On the power of parallel communicating Watson–Crick automata systems

AbstractParallel communicating Watson–Crick automata systems were introduced in [E. Czeizler, E. Czeizler, Parallel communicating Watson–Crick automata systems, in: Z. Ésik, Z. Fülöp (Eds.), Proc. Automata and Formal Languages, Dobogókő, Hungary, 2005, pp. 83–96] as possible models of DNA computations. This combination of Watson–Crick automata and parallel communicating systems comes as a natural extension due to the new developments in DNA manipulation techniques. It is already known, see [D. Kuske, P. Weigel, The Role of the Complementarity Relation in Watson–Crick Automata and Sticker Systems, DLT 2004, Lecture Notes in Computer Science, Vol. 3340, Auckland, New Zealand, 2004, pp. 272–283], that for Watson–Crick finite automata, the complementarity relation plays no active role. However, this is not the case when considering parallel communicating Watson–Crick automata systems. In this paper we prove that non-injective complementarity relations increase the accepting power of these systems. We also prove that although Watson–Crick automata are equivalent to two-head finite automata, this equivalence is not preserved when comparing parallel communicating Watson–Crick automata systems and multi-head finite automata

Quantitative Model Refinement as a Solution to the Combinatorial Size Explosion of Biomodels

AbstractBuilding a large system through a systematic, step-by-step refinement of an initial abstract specification is a well established technique in software engineering, not yet much explored in systems biology. In the case of systems biology, one starts from an abstract, high-level model of a biological system and aims to add more and more details about its reactants and/or reactions, through a number of consecutive refinement steps. The refinement should be done in a quantitatively correct way, so that (some of) the numerical properties of the model (such as the experimental fit and validation) are preserved. In this study, we focus on the data-refinement mechanism where the aim is to increase the level of details of some of the reactants of a given model. That is, we analyse the case when a model is refined by substituting a given species by several types of subspecies. We show in this paper how the refined model can be systematically obtained from the original one. As a case study for this methodology we choose a recently introduced model for the eukaryotic heat shock response, [I. Petre, A. Mizera, C. L. Hyder, A. Meinander, A. Mikhailov, R.I. Morimoto, L. Sistonen, J. E. Eriksson, R.-J. Back, A simple mass-action model for the eukaryotic heat shock response and its mathematical validation, Natural Computing, 10(1), 595–612, 2011.]. We refine this model by including details about the acetylation of the heat shock factors and its influence on the heat shock response. The refined model has a significantly higher number of kinetic parameters and variables. However, we show that our methodology allows us to preserve the experimental fit/validation of the model with minimal computational effort

An extension of the Lyndon–Schützenberger result to pseudoperiodic words

AbstractOne of the particularities of information encoded as DNA strands is that a string u contains basically the same information as its Watson–Crick complement, denoted here as θ(u). Thus, any expression consisting of repetitions of u and θ(u) can be considered in some sense periodic. In this paper, we give a generalization of Lyndon and Schützenberger’s classical result about equations of the form ul=vnwm, to cases where both sides involve repetitions of words as well as their complements. Our main results show that, for such extended equations, if l⩾5,n,m⩾3, then all three words involved can be expressed in terms of a common word t and its complement θ(t). Moreover, if l⩾5, then n=m=3 is an optimal bound. These results are established based on a complete characterization of all possible overlaps between two expressions that involve only some word u and its complement θ(u), which is also obtained in this paper

Biclustering Methods: Biological Relevance and Application in Gene Expression Analysis

Peer reviewe

Parallel Communicating Watson-Crick Automata Systems

Watson-Crick automata are finite state automata working on doublestranded tapes, introduced to investigate the potential of DNA molecules for computing. In this paper we introduce the concept of parallel communicating Watson-Crick automata systems. It consists of several Watson-Crick finite automata parsing independently the same input and exchanging information on request, by communicating states to each other. We investigate the computational power of these systems and prove that they are more powerful than classical Watson-Crick finite automata, but still accepting at most context-sensitive languages. Moreover, if the complementarity relation is injective, then we obtain that this inclusion is strict. For the general case, we also give some closure properties, as well as a characterization of recursively enumerable languages based on these systems.

The non-parametrizability of the word equation xyz=zvx: A short proof

AbstractAlthough Makanin proved the problem of satisfiability of word equations to be decidable, the general structure of solutions is difficult to describe. In particular, Hmelevskii proved that the set of solutions of xyz=zvx cannot be described using only finitely many parameters, contrary to the case of equations in three unknowns. In this paper we give a short, elementary proof of Hmelevskii's result

Computational modelling of the kinetic Tile Assembly Model using a rule-based approach

The (abstract) Tile Assembly Model (aTAM), is a mathematical paradigm for the study and algorithmic design of DNA self-assembly systems. It employs the use of so-called DNA-tiles, which are abstractions of experimentally achievable DNA nanostructure complexes with similar inter-matching behaviours. To this day, there are about half-dozen different experimental implementations of DNA tiles and their sub-sequent algorithmic assembly into larger complexes, see e.g. Reif et al. (2012) In order to provide further insight into the assembly process, the aTAM model has been extended to a kinetic counterpart (kTAM). Although there is a wide abundance of different variants of the abstract model, e.g., stage, step, hierarchical, temperature-k, signal-passing, etc. (see e.g. Patitz (2012) ), numerical simulations of the kinetic counterpart have been performed only for a few types of these systems. This might be due to the fact that the numerical models and simulations of kTAM were almost exclusively implemented using classical stochastic simulation algorithms frameworks, which are not designed for capturing models with theoretically un-bounded number of species. In this paper we introduce an agent- and rule-based modelling approach for kTAM, and its implementation on NFsim, one of the available platforms for such type of modelling. We show not only how the modelling of kTAM can be implemented, but we also explore the advantages of this modelling framework for kinetic simulations of kTAM and the easy way such models can be updated and modified. We present numerical comparisons both with classical numerical simulations of kTAM, as well as comparison in between four different kinetic variant of the TAM model, all implemented in NFsim as stand-alone rule-based models.Peer reviewe

Computational methods for quantitative submodel comparison

Abstract Comparing alternative models for a given biochemical system is in general a very difficult problem: the models may focus on different aspects of the same system and may consist of very different species and reactions. The numerical setups of the models also play a crucial role in the quantitative comparison. When the alternative designs are submodels of a reference model, e.g. knockdown mutants of a model, the problem of comparing them becomes simpler: they all have very similar, although not identical, underlying reaction networks, and the biological constraints are given by the ones in the reference model. In the first part of our study we review several known methods for model decomposition and for quantitative comparison of submodels. In the second part of the paper, we consider as a case study the eukaryotic heat shock response, an evolutionary well conserved defence mechanism against the accumulation of misfolded proteins. Keywords: Model comparison; model decomposition; computational knockdown analysis; control-based decomposition; quantitative model refinement; heat shock response

Contents lists available at ScienceDirect Theoretical Computer Science journal homepage: www.elsevier.com/locate/tcs

AbstractWhen representing DNA molecules as words, it is necessary to take into account the fact that a word u encodes basically the same information as its Watson–Crick complement θ(u), where θ denotes the Watson–Crick complementarity function. Thus, an expression which involves only a word u and its complement can be still considered as a repeating sequence. In this context, we define and investigate the properties of a special class of primitive words, called pseudo-primitive words relative to θ or simply θ-primitive words, which cannot be expressed as such repeating sequences. For instance, we prove the existence of a unique θ-primitive root of a given word, and we give some constraints forcing two distinct words to share their θ-primitive root. Also, we present an extension of the well-known Fine and Wilf theorem, for which we give an optimal bound