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Cognitive disorders, including Down syndrome (DS), present significant morphological alterations in neuron architectural complexity. However, the relationship between neuromorphological alterations and impaired brain function is not fully understood. To address this gap, we propose a novel computational model that accounts for the observed cell deformations in DS. The model consists of a cross-sectional layer of the mouse motor cortex, composed of 3000 neurons. The network connectivity is obtained by accounting explicitly for two single-neuron morphological parameters: the mean dendritic tree radius and the spine density in excitatory pyramidal cells. We obtained these values by fitting reconstructed neuron data corresponding to three mouse models: wild-type (WT), transgenic (TgDyrk1A), and trisomic (Ts65Dn). Our findings reveal a dynamic interplay between pyramidal and fast-spiking interneurons leading to the emergence of gamma activity (∼40 Hz). In the DS models this gamma activity is diminished, corroborating experimental observations and validating our computational methodology. We further explore the impact of disrupted excitation-inhibition balance by mimicking the reduction recurrent inhibition present in DS. In this case, gamma power exhibits variable responses as a function of the external input to the network. Finally, we perform a numerical exploration of the morphological parameter space, unveiling the direct influence of each structural parameter on gamma frequency and power. Our research demonstrates a clear link between changes in morphology and the disruption of gamma oscillations in DS. This work underscores the potential of computational modeling to elucidate the relationship between neuron architecture and brain function, and ultimately improve our understanding of cognitive disorders.

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.

Summary: Individual cells exhibit substantial heterogeneity in protein abundance and activity, which is frequently reflected in broad distributions of fluorescently labeled reporters. Since all cellular components are intrinsically fluorescent to some extent, the observed distributions contain background noise that masks the natural heterogeneity of cellular populations. This limits our ability to characterize cell-fate decision processes that are key for development, immune response, tissue homeostasis, and many other biological functions. It is therefore important to separate the contributions from signal and noise in single-cell measurements. Addressing this issue rigorously requires deconvolving the noise distribution from the signal, but approaches in that direction are still limited. Here, we present a non-parametric Bayesian formalism that performs such a deconvolution efficiently on multidimensional measurements, providing unbiased estimates of the resulting confidence intervals. We use this approach to study the expression of the mesodermal transcription factor Brachyury in mouse embryonic stem cells undergoing differentiation.

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.

Summary: Quality control of offspring is important for the survival of cells. However, the mechanisms by which quality of offspring cells may be checked while running genetic programs of cellular differentiation remain unclear. Here we investigated quality control during sporulating in Bacillus subtilis by combining single-cell time-lapse microscopy, molecular biology, and mathematical modeling. Our results revealed that the quality control via premature germination is coupled with the electrical polarization of outer membranes of developing forespores. The forespores that accumulate fewer cations on their surface are more likely to be aborted. This charge accumulation enables the projection of multi-dimensional information about the external environment and morphological development of the forespore into one-dimensional information of cation accumulation. We thus present a paradigm of cellular regulation by bacterial electrical signaling. Moreover, based on the insight we gain, we propose an electrophysiology-based approach of reducing the yield and quality of Bacillus endospores. : Microbiology; Microbial Physiology; Bioinformatics; Mathematical Biosciences Subject Areas: Microbiology, Microbial Physiology, Bioinformatics, Mathematical Biosciences

Summary: Processing time-dependent information requires cells to quantify the duration of past regulatory events and program the time span of future signals. At the single-cell level, timer mechanisms can be implemented with genetic circuits. However, such systems are difficult to implement in single cells due to saturation in molecular components and stochasticity in the limited intracellular space. In contrast, multicellular implementations outsource some of the components of information-processing circuits to the extracellular space, potentially escaping these constraints. Here, we develop a theoretical framework, based on trilinear coordinate representation, to study the collective behavior of populations composed of three cell types under stationary conditions. This framework reveals that distributing different processes (in our case the production, detection and degradation of a time-encoding signal) across distinct strains enables the implementation of a multicellular timer. Our analysis also shows that the circuit can be easily tunable by varying the cellular composition of the consortium.

We sought to investigate differential phenotypic characteristics according to neutrophil counts, using a biostatistics approach in a large-cohort study from the Spanish Online Bronchiectasis Registry (RIBRON). The 1034 patients who met the inclusion criteria were clustered into two groups on the basis of their blood neutrophil levels. Using the Mann–Whitney U test to explore potential differences according to FACED and EFACED scores between the two groups, a neutrophil count of 4990 cells/µL yielded the most balanced cluster sizes: (1) above-threshold (n = 337) and (2) below-threshold (n = 697) groups. Patients above the threshold showed significantly worse lung function parameters and nutritional status, while systemic inflammation levels were higher than in the below-threshold patients. In the latter group, the proportions of patients with mild disease were greater, while a more severe disease was present in the above-threshold patients. According to the blood neutrophil counts using biostatistics analyses, two distinct clinical phenotypes of stable patients with non-CF bronchiectasis were defined. Patients falling into the above-threshold cluster were more severe. Severity was characterized by a significantly impaired lung function parameters and nutritional status, and greater systemic inflammation. Phenotypic profiles of bronchiectasis patients are well defined as a result of the cluster analysis of combined systemic and respiratory variables.

Precise control and maintenance of population size is fundamental for organismal development and homeostasis. The three cell types of the mammalian blastocyst are generated in precise proportions over a short time, suggesting a mechanism to ensure a reproducible outcome. We developed a minimal mathematical model demonstrating growth factor signaling is sufficient to guarantee this robustness and which anticipates an embryo's response to perturbations in lineage composition. Addition of lineage-restricted cells both in vivo and in silico, causes a shift of the fate of progenitors away from the supernumerary cell type, while eliminating cells using laser ablation biases the specification of progenitors toward the targeted cell type. Finally, FGF4 couples fate decisions to lineage composition through changes in local growth factor concentration, providing a basis for the regulative abilities of the early mammalian embryo whereby fate decisions are coordinated at the population level to robustly generate tissues in the right proportions.

Differential phenotypic characteristics using data mining approaches were defined in a large cohort of patients from the Spanish Online Bronchiectasis Registry (RIBRON). Three differential phenotypic clusters (hierarchical clustering, scikit-learn library for Python, and agglomerative methods) according to systemic biomarkers: neutrophil, eosinophil, and lymphocyte counts, C reactive protein, and hemoglobin were obtained in a patient large-cohort (n = 1092). Clusters #1–3 were named as mild, moderate, and severe on the basis of disease severity scores. Patients in cluster #3 were significantly more severe (FEV1, age, colonization, extension, dyspnea (FACED), exacerbation (EFACED), and bronchiectasis severity index (BSI) scores) than patients in clusters #1 and #2. Exacerbation and hospitalization numbers, Charlson index, and blood inflammatory markers were significantly greater in cluster #3 than in clusters #1 and #2. Chronic colonization by Pseudomonas aeruginosa and COPD prevalence were higher in cluster # 3 than in cluster #1. Airflow limitation and diffusion capacity were reduced in cluster #3 compared to clusters #1 and #2. Multivariate ordinal logistic regression analysis further confirmed these results. Similar results were obtained after excluding COPD patients. Clustering analysis offers a powerful tool to better characterize patients with bronchiectasis. These results have clinical implications in the management of the complexity and heterogeneity of bronchiectasis patients.

State Visual Evoked Potentials (SSVEPs) arise from a resonance phenomenon in the visual cortex that is produced by a repetitive visual stimulus. SSVEPs have long been considered a steady-state response resulting from purely oscillatory components phase locked with the stimulation source, matching the stimulation frequency and its harmonics. Here we explore the dynamical character of the SSVEP response by proposing a novel non-stationary methodology for SSVEP detection based on an ensemble of Echo State Networks (ESN). The performance of this dynamical approach is compared to stationary canonical correlation analysis (CCA) for the detection of 6 visual stimulation frequencies ranging from 12 to 22 Hz. ESN-based methodology outperformed CCA, achieving an average information transfer rate of 47 bits/minute when simulating a BCI system of 6 degrees of freedom. However, for some subjects and stimulation frequencies the detection accuracy of CCA exceeds that of ESN. The comparison suggests that each methodology captures different features of the SSVEP response: while CCA captures purely stationary patterns, the ESN-based approach presented here is capable of detecting the non-stationary nature of the SSVEP.

Data assimilation, defined as the fusion of data with preexisting knowledge, is particularly suited to elucidating underlying phenomena from noisy/insufficient observations. Although this approach has been widely used in diverse fields, only recently have efforts been directed to problems in neuroscience, using mainly intracranial data and thus limiting its applicability to invasive measurements involving electrode implants. Here we intend to apply data assimilation to non-invasive electroencephalography (EEG) measurements to infer brain states and their characteristics. For this purpose, we use Kalman filtering to combine synthetic EEG data with a coupled neural-mass model together with Ary's model of the head, which projects intracranial signals onto the scalp. Our results show that using several extracranial electrodes allows to successfully estimate the state and a specific parameter of the model, whereas one single electrode provides only a very partial and insufficient view of the system. The superiority of using multiple extracranial electrodes over using only one, be it intra- or extra-cranial, is shown in different dynamical behaviours. Our results show potential toward future clinical applications of the method.

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.

Abstract Pluripotency in embryonic stem cells is maintained through the activity of a small set of transcription factors centred around Oct4 and Nanog, which control the expression of ‘self‐renewal’ and ‘differentiation’ genes. Here, we combine single‐cell quantitative immunofluorescence microscopy and gene expression analysis, together with theoretical modelling, to investigate how the activity of those factors is regulated. We uncover a key role for post‐translational regulation in the maintenance of pluripotency, which complements the well‐established transcriptional regulatory layer. Specifically, we find that the activity of a network of protein complexes involving Nanog, Oct4, Tcf3, and β‐catenin suffices to account for the behavior of ES cells under different conditions. Our results suggest that the function of the network is to buffer the transcriptional activity of Oct4, which appears to be the main determinant to exit pluripotency. The protein network explains the mechanisms underlying the gain and loss of function in different mutants, and brings us closer to a full understanding of the molecular basis of pluripotency.

The thalamus is a key brain element in the processing of sensory information. During the sleep and awake states, this brain area is characterized by the presence of two distinct dynamical regimes: in the sleep state activity is dominated by spindle oscillations (7 - 15 Hz) weakly affected by external stimuli, while in the awake state the activity is primarily driven by external stimuli. Here we develop a simple and computationally efficient model of the thalamus that exhibits two dynamical regimes with different information-processing capabilities, and study the transition between them. The network model includes glutamatergic thalamocortical (TC) relay neurons and GABAergic reticular (RE) neurons described by adaptive integrate-and-fire models in which spikes are induced by either depolarization or hyperpolarization rebound. We found a range of connectivity conditions under which the thalamic network composed by these neurons displays the two aforementioned dynamical regimes. Our results show that TC-RE loops generate spindle-like oscillations and that a minimum level of clustering (i.e. local connectivity density) in the RE-RE connections is necessary for the coexistence of the two regimes. We also observe that the transition between the two regimes occurs when the external excitatory input on TC neurons (mimicking sensory stimulation) is large enough to cause a significant fraction of them to switch from hyperpolarization-rebound-driven firing to depolarization-driven firing. Overall, our model gives a novel and clear description of the role that the two types of neurons and their connectivity play in the dynamical regimes observed in the thalamus, and in the transition between them. These results pave the way for the development of efficient models of the transmission of sensory information from periphery to cortex.

Abstract Multipotent differentiation, where cells adopt one of several possible fates, occurs in diverse systems ranging from bacteria to mammals. This decision‐making process is driven by multiple differentiation programs that operate simultaneously in the cell. How these programs interact to govern cell fate choice is poorly understood. To investigate this issue, we simultaneously measured activities of the competing sporulation and competence programs in single Bacillus subtilis cells. This approach revealed that these competing differentiation programs progress independently without cross‐regulation before the decision point. Cells seem to arrive at a fate choice through differences in the relative timing between the two programs. To test this proposed dynamic mechanism, we altered the relative timing by engineering artificial cross‐regulation between the sporulation and competence circuits. Results suggest a simple model that does not require a checkpoint or intricate cross‐regulation before cellular decision‐making. Rather, cell fate choice appears to be the outcome of a ‘molecular race’ between differentiation programs that compete in time, providing a simple dynamic mechanism for decision‐making.

Neurons in the brain are known to operate under a careful balance of excitation and inhibition, which maintains neural microcircuits within the proper operational range. How this balance is played out at the mesoscopic level of neuronal populations is, however, less clear. In order to address this issue, here we use a coupled neural mass model to study computationally the dynamics of a network of cortical macrocolumns operating in a partially synchronized, irregular regime. The topology of the network is heterogeneous, with a few of the nodes acting as connector hubs while the rest are relatively poorly connected. Our results show that in this type of mesoscopic network excitation and inhibition spontaneously segregate, with some columns acting mainly in an excitatory manner while some others have predominantly an inhibitory effect on their neighbors. We characterize the conditions under which this segregation arises, and relate the character of the different columns with their topological role within the network. In particular, we show that the connector hubs are preferentially inhibitory, the more so the larger the node's connectivity. These results suggest a potential mesoscale organization of the excitation-inhibition balance in brain networks.

Synchronization between neuronal populations plays an important role in information transmission between brain areas. In particular, collective oscillations emerging from the synchronized activity of thousands of neurons can increase the functional connectivity between neural assemblies by coherently coordinating their phases. This synchrony of neuronal activity can take place within a cortical patch or between different cortical regions. While short-range interactions between neurons involve just a few milliseconds, communication through long-range projections between different regions could take up to tens of milliseconds. How these heterogeneous transmission delays affect communication between neuronal populations is not well known. To address this question, we have studied the dynamics of two bidirectionally delayed-coupled neuronal populations using conductance-based spiking models, examining how different synaptic delays give rise to in-phase/anti-phase transitions at particular frequencies within the gamma range, and how this behavior is related to the phase coherence between the two populations at different frequencies. We have used spectral analysis and information theory to quantify the information exchanged between the two networks. For different transmission delays between the two coupled populations, we analyze how the local field potential and multi-unit activity calculated from one population convey information in response to a set of external inputs applied to the other population. The results confirm that zero-lag synchronization maximizes information transmission, although out-of-phase synchronization allows for efficient communication provided the coupling delay, the phase lag between the populations, and the frequency of the oscillations are properly matched.

Cells must make reliable decisions under fluctuating extracellular conditions, but also be flexible enough to adapt to such changes. How cells reconcile these seemingly contradictory requirements through the dynamics of cellular decision-making is poorly understood. To study this issue we quantitatively measured gene expression and protein localization in single cells of the model organism Bacillus subtilis during the progression to spore formation. We found that sporulation proceeded through noisy and reversible steps towards an irreversible, all-or-none commitment point. Specifically, we observed cell-autonomous and spontaneous bursts of gene expression and transient protein localization events during sporulation. Based on these measurements we developed mathematical population models to investigate how the degree of reversibility affects cellular decision-making. In particular, we evaluated the effect of reversibility on the 1) reliability in the progression to sporulation, and 2) adaptability under changing extracellular stress conditions. Results show that reversible progression allows cells to remain responsive to long-term environmental fluctuations. In contrast, the irreversible commitment point supports reliable execution of cell fate choice that is robust against short-term reductions in stress. This combination of opposite dynamic behaviors (reversible and irreversible) thus maximizes both adaptable and reliable decision-making over a broad range of changes in environmental conditions. These results suggest that decision-making systems might employ a general hybrid strategy to cope with unpredictably fluctuating environmental conditions.

Developmental patterning requires juxtacrine signaling in order to tightly coordinate the fates of neighboring cells. Recent work has shown that Notch and Delta, the canonical metazoan juxtacrine signaling receptor and ligand, mutually inactivate each other in the same cell. This cis-interaction generates mutually exclusive sending and receiving states in individual cells. It generally remains unclear, however, how this mutual inactivation and the resulting switching behavior can impact developmental patterning circuits. Here we address this question using mathematical modeling in the context of two canonical pattern formation processes: boundary formation and lateral inhibition. For boundary formation, in a model motivated by Drosophila wing vein patterning, we find that mutual inactivation allows sharp boundary formation across a broader range of parameters than models lacking mutual inactivation. This model with mutual inactivation also exhibits robustness to correlated gene expression perturbations. For lateral inhibition, we find that mutual inactivation speeds up patterning dynamics, relieves the need for cooperative regulatory interactions, and expands the range of parameter values that permit pattern formation, compared to canonical models. Furthermore, mutual inactivation enables a simple lateral inhibition circuit architecture which requires only a single downstream regulatory step. Both model systems show how mutual inactivation can facilitate robust fine-grained patterning processes that would be difficult to implement without it, by encoding a difference-promoting feedback within the signaling system itself. Together, these results provide a framework for analysis of more complex Notch-dependent developmental systems.

Under conditions of nutrient limitation, Bacillus subtilis cells terminally differentiate into a dormant spore state. Progression to sporulation is controlled by a genetic circuit consisting of a phosphorelay embedded in multiple transcriptional feedback loops, which is used to activate the master regulator Spo0A by phosphorylation. These transcriptional regulatory interactions are "bandpass"-like, in the sense that activation occurs within a limited band of Spo0A∼P concentrations. Additionally, recent results show that the phosphorelay activation occurs in pulses, in a cell-cycle dependent fashion. However, the impact of these pulsed bandpass interactions on the circuit dynamics preceding sporulation remains unclear. In order to address this question, we measured key features of the bandpass interactions at the single-cell level and analyzed them in the context of a simple mathematical model. The model predicted the emergence of a delayed phase shift between the pulsing activity of the different sporulation genes, as well as the existence of a stable state, with elevated Spo0A activity but no sporulation, embedded within the dynamical structure of the system. To test the model, we used time-lapse fluorescence microscopy to measure dynamics of single cells initiating sporulation. We observed the delayed phase shift emerging during the progression to sporulation, while a re-engineering of the sporulation circuit revealed behavior resembling the predicted additional state. These results show that periodically-driven bandpass feedback loops can give rise to complex dynamics in the progression towards sporulation.

There is evidence that pluripotency of mouse embryonic stem (ES) cells is associated with the activity of a network of transcription factors with Sox2, Oct4, and Nanog at the core. Using fluorescent reporters for the expression of Nanog, we observed that a population of ES cells is best described by a dynamic distribution of Nanog expression characterized by two peaks defined by high (HN) and low (LN) Nanog expression. Typically, the LN state is 5%-20% of the total population, depending on the culture conditions. Modelling of the activity of Nanog reveals that a simple network of Oct4/Sox2 and Nanog activity can account for the observed distribution and its properties as long as the transcriptional activity is tuned by transcriptional noise. The model also predicts that the LN state is unstable, something that is born out experimentally. While in this state, cells can differentiate. We suggest that transcriptional fluctuations in Nanog expression are an essential element of the pluripotent state and that the function of Sox2, Oct4, and Nanog is to act as a network that promotes and maintains transcriptional noise to interfere with the differentiation signals.

Coupling frequently enhances noise-induced coherence and synchronization in interacting nonlinear systems, but it does so separately. In principle collective stochastic coherence and synchronizability are incompatible phenomena, since strongly synchronized elements behave identically and thus their response to noise is indistinguishable to that of a single element. Therefore one can expect systems that synchronize well to have a poor collective response to noise. Here we show that, in spite of this apparent conflict, a certain coupling architecture is able to reconcile the two properties. Specifically, our results reveal that weighted scale-free networks of diffusively coupled excitable elements exhibit both high synchronizability of their subthreshold dynamics and a good collective response to noise of their pulsed dynamics. This is established by comparing the behavior of this system to that of random, regular, and unweighted scale-free networks. We attribute the optimal response of weighted scale-free networks to a balance between degree heterogeneity, which ensures a good collective response to noise, and the coupling-strength weighting procedure, which overcomes the paradox of heterogeneity that would otherwise impair synchronization.