Anti-Hebbian plasticity drives sequence learning in striatum.

Spatio-temporal activity patterns have been observed in a variety of brain areas in spontaneous activity, prior to or during action, or in response to stimuli. Biological mechanisms endowing neurons with the ability to distinguish between different sequences remain largely unknown. Learning sequences of spikes raises multiple challenges, such as maintaining in memory spike history and discriminating partially overlapping sequences. Here, we show that anti-Hebbian spike-timing dependent plasticity (STDP), as observed at cortico-striatal synapses, can naturally lead to learning spike sequences. We design a spiking model of the striatal output neuron receiving spike patterns defined as sequential input from a fixed set of cortical neurons. We use a simple synaptic plasticity rule that combines anti-Hebbian STDP and non-associative potentiation for a subset of the presented patterns called rewarded patterns. We study the ability of striatal output neurons to discriminate rewarded from non-rewarded patterns by firing only after the presentation of a rewarded pattern. In particular, we show that two biological properties of striatal networks, spiking latency and collateral inhibition, contribute to an increase in accuracy, by allowing a better discrimination of partially overlapping sequences. These results suggest that anti-Hebbian STDP may serve as a biological substrate for learning sequences of spikes.

Pattern Formation in Mesic Savannas.

We analyze a spatially extended version of a well-known model of forest-savanna dynamics, which presents as a system of nonlinear partial integro-differential equations, and study necessary conditions for pattern-forming bifurcations. Homogeneous solutions dominate the dynamics of the standard forest-savanna model, regardless of the length scales of the various spatial processes considered. However, several different pattern-forming scenarios are possible upon including spatial resource limitation, such as competition for water, soil nutrients, or herbivory effects. Using numerical simulations and continuation, we study the nature of the resulting patterns as a function of system parameters and length scales, uncovering subcritical pattern-forming bifurcations and observing significant regions of multistability for realistic parameter regimes. Finally, we discuss our results in the context of extant savanna-forest modeling efforts and highlight ongoing challenges in building a unifying mathematical model for savannas across different rainfall levels.

Reliability and robustness of oscillations in some slow-fast chaotic systems.

A variety of nonlinear models of biological systems generate complex chaotic behaviors that contrast with biological homeostasis, the observation that many biological systems prove remarkably robust in the face of changing external or internal conditions. Motivated by the subtle dynamics of cell activity in a crustacean central pattern generator (CPG), this paper proposes a refinement of the notion of chaos that reconciles homeostasis and chaos in systems with multiple timescales. We show that systems displaying relaxation cycles while going through chaotic attractors generate chaotic dynamics that are regular at macroscopic timescales and are, thus, consistent with physiological function. We further show that this relative regularity may break down through global bifurcations of chaotic attractors such as crises, beyond which the system may also generate erratic activity at slow timescales. We analyze these phenomena in detail in the chaotic Rulkov map, a classical neuron model known to exhibit a variety of chaotic spike patterns. This leads us to propose that the passage of slow relaxation cycles through a chaotic attractor crisis is a robust, general mechanism for the transition between such dynamics. We validate this numerically in three other models: a simple model of the crustacean CPG neural network, a discrete cubic map, and a continuous flow.

The use of AI in legal systems: determining independent contractor vs. employee status.

The use of artificial intelligence (AI) to aid legal decision making has become prominent. This paper investigates the use of AI in a critical issue in employment law, the determination of a worker's status-employee vs. independent contractor-in two common law countries (the U.S. and Canada). This legal question has been a contentious labor issue insofar as independent contractors are not eligible for the same benefits as employees. It has become an important societal issue due to the ubiquity of the gig economy and the recent disruptions in employment arrangements. To address this problem, we collected, annotated, and structured the data for all Canadian and Californian court cases related to this legal question between 2002 and 2021, resulting in 538 Canadian cases and 217 U.S. cases. In contrast to legal literature focusing on complex and correlated characteristics of the employment relationship, our statistical analyses of the data show very strong correlations between the worker's status and a small subset of quantifiable characteristics of the employment relationship. In fact, despite the variety of situations in the case law, we show that simple, off-the-shelf AI models classify the cases with an out-of-sample accuracy of more than 90%. Interestingly, the analysis of misclassified cases reveals consistent misclassification patterns by most algorithms. Legal analyses of these cases led us to identify how equity is ensured by judges in ambiguous situations. Finally, our findings have practical implications for access to legal advice and justice. We deployed our AI model via the open-access platform, https://MyOpenCourt.org/, to help users answer employment legal questions. This platform has already assisted many Canadian users, and we hope it will help democratize access to legal advice to large crowds.

Pattern formation in a four-ring reaction-diffusion network with heterogeneity.

In networks of nonlinear oscillators, symmetries place hard constraints on the system that can be exploited to predict universal dynamical features and steady states, providing a rare generic organizing principle for far-from-equilibrium systems. However, the robustness of this class of theories to symmetry-disrupting imperfections is untested in free-running (i.e., non-computer-controlled) systems. Here, we develop a model experimental reaction-diffusion network of chemical oscillators to test applications of the theory of dynamical systems with symmeries in the context of self-organizing systems relevant to biology and soft robotics. The network is a ring of four microreactors containing the oscillatory Belousov-Zhabotinsky reaction coupled to nearest neighbors via diffusion. Assuming homogeneity across the oscillators, theory predicts four categories of stable spatiotemporal phase-locked periodic states and four categories of invariant manifolds that guide and structure transitions between phase-locked states. In our experiments, we observed that three of the four phase-locked states were displaced from their idealized positions and, in the ensemble of measurements, appeared as clusters of different shapes and sizes, and that one of the predicted states was absent. We also observed the predicted symmetry-derived synchronous clustered transients that occur when the dynamical trajectories coincide with invariant manifolds. Quantitative agreement between experiment and numerical simulations is found by accounting for the small amount of experimentally determined heterogeneity in intrinsic frequency. We further elucidate how different patterns of heterogeneity impact each attractor differently through a bifurcation analysis. We show that examining bifurcations along invariant manifolds provides a general framework for developing intuition about how chemical-specific dynamics interact with topology in the presence of heterogeneity that can be applied to other oscillators in other topologies.

Striatum expresses region-specific plasticity consistent with distinct memory abilities.

The striatum mediates two learning modalities: goal-directed behavior in dorsomedial (DMS) and habits in dorsolateral (DLS) striata. The synaptic bases of these learnings are still elusive. Indeed, while ample research has described DLS plasticity, little remains known about DMS plasticity and its involvement in procedural learning. Here, we find symmetric and asymmetric anti-Hebbian spike-timing-dependent plasticity (STDP) in DMS and DLS, respectively, with opposite plasticity dominance upon increasing corticostriatal activity. During motor-skill learning, plasticity is engaged in DMS and striatonigral DLS neurons only during early learning stages, whereas striatopallidal DLS neurons are mobilized only during late phases. With a mathematical modeling approach, we find that symmetric anti-Hebbian STDP favors memory flexibility, while asymmetric anti-Hebbian STDP favors memory maintenance, consistent with memory processes at play in procedural learning.

COUP-TFI specifies the medial entorhinal cortex identity and induces differential cell adhesion to determine the integrity of its boundary with neocortex.

Development of cortical regions with precise, sharp, and regular boundaries is essential for physiological function. However, little is known of the mechanisms ensuring these features. Here, we show that determination of the boundary between neocortex and medial entorhinal cortex (MEC), two abutting cortical regions generated from the same progenitor lineage, relies on COUP-TFI (chicken ovalbumin upstream promoter-transcription factor I), a patterning transcription factor with graded expression in cortical progenitors. In contrast with the classical paradigm, we found that increased COUP-TFI expression expands MEC, creating protrusions and disconnected ectopic tissue. We further developed a mathematical model that predicts that neuronal specification and differential cell affinity contribute to the emergence of an instability region and boundary sharpness. Correspondingly, we demonstrated that high expression of COUP-TFI induces MEC cell fate and protocadherin 19 expression. Thus, we conclude that a sharp boundary requires a subtle interplay between patterning transcription factors and differential cell affinity.

Is There Sufficient Evidence for Criticality in Cortical Systems?

Numerous studies have proposed that specific brain activity statistics provide evidence that the brain operates at a critical point, which could have implications for the brain's information processing capabilities. A recent paper reported that identical scalings and criticality signatures arise in a variety of different neural systems (neural cultures, cortical slices, anesthetized or awake brains, across both reptiles and mammals). The diversity of these states calls into question the claimed role of criticality in information processing. We analyze the methodology used to assess criticality and replicate this analysis for spike trains of two non-critical systems. These two non-critical systems pass all the tests used to assess criticality in the aforementioned recent paper. This analysis provides a crucial control (which is absent from the original study) and suggests that the methodology used may not be sufficient to establish that a system operates at criticality. Hence whether the brain operates at criticality or not remains an open question and it is of evident interest to develop more robust methods to address these questions.

Engrams of Fast Learning.

Fast learning designates the behavioral and neuronal mechanisms underlying the acquisition of a long-term memory trace after a unique and brief experience. As such it is opposed to incremental, slower reinforcement or procedural learning requiring repetitive training. This learning process, found in most animal species, exists in a large spectrum of natural behaviors, such as one-shot associative, spatial, or perceptual learning, and is a core principle of human episodic memory. We review here the neuronal and synaptic long-term changes associated with fast learning in mammals and discuss some hypotheses related to their underlying mechanisms. We first describe the variety of behavioral paradigms used to test fast learning memories: those preferentially involve a single and brief (from few hundred milliseconds to few minutes) exposures to salient stimuli, sufficient to trigger a long-lasting memory trace and new adaptive responses. We then focus on neuronal activity patterns observed during fast learning and the emergence of long-term selective responses, before documenting the physiological correlates of fast learning. In the search for the engrams of fast learning, a growing body of evidence highlights long-term changes in gene expression, structural, intrinsic, and synaptic plasticities. Finally, we discuss the potential role of the sparse and bursting nature of neuronal activity observed during the fast learning, especially in the induction plasticity mechanisms leading to the rapid establishment of long-term synaptic modifications. We conclude with more theoretical perspectives on network dynamics that could enable fast learning, with an overview of some theoretical approaches in cognitive neuroscience and artificial intelligence.

A "Numerical Evo-Devo" Synthesis for the Identification of Pattern-Forming Factors.

Animals display extensive diversity in motifs adorning their coat, yet these patterns have reproducible orientation and periodicity within species or groups. Morphological variation has been traditionally used to dissect the genetic basis of evolutionary change, while pattern conservation and stability in both mathematical and organismal models has served to identify core developmental events. Two patterning theories, namely instruction and self-organisation, emerged from this work. Combined, they provide an appealing explanation for how natural patterns form and evolve, but in vivo factors underlying these mechanisms remain elusive. By bridging developmental biology and mathematics, novel frameworks recently allowed breakthroughs in our understanding of pattern establishment, unveiling how patterning strategies combine in space and time, or the importance of tissue morphogenesis in generating positional information. Adding results from surveys of natural variation to these empirical-modelling dialogues improves model inference, analysis, and in vivo testing. In this evo-devo-numerical synthesis, mathematical models have to reproduce not only given stable patterns but also the dynamics of their emergence, and the extent of inter-species variation in these dynamics through minimal parameter change. This integrative approach can help in disentangling molecular, cellular and mechanical interaction during pattern establishment.

Deep brain stimulation-guided optogenetic rescue of parkinsonian symptoms.

Deep brain stimulation (DBS) of the subthalamic nucleus is a symptomatic treatment of Parkinson's disease but benefits only to a minority of patients due to stringent eligibility criteria. To investigate new targets for less invasive therapies, we aimed at elucidating key mechanisms supporting deep brain stimulation efficiency. Here, using in vivo electrophysiology, optogenetics, behavioral tasks and mathematical modeling, we found that subthalamic stimulation normalizes pathological hyperactivity of motor cortex pyramidal cells, while concurrently activating somatostatin and inhibiting parvalbumin interneurons. In vivo opto-activation of cortical somatostatin interneurons alleviates motor symptoms in a parkinsonian mouse model. A computational model highlights that a decrease in pyramidal neuron activity induced by DBS or by a stimulation of cortical somatostatin interneurons can restore information processing capabilities. Overall, these results demonstrate that activation of cortical somatostatin interneurons may constitute a less invasive alternative than subthalamic stimulation.

Concurrent Thalamostriatal and Corticostriatal Spike-Timing-Dependent Plasticity and Heterosynaptic Interactions Shape Striatal Plasticity Map.

The striatum integrates inputs from the cortex and thalamus, which display concomitant or sequential activity. The striatum assists in forming memory, with acquisition of the behavioral repertoire being associated with corticostriatal (CS) plasticity. The literature has mainly focused on that CS plasticity, and little remains known about thalamostriatal (TS) plasticity rules or CS and TS plasticity interactions. We undertook here the study of these plasticity rules. We found bidirectional Hebbian and anti-Hebbian spike-timing-dependent plasticity (STDP) at the thalamic and cortical inputs, respectively, which were driving concurrent changes at the striatal synapses. Moreover, TS- and CS-STDP induced heterosynaptic plasticity. We developed a calcium-based mathematical model of the coupled TS and CS plasticity, and simulations predict complex changes in the CS and TS plasticity maps depending on the precise cortex-thalamus-striatum engram. These predictions were experimentally validated using triplet-based STDP stimulations, which revealed the significant remodeling of the CS-STDP map upon TS activity, which is notably the induction of the LTD areas in the CS-STDP for specific timing regimes. TS-STDP exerts a greater influence on CS plasticity than CS-STDP on TS plasticity. These findings highlight the major impact of precise timing in cortical and thalamic activity for the memory engram of striatal synapses.

Progressive alignment of inhibitory and excitatory delay may drive a rapid developmental switch in cortical network dynamics.

Nervous system maturation occurs on multiple levels-synaptic, circuit, and network-at divergent timescales. For example, many synaptic properties mature gradually, whereas emergent network dynamics can change abruptly. Here we combine experimental and theoretical approaches to investigate a sudden transition in spontaneous and sensory evoked thalamocortical activity necessary for the development of vision. Inspired by in vivo measurements of timescales and amplitudes of synaptic currents, we extend the Wilson and Cowan model to take into account the relative onset timing and amplitudes of inhibitory and excitatory neural population responses. We study this system as these parameters are varied within amplitudes and timescales consistent with developmental observations to identify the bifurcations of the dynamics that might explain the network behaviors in vivo. Our findings indicate that the inhibitory timing is a critical determinant of thalamocortical activity maturation; a gradual decay of the ratio of inhibitory to excitatory onset time drives the system through a bifurcation that leads to a sudden switch of the network spontaneous activity from high-amplitude oscillations to a nonoscillatory active state. This switch also drives a change from a threshold bursting to linear response to transient stimuli, also consistent with in vivo observation. Thus we show that inhibitory timing is likely critical to the development of network dynamics and may underlie rapid changes in activity without similarly rapid changes in the underlying synaptic and cellular parameters.NEW & NOTEWORTHY Relying on a generalization of the Wilson-Cowan model, which allows a solid analytic foundation for the understanding of the link between maturation of inhibition and network dynamics, we propose a potential explanation for the role of developing excitatory/inhibitory synaptic delays in mediating a sudden switch in thalamocortical visual activity preceding vision onset.

In vitro characterization of the human segmentation clock.

The segmental organization of the vertebral column is established early in embryogenesis, when pairs of somites are rhythmically produced by the presomitic mesoderm (PSM). The tempo of somite formation is controlled by a molecular oscillator known as the segmentation clock1,2. Although this oscillator has been well-characterized in model organisms1,2, whether a similar oscillator exists in humans remains unknown. Genetic analyses of patients with severe spine segmentation defects have implicated several human orthologues of cyclic genes that are associated with the mouse segmentation clock, suggesting that this oscillator might be conserved in humans3. Here we show that human PSM cells derived in vitro-as well as those of the mouse4-recapitulate the oscillations of the segmentation clock. Human PSM cells oscillate with a period two times longer than that of mouse cells (5 h versus 2.5 h), but are similarly regulated by FGF, WNT, Notch and YAP signalling5. Single-cell RNA sequencing reveals that mouse and human PSM cells in vitro follow a developmental trajectory similar to that of mouse PSM in vivo. Furthermore, we demonstrate that FGF signalling controls the phase and period of oscillations, expanding the role of this pathway beyond its classical interpretation in 'clock and wavefront' models1. Our work identifying the human segmentation clock represents an important milestone in understanding human developmental biology.

Symmetry breaking in the embryonic skin triggers directional and sequential plumage patterning.

The development of an organism involves the formation of patterns from initially homogeneous surfaces in a reproducible manner. Simulations of various theoretical models recapitulate final states of natural patterns, yet drawing testable hypotheses from those often remains difficult. Consequently, little is known about pattern-forming events. Here, we surveyed plumage patterns and their emergence in Galliformes, ratites, passerines, and penguins, together representing the three major taxa of the avian phylogeny, and built a unified model that not only reproduces final patterns but also intrinsically generates shared and varying directionality, sequence, and duration of patterning. We used in vivo and ex vivo experiments to test its parameter-based predictions. We showed that directional and sequential pattern progression depends on a species-specific prepattern: an initial break in surface symmetry launches a travelling front of sharply defined, oriented domains with self-organising capacity. This front propagates through the timely transfer of increased cell density mediated by cell proliferation, which controls overall patterning duration. These results show that universal mechanisms combining prepatterning and self-organisation govern the timely emergence of the plumage pattern in birds.

Interplay of multiple pathways and activity-dependent rules in STDP.

Hebbian plasticity describes a basic mechanism for synaptic plasticity whereby synaptic weights evolve depending on the relative timing of paired activity of the pre- and postsynaptic neurons. Spike-timing-dependent plasticity (STDP) constitutes a central experimental and theoretical synaptic Hebbian learning rule. Various mechanisms, mostly calcium-based, account for the induction and maintenance of STDP. Classically STDP is assumed to gradually emerge in a monotonic way as the number of pairings increases. However, non-monotonic STDP accounting for fast associative learning led us to challenge this monotonicity hypothesis and explore how the existence of multiple plasticity pathways affects the dynamical establishment of plasticity. To account for distinct forms of STDP emerging from increasing numbers of pairings and the variety of signaling pathways involved, we developed a general class of simple mathematical models of plasticity based on calcium transients and accommodating various calcium-based plasticity mechanisms. These mechanisms can either compete or cooperate for the establishment of long-term potentiation (LTP) and depression (LTD), that emerge depending on past calcium activity. Our model reproduces accurately the striatal STDP that involves endocannabinoid and NMDAR signaling pathways. Moreover, we predict how stimulus frequency alters plasticity, and how triplet rules are affected by the number of pairings. We further investigate the general model with an arbitrary number of pathways and show that depending on those pathways and their properties, a variety of plasticities may emerge upon variation of the number and/or the frequency of pairings, even when the outcome after large numbers of pairings is identical. These findings, built upon a biologically realistic example and generalized to other applications, argue that in order to fully describe synaptic plasticity it is not sufficient to record STDP curves at fixed pairing numbers and frequencies. In fact, considering the whole spectrum of activity-dependent parameters could have a great impact on the description of plasticity, and a better understanding of the engram.

On the complex dynamics of savanna landscapes.

Simple mathematical models can exhibit rich and complex behaviors. Prototypical examples of these drawn from biology and other disciplines have provided insights that extend well beyond the situations that inspired them. Here, we explore a set of simple, yet realistic, models for savanna-forest vegetation dynamics based on minimal ecological assumptions. These models are aimed at understanding how vegetation interacts with both climate (a primary global determinant of vegetation structure) and feedbacks with chronic disturbances from fire. The model includes three plant functional types-grasses, savanna trees, and forest trees. Grass and (when they allow grass to persist in their subcanopy) savanna trees promote the spread of fires, which in turn, demographically limit trees. The model exhibits a spectacular range of behaviors. In addition to bistability, analysis reveals (i) that diverse cyclic behaviors (including limit and homo- and heteroclinic cycles) occur for broad ranges of parameter space, (ii) that large shifts in landscape structure can result from endogenous dynamics and not just from external drivers or from noise, and (iii) that introducing noise into this system induces resonant and inverse resonant phenomena, some of which have never been previously observed in ecological models. Ecologically, these results raise questions about how to evaluate complicated dynamics with data. Mathematically, they lead to classes of behaviors that are likely to occur in other models with similar structure.

The hemodynamic signal as a first-order low-pass temporal filter: Evidence and implications for neuroimaging studies.

Neuronal activation triggers local changes in blood flow and hemoglobin oxygenation. These hemodynamic signals can be recorded through functional magnetic resonance imaging or intrinsic optical imaging, and allows inferring neural activity in response to stimuli. These techniques are widely used to uncover functional brain architectures. However, their accuracy suffers from distortions inherent to hemodynamic responses and noise. The analysis of these signals currently relies on models of impulse hemodynamic responses to brief stimuli. Here, in order to infer precise functional architectures, we focused on integrated signals associated to the dynamic response of functional maps. To this end, we recorded orientation and direction maps in cat primary visual cortex and compared two protocols: the conventional episodic stimulation technique and a continuous, periodic stimulation paradigm. Conventional methods show that the dynamics of activation and deactivation of the functional maps follows a linear first-order differential equation representing a low-pass filter. Comparison with the periodic stimulation methods confirmed this observation: the phase shifts and magnitude attenuations extracted at various frequencies were consistent with a low-pass filter with a 5s time constant. This dynamics presumably reflects the variations in deoxyhemoglobin mediated by arterial dilations. This dynamics open new avenues in the analysis of neuroimaging data that differs from common methods based on the hemodynamic response function. In particular, we demonstrate that inverting this first-order low-pass filter minimized the distortions of the signal and enabled a much faster and accurate reconstruction of functional maps.

Power-law statistics and universal scaling in the absence of criticality.

Critical states are sometimes identified experimentally through power-law statistics or universal scaling functions. We show here that such features naturally emerge from networks in self-sustained irregular regimes away from criticality. In these regimes, statistical physics theory of large interacting systems predict a regime where the nodes have independent and identically distributed dynamics. We thus investigated the statistics of a system in which units are replaced by independent stochastic surrogates and found the same power-law statistics, indicating that these are not sufficient to establish criticality. We rather suggest that these are universal features of large-scale networks when considered macroscopically. These results put caution on the interpretation of scaling laws found in nature.

On the Dynamical Interplay of Positive and Negative Affects.

Emotional disorders and psychological flourishing are the result of complex interactions between positive and negative affects that depend on external events and the subject's internal representations. Based on psychological data, we mathematically model the dynamical balance between positive and negative affects as a function of the response to external positive and negative events. This modeling allows the investigation of the relative impact of two leading forms of therapy on affect balance. The model uses a delay differential equation to analytically study the bifurcation diagram of the system. We compare the results of the model to psychological data on a single, recurrently depressed patient who was administered the two types of therapies considered (coping focused versus affect focused). The model leads to the prediction that stabilization at a normal state may rely on evaluating one's emotional state through a historical ongoing emotional state rather than in a narrow present window. The simple mathematical model proposed here offers a theoretical framework for investigating the temporal process of change and parameters of resilience to relapse.