Stochastic Turing patterns of trichomes in Arabidopsis leaves.

Biological patterns that emerge during the morphogenesis of multicellular organisms can display high precision at large scales, while at cellular scales, cells exhibit large fluctuations stemming from cell-cell differences in molecular copy numbers also called demographic noise. We study the conflicting interplay between high precision and demographic noise in trichome patterns on the epidermis of wild-type Arabidopsis thaliana leaves, as a two-dimensional model system. We carry out a statistical characterization of these patterns and show that their power spectra display fat tails-a signature compatible with noise-driven stochastic Turing patterns-which are absent in power spectra of patterns driven by deterministic instabilities. We then present a theoretical model that includes demographic noise stemming from birth-death processes of genetic regulators which we study analytically and by stochastic simulations. The model captures the observed experimental features of trichome patterns.

A unique circulating miRNA profile highlights thrombo-inflammation in Behçet's syndrome.

OBJECTIVES: Behçet's syndrome (BS) is a rare systemic vasculitis often complicated by thrombotic events. Given the lack of validated biomarkers, BS diagnosis relies on clinical criteria.In search of novel biomarkers for BS diagnosis, we determined the profile of plasmatic circulating microRNAs (ci-miRNAs) in patients with BS compared with healthy controls (HCs). METHODS: ci-miRNA profile was evaluated by microarray in a screening cohort (16 patients with BS and 18 HCs) and then validated by poly(T) adaptor PCR (PTA-PCR) in a validation cohort (30 patients with BS and 30 HCs). Two disease control groups (30 patients with systemic lupus erythematosus (SLE) and 30 patients with giant cell arteritis (GCA) were also analysed. RESULTS: From the microarray screening, 29 deregulated (differentially expressed (DE)) human ci-miRNAs emerged. A hierarchical cluster analysis indicated that DE ci-miRNAs clearly segregated patients from controls, independently of clinical features. PTA-PCR analysis on the validation cohort confirmed the deregulation of miR-224-5p, miR-206 and miR-653-5p. The combined receiver operating characteristic (ROC) curve analyses showed that such ci-miRNAs discriminate BS from HCs (and BS with active vs inactive disease), as well as BS from patients with SLE and GCA.The functional annotation analyses (FAAs) showed that the most enriched pathways affected by DE ci-miRNAs (ie, cell-matrix interaction, oxidative stress and blood coagulation) are related to thrombo-inflammatory mechanisms. Accordingly, the expression of the three ci-miRNAs from the validation cohort significantly correlated with leucocyte reactive oxygen species production and plasma lipid peroxidation. CONCLUSIONS: The ci-miRNA profile identified in this study may represent a novel, poorly invasive BS biomarker, while suggesting an epigenetic control of BS-related thrombo-inflammation.

Circulating miRNome profiling data in Behçet's syndrome.

We conducted a screening analysis to assess the presence of a characteristic extracellular circulating microRNAs (ci-miRNAs) profile in Behçet's syndrome (BS). Total RNA was extracted from platelets-free plasma (PFP) samples obtained from 16 BS patients and 18 healthy controls. Ci-miRNAs profiling was conducted by using dedicated Agilent microarray hybridization and data extraction technology. Statistical analysis of data extracted from microarray scanning revealed the deregulation of 36 ci-miRNAs, which turned out be differentially expressed between BS patients and healthy controls. Detailed experimental methods and data analysis were described here. The raw and normalized microarray data were deposited into Gene Expression Omnibus (GEO) under accession number GSE145191.

Robust, coherent, and synchronized circadian clock-controlled oscillations along Anabaena filaments.

Circadian clocks display remarkable reliability despite significant stochasticity in biomolecular reactions. We study the dynamics of a circadian clock-controlled gene at the individual cell level in Anabaena sp. PCC 7120, a multicellular filamentous cyanobacterium. We found significant synchronization and spatial coherence along filaments, clock coupling due to cell-cell communication, and gating of the cell cycle. Furthermore, we observed low-amplitude circadian oscillatory transcription of kai genes encoding the post-transcriptional core oscillatory circuit and high-amplitude oscillations of rpaA coding for the master regulator transducing the core clock output. Transcriptional oscillations of rpaA suggest an additional level of regulation. A stochastic one-dimensional toy model of coupled clock cores and their phosphorylation states shows that demographic noise can seed stochastic oscillations outside the region where deterministic limit cycles with circadian periods occur. The model reproduces the observed spatio-temporal coherence along filaments and provides a robust description of coupled circadian clocks in a multicellular organism.

Diauxie and co-utilization of carbon sources can coexist during bacterial growth in nutritionally complex environments.

It is commonly thought that when multiple carbon sources are available, bacteria metabolize them either sequentially (diauxic growth) or simultaneously (co-utilization). However, this view is mainly based on analyses in relatively simple laboratory settings. Here we show that a heterotrophic marine bacterium, Pseudoalteromonas haloplanktis, can use both strategies simultaneously when multiple possible nutrients are provided in the same growth experiment. The order of nutrient uptake is partially determined by the biomass yield that can be achieved when the same compounds are provided as single carbon sources. Using transcriptomics and time-resolved intracellular 1H-13C NMR, we reveal specific pathways for utilization of various amino acids. Finally, theoretical modelling indicates that this metabolic phenotype, combining diauxie and co-utilization of substrates, is compatible with a tight regulation that allows the modulation of assimilatory pathways.

A Method for the Structure-Based, Genome-Wide Analysis of Bacterial Intergenic Sequences Identifies Shared Compositional and Functional Features.

In this paper, we propose a computational strategy for performing genome-wide analyses of intergenic sequences in bacterial genomes. Following similar directions of a previous paper, where a method for genome-wide analysis of eucaryotic Intergenic sequences was proposed, here we developed a tool for implementing similar concepts in bacteria genomes. This allows us to (i) classify intergenic sequences into clusters, characterized by specific global structural features and (ii) draw possible relations with their functional features.

Noise⁻Seeded Developmental Pattern Formation in Filamentous Cyanobacteria.

Under nitrogen-poor conditions, multicellular cyanobacteria such as Anabaena sp. PCC 7120 undergo a process of differentiation, forming nearly regular, developmental patterns of individual nitrogen-fixing cells, called heterocysts, interspersed between intervals of vegetative cells that carry out photosynthesis. Developmental pattern formation is mediated by morphogen species that can act as activators and inhibitors, some of which can diffuse along filaments. We survey the limitations of the classical, deterministic Turing mechanism that has been often invoked to explain pattern formation in these systems, and then, focusing on a simpler system governed by birth-death processes, we illustrate pedagogically a recently proposed paradigm that provides a much more robust description of pattern formation: stochastic Turing patterns. We emphasize the essential role that cell-to-cell differences in molecular numbers-caused by inevitable fluctuations in gene expression-play, the so called demographic noise, in seeding the formation of stochastic Turing patterns over a much larger region of parameter space, compared to their deterministic counterparts.

Hopping in the Crowd to Unveil Network Topology.

We introduce a nonlinear operator to model diffusion on a complex undirected network under crowded conditions. We show that the asymptotic distribution of diffusing agents is a nonlinear function of the nodes' degree and saturates to a constant value for sufficiently large connectivities, at variance with standard diffusion in the absence of excluded-volume effects. Building on this observation, we define and solve an inverse problem, aimed at reconstructing the a priori unknown connectivity distribution. The method gathers all the necessary information by repeating a limited number of independent measurements of the asymptotic density at a single node, which can be chosen randomly. The technique is successfully tested against both synthetic and real data and is also shown to estimate with great accuracy the total number of nodes.

Robust stochastic Turing patterns in the development of a one-dimensional cyanobacterial organism.

Under nitrogen deprivation, the one-dimensional cyanobacterial organism Anabaena sp. PCC 7120 develops patterns of single, nitrogen-fixing cells separated by nearly regular intervals of photosynthetic vegetative cells. We study a minimal, stochastic model of developmental patterns in Anabaena that includes a nondiffusing activator, two diffusing inhibitor morphogens, demographic fluctuations in the number of morphogen molecules, and filament growth. By tracking developing filaments, we provide experimental evidence for different spatiotemporal roles of the two inhibitors during pattern maintenance and for small molecular copy numbers, justifying a stochastic approach. In the deterministic limit, the model yields Turing patterns within a region of parameter space that shrinks markedly as the inhibitor diffusivities become equal. Transient, noise-driven, stochastic Turing patterns are produced outside this region, which can then be fixed by downstream genetic commitment pathways, dramatically enhancing the robustness of pattern formation, also in the biologically relevant situation in which the inhibitors' diffusivities may be comparable.

Noise processing by microRNA-mediated circuits: The Incoherent Feed-Forward Loop, revisited.

The intrinsic stochasticity of gene expression is usually mitigated in higher eukaryotes by post-transcriptional regulation channels that stabilise the output layer, most notably protein levels. The discovery of small non-coding RNAs (miRNAs) in specific motifs of the genetic regulatory network has led to identifying noise buffering as the possible key function they exert in regulation. Recent in vitro and in silico studies have corroborated this hypothesis. It is however also known that miRNA-mediated noise reduction is hampered by transcriptional bursting in simple topologies. Here, using stochastic simulations validated by analytical calculations based on van Kampen's expansion, we revisit the noise-buffering capacity of the miRNA-mediated Incoherent Feed Forward Loop (IFFL), a small module that is widespread in the gene regulatory networks of higher eukaryotes, in order to account for the effects of intermittency in the transcriptional activity of the modulator gene. We show that bursting considerably alters the circuit's ability to control static protein noise. By comparing with other regulatory architectures, we find that direct transcriptional regulation significantly outperforms the IFFL in a broad range of kinetic parameters. This suggests that, under pulsatile inputs, static noise reduction may be less important than dynamical aspects of noise and information processing in characterising the performance of regulatory elements.

The second will be first: competition on directed networks.

Multiple sinks competition is investigated for a walker diffusing on directed complex networks. The asymmetry of the imposed spatial support makes the system non transitive. As a consequence, it is always possible to identify a suitable location for the second absorbing sink that screens at most the flux of agents directed against the first trap, whose position has been preliminarily assigned. The degree of mutual competition between pairs of nodes is analytically quantified through apt indicators that build on the topological characteristics of the hosting graph. Moreover, the positioning of the second trap can be chosen so as to minimize, at the same time, the probability of being in turn shaded by a thirdly added trap. Supervised placing of absorbing traps on a asymmetric disordered and complex graph is hence possible, as follows a robust optimization protocol. This latter is here discussed and successfully tested against synthetic data.

Multiple-scale theory of topology-driven patterns on directed networks.

Dynamical processes on networks are currently being considered in different domains of cross-disciplinary interest. Reaction-diffusion systems hosted on directed graphs are in particular relevant for their widespread applications, from computer networks to traffic systems. Due to the peculiar spectrum of the discrete Laplacian operator, homogeneous fixed points can turn unstable, on a directed support, because of the topology of the network, a phenomenon which cannot be induced on undirected graphs. A linear analysis can be performed to single out the conditions that underly the instability. The complete characterization of the patterns, which are eventually attained beyond the linear regime of exponential growth, calls instead for a full nonlinear treatment. By performing a multiple time scale perturbative calculation, we here derive an effective equation for the nonlinear evolution of the amplitude of the most unstable mode, close to the threshold of criticality. This is a Stuart-Landau equation the complex coefficients of which appear to depend on the topological features of the embedding directed graph. The theory proves adequate versus simulations, as confirmed by operating with a paradigmatic reaction-diffusion model.

Optimal search strategies on complex multi-linked networks.

In this paper we consider the problem of optimal search strategies on multi-linked networks, i.e. graphs whose nodes are endowed with several independent sets of links. We focus preliminarily on agents randomly hopping along the links of a graph, with the additional possibility of performing non-local hops to randomly chosen nodes with a given probability. We show that an optimal combination of the two jump rules exists that maximises the efficiency of target search, the optimum reflecting the topology of the network. We then generalize our results to multi-linked networks with an arbitrary number of mutually interfering link sets.

Genome-wide analysis of promoters: clustering by alignment and analysis of regular patterns.

In this paper we perform a genome-wide analysis of H. sapiens promoters. To this aim, we developed and combined two mathematical methods that allow us to (i) classify promoters into groups characterized by specific global structural features, and (ii) recover, in full generality, any regular sequence in the different classes of promoters. One of the main findings of this analysis is that H. sapiens promoters can be classified into three main groups. Two of them are distinguished by the prevalence of weak or strong nucleotides and are characterized by short compositionally biased sequences, while the most frequent regular sequences in the third group are strongly correlated with transposons. Taking advantage of the generality of these mathematical procedures, we have compared the promoter database of H. sapiens with those of other species. We have found that the above-mentioned features characterize also the evolutionary content appearing in mammalian promoters, at variance with ancestral species in the phylogenetic tree, that exhibit a definitely lower level of differentiation among promoters.

Stochastic Turing patterns on a network.

The process of stochastic Turing instability on a scale-free network is discussed for a specific case study: the stochastic Brusselator model. The system is shown to spontaneously differentiate into activator-rich and activator-poor nodes outside the region of parameters classically deputed to the deterministic Turing instability. This phenomenon, as revealed by direct stochastic simulations, is explained analytically and eventually traced back to the finite-size corrections stemming from the inherent graininess of the scrutinized medium.

System size expansion for systems with an absorbing state.

The well-known van Kampen system size expansion, while of rather general applicability, is shown to fail to reproduce some qualitative features of the time evolution for systems with an absorbing state, apart from a transient initial time interval. We generalize the van Kampen ansatz by introducing a new prescription leading to non-Gaussian fluctuations around the absorbing state. The two expansion predictions are explicitly compared for the infinite range voter model with speciation as a paradigmatic model with an absorbing state. The new expansion, both for a finite size system in the large time limit and at finite time in the large size limit, converges to the exact solution as obtained in a numerical implementation using the Gillespie algorithm. Furthermore, the predicted lifetime distribution is shown to have the correct asymptotic behavior.

Deterministic and stochastic aspects of VEGF-A production and the cooperative behavior of tumoral cell colony.

A model is proposed to study the process of hypoxia-induced angiogenesis in cancer cells. The model accounts for the role played by the vascular endothelial growth factor (VEGF)-A in regulating the oxygen intake. VEGF-A is dynamically controlled by the HIF-1α concentration. If not degraded, HIF-1α can bind to the subunit termed HIF-1ß and so experience translocation to the nucleus, to exert its proper transcriptional activity. The delicate balance between these opposing tendencies translates into the emergence of distinct macroscopic behaviors in terms of the associated molecular concentrations that we here trace back to normoxia, hypoxia and death regimes. These aspects are firstly analyzed with reference to the ideal mean-field scenario. Stochastic fluctuations are also briefly discussed and shown to seed a cooperative interaction among cellular units, competing for the same oxygen reservoir.

Spatial model of autocatalytic reactions.

Biological cells with all of their surface structure and complex interior stripped away are essentially vesicles--membranes composed of lipid bilayers which form closed sacs. Vesicles are thought to be relevant as models of primitive protocells, and they could have provided the ideal environment for prebiotic reactions to occur. In this paper, we investigate the stochastic dynamics of a set of autocatalytic reactions, within a spatially bounded domain, so as to mimic a primordial cell. The discreteness of the constituents of the autocatalytic reactions gives rise to large sustained oscillations even when the number of constituents is quite large. These oscillations are spatiotemporal in nature, unlike those found in previous studies, which consisted only of temporal oscillations. We speculate that these oscillations may have a role in seeding membrane instabilities which lead to vesicle division. In this way synchronization could be achieved between protocell growth and the reproduction rate of the constituents (the protogenetic material) in simple protocells.

Stochastic Turing patterns in the Brusselator model.

A stochastic version of the Brusselator model is proposed and studied via the system size expansion. The mean-field equations are derived and shown to yield to organized Turing patterns within a specific parameters region. When determining the Turing condition for instability, we pay particular attention to the role of cross-diffusive terms, often neglected in the heuristic derivation of reaction-diffusion schemes. Stochastic fluctuations are shown to give rise to spatially ordered solutions, sharing the same quantitative characteristic of the mean-field based Turing scenario, in term of excited wavelengths. Interestingly, the region of parameter yielding to the stochastic self-organization is wider than that determined via the conventional Turing approach, suggesting that the condition for spatial order to appear can be less stringent than customarily believed.

Enhanced stochastic oscillations in autocatalytic reactions.

We study a simplified scheme of k coupled autocatalytic reactions, previously introduced by Togashi and Kaneko. The role of stochastic fluctuations is elucidated through the use of the van Kampen system-size expansion and the results compared with direct stochastic simulations. Regular temporal oscillations are predicted to occur for the concentration of the various chemical constituents, with an enhanced amplitude resulting from a resonance which is induced by the intrinsic graininess of the system. The associated power spectra are determined and have a different form depending on the number of chemical constituents k . We make detailed comparisons in the two cases k=4 and k=8 . Agreement between the theoretical and numerical results for the power spectrum is good in both cases. The resulting spectrum is especially interesting in the k=8 system, since it has two peaks, which the system-size expansion is still able to reproduce accurately.