Lactate supply overtakes glucose when neural computational and cognitive loads scale up.

Neural computational power is determined by neuroenergetics, but how and which energy substrates are allocated to various forms of memory engram is unclear. To solve this question, we asked whether neuronal fueling by glucose or lactate scales differently upon increasing neural computation and cognitive loads. Here, using electrophysiology, two-photon imaging, cognitive tasks, and mathematical modeling, we show that both glucose and lactate are involved in engram formation, with lactate supporting long-term synaptic plasticity evoked by high-stimulation load activity patterns and high attentional load in cognitive tasks and glucose being sufficient for less demanding neural computation and learning tasks. Indeed, we show that lactate is mandatory for demanding neural computation, such as theta-burst stimulation, while glucose is sufficient for lighter forms of activity-dependent long-term potentiation (LTP), such as spike timing-dependent plasticity (STDP). We find that subtle variations of spike number or frequency in STDP are sufficient to shift the on-demand fueling from glucose to lactate. Finally, we demonstrate that lactate is necessary for a cognitive task requiring high attentional load, such as the object-in-place task, and for the corresponding in vivo hippocampal LTP expression but is not needed for a less demanding task, such as a simple novel object recognition. Overall, these results demonstrate that glucose and lactate metabolism are differentially engaged in neuronal fueling depending on the complexity of the activity-dependent plasticity and behavior.

A coupled neural field model for the standard consolidation theory.

The standard consolidation theory states that short-term memories located in the hippocampus enable the consolidation of long-term memories in the neocortex. In other words, the neocortex slowly learns long-term memories with a transient support of the hippocampus that quickly learns unstable memories. However, it is not clear yet what could be the neurobiological mechanisms underlying these differences in learning rates and memory time-scales. Here, we propose a novel modeling approach of the standard consolidation theory, that focuses on its potential neurobiological mechanisms. In addition to synaptic plasticity and spike frequency adaptation, our model incorporates adult neurogenesis in the dentate gyrus as well as the difference in size between the neocortex and the hippocampus, that we associate with distance-dependent synaptic plasticity. We also take into account the interconnected spatial structure of the involved brain areas, by incorporating the above neurobiological mechanisms in a coupled neural field framework, where each area is represented by a separate neural field with intra- and inter-area connections. To our knowledge, this is the first attempt to apply neural fields to this process. Using numerical simulations and mathematical analysis, we explore the short-term and long-term dynamics of the model upon alternance of phases of hippocampal replay and retrieval cue of an external input. This external input is encodable as a memory pattern in the form of a multiple bump attractor pattern in the individual neural fields. In the model, hippocampal memory patterns become encoded first, before neocortical ones, because of the smaller distances between the bumps of the hippocampal memory patterns. As a result, retrieval of the input pattern in the neocortex at short time-scales necessitates the additional input delivered by the memory pattern of the hippocampus. Neocortical memory patterns progressively consolidate at longer times, up to a point where their retrieval does not need the support of the hippocampus anymore. At longer times, perturbation of the hippocampal neural fields by neurogenesis erases the hippocampus pattern, leading to a final state where the memory pattern is exclusively evoked in the neocortex. Therefore, the dynamics of our model successfully reproduces the main features of the standard consolidation theory. This suggests that neurogenesis in the hippocampus and distance-dependent synaptic plasticity coupled to synaptic depression and spike frequency adaptation, are indeed critical neurobiological processes in memory consolidation.

Astroglial Kir4.1 in the lateral habenula drives neuronal bursts in depression.

Enhanced bursting activity of neurons in the lateral habenula (LHb) is essential in driving depression-like behaviours, but the cause of this increase has been unknown. Here, using a high-throughput quantitative proteomic screen, we show that an astroglial potassium channel (Kir4.1) is upregulated in the LHb in rat models of depression. Kir4.1 in the LHb shows a distinct pattern of expression on astrocytic membrane processes that wrap tightly around the neuronal soma. Electrophysiology and modelling data show that the level of Kir4.1 on astrocytes tightly regulates the degree of membrane hyperpolarization and the amount of bursting activity of LHb neurons. Astrocyte-specific gain and loss of Kir4.1 in the LHb bidirectionally regulates neuronal bursting and depression-like symptoms. Together, these results show that a glia-neuron interaction at the perisomatic space of LHb is involved in setting the neuronal firing mode in models of a major psychiatric disease. Kir4.1 in the LHb might have potential as a target for treating clinical depression.

Quantifying membrane binding and diffusion with fluorescence correlation spectroscopy diffusion laws.

Many transient processes in cells arise from the binding of cytosolic proteins to membranes. Quantifying this membrane binding and its associated diffusion in the living cell is therefore of primary importance. Dynamic photonic microscopies, e.g., single/multiple particle tracking, fluorescence recovery after photobleaching, and fluorescence correlation spectroscopy (FCS), enable non-invasive measurement of molecular mobility in living cells and their plasma membranes. However, FCS with a single beam waist is of limited applicability with complex, non-Brownian, motions. Recently, the development of FCS diffusion laws methods has given access to the characterization of these complex motions, although none of them is applicable to the membrane binding case at the moment. In this study, we combined computer simulations and FCS experiments to propose an FCS diffusion law for membrane binding. First, we generated computer simulations of spot-variation FCS (svFCS) measurements for a membrane binding process combined to 2D and 3D diffusion at the membrane and in the bulk/cytosol, respectively. Then, using these simulations as a learning set, we derived an empirical diffusion law with three free parameters: the apparent binding constant KD, the diffusion coefficient on the membrane D2D, and the diffusion coefficient in the cytosol, D3D. Finally, we monitored, using svFCS, the dynamics of retroviral Gag proteins and associated mutants during their binding to supported lipid bilayers of different lipid composition or at plasma membranes of living cells, and we quantified KD and D2D in these conditions using our empirical diffusion law. Based on these experiments and numerical simulations, we conclude that this new approach enables correct estimation of membrane partitioning and membrane diffusion properties (KD and D2D) for peripheral membrane molecules.

Modelling the modulation of cortical Up-Down state switching by astrocytes.

Up-Down synchronization in neuronal networks refers to spontaneous switches between periods of high collective firing activity (Up state) and periods of silence (Down state). Recent experimental reports have shown that astrocytes can control the emergence of such Up-Down regimes in neural networks, although the molecular or cellular mechanisms that are involved are still uncertain. Here we propose neural network models made of three populations of cells: excitatory neurons, inhibitory neurons and astrocytes, interconnected by synaptic and gliotransmission events, to explore how astrocytes can control this phenomenon. The presence of astrocytes in the models is indeed observed to promote the emergence of Up-Down regimes with realistic characteristics. Our models show that the difference of signalling timescales between astrocytes and neurons (seconds versus milliseconds) can induce a regime where the frequency of gliotransmission events released by the astrocytes does not synchronize with the Up and Down phases of the neurons, but remains essentially stable. However, these gliotransmission events are found to change the localization of the bifurcations in the parameter space so that with the addition of astrocytes, the network enters a bistability region of the dynamics that corresponds to Up-Down synchronization. Taken together, our work provides a theoretical framework to test scenarios and hypotheses on the modulation of Up-Down dynamics by gliotransmission from astrocytes.

Control of Ca2+ signals by astrocyte nanoscale morphology at tripartite synapses.

Much of the Ca2+ activity in astrocytes is spatially restricted to microdomains and occurs in fine processes that form a complex anatomical meshwork, the so-called spongiform domain. A growing body of literature indicates that those astrocytic Ca2+ signals can influence the activity of neuronal synapses and thus tune the flow of information through neuronal circuits. Because of technical difficulties in accessing the small spatial scale involved, the role of astrocyte morphology on Ca2+ microdomain activity remains poorly understood. Here, we use computational tools and idealized 3D geometries of fine processes based on recent super-resolution microscopy data to investigate the mechanistic link between astrocytic nanoscale morphology and local Ca2+ activity. Simulations demonstrate that the nano-morphology of astrocytic processes powerfully shapes the spatio-temporal properties of Ca2+ signals and promotes local Ca2+ activity. The model predicts that this effect is attenuated upon astrocytic swelling, hallmark of brain diseases, which we confirm experimentally in hypo-osmotic conditions. Upon repeated neurotransmitter release events, the model predicts that swelling hinders astrocytic signal propagation. Overall, this study highlights the influence of the complex morphology of astrocytes at the nanoscale and its remodeling in pathological conditions on neuron-astrocyte communication at so-called tripartite synapses, where astrocytic processes come into close contact with pre- and postsynaptic structures.

BDNF Controls Bidirectional Endocannabinoid Plasticity at Corticostriatal Synapses.

The dorsal striatum exhibits bidirectional corticostriatal synaptic plasticity, NMDAR and endocannabinoids (eCB) mediated, necessary for the encoding of procedural learning. Therefore, characterizing factors controlling corticostriatal plasticity is of crucial importance. Brain-derived neurotrophic factor (BDNF) and its receptor, the tropomyosine receptor kinase-B (TrkB), shape striatal functions, and their dysfunction deeply affects basal ganglia. BDNF/TrkB signaling controls NMDAR plasticity in various brain structures including the striatum. However, despite cross-talk between BDNF and eCBs, the role of BDNF in eCB plasticity remains unknown. Here, we show that BDNF/TrkB signaling promotes eCB-plasticity (LTD and LTP) induced by rate-based (low-frequency stimulation) or spike-timing-based (spike-timing-dependent plasticity, STDP) paradigm in striatum. We show that TrkB activation is required for the expression and the scaling of both eCB-LTD and eCB-LTP. Using 2-photon imaging of dendritic spines combined with patch-clamp recordings, we show that TrkB activation prolongs intracellular calcium transients, thus increasing eCB synthesis and release. We provide a mathematical model for the dynamics of the signaling pathways involved in corticostriatal plasticity. Finally, we show that TrkB activation enlarges the domain of expression of eCB-STDP. Our results reveal a novel role for BDNF/TrkB signaling in governing eCB-plasticity expression in striatum and thus the engram of procedural learning.

Simulation of calcium signaling in fine astrocytic processes: Effect of spatial properties on spontaneous activity.

Astrocytes, a glial cell type of the central nervous system, have emerged as detectors and regulators of neuronal information processing. Astrocyte excitability resides in transient variations of free cytosolic calcium concentration over a range of temporal and spatial scales, from sub-microdomains to waves propagating throughout the cell. Despite extensive experimental approaches, it is not clear how these signals are transmitted to and integrated within an astrocyte. The localization of the main molecular actors and the geometry of the system, including the spatial organization of calcium channels IP3R, are deemed essential. However, as most calcium signals occur in astrocytic ramifications that are too fine to be resolved by conventional light microscopy, most of those spatial data are unknown and computational modeling remains the only methodology to study this issue. Here, we propose an IP3R-mediated calcium signaling model for dynamics in such small sub-cellular volumes. To account for the expected stochasticity and low copy numbers, our model is both spatially explicit and particle-based. Extensive simulations show that spontaneous calcium signals arise in the model via the interplay between excitability and stochasticity. The model reproduces the main forms of calcium signals and indicates that their frequency crucially depends on the spatial organization of the IP3R channels. Importantly, we show that two processes expressing exactly the same calcium channels can display different types of calcium signals depending on the spatial organization of the channels. Our model with realistic process volume and calcium concentrations successfully reproduces spontaneous calcium signals that we measured in calcium micro-domains with confocal microscopy and predicts that local variations of calcium indicators might contribute to the diversity of calcium signals observed in astrocytes. To our knowledge, this model is the first model suited to investigate calcium dynamics in fine astrocytic processes and to propose plausible mechanisms responsible for their variability.

Endocannabinoids mediate bidirectional striatal spike-timing-dependent plasticity.

KEY POINTS: Although learning can arise from few or even a single trial, synaptic plasticity is commonly assessed under prolonged activation. Here, we explored the existence of rapid responsiveness of synaptic plasticity at corticostriatal synapses in a major synaptic learning rule, spike-timing-dependent plasticity (STDP). We found that spike-timing-dependent depression (tLTD) progressively disappears when the number of paired stimulations (below 50 pairings) is decreased whereas spike-timing-dependent potentiation (tLTP) displays a biphasic profile: tLTP is observed for 75-100 pairings, is absent for 25-50 pairings and re-emerges for 5-10 pairings. This tLTP induced by low numbers of pairings (5-10) depends on activation of the endocannabinoid system, type-1 cannabinoid receptor and the transient receptor potential vanilloid type-1. Endocannabinoid-tLTP may represent a physiological mechanism operating during the rapid learning of new associative memories and behavioural rules characterizing the flexible behaviour of mammals or during the initial stages of habit learning. ABSTRACT: Synaptic plasticity, a main substrate for learning and memory, is commonly assessed with prolonged stimulations. Since learning can arise from few or even a single trial, synaptic strength is expected to adapt rapidly. However, whether synaptic plasticity occurs in response to limited event occurrences remains elusive. To answer this question, we investigated whether a low number of paired stimulations can induce plasticity in a major synaptic learning rule, spike-timing-dependent plasticity (STDP). It is known that 100 pairings induce bidirectional STDP, i.e. spike-timing-dependent potentiation (tLTP) and depression (tLTD) at most central synapses. In rodent striatum, we found that tLTD progressively disappears when the number of paired stimulations is decreased (below 50 pairings) whereas tLTP displays a biphasic profile: tLTP is observed for 75-100 pairings, absent for 25-50 pairings and re-emerges for 5-10 pairings. This tLTP, induced by very few pairings (∼5-10) depends on the endocannabinoid (eCB) system. This eCB-dependent tLTP (eCB-tLTP) involves postsynaptic endocannabinoid synthesis, requires paired activity (post- and presynaptic) and the activation of type-1 cannabinoid receptor (CB1R) and transient receptor potential vanilloid type-1 (TRPV1). eCB-tLTP occurs in both striatopallidal and striatonigral medium-sized spiny neurons (MSNs) and is dopamine dependent. Lastly, we show that eCB-LTP and eCB-LTD can be induced sequentially in the same neuron, depending on the cellular conditioning protocol. Thus, while endocannabinoids are usually thought simply to depress synaptic function, they also constitute a versatile system underlying bidirectional plasticity. Our results reveal a novel form of synaptic plasticity, eCB-tLTP, which may underlie rapid learning capabilities characterizing behavioural flexibility.

Glutamate mediated astrocytic filtering of neuronal activity.

Neuron-astrocyte communication is an important regulatory mechanism in various brain functions but its complexity and role are yet to be fully understood. In particular, the temporal pattern of astrocyte response to neuronal firing has not been fully characterized. Here, we used neuron-astrocyte cultures on multi-electrode arrays coupled to Ca2+ imaging and explored the range of neuronal stimulation frequencies while keeping constant the amount of stimulation. Our results reveal that astrocytes specifically respond to the frequency of neuronal stimulation by intracellular Ca2+ transients, with a clear onset of astrocytic activation at neuron firing rates around 3-5 Hz. The cell-to-cell heterogeneity of the astrocyte Ca2+ response was however large and increasing with stimulation frequency. Astrocytic activation by neurons was abolished with antagonists of type I metabotropic glutamate receptor, validating the glutamate-dependence of this neuron-to-astrocyte pathway. Using a realistic biophysical model of glutamate-based intracellular calcium signaling in astrocytes, we suggest that the stepwise response is due to the supralinear dynamics of intracellular IP3 and that the heterogeneity of the responses may be due to the heterogeneity of the astrocyte-to-astrocyte couplings via gap junction channels. Therefore our results present astrocyte intracellular Ca2+ activity as a nonlinear integrator of glutamate-dependent neuronal activity.

Effects of cellular homeostatic intrinsic plasticity on dynamical and computational properties of biological recurrent neural networks.

Homeostatic intrinsic plasticity (HIP) is a ubiquitous cellular mechanism regulating neuronal activity, cardinal for the proper functioning of nervous systems. In invertebrates, HIP is critical for orchestrating stereotyped activity patterns. The functional impact of HIP remains more obscure in vertebrate networks, where higher order cognitive processes rely on complex neural dynamics. The hypothesis has emerged that HIP might control the complexity of activity dynamics in recurrent networks, with important computational consequences. However, conflicting results about the causal relationships between cellular HIP, network dynamics, and computational performance have arisen from machine-learning studies. Here, we assess how cellular HIP effects translate into collective dynamics and computational properties in biological recurrent networks. We develop a realistic multiscale model including a generic HIP rule regulating the neuronal threshold with actual molecular signaling pathways kinetics, Dale's principle, sparse connectivity, synaptic balance, and Hebbian synaptic plasticity (SP). Dynamic mean-field analysis and simulations unravel that HIP sets a working point at which inputs are transduced by large derivative ranges of the transfer function. This cellular mechanism ensures increased network dynamics complexity, robust balance with SP at the edge of chaos, and improved input separability. Although critically dependent upon balanced excitatory and inhibitory drives, these effects display striking robustness to changes in network architecture, learning rates, and input features. Thus, the mechanism we unveil might represent a ubiquitous cellular basis for complex dynamics in neural networks. Understanding this robustness is an important challenge to unraveling principles underlying self-organization around criticality in biological recurrent neural networks.

Localization of protein aggregation in Escherichia coli is governed by diffusion and nucleoid macromolecular crowding effect.

Aggregates of misfolded proteins are a hallmark of many age-related diseases. Recently, they have been linked to aging of Escherichia coli (E. coli) where protein aggregates accumulate at the old pole region of the aging bacterium. Because of the potential of E. coli as a model organism, elucidating aging and protein aggregation in this bacterium may pave the way to significant advances in our global understanding of aging. A first obstacle along this path is to decipher the mechanisms by which protein aggregates are targeted to specific intercellular locations. Here, using an integrated approach based on individual-based modeling, time-lapse fluorescence microscopy and automated image analysis, we show that the movement of aging-related protein aggregates in E. coli is purely diffusive (Brownian). Using single-particle tracking of protein aggregates in live E. coli cells, we estimated the average size and diffusion constant of the aggregates. Our results provide evidence that the aggregates passively diffuse within the cell, with diffusion constants that depend on their size in agreement with the Stokes-Einstein law. However, the aggregate displacements along the cell long axis are confined to a region that roughly corresponds to the nucleoid-free space in the cell pole, thus confirming the importance of increased macromolecular crowding in the nucleoids. We thus used 3D individual-based modeling to show that these three ingredients (diffusion, aggregation and diffusion hindrance in the nucleoids) are sufficient and necessary to reproduce the available experimental data on aggregate localization in the cells. Taken together, our results strongly support the hypothesis that the localization of aging-related protein aggregates in the poles of E. coli results from the coupling of passive diffusion-aggregation with spatially non-homogeneous macromolecular crowding. They further support the importance of "soft" intracellular structuring (based on macromolecular crowding) in diffusion-based protein localization in E. coli.

Anomalous versus slowed-down Brownian diffusion in the ligand-binding equilibrium.

Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) that converges back to a Brownian motion with reduced diffusion coefficient at long times after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in two dimensions. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law-distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte Carlo simulations, we show that these three scenarios have distinctive effects on the apparent affinity of the reaction. Whereas continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hindrance by obstacles both improve it. However, only in the case of slowed-down Brownian motion is the affinity maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes.

A tale of two stories: astrocyte regulation of synaptic depression and facilitation.

Short-term presynaptic plasticity designates variations of the amplitude of synaptic information transfer whereby the amount of neurotransmitter released upon presynaptic stimulation changes over seconds as a function of the neuronal firing activity. While a consensus has emerged that the resulting decrease (depression) and/or increase (facilitation) of the synapse strength are crucial to neuronal computations, their modes of expression in vivo remain unclear. Recent experimental studies have reported that glial cells, particularly astrocytes in the hippocampus, are able to modulate short-term plasticity but the mechanism of such a modulation is poorly understood. Here, we investigate the characteristics of short-term plasticity modulation by astrocytes using a biophysically realistic computational model. Mean-field analysis of the model, supported by intensive numerical simulations, unravels that astrocytes may mediate counterintuitive effects. Depending on the expressed presynaptic signaling pathways, astrocytes may globally inhibit or potentiate the synapse: the amount of released neurotransmitter in the presence of the astrocyte is transiently smaller or larger than in its absence. But this global effect usually coexists with the opposite local effect on paired pulses: with release-decreasing astrocytes most paired pulses become facilitated, namely the amount of neurotransmitter released upon spike i+1 is larger than that at spike i, while paired-pulse depression becomes prominent under release-increasing astrocytes. Moreover, we show that the frequency of astrocytic intracellular Ca(2+) oscillations controls the effects of the astrocyte on short-term synaptic plasticity. Our model explains several experimental observations yet unsolved, and uncovers astrocytic gliotransmission as a possible transient switch between short-term paired-pulse depression and facilitation. This possibility has deep implications on the processing of neuronal spikes and resulting information transfer at synapses.

Nonlinear gap junctions enable long-distance propagation of pulsating calcium waves in astrocyte networks.

A new paradigm has recently emerged in brain science whereby communications between glial cells and neuron-glia interactions should be considered together with neurons and their networks to understand higher brain functions. In particular, astrocytes, the main type of glial cells in the cortex, have been shown to communicate with neurons and with each other. They are thought to form a gap-junction-coupled syncytium supporting cell-cell communication via propagating Ca(2+) waves. An identified mode of propagation is based on cytoplasm-to-cytoplasm transport of inositol trisphosphate (IP(3)) through gap junctions that locally trigger Ca(2+) pulses via IP(3)-dependent Ca(2+)-induced Ca(2+) release. It is, however, currently unknown whether this intracellular route is able to support the propagation of long-distance regenerative Ca(2+) waves or is restricted to short-distance signaling. Furthermore, the influence of the intracellular signaling dynamics on intercellular propagation remains to be understood. In this work, we propose a model of the gap-junctional route for intercellular Ca(2+) wave propagation in astrocytes. Our model yields two major predictions. First, we show that long-distance regenerative signaling requires nonlinear coupling in the gap junctions. Second, we show that even with nonlinear gap junctions, long-distance regenerative signaling is favored when the internal Ca(2+) dynamics implements frequency modulation-encoding oscillations with pulsating dynamics, while amplitude modulation-encoding dynamics tends to restrict the propagation range. As a result, spatially heterogeneous molecular properties and/or weak couplings are shown to give rise to rich spatiotemporal dynamics that support complex propagation behaviors. These results shed new light on the mechanisms implicated in the propagation of Ca(2+) waves across astrocytes and the precise conditions under which glial cells may participate in information processing in the brain.

A model of on/off transitions in neurons of the deep cerebellar nuclei: deciphering the underlying ionic mechanisms.

The neurons of the deep cerebellar nuclei (DCNn) represent the main functional link between the cerebellar cortex and the rest of the central nervous system. Therefore, understanding the electrophysiological properties of DCNn is of fundamental importance to understand the overall functioning of the cerebellum. Experimental data suggest that DCNn can reversibly switch between two states: the firing of spikes (F state) and a stable depolarized state (SD state). We introduce a new biophysical model of the DCNn membrane electro-responsiveness to investigate how the interplay between the documented conductances identified in DCNn give rise to these states. In the model, the F state emerges as an isola of limit cycles, i.e. a closed loop of periodic solutions disconnected from the branch of SD fixed points. This bifurcation structure endows the model with the ability to reproduce the [Formula: see text] transition triggered by hyperpolarizing current pulses. The model also reproduces the [Formula: see text] transition induced by blocking Ca currents and ascribes this transition to the blocking of the high-threshold Ca current. The model suggests that intracellular current injections can trigger fully reversible [Formula: see text] transitions. Investigation of low-dimension reduced models suggests that the voltage-dependent Na current is prominent for these dynamical features. Finally, simulations of the model suggest that physiological synaptic inputs may trigger [Formula: see text] transitions. These transitions could explain the puzzling observation of positively correlated activities of connected Purkinje cells and DCNn despite the former inhibit the latter.

Dendritic signals command firing dynamics in a mathematical model of cerebellar Purkinje cells.

Dendrites of cerebellar Purkinje cells (PCs) respond to brief excitations from parallel fibers with lasting plateau depolarizations. It is unknown whether these plateaus are local events that boost the synaptic signals or they propagate to the soma and directly take part in setting the cell firing dynamics. To address this issue, we analyzed a likely mechanism underlying plateaus in three representations of a reconstructed PC with increasing complexity. Analysis in an infinite cable suggests that Ca plateaus triggered by direct excitatory inputs from parallel fibers and their mirror signals, valleys (putatively triggered by the local feed forward inhibitory network), cannot propagate. However, simulations of the model in electrotonic equivalent cables prove that Ca plateaus (resp. valleys) are conducted over the entire cell with velocities typical of passive events once they are triggered by threshold synaptic inputs that turn the membrane current inward (resp. outward) over the whole cell surface. Bifurcation analysis of the model in equivalent cables, and simulations in a fully reconstructed PC both indicate that dendritic Ca plateaus and valleys, respectively, command epochs of firing and silencing of PCs.

Erratum to: Glutamate regulation of calcium and IP(3) oscillating and pulsating dynamics in astrocytes.

[This corrects the article DOI: 10.1007/s10867-009-9155-y.].

Interdisciplinary Research in Artificial Intelligence: Challenges and Opportunities.

The use of artificial intelligence (AI) in a variety of research fields is speeding up multiple digital revolutions, from shifting paradigms in healthcare, precision medicine and wearable sensing, to public services and education offered to the masses around the world, to future cities made optimally efficient by autonomous driving. When a revolution happens, the consequences are not obvious straight away, and to date, there is no uniformly adapted framework to guide AI research to ensure a sustainable societal transition. To answer this need, here we analyze three key challenges to interdisciplinary AI research, and deliver three broad conclusions: 1) future development of AI should not only impact other scientific domains but should also take inspiration and benefit from other fields of science, 2) AI research must be accompanied by decision explainability, dataset bias transparency as well as development of evaluation methodologies and creation of regulatory agencies to ensure responsibility, and 3) AI education should receive more attention, efforts and innovation from the educational and scientific communities. Our analysis is of interest not only to AI practitioners but also to other researchers and the general public as it offers ways to guide the emerging collaborations and interactions toward the most fruitful outcomes.