A segmentation clock patterns cellular differentiation in a bacterial biofilm.

Contrary to multicellular organisms that display segmentation during development, communities of unicellular organisms are believed to be devoid of such sophisticated patterning. Unexpectedly, we find that the gene expression underlying the nitrogen stress response of a developing Bacillus subtilis biofilm becomes organized into a ring-like pattern. Mathematical modeling and genetic probing of the underlying circuit indicate that this patterning is generated by a clock and wavefront mechanism, similar to that driving vertebrate somitogenesis. We experimentally validated this hypothesis by showing that predicted nutrient conditions can even lead to multiple concentric rings, resembling segments. We additionally confirmed that this patterning mechanism is driven by cell-autonomous oscillations. Importantly, we show that the clock and wavefront process also spatially patterns sporulation within the biofilm. Together, these findings reveal a biofilm segmentation clock that organizes cellular differentiation in space and time, thereby challenging the paradigm that such patterning mechanisms are exclusive to plant and animal development.

Magnesium Flux Modulates Ribosomes to Increase Bacterial Survival.

Bacteria exhibit cell-to-cell variability in their resilience to stress, for example, following antibiotic exposure. Higher resilience is typically ascribed to "dormant" non-growing cellular states. Here, by measuring membrane potential dynamics of Bacillus subtilis cells, we show that actively growing bacteria can cope with ribosome-targeting antibiotics through an alternative mechanism based on ion flux modulation. Specifically, we observed two types of cellular behavior: growth-defective cells exhibited a mathematically predicted transient increase in membrane potential (hyperpolarization), followed by cell death, whereas growing cells lacked hyperpolarization events and showed elevated survival. Using structural perturbations of the ribosome and proteomic analysis, we uncovered that stress resilience arises from magnesium influx, which prevents hyperpolarization. Thus, ion flux modulation provides a distinct mechanism to cope with ribosomal stress. These results suggest new approaches to increase the effectiveness of ribosome-targeting antibiotics and reveal an intriguing connection between ribosomes and the membrane potential, two fundamental properties of cells.

On time: developmental timing within and across species.

Organisms across species differ in the relative size and complexity of their tissues to serve the specific purposes of the host. Correct timing is a crucial ingredient in the development of tissues, as reaching the right size and complexity requires a careful balance between cellular proliferation and differentiation. Premature or delayed differentiation, for instance, can result in tissue imbalance, malformation or malfunction. Despite seemingly rigid constraints on development, however, there is flexibility in both the timing and differentiation trajectories within and between species. In this Spotlight, we discuss how time is measured and regulated in development, and question whether developmental timing is in fact different between species.

Multiscale networks in multiple sclerosis.

Complex diseases such as Multiple Sclerosis (MS) cover a wide range of biological scales, from genes and proteins to cells and tissues, up to the full organism. In fact, any phenotype for an organism is dictated by the interplay among these scales. We conducted a multilayer network analysis and deep phenotyping with multi-omics data (genomics, phosphoproteomics and cytomics), brain and retinal imaging, and clinical data, obtained from a multicenter prospective cohort of 328 patients and 90 healthy controls. Multilayer networks were constructed using mutual information for topological analysis, and Boolean simulations were constructed using Pearson correlation to identified paths within and among all layers. The path more commonly found from the Boolean simulations connects protein MK03, with total T cells, the thickness of the retinal nerve fiber layer (RNFL), and the walking speed. This path contains nodes involved in protein phosphorylation, glial cell differentiation, and regulation of stress-activated MAPK cascade, among others. Specific paths identified were subsequently analyzed by flow cytometry at the single-cell level. Combinations of several proteins (GSK3AB, HSBP1 or RS6) and immune cells (Th17, Th1 non-classic, CD8, CD8 Treg, CD56 neg, and B memory) were part of the paths explaining the clinical phenotype. The advantage of the path identified from the Boolean simulations is that it connects information about these known biological pathways with the layers at higher scales (retina damage and disability). Overall, the identified paths provide a means to connect the molecular aspects of MS with the overall phenotype.

A multiscale sensorimotor model of experience-dependent behavior in a minimal organism.

To survive in ever-changing environments, living organisms need to continuously combine the ongoing external inputs they receive, representing present conditions, with their dynamical internal state, which includes influences of past experiences. It is still unclear in general, however 1) how this happens at the molecular and cellular levels and 2) how the corresponding molecular and cellular processes are integrated with the behavioral responses of the organism. Here, we address these issues by modeling mathematically a particular behavioral paradigm in a minimal model organism, namely chemotaxis in the nematode C. elegans. Specifically, we use a long-standing collection of elegant experiments on salt chemotaxis in this animal, in which the migration direction varies depending on its previous experience. Our model integrates the molecular, cellular, and organismal levels to reproduce the experimentally observed experience-dependent behavior. The model proposes specific molecular mechanisms for the encoding of current conditions and past experiences in key neurons associated with this response, predicting the behavior of various mutants associated with those molecular circuits.

Shared Proteins and Pathways of Cardiovascular and Cognitive Diseases: Relation to Vascular Cognitive Impairment.

One of the primary goals of systems medicine is the detection of putative proteins and pathways involved in disease progression and pathological phenotypes. Vascular cognitive impairment (VCI) is a heterogeneous condition manifesting as cognitive impairment resulting from vascular factors. The precise mechanisms underlying this relationship remain unclear, which poses challenges for experimental research. Here, we applied computational approaches like systems biology to unveil and select relevant proteins and pathways related to VCI by studying the crosstalk between cardiovascular and cognitive diseases. In addition, we specifically included signals related to oxidative stress, a common etiologic factor tightly linked to aging, a major determinant of VCI. Our results show that pathways associated with oxidative stress are quite relevant, as most of the prioritized vascular cognitive genes and proteins were enriched in these pathways. Our analysis provided a short list of proteins that could be contributing to VCI: DOLK, TSC1, ATP1A1, MAPK14, YWHAZ, CREB3, HSPB1, PRDX6, and LMNA. Moreover, our experimental results suggest a high implication of glycative stress, generating oxidative processes and post-translational protein modifications through advanced glycation end-products (AGEs). We propose that these products interact with their specific receptors (RAGE) and Notch signaling to contribute to the etiology of VCI.

Complex spatiotemporal oscillations emerge from transverse instabilities in large-scale brain networks.

Spatiotemporal oscillations underlie all cognitive brain functions. Large-scale brain models, constrained by neuroimaging data, aim to trace the principles underlying such macroscopic neural activity from the intricate and multi-scale structure of the brain. Despite substantial progress in the field, many aspects about the mechanisms behind the onset of spatiotemporal neural dynamics are still unknown. In this work we establish a simple framework for the emergence of complex brain dynamics, including high-dimensional chaos and travelling waves. The model consists of a complex network of 90 brain regions, whose structural connectivity is obtained from tractography data. The activity of each brain area is governed by a Jansen neural mass model and we normalize the total input received by each node so it amounts the same across all brain areas. This assumption allows for the existence of an homogeneous invariant manifold, i.e., a set of different stationary and oscillatory states in which all nodes behave identically. Stability analysis of these homogeneous solutions unveils a transverse instability of the synchronized state, which gives rise to different types of spatiotemporal dynamics, such as chaotic alpha activity. Additionally, we illustrate the ubiquity of this route towards complex spatiotemporal activity in a network of next generation neural mass models. Altogehter, our results unveil the bifurcation landscape that underlies the emergence of function from structure in the brain.

Architecture-dependent noise discriminates functionally analogous differentiation circuits.

Gene regulatory circuits with different architectures (patterns of regulatory interactions) can generate similar dynamics. This raises the question of why a particular circuit architecture is selected to implement a given cellular process. To investigate this problem, we compared the Bacillus subtilis circuit that regulates differentiation into the competence state to an engineered circuit with an alternative architecture (SynEx) in silico and in vivo. Time-lapse microscopy measurements showed that SynEx cells generated competence dynamics similar to native cells and reconstituted the physiology of differentiation. However, architectural differences between the circuits altered the dynamic distribution of stochastic fluctuations (noise) during circuit operation. This distinction in noise causes functional differences between the circuits by selectively controlling the timing of competence episodes and response of the system to various DNA concentrations. These results reveal a tradeoff between temporal precision and physiological response range that is controlled by distinct noise characteristics of alternative circuit architectures.

Parametric modeling of mechanical effects on circadian oscillators.

Circadian rhythms are archetypal examples of nonlinear oscillations. While these oscillations are usually attributed to circuits of biochemical interactions among clock genes and proteins, recent experimental studies reveal that they are also affected by the cell's mechanical environment. Here, we extend a standard biochemical model of circadian rhythmicity to include mechanical effects in a parametric manner. Using experimental observations to constrain the model, we suggest specific ways in which the mechanical signal might affect the clock. Additionally, a bifurcation analysis of the system predicts that these mechanical signals need to be within an optimal range for circadian oscillations to occur.

Comparison between an exact and a heuristic neural mass model with second-order synapses.

Neural mass models (NMMs) are designed to reproduce the collective dynamics of neuronal populations. A common framework for NMMs assumes heuristically that the output firing rate of a neural population can be described by a static nonlinear transfer function (NMM1). However, a recent exact mean-field theory for quadratic integrate-and-fire (QIF) neurons challenges this view by showing that the mean firing rate is not a static function of the neuronal state but follows two coupled nonlinear differential equations (NMM2). Here we analyze and compare these two descriptions in the presence of second-order synaptic dynamics. First, we derive the mathematical equivalence between the two models in the infinitely slow synapse limit, i.e., we show that NMM1 is an approximation of NMM2 in this regime. Next, we evaluate the applicability of this limit in the context of realistic physiological parameter values by analyzing the dynamics of models with inhibitory or excitatory synapses. We show that NMM1 fails to reproduce important dynamical features of the exact model, such as the self-sustained oscillations of an inhibitory interneuron QIF network. Furthermore, in the exact model but not in the limit one, stimulation of a pyramidal cell population induces resonant oscillatory activity whose peak frequency and amplitude increase with the self-coupling gain and the external excitatory input. This may play a role in the enhanced response of densely connected networks to weak uniform inputs, such as the electric fields produced by noninvasive brain stimulation.

A Genome-Wide Functional Screen Identifies Enhancer and Protective Genes for Amyloid Beta-Peptide Toxicity.

Alzheimer's disease (AD) is known to be caused by amyloid ß-peptide (Aß) misfolded into ß-sheets, but this knowledge has not yet led to treatments to prevent AD. To identify novel molecular players in Aß toxicity, we carried out a genome-wide screen in Saccharomyces cerevisiae, using a library of 5154 gene knock-out strains expressing Aß1-42. We identified 81 mammalian orthologue genes that enhance Aß1-42 toxicity, while 157 were protective. Next, we performed interactome and text-mining studies to increase the number of genes and to identify the main cellular functions affected by Aß oligomers (oAß). We found that the most affected cellular functions were calcium regulation, protein translation and mitochondrial activity. We focused on SURF4, a protein that regulates the store-operated calcium channel (SOCE). An in vitro analysis using human neuroblastoma cells showed that SURF4 silencing induced higher intracellular calcium levels, while its overexpression decreased calcium entry. Furthermore, SURF4 silencing produced a significant reduction in cell death when cells were challenged with oAß1-42, whereas SURF4 overexpression induced Aß1-42 cytotoxicity. In summary, we identified new enhancer and protective activities for Aß toxicity and showed that SURF4 contributes to oAß1-42 neurotoxicity by decreasing SOCE activity.

Thalamocortical Spectral Transmission Relies on Balanced Input Strengths.

The thalamus is a key element of sensory transmission in the brain, as it gates and selects sensory streams through a modulation of its internal activity. A preponderant role in these functions is played by its internal activity in the alpha range ([8-14] Hz), but the mechanism underlying this process is not completely understood. In particular, how do thalamocortical connections convey stimulus driven information selectively over the back-ground of thalamic internally generated activity? Here we investigate this issue with a spiking network model of feedforward connectivity between thalamus and primary sensory cortex reproducing the local field potential of both areas. We found that in a feedforward network, thalamic oscillations in the alpha range do not entrain cortical activity for two reasons: (i) alpha range oscillations are weaker in neurons projecting to the cortex, (ii) the gamma resonance dynamics of cortical networks hampers oscillations over the 10-20 Hz range thus weakening alpha range oscillations. This latter mechanism depends on the balance of the strength of thalamocortical connections toward excitatory and inhibitory neurons in the cortex. Our results highlight the relevance of corticothalamic feedback to sustain alpha range oscillations and pave the way toward an integrated understanding of the sensory streams traveling between the periphery and the cortex.

Ion channels enable electrical communication in bacterial communities.

The study of bacterial ion channels has provided fundamental insights into the structural basis of neuronal signalling; however, the native role of ion channels in bacteria has remained elusive. Here we show that ion channels conduct long-range electrical signals within bacterial biofilm communities through spatially propagating waves of potassium. These waves result from a positive feedback loop, in which a metabolic trigger induces release of intracellular potassium, which in turn depolarizes neighbouring cells. Propagating through the biofilm, this wave of depolarization coordinates metabolic states among cells in the interior and periphery of the biofilm. Deletion of the potassium channel abolishes this response. As predicted by a mathematical model, we further show that spatial propagation can be hindered by specific genetic perturbations to potassium channel gating. Together, these results demonstrate a function for ion channels in bacterial biofilms, and provide a prokaryotic paradigm for active, long-range electrical signalling in cellular communities.

Metabolic co-dependence gives rise to collective oscillations within biofilms.

Cells that reside within a community can cooperate and also compete with each other for resources. It remains unclear how these opposing interactions are resolved at the population level. Here we investigate such an internal conflict within a microbial (Bacillus subtilis) biofilm community: cells in the biofilm periphery not only protect interior cells from external attack but also starve them through nutrient consumption. We discover that this conflict between protection and starvation is resolved through emergence of long-range metabolic co-dependence between peripheral and interior cells. As a result, biofilm growth halts periodically, increasing nutrient availability for the sheltered interior cells. We show that this collective oscillation in biofilm growth benefits the community in the event of a chemical attack. These findings indicate that oscillations support population-level conflict resolution by coordinating competing metabolic demands in space and time, suggesting new strategies to control biofilm growth.

Bistable emergence of oscillations in growing Bacillus subtilis biofilms.

Biofilm communities of Bacillus subtilis bacteria have recently been shown to exhibit collective growth-rate oscillations mediated by electrochemical signaling to cope with nutrient starvation. These oscillations emerge once the colony reaches a large enough number of cells. However, it remains unclear whether the amplitude of the oscillations, and thus their effectiveness, builds up over time gradually or if they can emerge instantly with a nonzero amplitude. Here we address this question by combining microfluidics-based time-lapse microscopy experiments with a minimal theoretical description of the system in the form of a delay-differential equation model. Analytical and numerical methods reveal that oscillations arise through a subcritical Hopf bifurcation, which enables instant high-amplitude oscillations. Consequently, the model predicts a bistable regime where an oscillating and a nonoscillating attractor coexist in phase space. We experimentally validate this prediction by showing that oscillations can be triggered by perturbing the media conditions, provided the biofilm size lies within an appropriate range. The model also predicts that the minimum size at which oscillations start decreases with stress, a fact that we also verify experimentally. Taken together, our results show that collective oscillations in cell populations can emerge suddenly with nonzero amplitude via a discontinuous transition.

Diversity of fate outcomes in cell pairs under lateral inhibition.

Cell fate determination by lateral inhibition via Notch/Delta signalling has been extensively studied. Most formalised models consider Notch/Delta interactions in fields of cells, with parameters that typically lead to symmetry breaking of signalling states between neighbouring cells, commonly resulting in salt-and-pepper fate patterns. Here, we consider the case of signalling between isolated cell pairs, and find that the bifurcation properties of a standard mathematical model of lateral inhibition can lead to stable symmetric signalling states. We apply this model to the adult intestinal stem cell (ISC) of Drosophila, the fate of which is stochastic but dependent on the Notch/Delta pathway. We observe a correlation between signalling state in cell pairs and their contact area. We interpret this behaviour in terms of the properties of our model in the presence of population variability in contact areas, which affects the effective signalling threshold of individual cells. Our results suggest that the dynamics of Notch/Delta signalling can contribute to explain stochasticity in stem cell fate decisions, and that the standard model for lateral inhibition can account for a wider range of developmental outcomes than previously considered.

Soft-wired long-term memory in a natural recurrent neuronal network.

Recurrent neuronal networks are known to be endowed with fading (short-term) memory, whereas long-term memory is usually considered to be hard-wired in the network connectivity via Hebbian learning, for instance. Here, we use the neuronal network of the roundworm C. elegans to show that recurrent architectures in living organisms can exhibit long-term memory without relying on specific hard-wired modules. We applied a genetic algorithm, using a binary genome that encodes for inhibitory-excitatory connectivity, to solve the unconstrained optimization problem of fitting the experimentally observed dynamics of the worm's neuronal network. Our results show that the network operates in a complex chaotic regime, as measured by the permutation entropy. In that complex regime, the response of the system to repeated presentations of a time-varying stimulus reveals a consistent behavior that can be interpreted as long-term memory. This memory is soft-wired, since it does not require structural changes in the network connectivity, but relies only on the system dynamics for encoding.

Dynamics and heterogeneity of brain damage in multiple sclerosis.

Multiple Sclerosis (MS) is an autoimmune disease driving inflammatory and degenerative processes that damage the central nervous system (CNS). However, it is not well understood how these events interact and evolve to evoke such a highly dynamic and heterogeneous disease. We established a hypothesis whereby the variability in the course of MS is driven by the very same pathogenic mechanisms responsible for the disease, the autoimmune attack on the CNS that leads to chronic inflammation, neuroaxonal degeneration and remyelination. We propose that each of these processes acts more or less severely and at different times in each of the clinical subgroups. To test this hypothesis, we developed a mathematical model that was constrained by experimental data (the expanded disability status scale [EDSS] time series) obtained from a retrospective longitudinal cohort of 66 MS patients with a long-term follow-up (up to 20 years). Moreover, we validated this model in a second prospective cohort of 120 MS patients with a three-year follow-up, for which EDSS data and brain volume time series were available. The clinical heterogeneity in the datasets was reduced by grouping the EDSS time series using an unsupervised clustering analysis. We found that by adjusting certain parameters, albeit within their biological range, the mathematical model reproduced the different disease courses, supporting the dynamic CNS damage hypothesis to explain MS heterogeneity. Our analysis suggests that the irreversible axon degeneration produced in the early stages of progressive MS is mainly due to the higher rate of myelinated axon degeneration, coupled to the lower capacity for remyelination. However, and in agreement with recent pathological studies, degeneration of chronically demyelinated axons is not a key feature that distinguishes this phenotype. Moreover, the model reveals that lower rates of axon degeneration and more rapid remyelination make relapsing MS more resilient than the progressive subtype. Therefore, our results support the hypothesis of a common pathogenesis for the different MS subtypes, even in the presence of genetic and environmental heterogeneity. Hence, MS can be considered as a single disease in which specific dynamics can provoke a variety of clinical outcomes in different patient groups. These results have important implications for the design of therapeutic interventions for MS at different stages of the disease.

Recurrence-based information processing in gene regulatory networks.

Cellular information processing is generally attributed to the complex networks of genes and proteins that regulate cell behavior. It is still unclear, however, what are the main features of those networks that allow a cell to encode and interpret its ever changing environment. Here, we address this question by studying the computational capabilities of the transcriptional regulatory networks of five evolutionary distant organisms. We identify in all cases a cyclic recurrent structure, formed by a small core of genes, that is essential for dynamical encoding and information integration. The recent history of the cell is projected nonlinearly into this recurrent reservoir of nodes, where it is encoded by its transient dynamics, while the rest of the network forms a readout layer devoted to decode and interpret the high-dimensional dynamical state of the recurrent core. In that way, gene regulatory networks act as echo-state networks that perform optimally in standard memory-demanding tasks, with most of their memory residing in the recurrent reservoir. The biological significance of these results is analyzed in the particular case of the bacterium Escherichia coli. Our work thus suggests that recurrent nonlinear dynamics is a key element for the processing of complex time-dependent information by cells.

Differentiating resting brain states using ordinal symbolic analysis.

Symbolic methods of analysis are valuable tools for investigating complex time-dependent signals. In particular, the ordinal method defines sequences of symbols according to the ordering in which values appear in a time series. This method has been shown to yield useful information, even when applied to signals with large noise contamination. Here, we use ordinal analysis to investigate the transition between eyes closed (EC) and eyes open (EO) resting states. We analyze two electroencephalography datasets (with 71 and 109 healthy subjects) with different recording conditions (sampling rates and the number of electrodes in the scalp). Using as diagnostic tools the permutation entropy, the entropy computed from symbolic transition probabilities, and an asymmetry coefficient (that measures the asymmetry of the likelihood of the transitions between symbols), we show that the ordinal analysis applied to the raw data distinguishes the two brain states. In both datasets, we find that, during the EC-EO transition, the EO state is characterized by higher entropies and lower asymmetry coefficient, as compared to the EC state. Our results thus show that these diagnostic tools have the potential for detecting and characterizing changes in time-evolving brain states.