Quantum Bio-Informatics II

The following sections are included:

• PREFACE

• CONTENTS

We outline our programme to create quantum-like representations in economy, cognitive science, psychology, genetics,….

In this paper, we discuss chaos observed in linear dynamical systems. Mainly, we address log-linear dynamics, which is a dynamical system on open simplex, and show chaotic behaviors near the boundary on the simplex.

In many models of perfect teleportation, maximum entangled states are usually used as resources. Kossakowski and Ohya showed that a linear teleportation map is defined mathematically even if a non-maximum entangled state is postulated. Based on K-O scheme, we design a perfect teleportation model by means of non-maximal entangled state.

A brief account of the quantum information dynamics and dynamical programming methods for the purpose of optimal control in quantum cybernetics with convex constraints and cońcave cost and bequest functions of the quantum state is given. Consideration is given to both open loop and feedback control schemes corresponding respectively to deterministic and stochastic semi-Markov dynamics of stable or unstable systems. For the quantum feedback control scheme with continuous observations we exploit the separation theorem of filtering and control aspects for quantum stochastic micro-dynamics of the total system. This allows to start with the Belavkin quantum filtering equation and derive the generalized Hamilton-Jacobi-Bellman equation using standard arguments of classical control theory. This is equivalent to a Hamilton-Jacobi equation with an extra linear dissipative term if the control is restricted to only Hamiltonian terms in the filtering equation. A controlled qubit is considered as an example throughout the development of the formalism. Finally, we discuss optimum observation strategies to obtain a pure quantum qubit state from a mixed one.

We provide a large class of quantum d ⊗ d states which are positive under partial transposition (so called PPT states). The construction is based on certain direct sum decomposition of the total Hilbert space which is governed by a cyclic permutation from the symmetric group S_d-1. It turns out that partial transposition maps any such decomposition into another one corresponding to 'complementary' permutation. This class contains many well known examples of PPT states from the literature and gives rise to a huge family of completely new states. The class of circulat states gives rise to a nice example for the linear lifting and transition expectation.

We introduce the compound Fock space as the Fock space over the Fock space. Though this investigation might be of some interest by itself the main purpose to deal with the compound Fock space was to model the space of the memory in a quantum statistical model of the recognition process.

For an arbitrary finite measurable decomposition of a finite measure space G into disjoint G₁,…,G_n the corresponding Fock space Γ(L²(G)) factorises as . We study unitary operators V on Γ(L²(G)) ⊗ Γ(L²(G)) that also factorise into , where V_Gk are unitary, vacuum preserving operators on Γ(L²(G_k)) ⊗ Γ(L²(G_k)). It is shown, that the only operators having this property are the unitary beam splitters well-known in quantum optics. The result is related to a quantum model of recognition and brain activities introduced in [6].

Quantum baker's map is a theoretical model that produces chaos in a quantum system. We have been studied quantum dynamics for the quantum baker's map. We used the Schack and Caves symbolic description of the quantum baker's map. We showed an exact expression for the expectation value of the time dependent position operator in the previous paper. In this paper, we introduce a combined quantum baker's map. Chaos of the combined dynamics for quantum baker's map is studied by the entropic chaos degree.

The alignment of genome sequences or amino acid sequences is one of fundamental operations for the study of life. Usual computational complexity for the multiple alignment of N sequences with common length L by dynamic programming is O(L^N). This alignment is considered as one of the NP problems, so that it is desirable to find a nice algorithm of the multiple alignment. Thus in this paper we propose the quantum algorithm for the multiple alignment based on the works^12,1,2 in which the NP complete problem was shown to be the P problem by means of quantum algorithm and chaos information dynamics.

We show that (in contrast to rather common opinion) the domain of applications of the mathematical formalism of quantum mechanics is not restricted to physics. This formalism can be applied to the description of various quantum-like (QL) information processing. In particular, the calculus of quantum (and more general QL) probabilities can be used to explain some paradoxical statistical data which was collected in psychology and cognitive science. The main lesson of our study is that one should sharply distinguish the mathematical apparatus of QM from QM as a physical theory. The domain of application of the mathematical apparatus is essentially wider than quantum physics. Quantum-like representation algorithm, formula of total probability, interference of probabilities, psychology, cognition, decision making.

A sufficient condition for non-Markovian master equation which ensures the complete positivity of the resulting time evolution is presented.

We present the description of positive partially transposed (PPT) states. Our approach is based on Tomita-Takesaki theory. The discussion about effectiveness of this approach is given. The notion degrees of entanglement are introduced.

Recently some descriptions to characterize partially transposed (PPT) sates were obtained. In this note we focus the two of them and discuss their relation.

We study patterns of creation, temporal evolution, and transport of entanglement in quantum spin chains. The model used is an isotropic Heisenberg chain with periodic boundary conditions, and we obtain analytic form of time dependence of concurrence and negativity of various spin pairs in the system. The objective of the present study is to assess the usefulness of various averaged entanglement measures in the characterization of entangling properties of quantum evolutions.

The problem of renormalization procedure is re-examied from the viewpoint of Micro-Macro duality.

The RNA-Crypto System (shortly RCS) is a symmetric key algorithm to cipher data. The idea for this new algorithm starts from the observation of nature. In particular from the observation of RNA behavior and some of its properties. The RNA sequences has some sections called Introns. Introns, derived from the term "intragenic regions", are non-coding sections of precursor mRNA (pre-mRNA) or other RNAs, that are removed (spliced out of the RNA) before the mature RNA is formed. Once the introns have been spliced out of a pre-mRNA, the resulting mRNA sequence is ready to be translated into a protein. The corresponding parts of a gene are known as introns as well. The nature and the role of Introns in the pre-mRNA is not clear and it is under ponderous researches by Biologists but, in our case, we will use the presence of Introns in the RNA-Crypto System output as a strong method to add chaotic non coding information and an unnecessary behaviour in the access to the secret key to code the messages. In the RNA-Crypto System algoritnm the introns are sections of the ciphered message with non-coding information as well as in the precursor mRNA.

We shall discuss some particular roles of quadratic generalized white noise functionals. First observation is made from the viewpoint of the so-called "la passage du fini à l'infini". We then come to a dual pairing of spaces formed by quadratic generalized white noise functionals. In this line, we can further discuss quadratic forms of differential operators acting on the space of white noise functionals.

For the analysis of square contingency tables with the same row and column classifications, the symmetry model is applied. This paper (1) reviews the measure for representing the degree of departure from the symmetry and (2) using the measure, compares five sets of social-mobility data on the father's and son's occupational status (i) for British in 1954, (ii) for Denmark in 1954, (iii) for Japan in 1955, (iv) for Japan in 1965, and (v) for Japan in 1975.

Some mathematical aspects of the concept of time in physics and life science are discussed. A theoretical model of time machine is a spacetime region with closed timelike curves. Possible production of mini time machines at CERN's Large Hadron Collider (LHC) is considered. It is argued that if the scale of quantum gravity is of the order of few TeVs, proton-proton collisions at the LHC could lead to the formation of traversable wormhole which is a model for the time machine. The wormhole production cross section at the LHC is of the same order as the cross section for the black hole production. We make also some comments on the role of time in life science. It is proposed to describe cells and other life phenomena by using framework of quantum field theory.

We treat the quantum processes of state changes, which can be expressed by quantum channels. In order to investigate the efficiency of information transmission under these quantum processes, three kind of mutual entropy-type measures are used. The quantum mutual entropy, which is called Ohya mutual entropy, for quantum input and output by using the quantum relative entropy was defined by Ohya in 1983. It denotes an amount of quantum information transmitted correctly from the input system to the output system through a quantum process. In this paper, we compare with mutual entropy-type measures for some quantum processes.

Molecular simulation provides useful information from microscopic view for understanding the properties of molecules. Now molecular dynamics (MD) simulations of large biomolecules can be performed easily on parallel computers. However, accuracy of force field parameters and simulation time scale remain as hard obstacles to biomolecular simulation. In this paper, we will briefly describe basics of MD simulation for biomolecules and discuss the problems of the method. Then, we introduce protein folding problem as a grand challenge of biomolecular simulation. Finally, we will present our approach to overcome the difficulties, a Brownian dynamics, which is able to simulate long-time folding dynamics of some peptides.

This paper consists of three sections. After the Introduction of Section 1, in Section 2 we describe a quantum mechanical mechanism of proton-induced ionic conduction in the superionic phase in zero-dimensional hydrogen-bonded M₃H(XO₄)₂ [M=K,Rb,Cs, X=S,Se] materials, by giving a review on the theory developed by Ito and Kamimura. Then we discuss the characteristic difference between quantum mechanical and classical mechanisms in the case of proton-induced superionic conducction, in paticular, by comparing characteristic time scales in quantum mechanical and classical diffusions in hydrogen-bonded systems. In Section 3 a theory is proposed with regard to the origin of the divergent behavior of ionic conductivity near the phase-transition temperature in the ferroelatic phase of M₃H(XO₄)₂.

Completion of the high-precision genome sequence analysis of rice led to the collection of about 35,000 full-length cDNA clones and the determination of their complete sequences. Mapping of these full-length cDNA sequences has given us information on (1) the number of genes expressed in the rice genome; (2) the start and end positions and exon–intron structures of rice genes; (3) alternative transcripts; (4) possible encoded proteins; (5) non-protein-coding (np) RNAs; (6) the density of gene localization on the chromosome; (7) setting the parameters of gene prediction programs; and (8) the construction of a microarray system that monitors global gene expression. Manual curation for rice gene annotation by using mapping information on full-length cDNA and EST assemblies has revealed about 32,000 expressed genes in the rice genome. Analysis of major gene families, such as those encoding membrane transport proteins (pumps, ion channels, and secondary transporters), along with the evolution from bacteria to higher animals and plants, reveals how gene numbers have increased through adaptation to circumstances. Family-based gene annotation also gives us a new way of comparing organisms. Massive amounts of data on gene expression under many kinds of physiological conditions are being accumulated in rice oligoarrays (22K and 44K) based on full-length cDNA sequences. Cluster analyses of genes that have the same promoter cis-elements, that have similar expression profiles, or that encode enzymes in the same metabolic pathways or signal transduction cascades give us clues to understanding the networks of gene expression in rice. As a tool for that purpose, we recently developed "RiCES", a tool for searching for cis-elements in the promoter regions of clustered genes.

To understand how influenza A H5 viruses change and how we can classify the viruses, we applied the entropic chaos degree introduced in information dynamics to the course of sequence changes in hemagglutinin (HA1) protein of all H5 viruses. Phylogenetic analysis of HA1 amino acid sequences of H5 viruses revealed that the HPAI H5N1 viruses appeared after A/Goose/Guangdong/1/96 were different from the cluster made of the LPAI H5 viruses, the HPAI H5N2 and H5N9 viruses and the HPAI H5N1 viruses before 1996. Moreover, the characteristics of the HA1 sequences of H5 viruses are discussed in this paper.

The genome sequences are one of the most fundamental data among various omics analyses. So far, basic bioinformatics tools have developing to treat genome sequences. First step of genome sequence analysis is to predict or assign "genes" on genome sequences. In the case of Eukaryotes, we can identify genes by use of full length cDNA sequences with local alignment tools such as search, blast and fasta, etc. However, it is difficult to catch mRNAs (transcripts) in Prokaryotes. Therefore, computational prediction for gene identification is first choice to start genome sequence analysis. In this review, we pick up methods for computational gene prediction first. Once genes are predicted, next step is to functions for proteins or RNAs encoded on a gene. Then, how we can define the distance between gene sequences is very important for the further analysis. So, we describe the basics of mathematical concept for gene comparison. And we also introduce our novel concept for biological sequence comparisons for the view point of informational theory.

In the post genome era, many researchers are very interested in not only gene functions but also the gene regulations whose information is also on genome sequences. Cis-regulatory elements, however, is too short to find some mathematical rules. Therefore, computationally predicted cis-elements tend to include many false-positives. To reduce the ratio false-positives, we need reliable database of set of cis-regulatory elements called cis-regulatory modules for a gene. So, we are trying to develop the Cis-Regulatory Elements Module Reference Database. In the third section, we introduce you the procedure to construct the Cis-Regulatory Elements Module Reference Database and its user interfaces.

The following sections are included:

• Introduction

• Transcription: From genes to RNA

• Microarray expression analysis: Quantification of RNA amounts

• AtGenExpress: Arabidopsis thaliana as a model organism for expression profile analysis

• Displaying and analyzing microarray expression data
  • Displaying expression data
  • Biologically simple but mathematically complex experimental design
  • Mining for meaningful data

• Conclusions & Outlook

• References

Biologists and bioinformatic scientists cope with the analysis of transcript abundance and the extraction of meaningful information from microarray expression data. By exploiting biological information accessible in public databases, we try to extend our current knowledge over the plant model organism Arabidopsis thaliana. Here, we give two examples of increasing the quality of information gained from large scale expression experiments by the integration of microarray-unrelated biological information: First, we utilize Arabidopsis microarray data to demonstrate that expression profiles are usually conserved between orthologous genes of different organisms. In an initial step of the analysis, orthology has to be inferred unambiguously, which then allows comparison of expression profiles between orthologs. We make use of the publicly available microarray expression data of Arabidopsis and barley, Hordeum vulgare. We found a generally positive correlation in expression trajectories between true orthologs although both organisms are only distantly related in evolutionary time scale. Second, extracting clusters of co-regulated genes implies similarities in transcriptional regulation via similar cis-regulatory elements (CREs). Vice versa approaches, where co-regulated gene clusters are found by investigating on CREs were not successful in general. Nonetheless, in some cases the presence of CREs in a defined position, orientation or CRE-combinations is positively correlated with co-regulated gene clusters. Here, we make use of genes involved in the phenylpropanoid biosynthetic pathway, to give one positive example for this approach.