Reducing model uncertainty effects in flexible manipulators through the addition of passive damping

An important issue in the control of practical systems is the effect of model uncertainty on closed loop performance. This is of particular concern when flexible structures are to be controlled, due to the fact that states associated with higher frequency vibration modes are truncated in order to make the control problem tractable. Digital simulations of a single-link manipulator system are employed to demonstrate that passive damping added to the flexible member reduces adverse effects associated with model uncertainty. A controller was designed based on a model including only one flexible mode. This controller was applied to larger order systems to evaluate the effects of modal truncation. Simulations using a Linear Quadratic Regulator (LQR) design assuming full state feedback illustrate the effect of control spillover. Simulations of a system using output feedback illustrate the destabilizing effect of observation spillover. The simulations reveal that the system with passive damping is less susceptible to these effects than the untreated case

Elastic Correlations in Nucleosomal DNA Structure

The structure of DNA in the nucleosome core particle is studied using an elastic model that incorporates anisotropy in the bending energetics and twist-bend coupling. Using the experimentally determined structure of nucleosomal DNA [T.J. Richmond and C.A. Davey, Nature {\bf 423}, 145 (2003)], it is shown that elastic correlations exist between twist, roll, tilt, and stretching of DNA, as well as the distance between phosphate groups. The twist-bend coupling term is shown to be able to capture these correlations to a large extent, and a fit to the experimental data yields a new estimate of G=25 nm for the value of the twist-bend coupling constant

Phase Coexistence in Driven One Dimensional Transport

We study a one-dimensional totally asymmetric exclusion process with random particle attachments and detachments in the bulk. The resulting dynamics leads to unexpected stationary regimes for large but finite systems. Such regimes are characterized by a phase coexistence of low and high density regions separated by domain walls. We use a mean-field approach to interpret the numerical results obtained by Monte-Carlo simulations and we predict the phase diagram of this non-conserved dynamics in the thermodynamic limit.Comment: 4 pages, 3 figures. Accepted for publication on Phys. Rev. Let

Clustered bottlenecks in mRNA translation and protein synthesis

We construct an algorithm that generates large, band-diagonal transition matrices for a totally asymmetric exclusion process (TASEP) with local hopping rate inhomogeneities. The matrices are diagonalized numerically to find steady-state currents of TASEPs with local variations in hopping rate. The results are then used to investigate clustering of slow codons along mRNA. Ribosome density profiles near neighboring clusters of slow codons interact, enhancing suppression of ribosome throughput when such bottlenecks are closely spaced. Increasing the slow codon cluster size, beyond $\approx 3-4$, does not significantly reduce ribosome current. Our results are verified by extensive Monte-Carlo simulations and provide a biologically-motivated explanation for the experimentally-observed clustering of low-usage codons

Quenched central limit theorem for the stochastic heat equation in weak disorder

We continue with the study of the mollified stochastic heat equation in $d\geq 3$ given by $d u_{\epsilon,t}=\frac 12\Delta u_{\epsilon,t}+ \beta \epsilon^{(d-2)/2} \,u_{\epsilon,t} \,d B_{\epsilon,t}$ with spatially smoothened cylindrical Wiener process $B$, whose (renormalized) Feynman-Kac solution describes the partition function of the continuous directed polymer. In an earlier work (\cite{MSZ16}), a phase transition was obtained, depending on the value of $\beta>0$ in the limiting object of the smoothened solution $u_\epsilon$ as the smoothing parameter $\epsilon\to 0$ This partition function naturally defines a quenched polymer path measure and we prove that as long as $\beta>0$ stays small enough while $u_\epsilon$ converges to a strictly positive non-degenerate random variable, the distribution of the diffusively rescaled Brownian path converges under the aforementioned polymer path measure to standard Gaussian distribution.Comment: Minor revisio

Influence of correlations on molecular recognition

The influence of the patchiness and correlations in the distribution of hydrophobic and polar residues at the interface between two rigid biomolecules on their recognition ability is investigated in idealised coarse-grained lattice models. A general two-stage approach is utilised where an ensemble of probe molecules is designed first and the recognition ability of the probe ensemble is related to the free energy of association with both the target molecule and a different rival molecule in a second step. The influence of correlation effects are investigated using numerical Monte Carlo techniques and mean field methods. Correlations lead to different optimum characteristic lengths of the hydrophobic and polar patches for the mutual design of the two biomolecules on the one hand and their recognition ability in the presence of other molecules on the other hand.Comment: 15 pages, 5 figure

Effective affinities in microarray data

In the past couple of years several studies have shown that hybridization in Affymetrix DNA microarrays can be rather well understood on the basis of simple models of physical chemistry. In the majority of the cases a Langmuir isotherm was used to fit experimental data. Although there is a general consensus about this approach, some discrepancies between different studies are evident. For instance, some authors have fitted the hybridization affinities from the microarray fluorescent intensities, while others used affinities obtained from melting experiments in solution. The former approach yields fitted affinities that at first sight are only partially consistent with solution values. In this paper we show that this discrepancy exists only superficially: a sufficiently complete model provides effective affinities which are fully consistent with those fitted to experimental data. This link provides new insight on the relevant processes underlying the functioning of DNA microarrays.Comment: 8 pages, 6 figure

Specific protein-protein binding in many-component mixtures of proteins

Proteins must bind to specific other proteins in vivo in order to function. The proteins must bind only to one or a few other proteins of the of order a thousand proteins typically present in vivo. Using a simple model of a protein, specific binding in many component mixtures is studied. It is found to be a demanding function in the sense that it demands that the binding sites of the proteins be encoded by long sequences of bits, and the requirement for specific binding then strongly constrains these sequences. This is quantified by the capacity of proteins of a given size (sequence length), which is the maximum number of specific-binding interactions possible in a mixture. This calculation of the maximum number possible is in the same spirit as the work of Shannon and others on the maximum rate of communication through noisy channels.Comment: 13 pages, 3 figures (changes for v2 mainly notational - to be more in line with notation in information theory literature

The Continuum Directed Random Polymer

Motivated by discrete directed polymers in one space and one time dimension, we construct a continuum directed random polymer that is modeled by a continuous path interacting with a space-time white noise. The strength of the interaction is determined by an inverse temperature parameter beta, and for a given beta and realization of the noise the path evolves in a Markovian way. The transition probabilities are determined by solutions to the one-dimensional stochastic heat equation. We show that for all beta > 0 and for almost all realizations of the white noise the path measure has the same Holder continuity and quadratic variation properties as Brownian motion, but that it is actually singular with respect to the standard Wiener measure on C([0,1]).Comment: 21 page

Influence of non-universal effects on dynamical scaling in driven polymer translocation

We study the dynamics of driven polymer translocation using both molecular dynamics (MD) simulations and a theoretical model based on the non-equilibrium tension propagation on the cis side subchain. We present theoretical and numerical evidence that the non-universal behavior observed in experiments and simulations are due to finite chain length effects that persist well beyond the relevant experimental and simulation regimes. In particular, we consider the influence of the pore-polymer interactions and show that they give a major contribution to the non-universal effects. In addition, we present comparisons between the theory and MD simulations for several quantities, showing extremely good agreement in the relevant parameter regimes. Finally, we discuss the potential limitations of the present theories.Peer reviewe