Ion Petre

String and graph reduction systems for gene assembly in ciliates

Ciliates have developed a unique nuclear dualism, having two nuclei of different 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 excisionsreinsertion used in the assembly process. In particular, we consider three levels of formalization of this process, culminating in graph reduction systems.

Universal and simple operations for gene assembly in ciliates

The way that ciliates transform genes from their micronuclear to their macronuclear form is very interesting (and unique), particularly from a computational point of view. In this paper, we describe the model of gene assembly in ciliates presented in [2], [4], and [3]. Moreover, we prove that the set of three operations underlying this model is universal, in the sense that it suffices for gene assembly from any micronuclear pattern. We also prove that the set of simple versions of these operations is not universal — this fact is interesting from the experimental point of view.

A simple mass-action model for the eukaryotic heat shock response and its mathematical validation

The heat shock response is a primordial defense mechanism against cell stress and protein misfolding. It proceeds with the minimum number of mechanisms that any regulatory network must include, a stress-induced activation and a feedback regulation, and can thus be regarded as the archetype for a cellular regulatory process. We propose here a simple mechanistic model for the eukaryotic heat shock response, including its mathematical validation. Based on numerical predictions of the model and on its sensitivity analysis, we minimize the model by identifying the reactions with marginal contribution to the heat shock response. As the heat shock response is a very basic and conserved regulatory network, our analysis of the network provides a useful foundation for modeling strategies of more complex cellular processes.

Characterizing the Micronuclear Gene Patterns in Ciliates

Abstract The process of gene assembly in ciliates is one of the most complex examples of DNA processing known in any organism, and it is fascinating from the computational point of view—it is a prime example of DNA computing in vivo. In this paper we continue to investigate the three molecular operations (ld, hi , and dlad ) that were postulated to carry out the gene assembly process in the intramolecular fashion. In particular, we focus on the understanding of the IES/ MDS patterns of micronuclear genes, which is one of the important goals of research on gene assembly in ciliates. We succeed in characterizing for each subset S of the three molecular operations those patterns that can be assembled using operations in S. These results enhance our understanding of the structure of micronuclear genes (and of the nature of molecular operations). They allow one to establish both similarity and complexity measures for micronuclear genes.

Conway's problem for three-word sets

We prove two results on commutation of languages. First, we show that the maximal language commuting with a three-element language, i.e. its centralizer, is rational, thus giving an affirmative answer to a special case of a problem proposed by Conway in 1971. Second, we characterize all languages commuting with a three-element code. The characterization is similar to the one proved by Bergman for polynomials over noncommuting variables (see Trans. Am. Math. Soc. 137 (1969) 327 and Algebraic Combinatorics on Words, Cambridge University Press, Cambridge, 2000): A language commutes with a three-element code X if and only if it is a union of powers of X.

Algebraic Systems and Pushdown Automata

We concentrate in this chapter on the core aspects of algebraic series, pushdown automata, and their relation to formal languages. We choose to follow here a presentation of their theory based on the concept of properness. We introduce in Sect. 2 some auxiliary notions and results needed throughout the chapter, in particular the notions of discrete convergence in semirings and C-cycle free infinite matrices. In Sect. 3 we introduce the algebraic power series in terms of algebraic systems of equations. We focus on interconnections with context-free grammars and on normal forms. We then conclude the section with a presentation of the theorems of Shamir and Chomsky–Schutzenberger. We discuss in Sect. 4 the algebraic and the regulated rational transductions, as well as some representation results related to them. Section 5 is dedicated to pushdown automata and focuses on the interconnections with classical (non-weighted) pushdown automata and on the interconnections with algebraic systems. We then conclude the chapter with a brief discussion of some of the other topics related to algebraic systems and pushdown automata.

Matrix insertion-deletion systems

We investigate in this article the operations of insertion and deletion working in a matrix-controlled manner. We show that this allows to us strictly increase the computational power: in the case of systems that are not computationally complete (with total size equal to 4), the computational completeness can be obtained by introducing the matrix control and using only binary matrices.

Parallelism in Gene Assembly

The process of gene assembly in ciliates, an ancient group of organisms, is one of the most complex instances of DNA manipulation known in any organisms. This process is fascinating from the computational point of view, with ciliates even using the linked lists data structure. Three molecular operations (ld, hi, and dlad) have been postulated for the gene assembly process. We initiate here the study of parallelism in this process, raising several natural questions, such as: when can a number of operations be applied in parallel to a gene pattern; or how many steps are needed to assemble (in parallel) a micronuclear gene. In particular, this gives rise to a new measure of complexity for the process of gene assembly in ciliates.

Modelling Simple Operations for Gene Assembly

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. TUCS Laboratory Computational Biomodelling Discrete Mathematics for Information Technology

Patterns of Micronuclear Genes in ciliates

The process of gene assembly in ciliates is one of the most complex examples of DNA processing known in any organism, and it is fascinating from the computational point-of-view -- it is a prime example of DNA computing in vivo. In this paper we continue to investigate the three molecular operations (ld, hi, and dlad) that were postulated to carry out the gene assembly process in the intramolecular fashion. In particular, we focus on the understanding of the IES/MDS patterns of micronuclear genes, which is one of the important goals of research on gene assembly in ciliates. We succeed in characterizing for each subset S of the three molecular operations those patterns that can be assembled using operations in S. These results enhance our understanding of the structure of micronuclear genes (and of the nature of molecular operations). They allow one to establish both similarity and complexity measures for micronuclear genes.