arXiv subjects

Alexander Y. Grosberg

Publications and source records attributed to Alexander Y. Grosberg.

32 records · Page 2Linked to original sources

arXiv2014

Exact expressions for the mobility and electrophoretic mobility of a weakly charged sphere in a simple electrolyte

We present (asymptotically) exact expressions for the mobility and electrophoretic mobility of a weakly charged spherical particle in an $1:1$ electrolyte solution. This is done by analytically solving the electro and hydrodynamic equations governing the electric potential and fluid flow with respect to an electric field and a nonelectric force. The resulting formulae are cumbersome, but fully explicit and trivial for computation. In the case of a very small particle compared to the Debye screening length ($R \ll r_D$) our results reproduce proper limits of the classical Debye and Onsager theories, while in the case of a very large particle ($R \gg r_D$) we recover, both, the non-monotonous charge dependence discovered by Levich (1958) as well as the scaling estimate given by Long, Viovy, and Ajdari (1996), while adding the previously unknown coefficients and corrections. The main applicability condition of our solution is charge smallness in the sense that screening remains linear.

cond-mat.soft↗

arXiv2014

From a melt of rings to chromosome territories: The role of topological constraints in genome folding

We review pro and contra of the hypothesis that generic polymer properties of topological constraints are behind many aspects of chromatin folding in eukaryotic cells. For that purpose, we review, first, recent theoretical and computational findings in polymer physics related to concentrated, topologically-simple (unknotted and unlinked) chains or a system of chains. Second, we review recent experimental discoveries related to genome folding. Understanding in these fields is far from complete, but we show how looking at them in parallel sheds new light on both.

q-bio.BM↗

arXiv2013

Annealed lattice animal model and Flory theory for the melt of non-concatenated rings: Towards the physics of crumpling

A Flory theory is constructed for a long polymer ring in a melt of unknotted and non-concatenated rings. The theory assumes that the ring forms an effective annealed branched object and computes its primitive path. It is shown that the primitive path follows self-avoiding statistics and is characterized by the corresponding Flory exponent of a polymer with excluded volume. Based on that, it is shown that rings in the melt are compact objects with overall size proportional to their length raised to the 1/3 power. Furthermore, the contact probability exponent is estimated, albeit by a poorly controlled approximation, with the result consistent with both numerical and experimental data.

cond-mat.soft↗

arXiv2013

Propagation of Tension along a Polymer Chain

We study the propagation of tension caused by an external force along a long polymeric molecule in two different settings, namely along a free polymer in 3d space being pulled from one end, and along a pre-stretched circular polymer, confined in a narrow circular tube. We show that in both cases, the tension propagation is governed by a diffusion equation, and in particular, the tension front propagates as $t^{1/2}$ along the contour of the chain. The results are confirmed numerically, and by molecular dynamics simulations in the case of the 3d polymer. We also compare our results with the previously suggested ones for the translocation setting, and discuss why tension propagation is slower in that case.

cond-mat.soft↗

arXiv2013

Electrophoretic Capture of a DNA Chain into a Nanopore

Based on our formulation of the DNA electrophoresis near a pore [P. Rowghanian and A. Y. Grosberg, Phys. Rev. E 87, 042723 (2013)], we address the electrophoretic DNA capture into a nanopore as a steady-state process of particle absorption to a sink placed on top of an energy barrier. Reproducing the previously observed diffusion-limited and barrier-limited regimes as two different limits of the particle absorption process and matching the data, our model suggests a slower growth of the capture rate with the DNA length for very large DNA molecules than the previous model, motivating more experiments beyond the current range of electric field and DNA length. At moderately weak electric fields, our model predicts a different effect, stating that the DNA length dependence of the capture rate first disappears as the field is reduced and eventually reverses to a decreasing trend with $N$.

physics.bio-ph↗

arXiv2013

Electrophoresis of a DNA Coil Near a Nanopore

Motivated by DNA electrophoresis near a nanopore, we consider the flow field around an "elongated jet", a long thin source which injects momentum into a liquid. This solution qualitatively describes the electro-osmotic flow around a long rigid polymer, where due to electrohydrodynamic coupling, the solvent receives momentum from the electric field. Based on the qualitative behavior of the elongated jet solution, we develop a coarse-grained scheme which reproduces the known theoretical results regarding the electrophoretic behavior of a long rigid polymer and a polymer coil in a uniform field, which we then exploit to analyze the electrophoresis of a polymer coil in the non-uniform field near a nanopore.

physics.bio-ph↗

arXiv2011

Rheology of Ring Polymer Melts: From Linear Contaminants to Ring/Linear Blends

Ring polymers remain a major challenge to our current understanding of polymer dynamics. Experimental results are difficult to interpret because of the uncertainty in the purity and dispersity of the sample. Using both equilibrium and non-equilibrium molecular dynamics simulations we have systematically investigated the structure, dynamics and rheology of perfectly controlled ring/linear polymer blends with chains of such length and flexibility that the number of entanglements is up to about 14 per chain, which is comparable to experimental systems examined in the literature. The smallest concentration at which linear contaminants increase the zero-shear viscosity of a ring polymer melt of these chain lengths by 10% is approximately one-fifth of their overlap concentration. When the two architectures are present in equal amounts the viscosity of the blend is approximately twice as large as that of the pure linear melt. At this concentration the diffusion coefficient of the rings is found to decrease dramatically, while the static and dynamic properties of the linear polymers are mostly unaffected. Our results are supported by a primitive path analysis.

cond-mat.soft↗

arXiv2011

Molecular Dynamics Simulation Study of Nonconcatenated Ring Polymers in a Melt: I. Statics

Molecular dynamics simulations were conducted to investigate the structural properties of melts of nonconcatenated ring polymers and compared to melts of linear polymers. The longest rings were composed of N=1600 monomers per chain which corresponds to roughly 57 entanglement lengths for comparable linear polymers. For the rings, the radius of gyration squared was found to scale as N to the 4/5 power for an intermediate regime and N to the 2/3 power for the larger rings indicating an overall conformation of a crumpled globule. However, almost all beads of the rings are "surface beads" interacting with beads of other rings, a result also in agreement with a primitive path analysis performed in the following paper (DOI: 10.1063/1.3587138). Details of the internal conformational properties of the ring and linear polymers as well as their packing are analyzed and compared to current theoretical models.

cond-mat.soft↗

arXiv2011

Molecular Dynamics Simulation Study of Nonconcatenated Ring Polymers in a Melt: II. Dynamics

Molecular dynamics simulations were conducted to investigate the dynamic properties of melts of nonconcatenated ring polymers and compared to melts of linear polymers. The longest rings were composed of N=1600 monomers per chain which corresponds to roughly 57 entanglement lengths for comparable linear polymers. The ring melts were found to diffuse faster than their linear counterparts, with the self-diffusion coefficient for both architectures scaling as approximately N to the -2.4 power for large N. The mean-square displacement of the center-of-mass of the rings follows a sub-diffusive behavior for times and distances beyond the mean-square gyration radius, neither compatible with the Rouse nor the reptation model. The rings relax stress much faster than linear polymers and the zero-shear viscosity was found to vary as approximately N to the 1.4 power which is much weaker than the N to the 3.4 power of linear chains, not matching any commonly known model for polymer dynamics when compared to the observed mean-square displacements. These findings are discussed in view of the conformational properties of the rings presented in the preceding paper (DOI: 10.1063/1.3587137).

cond-mat.soft↗

arXiv2009

Brownian Vortexes

A particle diffusing around a point of stable mechanical equilibrium in a static but non-conservative force field enters into a steady state characterized by circulation in the probability flux. Circulation in such a Brownian vortex is not simply a deterministic response to the solenoidal component of the force, but rather reflects an interplay between force-driven probability currents and diffusion. As an example of this previously unrecognized class of stochastic heat engines, we consider a colloidal sphere stably trapped in a conventional optical tweezer. Rather than coming into thermodynamic equilibrium with the surrounding heat bath, the particle's Brownian fluctuations are biased into a toroidal roll. We demonstrate both theoretically and experimentally that the circulation in this practical realization of the Brownian vortex can undergo flux reversal.

cond-mat.soft↗

arXiv2007

Thermodynamic restrictions on evolutionary optimization of transcription factor proteins

Conformational fluctuations are believed to play an important role in the process by which transcription factor proteins locate and bind their target site on the genome of a bacterium. Using a simple model, we show that the binding time can be minimized, under selective pressure, by adjusting the spectrum of conformational states so that the fraction of time spent in more mobile conformations is matched with the target recognition rate. The associated optimal binding time is then within an order of magnitude of the limiting binding time imposed by thermodynamics, corresponding to an idealized protein with instant target recognition. Numerical estimates suggest that typical bacteria operate in this regime of optimized conformational fluctuations.

cond-mat.soft↗

arXiv2007

Metastable tight knots in a worm-like polymer

Based on an estimate of the knot entropy of a worm-like chain we predict that the interplay of bending energy and confinement entropy will result in a compact metastable configuration of the knot that will diffuse, without spreading, along the contour of the semi-flexible polymer until it reaches one of the chain ends. Our estimate of the size of the knot as a function of its topological invariant (ideal aspect ratio) agrees with recent experimental results of knotted dsDNA. Further experimental tests of our ideas are proposed.

cond-mat.soft↗

arXiv2007

Heteropolymer Sequence Design and Preferential Solvation of Hydrophilic Monomers: One More Application of Random Energy Model

In this paper, we study the role of surface of the globule and the role of interactions with the solvent for designed sequence heteropolymers using random energy model (REM). We investigate the ground state energy and surface monomer composition distribution. By comparing the freezing transition in random and designed sequence heteropolymers, we discuss the effects of design. Based on our results, we are able to show under which conditions solvation effect improves the quality of sequence design. Finally, we study sequence space entropy and discuss the number of available sequences as a function of imposed requirements for the design quality.

cond-mat.soft↗

arXiv2005

First passage times and asymmetry of DNA translocation

Motivated by experiments in which single-stranded DNA with a short hairpin loop at one end undergoes unforced diffusion through a narrow pore, we study the first passage times for a particle, executing one-dimensional brownian motion in an asymmetric sawtooth potential, to exit one of the boundaries. We consider the first passage times for the case of classical diffusion, characterized by a mean-square displacement of the form $< (Δx)^2> \sim t$, and for the case of anomalous diffusion or subdiffusion, characterized by a mean-square displacement of the form $< (Δx)^2> \sim t^γ$ with $0<γ<1$. In the context of classical diffusion, we obtain an expression for the mean first passage time and show that this quantity changes when the direction of the sawtooth is reversed or, equivalently, when the reflecting and absorbing boundaries are exchanged. We discuss at which numbers of `teeth' $N$ (or number of DNA nucleotides) and at which heights of the sawtooth potential this difference becomes significant. For large $N$, it is well known that the mean first passage time scales as $N^2$. In the context of subdiffusion, the mean first passage time does not exist. Therefore we obtain instead the distribution of first passage times in the limit of long times. We show that the prefactor in the power relation for this distribution is simply the expression for the mean first passage time in classical diffusion. We also describe a hypothetical experiment to calculate the average of the first passage times for a fraction of passage events that each end within some time $t^*$. We show that this average first passage time scales as $N^{2/γ}$ in subdiffusion.

q-bio.BM↗