arXiv subjects

Tobias Ambjornsson

Publications and source records attributed to Tobias Ambjornsson.

At least 19 recordsLinked to original sources

arXiv2020

Stochastic unfolding of nanoconfined DNA: experiments, model and Bayesian analysis

Nanochannels provide means for detailed experiments on the effect of confinement on biomacromolecules, such as DNA. We here introduce a model for the complete unfolding of DNA from the circular to linear configuration. Two main ingredients are the entropic unfolding force as well as the friction coefficient for the unfolding process, and we describe the associated dynamics by a non-linear Langevin equation. By analyzing experimental data where DNA molecules are photo-cut and unfolded inside a nanochannel, our model allows us to extract values for the unfolding force as well as the friction coefficient for the first time. In order to extract numerical values for these physical quantities, we employ a recently introduced Bayesian inference framework. We find that the determined unfolding force is in agreement with estimates from a simple Flory type argument. The estimated friction coefficient is in agreement with theoretical estimates for motion of a cylinder in a channel. We further validate the estimated friction constant by extracting this parameter from DNA's center-of-mass motion before and after unfolding, yielding decent agreement.

physics.bio-ph↗

arXiv2018

Fitting a function to time-dependent ensemble averaged data

Time-dependent ensemble averages, i.e., trajectory-based averages of some observable, are of importance in many fields of science. A crucial objective when interpreting such data is to fit these averages (for instance, squared displacements) with a function and extract parameters (such as diffusion constants). A commonly overlooked challenge in such function fitting procedures is that fluctuations around mean values, by construction, exhibit temporal correlations. We show that the only available general purpose function fitting methods, correlated chi-square method and the weighted least squares method (which neglects correlation), fail at either robust parameter estimation or accurate error estimation. We remedy this by deriving a new closed-form error estimation formula for weighted least square fitting. The new formula uses the full covariance matrix, i.e., rigorously includes temporal correlations, but is free of the robustness issues, inherent to the correlated chi-square method. We demonstrate its accuracy in four examples of importance in many fields: Brownian motion, damped harmonic oscillation, fractional Brownian motion and continuous time random walks. We also successfully apply our method, weighted least squares including correlation in error estimation (WLS-ICE), to particle tracking data. The WLS-ICE method is applicable to arbitrary fit functions, and we provide a publically available WLS-ICE software.

physics.data-an↗

arXiv2015

How nanochannel confinement affects the DNA melting transition within the Poland-Scheraga model

When double-stranded DNA molecules are heated, or exposed to denaturing agents, the two strands get separated. The statistical physics of this process has a long history, and is commonly described in term of the Poland-Scheraga (PS) model. Crucial to this model is the configurational entropy for a melted region (compared to the entropy of an intact region of the same size), quantified by the loop factor. In this study we investigate how confinement affects the DNA melting transition, by using the loop factor for an ideal Gaussian chain. By subsequent numerical solutions of the PS model, we demonstrate that the melting temperature depends on the persistence lengths of single-stranded and double-stranded DNA. For realistic values of the persistence lengths the melting temperature is predicted to decrease with decreasing channel diameter. We also demonstrate that confinement broadens the melting transition. These general findings hold for the three scenarios investigated: namely 1. homo-DNA, i.e. identical basepairs along the DNA molecule; 2. random sequence DNA, and 3. "real" DNA, here T4 phage DNA. We show that cases 2 and 3 in general give rise to broader transitions than case 1. Case 3 exhibits a similar phase transition as case 2 provided the random sequence DNA has the same ratio of AT to GC basepairs. A simple analytical estimate for the shift in melting temperature is provided as a function of nanochannel diameter. For homo-DNA, we also present an analytical prediction of the melting probability as a function of temperature.

q-bio.BM↗

arXiv2014

Universality and non-universality of mobility in heterogeneous single-file systems and Rouse chains

We study analytically the tracer particle mobility in single-file systems with distributed friction constants. Our system serves as a prototype for non-equilibrium, heterogeneous, strongly interacting Brownian systems. The long time dynamics for such a single-file setup belongs to the same universality class as the Rouse model with dissimilar beads. The friction constants are drawn from a density $\varrho(ξ)$ and we derive an asymptotically exact solution for the mobility distribution $P[μ_0(s)]$, where $μ_0(s)$ is the Laplace-space mobility. If $\varrho$ is light-tailed (first moment exists) we find a self-averaging behaviour: $P[μ_0(s)]=δ[μ_0(s)-μ(s)]$ with $μ(s)\propto s^{1/2}$. When $\varrho(ξ)$ is heavy-tailed, $\varrho(ξ)\simeq ξ^{-1-α} \ (0<α<1)$ for large $ξ$ we obtain moments $\langle [μ_s(0)]^n\rangle \propto s^{βn}$ where $β=1/(1+α)$ and no self-averaging. The results are corroborated by simulations.

cond-mat.stat-mech↗

arXiv2013

Transition dynamics in aging systems: microscopic origin of logarithmic time evolution

There exists compelling experimental evidence in numerous systems for logarithmically slow time evolution, yet its theoretical understanding remains elusive. We here introduce and study a generic transition process in complex systems, based on non-renewal, aging waiting times. Each state n of the system follows a local clock initiated at t=0. The random time τbetween clock ticks follows the waiting time density ψ(τ). Transitions between states occur only at local clock ticks and are hence triggered by the local forward waiting time, rather than by ψ(τ). For power-law forms ψ(τ) ~ τ^{-1-α} (0<α<1) we obtain a logarithmic time evolution of the state number ~ log(t/t_0), while for α>2 the process becomes normal in the sense that ~ t. In the intermediate range 1<α<2 we find the power-law growth ~ t^{α-1}. Our model provides a universal description for transition dynamics between aging and non-aging states.

cond-mat.stat-mech↗

arXiv2012

First Passage Times for a Tracer Particle in Single File Diffusion and Fractional Brownian Motion

We investigate the full functional form of the first passage time density (FPTD) of a tracer particle in a single-file diffusion (SFD) system whose population is: (i) homogeneous, i.e., all particles having the same diffusion constant and (ii) heterogeneous, with diffusion constants drawn from a heavy-tailed power-law distribution. In parallel, the full FPTD for fractional Brownian motion [fBm - defined by the Hurst parameter, 0 = 1/3, as predicted by Molchan [1999] for fBm. When H<1/3, which includes homogeneous SFD (H=1/4), and heterogeneous SFD (H<1/4), the WFA fails to agree with any temporal scale of the simulations and Molchan's long-time result. SFD systems are compared to their fBm counter parts; and in the homogeneous system both scaled FPTDs agree on all temporal scales including also, the result by Molchan, thus affirming that SFD and fBm dynamics belong to the same universality class. In the heterogeneous case SFD and fBm results for heterogeneity-averaged FPTDs agree in the asymptotic time limit. The non-averaged heterogeneous SFD systems display a lack of self-averaging. An exponential with a power-law argument, multiplied by a power-law pre-factor is shown to describe well the FPTD for all times for homogeneous SFD and sub-diffusive fBm systems.

physics.bio-ph↗

arXiv2010

Dissimilar bouncy walkers

We consider the dynamics of a one-dimensional system consisting of dissimilar hardcore interacting (bouncy) random walkers. The walkers' (diffusing particles') friction constants xi_n, where n labels different bouncy walkers, are drawn from a distribution rho(xi_n). We provide an approximate analytic solution to this recent single-file problem by combining harmonization and effective medium techniques. Two classes of systems are identified: when rho(xi_n) is heavy-tailed, rho(xi_n)=A xi_n^(-1-α) (0<alpha<1) for large xi_n, we identify a new universality class in which density relaxations, characterized by the dynamic structure factor S(Q,t), follows a Mittag-Leffler relaxation, and the the mean square displacement of a tracer particle (MSD) grows as t^delta with time t, where delta=alpha/(1+α). If instead rho is light-tailedsuch that the mean friction constant exist, S(Q,t) decays exponentially and the MSD scales as t^(1/2). We also derive tracer particle force response relations. All results are corroborated by simulations and explained in a simplified model.

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↗

arXiv2009

Diffusion of Finite-Sized Hard-Core Interacting Particles In a One-Dimensional Box - Tagged Particle Dynamics

We solve a non-equilibrium statistical mechanics problem exactly, namely, the single-file dynamics of N hard-core interacting particles (the particles cannot pass each other) of size Δdiffusing in a one dimensional system of finite length L with reflecting boundaries at the ends. We obtain an exact expression for the conditional probability density function P_T(y_T,t|y_{T,0}) that a tagged particle T (T=1,...,N) is at position y_T at time t given that it at time t=0 was at position y_{T,0}. Going beyond previous studies, we consider the asymptotic limit of large N, maintaining L finite, using a non-standard asymptotic technique. We derive an exact expression for P_T(y_T,t|y_{T,0}) for a a tagged particle located roughly in the middle of the system, from which we find that there are three time regimes of interest for finite-sized systems: (A) For times much smaller than the collision time t<< t_coll=1/(ρ^2D), where ρ=N/L is the particle concentration and D the diffusion constant for each particle, the tagged particle undergoes normal diffusion; (B) for times much larger than the collision time t>> t_coll but times smaller than the equilibrium time t<< t_eq=L^2/D we find a single-file regime where P_T(y_T,t|y_{T,0}) is a Gaussian with a mean square displacement scaling as t^{1/2}; (C) For times longer than the equilibrium time $t>> t_eq, P_T(y_T,t|y_{T,0}) approaches a polynomial-type equilibrium probability density function.

cond-mat.stat-mech↗

arXiv2009

Bubble merging in breathing DNA as a vicious walker problem in opposite potentials

We investigate the coalescence of two DNA-bubbles initially located at weak domains and separated by a more stable barrier region in a designed construct of double-stranded DNA. In a continuum Fokker-Planck approach, the characteristic time for bubble coalescence and the corresponding distribution are derived, as well as the distribution of coalescence positions along the barrier. Below the melting temperature, we find a Kramers-type barrier crossing behavior, while at high temperatures, the bubble corners perform drift-diffusion towards coalescence. In the calculations, we map the bubble dynamics on the problem of two vicious walkers in opposite potentials. We also present a discrete master equation approach to the bubble coalescence problem. Numerical evaluation and stochastic simulation of the master equation show excellent agreement with the results from the continuum approach. Given that the coalesced state is thermodynamically stabilized against a state where only one or a few base pairs of the barrier region are re-established, it appears likely that this type of setup could be useful for the quantitative investigation of thermodynamic DNA stability data as well as the rate constants involved in the unzipping and zipping dynamics of DNA, in single molecule fluorescence experiments.

cond-mat.stat-mech↗

arXiv2008

Diffusion of two particles with a finite interaction potential in one dimension

We investigate the dynamics of two interacting diffusing particles in an infinite effectively one dimensional system; the particles interact through a step-like potential of width b and height phi_0 and are allowed to pass one another. By solving the corresponding 2+1-variate Fokker-Planck equation an exact result for the two particle conditional probability density function (PDF) is obtained for arbitrary initial particle positions. From the two-particle PDF we obtain the overtake probability, i.e. the probability that the two particles has exchanged positions at time t compared to the initial configuration. In addition, we calculate the trapping probability, i.e. the probability that the two particles are trapped close to each other (within the barrier width b) at time t, which is mainly of interest for an attractive potential, phi_0<0. We also investigate the tagged particle PDF, relevant for describing the dynamics of one particle which is fluorescently labeled. Our analytic results are in excellent agreement with the results of stochastic simulations, which are performed using the Gillespie algorithm.

q-bio.BM↗

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

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

Breathing dynamics in heteropolymer DNA

While the statistical mechanical description of DNA has a long tradition, renewed interest in DNA melting from a physics perspective is nourished by measurements of the fluctuation dynamics of local denaturation bubbles by single molecule spectroscopy. The dynamical opening of DNA bubbles (DNA breathing) is supposedly crucial for biological functioning during, for instance, transcription initiation and DNA's interaction with selectively single-stranded DNA binding proteins. Motivated by this, we consider the bubble breathing dynamics in a heteropolymer DNA based on a (2+1)-variable master equation and complementary stochastic Gillespie simulations, providing the bubble size and the position of the bubble along the sequence as a function of time. We utilize new experimental data that independently obtain stacking and hydrogen bonding contributions to DNA stability. We calculate the spectrum of relaxation times and the experimentally measurable autocorrelation function of a fluorophore-quencher tagged base-pair, and demonstrate good agreement with fluorescence correlation experiments. A significant dependence of opening probability and waiting time between bubble events on the local DNA sequence is revealed and quantified for a promoter sequence of the T7 phage. The strong dependence on sequence, temperature and salt concentration for the breathing dynamics of DNA found here points at a good potential for nanosensing applications by utilizing short fluorophore-quencher dressed DNA constructs.

q-bio.BM↗

arXiv2006

Bubble coalescence in breathing DNA: Two vicious walkers in opposite potentials

We investigate the coalescence of two DNA-bubbles initially located at weak segments and separated by a more stable barrier region in a designed construct of double-stranded DNA. The characteristic time for bubble coalescence and the corresponding distribution are derived, as well as the distribution of coalescence positions along the barrier. Below the melting temperature, we find a Kramers-type barrier crossing behaviour, while at high temperatures, the bubble corners perform drift-diffusion towards coalescence. The results are obtained by mapping the bubble dynamics on the problem of two vicious walkers in opposite potentials.

cond-mat.stat-mech↗

arXiv2006

Master equation approach to DNA-breathing in heteropolymer DNA

After crossing an initial barrier to break the first base-pair (bp) in double-stranded DNA, the disruption of further bps is characterized by free energies between less than one to a few kT. This causes the opening of intermittent single-stranded bubbles. Their unzipping and zipping dynamics can be monitored by single molecule fluorescence or NMR methods. We here establish a dynamic description of this DNA-breathing in a heteropolymer DNA in terms of a master equation that governs the time evolution of the joint probability distribution for the bubble size and position along the sequence. The transfer coefficients are based on the Poland-Scheraga free energy model. We derive the autocorrelation function for the bubble dynamics and the associated relaxation time spectrum. In particular, we show how one can obtain the probability densities of individual bubble lifetimes and of the waiting times between successive bubble events from the master equation. A comparison to results of a stochastic Gillespie simulation shows excellent agreement.

cond-mat.stat-mech↗

arXiv2006

Sequence sensitivity of breathing dynamics in heteropolymer DNA

We study the fluctuation dynamics of localized denaturation bubbles in heteropolymer DNA with a master equation and complementary stochastic simulation based on novel DNA stability data. A significant dependence of opening probability and waiting time between bubble events on the local DNA sequence is revealed and quantified for a biological sequence of the T7 bacteriophage. Quantitative agreement with data from fluorescence correlation spectroscopy (FCS) is demonstrated.

q-bio.BM↗

arXiv2006

Resonant coupling between localized plasmons and anisotropic molecular coatings in ellipsoidal metal nanoparticles

We present an analytic theory for the optical properties of ellipsoidal plasmonic particles covered by anisotropic molecular layers. The theory is applied to the case of a prolate spheroid covered by chromophores oriented parallel and perpendicular to the metal surface. For the case that the molecular layer resonance frequency is close to being degenerate with one of the particle plasmon resonances strong hybridization between the two resonances occur. Approximate analytic expressions for the hybridized resonance frequencies, their extinction cross section peak heights and widths are derived. The strength of the molecular - plasmon interaction is found to be strongly dependent on molecular orientation and suggest that this sensitivity could be the basis for novel nanoparticle based bio/chemo-sensing applications.

physics.optics↗