Effect of sequence-dependent rigidity on plectoneme localization in dsDNA.

We use Monte-Carlo simulations to study the effect of variable rigidity on plectoneme formation and localization in supercoiled double-stranded DNA. We show that the presence of soft sequences increases the number of plectoneme branches and that the edges of the branches tend to be localized at these sequences. We propose an experimental approach to test our results in vitro, and discuss the possible role played by plectoneme localization in the search process of transcription factors for their targets (promoter regions) on the bacterial genome.

Effect of knots on binding of intercalators to DNA.

We study the effect of knots in circular dsDNA molecules on the binding of intercalating ligands. Using Monte Carlo simulations we show that depending on their handedness, the presence of knots can either suppress or enhance intercalation in supercoiled DNA. When the occupancy of intercalators on DNA is low, the effect of knots on intercalation can be captured by introducing a shift in the mean writhe of the chain that accounts for the writhe of the corresponding ideal knot. In the limit of high intercalator occupancy, the writhe distribution of different knots is strongly affected by excluded volume effects and therefore by salt concentration. Based on the finding that different knots yield well-separated probability distributions of bound intercalators, we propose a new experimental approach to determine DNA topology by monitoring the intensity of fluorescence emitted by dye molecules intercalated into knotted DNA molecules.

On binding of DNA-bending proteins to DNA minicircles.

We present a theoretical study of binding of DNA-bending proteins to circular DNA, using computer simulations of the wormlike chain model of DNA. We find that the binding affinity is affected by the bending elasticity and the conformational entropy of the polymer and that while protein adsorption is identical on open and closed long DNA molecules, there is significant enhancement of binding on DNA minicircles, compared to their linear counterparts. We also find that the ratio of the radii of gyration of open and closed chains depends on protein concentration for short DNA molecules. Experimental tests of our predictions are proposed.

Cancer detection from stained biopsies using high-speed spectral imaging.

The escalating demand for diagnosing pathological biopsies requires the procedures to be expedited and automated. The existing imaging systems for measuring biopsies only measure color, and even though a lot of effort is invested in deep learning analysis, there are still serious challenges regarding the performance and validity of the data for the intended medical setting. We developed a system that rapidly acquires spectral images from biopsies, followed by spectral classification algorithms. The spectral information is remarkably more informative than the color information, and leads to very high accuracy in identifying cancer cells, as tested on tens of cancer cases. This was improved even more by using artificial intelligence algorithms that required a rather small training set, indicating the high level of information that exists in the spectral images. The most important spectral differences are observed in the nucleus and they are related to aneuploidy in tumor cells. Rapid spectral imaging measurement therefore can bridge the gap in the machine-aided diagnostics of whole biopsies, thus improving patient care, and expediting the treatment procedure.

Effect of spontaneous twist on DNA minicircles.

Monte Carlo simulations are used to study the effect of spontaneous (intrinsic) twist on the conformation of topologically equilibrated minicircles of dsDNA. The twist, writhe, and radius of gyration distributions and their moments are calculated for different spontaneous twist angles and DNA lengths. The average writhe and twist deviate in an oscillatory fashion (with the period of the double helix) from their spontaneous values, as one spans the range between two neighboring integer values of intrinsic twist. Such deviations vanish in the limit of long DNA plasmids.

Coupling of twist and writhe in short DNA loops.

While bending and twist can be treated as independent degrees of freedom for linear DNA molecules, the loop closure constraint introduces a coupling between these variables in circular DNA. We performed Monte Carlo simulations of wormlike rods with both bending and twist rigidity in order to study the coupling between the writhe and twist distributions for various DNA lengths. We find that for sufficiently short DNA, the writhe distribution differs from that of a model with bending energy only. We show that the factorization approximation introduced by previous researchers coincides, within numerical accuracy, with our simulation results, and conclude that the closure constraint is fully accounted for by the White-Fuller relation. Experimental tests of our results for short DNA plasmids are proposed.

Size distribution of ring polymers.

We present an exact solution for the distribution of sample averaged monomer to monomer distance of ring polymers. For non-interacting and local-interaction models these distributions correspond to the distribution of the area under the reflected Bessel bridge and the Bessel excursion respectively, and are shown to be identical in dimension d ≥ 2, albeit with pronounced finite size effects at the critical dimension, d = 2. A symmetry of the problem reveals that dimension d and 4 - d are equivalent, thus the celebrated Airy distribution describing the areal distribution of the d = 1 Brownian excursion describes also a polymer in three dimensions. For a self-avoiding polymer in dimension d we find numerically that the fluctuations of the scaled averaged distance are nearly identical in dimension d = 2, 3 and are well described to a first approximation by the non-interacting excursion model in dimension 5.

Fractional Edgeworth expansion: Corrections to the Gaussian-Lévy central-limit theorem.

In this article we generalize the classical Edgeworth expansion for the probability density function (PDF) of sums of a finite number of symmetric independent identically distributed random variables with a finite variance to PDFs with a diverging variance, which converge to a Lévy α-stable density function. Our correction may be written by means of a series of fractional derivatives of the Lévy and the conjugate Lévy PDFs. This series expansion is general and applies also to the Gaussian regime. To describe the terms in the series expansion, we introduce a new family of special functions and briefly discuss their properties. We implement our generalization to the distribution of the momentum for atoms undergoing Sisyphus cooling, and show the improvement of our leading order approximation compared to previous approximations. In vicinity of the transition between Lévy and Gauss behaviors, convergence to asymptotic results slows down.

Force-free measurements of the conformations of DNA molecules tethered to a wall.

Using an optimized combination of tethered particle motion method, total internal reflection, and a gold nanobead, we measured the three-dimensional distribution of the free end of a tethered DNA molecule. The distribution along the axial z direction (perpendicular to the surface) is found to be Rayleigh-like, in agreement with wormlike chain and freely jointed chain simulations. Using these simulations, we show that the presence of the wall increases the correlations between the orientations of neighboring chain segments compared to free DNA. While the measured and the simulated planar (xy) distributions always agree with that of a Gaussian-random-walk (GRW) model, for short DNA lengths (1 µm) studied in our experiment, the corresponding axial (z) distributions deviate from those predicted for a GRW confined to half-space.