Computational neuroscience: beyond the local circuit

Relationships and representations of brain structures, connectivity, dynamics and functions

The review explores the complex interplay between brain structures and their associated functions, presenting a diversity of hierarchical models that enhances our understanding of these relationships. Central to this approach are structure-function flow diagrams, which offer a visual representation of how specific neuroanatomical structures are linked to their functional roles. These diagrams are instrumental in mapping the intricate connections between different brain regions, providing a clearer understanding of how functions emerge from the underlying neural architecture. The study details innovative attempts to develop new functional hierarchies that integrate structural and functional data. These efforts leverage recent advancements in neuroimaging techniques such as fMRI, EEG, MEG, and PET, as well as computational models that simulate neural dynamics. By combining these approaches, the study seeks to create a more refined and dynamic hierarchy that can accommodate the brain's complexity, including its capacity for plasticity and adaptation. A significant focus is placed on the overlap of structures and functions within the brain. The manuscript acknowledges that many brain regions are multifunctional, contributing to different cognitive and behavioral processes depending on the context. This overlap highlights the need for a flexible, non-linear hierarchy that can capture the brain's intricate functional landscape. Moreover, the study examines the interdependence of these functions, emphasizing how the loss or impairment of one function can impact others. Another crucial aspect discussed is the brain's ability to compensate for functional deficits following neurological diseases or injuries. The investigation explores how the brain reorganizes itself, often through the recruitment of alternative neural pathways or the enhancement of existing ones, to maintain functionality despite structural damage. This compensatory mechanism underscores the brain's remarkable plasticity, demonstrating its ability to adapt and reconfigure itself in response to injury, thereby ensuring the continuation of essential functions. In conclusion, the study presents a system of brain functions that integrates structural, functional, and dynamic perspectives. It offers a robust framework for understanding how the brain's complex network of structures supports a wide range of cognitive and behavioral functions, with significant implications for both basic neuroscience and clinical applications.

Efficient models of cortical activity via local dynamic equilibria and coarse-grained interactions

Biologically detailed models of brain circuitry are challenging to build and simulate due to the large number of neurons, their complex interactions, and the many unknown physiological parameters. Simplified mathematical models are more tractable, but harder to evaluate when too far removed from neuroanatomy/physiology. We propose that a multiscale model, coarse-grained (CG) while preserving local biological details, offers the best balance between biological realism and computability. This paper presents such a model. Generally, CG models focus on the interaction between groups of neurons-here termed "pixels"-rather than individual cells. In our case, dynamics are alternately updated at intra- and interpixel scales, with one informing the other, until convergence to equilibrium is achieved on both scales. An innovation is how we exploit the underlying biology: Taking advantage of the similarity in local anatomical structures across large regions of the cortex, we model intrapixel dynamics as a single dynamical system driven by "external" inputs. These inputs vary with events external to the pixel, but their ranges can be estimated a priori. Precomputing and tabulating all potential local responses speed up the updating procedure significantly compared to direct multiscale simulation. We illustrate our methodology using a model of the primate visual cortex. Except for local neuron-to-neuron variability (necessarily lost in any CG approximation) our model reproduces various features of large-scale network models at a tiny fraction of the computational cost. These include neuronal responses as a consequence of their orientation selectivity, a primary function of visual neurons.

Neurodynamical Computing at the Information Boundaries of Intelligent Systems

Artificial intelligence has not achieved defining features of biological intelligence despite models boasting more parameters than neurons in the human brain. In this perspective article, we synthesize historical approaches to understanding intelligent systems and argue that methodological and epistemic biases in these fields can be resolved by shifting away from cognitivist brain-as-computer theories and recognizing that brains exist within large, interdependent living systems. Integrating the dynamical systems view of cognition with the massive distributed feedback of perceptual control theory highlights a theoretical gap in our understanding of nonreductive neural mechanisms. Cell assemblies-properly conceived as reentrant dynamical flows and not merely as identified groups of neurons-may fill that gap by providing a minimal supraneuronal level of organization that establishes a neurodynamical base layer for computation. By considering information streams from physical embodiment and situational embedding, we discuss this computational base layer in terms of conserved oscillatory and structural properties of cortical-hippocampal networks. Our synthesis of embodied cognition, based in dynamical systems and perceptual control, aims to bypass the neurosymbolic stalemates that have arisen in artificial intelligence, cognitive science, and computational neuroscience.

BrainFreeze: Expanding the Capabilities of Neuromorphic Systems Using Mixed-Signal Superconducting Electronics

Superconducting electronics (SCE) is uniquely suited to implement neuromorphic systems. As a result, SCE has the potential to enable a new generation of neuromorphic architectures that can simultaneously provide scalability, programmability, biological fidelity, on-line learning support, efficiency and speed. Supporting all of these capabilities simultaneously has thus far proven to be difficult using existing semiconductor technologies. However, as the fields of computational neuroscience and artificial intelligence (AI) continue to advance, the need for architectures that can provide combinations of these capabilities will grow. In this paper, we will explain how superconducting electronics could be used to address this need by combining analog and digital SCE circuits to build large scale neuromorphic systems. In particular, we will show through detailed analysis that the available SCE technology is suitable for near term neuromorphic demonstrations. Furthermore, this analysis will establish that neuromorphic architectures built using SCE will have the potential to be significantly faster and more efficient than current approaches, all while supporting capabilities such as biologically suggestive neuron models and on-line learning. In the future, SCE-based neuromorphic systems could serve as experimental platforms supporting investigations that are not feasible with current approaches. Ultimately, these systems and the experiments that they support would enable the advancement of neuroscience and the development of more sophisticated AI.

A markerless platform for ambulatory systems neuroscience

Motor systems neuroscience seeks to understand how the brain controls movement. To minimize confounding variables, large-animal studies typically constrain body movement from areas not under observation, ensuring consistent, repeatable behaviors. Such studies have fueled decades of research, but they may be artificially limiting the richness of neural data observed, preventing generalization to more natural movements and settings. Neuroscience studies of unconstrained movement would capture a greater range of behavior and a more complete view of neuronal activity, but instrumenting an experimental rig suitable for large animals presents substantial engineering challenges. Here, we present a markerless, full-body motion tracking and synchronized wireless neural electrophysiology platform for large, ambulatory animals. Composed of four depth (RGB-D) cameras that provide a 360° view of a 4.5-square-meters enclosed area, this system is designed to record a diverse range of neuroethologically relevant behaviors. This platform also allows for the simultaneous acquisition of hundreds of wireless neural recording channels in multiple brain regions. As behavioral and neuronal data are generated at rates below 200 megabytes per second, a single desktop can facilitate hours of continuous recording. This setup is designed for systems neuroscience and neuroengineering research, where synchronized kinematic behavior and neural data are the foundation for investigation. By enabling the study of previously unexplored movement tasks, this system can generate insights into the functioning of the mammalian motor system and provide a platform to develop brain-machine interfaces for unconstrained applications.

Personalizing neuromodulation

In the era of "big data", we are gaining rich person-specific information about neuroanatomy, neural function, and cognitive functions. However, the optimal ways to create precise approaches to optimize individuals' mental functions in health and disease are unclear. Multimodal analysis and modeling approaches can guide neuromodulation by combining anatomical networks, functional signal analysis, and cognitive neuroscience paradigms in single subjects. Our progress could be improved by progressing from statistical fits to mechanistic models. Using transcranial magnetic stimulation as an example, we discuss how integrating methods with a focus on mechanisms could improve our predictions TMS effects within individuals, refine our models of health and disease, and improve our treatments.

Separability and geometry of object manifolds in deep neural networks

Stimuli are represented in the brain by the collective population responses of sensory neurons, and an object presented under varying conditions gives rise to a collection of neural population responses called an ‘object manifold’. Changes in the object representation along a hierarchical sensory system are associated with changes in the geometry of those manifolds, and recent theoretical progress connects this geometry with ‘classification capacity’, a quantitative measure of the ability to support object classification. Deep neural networks trained on object classification tasks are a natural testbed for the applicability of this relation. We show how classification capacity improves along the hierarchies of deep neural networks with different architectures. We demonstrate that changes in the geometry of the associated object manifolds underlie this improved capacity, and shed light on the functional roles different levels in the hierarchy play to achieve it, through orchestrated reduction of manifolds’ radius, dimensionality and inter-manifold correlations.

Neural activity space or manifold that represents object information changes across the layers of a deep neural network. Here the authors present a theoretical account of the relationship between the geometry of the manifolds and the classification capacity of the neural networks.

Volumetric Ca2+ Imaging in the Mouse Brain Using Hybrid Multiplexed Sculpted Light Microscopy

Calcium imaging using two-photon scanning microscopy has become an essential tool in neuroscience. However, in its typical implementation, the tradeoffs between fields of view, acquisition speeds, and depth restrictions in scattering brain tissue pose severe limitations. Here, using an integrated systems-wide optimization approach combined with multiple technical innovations, we introduce a new design paradigm for optical microscopy based on maximizing biological information while maintaining the fidelity of obtained neuron signals. Our modular design utilizes hybrid multi-photon acquisition and allows volumetric recording of neuroactivity at single-cell resolution within up to 1 × 1 × 1.22 mm volumes at up to 17 Hz in awake behaving mice. We establish the capabilities and potential of the different configurations of our imaging system at depth and across brain regions by applying it to in vivo recording of up to 12,000 neurons in mouse auditory cortex, posterior parietal cortex, and hippocampus.

Functional mechanisms underlie the emergence of a diverse range of plasticity phenomena

Diverse plasticity mechanisms are orchestrated to shape the spatiotemporal dynamics underlying brain functions. However, why these plasticity rules emerge and how their dynamics interact with neural activity to give rise to complex neural circuit dynamics remains largely unknown. Here we show that both Hebbian and homeostatic plasticity rules emerge from a functional perspective of neuronal dynamics whereby each neuron learns to encode its own activity in the population activity, so that the activity of the presynaptic neuron can be decoded from the activity of its postsynaptic neurons. We explain how a range of experimentally observed plasticity phenomena with widely separated time scales emerge from learning this encoding function, including STDP and its frequency dependence, and metaplasticity. We show that when implemented in neural circuits, these plasticity rules naturally give rise to essential neural response properties, including variable neural dynamics with balanced excitation and inhibition, and approximately log-normal distributions of synaptic strengths, while simultaneously encoding a complex real-world visual stimulus. These findings establish a novel function-based account of diverse plasticity mechanisms, providing a unifying framework relating plasticity, dynamics and neural computation.

Many experiments have documented a variety of ways in which the connectivity strengths between neurons change in response to the activity of neurons. These changes are an important part of learning. However, it is not understood how such a diverse range of observations can be understood as consequences of an underlying algorithm used by brains for learning. In order to understand such a learning algorithm it is also necessary to understand the neural computation that is being learned, that is, how the functions of the brain are encoded in the activity of its neurons and its connectivity. In this work we propose a simple way in which information can be encoded and decoded in a network of neurons for operating on real-world stimuli, and how this can be learned using two fundamental plasticity rules that change the strength of connections between neurons in response to neural activity. Surprisingly, many experimental observations result as consequences of this approach, indicating that studying the learning of function provides a novel framework for unifying plasticity, dynamics, and neural computation.

How the Hippocampus Represents Memories: Making Sense of Memory Allocation Studies

In recent years there has been a wealth of studies investigating how memories are allocated in the hippocampus. Some of those studies showed that it is possible to manipulate the identity of neurons recruited to represent a given memory without affecting the memory's behavioral expression. Those findings raised questions about how the hippocampus represents memories, with some researchers arguing that hippocampal neurons do not represent fixed stimuli. Herein, an alternative hypothesis is argued. Neurons in high-order brain regions can be tuned to multiple dimensions, forming complex, abstract representations. It is argued that such complex receptive fields allow those neurons to show some flexibility in their responses while still representing relatively fixed sets of stimuli. Moreover, it is pointed out that changes induced by artificial manipulation of cell assemblies are not completely redundant-the observed behavioral redundancy does not imply cognitive redundancy, as different, but similar, memories may induce the same behavior.

Data and Power Efficient Intelligence with Neuromorphic Learning Machines

The success of deep networks and recent industry involvement in brain-inspired computing is igniting a widespread interest in neuromorphic hardware that emulates the biological processes of the brain on an electronic substrate. This review explores interdisciplinary approaches anchored in machine learning theory that enable the applicability of neuromorphic technologies to real-world, human-centric tasks. We find that (1) recent work in binary deep networks and approximate gradient descent learning are strikingly compatible with a neuromorphic substrate; (2) where real-time adaptability and autonomy are necessary, neuromorphic technologies can achieve significant advantages over main-stream ones; and (3) challenges in memory technologies, compounded by a tradition of bottom-up approaches in the field, block the road to major breakthroughs. We suggest that a neuromorphic learning framework, tuned specifically for the spatial and temporal constraints of the neuromorphic substrate, will help guiding hardware algorithm co-design and deploying neuromorphic hardware for proactive learning of real-world data.

Embedded ensemble encoding hypothesis: The role of the "Prepared" cell

We here reconsider current theories of neural ensembles in the context of recent discoveries about neuronal dendritic physiology. The key physiological observation is that the dendritic plateau potential produces sustained depolarization of the cell body (amplitude 10-20 mV, duration 200-500 ms). Our central hypothesis is that synaptically-evoked dendritic plateau potentials lead to a prepared state of a neuron that favors spike generation. The plateau both depolarizes the cell toward spike threshold, and provides faster response to inputs through a shortened membrane time constant. As a result, the speed of synaptic-to-action potential (AP) transfer is faster during the plateau phase. Our hypothesis relates the changes from "resting" to "depolarized" neuronal state to changes in ensemble dynamics and in network information flow. The plateau provides the Prepared state (sustained depolarization of the cell body) with a time window of 200-500 ms. During this time, a neuron can tune into ongoing network activity and synchronize spiking with other neurons to provide a coordinated Active state (robust firing of somatic APs), which would permit "binding" of signals through coordination of neural activity across a population. The transient Active ensemble of neurons is embedded in the longer-lasting Prepared ensemble of neurons. We hypothesize that "embedded ensemble encoding" may be an important organizing principle in networks of neurons.

Computational Models for Calcium-Mediated Astrocyte Functions

The computational neuroscience field has heavily concentrated on the modeling of neuronal functions, largely ignoring other brain cells, including one type of glial cell, the astrocytes. Despite the short history of modeling astrocytic functions, we were delighted about the hundreds of models developed so far to study the role of astrocytes, most often in calcium dynamics, synchronization, information transfer, and plasticity in vitro, but also in vascular events, hyperexcitability, and homeostasis. Our goal here is to present the state-of-the-art in computational modeling of astrocytes in order to facilitate better understanding of the functions and dynamics of astrocytes in the brain. Due to the large number of models, we concentrated on a hundred models that include biophysical descriptions for calcium signaling and dynamics in astrocytes. We categorized the models into four groups: single astrocyte models, astrocyte network models, neuron-astrocyte synapse models, and neuron-astrocyte network models to ease their use in future modeling projects. We characterized the models based on which earlier models were used for building the models and which type of biological entities were described in the astrocyte models. Features of the models were compared and contrasted so that similarities and differences were more readily apparent. We discovered that most of the models were basically generated from a small set of previously published models with small variations. However, neither citations to all the previous models with similar core structure nor explanations of what was built on top of the previous models were provided, which made it possible, in some cases, to have the same models published several times without an explicit intention to make new predictions about the roles of astrocytes in brain functions. Furthermore, only a few of the models are available online which makes it difficult to reproduce the simulation results and further develop the models. Thus, we would like to emphasize that only via reproducible research are we able to build better computational models for astrocytes, which truly advance science. Our study is the first to characterize in detail the biophysical and biochemical mechanisms that have been modeled for astrocytes.

Computational Foundations of Natural Intelligence

New developments in AI and neuroscience are revitalizing the quest to understanding natural intelligence, offering insight about how to equip machines with human-like capabilities. This paper reviews some of the computational principles relevant for understanding natural intelligence and, ultimately, achieving strong AI. After reviewing basic principles, a variety of computational modeling approaches is discussed. Subsequently, I concentrate on the use of artificial neural networks as a framework for modeling cognitive processes. This paper ends by outlining some of the challenges that remain to fulfill the promise of machines that show human-like intelligence.

Coupled variability in primary sensory areas and the hippocampus during spontaneous activity

The cerebral cortex is an anatomically divided and functionally specialized structure. It includes distinct areas, which work on different states over time. The structural features of spiking activity in sensory cortices have been characterized during spontaneous and evoked activity. However, the coordination among cortical and sub-cortical neurons during spontaneous activity across different states remains poorly characterized. We addressed this issue by studying the temporal coupling of spiking variability recorded from primary sensory cortices and hippocampus of anesthetized or freely behaving rats. During spontaneous activity, spiking variability was highly correlated across primary cortical sensory areas at both small and large spatial scales, whereas the cortico-hippocampal correlation was modest. This general pattern of spiking variability was observed under urethane anesthesia, as well as during waking, slow-wave sleep and rapid-eye-movement sleep, and was unchanged by novel stimulation. These results support the notion that primary sensory areas are strongly coupled during spontaneous activity.

From Whole-Brain Data to Functional Circuit Models: The Zebrafish Optomotor Response

Detailed descriptions of brain-scale sensorimotor circuits underlying vertebrate behavior remain elusive. Recent advances in zebrafish neuroscience offer new opportunities to dissect such circuits via whole-brain imaging, behavioral analysis, functional perturbations, and network modeling. Here, we harness these tools to generate a brain-scale circuit model of the optomotor response, an orienting behavior evoked by visual motion. We show that such motion is processed by diverse neural response types distributed across multiple brain regions. To transform sensory input into action, these regions sequentially integrate eye- and direction-specific sensory streams, refine representations via interhemispheric inhibition, and demix locomotor instructions to independently drive turning and forward swimming. While experiments revealed many neural response types throughout the brain, modeling identified the dimensions of functional connectivity most critical for the behavior. We thus reveal how distributed neurons collaborate to generate behavior and illustrate a paradigm for distilling functional circuit models from whole-brain data.

A new neuroinformatics approach to personalized medicine in neurology: The Virtual Brain

PURPOSE OF REVIEW

An exciting advance in the field of neuroimaging is the acquisition and processing of very large data sets (so called 'big data'), permitting large-scale inferences that foster a greater understanding of brain function in health and disease. Yet what we are clearly lacking are quantitative integrative tools to translate this understanding to the individual level to lay the basis for personalized medicine.

RECENT FINDINGS

Here we address this challenge through a review on how the relatively new field of neuroinformatics modeling has the capacity to track brain network function at different levels of inquiry, from microscopic to macroscopic and from the localized to the distributed. In this context, we introduce a new and unique multiscale approach, The Virtual Brain (TVB), that effectively models individualized brain activity, linking large-scale (macroscopic) brain dynamics with biophysical parameters at the microscopic level. We also show how TVB modeling provides unique biological interpretable data in epilepsy and stroke.

SUMMARY

These results establish the basis for a deliberate integration of computational biology and neuroscience into clinical approaches for elucidating cellular mechanisms of disease. In the future, this can provide the means to create a collection of disease-specific models that can be applied on the individual level to personalize therapeutic interventions. VIDEO ABSTRACT.

Biologically based neural circuit modelling for the study of fear learning and extinction

The neuronal systems that promote protective defensive behaviours have been studied extensively using Pavlovian conditioning. In this paradigm, an initially neutral-conditioned stimulus is paired with an aversive unconditioned stimulus leading the subjects to display behavioural signs of fear. Decades of research into the neural bases of this simple behavioural paradigm uncovered that the amygdala, a complex structure comprised of several interconnected nuclei, is an essential part of the neural circuits required for the acquisition, consolidation and expression of fear memory. However, emerging evidence from the confluence of electrophysiological, tract tracing, imaging, molecular, optogenetic and chemogenetic methodologies, reveals that fear learning is mediated by multiple connections between several amygdala nuclei and their distributed targets, dynamical changes in plasticity in local circuit elements as well as neuromodulatory mechanisms that promote synaptic plasticity. To uncover these complex relations and analyse multi-modal data sets acquired from these studies, we argue that biologically realistic computational modelling, in conjunction with experiments, offers an opportunity to advance our understanding of the neural circuit mechanisms of fear learning and to address how their dysfunction may lead to maladaptive fear responses in mental disorders.

Fast volumetric calcium imaging across multiple cortical layers using sculpted light

Although whole-organism calcium imaging in small and semi-transparent animals has been demonstrated, capturing the functional dynamics of large-scale neuronal circuits in awake behaving mammals at high speed and resolution has remained one of the main frontiers in systems neuroscience. Here we present a method based on light sculpting that enables unbiased single- and dual-plane high-speed (up to 160 Hz) calcium imaging as well as in vivo volumetric calcium imaging of a mouse cortical column (0.5 mm × 0.5 mm × 0.5 mm) at single-cell resolution and fast volume rates (3-6 Hz). We achieved this by tailoring the point-spread function of our microscope to the structures of interest while maximizing the signal-to-noise ratio using a home-built fiber laser amplifier with pulses that are synchronized to the imaging voxel speed. This enabled in vivo recording of calcium dynamics of several thousand neurons across cortical layers and in the hippocampus of awake behaving mice.

Breeding novel solutions in the brain: a model of Darwinian neurodynamics

Background: The fact that surplus connections and neurons are pruned during development is well established. We complement this selectionist picture by a proof-of-principle model of evolutionary search in the brain, that accounts for new variations in theory space. We present a model for Darwinian evolutionary search for candidate solutions in the brain.

Methods: We combine known components of the brain – recurrent neural networks (acting as attractors), the action selection loop and implicit working memory – to provide the appropriate Darwinian architecture. We employ a population of attractor networks with palimpsest memory. The action selection loop is employed with winners-share-all dynamics to select for candidate solutions that are transiently stored in implicit working memory.

Results: We document two processes: selection of stored solutions and evolutionary search for novel solutions. During the replication of candidate solutions attractor networks occasionally produce recombinant patterns, increasing variation on which selection can act. Combinatorial search acts on multiplying units (activity patterns) with hereditary variation and novel variants appear due to (i) noisy recall of patterns from the attractor networks, (ii) noise during transmission of candidate solutions as messages between networks, and, (iii) spontaneously generated, untrained patterns in spurious attractors.

Conclusions: Attractor dynamics of recurrent neural networks can be used to model Darwinian search. The proposed architecture can be used for fast search among stored solutions (by selection) and for evolutionary search when novel candidate solutions are generated in successive iterations. Since all the suggested components are present in advanced nervous systems, we hypothesize that the brain could implement a truly evolutionary combinatorial search system, capable of generating novel variants.

Breeding novel solutions in the brain: a model of Darwinian neurodynamics

Background: The fact that surplus connections and neurons are pruned during development is well established. We complement this selectionist picture by a proof-of-principle model of evolutionary search in the brain, that accounts for new variations in theory space. We present a model for Darwinian evolutionary search for candidate solutions in the brain. Methods: We combine known components of the brain - recurrent neural networks (acting as attractors), the action selection loop and implicit working memory - to provide the appropriate Darwinian architecture. We employ a population of attractor networks with palimpsest memory. The action selection loop is employed with winners-share-all dynamics to select for candidate solutions that are transiently stored in implicit working memory. Results: We document two processes: selection of stored solutions and evolutionary search for novel solutions. During the replication of candidate solutions attractor networks occasionally produce recombinant patterns, increasing variation on which selection can act. Combinatorial search acts on multiplying units (activity patterns) with hereditary variation and novel variants appear due to (i) noisy recall of patterns from the attractor networks, (ii) noise during transmission of candidate solutions as messages between networks, and, (iii) spontaneously generated, untrained patterns in spurious attractors. Conclusions: Attractor dynamics of recurrent neural networks can be used to model Darwinian search. The proposed architecture can be used for fast search among stored solutions (by selection) and for evolutionary search when novel candidate solutions are generated in successive iterations. Since all the suggested components are present in advanced nervous systems, we hypothesize that the brain could implement a truly evolutionary combinatorial search system, capable of generating novel variants.

Genetic variants in Alzheimer disease - molecular and brain network approaches

Genetic studies in late-onset Alzheimer disease (LOAD) are aimed at identifying core disease mechanisms and providing potential biomarkers and drug candidates to improve clinical care of AD. However, owing to the complexity of LOAD, including pathological heterogeneity and disease polygenicity, extraction of actionable guidance from LOAD genetics has been challenging. Past attempts to summarize the effects of LOAD-associated genetic variants have used pathway analysis and collections of small-scale experiments to hypothesize functional convergence across several variants. In this Review, we discuss how the study of molecular, cellular and brain networks provides additional information on the effects of LOAD-associated genetic variants. We then discuss emerging combinations of these omic data sets into multiscale models, which provide a more comprehensive representation of the effects of LOAD-associated genetic variants at multiple biophysical scales. Furthermore, we highlight the clinical potential of mechanistically coupling genetic variants and disease phenotypes with multiscale brain models.

Analysis of complex neural circuits with nonlinear multidimensional hidden state models

A universal need in understanding complex networks is the identification of individual information channels and their mutual interactions under different conditions. In neuroscience, our premier example, networks made up of billions of nodes dynamically interact to bring about thought and action. Granger causality is a powerful tool for identifying linear interactions, but handling nonlinear interactions remains an unmet challenge. We present a nonlinear multidimensional hidden state (NMHS) approach that achieves interaction strength analysis and decoding of networks with nonlinear interactions by including latent state variables for each node in the network. We compare NMHS to Granger causality in analyzing neural circuit recordings and simulations, improvised music, and sociodemographic data. We conclude that NMHS significantly extends the scope of analyses of multidimensional, nonlinear networks, notably in coping with the complexity of the brain.

The effects of neuron morphology on graph theoretic measures of network connectivity: the analysis of a two-level statistical model

We developed a two-level statistical model that addresses the question of how properties of neurite morphology shape the large-scale network connectivity. We adopted a low-dimensional statistical description of neurites. From the neurite model description we derived the expected number of synapses, node degree, and the effective radius, the maximal distance between two neurons expected to form at least one synapse. We related these quantities to the network connectivity described using standard measures from graph theory, such as motif counts, clustering coefficient, minimal path length, and small-world coefficient. These measures are used in a neuroscience context to study phenomena from synaptic connectivity in the small neuronal networks to large scale functional connectivity in the cortex. For these measures we provide analytical solutions that clearly relate different model properties. Neurites that sparsely cover space lead to a small effective radius. If the effective radius is small compared to the overall neuron size the obtained networks share similarities with the uniform random networks as each neuron connects to a small number of distant neurons. Large neurites with densely packed branches lead to a large effective radius. If this effective radius is large compared to the neuron size, the obtained networks have many local connections. In between these extremes, the networks maximize the variability of connection repertoires. The presented approach connects the properties of neuron morphology with large scale network properties without requiring heavy simulations with many model parameters. The two-steps procedure provides an easier interpretation of the role of each modeled parameter. The model is flexible and each of its components can be further expanded. We identified a range of model parameters that maximizes variability in network connectivity, the property that might affect network capacity to exhibit different dynamical regimes.

Simple, biologically-constrained CA1 pyramidal cell models using an intact, whole hippocampus context

The hippocampus is a heavily studied brain structure due to its involvement in learning and memory. Detailed models of excitatory, pyramidal cells in hippocampus have been developed using a range of experimental data. These models have been used to help us understand, for example, the effects of synaptic integration and voltage gated channel densities and distributions on cellular responses. However, these cellular outputs need to be considered from the perspective of the networks in which they are embedded. Using modeling approaches, if cellular representations are too detailed, it quickly becomes computationally unwieldy to explore large network simulations. Thus, simple models are preferable, but at the same time they need to have a clear, experimental basis so as to allow physiologically based understandings to emerge. In this article, we describe the development of simple models of CA1 pyramidal cells, as derived in a well-defined experimental context of an intact, whole hippocampus preparation expressing population oscillations. These models are based on the intrinsic properties and frequency-current profiles of CA1 pyramidal cells, and can be used to build, fully examine, and analyze large networks.