An Adaptive Generalized Leaky Integrate-and-Fire Model for Hippocampal CA1 Pyramidal Neurons and Interneurons.

Full-scale morphologically and biophysically realistic model networks, aiming at modeling multiple brain areas, provide an invaluable tool to make significant scientific advances from in-silico experiments on cognitive functions to digital twin implementations. Due to the current technical limitations of supercomputer systems in terms of computational power and memory requirements, these networks must be implemented using (at least) simplified neurons. A class of models which achieve a reasonable compromise between accuracy and computational efficiency is given by generalized leaky integrate-and fire models complemented by suitable initial and update conditions. However, we found that these models cannot reproduce the complex and highly variable firing dynamics exhibited by neurons in several brain regions, such as the hippocampus. In this work, we propose an adaptive generalized leaky integrate-and-fire model for hippocampal CA1 neurons and interneurons, in which the nonlinear nature of the firing dynamics is successfully reproduced by linear ordinary differential equations equipped with nonlinear and more realistic initial and update conditions after each spike event, which strictly depends on the external stimulation current. A mathematical analysis of the equilibria stability as well as the monotonicity properties of the analytical solution for the membrane potential allowed (i) to determine general constraints on model parameters, reducing the computational cost of an optimization procedure based on spike times in response to a set of constant currents injections; (ii) to identify additional constraints to quantitatively reproduce and predict the experimental traces from 85 neurons and interneurons in response to any stimulation protocol using constant and piecewise constant current injections. Finally, this approach allows to easily implement a procedure to create infinite copies of neurons with mathematically controlled firing properties, statistically indistinguishable from experiments, to better reproduce the full range and variability of the firing scenarios observed in a real network.

A mathematical approach to study and forecast racial groups interactions: deterministic modeling and scenario method.

Globalization and migratory fluxes are increasing the ethnic and racial diversity within many countries. Therefore, describing social dynamics requires models that are apt to capture multi-groups interactions. Building on the assumption of a relationship between multi-racial dynamics and socioeconomic status (SES), we introduce an aggregate, contextual, and continuous index of SES accounting for measures of income, employment, expected life, and group numerosity. After, taking into account that groups' SES assumes the form of a logit model, we propose a Lotka-Volterra system to study and forecast the interaction among racial groups. Last, we apply our methodology to describe the racial dynamics in the US society. In particular, we study the kind and the intensity of Asians-Blacks-Natives-Whites interactions in the US between 2002 and 2013. Moreover, we forecast the evolution of groups' SES and how interracial relations will unfold between 2013 and 2018 and in three alternative stylized scenarios.

Weathering of a Roman Mosaic-A Biological and Quantitative Study on In Vitro Colonization of Calcareous Tesserae by Phototrophic Microorganisms.

The potential impact of cyanobacteria and microalgae on the weathering of calcareous tesserae from a Roman mosaic of the II Century CE has been followed through in vitro experiments. Laboratory tests were carried out by inoculating mosaic tiles with single strains of Cyanobacteria or Chlorophyta to evaluate the roles of pioneer phototrophic microrganism on the resulting architecture of biofilms. The interaction between tesserae and strains was assessed at the whole substratum and micrometer scales, by image analysis and Confocal Laser Scanning (CLS) microscopy, respectively. The biofilm surface coverage on each tessera varied from 19% (Fischerella ambigua) to 97% (Microcoleus autumnalis). Cyanobacteria showed a better growth on calcareous tesserae, whereas the only green alga attaining a superficial coverage higher than 50% was Coelastrella rubescens. CLS microscopy evidenced two different types of spatial arrangement of the phototrophic organisms on the tesserae, that were defined as compact or porous, respectively. In the first one was measured a reduced number of empty spaces between cells or filaments, whereas in the second type, a reticulate texture allowed the presence of numerous empty volumes. The colonization processes observed are an intrinsic characteristic of each strain. We have proposed a colonization index IC as a sensible tool to describe, in a quantitative way, the pioneering attitude of each photosynthetic microorganism to colonize lithic substrates under laboratory conditions.

Glomerular and Mitral-Granule Cell Microcircuits Coordinate Temporal and Spatial Information Processing in the Olfactory Bulb.

The olfactory bulb processes inputs from olfactory receptor neurons (ORNs) through two levels: the glomerular layer at the site of input, and the granule cell level at the site of output to the olfactory cortex. The sequence of action of these two levels has not yet been examined. We analyze this issue using a novel computational framework that is scaled up, in three-dimensions (3D), with realistic representations of the interactions between layers, activated by simulated natural odors, and constrained by experimental and theoretical analyses. We suggest that the postulated functions of glomerular circuits have as their primary role transforming a complex and disorganized input into a contrast-enhanced and normalized representation, but cannot provide for synchronization of the distributed glomerular outputs. By contrast, at the granule cell layer, the dendrodendritic interactions mediate temporal decorrelation, which we show is dependent on the preceding contrast enhancement by the glomerular layer. The results provide the first insights into the successive operations in the olfactory bulb, and demonstrate the significance of the modular organization around glomeruli. This layered organization is especially important for natural odor inputs, because they activate many overlapping glomeruli.

Predicting the response of olfactory sensory neurons to odor mixtures from single odor response.

The response of olfactory receptor neurons to odor mixtures is not well understood. Here, using experimental constraints, we investigate the mathematical structure of the odor response space and its consequences. The analysis suggests that the odor response space is 3-dimensional, and predicts that the dose-response curve of an odor receptor can be obtained, in most cases, from three primary components with specific properties. This opens the way to an objective procedure to obtain specific olfactory receptor responses by manipulating mixtures in a mathematically predictable manner. This result is general and applies, independently of the number of odor components, to any olfactory sensory neuron type with a response curve that can be represented as a sigmoidal function of the odor concentration.

Synaptic clusters function as odor operators in the olfactory bulb.

How the olfactory bulb organizes and processes odor inputs through fundamental operations of its microcircuits is largely unknown. To gain new insight we focus on odor-activated synaptic clusters related to individual glomeruli, which we call glomerular units. Using a 3D model of mitral and granule cell interactions supported by experimental findings, combined with a matrix-based representation of glomerular operations, we identify the mechanisms for forming one or more glomerular units in response to a given odor, how and to what extent the glomerular units interfere or interact with each other during learning, their computational role within the olfactory bulb microcircuit, and how their actions can be formalized into a theoretical framework in which the olfactory bulb can be considered to contain "odor operators" unique to each individual. The results provide new and specific theoretical and experimentally testable predictions.

Vegetation pattern formation due to interactions between water availability and toxicity in plant-soil feedback.

Development of a comprehensive theory of the formation of vegetation patterns is still in progress. A prevailing view is to treat water availability as the main causal factor for the emergence of vegetation patterns. While successful in capturing the occurrence of multiple vegetation patterns in arid and semiarid regions, this hypothesis fails to explain the presence of vegetation patterns in humid environments. We explore the rich structure of a toxicity-mediated model of the vegetation pattern formation. This model consists of three PDEs accounting for a dynamic balance between biomass, water, and toxic compounds. Different (ecologically feasible) regions of the model's parameter space give rise to stable spatial vegetation patterns in Turing and non-Turing regimes. Strong negative feedback gives rise to dynamic spatial patterns that continuously move in space while retaining their stable topology.

Using Strahler's analysis to reduce up to 200-fold the run time of realistic neuron models.

The cellular mechanisms underlying higher brain functions/dysfunctions are extremely difficult to investigate experimentally, and detailed neuron models have proven to be a very useful tool to help these kind of investigations. However, realistic neuronal networks of sizes appropriate to study brain functions present the major problem of requiring a prohibitively high computational resources. Here, building on our previous work, we present a general reduction method based on Strahler's analysis of neuron morphologies. We show that, without any fitting or tuning procedures, it is possible to map any morphologically and biophysically accurate neuron model into an equivalent reduced version. Using this method for Purkinje cells, we demonstrate how run times can be reduced up to 200-fold, while accurately taking into account the effects of arbitrarily located and activated synaptic inputs.

Fast and accurate low-dimensional reduction of biophysically detailed neuron models.

Realistic modeling of neurons are quite successful in complementing traditional experimental techniques. However, their networks require a computational power beyond the capabilities of current supercomputers, and the methods used so far to reduce their complexity do not take into account the key features of the cells nor critical physiological properties. Here we introduce a new, automatic and fast method to map realistic neurons into equivalent reduced models running up to > 40 times faster while maintaining a very high accuracy of the membrane potential dynamics during synaptic inputs, and a direct link with experimental observables. The mapping of arbitrary sets of synaptic inputs, without additional fine tuning, would also allow the convenient and efficient implementation of a new generation of large-scale simulations of brain regions reproducing the biological variability observed in real neurons, with unprecedented advances to understand higher brain functions.

Negative plant soil feedback explaining ring formation in clonal plants.

Ring shaped patches of clonal plants have been reported in different environments, but the mechanisms underlying such pattern formation are still poorly explained. Water depletion in the inner tussocks zone has been proposed as a possible cause, although ring patterns have been also observed in ecosystems without limiting water conditions. In this work, a spatially explicit model is presented in order to investigate the role of negative plant-soil feedback as an additional explanation for ring formation. The model describes the dynamics of the plant biomass in the presence of toxicity produced by the decomposition of accumulated litter in the soil. Our model qualitatively reproduces the emergence of ring patterns of a single clonal plant species during colonisation of a bare substrate. The model admits two homogeneous stationary solutions representing bare soil and uniform vegetation cover which depend only on the ratio between the biomass death and growth rates. Moreover, differently from other plant spatial patterns models, but in agreement with real field observations of vegetation dynamics, we demonstrated that the pattern dynamics always lead to spatially homogeneous vegetation covers without creation of stable Turing patterns. Analytical results show that ring formation is a function of two main components, the plant specific susceptibility to toxic compounds released in the soil by the accumulated litter and the decay rate of these same compounds, depending on environmental conditions. These components act at the same time and their respective intensities can give rise to the different ring structures observed in nature, ranging from slight reductions of biomass in patch centres, to the appearance of marked rings with bare inner zones, as well as the occurrence of ephemeral waves of plant cover. Our results highlight the potential role of plant-soil negative feedback depending on decomposition processes for the development of transient vegetation patterns.

On the mechanisms underlying the depolarization block in the spiking dynamics of CA1 pyramidal neurons.

Under sustained input current of increasing strength neurons eventually stop firing, entering a depolarization block. This is a robust effect that is not usually explored in experiments or explicitly implemented or tested in models. However, the range of current strength needed for a depolarization block could be easily reached with a random background activity of only a few hundred excitatory synapses. Depolarization block may thus be an important property of neurons that should be better characterized in experiments and explicitly taken into account in models at all implementation scales. Here we analyze the spiking dynamics of CA1 pyramidal neuron models using the same set of ionic currents on both an accurate morphological reconstruction and on its reduction to a single-compartment. The results show the specific ion channel properties and kinetics that are needed to reproduce the experimental findings, and how their interplay can drastically modulate the neuronal dynamics and the input current range leading to a depolarization block. We suggest that this can be one of the rate-limiting mechanisms protecting a CA1 neuron from excessive spiking activity.