A novel methodology to describe neuronal networks activity reveals spatiotemporal recruitment dynamics of synchronous bursting states.

We propose a novel phase based analysis with the purpose of quantifying the periodic bursts of activity observed in various neuronal systems. The way bursts are intiated and propagate in a spatial network is still insufficiently characterized. In particular, we investigate here how these spatiotemporal dynamics depend on the mean connection length. We use a simplified description of a neuron's state as a time varying phase between firings. This leads to a definition of network bursts, that does not depend on the practitioner's individual judgment as the usage of subjective thresholds and time scales. This allows both an easy and objective characterization of the bursting dynamics, only depending on system's proper scales. Our approach thus ensures more reliable and reproducible measurements. We here use it to describe the spatiotemporal processes in networks of intrinsically oscillating neurons. The analysis rigorously reveals the role of the mean connectivity length in spatially embedded networks in determining the existence of "leader" neurons during burst initiation, a feature incompletely understood observed in several neuronal cultures experiments. The precise definition of a burst with our method allowed us to rigorously characterize the initiation dynamics of bursts and show how it depends on the mean connectivity length. Although presented with simulations, the methodology can be applied to other forms of neuronal spatiotemporal data. As shown in a preliminary study with MEA recordings, it is not limited to in silico modeling.

Gene dosage effects: nonlinearities, genetic interactions, and dosage compensation.

High-throughput genomic analyses have shown that many mutations, including loss-of-function (LOF) mutations, are present in diseased as well as in healthy individuals. Gene dosage effects due to deletions, duplications, and LOF mutations provide avenues to explore oligo- and multigenic inheritance. Here, we focus on several mechanisms that mediate gene dosage effects and analyze biochemical interactions among multiple gene products that are sources of nonlinear relations connecting genotypes and phenotypes. We also explore potential mechanisms that compensate for gene dosage effects. Understanding these issues is critical to understanding why an individual bearing a few damaging mutations can be severely diseased, whereas others harboring tens of potentially deleterious mutations can appear quite healthy.

Severe osmotic compression triggers a slowdown of intracellular signaling, which can be explained by molecular crowding.

Regulation of the cellular volume is fundamental for cell survival and function. Deviations from equilibrium trigger dedicated signaling and transcriptional responses that mediate water homeostasis and volume recovery. Cells are densely packed with proteins, and molecular crowding may play an important role in cellular processes. Indeed, increasing molecular crowding has been shown to modify the kinetics of biochemical reactions in vitro; however, the effects of molecular crowding in living cells are mostly unexplored. Here, we report that, in yeast, a sudden reduction in cellular volume, induced by severe osmotic stress, slows down the dynamics of several signaling cascades, including the stress-response pathways required for osmotic adaptation. We show that increasing osmotic compression decreases protein mobility and can eventually lead to a dramatic stalling of several unrelated signaling and cellular processes. The rate of these cellular processes decreased exponentially with protein density when approaching stalling osmotic compression. This suggests that, under compression, the cytoplasm behaves as a soft colloid undergoing a glass transition. Our results shed light on the physical mechanisms that force cells to cope with volume fluctuations to maintain an optimal protein density compatible with cellular functions.

Long-term model predictive control of gene expression at the population and single-cell levels.

Gene expression plays a central role in the orchestration of cellular processes. The use of inducible promoters to change the expression level of a gene from its physiological level has significantly contributed to the understanding of the functioning of regulatory networks. However, from a quantitative point of view, their use is limited to short-term, population-scale studies to average out cell-to-cell variability and gene expression noise and limit the nonpredictable effects of internal feedback loops that may antagonize the inducer action. Here, we show that, by implementing an external feedback loop, one can tightly control the expression of a gene over many cell generations with quantitative accuracy. To reach this goal, we developed a platform for real-time, closed-loop control of gene expression in yeast that integrates microscopy for monitoring gene expression at the cell level, microfluidics to manipulate the cells' environment, and original software for automated imaging, quantification, and model predictive control. By using an endogenous osmostress responsive promoter and playing with the osmolarity of the cells environment, we show that long-term control can, indeed, be achieved for both time-constant and time-varying target profiles at the population and even the single-cell levels. Importantly, we provide evidence that real-time control can dynamically limit the effects of gene expression stochasticity. We anticipate that our method will be useful to quantitatively probe the dynamic properties of cellular processes and drive complex, synthetically engineered networks.

Rich dynamics and functional organization on topographically designed neuronal networks in vitro.

Neuronal cultures are a prominent experimental tool to understand complex functional organization in neuronal assemblies. However, neurons grown on flat surfaces exhibit a strongly coherent bursting behavior with limited functionality. To approach the functional richness of naturally formed neuronal circuits, here we studied neuronal networks grown on polydimethylsiloxane (PDMS) topographical patterns shaped as either parallel tracks or square valleys. We followed the evolution of spontaneous activity in these cultures along 20 days in vitro using fluorescence calcium imaging. The networks were characterized by rich spatiotemporal activity patterns that comprised from small regions of the culture to its whole extent. Effective connectivity analysis revealed the emergence of spatially compact functional modules that were associated with both the underpinned topographical features and predominant spatiotemporal activity fronts. Our results show the capacity of spatial constraints to mold activity and functional organization, bringing new opportunities to comprehend the structure-function relationship in living neuronal circuits.

Cellular reactions to gene dosage imbalance: genomic, transcriptomic and proteomic effects.

There is increasing evidence suggesting that stoichiometric imbalances in macromolecular complexes and in signaling/transcriptional networks are a source of dosage-dependent phenotypes. Such alterations can result from total or partial aneuploidy, gene copy number variants or regulatory alterations. Thus, some gene balance is required to ensure a normal function. This balance also dictates which genes are preferentially over- or underretained after single gene, segmental or whole genome duplications. Here, we review the mechanisms leading to dosage effects and compensation at the transcriptional and translational levels. Moreover, we propose that the involvement of a protein in a complex can affect its stability: formation of complexes might mask degradation signals in the monomers leading to their preferential degradation when in excess, alleviating dosage imbalances.

Gene Expression Dominance in Allopolyploids: Hypotheses and Models.

The classical example of nonadditive contributions of the two parents to allopolyploids is nucleolar dominance, which entails silencing of one parental set of ribosomal RNA genes. This has been observed for many other loci. The prevailing explanation for this genome-wide expression disparity is that the two merged genomes differ in their transposable element (TE) complement and in their level of TE-mediated repression of gene expression. Alternatively, and not exclusively, gene expression dominance may arise from mismatches between trans effectors and their targets. Here, we explore quantitative models of regulatory mismatches leading to gene expression dominance. We also suggest that, when pairs of merged genomes are similar from one allopolyploidization event to another, gene-level and genome dominance patterns should also be similar.

Understanding the Generation of Network Bursts by Adaptive Oscillatory Neurons.

Experimental and numerical studies have revealed that isolated populations of oscillatory neurons can spontaneously synchronize and generate periodic bursts involving the whole network. Such a behavior has notably been observed for cultured neurons in rodent's cortex or hippocampus. We show here that a sufficient condition for this network bursting is the presence of an excitatory population of oscillatory neurons which displays spike-driven adaptation. We provide an analytic model to analyze network bursts generated by coupled adaptive exponential integrate-and-fire neurons. We show that, for strong synaptic coupling, intrinsically tonic spiking neurons evolve to reach a synchronized intermittent bursting state. The presence of inhibitory neurons or plastic synapses can then modulate this dynamics in many ways but is not necessary for its appearance. Thanks to a simple self-consistent equation, our model gives an intuitive and semi-quantitative tool to understand the bursting behavior. Furthermore, it suggests that after-hyperpolarization currents are sufficient to explain bursting termination. Through a thorough mapping between the theoretical parameters and ion-channel properties, we discuss the biological mechanisms that could be involved and the relevance of the explored parameter-space. Such an insight enables us to propose experimentally-testable predictions regarding how blocking fast, medium or slow after-hyperpolarization channels would affect the firing rate and burst duration, as well as the interburst interval.

Hill function-based models of transcriptional switches: impact of specific, nonspecific, functional and nonfunctional binding.

We explore minimalist models of transcription in which we take into account that a cis-regulatory sequence is embedded in, and interacts with, a complex genome. The classical Hill equation is the simplest way to represent a transcriptional response. However, it may overlook the fact that a transcription factor (TF) establishes specific and nonspecific nonfunctional interactions with chromatin. Classical papers have shown that nonfunctional binding (not leading to transcription) may influence gene expression. We examine how the presence of additional binding sites for a TF, besides those on the gene(s) of interest, affect the shape and parameters of the transcriptional response. We consider two conditions: at equilibrium and at steady-state. In many cases the TF level is determined by the position of the cell within a spatial or temporal gradient. We show that such gradients can be adjusted by evolutionary selection to compensate for the alteration of the gene transcription response by the presence of nonfunctional binding sites. Finally, we analyse how the transcriptional response is affected by a decrease in TF concentration, as in cases of haploinsufficiency. We show that the nonlinearity of the transcriptional response as a function of [TF] exacerbates the effect of a decrease in the latter, at least for weakly expressed TFs. Although decades of work on TFs have led to the impression that almost everything is known about the control of gene expression, we show that even the simplest models of transcription control have not delivered all their secrets yet.

Aging: Somatic Mutations, Epigenetic Drift and Gene Dosage Imbalance.

Aging involves a progressive decline of metabolic function and an increased incidence of late-onset degenerative disorders and cancer. To a large extent, these processes are influenced by alterations affecting the integrity of genome architecture and, ultimately, its phenotypic expression. Despite the progress made towards establishing causal links between genomic and epigenomic changes and aging, mechanisms underlying metabolic dysregulation and age-related phenotypes remain obscure. Here, we present a model linking genome-wide changes and their age-related phenotypic consequences via the alteration of macromolecular complexes and cellular networks. This approach may provide a better understanding of the dynamically changing genome-phenome map with age, but also deeper insights to developing more targeted therapies to prevent and/or manage late-onset degenerative disorders as well as decelerate aging.

Effect of threshold disorder on the quorum percolation model.

We study the modifications induced in the behavior of the quorum percolation model on neural networks with Gaussian in-degree by taking into account an uncorrelated Gaussian thresholds variability. We derive a mean-field approach and show its relevance by carrying out explicit Monte Carlo simulations. It turns out that such a disorder shifts the position of the percolation transition, impacts the size of the giant cluster, and can even destroy the transition. Moreover, we highlight the occurrence of disorder independent fixed points above the quorum critical value. The mean-field approach enables us to interpret these effects in terms of activation probability. A finite-size analysis enables us to show that the order parameter is weakly self-averaging with an exponent independent on the thresholds disorder. Last, we show that the effects of the thresholds and connectivity disorders cannot be easily discriminated from the measured averaged physical quantities.

X chromosome inactivation and active X upregulation in therian mammals: facts, questions, and hypotheses.

X chromosome inactivation is a mechanism that modulates the expression of X-linked genes in eutherian females (XX). Ohno proposed that to achieve a proper balance between X-linked and autosomal genes, those on the active X should also undergo a 2-fold upregulation. Although some support for Ohno's hypothesis has been provided through the years, recent genomic studies testing this hypothesis have brought contradictory results and fueled debate. Thus far, there are as many results in favor as against Ohno's hypothesis, depending on the nature of the datasets and the various assumptions and thresholds involved in the analyses. However, they have confirmed the importance of dosage balance between X-linked and autosomal genes involved in stoichiometric relationships. These facts as well as questions and hypotheses are discussed below.

In silico control of biomolecular processes.

By implementing an external feedback loop one can tightly control the expression of a gene over many cell generations with quantitative accuracy. Controlling precisely the level of a protein of interest will be useful to probe quantitatively the dynamical properties of cellular processes and to drive complex, synthetically-engineered networks. In this chapter we describe a platform for real-time closed-loop control of gene expression in yeast that integrates microscopy for monitoring gene expression at the cell level, microfluidics to manipulate the cells environment, and original software for automated imaging, quantification, and model predictive control. By using an endogenous osmo-stress responsive promoter and playing with the osmolarity of the cells environment, we demonstrate that long-term control can indeed be achieved for both time-constant and time-varying target profiles, at the population level, and even at the single-cell level.

Combining microfluidics, optogenetics and calcium imaging to study neuronal communication in vitro.

In this paper we report the combination of microfluidics, optogenetics and calcium imaging as a cheap and convenient platform to study synaptic communication between neuronal populations in vitro. We first show that Calcium Orange indicator is compatible in vitro with a commonly used Channelrhodopsine-2 (ChR2) variant, as standard calcium imaging conditions did not alter significantly the activity of transduced cultures of rodent primary neurons. A fast, robust and scalable process for micro-chip fabrication was developed in parallel to build micro-compartmented cultures. Coupling optical fibers to each micro-compartment allowed for the independent control of ChR2 activation in the different populations without crosstalk. By analyzing the post-stimuli activity across the different populations, we finally show how this platform can be used to evaluate quantitatively the effective connectivity between connected neuronal populations.

Memory decay and loss of criticality in quorum percolation.

In this paper, we present the effects of memory decay on a bootstrap percolation model applied to random directed graphs (quorum percolation). The addition of decay was motivated by its natural occurrence in physical systems previously described by percolation theory, such as cultured neuronal networks, where decay originates from ionic leakage through the membrane of neurons and/or synaptic depression. Surprisingly, this feature alone appears to change the critical behavior of the percolation transition, where discontinuities are replaced by steep but finite slopes. Using different numerical approaches, we show evidence for this qualitative change even for very small decay values. In experiments where the steepest slopes can not be resolved and still appear as discontinuities, decay produces nonetheless a quantitative difference on the location of the apparent critical point. We discuss how this shift impacts network connectivity previously estimated without considering decay. In addition to this particular example, we believe that other percolation models are worth reinvestigating, taking into account similar sorts of memory decay.

Towards real-time control of gene expression: controlling the HOG signaling cascade.

To decipher the dynamical functioning of cellular processes, the method of choice is to observe the time response of cells subjected to well controlled perturbations in time and amplitude. Efficient methods, based on molecular biology, are available to monitor quantitatively and dynamically many cellular processes. In contrast, it is still a challenge to perturb cellular processes - such as gene expression - in a precise and controlled manner. Here, we propose a first step towards in vivo control of gene expression: in real-time, we dynamically control the activity of a yeast signaling cascade thanks to an experimental platform combining a micro-fluidic device, an epi-fluorescence microscope and software implementing control approaches. We experimentally demonstrate the feasibility of this approach, and we investigate computationally some possible improvements of our control strategy using a model of the yeast osmo-adaptation response fitted to our data.

Whole genome duplications and a 'function' for junk DNA? Facts and hypotheses.

BACKGROUND: The lack of correlation between genome size and organismal complexity is understood in terms of the massive presence of repetitive and non-coding DNA. This non-coding subgenome has long been called "junk" DNA. However, it might have important functions. Generation of junk DNA depends on proliferation of selfish DNA elements and on local or global DNA duplication followed by genic non-functionalization. METHODOLOGY/PRINCIPAL FINDINGS: Evidence from genomic analyses and experimental data indicates that Whole Genome Duplications (WGD) are often followed by a return to the diploid state, through DNA deletions and intra/interchromosomal rearrangements. We use simple theoretical models and simulations to explore how a WGD accompanied by sequence deletions might affect the dosage balance often required among several gene products involved in regulatory processes. We find that potential genomic deletions leading to changes in nuclear and cell volume might potentially perturb gene dosage balance. CONCLUSIONS/SIGNIFICANCE: The potentially negative impact of DNA deletions can be buffered if deleted genic DNA is, at least temporarily, replaced by repetitive DNA so that the nuclear/cell volume remains compatible with normal living. Thus, we speculate that retention of non-functionalized non-coding DNA, and replacement of deleted DNA through proliferation of selfish elements, might help avoid dosage imbalances in cycles of polyploidization and diploidization, which are particularly frequent in plants.

Analysis of a minimal model for p53 oscillations.

Oscillatory behaviours in genetic networks are important examples for studying the principles underlying the dynamics of cellular regulation. Recently the team of Alon has reported a surprisingly rich oscillatory response of the p53 tumor suppressor to irradiation stress et al. [Lahav, G., Rosenfeld, N., Sigal, A., Geva-Zatorsky, N., Levine, A.J., Elowitz, M.B., Alon, U., 2004. Dynamics of the p53-Mdm2 feedback loop in individual cells. Nat. Genet. 36 (2), 147-150; Geva-Zatorsky, N., Rosenfeld, N., Itzkovitz, S., Milo, R., Sigal, A., Dekel, E., Yarnitzky, T., Liron, Y., Polak, P., Lahav, G., Alon, U., 2006. Oscillations and variability in the p53 system. Mol. Syst. Biol. 2, 2006.0033]. Several models for this system have been proposed by different groups, based essentially on negative feedback loops. In this paper we investigate in detail oscillations and stability in a deterministic time delayed differential model of the core circuit for p53 expression. This model is representative of a class of modelling approaches of this system, based on a "minimal" set of well-established biomolecular regulations. Depending on the protein degradation rates we show the existence of bifurcations between a stable steady state and oscillations both in presence and absence of stress.

An evolutionary and functional assessment of regulatory network motifs.

BACKGROUND: Cellular functions are regulated by complex webs of interactions that might be schematically represented as networks. Two major examples are transcriptional regulatory networks, describing the interactions among transcription factors and their targets, and protein-protein interaction networks. Some patterns, dubbed motifs, have been found to be statistically over-represented when biological networks are compared to randomized versions thereof. Their function in vitro has been analyzed both experimentally and theoretically, but their functional role in vivo, that is, within the full network, and the resulting evolutionary pressures remain largely to be examined. RESULTS: We investigated an integrated network of the yeast Saccharomyces cerevisiae comprising transcriptional and protein-protein interaction data. A comparative analysis was performed with respect to Candida glabrata, Kluyveromyces lactis, Debaryomyces hansenii and Yarrowia lipolytica, which belong to the same class of hemiascomycetes as S. cerevisiae but span a broad evolutionary range. Phylogenetic profiles of genes within different forms of the motifs show that they are not subject to any particular evolutionary pressure to preserve the corresponding interaction patterns. The functional role in vivo of the motifs was examined for those instances where enough biological information is available. In each case, the regulatory processes for the biological function under consideration were found to hinge on post-transcriptional regulatory mechanisms, rather than on the transcriptional regulation by network motifs. CONCLUSION: The overabundance of the network motifs does not have any immediate functional or evolutionary counterpart. A likely reason is that motifs within the networks are not isolated, that is, they strongly aggregate and have important edge and/or node sharing with the rest of the network.