An exact steady-state solution of the stochastic equations governing the behavior of a gene regulated by a self-generated proteomic atmosphere is presented. The solutions depend on an adiabaticity parameter measuring the relative rate of DNA-protein unbinding and protein degradation. The steady-state solution reveals deviations from the commonly used Ackers et al approximation based on the equilibrium law of mass action, allowing anticooperative behavior in the "nonadiabatic" limit of slow binding and unbinding rates. Noise from binding and unbinding events dominates the shot noise of protein synthesis and degradation up to quite high values of the adiabaticity parameter.
A search for symmetries based on the compact simple Lie algebras is performed to verify to what extent the genetic code is a manifestation of some underlying symmetry. An exact continuous symmetry group cannot be found to reproduce the present genetic code. However, a unique approximate symmetry group is compatible with codon assignment for the fundamental amino acids and the termination codon. In order to obtain the actual genetic code, the symmetry must be slightly broken.The storage of genetic information in a cell is governed by deoxyribonucleic acid (DNA). The DNA molecules are large polymers composed of deoxyribonucleotides which contain a base, a sugar (deoxyribose), and a phosphate. The sugar and the phosphate groups are responsible for the well known helical backbone of DNA, and the bases sequence carries the genetic information. In DNA there are only four bases derived from purine and pyrimidine. The purines, adenine {A) and guanine (G), and the pyrimidines, thymine iT) and cytosine (C), form the double helix through the base pairs C-G and A-T bonded, respectively, by 3 and 2 hydrogen bonds. This pairing rule manifests itself not only by the spatial conformation on DNA, but also by the equal rate of cytosine to guanine and adenine to thymine. It is this pairing rule that makes one of the helices the exact template of the other one, so replication can be understood.The transmission of information from DNA to protein building is a complex process of transcription and translation. In eucariotic cells DNA molecules are inside the nucleus of the cell and the proteins which they code are made outside of the nucleus in the citoplasma, more specifically in the ribosomes. The flow of information from DNA to the ribosomes requires another class of molecules, the ribonucleic acid (RNA) which are also constructed inside the nucleus. These molecules, rather than DNA, are the templates for protein synthesis; they leave the nucleus to the ribosomes to guide the synthesis.RNA are unbranched polymers, much smaller than DNA, and are also composed of a sugar (ribose), a phosphate group, and a base. Different from DNA's, RNA's subdivide into classes, messenger mRNA, transfer /RNA, and ribosomal rRNA. While /RNA and rRNA are part of the protein-synthesizing machinery, mRNA's are the information carrying intermediates in protein synthesis. The size of RNA varies from as few as 75 to many thousands of nucleotides. /RNA's are smaller and they carry amino acids (a.a.) in an active form to the ribosome for peptide-bond formation in a sequence determined by the mRNA template. Ribosomal RNA's are the major component of ribosomes, but their precise role in protein synthesis is not yet known. The concept of mRNA was formulated by Jacob and Monod 111 in 1961. The genetic information from DNA is transcripted by RNA polym-
We investigate the use of continuously-applied external fields to maximize the fidelity of quantum logic operations performed on a decohering qubit. Assuming a known error operator and an environment represented by a scalar boson field at a finite temperature, we show how decoherence during logical operations can be efficiently reduced by applying a superposition of two external vector fields: one rotating orthogonally to the direction of the other, which remains static. The required field directions, frequency of rotation and amplitudes to decouple noise dynamically are determined by the coupling constants and the desired logical operation. We illustrate these findings numerically for a Hadamard quantum gate and an environment with ohmic spectral density.A quantum computer, when finally built, will be more efficient than current classical computers to solve certain kinds of problems [1]. The theory of quantum information processing generally takes advantage of the inherent parallelism exhibited by unitary operations on quantumstate superpositions. The terms of these linear combinations are tensor products of quantum bits, or "qubits" [2], which, linearly superposed, result in states with the desired properties of entanglement and interference [3]. In principle, the choice of an appropriate external field would guarantee a correct dynamics for the system, selected among those exhibiting unitary symmetry. However, during the actual quantum evolution of the system, since it cannot be completely separated from its environment, the unitary symmetry breaks down. The consequent decay of the quantum state purity is a manifestation of the ubiquitous phenomenon of decoherence [4].There are at least three major classes of strategic devices proposed to counteract the deleterious and unavoidable effects of decoherence: quantum error correcting codes [5], decoherence-free subspaces and subsystems [6], and dynamical decoupling [7,8,9,10]. Because the first two of these strategies require more than one physical qubit to protect each logical qubit, dynamical decoupling is the simplest of the three, since it requires, in principle, only controllable external fields to directly protect each physical qubit. Even without precise knowledge of the error structure and strengths, the pulsed dynamicaldecoupling scheme is effective, but usually employ an articulate time sequence of external-field pulses which, for experimental implementations, requires sophisticated control procedures. Moreover, the pulses have to be so short as to start and finish well within the environmental correlation time interval, so the field intensities involved must be high. Initial attempts to use continuously- * Electronic address: felipe@ifsc.usp.br applied fields instead of pulses have appeared recently [11] and these preliminary analyses show that, although pulses are not necessary for protecting against the effects of particular error structures assumed known, employing fast control cycles is inevitable. From the practical point of view of experimental rea...
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