arXiv subjects

Michael A. Lomholt

Publications and source records attributed to Michael A. Lomholt.

35 records · Page 2Linked to original sources

arXiv2010

Elastic moderation of intrinsically applied tension in lipid membranes

Tension in lipid membranes is often controlled externally, by pulling on the boundary of the membrane or changing osmotic pressure across a curved membrane. But modifications of the tension can also be induced in an internal fashion, for instance as a byproduct of changing a membranes electric potential or, as observed experimentally, by activity of membrane proteins. Here we develop a theory which demonstrate how such internal contributions to the tension are moderated through elastic stretching of the membrane when the membrane is initially in a low tension floppy state.

cond-mat.soft↗

arXiv2010

Foundation of Fractional Langevin Equation: Harmonization of a Many Body Problem

In this study we derive a single-particle equation of motion, from first-principles, starting out with a microscopic description of a tracer particle in a one-dimensional many-particle system with a general two-body interaction potential. Using a new harmonization technique, we show that the resulting dynamical equation belongs to the class of fractional Langevin equations, a stochastic framework which has been proposed in a large body of works as a means of describing anomalous dynamics. Our work sheds light on the fundamental assumptions of these phenomenological models.

cond-mat.stat-mech↗

arXiv2008

Bulk-mediated surface diffusion on a cylinder: propagators and crossovers

We consider the effective surface motion of a particle that freely diffuses in the bulk and intermittently binds to that surface. From an exact approach we derive various regimes of the effective surface motion characterized by physical rates for binding/unbinding and the bulk diffusivity. We obtain a transient regime of superdiffusion and, in particular, a saturation regime characteristic for the cylindrical geometry. This saturation, however, in a finite system is not terminal but eventually turns over to normal surface diffusion. The first passage behavior of particles to the cylinder surface is derived. Consequences for actual systems are discussed.

cond-mat.stat-mech↗

arXiv2008

Quantitative approach to facilitated diffusion with intersegmental jumping

We study the impact of DNA coiling on the search rate of proteins moving along the DNA contour interspersed by three-dimensional (3D) bulk excursions. When the DNA is coiled proteins performing short 3D hops along a DNA segment can be captured by foreign DNA segments that have looped back close to the original segment. These intersegmental jumps are shown to enhance the search rate for a specific site on the DNA by lowering the tendency to resample previously visited sites on the DNA. The model developed here offers a quantitative description of recent single molecule experiments on facilitated diffusion of restriction enzymes EcoRV.

cond-mat.stat-mech↗

arXiv2008

Langevin formulation for single-file diffusion

We introduce a stochastic equation for the microscopic motion of a tagged particle in the single file model. This equation provides a compact representation of several of the system's properties such as Fluctuation-Dissipation and Linear Response relations, achieved by means of a diffusion noise approach. Most important, the proposed Langevin Equation reproduces quantitatively the \emph{three} temporal regimes and the corresponding time scales: ballistic, diffusive and subdiffusive.

cond-mat.stat-mech↗

arXiv2008

Single-file dynamics with different diffusion constants

We investigate the single-file dynamics of a tagged particle in a system consisting of N hardcore interacting particles (the particles cannot pass each other) which are diffusing in a one-dimensional system where the particles have different diffusion constants. For the two particle case an exact result for the conditional probability density function (PDF) is obtained for arbitrary initial particle positions and all times. The two-particle PDF is used to obtain the tagged particle PDF. For the general N-particle case (N large) we perform stochastic simulations using our new computationally efficient stochastic simulation technique based on the Gillespie algorithm. We find that the mean square displacement for a tagged particle scales as the square root of time (as for identical particles) for long times, with a prefactor which depends on the diffusion constants for the particles; these results are in excellent agreement with very recent analytic predictions in the mathematics literature.

cond-mat.stat-mech↗

arXiv2007

The advantage of Lévy strategies in intermittent search processes

Search strategies based on random walk processes with long-tailed jump length distributions (Levy walks) on the one hand and intermittent behavior switching between local search and ballistic relocation phases on the other, have been previously shown to be beneficial in stochastic target finding problems. We here study a combination of both mechanisms: an intermittent process with Levy distributed relocations. We demonstrate how Levy distributed relocations reduce oversampling and thus further optimize the intermittent search strategy in the critical situation of rare targets.

cond-mat.stat-mech↗

arXiv2007

Leapover lengths and first passage time statistics for Lévy flights

Exact results for the first passage time and leapover statistics of symmetric and one-sided Levy flights (LFs) are derived. LFs with stable index alpha are shown to have leapover lengths, that are asymptotically power-law distributed with index alpha for one-sided LFs and, surprisingly, with index alpha/2 for symmetric LFs. The first passage time distribution scales like a power-law with index 1/2 as required by the Sparre Andersen theorem for symmetric LFs, whereas one-sided LFs have a narrow distribution of first passage times. The exact analytic results are confirmed by extensive simulations.

cond-mat.stat-mech↗

arXiv2007

Subdiffusion and weak ergodicity breaking in the presence of a reactive boundary

We derive the boundary condition for a subdiffusive particle interacting with a reactive boundary with finite reaction rate. Molecular crowding conditions, that are found to cause subdiffusion of larger molecules in biological cells, are shown to effect long-tailed distributions with identical exponent for both the unbinding times from the boundary to the bulk and the rebinding times from the bulk. This causes a weak ergodicity breaking: typically, an individual particle either stays bound or remains in the bulk for very long times. We discuss why this may be beneficial for in vivo gene regulation by DNA-binding proteins, whose typical concentrations are nanomolar

cond-mat.stat-mech↗

arXiv2007

Manipulating single enzymes by an external harmonic force

We study a Michaelis-Menten reaction for a single two-state enzyme molecule, whose transition rates between the two conformations are modulated by an harmonically oscillating external force. In particular, we obtain a range of optimal driving frequencies for changing the conformation of the enzyme thereby controlling the enzymatic activity (i.e. product formation). This analysis demonstrates that it is, in principle, possible to obtain information about particular rates within the kinetic scheme.

q-bio.BM↗

arXiv2007

Applying a potential across a biomembrane: electrostatic contribution to the bending rigidity and membrane instability

We investigate the effect on biomembrane mechanical properties due to the presence an external potential for a non-conductive non-compressible membrane surrounded by different electrolytes. By solving the Debye-Huckel and Laplace equations for the electrostatic potential and using the relevant stress-tensor we find: in (1.) the small screening length limit, where the Debye screening length is smaller than the distance between the electrodes, the screening certifies that all electrostatic interactions are short-range and the major effect of the applied potential is to decrease the membrane tension and increase the bending rigidity; explicit expressions for electrostatic contribution to the tension and bending rigidity are derived as a function of the applied potential, the Debye screening lengths and the dielectric constants of the membrane and the solvents. For sufficiently large voltages the negative contribution to the tension is expected to cause a membrane stretching instability. For (2.) the dielectric limit, i.e. no salt (and small wavevectors compared to the distance between the electrodes), when the dielectric constant on the two sides are different the applied potential induces an effective (unscreened) membrane charge density, whose long-range interaction is expected to lead to a membrane undulation instability.

cond-mat.soft↗

arXiv2006

Mechanics of non-planar membranes with force-dipole activity

A study is made of how active membrane proteins can modify the long wavelength mechanics of fluid membranes. The activity of the proteins is modelled as disturbing the protein surroundings through non-local force distributions of which a force-dipole distribution is the simplest example. An analytic expression describing how the activity modifies the force-balance equation for the membrane surface is obtained in the form of a moment expansion of the force distribution. This expression allows for further studies of the consequences of the activity for non-planar membranes. In particular the active contributions to mechanical properties such as tension and bending moments become apparent. It is also explained how the activity can induce a hydrodynamic attraction between the active proteins in the membrane.

cond-mat.soft↗

arXiv2006

Descriptions of membrane mechanics from microscopic and effective two-dimensional perspectives

Mechanics of fluid membranes may be described in terms of the concepts of mechanical deformations and stresses, or in terms of mechanical free-energy functions. In this paper, each of the two descriptions is developed by viewing a membrane from two perspectives: a microscopic perspective, in which the membrane appears as a thin layer of finite thickness and with highly inhomogeneous material and force distributions in its transverse direction, and an effective, two-dimensional perspective, in which the membrane is treated as an infinitely thin surface, with effective material and mechanical properties. A connection between these two perspectives is then established. Moreover, the functional dependence of the variation in the mechanical free energy of the membrane on its mechanical deformations is first studied in the microscopic perspective. The result is then used to examine to what extent different, effective mechanical stresses and forces can be derived from a given, effective functional of the mechanical free energy.

cond-mat.soft↗

arXiv2006

Fluctuation spectrum of quasispherical membranes with force-dipole activity

The fluctuation spectrum of a quasi-spherical vesicle with active membrane proteins is calculated. The activity of the proteins is modeled as the proteins pushing on their surroundings giving rise to non-local force distributions. Both the contributions from the thermal fluctuations of the active protein densities and the temporal noise in the individual active force distributions of the proteins are taken into account. The noise in the individual force distributions is found to become significant at short wavelengths.

cond-mat.soft↗

arXiv2006

Optimal target search on a fast folding polymer chain with volume exchange

We study the search process of a target on a rapidly folding polymer (`DNA') by an ensemble of particles (`proteins'), whose search combines 1D diffusion along the chain, Levy type diffusion mediated by chain looping, and volume exchange. A rich behavior of the search process is obtained with respect to the physical parameters, in particular, for the optimal search.

cond-mat.soft↗

arXiv2005

A General Theory of Non-equilibrium Dynamics of Lipid-protein Fluid Membranes

We present a general and systematic theory of non-equilibrium dynamics of multi-component fluid membranes, in general, and membranes containing transmembrane proteins, in particular. Developed based on a minimal number of principles of statistical physics and designed to be a meso/macroscopic-scale effective description, the theory is formulated in terms of a set of equations of hydrodynamics and linear constitutive relations. As a particular emphasis of the theory, the equations and the constitutive relations address both the thermodynamic and the hydrodynamic consequences of the unconventional material characteristics of lipid-protein membranes and contain proposals as well as predictions which have not yet been made in already existed work on membrane hydrodynamics and which may have experimental relevance. The framework structure of the theory makes possible its applications to a range of non-equilibrium phenomena in a range of membrane systems, as discussions in the paper of a few limit cases demonstrate.

cond-mat.soft↗

arXiv2002

Dynamics of shape fluctuations of quasi-spherical vesicles revisited

In this paper, the dynamics of spontaneous shape fluctuations of a single, giant quasi-spherical vesicle formed of a single lipid species is revisited theoretically. A coherent physical theory for the dynamics is developed based on a number of fundamental principles and considerations and a systematic formulation of the theory is also established. From the systematic theoretical formulation, an analytical description of the dynamics of shape fluctuations of quasi-spherical vesicles is derived. In particular, in developing the theory we have made a new interpretation of some of the phenomenological constants in a canonical continuum description of fluid lipid-bilayer membranes and shown the consequences of this new interpretation in terms of the characteristics of the dynamics of vesicle shape fluctuations. Moreover, we have used the systematic formulation of our theory as a framework against which we have discussed the previously existing theories and their discrepancies. Finally, we have made a systematic prediction about the system-dependent characteristics of the relaxation dynamics of shape fluctuations of quasi-spherical vesicles with a view of experimental studies of the phenomenon and also discussed, based on our theory, a recently published experimental work on the topic.

cond-mat.soft↗