimum. The master curve may indicate a simplifying principle during mastication and subsequent swallowing. We have also calculated a particular complexity measure. This measure displays an increase just before swallowing.

eess.SP↗

arXiv2016

Material Line Fluctuations Slaved to Bulk Correlations in Two-Dimensional Turbulence

An analogy is pointed out between a polymer chain fluctuating in a two-dimensional nematic background and a freely floating material line buffeted by a two-dimensional turbulent fluid in the inertial (Kraichnan) regime. Under certain conditions, the back-reaction of the line on the turbulent flow may be neglected. The fractal exponent related to the size-contour relation of the material line is connected to a "nematic" correlation function in the bulk.

cond-mat.soft↗

arXiv2014

A Tree Swaying in a Turbulent Wind: A Scaling Analysis

A tentative scaling theory is presented of a tree swaying in a turbulent wind. It is argued that the turbulence of the air within the crown is in the inertial regime. An eddy causes a dynamic bending response of the branches according to a time criterion. The resulting expression for the penetration depth of the wind yields an exponent which appears to be consistent with that pertaining to the morphology of the tree branches. An energy criterion shows that the dynamics of the branches is basically passive. The possibility of hydrodynamic screening by the leaves is discussed.

cond-mat.soft↗

arXiv2009

Longitudinal dispersion of DNA in nanochannels

A theory is presented of the longitudinal dispersion of DNA under equilibrium confined in a nanochannel. Orientational fluctuations of the DNA chain build up to give rise to substantial fluctuations of the coil in the longitudinal direction of the channel. The translational and orientational degrees of freedom of the polymer are described by the Green function satisfying the usual Fokker-Planck equation. It is argued that this is analogous to the transport equation occurring in the theory of convective diffusion of particles in pipe flow. Moreover, Taylor's method may be used to reduce the Fokker-Planck equation to a diffusion equation for long DNA although subtleties arise connected with the orientational distribution of segments within the channel. The longitudinal "step length" turns out to be proportional to the typical angle of a DNA segment to the sixth power. The dispersion is underestimated compared to experiment, probably because the harmonic approximation is used to describe the polymer confinement.

cond-mat.soft↗

arXiv2008

Depletion theory and the precipitation of protein by polymer

The depletion theory of nanoparticles immersed in a semidilute polymer solution is reinterpreted in terms of depleted chains of polymer segments. Limitations and extensions of mean-field theory are discussed. An explicit expression for the interaction between two small spheres is derived. The depletion free energy for a particle of general shape is given in terms of the capacitance or effective Stokes radius. This affords a close to quantitative explanation for the effect of polymer on protein precipitation.

cond-mat.soft↗

arXiv2007

Collective diffusion coefficient of proteins with hydrodynamic, electrostatic and adhesive interactions

A theory is presented for lambda_C, the coefficient of the first-order correction in the density of the collective diffusion coefficient, for protein spheres interacting by electrostatic and adhesive forces. An extensive numerical analysis of the Stokesian hydrodynamics of two moving spheres is given so as to gauge the precise impact of lubrication forces. An effective stickiness is introduced and a simple formula for lambda_C in terms of this variable is put forward. A precise though more elaborate approximation for lambda_C is also developed. These and numerically exact expressions for lambda_C are compared with experimental data on lysozyme at pH 4.5 and a range of ionic strengths between 0.05 M and 2 M.

cond-mat.soft↗

arXiv2006

DNA Confined in Nanochannels: Hairpin Tightening by Entropic Depletion

A theory is presented of DNA hairpins enclosed in a nanochannel. A hairpin becomes constrained as it approaches the wall of a channel which leads to an entropic force causing the hairpin to tighten. The free energy of the hairpin computed in the classical limit is significantly larger than what one would expect. As a result, the distance between hairpins or the global persistence length is often tens of micrometers long and may even reach mm sizes for 10 nm thin channels. The hairpin shape and size, and the DNA elongation are computed for nanoslits, and circular and square nanoschannels. A comparison with experiment is given.

cond-mat.soft↗

arXiv2006

Fluid-crystal coexistence for proteins and inorganic nanocolloids: dependence on ionic strength

We investigate theoretically the fluid-crystal coexistence of solutions of globular charged nanoparticles like proteins and inorganic colloids. The thermodynamic properties of the fluid phase are computed via the optimized Baxter model. This is done specifically for lysozyme and silicotungstates for which the bare adhesion parameters are evaluated via the experimental second virial coefficients. The electrostatic free energy of the crystal is approximated by supposing the cavities in the interstitial phase between the particles are spherical in form. In the salt-free case a Poisson-Boltzmann equation is solved to calculate the effective charge on a particle and a Donnan approximation is used to derive the chemical potential and osmotic pressure in the presence of salt. The coexistence data of lysozyme and silicotungstates are analyzed within this scheme, especially with regard to the ionic-strength dependence of the chemical potentials. The latter agree within the two phases provided some upward adjustment of the effective charge is allowed for.

cond-mat.soft↗

arXiv2006

Application of the Optimized Baxter Model to the hard-core attractive Yukawa system

We perform Monte Carlo simulations on the hard-core attractive Yukawa system to test the Optimized Baxter Model that was introduced in [P.Prinsen and T. Odijk, J. Chem. Phys. 121, p.6525 (2004)] to study a fluid phase of spherical particles interacting through a short-range pair potential. We compare the chemical potentials and pressures from the simulations with analytical predictions from the Optimized Baxter Model. We show that the model is accurate to within 10 percent over a range of volume fractions from 0.1 to 0.4, interaction strengths up to three times the thermal energy and interaction ranges from 6 to 20 % of the particle diameter, and performs even better in most cases. We furthermore establish the consistency of the model by showing that the thermodynamic properties of the Yukawa fluid computed via simulations may be understood on the basis of one similarity variable, the stickiness parameter defined within the Optimized Baxter Model. Finally we show that the Optimized Baxter Model works significantly better than an often used, naive method determining the stickiness parameter by equating the respective second virial coefficients based on the attractive Yukawa and Baxter potentials.

cond-mat.soft↗

arXiv2004

Optimized Baxter Model of Protein Solutions: Electrostatics versus Adhesion

A theory is set up of spherical proteins interacting by screened electrostatics and constant adhesion, in which the effective adhesion parameter is optimized by a variational principle for the free energy. An analytical approach to the second virial coefficient is first outlined by balancing the repulsive electrostatics against part of the bare adhesion. A theory similar in spirit is developed at nonzero concentrations by assuming an appropriate Baxter model as the reference state. The first-order term in a functional expansion of the free energy is set equal to zero which determines the effective adhesion as a function of salt and protein concentrations. The resulting theory is shown to have fairly good predictive power for the ionic-strength dependence of both the second virial coefficient and the osmotic pressure or compressibility of lysozyme up to about 0.2 volume fraction.

cond-mat.soft↗

arXiv2003

Convective Depletion During The Fast Propagation Of A Nanosphere Through A Polymer Solution

A theory of nonlinear convective depletion is set up as a nanosphere translates fast through a semidilute polymer solution. For nanospheres a self-consistent field theory in the Rouse approximation is often legitimate. A self-similar solution of the convective depletion equation is argued to be feasible at high velocities. The nature of the thin boundary layer in front of the propagating particle is analyzed. One example of convective depletion is when a charged protein moves through a semidilute polymer under the influence of a high electric field. The protein velocity is then proportional to the fifth power of the field. The theory could be useful in interpreting the separation of protein mixtures by microchip electrophoresis.

cond-mat.soft↗

arXiv2003

Statics and Dynamics of Condensed DNA within Phages and Globules

Several controversial issues concerning the packing of linear DNA in bacteriophages and globules are discussed. Exact relations for the osmotic pressure, capsid pressure and loading force are derived in terms of the hole size inside phages under the assumption that the DNA globule has a uniform density. A new electrostatic model is introduced for computing the osmotic pressure of rodlike polyelectrolytes at very high concentrations. At intermediate packing, a reptation model is considered for DNA diffusing within a toroidal globule. Under tight packing conditions, a model of Coulomb sliding friction is proposed. A general discussion is given of our current understanding of the statics and dynamics of confined DNA in the context of to the following experiments: characterization of the liquid crystalline phases, X-ray scattering by phages, osmotic stress measurements, cyclization within globules and single-molecule determination ofthe loading forces.

cond-mat.soft↗

arXiv2003

Nonuniform Donnan Equilibrium within Bacteriophages Packed with Dna

The curvature stress of DNA packed inside a phage is balanced against its electrostatic self-interaction. The DNA density is supposed nonuniform and as a result the Donnan effect is also inhomogeneous. The coarse-grained DNA density is a nonlinear function of the DNA radius of curvature at a given position inside the bacteriophage. It turns out that a region (or regions) exists totally free from DNA. The size of such holes is computed.

cond-mat.soft↗