Ciliates have developed a unique nuclear dualism- two nuclei of di erent functionality: the germline micronucleus and the somatic macronucleus. The way that ciliates assemble the macronuclear genes after cell mating constitutes one of the most intricate DNA processings in living organisms. This processing is also very interesting from the computational point of view. In this paper, we investigate the operations of loop excision and hairpin excision/reinsertion used in the assembly process. In particular, we consider three levels of formalization of this process, culminating in graph reduction systems.

Abstract. One of the most complex DNA processing in nature known to us is carried out by ciliates during the sexual reproduction when their micronuclear genome is transformed to the macronuclear genome. This process of gene assembly is intriguing and captivating also from the computational point of view. We investigate here three intramolecular molecular operations (ld, hi, and dlad) postulated to accomplish gene assembly. The formal models for these operations are formulated on three different abstraction levels: MDS descriptors, legals strings and overlap graphs. In general both legal strings and overlap graphs contain strings and graphs that do not model any micronuclear gene. After a short survey of gene assembly we study the problem of recognizing whether a general legal string or a general overlap graph is a formalization of a micronuclear gene. 1

This paper provides a description of the recent evolution in the US of an emerging technology known as DNA Computation or more generally as Biomolecular Computation from its early stages to its development and extension into other areas such as nanotechnology, emerging as a viable sub-discipline of science and engineering.

Summary. Gene assembly in ciliates is a life process fascinating from both the biological and the computational points of view. Several formal models of this process have been formulated and investigated, among them a model based on (legal) strings and a model based on (overlap) graphs. The latter is more abstract because the translation of legal strings into overlap graphs is not injective. In this paper we consider and solve the overlap equivalence problem for realistic strings: when do two different realistic legal strings translate into the same overlap graph? Realistic legal strings are legal strings that “really ” correspond to genes generated during the gene assembly process. 1

Abstract. The simple intramolecular model for gene assembly in ciliates is particularly interesting because it can predict the correct assembly of all available experimental data, although it is not universal. The simple model also has a confluence property that is not shared by the general model. A previous formalization of the simple model through sorting of signed permutations is unsatisfactory because it effectively ignores one operation of the model and thus, it cannot be used to answer questions about parallelism in the model, or about measures of complexity. We propose in this paper a string-based model in which a gene is represented through its sequence of pointers and markers and its assembly is represented as a string rewriting process. We prove that this stringbased model is equivalent to the permutation-based model as far as gene assembly is concerned, while it tracks all operations of the model. 1

The intramolecular model (Ehrenfeucht et al, 2001) for gene assembly in ciliates considers three operations, ld, hi, and dlad that can assemble any micronuclear gene pattern through folding and recombination: the molecule is folded so that two occurrences of a pointer (short nucleotide sequence) get aligned and then the sequence is rearranged through recombination of pointers. In general, the sequence rearranged by one operation can be arbitrarily long and may consist of many coding and non-coding blocks. We consider in this paper some restricted variants of the three operations, where only one coding block is rearranged at a time. We present in this paper the molecular model of these simple operations. We also introduce a mathematical model for the simple operations, on three levels of abstractions: MDS descriptors, signed permutations, and signed double occurrence strings. Interestingly, we show that simple assemblies possess rather involved properties: a gene pattern may have both successful and unsuccessful assemblies and also more than one successful strategy.

Natural Computing is concerned with computing taking place in nature and with human-designed computing inspired by nature. It is an interdisciplinary research area that has already had a significant effect on the development of computer science: human-designed computing inspired by nature includes areas such as neural computing, evolutionary algorithms, DNA computing and quantum computing. Also, there is a growing research trend spread throughout the disciplines of bioinformatics, computational biology and DNA computing (among others) that investigates computational nature of complex biological phenomena. As a matter of fact, part of this research considers some of the basic life processes as computations. One of such processes that has recently attracted the attention

We shall give an introduction to gene assembly based on operations on signed permutations. These operations sort signed permutations to a conjugate of an identity permutation or of its inversion, and they are faithful to the molecular model of gene assembly in ciliates introduced by Ehrenfeucht, Prescott, and Rozenberg. In particular, the operations on signed permutations are not reductive, that is, the result of an application of an operation corresponds to a full molecule of the molecular model. For the molecular model there are formal reductive models based on strings and graphs.

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