Getting DNA twist rigidity from single molecule experiments

We use an elastic rod model with contact to study the extension versus rotation diagrams of single supercoiled DNA molecules. We reproduce quantitatively the supercoiling response of overtwisted DNA and, using experimental data, we get an estimation of the effective supercoiling radius and of the twist rigidity of B-DNA. We find that unlike the bending rigidity, the twist rigidity of DNA seems to vary widely with the nature and concentration of the salt buffer in which it is immerged

Mechanical response of plectonemic DNA: an analytical solution

We consider an elastic rod model for twisted DNA in the plectonemic regime. The molecule is treated as an impenetrable tube with an effective, adjustable radius. The model is solved analytically and we derive formulas for the contact pressure, twisting moment and geometrical parameters of the supercoiled region. We apply our model to magnetic tweezer experiments of a DNA molecule subjected to a tensile force and a torque, and extract mechanical and geometrical quantities from the linear part of the experimental response curve. These reconstructed values are derived in a self-contained manner, and are found to be consistent with those available in the literature.Comment: 14 pages, 4 figure

Molecular determinants of avoidance and inhibition of Pseudomonas aeruginosa MexB efflux pump

: Transporters of the resistance-nodulation-cell division (RND) superfamily of proteins are the dominant multidrug efflux power of Gram-negative bacteria. The major RND efflux pump of Pseudomonas aeruginosa is MexAB-OprM, in which the inner membrane transporter MexB is responsible for the recognition and binding of compounds. The high importance of this pump in clinical antibiotic resistance made it a subject of intense investigations and a promising target for the discovery of efflux pump inhibitors. This study is focused on a series of peptidomimetic compounds developed as effective inhibitors of MexAB-OprM. We performed multi-copy molecular dynamics simulations, machine-learning (ML) analyses, and site-directed mutagenesis of MexB to investigate interactions of MexB with representatives of efflux avoiders, substrates, and inhibitors. The analysis of both direct and water-mediated protein-ligand interactions revealed characteristic patterns for each class, highlighting significant differences between them. We found that efflux avoiders poorly interact with the access binding site of MexB, and inhibition engages amino acid residues that are not directly involved in binding and transport of substrates. In agreement, machine-learning models selected different residues predictive of MexB substrates and inhibitors. The differences in interactions were further validated by site-directed mutagenesis. We conclude that the substrate translocation and inhibition pathways of MexB split at the interface (between the main putative binding sites) and at the deep binding pocket and that interactions outside of the hydrophobic patch contribute to the inhibition of MexB. This molecular-level information could help in the rational design of new inhibitors and antibiotics less susceptible to the efflux mechanism. IMPORTANCE Multidrug transporters recognize and expel from cells a broad range of ligands including their own inhibitors. The difference between the substrate translocation and inhibition routes remains unclear. In this study, machine learning and computational and experimental approaches were used to understand dynamics of MexB interactions with its ligands. Our results show that some ligands engage a certain combination of polar and charged residues in MexB binding sites to be effectively expelled into the exit funnel, whereas others engage aromatic and hydrophobic residues that slow down or hinder the next step in the transporter cycle. These findings suggest that all MexB ligands fit into this substrate-inhibitor spectrum depending on their physico-chemical structures and properties

СИНТЕЗ ПАРАУНИТАРНЫХ БАНКОВ ФИЛЬТРОВ В АЛГЕБРЕ КВАТЕРНИОНОВ ДЛЯ ВЫЧИСЛИТЕЛЬНЫХ СТРУКТУР С ФИКСИРОВАННОЙ ЗАПЯТОЙ

The synthesis method of paraunitary filter banks based on the quaternion algebra (Q-PUBF) for computing structures constrained by fixed point arithmetic is proposed. Synthesis problem using method of Lagrange multipliers is solved. It is shown that the Q-PUBF represents integer transform and can be used for image coding by scheme L2L (lossless-to-lossy).Предлагается метод синтеза параунитарных банков фильтров на основе алгебры кватернионов (Q-ПУБФ) для вычислительных структур с фиксированной запятой. Задача синтеза решается с помощью метода множителей Лагранжа. Показано, что Q-ПУБФ представляет собой целочисленное преобразование и может быть использовано для кодирования изображений по схеме L2L (lossless-to-lossy)

СИНТЕЗ FPGA-АРХИТЕКТУР БАНКОВ ФИЛЬТРОВ НА ОСНОВЕ БЛОЧНОЙ ЛЕСТНИЧНОЙ ФАКТОРИЗАЦИИ В АЛГЕБРЕ КВАТЕРНИОНОВ (ЧАСТЬ 1)

Nowadays the methodology for designing systems on a chip is based on highly parameterized IP components which provide a wide range of adjustment of costs in resources, fixed point arithmetic data formats and system performance for a specific target application. The article presents a systematic approach for synthesizing FPGA architectures of integer reversible paraunitary filter banks in quaternion algebra (Int-Q-PUBB) for L2L (lossless-to-lossy) image transformed encoding. It is shown that the basic elementary transformation of the filter bank is the operation of quaternion multiplication (Q-MUL), the block-lifting factorization of which and the distributed arithmetic on the adder are the basis of the parametrizable Q-MUL IP-component.В настоящее время методологии проектирования систем на кристалле основываются на высокопараметризированных IP-компонентах (IP – intellectual property), которые для конкретного целевого приложения обеспечивают широкий диапазон регулировки затрат ресурсов, форматов данных арифметики с фиксированной запятой и производительности системы. В статье представлен систематический подход к синтезу FPGA-архитектур целочисленных обратимых параунитарных банков фильтров в алгебре кватернионов (Int-Q-ПУБФ) для трансформационного кодирования изображений по схеме L2L (lossless-to-lossy). Показывается, что базовым элементарным преобразованием банка фильтров является операция умножения кватернионов (Q-MUL). Блочная лестничная факторизация данной операции и распределенная арифметика на сумматорах положены в основу параметризируемого Q-MUL IP-компонента

Critical exponents for random knots

The size of a zero thickness (no excluded volume) polymer ring is shown to scale with chain length $N$ in the same way as the size of the excluded volume (self-avoiding) linear polymer, as $N^{\nu}$, where $\nu \approx 0.588$. The consequences of that fact are examined, including sizes of trivial and non-trivial knots.Comment: 4 pages, 0 figure

Topological entropy of a stiff ring polymer and its connection to DNA knots

We discuss the entropy of a circular polymer under a topological constraint. We call it the {\it topological entropy} of the polymer, in short. A ring polymer does not change its topology (knot type) under any thermal fluctuations. Through numerical simulations using some knot invariants, we show that the topological entropy of a stiff ring polymer with a fixed knot is described by a scaling formula as a function of the thickness and length of the circular chain. The result is consistent with the viewpoint that for stiff polymers such as DNAs, the length and diameter of the chains should play a central role in their statistical and dynamical properties. Furthermore, we show that the new formula extends a known theoretical formula for DNA knots.Comment: 14pages,11figure

Inferring the effective thickness of polyelectrolytes from stretching measurements at various ionic strengths: applications to DNA and RNA

By resorting to the thick-chain model we discuss how the stretching response of a polymer is influenced by the self-avoidance entailed by its finite thickness. The characterization of the force versus extension curve for a thick chain is carried out through extensive stochastic simulations. The computational results are captured by an analytic expression that is used to fit experimental stretching measurements carried out on DNA and single-stranded RNA (poly-U) in various solutions. This strategy allows us to infer the apparent diameter of two biologically-relevant polyelectrolytes, namely DNA and poly-U, for different ionic strengths. Due to the very different degree of flexibility of the two molecules, the results provide insight into how the apparent diameter is influenced by the interplay between the (solution-dependent) Debye screening length and the polymers' ``bare'' thickness. For DNA, the electrostatic contribution to the effective radius, $\Delta$, is found to be about 5 times larger than the Debye screening length, consistently with previous theoretical predictions for highly-charged stiff rods. For the more flexible poly-U chains the electrostatic contribution to $\Delta$ is found to be significantly smaller than the Debye screening length.Comment: iopart, 14 pages, 13 figures, to appear in J. Phys.: Condens. Matte

Abundance of unknots in various models of polymer loops

A veritable zoo of different knots is seen in the ensemble of looped polymer chains, whether created computationally or observed in vitro. At short loop lengths, the spectrum of knots is dominated by the trivial knot (unknot). The fractional abundance of this topological state in the ensemble of all conformations of the loop of $N$ segments follows a decaying exponential form, $\sim \exp (-N/N_0)$, where $N_0$ marks the crossover from a mostly unknotted (ie topologically simple) to a mostly knotted (ie topologically complex) ensemble. In the present work we use computational simulation to look closer into the variation of $N_0$ for a variety of polymer models. Among models examined, $N_0$ is smallest (about 240) for the model with all segments of the same length, it is somewhat larger (305) for Gaussian distributed segments, and can be very large (up to many thousands) when the segment length distribution has a fat power law tail.Comment: 13 pages, 6 color figure