Calculation of π and Classification of Self-avoiding Lattices via DNA Configuration

Abstract

Numerical simulation (e.g. Monte Carlo simulation) is an efficient computational algorithm establishing an integral part in science to understand complex physical and biological phenomena related with stochastic problems. Aside from the typical numerical simulation applications, studies calculating numerical constants in mathematics, and estimation of growth behavior via a non-conventional self-assembly in connection with DNA nanotechnology, open a novel perspective to DNA related to computational physics. Here, a method to calculate the numerical value of π, and way to evaluate possible paths of self-avoiding walk with the aid of Monte Carlo simulation, are addressed. Additionally, experimentally obtained variation of the π as functions of DNA concentration and the total number of trials, and the behaviour of self-avoiding random DNA lattice growth evaluated through number of growth steps, are discussed. From observing experimental calculations of π (πexp) obtained by double crossover DNA lattices and DNA rings, fluctuation of πexp tends to decrease as either DNA concentration or the number of trials increases. Based upon experimental data of self-avoiding random lattices grown by the three-point star DNA motifs, various lattice configurations are examined and analyzed. This new kind of study inculcates a novel perspective for DNA nanostructures related to computational physics and provides clues to solve analytically intractable problems.

Programming Biomimetically Confined Aptamers with DNA Frameworks

“…Following this model, we first predicted the length of the aptamer in both native and nonnative conformations via a selfavoiding method, in which each oligonucleotide is represented by a hard sphere, and those spheres are linked to each other with a fixed bond length without overlapping (1.7 base for a single strand and 1 base for a double strand). 51 Specifically, by randomly picking polar angle coordinates in relation to the previous monomers, we calculated the maximum length between the starting point and a random point based on these generated coordinates for the aptamer (N = 1000). As shown in Figure 5b, the maximum length distribution for the native conformation is much narrower than that of nonnative conformation, as expected.…”

Multi-Domains in a Single Lattice Formed by DNA Self-Assembly

“…Although it might be possible to design unit building blocks with six binding domains (e.g., a honeycomb shaped building block), double-rectangular shaped building blocks such as double DX (dDX) tiles could also provide six binding domains. 37 To use dDX tiles, mapping from hexagonal to square systems had to be conducted. Among the various coordinate systems in a hexagonal grid, such as the offset, cube, doubled, and axial coordinate systems, the commonly used axial coordinate system was adapted.…”

“…Figure a shows hexadomain lattices with ON and XOR patterns in hexagonal and square systems. Although it might be possible to design unit building blocks with six binding domains (e.g., a honeycomb shaped building block), double-rectangular shaped building blocks such as double DX (dDX) tiles could also provide six binding domains . To use dDX tiles, mapping from hexagonal to square systems had to be conducted.…”