Tobias Ambjörnsson

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 occurs. 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 suggests that this sensitivity could be the basis for novel nanoparticle based bio- and chemo-sensing applications.

Chaperone-assisted translocation

We investigate the translocation of a stiff polymer through a nanopore in a membrane, in the presence of binding particles (chaperones) that bind reversibly to the polymer on both sides of the membrane. A bound chaperone covers one (univalent binding) or many (multivalent binding) binding sites. Assuming that the diffusion of the chaperones is fast compared to the rate of translocation we describe the process by a one-dimensional master equation. We expand previous models by a detailed study of the effective force in the master equation, which is obtained by the appropriate statistical mechanical average over the chaperone states. The dependence of the force on the degree of valency (the number of binding sites occupied by a chaperone) is studied in detail. We obtain finite size corrections (to the thermodynamical expression for the force), which, for univalent binding, can be expressed analytically. We finally investigate the mean velocity for translocation as a function of chaperone binding strength and size. For both univalent and multivalent binding simple results are obtained for the case of a sufficiently long translocating polymer.

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 DNAs 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 basepair, 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.

Directed motion emerging from two coupled random processes : translocation of a chain through a membrane nanopore driven by binding proteins

We investigate the translocation of a stiff polymer consisting of M monomers through a nanopore in a membrane, in the presence of binding particles (chaperones) that bind onto the polymer, and partially prevent backsliding of the polymer through the pore. The process is characterized by the rates: k for the polymer to make a diffusive jump through the pore, q for unbinding of a chaperone, and the rate qκ for binding (with a binding strength κ); except for the case of no binding κ = 0 the presence of the chaperones gives rise to an effective force that drives the translocation process. In more detail, we develop a dynamical description of the process in terms of a (2+1)-variable master equation for the probability of having m monomers on the target side of the membrane with n bound chaperones at time t. Emphasis is put on the calculation of the mean first passage time [Formula: see text] as a function of total chain length M. The transfer coefficients in the master equation are determined through detailed balance, and depend on the relative chaperone size λ and binding strength κ, as well as the two rate constants k and q. The ratio γ = q/k between the two rates determines, together with κ and λ, three limiting cases, for which analytic results are derived: (i) for the case of slow binding ([Formula: see text]), the motion is purely diffusive, and [Formula: see text] for large M; (ii) for fast binding ([Formula: see text]) but slow unbinding ([Formula: see text]), the motion is, for small chaperones λ = 1, ratchet-like, and [Formula: see text]; (iii) for the case of fast binding and unbinding dynamics ([Formula: see text] and [Formula: see text]), we perform the adiabatic elimination of the fast variable n, and find that for a very long polymer [Formula: see text], but with a smaller prefactor than for ratchet-like dynamics. We solve the general case numerically as a function of the dimensionless parameters λ, κ and γ, and compare to the three limiting cases.

Stochastic approach to DNA breathing dynamics

We propose a stochastic Gillespie scheme to describe the temporal fluctuations of local denaturation zones in double-stranded DNA as a single-molecule time series. It is demonstrated that the model recovers the equilibrium properties. We also study measurable dynamical quantities such as the bubble size autocorrelation function. This efficient computational approach will be useful to analyse in detail recent single-molecule experiments on clamped homopolymer breathing domains, to probe the parameter values of the underlying Poland-Scheraga model, as well as to design experimental conditions for similar setups.

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 up to a few k(B)T. Thermal motion within the DNA double strand therefore causes the opening of intermittent single-stranded denaturation zones, the DNA bubbles. The unzipping and zipping dynamics of bps at the two zipper forks of a bubble, where the single strand of the denatured zone joins the still intact double strand, can be monitored by single molecule fluorescence or NMR methods. We here establish a dynamic description of this DNA breathing in a heteropolymer DNA with given sequence 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.

Binding dynamics of single-stranded DNA binding proteins to fluctuating bubbles in breathing DNA

We investigate the dynamics of a single local denaturation zone in a DNA molecule, a so-called DNA bubble, in the presence of single-stranded DNA binding proteins (SSBs). In particular, we develop a dynamical description of the process in terms of a two-dimensional master equation for the time evolution of the probability distribution of having a bubble of size m with n bound SSBs, for the case when m and n are the slowest variables in the system. We derive explicit expressions for the equilibrium statistical weights for a given m and n, which depend on the statistical weight u associated with breaking a base-pair interaction, the loop closure exponent c, the cooperativity parameter σ0, the SSB size λ, and binding strength κ. These statistical weights determine, through the detailed balance condition, the transfer coefficient in the master equation. For the case of slow and fast binding dynamics the problem can be reduced to one-dimensional master equations. In the latter case, we perform explicitly the adiabatic elimination of the fast variable n. Furthermore, we find that for the case that the loop closure is neglected and the binding dynamics is vanishing (but with arbitrary σ0) the eigenvalues and the eigenvectors of the master equation can be obtained analytically, using an orthogonal polynomial approach. We solve the general case numerically (i.e., including SSB binding and the loop closure) as a function of statistical weight u, binding protein size λ, and binding strength κ, and compare to the fast and slow binding limits. In particular, we find that the presence of SSBs in general increases the relaxation time, compared to the case when no binding proteins are present. By tuning the parameters, we can drive the system from regular bubble fluctuation in the absence of SSBs to full denaturation, reflecting experimental and in vivo situations.

Dynamic Approach to DNA Breathing

Even under physiological conditions, the DNA double-helix spontaneously denatures locally, opening up fluctuating, flexible, single-stranded zones called DNA-bubbles. We present a dynamical description of this DNA-bubble breathing in terms of a Fokker-Planck equation for the bubble size, based on the Poland-Scheraga free energy for DNA denaturation. From this description, we can obtain basic quantities such as the lifetime, an important measure for the description of the interaction of a breathing DNA molecule and selectively single-stranded DNA binding proteins. Our approach is consistent with recent single molecule measurements of bubble fluctuation. We also introduce a master equation approach to model DNA breathing, and discuss its differences from the continuous Fokker-Planck description.

Blinking statistics of a molecular beacon triggered by end-denaturation of DNA

We use a master equation approach based on the Poland–Scheraga free energy for DNA denaturation to investigate the (un)zipping dynamics of a denaturation wedge in a stretch of DNA that is clamped at one end. In particular, we quantify the blinking dynamics of a fluorophore–quencher pair mounted within the denaturation wedge. We also study the behavioural changes in the presence of proteins that selectively bind to single-stranded DNA. We show that such a set-up could be well suited as an easy-to-implement nanodevice for sensing environmental conditions in small volumes.