Kazumoto Iguchi

π-ELECTRONS IN A SINGLE STRAND OF DNA: A PHENOMENOLOGICAL APPROACH

We revisit the problem of the electronic properties of a single strand of DNA, formulating the Huckel approximation for π-electrons in both the sugar-phosphate backbone chain and the π-stacking of nitrogenous bases in a single strand of DNA where the nitrogenous bases are adenine (A), guanine (G), cytosine (C) and thymine (T), respectively. We calculate the electronic band structure of π-electrons: (i) in the single nitrogenous base molecules such as A, G, C and T, (ii) in the single sugar-phosphate molecule, (iii) in the single nucleotide systems such as A, G, C, T with the single sugar-phosphate group, and (iv) in the system of a single strand of DNA with an infinite repetition of a nucleotide such as A, G, C and T, respectively. We find the following: In the case of (i), there is an energy gap between the energy levels for the HOMO and LUMO in the nitrogenous base. This guarantees the semiconducting character of the bases as a mother material. In the case of (ii), there are the HOMO localized at the ox...

Tight-Binding Model for DNA Double Chains: Metal–Insulator Transition Due to the Formation of a Double Strand of DNA

A tight-binding model is formulated for the calculation of the electronic structure of a double strand of deoxyribonucleic acid (DNA). The theory is applied to DNA with a particular structure such as the ladder and decorated ladder structures. It is found that there is a novel type of metal–insulator transitions due to the hopping anisotropy of the system. A metal-semimetal-semiconductor transition is found in the former and an effective semiconductor-metal transition at finite temperature in the latter, as the effect of base paring between two strands of DNA is increased. The latter mechanism may be responsible for explaining the Meade and Kayyems recent observation.

Extrinsic Semiconductor Character of a Double Strand of DNA: Holstein's Polarons as Donors and Acceptors

We study the electrical conductivity problem of DNA, applying the Holsteins polaron model to a double strand of DNA. We show that the Holsteins polarons act as donors and acceptors in DNA and that the existence of such donors and acceptors provides us the extrinsic semiconductor character of DNA. This character of DNA may explain with a unified point of view almost all the known results recently obtained by experiments in the study of conductivity problems of DNA, which seem so controversial so far.

Intrinsic properties of Boolean dynamics in complex networks

We study intrinsic properties of attractor in Boolean dynamics of complex networks with scale-free topology, comparing with those of the so-called Kauffmans random Boolean networks. We numerically study both frozen and relevant nodes in each attractor in the dynamics of relatively small networks (20<or=N<or=200). We investigate numerically robustness of an attractor to a perturbation. An attractor with cycle length of l(c) in a network of size N consists of l(c) states in the state space of 2(N) states; each attractor has the arrangement of N nodes, where the cycle of attractor sweeps l(c) states. We define a perturbation as a flip of the state on a single node in the attractor state at a given time step. We show that the rate between unfrozen and relevant nodes in the dynamics of a complex network with scale-free topology is larger than that in Kauffmans random Boolean network model. Furthermore, we find that in a complex scale-free network with fluctuation of the in-degree number, attractors are more sensitive to a state flip for a highly connected node (i.e. input-hub node) than to that for a less connected node. By some numerical examples, we show that the number of relevant nodes increases, when an input-hub node is coincident with and/or connected with an output-hub node (i.e. a node with large output-degree) one another.

Some Effective Tight-Binding Models for Electrons in DNA Conduction:A Review

Quantum transport for DNA conduction has been widely studied with interest in application as a candidate in making nanowires as well as interest in the scientific mechanism. In this paper, we review recent works concerning the electronic states and the conduction/transfer in DNA polymers. We have mainly investigated the energy-band structure and the correlation effects of localization property in the two- and three-chain systems (ladder model) with long-range correlation as a simple model for electronic property in a double strand of DNA by using the tight-bindingmodel. In addition, we investigated the localization properties of electronic states in several actual DNA sequences such as bacteriophages of Escherichia coli, human-chromosome 22, compared with those of the artificial disordered sequences with correlation. The charge-transfer properties for poly(dA)-poly(dT) and poly(dG)-poly(dC) DNA polymers are also presented in terms of localization lengths within the frameworks of the polaron models due to the coupling between the charge carriers and the lattice vibrations of the double strand of DNA.

A class of new invariant surfaces under the trace maps for nary Fibonacci lattices

A class of new noncompact surfaces that are invariant under the trace maps for a series of nary Fibonacci lattices is derived herein. When n is fixed the lattice is constructed by a substitution scheme of n letters: A →ABCD...Z,B→A,C→B,D→C,... ,Z→Y, where the trace map is given by an n(n+1)/2‐dimensional dynamical map. The invariant surface is of the (n+1)th degree and exists in Rn(n+1)/2. The existence of such surfaces is relevant to prove the universal criticality of the spectrum—whether or not all the states in the system belong to critical states, where the wave function is self‐similar or fractal.

Optical property of a quasi-periodic multilayer

Abstract An optical property of a quasi-periodic multilayer constructed of two types of layer, A and B, is discussed. For light propagation through a quasi-periodic medium, we find that the transmission coefficient has, for the wavelength of light, many barriers where the transmission coefficient vanishes.

Exact wave functions of an electron on a quasiperiodic lattice: Definition of an infinite‐dimensional Riemann theta function

A scheme for obtaining the exact wave functions of an electron on a quasiperiodic lattice is presented. It is shown that the trace map plays a very important role for construction of the infinite‐dimensional Riemann theta function in terms of which the wave functions can be represented.

Quasiperiodic systems without Cantor‐set‐like energy bands

A class of quasiperiodic systems is proposed that does not show the Cantor‐set‐like energy bands. The general aspects of such systems are investigated.

Robustness of Attractor States in Complex Networks

We study the intrinsic properties of attractors in the Boolean dynamics in complex network with scale‐free topology, comparing with those of the so‐called random Kauffman networks. We have numerically investigated the frozen and relevant nodes for each attractor, and the robustness of the attractors to the perturbation that flips the state of a single node of attractors in the relatively small network (N = 30∼200). It is shown that the rate of frozen nodes in the complex networks with scale‐free topology is larger than that in the random Kauffman model. Furthermore, we have found that in the complex scale‐free networks with fluctuations of in‐degree number the attractors are more sensitive to the state flip of a highly connected node than to the state flip of a less connected node.