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Joseph Rudnick

Publications and source records attributed to Joseph Rudnick.

At least 55 records · Page 3Linked to original sources
arXiv2003

Viral self-assembly as a thermodynamic process

The protein shells, or capsids, of all sphere-like viruses adopt icosahedral symmetry. In the present paper we propose a statistical thermodynamic model for viral self-assembly. We find that icosahedral symmetry is not expected for viral capsids constructed from structurally identical protein subunits and that this symmetry requires (at least) two internal "switching" configurations of the protein. Our results indicate that icosahedral symmetry is not a generic consequence of free energy minimization but requires optimization of internal structural parameters of the capsid proteins.

cond-mat.soft↗
arXiv2003

Anomalous bending of a polyelectrolyte

We report on a study of the shape of a stiff, charged rod that is subjected to equal and opposite force couples at its two ends. Unlike a neutral elastic rod, which forms a constant curvature configuration under such influences, the charged rod tends to flatten in the interior and accumulate the curvature in the end points, to maximally reduce the electrostatic self-repulsion. The effect of this nonuniform bending on the effective elasticity and on the statistical conformations of a fluctuating charged rod is discussed. An alternative definition for the electrostatic persistence length is suggested. This new definition is found to be consistent with a corresponding length that can be deduced from the end-to-end distribution function of a fluctuating polyelectrolyte.

cond-mat.soft↗
arXiv2003

What drives the translocation of stiff chains?

We study the dynamics of the passage of a stiff chain through a pore into a cell containing particles that bind reversibly to it. Using Brownian Molecular Dynamics simulations we investigate the mean-first-passage time as a function of the length of the chain inside, for different concentrations of binding particles. As a consequence of the interactions with these particles, the chain experiences a net force along its length whose calculated value from the simulations accounts for the velocity at which it enters the cell. This force can in turn be obtained from the solution of a generalized diffusion equation incorporating an effective Langmuir adsorption free energy for the chain plus binding particles. These results suggest a role of binding particles in the translocation process which is in general quite different from that of a Brownian ratchet. Furthermore, non-equilibrium effects contribute significantly to the dynamics, \emph{e.g.}, the chain often enters the cell faster than particle binding can be saturated, resulting in a force several times smaller than the equilibrium value.

cond-mat.soft↗
arXiv2003

Icosahedral packing of RNA viral genomes

Recent studies reveal that certain viruses package a portion of their genome in a manner that mirrors the icosahedral symmetry of the protein container, or capsid. Graph theoretical constraints forbid exact realization of icosahedral symmetry. This paper proposes a model for the determination of quasi-icosahedral genome structures and discusses the connection between genomic structure and viral assembly kinetics.

cond-mat.soft↗
arXiv2003

Probing Polyelectrolyte Elasticity Using Radial Distribution Function

We study the effect of electrostatic interactions on the distribution function of the end-to-end distance of a single polyelectrolyte chain in the rodlike limit. The extent to which the radial distribution function of a polyelectrolyte is reproduced by that of a wormlike chain with an adjusted persistence length is investigated. Strong evidence is found for a universal scaling formula connecting the effective persistence length of a polyelectrolyte with its linear charge density and the Debye screening of its self-interaction. An alternative definition of the electrostatic persistence length is proposed based on matching of the maximum of the distribution with that of an effective wormlike chain, as opposed to the traditional matching of the first or the second moments of the distributions. It is shown that this definition provides a more accurate probe of the affinity of the distribution to that of the wormlike chains, as compared to the traditional definition. It is also found that the length of a polyelectrolyte segment can act as a crucial parameter in determining its elastic properties.

cond-mat.soft↗
arXiv2002

Radial Distribution Function of Rodlike Polyelectrolytes

We study the effect of electrostatic interactions on the distribution function of the end-to-end distance of a single polyelectrolyte chain in a rodlike configuration. We investigate the validity of the concept of electrostatic persistence length for uniformly charged wormlike chains for both screened and unscreened Coulomb interactions. We find that the distribution function of a polyelectrolyte often differs significantly from the distribution function of a wormlike chain.

cond-mat.soft↗
arXiv2002

Two-level system with a thermally fluctuating transfer matrix element: Application to the problem of DNA charge transfer

Charge transfer along the base-pair stack in DNA is modeled in terms of thermally-assisted tunneling between adjacent base pairs. Central to our approach is the notion that tunneling between fluctuating pairs is rate-limited by the requirement of their optimal alignment. We focus on this aspect of the process by modeling two adjacent base pairs in terms of a classical damped oscillator subject to thermal fluctuations as described by a Fokker-Planck equation. We find that the process is characterized by two time scales, a result that is in accord with experimental findings.

cond-mat.soft↗
arXiv2001

Effects of mechanical strain on thermal denaturation of DNA

As sections of a strand duplexed DNA denature when exposed to high temperature, the excess linking number is taken up by the undenatured portions of the molecule. The mechanical energy that arises because of the overwinding of the undenatured sections can, in principle, alter the nature of the thermal denaturation process. Assuming that the strains associated with this overwinding are not relieved, we find that a simple model of strain-altered melting leads to a suppression of the melting transition when the unaltered transition is continuous. When the melting transition is first order in the absence of strain associated with overwinding, the modification is to a third order phase transition.

cond-mat.soft↗
arXiv2001

Analysis of a continuous field theory in two dimensions with use of the Density Matrix Renormalization Group

A formulation of the Ginzburg-Landau-Wilson version of the partition function of a system with a continuously varying order parameter as a transfer matrix calculation allows for the application of methods based on the Density Matrix Renormalization Group (DMRG) to the calculation of the free energy of the O(1) model. The essence of both the mapping and the DMRG calculation is laid out, along with results that validate this strategy. This method forms the basis of a unified approach to the crossover from three to two dimensions in an O(1) system with a slab-like geometry.

cond-mat.stat-mech↗
arXiv2001

Constraints, Histones, and the 30 Nanometer Spiral

We investigate the mechanical stability of a segment of DNA wrapped around a histone in the nucleosome configuration. The assumption underlying this investigation is that the proper model for this packaging arrangement is that of an elastic rod that is free to twist and that writhes subject to mechanical constraints. We find that the number of constraints required to stabilize the nuclesome configuration is determined by the length of the segment, the number of times the DNA wraps around the histone spool, and the specific constraints utilized. While it can be shown that four constraints suffice, in principle, to insure stability of the nucleosome, a proper choice must be made to guarantee the effectiveness of this minimal number. The optimal choice of constraints appears to bear a relation to the existence of a spiral ridge on the surface of the histone octamer. The particular configuration that we investigate is related to the 30 nanometer spiral, a higher-order organization of DNA in chromatin.

cond-mat.soft↗
arXiv2001

Subleading long-range interactions and violations of finite size scaling

We study the behavior of systems in which the interaction contains a long-range component that does not dominate the critical behavior. Such a component is exemplified by the van der Waals force between molecules in a simple liquid-vapor system. In the context of the mean spherical model with periodic boundary conditions we are able to identify, for temperatures close above $T_c$, finite-size contributions due to the {\it subleading} term in the interaction that are {\it dominant} in this region decaying algebraically as a function of $L$. This mechanism goes beyond the standard formulation of the finite-size scaling but is to be expected in real physical systems. We also discuss other ways in which critical point behavior is modified that are of relevance for analysis of Monte Carlo simulations of such systems.

cond-mat.stat-mech↗
arXiv2000

Numerical studies of domains and bubbles of Langmuir monolayers

A numerical algorithm based on the finite element methods has been developed to accurately determine the shape of the boundary of a domain containing ``boojum'' textures. Within the context of the simple model we adopt, the effects of both bulk elastic anisotropy and line-tension anisotropy on the domain boundary can be examined. It is found that line-tension anisotropy must be present in order to account for domains with protruding features. Both elastic anisotropy and anisotropic line-tension can result in domains with indentations. The numerical algorithm has been extended to investigate the problem of a bubble in extended region ordered phase.

cond-mat.soft↗
arXiv1999

Theory of monolayers with boundaries: Exact results and Perturbative analysis

Domains and bubbles in tilted phases of Langmuir monolayers contain a class of textures knows as boojums. The boundaries of such domains and bubbles may display either cusp-like features or indentations. We derive analytic expressions for the textures within domains and surrounding bubbles, and for the shapes of the boundaries of these regions. The derivation is perturbative in the deviation of the bounding curve from a circle. This method is not expected to be accurate when the boundary suffers large distortions, but it does provide important clues with regard to the influence of various energetic terms on the order-parameter texture and the shape of the domain or bubble bounding curve. We also look into the effects of thermal fluctuations, which include a sample-size-dependent effective line tension.

cond-mat.soft↗
arXiv1999

Modified Extrapolation Length Renormalization Group Equation

A modified renormalization group equation for the inverse extrapolation length $c$ is derived by considering the phase shifts of order parameter fluctuations. The resulting non-linear equation is also derived using standard methods and some additional assumptions. The associated renormalized flow $c(l)$ exhibits the correct behavior near both the special and ordinary fixed points and in particular yields a canonical scaling of $c$ with cross-over exponent $ϕ_{\rm ord} = -ν$ near the ordinary transition.

cond-mat.stat-mech↗
arXiv1999

Boojums and the Shapes of Domains in Monolayer Films

Domains in Langmuir monolayers support a texture that is the two-dimensional version of the feature known as a boojum. Such a texture has a quantifiable effect on the shape of the domain with which it is associated. The most noticeable consequence is a cusp-like feature on the domain boundary. We report the results of an experimental and theoretical investigation of the shape of a domain in a Langmuir monolayer. A further aspect of the investigation is the study of the shape of a ``bubble'' of gas-like phase in such a monolayer. This structure supports a texture having the form of an inverse boojum. The distortion of a bubble resulting from this texture is also studied. The correspondence between theory and experiment, while not perfect, indicates that a qualitative understanding of the relationship between textures and domain shapes has been achieved.

cond-mat.soft↗
arXiv1999

Textures and the shapes of domains in Langmuir monolayers

Two-dimensional domains containing an XY-like order parameter exhibit non-trivial internal structure and take on shapes controlled by the configuration that the order parameter adopts. The textures exhibited by the order parameter in such domains are controlled by the interplay between bulk and surface contributions to the energy. We report calculations of the internal texture and the shape of such domains. These calculations lead to the determination of the equilibrium properties of two-dimensional domains, such as those observed in Langmuir monolayers. This allows for the unambiguous exploration of the implications of experimental findings.

cond-mat.soft↗
arXiv1999

Conformations of closed DNA

We examine the conformations of a model for a short segment of closed DNA. The molecule is represented as a cylindrically symmetric elastic rod with a constraint corresponding to a specification of the linking number. We obtain analytic expressions leading to the spatial configuration of a family of solutions representing distortions that interpolate between the circular form of DNA and a figure-eight form that represents the onset of interwinding. We are also able to generate knotted loops. We suggest ways to use our approach to produce other configurations relevant to studies of DNA structure. The stability of the distorted configurations is assessed, along with the effects of fluctuations on the free energy of the various configurations.

cond-mat.soft↗