Self Organization of Interacting Polya Urns

We introduce a simple model which shows non-trivial self organized critical properties. The model describes a system of interacting units, modelled by Polya urns, subject to perturbations and which occasionally break down. Three equivalent formulations - stochastic, quenched and deterministic - are shown to reproduce the same dynamics. Among the novel features of the model are a non-homogeneous stationary state, the presence of a non-stationary critical phase and non-trivial exponents even in mean field. We discuss simple interpretations in term of biological evolution and earthquake dynamics and we report on extensive numerical simulations in dimensions $d=1,2$ as well as in the random neighbors limit.Comment: 4 pages 1 figur

Predict or classify: The deceptive role of time-locking in brain signal classification

Several experimental studies claim to be able to predict the outcome of simple decisions from brain signals measured before subjects are aware of their decision. Often, these studies use multivariate pattern recognition methods with the underlying assumption that the ability to classify the brain signal is equivalent to predict the decision itself. Here we show instead that it is possible to correctly classify a signal even if it does not contain any predictive information about the decision. We first define a simple stochastic model that mimics the random decision process between two equivalent alternatives, and generate a large number of independent trials that contain no choice-predictive information. The trials are first time-locked to the time point of the final event and then classified using standard machine-learning techniques. The resulting classification accuracy is above chance level long before the time point of time-locking. We then analyze the same trials using information theory. We demonstrate that the high classification accuracy is a consequence of time-locking and that its time behavior is simply related to the large relaxation time of the process. We conclude that when time-locking is a crucial step in the analysis of neural activity patterns, both the emergence and the timing of the classification accuracy are affected by structural properties of the network that generates the signal.Comment: 23 pages, 5 figure

Biodiversity in model ecosystems, II: Species assembly and food web structure

This is the second of two papers dedicated to the relationship between population models of competition and biodiversity. Here we consider species assembly models where the population dynamics is kept far from fixed points through the continuous introduction of new species, and generalize to such models thecoexistence condition derived for systems at the fixed point. The ecological overlap between species with shared preys, that we define here, provides a quantitative measure of the effective interspecies competition and of the trophic network topology. We obtain distributions of the overlap from simulations of a new model based both on immigration and speciation, and show that they are in good agreement with those measured for three large natural food webs. As discussed in the first paper, rapid environmental fluctuations, interacting with the condition for coexistence of competing species, limit the maximal biodiversity that a trophic level can host. This horizontal limitation to biodiversity is here combined with either dissipation of energy or growth of fluctuations, which in our model limit the length of food webs in the vertical direction. These ingredients yield an effective model of food webs that produce a biodiversity profile with a maximum at an intermediate trophic level, in agreement with field studies

Biodiversity in model ecosystems, I: Coexistence conditions for competing species

This is the first of two papers where we discuss the limits imposed by competition to the biodiversity of species communities. In this first paper we study the coexistence of competing species at the fixed point of population dynamic equations. For many simple models, this imposes a limit on the width of the productivity distribution, which is more severe the more diverse the ecosystem is (Chesson, 1994). Here we review and generalize this analysis, beyond the ``mean-field''-like approximation of the competition matrix used in previous works, and extend it to structured food webs. In all cases analysed, we obtain qualitatively similar relations between biodiversity and competition: the narrower the productivity distribution is, the more species can stably coexist. We discuss how this result, considered together with environmental fluctuations, limits the maximal biodiversity that a trophic level can host

Single-molecule modeling of mRNA degradation by miRNA: Lessons from data

Recent experimental results on the effect of miRNA on the decay of its target mRNA have been analyzed against a previously hypothesized single molecule degradation pathway. According to that hypothesis, the silencing complex (miRISC) first interacts with its target mRNA and then recruits the protein complexes associated with NOT1 and PAN3 to trigger deadenylation (and subsequent degradation) of the target mRNA. Our analysis of the experimental decay patterns allowed us to refine the structure of the degradation pathways at the single molecule level. Surprisingly, we found that if the previously hypothesized network was correct, only about 7% of the target mRNA would be regulated by the miRNA mechanism, which is inconsistent with the available knowledge. Based on systematic data analysis, we propose the alternative hypothesis that NOT1 interacts with miRISC before binding to the target mRNA. Moreover, we show that when miRISC binds alone to the target mRNA, the mRNA is degraded more slowly, probably through a deadenylation-independent pathway. The new biochemical pathway we propose both fits the data and paves the way for new experimental work to identify new interactions.Comment: It contains also the Supplementary Materials as appendix

Global and local depletion of ternary complex limits translational elongation

The translation of genetic information according to the sequence of the mRNA template occurs with high accuracy and fidelity. Critical events in each single step of translation are selection of transfer RNA (tRNA), codon reading and tRNA-regeneration for a new cycle. We developed a model that accurately describes the dynamics of single elongation steps, thus providing a systematic insight into the sensitivity of the mRNA translation rate to dynamic environmental conditions. Alterations in the concentration of the aminoacylated tRNA can transiently stall the ribosomes during translation which results, as suggested by the model, in two outcomes: either stress-induced change in the tRNA availability triggers the premature termination of the translation and ribosomal dissociation, or extensive demand for one tRNA species results in a competition between frameshift to an aberrant open-reading frame and ribosomal drop-off. Using the bacterial Escherichia coli system, we experimentally draw parallels between these two possible mechanisms

Transient Phenomena in Gene Expression after Induction of Transcription

When transcription of a gene is induced by a stimulus, the number of its mRNA molecules changes with time. Here we discuss how this time evolution depends on the shape of the mRNA lifetime distribution. Analysis of the statistical properties of this change reveals transient effects on polysomes, ribosomal profiles, and rate of protein synthesis. Our studies reveal that transient phenomena in gene expression strongly depend on the specific form of the mRNA lifetime distribution

The shape of ecological networks

We study the statistics of ecosystems with a variable number of co-evolving species. The species interact in two ways: by prey-predator relationships and by direct competition with similar kinds. The interaction coefficients change slowly through successful adaptations and speciations. We treat them as quenched random variables. These interactions determine long-term topological features of the species network, which are found to agree with those of biological systems.Comment: 4 pages, 2 figure

Self-Organized Criticality Driven by Deterministic Rules

We have investigated the essential ingredients allowing a system to show Self Organized Criticality (SOC) in its collective behavior. Using the Bak-Sneppen model of biological evolution as our paradigm, we show that the random microscopic rules of update can be effectively substituted with a chaotic map without changing the universality class. Using periodic maps SOC is preserved, but in a different universality class, as long as the spectrum of frequencies is broad enough.Comment: 4 pages, RevTex (tar.gz), 4 eps-figures include

Self-organized criticality in deterministic systems with disorder

Using the Bak-Sneppen model of biological evolution as our paradigm, we investigate in which cases noise can be substituted with a deterministic signal without destroying Self-Organized Criticality (SOC). If the deterministic signal is chaotic the universality class is preserved; some non-universal features, such as the threshold, depend on the time correlation of the signal. We also show that, if the signal introduced is periodic, SOC is preserved but in a different universality class, as long as the spectrum of frequencies is broad enough.Comment: RevTex, 8 pages, 8 figure