arXiv subjects

R. Bundschuh

Publications and source records attributed to R. Bundschuh.

8 recordsLinked to original sources

arXiv2004

A Statistical Analysis of RNA Folding Algorithms Through Thermodynamic Parameter Perturbation

Computational RNA secondary structure prediction is rather well established. However, such prediction algorithms always depend on a large number of experimentally measured parameters. Here, we study how sensitive structure prediction algorithms are to changes in these parameters. We find that already for changes corresponding to the actual experimental error to which these parameters have been determined 30% of the structure are falsly predicted and the ground state structure is preserved under parameter perturbation in only 5% of all cases. We establish that base pairing probabilities calculated in a thermal ensemble are a viable though not perfect measure for the reliability of the prediction of individual structure elements. A new measure of stability using parameter perturbation is proposed, and its limitations discussed.

q-bio.QM↗

arXiv2001

Statistical mechanics of secondary structures formed by random RNA sequences

The formation of secondary structures by a random RNA sequence is studied as a model system for the sequence-structure problem omnipresent in biopolymers. Several toy energy models are introduced to allow detailed analytical and numerical studies. First, a two-replica calculation is performed. By mapping the two-replica problem to the denaturation of a single homogeneous RNA in 6-dimensional embedding space, we show that sequence disorder is perturbatively irrelevant, i.e., an RNA molecule with weak sequence disorder is in a molten phase where many secondary structures with comparable total energy coexist. A numerical study of various models at high temperature reproduces behaviors characteristic of the molten phase. On the other hand, a scaling argument based on the extremal statistics of rare regions can be constructed to show that the low temperature phase is unstable to sequence disorder. We performed a detailed numerical study of the low temperature phase using the droplet theory as a guide, and characterized the statistics of large-scale, low-energy excitations of the secondary structures from the ground state structure. We find the excitation energy to grow very slowly (i.e., logarithmically) with the length scale of the excitation, suggesting the existence of a marginal glass phase. The transition between the low temperature glass phase and the high temperature molten phase is also characterized numerically. It is revealed by a change in the coefficient of the logarithmic excitation energy, from being disorder dominated to entropy dominated.

cond-mat.stat-mech↗

arXiv2001

High precision simulations of the longest common subsequence problem

The longest common subsequence problem is a long studied prototype of pattern matching problems. In spite of the effort dedicated to it, the numerical value of its central quantity, the Chvatal-Sankoff constant, is not yet known. Numerical estimations of this constant are very difficult due to finite size effects. We propose a numerical method to estimate the Chvatal-Sankoff constant which combines the advantages of an analytically known functional form of the finite size effects with an efficient multi-spin coding scheme. This method yields very high precision estimates of the Chvatal-Sankoff constant. Our results correct earlier estimates for small alphabet size while they are consistent with (albeit more precise than) earlier results for larger alphabet size.

cond-mat.stat-mech↗

arXiv2001

Glass transition in secondary structures formed by random RNA sequences

Formation of RNA secondary structures is an example of the sequence-structure problem omnipresent in biopolymers. A theoretical question of recent interest is whether a random RNA sequence undergoes a finite temperature glass transition. We answer this question affirmatively by first establishing the perturbative stability of the high temperature phase via a two replica calculation. Subsequently, we show that this phase cannot persist down to zero temperature by considering energetic contributions due to rare regions of complementary subsequences.

cond-mat.stat-mech↗

arXiv1999

Asymmetric exclusion process and extremal statistics of random sequences

An exact mapping is established between sequence alignment, one of the most commonly used tools of computational biology, and the asymmetric exclusion process, one of the few exactly solvable models of nonequilibrium physics. The statistical significance of sequence alignments is characterized through studying the total hopping current of the discrete time and space version of the asymmetric exclusion process.

cond-mat.stat-mech↗

arXiv1999

RNA secondary structure formation: a solvable model of heteropolymer folding

The statistical mechanics of heteropolymer structure formation is studied in the context of RNA secondary structures. A designed RNA sequence biased energetically towards a particular native structure (a hairpin) is used to study the transition between the native and molten phase of the RNA as a function of temperature. The transition is driven by a competition between the energy gained from the polymer's overlap with the native structure and the entropic gain of forming random contacts. A simplified Go-like model is proposed and solved exactly. The predicted critical behavior is verified via exact numerical enumeration of a large ensemble of similarly designed sequences.

cond-mat.stat-mech↗

arXiv1999

Weak localization of disordered quasiparticles in the mixed superconducting state

Starting from a random matrix model, we construct the low-energy effective field theory for the noninteracting gas of quasiparticles of a disordered superconductor in the mixed state. The theory is a nonlinear sigma model, with the order parameter field being a supermatrix whose form is determined solely on symmetry grounds. The weak localization correction to the field-axis thermal conductivity is computed for a dilute array of s-wave vortices near the lower critical field H_c1. We propose that weak localization effects, cut off at low temperatures by the Zeeman splitting, are responsible for the field dependence of the thermal conductivity seen in recent high-T_c experiments by Aubin et al.

cond-mat.supr-con↗

arXiv1998

Localization of quasiparticles in a disordered vortex

We study the diffusive motion of low-energy normal quasiparticles along the core of a single vortex in a dirty, type-II, s-wave superconductor. The physics of this system is argued to be described by a one-dimensional supersymmetric nonlinear sigma model, which differs from the sigma models known for disordered metallic wires. For an isolated vortex and quasiparticle energies less than the Thouless energy, we recover the spectral correlations that are predicted by random matrix theory for the universality class C. We then consider the transport problem of transmission of quasiparticles through a vortex connected to particle reservoirs at both ends. The transmittance at zero energy exhibits a weak localization correction reminiscent of quasi-one-dimensional metallic systems with symmetry index beta = 1. Weak localization disappears with increasing energy over a scale set by the Thouless energy. This crossover should be observable in measurements of the longitudinal heat conductivity of an ensemble of vortices under mesoscopic conditions. In the regime of strong localization, the localization length is shown to decrease by a factor of 8 as the quasiparticle energy goes to zero.

cond-mat.mes-hall↗