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Within biology, it is of interest to construct DNA complexes of a certain shape. These complexes can be represented through graph theory, using edges to model strands of DNA joined at junctions, represented by vertices. Because guided…
A new set of DNA base-nucleic acid codes and their hypercomplex number representation have been introduced for taking the probability of each nucleotide into full account. A new scoring system has been proposed to suit the hypercomplex…
DNA looping plays a fundamental role in a wide variety of biological processes, providing the backbone for long range interactions on DNA. Here we develop the first model for DNA looping by an arbitrarily large number of proteins and solve…
We use a coarse-grained molecular model to study the self-assembly process of complexes of cationic and neutral lipids with DNA molecules ("lipoplexes") - a promising nonviral carrier of DNA for gene therapy. We identify the resulting…
In this paper, a new method to efficiently simulate diffusion controlled second order chemical reactions is derived and applied to site-specific DNA-binding proteins. The protein enters a spherical cell and propagates via two competing…
Surfaces are at the frontier of every known solid. They provide versatile supports for functional nanostructures and mediate essential physicochemical processes. Being intimately related with 2D materials, interfaces and atomically thin…
In an exploration paper, {\it L. Chen, Algorithms for Deforming and Contracting Simply Connected Discrete Closed Manifolds (I)}, we designed algorithms for deforming and contracting a simply connected discrete closed manifold to a discrete…
We report model calculations on DNA single strands which describe the equilibrium dynamics and kinetics of hairpin formation and melting. Modeling is at the level of single bases. Strand rigidity is described in terms of simple polymer…
Structural DNA nanotechnology has advanced to the extent that extremely complex structures can be designed. Much of this advancement has been due to the development of automated DNA design and simulation tools. Typically, the tools (e.g.…
DNA loop formation is one of several mechanisms used by organisms to regulate genes. The free energy of forming a loop is an important factor in determining whether the associated gene is switched on or off. In this paper we use an elastic…
We propose a dynamical model depicting the interactions between DNA and a specific binding protein involving long range transmissions. The dynamics rely on the coupling between Hydrogen bonds formed between DNA and protein and between the…
The histone-DNA interaction in the nucleosome is a fundamental mechanism of genomic compaction and regulation, which remains largely unkown despite a growing structural knowledge of the complex. Here, we propose a framework for the…
Many fundamental biological processes are regulated by protein-DNA complexes called {\it synaptosomes}, which possess multiple interaction sites. Despite the critical importance of synaptosomes, the mechanisms of their formation remain not…
We introduce a novel concept, the minimal molecular surface (MMS), as a new paradigm for the theoretical modeling of biomolecule-solvent interfaces. When a less polar macromolecule is immersed in a polar environment, the surface free energy…
The denaturation of the double helix is a template for fundamental biological functions such as replication and transcription involving the formation of local fluctuational openings. The denaturation transition is studied for heterogeneous…
The equilibrium structure of a Dinucleosome is studied using an elastic model that takes into account the force and torque balance conditions. Using the proper boundary conditions, it is found that the conformational energy of the problem…
We categorise coherent band (aka nullification) pathways between knots and 2-component links. Additionally, we characterise the minimal coherent band pathways (with intermediates) between any two knots or 2-component links with small…
Planar/flat configurations of fixed-angle chains and trees are well studied in the context of polymer science, molecular biology, and puzzles. In this paper, we focus on a simple type of fixed-angle linkage: every edge has unit length…
The interaction between metal atoms and nucleobases has been a topic of high interest due to the wide scientific and technological implications. Combining density functional theory simulations with a literature overview, we achieved an…
Chromosomes are crumpled polymer chains further folded into a sequence of stochastic loops via loop extrusion. While extrusion has been verified experimentally, the particular means by which the extruding complexes bind DNA polymer remains…