Construction of minimal DFAs from biological motifs

Deterministic finite automata (DFAs) are constructed for various purposes in computational biology. Little attention, however, has been given to the efficient construction of minimal DFAs. In this article, we define simple non-deterministic finite automata (NFAs) and prove that the standard subset construction transforms NFAs of this type into minimal DFAs. Furthermore, we show how simple NFAs can be constructed from two types of patterns popular in bioinformatics, namely (sets of) generalized strings and (generalized) strings with a Hamming neighborhood

Sparse approaches for the exact distribution of patterns in long state sequences generated by a Markov source

We present two novel approaches for the computation of the exact distribution of a pattern in a long sequence. Both approaches take into account the sparse structure of the problem and are two-part algorithms. The first approach relies on a partial recursion after a fast computation of the second largest eigenvalue of the transition matrix of a Markov chain embedding. The second approach uses fast Taylor expansions of an exact bivariate rational reconstruction of the distribution. We illustrate the interest of both approaches on a simple toy-example and two biological applications: the transcription factors of the Human Chromosome 5 and the PROSITE signatures of functional motifs in proteins. On these example our methods demonstrate their complementarity and their hability to extend the domain of feasibility for exact computations in pattern problems to a new level

Significance Score of Motifs in Biological Sequences

Available from: http://www.intechopen.com/books/bioinformatics-trends-and-methodologies/significance-score-of-motifs-in-biological-sequence

General Iteration graphs and Boolean automata circuits

This article is set in the field of regulation networks modeled by discrete dynamical systems. It focuses on Boolean automata networks. In such networks, there are many ways to update the states of every element. When this is done deterministically, at each time step of a discretised time flow and according to a predefined order, we say that the network is updated according to block-sequential update schedule (blocks of elements are updated sequentially while, within each block, the elements are updated synchronously). Many studies, for the sake of simplicity and with some biologically motivated reasons, have concentrated on networks updated with one particular block-sequential update schedule (more often the synchronous/parallel update schedule or the sequential update schedules). The aim of this paper is to give an argument formally proven and inspired by biological considerations in favour of the fact that the choice of a particular update schedule does not matter so much in terms of the possible and likely dynamical behaviours that networks may display

An Ansatz for undecidable computation in RNA-world automata

In this Ansatz we consider theoretical constructions of RNA polymers into automata, a form of computational structure. The basis for transitions in our automata are plausible RNA-world enzymes that may perform ligation or cleavage. Limited to these operations, we construct RNA automata of increasing complexity; from the Finite Automaton (RNA-FA) to the Turing Machine equivalent 2-stack PDA (RNA-2PDA) and the universal RNA-UPDA. For each automaton we show how the enzymatic reactions match the logical operations of the RNA automaton, and describe how biological exploration of the corresponding evolutionary space is facilitated by the efficient arrangement of RNA polymers into a computational structure. A critical theme of the Ansatz is the self-reference in RNA automata configurations which exploits the program-data duality but results in undecidable computation. We describe how undecidable computation is exemplified in the self-referential Liar paradox that places a boundary on a logical system, and by construction, any RNA automata. We argue that an expansion of the evolutionary space for RNA-2PDA automata can be interpreted as a hierarchical resolution of the undecidable computation by a meta-system (akin to Turing's oracle), in a continual process analogous to Turing's ordinal logics and Post's extensible recursively generated logics. On this basis, we put forward the hypothesis that the resolution of undecidable configurations in RNA-world automata represents a mechanism for novelty generation in the evolutionary space, and propose avenues for future investigation of biological automata

A framework for the local information dynamics of distributed computation in complex systems

The nature of distributed computation has often been described in terms of the component operations of universal computation: information storage, transfer and modification. We review the first complete framework that quantifies each of these individual information dynamics on a local scale within a system, and describes the manner in which they interact to create non-trivial computation where "the whole is greater than the sum of the parts". We describe the application of the framework to cellular automata, a simple yet powerful model of distributed computation. This is an important application, because the framework is the first to provide quantitative evidence for several important conjectures about distributed computation in cellular automata: that blinkers embody information storage, particles are information transfer agents, and particle collisions are information modification events. The framework is also shown to contrast the computations conducted by several well-known cellular automata, highlighting the importance of information coherence in complex computation. The results reviewed here provide important quantitative insights into the fundamental nature of distributed computation and the dynamics of complex systems, as well as impetus for the framework to be applied to the analysis and design of other systems.Comment: 44 pages, 8 figure

Boolean networks with reliable dynamics

We investigated the properties of Boolean networks that follow a given reliable trajectory in state space. A reliable trajectory is defined as a sequence of states which is independent of the order in which the nodes are updated. We explored numerically the topology, the update functions, and the state space structure of these networks, which we constructed using a minimum number of links and the simplest update functions. We found that the clustering coefficient is larger than in random networks, and that the probability distribution of three-node motifs is similar to that found in gene regulation networks. Among the update functions, only a subset of all possible functions occur, and they can be classified according to their probability. More homogeneous functions occur more often, leading to a dominance of canalyzing functions. Finally, we studied the entire state space of the networks. We observed that with increasing systems size, fixed points become more dominant, moving the networks close to the frozen phase.Comment: 11 Pages, 15 figure