Related papers: Role of boundary constraints in DNA cyclization
We have developed a generalized semi-analytic approach for efficiently computing cyclization and looping $J$ factors of DNA under arbitrary binding constraints. Many biological systems involving DNA-protein interactions impose precise…
DNA looping participates in transcriptional regulation, for instance, by allowing distal binding sites to act synergistically. Here we study this process and compare different regulatory mechanisms based on repression with and without…
The formation of DNA loops by proteins and protein complexes that bind at distal DNA sites plays a central role in many cellular processes, such as transcription, recombination, and replication. Here we review the basic thermodynamic…
We analyze the canonical treatment of classical constrained mechanical systems formulated with a discrete time. We prove that under very general conditions, it is possible to introduce nonsingular canonical transformations that preserve the…
We show the existence of a high interrelation between the different loops that may appear in a DNA segment. Conformational changes in a chain segment caused by the formation of a particular loop may either promote or prevent the appearance…
The formation of DNA loops by proteins and protein complexes is ubiquitous to many fundamental cellular processes, including transcription, recombination, and replication. Here we review recent advances in understanding the properties of…
Effects of sequence disorder on looping and cyclization of the double-stranded DNA are studied theoretically. Both random intrinsic curvature and inhomogeneous bending rigidity are found to result in a remarkably wide distribution of…
In the past few decades maximal regularity theory has successfully been applied to moving boundary problems. The basic idea is to reduce the system with varying domains to one in a fixed domain. This is done by a transformation (the…
Living cells provide a fluctuating, out-of-equilibrium environment in which genes must coordinate cellular function. DNA looping, which is a common means of regulating transcription, is very much a stochastic process; the loops arise from…
DNA cyclization is a powerful technique to gain insight into the nature of DNA bending. The worm-like chain model provides a good description of small to moderate bending fluctuations, but some experiments on strongly-bent shorter molecules…
In this article we show that boundary conditions can be treated as Lagrangian and Hamiltonian constraints. Using the Dirac method, we find that boundary conditions are equivalent to an infinite chain of second class constraints which is a…
A simple example is used to show that renormalization group limit cycles of effective quantum theories can be studied in a new way. The method is based on the similarity renormalization group procedure for Hamiltonians. The example contains…
One way to generalize the boundary Yamabe problem posed by Escobar is to ask if a given metric on a compact manifold with boundary can be conformally deformed to have vanishing $\sigma_k$-curvature in the interior and constant…
DNA strings and their properties are widely studied since last 20 years due to its applications in DNA computing. In this area, one designs a set of DNA strings (called DNA code) which satisfies certain thermodynamic and combinatorial…
For much of the last three decades Monte Carlo-simulation methods have been the standard approach for accurately calculating the cyclization probability, $J$, or J factor, for DNA models having sequence-dependent bends or inhomogeneous…
This paper focuses on the probability that a portion of DNA closes on itself through thermal fluctuations. We investigate the dependence of this probability upon the size r of a protein bridge and/or the presence of a kink at half DNA…
We present a boundary integral method for solving a certain class of Riemann-Hilbert problems known as the general conjugation problem. The method is based on a uniquely solvable boundary integral equation with the generalized Neumann…
We review pro and contra of the hypothesis that generic polymer properties of topological constraints are behind many aspects of chromatin folding in eukaryotic cells. For that purpose, we review, first, recent theoretical and computational…
We report a theoretical study of DNA flexibility and quantitatively predict the ring closure probability as a function of DNA contour length. Recent experimental studies show that the flexibility of short DNA fragments (as compared to the…
This paper proves that robustness implies generalization via data-dependent generalization bounds. As a result, robustness and generalization are shown to be connected closely in a data-dependent manner. Our bounds improve previous bounds…