Andrés Moreira

Complexity of Langton's ant

The virtual ant introduced by Langton [Physica D 22 (1986) 120] has an interesting behavior, which has been studied in several contexts. Here we give a construction to calculate any boolean circuit with the trajectory of a single ant. This proves the P-hardness of the system and implies, through the simulation of one-dimensional cellular automata and Turing machines, the universality of the ant and the undecidability of some problems associated to it.

Micro-RNAs: viral genome and robustness of gene expression in the host

For comparing RNA rings or hairpins with reference or random ring sequences, circular versions of distances and distributions like those of Hamming and Gumbel are needed. We define these circular versions and we apply these new tools to the comparison of RNA relics (such as micro-RNAs and tRNAs) with viral genomes that have coevolved with them. Then we show how robust are the regulation networks incorporating in their boundary micro-RNAs as sources or new feedback loops involving ubiquitous proteins like p53 (which is a micro-RNA transcription factor) or oligopeptides regulating protein translation. Eventually, we propose a new coevolution game between viral and host genomes.

RNA Relics and Origin of Life

A number of small RNA sequences, located in different non-coding sequences and highly preserved across the tree of life, have been suggested to be molecular fossils, of ancient (and possibly primordial) origin. On the other hand, recent years have revealed the existence of ubiquitous roles for small RNA sequences in modern organisms, in functions ranging from cell regulation to antiviral activity. We propose that a single thread can be followed from the beginning of life in RNA structures selected only for stability reasons through the RNA relics and up to the current coevolution of RNA sequences; such an understanding would shed light both on the history and on the present development of the RNA machinery and interactions. After presenting the evidence (by comparing their sequences) that points toward a common thread, we discuss a scenario of genome coevolution (with emphasis on viral infectious processes) and finally propose a plan for the reevaluation of the stereochemical theory of the genetic code; we claim that it may still be relevant, and not only for understanding the origin of life, but also for a comprehensive picture of regulation in present-day cells.

Genetic algorithms for the imitation of genomic styles in protein backtranslation

Abstract Several technological applications require the translation of a protein into a nucleic acid that codes for it (“backtranslation”). The degeneracy of the genetic code makes this translation ambiguous; moreover, not every translation is equally viable. The common answer to this problem is the imitation of the codon usage of the target species. Here we discuss several other features of coding sequences (“coding statistics”) that are relevant for the “genomic style” of different species. A genetic algorithm is then used to obtain backtranslations that mimic these styles, by minimizing the difference in the coding statistics. Possible improvements and applications are discussed.

Generalized Langton's Ant: Dynamical Behavior and Complexity

Langtons ant is a simple discrete dynamical system, with a surprisingly complex behavior. We study its extension to general planar graphs. First we give some relations between characteristics of finite graphs and the dynamics of the ant on them. Then we consider the infinite bi-regular graphs of degrees 3 and 4, where we prove the universality of the system, and in the particular cases of the square and the hexagonal grids, we associate a P-hard problem to the dynamics. Finally, we show strong spatial restrictions on the trajectory of the ant in infinite bi-regular graphs with degrees strictly greater than 4, which contrasts with the high unpredictability on the graphs of lower degrees.

Evolution and RNA Relics. A Systems Biology View

The genetic code has evolved from its initial non-degenerate wobble version until reaching its present state of degeneracy. By using the stereochemical hypothesis, we revisit the problem of codon assignations to the synonymy classes of amino-acids. We obtain these classes with a simple classifier based on physico-chemical properties of nucleic bases, like hydrophobicity and molecular weight. Then we propose simple RNA (or more generally XNA, with X for D, P or R) ring structures that present, overlap included, one and only one codon by synonymy class as solutions of a combinatory variational problem. We compare these solutions to sequences of present RNAs considered as relics, with a high interspecific invariance, like invariant parts of tRNAs and micro-RNAs. We conclude by emphasizing some optimal properties of the genetic code.

Dynamical behavior and complexity of Langton's ant

O ne of the first models of artificial life, proposed back in the 1980s by Christopher Langton, founder of the field, was the virtual ant [1,2]. This simple cellular automaton is defined on the square grid in the following way: each square (“cell”) of the grid can be in one of two states, white or black, and the ant is represented by a short arrow that stands on one cell and points to the north, the west, the east, or the south. At each time step, it moves to the cell it was pointing to, and it turns 90 degrees to the left if this cell is white or 90 degrees to the right if it is black; in addition, the state of the cell is switched. Figure 1a shows the situation after 5 time steps, starting with a background of only white cells. The interesting part starts when we let the ant go on with its walk. At iterations 96 and 184, rotational symmetry of order 2 is observed; at iteration 368 (Figure 1b), it is almost of order 4. When one could expect further symmetrical patterns, the symmetry breaks down, and after the step 500, the ant seems to walk at random, for more than 9000 iterations (Figure 1c). Again, when one would expect this chaos to go on forever, the ant suddenly starts building a pattern that is periodic but for a drift; it is the so called “highway,” and in the absence of obstacles, the ant will draw it forever (Figure 1d). This brief history involving a break of symmetry, a “chaotic” phase, and sudden order, all generated by a rule that could hardly be simpler, becomes more intriguing when we notice that it repeats with other initial patterns. In fact, the highway has appeared, sooner or later, in all the simulations that have been started with a finite amount of black (or of white) cells (we call them configurations with finite support). Nobody has demonstrated Langton’s ant, with its intriguing behavior, has been elusive to theoretical results, particularly from the point of view of the system’s complexity. We summarize here some recent work of our group, that sheds some new light on the ant.

Universal Time-Symmetric Number-Conserving Cellular Automaton

We show the existence of Turing-universal and intrinsically universal cellular automata exhibiting both time symmetry and number conservation; this is achieved by providing a way to simulate reversible CA with time-symmetric CA, which preserves the number-conserving property. We also provide some additional results and observations concerning the simulation relations between reversible, time-symmetric and number-conserving CA in the context of partitioned CA.