Showing papers in "Natural Computing in 2011"

Strand algebras for DNA computing

Abstract: We present a process algebra for DNA computing, discussing compilation of other formal systems into the algebra, and compilation of the algebra into DNA structures.

Approximating Mexican highways with slime mould

Abstract: Plasmodium of Physarum polycephalum is a single cell visible by unaided eye. During its foraging behavior the cell spans spatially distributed sources of nutrients with a protoplasmic network. The geometrical structure of the protoplasmic networks allows the plasmodium to optimize transport of nutrients between remote parts of its body. Assuming major Mexican cities are sources of nutrients that need to be distributed across Mexico, how much does the structure of the Physarum protoplasmic network correspond to the structure of Mexican Federal highway network? To address the issue we undertook a series of laboratory experiments with living P. polycephalum. We represent geographical locations of major cities (19 locations) by oat flakes, place a piece of plasmodium in the area corresponding to Mexico city, record the plasmodium's foraging behavior and extract topology of the resulting nutrient transport networks. Results of our experiments show that the protoplasmic network formed by Physarum is isomorphic, subject to limitations imposed, to a network of principal highways. Ideas and results in the paper may contribute towards future developments in bio-inspired road planning.

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

Abstract: 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.

A computational modeling for real ecosystems based on P systems

Abstract: In this paper, a P systems based general framework for modeling ecosystems dynamics is presented. Particularly, ecosystems are specified by means of multienvironment P systems composed of a finite number of environments, each of them having an extended P system with active membranes. The semantics is of a probabilistic type and it is implemented by assigning each rule of the system a probabilistic constant which depends on the environment and the run time. As a case study, two real ecosystems are described: scavenger birds in the Catalan Pyrenees and the zebra mussel (Dreissena Polymorpha) in Ribarroja reservoir (Spain).

The computational power of membrane systems under tight uniformity conditions

Abstract: We apply techniques from complexity theory to a model of biological cellular membranes known as membrane systems or P-systems. Like Boolean circuits, membrane systems are defined as uniform families of computational devices. To date, polynomial time uniformity has been the accepted uniformity notion for membrane systems. Here, we introduce the idea of using AC 0-uniformity and investigate the computational power of membrane systems under these tighter conditions. It turns out that the computational power of some systems is lowered from P to NL when using AC 0-semi-uniformity, so we argue that this is a more reasonable uniformity notion for these systems as well as others. Interestingly, other P-semi-uniform systems that are known to be lower-bounded by P are shown to retain their P lower-bound under the new tighter semi-uniformity condition. Similarly, a number of membrane systems that are known to solve PSPACE-complete problems retain their computational power under tighter uniformity conditions.

Spatial P systems

Abstract: We present Spatial P systems, a variant of P systems which embodies the concept of space and position inside a membrane. Objects in membranes are associated with positions. Rules specify, in the usual way, the objects which are consumed and the ones which are produced; in addition, they can specify the positions of the produced objects. Objects belong to two different sets: the set of ordinary objects and the set of mutually exclusive objects. Every position inside a membrane can accommodate an arbitrary number of ordinary objects, but at most one mutually exclusive object. We prove that Spatial P systems are universal even if only non-cooperating rules are allowed. We also show how Spatial P systems can be used to model the evolution of populations in presence of geographical separations.

Self-assembly of decidable sets

Abstract: The theme of this paper is computation in Winfree's Abstract Tile Assembly Model (TAM). We first review a simple, well-known tile assembly system (the "wedge construction") that is capable of universal computation. We then extend the wedge construction to prove the following result: if a set of natural numbers is decidable, then it and its complement's canonical two-dimensional representation self-assemble. This leads to a novel characterization of decidable sets of natural numbers in terms of self-assembly. Finally, we show that our characterization is robust with respect to various (restrictive) geometrical constraints.

Influences on the formation and evolution of Physarum polycephalum inspired emergent transport networks

Abstract: The single-celled organism Physarum polycephalum efficiently constructs and minimises dynamical nutrient transport networks resembling proximity graphs in the Toussaint hierarchy. We present a particle model which collectively approximates the behaviour of Physarum. We demonstrate spontaneous transport network formation and complex network evolution using the model and show that the model collectively exhibits quasi-physical emergent properties, allowing it to be considered as a virtual computing material. This material is used as an unconventional method to approximate spatially represented geometry problems by representing network nodes as nutrient sources. We demonstrate three different methods for the construction, evolution and minimisation of Physarum-like transport networks which approximate Steiner trees, relative neighbourhood graphs, convex hulls and concave hulls. We extend the model to adapt population size in response to nutrient availability and show how network evolution is dependent on relative node position (specifically inter-node angle), sensor scaling and nutrient concentration. We track network evolution using a real-time method to record transport network topology in response to global differences in nutrient concentration. We show how Steiner nodes are utilised at low nutrient concentrations whereas direct connections to nutrients are favoured when nutrient concentration is high. The results suggest that the foraging and minimising behaviour of Physarum-like transport networks reflect complex interplay between nutrient concentration, nutrient location, maximising foraging area coverage and minimising transport distance. The properties and behaviour of the synthetic virtual plasmodium may be useful in future physical instances of distributed unconventional computing devices, and may also provide clues to the generation of emergent computation behaviour by Physarum.

Petri net representation of multi-valued logical regulatory graphs

Abstract: Relying on a convenient logical representation of regulatory networks, we propose a generic method to qualitatively model regulatory interactions in the standard elementary and coloured Petri net frameworks. Logical functions governing the behaviours of the components of logical regulatory graphs are efficiently represented by Multivalued Decision Diagrams, which are also at the basis of the translation of logical models in terms of Petri nets. We further delineate a simple strategy to sort trajectories through the introduction of priority classes (in the logical framework) or priority functions (in the Petri net framework). We also focus on qualitative behaviours such as multistationarity or sustained oscillations, identified as specific structures in state transition graphs (for logical models) or in marking graphs (in Petri nets). Regulatory circuits are known to be at the origin of such properties. In this respect, we present a method that allows to determine the functionality contexts of regulatory circuits, i.e. constraints on external regulator states enabling the corresponding dynamical properties. Finally, this approach is illustrated through an application to the modelling of a regulatory network controlling T lymphocyte activation and differentiation.

Petri nets as a framework for the reconstruction and analysis of signal transduction pathways and regulatory networks

Abstract: Petri nets are directed, weighted bipartite graphs that have successfully been applied to the systems biology of metabolic and signal transduction pathways in modeling both stochastic (discrete) and deterministic (continuous) processes Here we exemplify how molecular mechanisms, biochemical or genetic, can be consistently respresented in the form of place/transition Petri nets We then describe the application of Petri nets to the reconstruction of molecular and genetic networks from experimental data and their power to represent biological processes with arbitrary degree of resolution of the subprocesses at the cellular and the molecular level Petri nets are executable formal language models that permit the unambiguous visualization of regulatory mechanisms, and they can be used to encode the results of mathematical algorithms for the reconstruction of causal interaction networks from experimental time series data

Computational power of insertion---deletion (P) systems with rules of size two

Abstract: This article investigates insertion---deletion systems of small size, where at most two symbols can be used in the description of insertion or deletion rules in a context-free or contextual manner. The basic result shows a characterization by context-free grammars of insertion---deletion systems, which insert or delete one symbol in one symbol left context (systems of size (1, 1, 0; 1, 1, 0)). If context-free insertion or deletion rules are considered (systems of size (2, 0, 0; 1, 1, 0) or (1, 1, 0; 2, 0, 0)), then we show that corresponding systems are not computationally complete. However, if the insertion and the deletion operations having same size as above are considered in the distributed framework of P systems, then the computational power strictly increases and the obtained models become computationally complete. The article also shows that if context-free insertion and deletion rules of two symbols (of size (2, 0, 0; 2, 0, 0)) are used in combination with P systems, then the obtained model is still not computationally complete. Finally some open problems are presented.

Evolutionary computation approaches to the Curriculum Sequencing problem

Abstract: Within the field of e-Learning, a learning path represents a match between a learner profile and his preferences from one side, and the learning content presentation and the pedagogical requirements from the other side. The Curriculum Sequencing problem (CS) concerns the dynamic generation of a personal optimal learning path for a learner. This problem has gained an increased research interest in the last decade, as it is not possible to have a single learning path that suits every learner in the widely heterogeneous e-Learning environment. Since this problem is NP-hard, heuristics and meta-heuristics are usually used to approximate its solutions, in particular Evolutionary Computation approaches (EC). In this paper, a review of recent developments in the application of EC approaches to the CS problem is presented. A classification of these approaches is provided with emphasis on the tools necessary for facilitating learning content reusability and automated sequencing.

Digital Ecosystems: Ecosystem-Oriented Architectures

Abstract: We view Digital Ecosystems to be the digital counterparts of biological ecosystems. Here, we are concerned with the creation of these Digital Ecosystems, exploiting the self-organising properties of biological ecosystems to evolve high-level software applications. Therefore, we created the Digital Ecosystem, a novel optimisation technique inspired by biological ecosystems, where the optimisation works at two levels: a first optimisation, migration of agents which are distributed in a decentralised peer-to-peer network, operating continuously in time; this process feeds a second optimisation based on evolutionary computing that operates locally on single peers and is aimed at finding solutions to satisfy locally relevant constraints. The Digital Ecosystem was then measured experimentally through simulations, with measures originating from theoretical ecology, evaluating its likeness to biological ecosystems. This included its responsiveness to requests for applications from the user base, as a measure of the ecological succession (ecosystem maturity). Overall, we have advanced the understanding of Digital Ecosystems, creating Ecosystem-Oriented Architectures (EOA) where the word ecosystem is more than just a metaphor.

Improving convergence of evolutionary multi-objective optimization with local search: a concurrent-hybrid algorithm

Abstract: A local search method is often introduced in an evolutionary optimization algorithm, to enhance its speed and accuracy of convergence to optimal solutions. In multi-objective optimization problems, the implementation of local search is a non-trivial task, as determining a goal for local search in presence of multiple conflicting objectives becomes a difficult task. In this paper, we borrow a multiple criteria decision making concept of employing a reference point based approach of minimizing an achievement scalarizing function and integrate it as a search operator with a concurrent approach in an evolutionary multi-objective algorithm. Simulation results of the new concurrent-hybrid algorithm on several two to four-objective problems compared to a serial approach, clearly show the importance of local search in aiding a computationally faster and accurate convergence to the Pareto optimal front.

Biocircuit design through engineering bacterial logic gates

Abstract: Designing synthetic biocircuits to perform desired purposes is a scientific field that has exponentially grown over the past decade. The advances in genome sequencing, bacteria gene regulatory networks, as well as the further knowledge of intraspecies bacterial communication through quorum sensing signals are the starting point for this work. Although biocircuits are mostly developed in a single cell, here we propose a model in which every bacterium is considered to be a single logic gate and chemical cell-to-cell connections are engineered to control circuit function. Having one genetically modified bacterial strain per logic process would allow us to develop circuits with different behaviors by mixing the populations instead of re-programming the whole genetic network within a single strain. Two principal advantages of this procedure are highlighted. First, the fully connected circuits obtained where every cellgate is able to communicate with all the rest. Second, the resistance to the noise produced by inappropriate gene expression. This last goal is achieved by modeling thresholds for input signals. Thus, if the concentration of input does not exceed the threshold, it is ignored by the logic function of the gate.

P systems with active membranes: trading time for space

Abstract: We consider recognizer P systems having three polarizations associated to the membranes, and we show that they are able to solve the PSPACE-complete problem Quantified 3SAT when working in polynomial space and exponential time. The solution is uniform (all the instances of a fixed size are solved by the same P system) and uses only communication rules: evolution rules, as well as membrane division and dissolution rules, are not used. Our result shows that, as it happens with Turing machines, this model of P systems can solve in exponential time and polynomial space problems that cannot be solved in polynomial time, unless P = SPACE.

Graph multiset transformation: a new framework for massively parallel computation inspired by DNA computing

Abstract: In this paper, graph multiset transformation is introduced and studied as a novel type of parallel graph transformation. The basic idea is that graph transformation rules may be applied to all or at least some members of a multiset of graphs simultaneously providing a computational step with the possibility of massive parallelism in this way. As a consequence, graph problems in the class NP can be solved by a single computation of polynomial length for each input graph.

Algorithmic applications of XPCR

Abstract: An emerging trend in DNA computing consists of the algorithmic analysis of new molecular biology technologies, and in general of more effective tools to tackle computational biology problems. An algorithmic understanding of the interaction between DNA molecules becomes the focus of some research which was initially addressed to solve mathematical problems by processing data within biomolecules. In this paper a novel mechanism of DNA recombination is discussed, that turned out to be a good implementation key to develop new procedures for DNA manipulation (Franco et al., DNA extraction by cross pairing PCR, 2005; Franco et al., DNA recombination by XPCR, 2006; Manca and Franco, Math Biosci 211:282---298, 2008). It is called XPCR as it is a variant of the polymerase chain reaction (PCR), which was a revolution in molecular biology as a technique for cyclic amplification of DNA segments. A few DNA algorithms are proposed, that were experimentally proven in different contexts, such as, mutagenesis (Franco, Biomolecular computing--combinatorial algorithms and laboratory experiments, 2006), multiple concatenation, gene driven DNA extraction (Franco et al., DNA extraction by cross pairing PCR, 2005), and generation of DNA libraries (Franco et al., DNA recombination by XPCR, 2006), and some related ongoing work is outlined.

(Tissue) P systems working in the k-restricted minimally or maximally parallel transition mode

Abstract: We investigate variants of the maximally and the minimally parallel transition mode, i.e., we allow only a bounded number of rules to be taken from every set of the partitioning of the whole set of rules. The 1-restricted minimally parallel transition mode especially fits to describe the way transitions take place in spiking neural P systems without delays, i.e., in every neuron where a rule is applicable exactly one rule has to be applied. Moreover, purely catalytic P systems working in the maximally parallel transition mode can be described as P systems using the corresponding rules without catalysts, i.e., noncooperative rules, when working in the 1-restricted minimally parallel transition mode. In contrast to these results for computationally complete models of P systems, with the k-restricted maximally parallel transition mode noncooperative rules only allow for the generation of semi-linear sets.

Petri net models for the semi-automatic construction of large scale biological networks

Abstract: For the implementation of the virtual cell, the fundamental question is how to model and simulate complex biological networks. During the last 15 years, Petri nets have attracted more and more attention to help to solve this key problem. Regarding the published papers, it seems clear that hybrid functional Petri nets are the adequate method to model complex biological networks. Today, a Petri net model of biological networks is built manually by drawing places, transitions and arcs with mouse events. Therefore, based on relevant molecular database and information systems biological data integration is an essential step in constructing biological networks. In this paper, we will motivate the application of Petri nets for modeling and simulation of biological networks. Furthermore, we will present a type of access to relevant metabolic databases such as KEGG, BRENDA, etc. Based on this integration process, the system supports semi-automatic generation of the correlated hybrid Petri net model. A case study of the cardio-disease related gene-regulated biological network is also presented. MoVisPP is available at http://agbi.techfak.uni-bielefeld.de/movispp/ .

On the hierarchy of conservation laws in a cellular automaton

Abstract: Conservation laws in cellular automata (CA) are studied as an abstraction of the conservation laws observed in nature. In addition to the usual real-valued conservation laws we also consider more general group-valued and semigroup-valued conservation laws. The (algebraic) conservation laws in a CA form a hierarchy, based on the range of the interactions they take into account. The conservation laws with smaller interaction ranges are the homomorphic images of those with larger interaction ranges, and for each specific range there is a most general law that incorporates all those with that range. For one-dimensional CA, such a most general conservation law has—even in the semigroup-valued case—an effectively constructible finite presentation, while for higher-dimensional CA such effective construction exists only in the group-valued case. It is even undecidable whether a given two-dimensional CA conserves a given semigroup-valued energy assignment. Although the local properties of this hierarchy are tractable in the one-dimensional case, its global properties turn out to be undecidable. In particular, we prove that it is undecidable whether this hierarchy is trivial or unbounded. We point out some interconnections between the structure of this hierarchy and the dynamical properties of the CA. In particular, we show that positively expansive CA do not have non-trivial real-valued conservation laws.

On discrete models and immunological algorithms for protein structure prediction

Abstract: Discrete models for protein structure prediction embed the protein amino acid sequence into a discrete spatial structure, usually a lattice, where an optimal tertiary structure is predicted on the basis of simple assumptions relating to the hydrophobic---hydrophilic character of amino acids in the sequence and to relevant interactions for free energy minimization. While the prediction problem is known to be NP complete even in the simple setting of Dill's model with a 2D-lattice, a variety of bio-inspired algorithms for this problem have been proposed in the literature. Immunological algorithms are inspired by the kind of optimization that immune systems perform when identifying and promoting the replication of the most effective antibodies against given antigens. A quick, state-of-the-art survey of discrete models and immunological algorithms for protein structure prediction is presented in this paper, and the main design and performance features of an immunological algorithm for this problem are illustrated in a tutorial fashion.

Data analysis pipeline from laboratory to MP models

Abstract: A workflow for data analysis is introduced to synthesize flux regulation maps of a Metabolic P system from time series of data observed in laboratory. The procedure is successfully tested on a significant case study, the photosynthetic phenomenon called NPQ, which determines plant accommodation to environmental light. A previously introduced MP model of such a photosynthetic process has been improved, by providing an MP system with a simpler regulative network that reproduces the observed behaviors of the natural system. Two regression techniques were employed to find out the regulation maps, and interesting experimental results came out in the context of their residual analysis for model validation.

Hybrid Petri net based modeling for biological pathway simulation

Abstract: Hybrid Petri net (HPN) is an extension of the Petri net formalism, which enables us to handle continuous information in addition to discrete information. Firstly, this paper demonstrates how biological pathways can be modeled by the integration of discrete and continuous elements, with an example of the ? phage genetic switch system including induction and retroregulation mechanisms. Although HPN allows intuitive modeling of biological pathways, some fundamental biological processes such as complex formation cannot be represented with HPN. Thus, this paper next provides the formal definition of hybrid functional Petri net with extension (HFPNe), which has high potential for modeling various kinds of biological processes. Cell Illustrator is a software tool developed on the basis of the definition of HFPNe. Hypothesis creation by Cell Illustrator is demonstrated with the example of the cyanobacterial circadian gene clock system. Finally, our ongoing tasks, which include the development of a computational platform for systems biology, are presented.

The combinatorics of modeling and analyzing biological systems

Abstract: The purpose of this paper is to present a strictly mathematical model for interaction networks, to address the question of steady-state analysis, and to outline an approach for reconstructing models from experimental data. Our expositions require notations and basic results from discrete mathematics. Therefore, we also introduce some elementary background material from this field.

NP-completeness of the energy barrier problem without pseudoknots and temporary arcs

Abstract: Knowledge of energy barriers between pairs of secondary structures for a given DNA or RNA molecule is useful, both in understanding RNA function in biological settings and in design of programmed molecular systems. Current heuristics are not guaranteed to find the exact energy barrier, raising the question whether the energy barrier can be calculated efficiently. In this paper, we study the computational complexity of a simple formulation of the energy barrier problem, in which each base pair contributes an energy of ?1 and only base pairs in the initial and final structures may be used on a folding pathway from initial to final structure. We show that this problem is NP-complete.

Boundedness analysis for open Chemical Reaction Networks with mass-action kinetics

Abstract: This paper describes the working principles of an algorithm for boundedness analysis of open Chemical Reaction Networks endowed with mass-action kinetics Such models can be thought of both as a special class of compartmental systems or a particular type of continuous Petri Nets, in which the firing rates of transitions are not constant or preassigned, but expressed as a function of the continuous marking of the network (function which in chemistry is referred to as the "kinetics") The algorithm can be applied to a broad class of such open networks, and returns, as an outcome, a classification of the possible dynamical behaviors that are compatible with the network structure, by classifying each variable either as bounded, converging to 0 or diverging to ? This can be viewed as a qualitative study of Input---Output Stability for chemical networks, or more precisely, as a classification of its possible I---O instability patterns Our goal is to analyze the system irrespectively of values of kinetic parameters More precisely, we attempt to analyze it simultaneously for all possible values Remarkably, tests on non-trivial examples (one of which is discussed in this paper) showed that, as the kinetic constants of the network are varied, all the compatible behaviors could be observed in simulations Finally, we discuss and illustrate how the results relate to previous works on the qualitative dynamics of closed reaction networks

DNA chips for species identification and biological phylogenies

Abstract: The codeword design problem is an important problem in DNA computing and its applications. Several theoretical analyses as well as practical solutions for short oligonucleotides (up to 20-mers) have been generated recently. These solutions have, in turn, suggested new applications to DNA-based indexing and natural language processing, in addition to the obvious applications to the problems of reliability and scalability that generated them. Here we continue the exploration of this type of DNA-based indexing for biological applications and show that DNA noncrosshybridizing (nxh) sets can be successfully applied to infer ab initio phylogenetic trees by providing a way to measure distances among different genomes indexed by sets of short oligonucleotides selected so as to minimize crosshybridization. These phylogenies are solidly established and well accepted in biology. The new technique is much more effective in terms of signal-to-noise ratio, cost and time than current methods. Second, it is demonstrated that DNA indexing does provide novel and principled insights into the phylogenesis of organisms hitherto inaccessible by current methods, such as a prediction of the origin of the Salmonella plasmid 50 as being acquired horizontally, likely from some bacteria somewhat related to Yesinia. Finally, DNA indexing can be scaled up to newly available universal DNA chips readily available both in vitro and in silico. In particular, we show how a recently obtained such set of nxh 16-mers can be used as a universal coordinate system in DNA spaces to characterize very large groups (families, genera, and even phylla) of organisms on a uniform biomarker reference system, a veritable and comprehensive "Atlas of Life", as it is or as it could be on earth.

Stochastic Petri net models of Ca2+ signaling complexes and their analysis

Abstract: Mathematical models of Ca2+ release sites derived from Markov chain models of intracellular Ca2+ channels exhibit collective gating reminiscent of the experimentally observed phenomenon of stochastic Ca2+ excitability (i.e., puffs and sparks). Ca2+ release site models are composed of a number of individual channel models whose dynamic behavior depends on the local Ca2+ concentration which is influenced by the state of all channels. We consider this application area to illustrate how stochastic Petri nets and in particular stochastic activity networks can be used to model dynamical phenomena in cell biology. We highlight how state-sharing composition operations as supported by the Mobius framework can represent both mean-field and spatial coupling assumptions in a natural manner. We investigate how state-of-the-art techniques for the numerical and simulative analysis of Markov chains associated with stochastic Petri nets scale when modeling Ca2+ signaling complexes of physiological size and complexity.

On stoichiometry for the assembly of flexible tile DNA complexes

Abstract: Given a set of flexible branched junction DNA molecules with sticky-ends (building blocks), called here "tiles", we consider the problem of determining the proper stoichiometry such that all sticky-ends could end up connected. In general, the stoichiometry is not uniform, and the goal is to determine the proper proportion (spectrum) of each type of molecule within a test tube to allow for complete assembly. According to possible components that assemble in complete complexes we partition multisets of tiles, called here "pots", into classes: unsatisfiable, weakly satisfiable, satisfiable and strongly satisfiable. This classification is characterized through the spectrum of the pot, and it can be computed in PTIME using the standard Gauss-Jordan elimination method. We also give a geometric description of the spectrum as a convex hull within the unit cube.