Top-down modulation in canonical cortical circuits with short-term plasticity

Cortical dynamics and computations are strongly influenced by diverse GABAergic interneurons, including those expressing parvalbumin (PV), somatostatin (SST), and vasoactive intestinal peptide (VIP). Together with excitatory (E) neurons, they form a canonical microcircuit and exhibit counterintuitive nonlinear phenomena. One instance of such phenomena is response reversal, whereby SST neurons show opposite responses to top-down modulation via VIP depending on the presence of bottom-up sensory input, indicating that the network may function in different regimes under different stimulation conditions. Combining analytical and computational approaches, we demonstrate that model networks with multiple interneuron subtypes and experimentally identified short-term plasticity mechanisms can implement response reversal. Surprisingly, despite not directly affecting SST and VIP activity, PV-to-E short-term depression has a decisive impact on SST response reversal. We show how response reversal relates to inhibition stabilization and the paradoxical effect in the presence of several short-term plasticity mechanisms demonstrating that response reversal coincides with a change in the indispensability of SST for network stabilization. In summary, our work suggests a role of short-term plasticity mechanisms in generating nonlinear phenomena in networks with multiple interneuron subtypes and makes several experimentally testable predictions.

Multifaceted luminance gain control beyond photoreceptors in Drosophila

Animals navigating in natural environments must handle vast changes in their sensory input. Visual systems, for example, handle changes in luminance at many timescales, from slow changes across the day to rapid changes during active behavior. To maintain luminance-invariant perception, visual systems must adapt their sensitivity to changing luminance at different timescales. We demonstrate that luminance gain control in photoreceptors alone is insufficient to explain luminance invariance at both fast and slow timescales and reveal the algorithms that adjust gain past photoreceptors in the fly eye. We combined imaging and behavioral experiments with computational modeling to show that downstream of photoreceptors, circuitry taking input from the single luminance-sensitive neuron type L3 implements gain control at fast and slow timescales. This computation is bidirectional in that it prevents the underestimation of contrasts in low luminance and overestimation in high luminance. An algorithmic model disentangles these multifaceted contributions and shows that the bidirectional gain control occurs at both timescales. The model implements a nonlinear interaction of luminance and contrast to achieve gain correction at fast timescales and a dark-sensitive channel to improve the detection of dim stimuli at slow timescales. Together, our work demonstrates how a single neuronal channel performs diverse computations to implement gain control at multiple timescales that are together important for navigation in natural environments.

Global change in brain state during spontaneous and forced walk in Drosophila is composed of combined activity patterns of different neuron classes

Movement-correlated brain activity has been found across species and brain regions. Here, we used fast whole-brain lightfield imaging in adult Drosophila to investigate the relationship between walk and brain-wide neuronal activity. We observed a global change in activity that tightly correlated with spontaneous bouts of walk. While imaging specific sets of excitatory, inhibitory, and neuromodulatory neurons highlighted their joint contribution, spatial heterogeneity in walk- and turning-induced activity allowed parsing unique responses from subregions and sometimes individual candidate neurons. For example, previously uncharacterized serotonergic neurons were inhibited during walk. While activity onset in some areas preceded walk onset exclusively in spontaneously walking animals, spontaneous and forced walk elicited similar activity in most brain regions. These data suggest a major contribution of walk and walk-related sensory or proprioceptive information to global activity of all major neuronal classes.

Single spikes drive sequential propagation and routing of activity in a cortical network

Single spikes can trigger repeatable firing sequences in cortical networks. The mechanisms that support reliable propagation of activity from such small events and their functional consequences remain unclear. By constraining a recurrent network model with experimental statistics from turtle cortex, we generate reliable and temporally precise sequences from single spike triggers. We find that rare strong connections support sequence propagation, while dense weak connections modulate propagation reliability. We identify sections of sequences corresponding to divergent branches of strongly connected neurons which can be selectively gated. Applying external inputs to specific neurons in the sparse backbone of strong connections can effectively control propagation and route activity within the network. Finally, we demonstrate that concurrent sequences interact reliably, generating a highly combinatorial space of sequence activations. Our results reveal the impact of individual spikes in cortical circuits, detailing how repeatable sequences of activity can be triggered, sustained, and controlled during cortical computations.

Adaptation of Drosophila larva foraging in response to changes in food resources

All animals face the challenge of finding nutritious resources in a changing environment. To maximize lifetime fitness, the exploratory behavior has to be flexible, but which behavioral elements adapt and what triggers those changes remain elusive. Using experiments and modeling, we characterized extensively how Drosophila larvae foraging adapts to different food quality and distribution and how the foraging genetic background influences this adaptation. Our work shows that different food properties modulated specific motor programs. Food quality controls the traveled distance by modulating crawling speed and frequency of pauses and turns. Food distribution, and in particular the food-no food interface, controls turning behavior, stimulating turns toward the food when reaching the patch border and increasing the proportion of time spent within patches of food. Finally, the polymorphism in the foraging gene (rover-sitter) of the larvae adjusts the magnitude of the behavioral response to different food conditions. This study defines several levels of control of foraging and provides the basis for the systematic identification of the neuronal circuits and mechanisms controlling each behavioral response.

Stability and learning in excitatory synapses by nonlinear inhibitory plasticity

Synaptic changes are hypothesized to underlie learning and memory formation in the brain. But Hebbian synaptic plasticity of excitatory synapses on its own is unstable, leading to either unlimited growth of synaptic strengths or silencing of neuronal activity without additional homeostatic mechanisms. To control excitatory synaptic strengths, we propose a novel form of synaptic plasticity at inhibitory synapses. Using computational modeling, we suggest two key features of inhibitory plasticity, dominance of inhibition over excitation and a nonlinear dependence on the firing rate of postsynaptic excitatory neurons whereby inhibitory synaptic strengths change with the same sign (potentiate or depress) as excitatory synaptic strengths. We demonstrate that the stable synaptic strengths realized by this novel inhibitory plasticity model affects excitatory/inhibitory weight ratios in agreement with experimental results. Applying a disinhibitory signal can gate plasticity and lead to the generation of receptive fields and strong bidirectional connectivity in a recurrent network. Hence, a novel form of nonlinear inhibitory plasticity can simultaneously stabilize excitatory synaptic strengths and enable learning upon disinhibition.

Regulation of circuit organization and function through inhibitory synaptic plasticity

Diverse inhibitory neurons in the mammalian brain shape circuit connectivity and dynamics through mechanisms of synaptic plasticity. Inhibitory plasticity can establish excitation/inhibition (E/I) balance, control neuronal firing, and affect local calcium concentration, hence regulating neuronal activity at the network, single neuron, and dendritic level. Computational models can synthesize multiple experimental results and provide insight into how inhibitory plasticity controls circuit dynamics and sculpts connectivity by identifying phenomenological learning rules amenable to mathematical analysis. We highlight recent studies on the role of inhibitory plasticity in modulating excitatory plasticity, forming structured networks underlying memory formation and recall, and implementing adaptive phenomena and novelty detection. We conclude with experimental and modeling progress on the role of interneuron-specific plasticity in circuit computation and context-dependent learning.

Formation and computational implications of assemblies in neural circuits

In the brain, patterns of neural activity represent sensory information and store it in non-random synaptic connectivity. A prominent theoretical hypothesis states that assemblies, groups of neurons that are strongly connected to each other, are the key computational units underlying perception and memory formation. Compatible with these hypothesised assemblies, experiments have revealed groups of neurons that display synchronous activity, either spontaneously or upon stimulus presentation, and exhibit behavioural relevance. While it remains unclear how assemblies form in the brain, theoretical work has vastly contributed to the understanding of various interacting mechanisms in this process. Here, we review the recent theoretical literature on assembly formation by categorising the involved mechanisms into four components: synaptic plasticity, symmetry breaking, competition and stability. We highlight different approaches and assumptions behind assembly formation and discuss recent ideas of assemblies as the key computational unit in the brain. Abstract figure legend Assembly Formation. Assemblies are groups of strongly connected neurons formed by the interaction of multiple mechanisms and with vast computational implications. Four interacting components are thought to drive assembly formation: synaptic plasticity, symmetry breaking, competition and stability. This article is protected by copyright. All rights reserved.

Emergence of synaptic organization and computation in dendrites

Single neurons in the brain exhibit astounding computational capabilities, which gradually emerge throughout development and enable them to become integrated into complex neural circuits. These capabilities derive in part from the precise arrangement of synaptic inputs on the neurons' dendrites. While the full computational benefits of this arrangement are still unknown, a picture emerges in which synapses organize according to their functional properties across multiple spatial scales. In particular, on the local scale (tens of microns), excitatory synaptic inputs tend to form clusters according to their functional similarity, whereas on the scale of individual dendrites or the entire tree, synaptic inputs exhibit dendritic maps where excitatory synapse function varies smoothly with location on the tree. The development of this organization is supported by inhibitory synapses, which are carefully interleaved with excitatory synapses and can flexibly modulate activity and plasticity of excitatory synapses. Here, we summarize recent experimental and theoretical research on the developmental emergence of this synaptic organization and its impact on neural computations.

The generation of cortical novelty responses through inhibitory plasticity

Animals depend on fast and reliable detection of novel stimuli in their environment. Neurons in multiple sensory areas respond more strongly to novel in comparison to familiar stimuli. Yet, it remains unclear which circuit, cellular, and synaptic mechanisms underlie those responses. Here, we show that spike-timing-dependent plasticity of inhibitory-to-excitatory synapses generates novelty responses in a recurrent spiking network model. Inhibitory plasticity increases the inhibition onto excitatory neurons tuned to familiar stimuli, while inhibition for novel stimuli remains low, leading to a network novelty response. The generation of novelty responses does not depend on the periodicity but rather on the distribution of presented stimuli. By including tuning of inhibitory neurons, the network further captures stimulus-specific adaptation. Finally, we suggest that disinhibition can control the amplification of novelty responses. Therefore, inhibitory plasticity provides a flexible, biologically plausible mechanism to detect the novelty of bottom-up stimuli, enabling us to make experimentally testable predictions.

Emergence of local and global synaptic organization on cortical dendrites

Synaptic inputs on cortical dendrites are organized with remarkable subcellular precision at the micron level. This organization emerges during early postnatal development through patterned spontaneous activity and manifests both locally where nearby synapses are significantly correlated, and globally with distance to the soma. We propose a biophysically motivated synaptic plasticity model to dissect the mechanistic origins of this organization during development and elucidate synaptic clustering of different stimulus features in the adult. Our model captures local clustering of orientation in ferret and receptive field overlap in mouse visual cortex based on the receptive field diameter and the cortical magnification of visual space. Including action potential back-propagation explains branch clustering heterogeneity in the ferret and produces a global retinotopy gradient from soma to dendrite in the mouse. Therefore, by combining activity-dependent synaptic competition and species-specific receptive fields, our framework explains different aspects of synaptic organization regarding stimulus features and spatial scales.

Efficient population coding depends on stimulus convergence and source of noise

Sensory organs transmit information to downstream brain circuits using a neural code comprised of spikes from multiple neurons. According to the prominent efficient coding framework, the properties of sensory populations have evolved to encode maximum information about stimuli given biophysical constraints. How information coding depends on the way sensory signals from multiple channels converge downstream is still unknown, especially in the presence of noise which corrupts the signal at different points along the pathway. Here, we calculated the optimal information transfer of a population of nonlinear neurons under two scenarios. First, a lumped-coding channel where the information from different inputs converges to a single channel, thus reducing the number of neurons. Second, an independent-coding channel when different inputs contribute independent information without convergence. In each case, we investigated information loss when the sensory signal was corrupted by two sources of noise. We determined critical noise levels at which the optimal number of distinct thresholds of individual neurons in the population changes. Comparing our system to classical physical systems, these changes correspond to first- or second-order phase transitions for the lumped- or the independent-coding channel, respectively. We relate our theoretical predictions to coding in a population of auditory nerve fibers recorded experimentally, and find signatures of efficient coding. Our results yield important insights into the diverse coding strategies used by neural populations to optimally integrate sensory stimuli in the presence of distinct sources of noise.

Adaptation of spontaneous activity in the developing visual cortex

Spontaneous activity drives the establishment of appropriate connectivity in different circuits during brain development. In the mouse primary visual cortex, two distinct patterns of spontaneous activity occur before vision onset: local low-synchronicity events originating in the retina and global high-synchronicity events originating in the cortex. We sought to determine the contribution of these activity patterns to jointly organize network connectivity through different activity-dependent plasticity rules. We postulated that local events shape cortical input selectivity and topography, while global events homeostatically regulate connection strength. However, to generate robust selectivity, we found that global events should adapt their amplitude to the history of preceding cortical activation. We confirmed this prediction by analyzing in vivo spontaneous cortical activity. The predicted adaptation leads to the sparsification of spontaneous activity on a slower timescale during development, demonstrating the remarkable capacity of the developing sensory cortex to acquire sensitivity to visual inputs after eye-opening.

Oxytocin Shapes Spontaneous Activity Patterns in the Developing Visual Cortex by Activating Somatostatin Interneurons

Spontaneous network activity shapes emerging neuronal circuits during early brain development prior to sensory perception. However, how neuromodulation influences this activity is not fully understood. Here, we report that the neuromodulator oxytocin differentially shapes spontaneous activity patterns across sensory cortices. In vivo, oxytocin strongly decreased the frequency and pairwise correlations of spontaneous activity events in the primary visual cortex (V1), but it did not affect the frequency of spontaneous network events in the somatosensory cortex (S1). Patch-clamp recordings in slices and RNAscope showed that oxytocin affects S1 excitatory and inhibitory neurons similarly, whereas in V1, oxytocin targets only inhibitory neurons. Somatostatin-positive (SST+) interneurons expressed the oxytocin receptor and were activated by oxytocin in V1. Accordingly, pharmacogenetic silencing of V1 SST+ interneurons fully blocked oxytocin's effect on inhibition in vitro as well its effect on spontaneous activity patterns in vivo. Thus, oxytocin decreases the excitatory/inhibitory (E/I) ratio by recruiting SST+ interneurons and modulates specific features of V1 spontaneous activity patterns that are crucial for the wiring and refining of developing sensory circuits.

Homeostatic mechanisms regulate distinct aspects of cortical circuit dynamics

Homeostasis is indispensable to counteract the destabilizing effects of Hebbian plasticity. Although it is commonly assumed that homeostasis modulates synaptic strength, membrane excitability, and firing rates, its role at the neural circuit and network level is unknown. Here, we identify changes in higher-order network properties of freely behaving rodents during prolonged visual deprivation. Strikingly, our data reveal that functional pairwise correlations and their structure are subject to homeostatic regulation. Using a computational model, we demonstrate that the interplay of different plasticity and homeostatic mechanisms can capture the initial drop and delayed recovery of firing rates and correlations observed experimentally. Moreover, our model indicates that synaptic scaling is crucial for the recovery of correlations and network structure, while intrinsic plasticity is essential for the rebound of firing rates, suggesting that synaptic scaling and intrinsic plasticity can serve distinct functions in homeostatically regulating network dynamics.

Autonomous emergence of connectivity assemblies via spike triplet interactions

Non-random connectivity can emerge without structured external input driven by activity-dependent mechanisms of synaptic plasticity based on precise spiking patterns. Here we analyze the emergence of global structures in recurrent networks based on a triplet model of spike timing dependent plasticity (STDP), which depends on the interactions of three precisely-timed spikes, and can describe plasticity experiments with varying spike frequency better than the classical pair-based STDP rule. We derive synaptic changes arising from correlations up to third-order and describe them as the sum of structural motifs, which determine how any spike in the network influences a given synaptic connection through possible connectivity paths. This motif expansion framework reveals novel structural motifs under the triplet STDP rule, which support the formation of bidirectional connections and ultimately the spontaneous emergence of global network structure in the form of self-connected groups of neurons, or assemblies. We propose that under triplet STDP assembly structure can emerge without the need for externally patterned inputs or assuming a symmetric pair-based STDP rule common in previous studies. The emergence of non-random network structure under triplet STDP occurs through internally-generated higher-order correlations, which are ubiquitous in natural stimuli and neuronal spiking activity, and important for coding. We further demonstrate how neuromodulatory mechanisms that modulate the shape of the triplet STDP rule or the synaptic transmission function differentially promote structural motifs underlying the emergence of assemblies, and quantify the differences using graph theoretic measures.

Emergent non-random connectivity structures in different brain regions are tightly related to specific patterns of neural activity and support diverse brain functions. For instance, self-connected groups of neurons, known as assemblies, have been proposed to represent functional units in brain circuits and can emerge even without patterned external instruction. Here we investigate the emergence of non-random connectivity in recurrent networks using a particular plasticity rule, triplet STDP, which relies on the interaction of spike triplets and can capture higher-order statistical dependencies in neural activity. We derive the evolution of the synaptic strengths in the network and explore the conditions for the self-organization of connectivity into assemblies. We demonstrate key differences of the triplet STDP rule compared to the classical pair-based rule in terms of how assemblies are formed, including the realistic asymmetric shape and influence of novel connectivity motifs on network plasticity driven by higher-order correlations. Assembly formation depends on the specific shape of the STDP window and synaptic transmission function, pointing towards an important role of neuromodulatory signals on formation of intrinsically generated assemblies.

Valence and State-Dependent Population Coding in Dopaminergic Neurons in the Fly Mushroom Body

Neuromodulation permits flexibility of synapses, neural circuits, and ultimately behavior. One neuromodulator, dopamine, has been studied extensively in its role as a reward signal during learning and memory across animal species. Newer evidence suggests that dopaminergic neurons (DANs) can modulate sensory perception acutely, thereby allowing an animal to adapt its behavior and decision making to its internal and behavioral state. In addition, some data indicate that DANs are not homogeneous but rather convey different types of information as a heterogeneous population. We have investigated DAN population activity and how it could encode relevant information about sensory stimuli and state by taking advantage of the confined anatomy of DANs innervating the mushroom body (MB) of the fly Drosophila melanogaster. Using in vivo calcium imaging and a custom 3D image registration method, we found that the activity of the population of MB DANs encodes innate valence information of an odor or taste as well as the physiological state of the animal. Furthermore, DAN population activity is strongly correlated with movement, consistent with a role of dopamine in conveying behavioral state to the MB. Altogether, our data and analysis suggest that DAN population activities encode innate odor and taste valence, movement, and physiological state in a MB-compartment-specific manner. We propose that dopamine shapes innate perception through combinatorial population coding of sensory valence, physiological, and behavioral context.

Heterosynaptic Plasticity Determines the Set Point for Cortical Excitatory-Inhibitory Balance

Excitation in neural circuits must be carefully controlled by inhibition to regulate information processing and network excitability. During development, cortical inhibitory and excitatory inputs are initially mismatched but become co-tuned or balanced with experience. However, little is known about how excitatory-inhibitory balance is defined at most synapses or about the mechanisms for establishing or maintaining this balance at specific set points. Here we show how coordinated long-term plasticity calibrates populations of excitatory-inhibitory inputs onto mouse auditory cortical pyramidal neurons. Pairing pre- and postsynaptic activity induced plasticity at paired inputs and different forms of heterosynaptic plasticity at the strongest unpaired synapses, which required minutes of activity and dendritic Ca²⁺ signaling to be computed. Theoretical analyses demonstrated how the relative rate of heterosynaptic plasticity could normalize and stabilize synaptic strengths to achieve any possible excitatory-inhibitory correlation. Thus, excitatory-inhibitory balance is dynamic and cell specific, determined by distinct plasticity rules across multiple excitatory and inhibitory synapses.

A Critical Role for Neocortical Processing of Threat Memory

Memory of cues associated with threat is critical for survival and a leading model for elucidating how sensory information is linked to adaptive behavior by learning. Although the brain-wide circuits mediating auditory threat memory have been intensely investigated, it remains unclear whether the auditory cortex is critically involved. Here we use optogenetic activity manipulations in defined cortical areas and output pathways, viral tracing, pathway-specific in vivo 2-photon calcium imaging, and computational analyses of population plasticity to reveal that the auditory cortex is selectively required for conditioning to complex stimuli, whereas the adjacent temporal association cortex controls all forms of auditory threat memory. More temporal areas have a stronger effect on memory and more neurons projecting to the lateral amygdala, which control memory to complex stimuli through a balanced form of population plasticity that selectively supports discrimination of significant sensory stimuli. Thus, neocortical processing plays a critical role in cued threat memory.

Functional diversity among sensory neurons from efficient coding principles

In many sensory systems the neural signal is coded by the coordinated response of heterogeneous populations of neurons. What computational benefit does this diversity confer on information processing? We derive an efficient coding framework assuming that neurons have evolved to communicate signals optimally given natural stimulus statistics and metabolic constraints. Incorporating nonlinearities and realistic noise, we study optimal population coding of the same sensory variable using two measures: maximizing the mutual information between stimuli and responses, and minimizing the error incurred by the optimal linear decoder of responses. Our theory is applied to a commonly observed splitting of sensory neurons into ON and OFF that signal stimulus increases or decreases, and to populations of monotonically increasing responses of the same type, ON. Depending on the optimality measure, we make different predictions about how to optimally split a population into ON and OFF, and how to allocate the firing thresholds of individual neurons given realistic stimulus distributions and noise, which accord with certain biases observed experimentally.

A Neural Circuit Arbitrates between Persistence and Withdrawal in Hungry Drosophila

In pursuit of food, hungry animals mobilize significant energy resources and overcome exhaustion and fear. How need and motivation control the decision to continue or change behavior is not understood. Using a single fly treadmill, we show that hungry flies persistently track a food odor and increase their effort over repeated trials in the absence of reward suggesting that need dominates negative experience. We further show that odor tracking is regulated by two mushroom body output neurons (MBONs) connecting the MB to the lateral horn. These MBONs, together with dopaminergic neurons and Dop1R2 signaling, control behavioral persistence. Conversely, an octopaminergic neuron, VPM4, which directly innervates one of the MBONs, acts as a brake on odor tracking by connecting feeding and olfaction. Together, our data suggest a function for the MB in internal state-dependent expression of behavior that can be suppressed by external inputs conveying a competing behavioral drive.

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Hunger motivates persistent food odor tracking even without reward

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Two synaptically connected MBONs, -γ1pedc>αβ and -α2sc, regulate odor tracking

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Octopamine neurons connect feeding and counteract MBON and odor tracking

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Dopaminergic neurons and Dop1R2 signaling promote persistent tracking

Special Issue from the 2017 International Conference on Mathematical Neuroscience

The ongoing acquisition of large and multifaceted data sets in neuroscience requires new mathematical tools for quantitatively grounding these experimental findings. Since 2015, the International Conference on Mathematical Neuroscience (ICMNS) has provided a forum for researchers to discuss current mathematical innovations emerging in neuroscience. This special issue assembles current research and tutorials that were presented at the 2017 ICMNS held in Boulder, Colorado from May 30 to June 2. Topics discussed at the meeting include correlation analysis of network activity, information theory for plastic synapses, combinatorics for attractor neural networks, and novel data assimilation methods for neuroscience-all of which are represented in this special issue.

Sensory experience inversely regulates feedforward and feedback excitation-inhibition ratio in rodent visual cortex

Brief (2-3d) monocular deprivation (MD) during the critical period induces a profound loss of responsiveness within binocular (V1b) and monocular (V1m) regions of rodent primary visual cortex. This has largely been ascribed to long-term depression (LTD) at thalamocortical synapses, while a contribution from intracortical inhibition has been controversial. Here we used optogenetics to isolate and measure feedforward thalamocortical and feedback intracortical excitation-inhibition (E-I) ratios following brief MD. Despite depression at thalamocortical synapses, thalamocortical E-I ratio was unaffected in V1b and shifted toward excitation in V1m, indicating that thalamocortical excitation was not effectively reduced. In contrast, feedback intracortical E-I ratio was shifted toward inhibition in V1m, and a computational model demonstrated that these opposing shifts produced an overall suppression of layer 4 excitability. Thus, feedforward and feedback E-I ratios can be independently tuned by visual experience, and enhanced feedback inhibition is the primary driving force behind loss of visual responsiveness.

Computational implications of biophysical diversity and multiple timescales in neurons and synapses for circuit performance

Despite advances in experimental and theoretical neuroscience, we are still trying to identify key biophysical details that are important for characterizing the operation of brain circuits. Biological mechanisms at the level of single neurons and synapses can be combined as 'building blocks' to generate circuit function. We focus on the importance of capturing multiple timescales when describing these intrinsic and synaptic components. Whether inherent in the ionic currents, the neuron's complex morphology, or the neurotransmitter composition of synapses, these multiple timescales prove crucial for capturing the variability and richness of circuit output and enhancing the information-carrying capacity observed across nervous systems.

Homeostatic Activity-Dependent Tuning of Recurrent Networks for Robust Propagation of Activity

Developing neuronal networks display spontaneous bursts of action potentials that are necessary for circuit organization and tuning. While spontaneous activity has been shown to instruct map formation in sensory circuits, it is unknown whether it plays a role in the organization of motor networks that produce rhythmic output. Using computational modeling, we investigate how recurrent networks of excitatory and inhibitory neuronal populations assemble to produce robust patterns of unidirectional and precisely timed propagating activity during organism locomotion. One example is provided by the motor network inDrosophilalarvae, which generates propagating peristaltic waves of muscle contractions during crawling. We examine two activity-dependent models, which tune weak network connectivity based on spontaneous activity patterns: a Hebbian model, where coincident activity in neighboring populations strengthens connections between them; and a homeostatic model, where connections are homeostatically regulated to maintain a constant level of excitatory activity based on spontaneous input. The homeostatic model successfully tunes network connectivity to generate robust activity patterns with appropriate timing relationships between neighboring populations. These timing relationships can be modulated by the properties of spontaneous activity, suggesting its instructive role for generating functional variability in network output. In contrast, the Hebbian model fails to produce the tight timing relationships between neighboring populations required for unidirectional activity propagation, even when additional assumptions are imposed to constrain synaptic growth. These results argue that homeostatic mechanisms are more likely than Hebbian mechanisms to tune weak connectivity based on spontaneous input in a recurrent network for rhythm generation and robust activity propagation.

SIGNIFICANCE STATEMENT

How are neural circuits organized and tuned to maintain stable function and produce robust output? This task is especially difficult during development, when circuit properties change in response to variable environments and internal states. Many developing circuits exhibit spontaneous activity, but its role in the synaptic organization of motor networks that produce rhythmic output is unknown. We studied a model motor network, that when appropriately tuned, generates propagating activity as during crawling inDrosophilalarvae. Based on experimental evidence of activity-dependent tuning of connectivity, we examined plausible mechanisms by which appropriate connectivity emerges. Our results suggest that activity-dependent homeostatic mechanisms are better suited than Hebbian mechanisms for organizing motor network connectivity, and highlight an important difference from sensory areas.

Intrinsic neuronal properties switch the mode of information transmission in networks

Diverse ion channels and their dynamics endow single neurons with complex biophysical properties. These properties determine the heterogeneity of cell types that make up the brain, as constituents of neural circuits tuned to perform highly specific computations. How do biophysical properties of single neurons impact network function? We study a set of biophysical properties that emerge in cortical neurons during the first week of development, eventually allowing these neurons to adaptively scale the gain of their response to the amplitude of the fluctuations they encounter. During the same time period, these same neurons participate in large-scale waves of spontaneously generated electrical activity. We investigate the potential role of experimentally observed changes in intrinsic neuronal properties in determining the ability of cortical networks to propagate waves of activity. We show that such changes can strongly affect the ability of multi-layered feedforward networks to represent and transmit information on multiple timescales. With properties modeled on those observed at early stages of development, neurons are relatively insensitive to rapid fluctuations and tend to fire synchronously in response to wave-like events of large amplitude. Following developmental changes in voltage-dependent conductances, these same neurons become efficient encoders of fast input fluctuations over few layers, but lose the ability to transmit slower, population-wide input variations across many layers. Depending on the neurons' intrinsic properties, noise plays different roles in modulating neuronal input-output curves, which can dramatically impact network transmission. The developmental change in intrinsic properties supports a transformation of a networks function from the propagation of network-wide information to one in which computations are scaled to local activity. This work underscores the significance of simple changes in conductance parameters in governing how neurons represent and propagate information, and suggests a role for background synaptic noise in switching the mode of information transmission.

Differences in ion channel composition endow different neuronal types with distinct computational properties. Understanding how these biophysical differences affect network-level computation is an important frontier. We focus on a set of biophysical properties, experimentally observed in developing cortical neurons, that allow these neurons to efficiently encode their inputs despite time-varying changes in the statistical context. Large-scale propagating waves are autonomously generated by the developing brain even before the onset of sensory experience. Using multi-layered feedforward networks, we examine how changes in intrinsic properties can lead to changes in the network's ability to represent and transmit information on multiple timescales. We demonstrate that measured changes in the computational properties of immature single neurons enable the propagation of slow-varying wave-like inputs. In contrast, neurons with more mature properties are more sensitive to fast fluctuations, which modulate the slow-varying information. While slow events are transmitted with high fidelity in initial network layers, noise degrades transmission in downstream network layers. Our results show how short-term adaptation and modulation of the neurons' input-output firing curves by background synaptic noise determine the ability of neural networks to transmit information on multiple timescales.

Relationship between individual neuron and network spontaneous activity in developing mouse cortex

Spontaneous synchronous activity (SSA) that propagates as electrical waves is found in numerous central nervous system structures and is critical for normal development, but the mechanisms of generation of such activity are not clear. In previous work, we showed that the ventrolateral piriform cortex is uniquely able to initiate SSA in contrast to the dorsal neocortex, which participates in, but does not initiate, SSA (Lischalk JW, Easton CR, Moody WJ. Dev Neurobiol 69: 407-414, 2009). In this study, we used Ca(2+) imaging of cultured embryonic day 18 to postnatal day 2 coronal slices (embryonic day 17 + 1-4 days in culture) of the mouse cortex to investigate the different activity patterns of individual neurons in these regions. In the piriform cortex where SSA is initiated, a higher proportion of neurons was active asynchronously between waves, and a larger number of groups of coactive cells was present compared with the dorsal cortex. When we applied GABA and glutamate synaptic antagonists, asynchronous activity and cellular clusters remained, while synchronous activity was eliminated, indicating that asynchronous activity is a result of cell-intrinsic properties that differ between these regions. To test the hypothesis that higher levels of cell-autonomous activity in the piriform cortex underlie its ability to initiate waves, we constructed a conductance-based network model in which three layers differed only in the proportion of neurons able to intrinsically generate bursting behavior. Simulations using this model demonstrated that a gradient of intrinsic excitability was sufficient to produce directionally propagating waves that replicated key experimental features, indicating that the higher level of cell-intrinsic activity in the piriform cortex may provide a substrate for SSA generation.

Neurobiology of Caenorhabditis elegans Locomotion: Where Do We Stand?

Animals use a nervous system for locomotion in some stage of their life cycle. The nematode Caenorhabditis elegans, a major animal model for almost all fields of experimental biology, has long been used for detailed studies of genetic and physiological locomotion mechanisms. Of its 959 somatic cells, 302 are neurons that are identifiable by lineage, location, morphology, and neurochemistry in every adult hermaphrodite. Of those, 75 motoneurons innervate body wall muscles that provide the thrust during locomotion. In this Overview, we concentrate on the generation of either forward- or backward-directed motion during crawling and swimming. We describe locomotion behavior, the parts constituting the locomotion system, and the relevant neuronal connectivity. Because it is not yet fully understood how these components combine to generate locomotion, we discuss competing hypotheses and models.

When do microcircuits produce beyond-pairwise correlations?

Describing the collective activity of neural populations is a daunting task. Recent empirical studies in retina, however, suggest a vast simplification in how multi-neuron spiking occurs: the activity patterns of retinal ganglion cell (RGC) populations under some conditions are nearly completely captured by pairwise interactions among neurons. In other circumstances, higher-order statistics are required and appear to be shaped by input statistics and intrinsic circuit mechanisms. Here, we study the emergence of higher-order interactions in a model of the RGC circuit in which correlations are generated by common input. We quantify the impact of higher-order interactions by comparing the responses of mechanistic circuit models vs. "null" descriptions in which all higher-than-pairwise correlations have been accounted for by lower order statistics; these are known as pairwise maximum entropy (PME) models. We find that over a broad range of stimuli, output spiking patterns are surprisingly well captured by the pairwise model. To understand this finding, we study an analytically tractable simplification of the RGC model. We find that in the simplified model, bimodal input signals produce larger deviations from pairwise predictions than unimodal inputs. The characteristic light filtering properties of the upstream RGC circuitry suppress bimodality in light stimuli, thus removing a powerful source of higher-order interactions. This provides a novel explanation for the surprising empirical success of pairwise models.

Neural circuits for peristaltic wave propagation in crawling Drosophila larvae: analysis and modeling

Drosophila larvae crawl by peristaltic waves of muscle contractions, which propagate along the animal body and involve the simultaneous contraction of the left and right side of each segment. Coordinated propagation of contraction does not require sensory input, suggesting that movement is generated by a central pattern generator (CPG). We characterized crawling behavior of newly hatched Drosophila larvae by quantifying timing and duration of segmental boundary contractions. We developed a CPG network model that recapitulates these patterns based on segmentally repeated units of excitatory and inhibitory (EI) neuronal populations coupled with immediate neighboring segments. A single network with symmetric coupling between neighboring segments succeeded in generating both forward and backward propagation of activity. The CPG network was robust to changes in amplitude and variability of connectivity strength. Introducing sensory feedback via "stretch-sensitive" neurons improved wave propagation properties such as speed of propagation and segmental contraction duration as observed experimentally. Sensory feedback also restored propagating activity patterns when an inappropriately tuned CPG network failed to generate waves. Finally, in a two-sided CPG model we demonstrated that two types of connectivity could synchronize the activity of two independent networks: connections from excitatory neurons on one side to excitatory contralateral neurons (E to E), and connections from inhibitory neurons on one side to excitatory contralateral neurons (I to E). To our knowledge, such I to E connectivity has not yet been found in any experimental system; however, it provides the most robust mechanism to synchronize activity between contralateral CPGs in our model. Our model provides a general framework for studying the conditions under which a single locally coupled network generates bilaterally synchronized and longitudinally propagating waves in either direction.

Modeling developmental patterns of spontaneous activity

Spontaneous activity is found in many regions of the developing nervous system; such activity is thought to be instructive for guiding developmental processes. In particular, the developing retina generates correlated patterns of activity known as retinal waves. We review the main theoretical models that have been developed to study the mechanisms for generation and propagation of retinal waves. Much of the progress in this field has been due to the close interaction between experimentalists and theorists in analyzing and modeling spontaneous activity. We conclude by describing spontaneous activity models in other systems and suggestions for future modeling work.

Self-organization in the developing nervous system: theoretical models

Sensory maps in the nervous system often connect to each other in a topographic fashion. This is most strikingly seen in the visual system, where neighboring neurons in the retina project to neighboring neurons in the target structure, such as the superior colliculus. This article discusses the developmental mechanisms that are involved in the formation of topographic maps, with an emphasis on the role of theoretical models in helping us to understand these mechanisms. Recent experimental advances in studying the roles of guidance molecules and patterns of spontaneous activity mean that there are new challenges to be addressed by theoretical models. Key questions include understanding what instructional cues are present in the patterns of spontaneous activity, and how activity and guidance molecules might interact. Our discussion concludes by comparing development of visual maps with development of maps in the olfactory system, where the influence of neural activity seems to differ.

The role of vaccination in the control of sars

We assess pre-outbreak and during-outbreak vaccination as control strategies for SARS epidemics using a mathematical model that includes susceptible, latent (traced and untraced), infectious, isolated and recovered individuals. Scenarios focusing on policies that include contact tracing and levels of self-isolation among untraced infected individuals are explored. Bounds on the proportion of pre-outbreak successfully vaccinated individuals are provided using the the basic reproductive number. Uncertainty and sensitivity analyses on the reproductive number are carried out. The final epidemic size under different vaccination scenarios is computed.