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The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…
We explore in detail the structural, mechanical and thermodynamic properties of a coarse-grained model of DNA similar to that introduced in Thomas E. Ouldridge, Ard A. Louis, Jonathan P.K. Doye, Phys. Rev. Lett. 104 178101 (2010). Effective…
The symmetries of the DNA double helix require a new term in its linear response to stress: the coupling between twist and stretch. Recent experiments with torsionally-constrained single molecules give the first direct measurement of this…
DNA polymerases are an essential class of enzymes or molecular motors that catalyze processive DNA syntheses during DNA replications. A critical issue for DNA polymerases is their molecular mechanism of processive DNA replication. We have…
We study the nonlinear dynamics of a deformed Deoxyribonucleic acid (DNA) molecular chain which is governed by a perturbed sine-Gordon equation coupled with a linear wave equation representing the lattice deformation. The DNA chain…
We investigate the presence of topological twistons in crystalline polyethylene. We describe crystalline polyethylene with a model that couples the torsional and longitudinal degrees of freedom of the polymeric chain by means of a system of…
In this paper we consider the multispecies stirring process on the discrete torus. We prove a large deviation principle for the trajectory of the vector of densities of the different species. The technique of proof consists in extending the…
Conformational transitions are ubiquitous in biomolecular systems, have significant functional roles and are subject to evolutionary pressures. Here we provide a first theoretical framework for topological transition, i.e. conformational…
Chain-like macromolecules in solution, whether biological or synthetic, transform from a spatially extended conformation to a compact one upon change of temperature or solvent qualities. This sharp transition plays a key role in various…
Transcription and translation retrieve and operationalize gene encoded information in cells. These processes are not instantaneous and incur significant delays. In this paper we study Goodwin models of both inducible and repressible operons…
The symmetries of the DNA double helix require a new term in its linear response to stress: the coupling between twist and stretch. Recent experiments with torsionally-constrained single molecules give the first direct measurement of this…
Our world is ambiguous and this is reflected in the data we use to train our algorithms. This is particularly true when we try to model natural processes where collected data is affected by noisy measurements and differences in measurement…
A couple of models are explained. Helicoidal PB model is studied in more details. It is shown that semi-discrete approximation yields to breather-type soliton moving along the chain. The model can explain local opening as a resonance mode.…
A simple model of DNA based on two interacting polymers has been used to study the unzipping of a double stranded DNA subjected to a periodic force. We propose a dynamical transition, where without changing the physiological condition, it…
We present a critique and extension of the mean-field approach to the mechanical pulling transition in bound polymer systems. Our model is motivated by the theoretically and experimentally important examples of adsorbed polymers and…
We present a very simple model for the study of charge transport in a molecule patterned on B-DNA. In this model we use a discrete non-linear Schr\"{o}dinger equation to describe electrons propagating along the sugar-phosphate backbone of…
We investigate the unfolding pathway of a cytosine-rich DNA hairpin structure via Molecular Dynamics simulations. Our results indicate a hidden complexity present in the unfolding process. W e show that this complex behavior arises due to…
We suggest that the DNA molecules could form the cholesteric phase owing to an interaction mediated by the network of the hydrogen bonds (H-network) in the solvent. The model admits of the dependence of the optical activity of the solution…
Genomic DNA is constantly subjected to various mechanical stresses arising from its biological functions and cell packaging. If the local mechanical properties of DNA change under torsional and tensional stress, the activity of…
The volume occupied by the unconstrained genomic DNA of prokaryotes in saline solutions is thousand times larger than the cell. Moreover, it is not separated from the rest of the cell by a membrane. Nevertheless, it occupies only a small…