An algorithm to predict the connectome of neural microcircuits

Experimentally mapping synaptic connections, in terms of the numbers and locations of their synapses and estimating connection probabilities, is still not a tractable task, even for small volumes of tissue. In fact, the six layers of the neocortex contain thousands of unique types of synaptic connections between the many different types of neurons, of which only a handful have been characterized experimentally. Here we present a theoretical framework and a data-driven algorithmic strategy to digitally reconstruct the complete synaptic connectivity between the different types of neurons in a small well-defined volume of tissue the micro scale connectome of a neural microcircuit. By enforcing a set of established principles of synaptic connectivity, and leveraging interdependencies between fundamental properties of neural microcircuits to constrain the reconstructed connectivity, the algorithm yields three parameters per connection type that predict the anatomy of all types of biologically viable synaptic connections. The predictions reproduce a spectrum of experimental data on synaptic connectivity not used by the algorithm. We conclude that an algorithmic approach to the connectome can serve as a tool to accelerate experimental mapping, indicating the minimal dataset required to make useful predictions, identifying the datasets required to improve their accuracy, testing the feasibility of experimental measurements, and making it possible to test hypotheses of synaptic connectivity

Data-driven model of the hippocampus using the HBP Brain Simulation Platform

The hippocampus is one of four brain regions being modeled in the ramp-up phase of the Human Brain Project (HBP), testing and guiding the development of the HBP Brain Simulation Platform (BSP) to be released in March 2016. Using preliminary versions of BSP applications developed at the Blue Brain Project, a first draft data-driven model of hippocampus was assembled, integrating data available from HBP and community sources. In brief, the building process started by populating the hippocampal volume, defined by the Allen Brain Atlas, with a series of reconstructions of well-characterized cell types according to experimentally observed densities and proportions. A connectome was generated as previously described [1], constrained by biological values for bouton density and synapses per connection. Single cell electrical models and synapse physiology were constrained by electrophysiological recordings and publicly available data. Further datasets not used as input during model building were used to validate the model. This first draft of the circuit model and the pipeline to build it are to be released with the HBP-BSP in March 2016, and they will be periodically updated. The model represents a resource for the community to integrate data, perform in silico experiments, and test hypotheses. Establishing a community process for the continued refinement of the model is planned for the next phase of the HBP. [1] Reimann, M. et al. An algorithm to predict the connectome of neural microcircuits. Front. Comput. Neurosci. (2015). http://dx.doi.org/10.3389/fncom.2015.0012

A realistic morpho-anatomical connection strategy for modelling full-scale point-neuron microcircuits

The modeling of extended microcircuits is emerging as an effective tool to simulate the neurophysiological correlates of brain activity and to investigate brain dysfunctions. However, for specific networks, a realistic modeling approach based on the combination of available physiological, morphological and anatomical data is still an open issue. One of the main problems in the generation of realistic networks lies in the strategy adopted to build network connectivity. Here we propose a method to implement a neuronal network at single cell resolution by using the geometrical probability volumes associated with pre- and postsynaptic neurites. This allows us to build a network with plausible connectivity properties without the explicit use of computationally intensive touch detection algorithms using full 3D neuron reconstructions. The method has been benchmarked for the mouse hippocampus CA1 area, and the results show that this approach is able to generate full-scale brain networks at single cell resolution that are in good agreement with experimental findings. This geometric reconstruction of axonal and dendritic occupancy, by effectively reflecting morphological and anatomical constraints, could be integrated into structured simulators generating entire circuits of different brain areas facilitating the simulation of different brain regions with realistic models

Comments and general discussion on “The anatomical problem posed by brain complexity and size: a potential solution”

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Cliques of Neurons Bound into Cavities Provide a Missing Link between Structure and Function

A recent publication provides the network graph for a neocortical microcircuit comprising 8 million connections between 31,000 neurons (H. Markram, et al., Reconstruction and simulation of neocortical microcircuitry, Cell, 163 (2015) no. 2, 456-492). Since traditional graph-theoretical methods may not be sufficient to understand the immense complexity of such a biological network, we explored whether methods from algebraic topology could provide a new perspective on its structural and functional organization. Structural topological analysis revealed that directed graphs representing connectivity among neurons in the microcircuit deviated significantly from different varieties of randomized graph. In particular, the directed graphs contained in the order of $10^7$ simplices {\DH} groups of neurons with all-to-all directed connectivity. Some of these simplices contained up to 8 neurons, making them the most extreme neuronal clustering motif ever reported. Functional topological analysis of simulated neuronal activity in the microcircuit revealed novel spatio-temporal metrics that provide an effective classification of functional responses to qualitatively different stimuli. This study represents the first algebraic topological analysis of structural connectomics and connectomics-based spatio-temporal activity in a biologically realistic neural microcircuit. The methods used in the study show promise for more general applications in network science

Reproducible Neural Network Simulations: Statistical Methods for Model Validation on the Level of Network Activity Data

Computational neuroscience relies on simulations of neural network models to bridge the gap between the theory of neural networks and the experimentally observed activity dynamics in the brain. The rigorous validation of simulation results against reference data is thus an indispensable part of any simulation workflow. Moreover, the availability of different simulation environments and levels of model description require also validation of model implementations against each other to evaluate their equivalence. Despite rapid advances in the formalized description of models, data, and analysis workflows, there is no accepted consensus regarding the terminology and practical implementation of validation workflows in the context of neural simulations. This situation prevents the generic, unbiased comparison between published models, which is a key element of enhancing reproducibility of computational research in neuroscience. In this study, we argue for the establishment of standardized statistical test metrics that enable the quantitative validation of network models on the level of the population dynamics. Despite the importance of validating the elementary components of a simulation, such as single cell dynamics, building networks from validated building blocks does not entail the validity of the simulation on the network scale. Therefore, we introduce a corresponding set of validation tests and present an example workflow that practically demonstrates the iterative model validation of a spiking neural network model against its reproduction on the SpiNNaker neuromorphic hardware system. We formally implement the workflow using a generic Python library that we introduce for validation tests on neural network activity data. Together with the companion study (Trensch et al., 2018), the work presents a consistent definition, formalization, and implementation of the verification and validation process for neural network simulations

Reconciliation of weak pairwise spike-train correlations and highly coherent local field potentials across space

Chronic and acute implants of multi-electrode arrays that cover several mm$^2$ of neural tissue provide simultaneous access to population signals like extracellular potentials and the spiking activity of 100 or more individual neurons. While the recorded data may uncover principles of brain function, its interpretation calls for multiscale computational models with corresponding spatial dimensions and signal predictions. Such models can facilitate the search of mechanisms underlying observed spatiotemporal activity patterns in cortex. Multi-layer spiking neuron network models of local cortical circuits covering ~1 mm$^2$ have been developed, integrating experimentally obtained neuron-type specific connectivity data and reproducing features of in-vivo spiking statistics. With forward models, local field potentials (LFPs) can be computed from the simulated spiking activity. To account for the spatial scale of common neural recordings, we extend a local network and LFP model to 4x4 mm$^2$. The upscaling preserves the neuron densities, and introduces distance-dependent connection probabilities and delays. As detailed experimental connectivity data is partially lacking, we address this uncertainty in model parameters by testing parameter combinations within biologically plausible bounds. Based on model predictions of spiking activity and LFPs, we find that the upscaling procedure preserves the overall spiking statistics of the original model and reproduces asynchronous irregular spiking across populations and weak pairwise spike-train correlations observed in sensory cortex. In contrast with the weak spike-train correlations, the correlation of LFP signals is strong and distance-dependent, compatible with experimental observations. Enhanced spatial coherence in the low-gamma band may explain the recent experimental report of an apparent band-pass filter effect in the spatial reach of the LFP.Comment: 44 pages, 9 figures, 5 table

A Brief History of Simulation Neuroscience

Our knowledge of the brain has evolved over millennia in philosophical, experimental and theoretical phases. We suggest that the next phase is simulation neuroscience. The main drivers of simulation neuroscience are big data generated at multiple levels of brain organization and the need to integrate these data to trace the causal chain of interactions within and across all these levels. Simulation neuroscience is currently the only methodology for systematically approaching the multiscale brain. In this review, we attempt to reconstruct the deep historical paths leading to simulation neuroscience, from the first observations of the nerve cell to modern efforts to digitally reconstruct and simulate the brain. Neuroscience began with the identification of the neuron as the fundamental unit of brain structure and function and has evolved towards understanding the role of each cell type in the brain, how brain cells are connected to each other, and how the seemingly infinite networks they form give rise to the vast diversity of brain functions. Neuronal mapping is evolving from subjective descriptions of cell types towards objective classes, subclasses and types. Connectivity mapping is evolving from loose topographic maps between brain regions towards dense anatomical and physiological maps of connections between individual genetically distinct neurons. Functional mapping is evolving from psychological and behavioral stereotypes towards a map of behaviors emerging from structural and functional connectomes. We show how industrialization of neuroscience and the resulting large disconnected datasets are generating demand for integrative neuroscience, how the scale of neuronal and connectivity maps is driving digital atlasing and digital reconstruction to piece together the multiple levels of brain organization, and how the complexity of the interactions between molecules, neurons, microcircuits and brain regions is driving brain simulation to understand the interactions in the multiscale brain

A study of cortical network models with realistic connectivity

Structure is fundamental in shaping the types of computations that neuronal circuits can perform. Explaining the laws that determine the connectivity properties of brain networks and their implications in neuronal dynamics is therefore an important step in the understanding of how brains operate. The local circuits of cortex, which are considered to carry out the basic and essential computations for brain functioning, exhibit a highly stereotyped and organized architecture, which is, in very general terms, conserved across different species, brain areas and individuals. An appropriate way to mathematically represent this family of networks is by means of models defined by a set of connectivity laws that include a certain degree of randomness. These laws reflect the common structural scaffold, whereas the randomness should be interpreted as the variability across the different networks in the ensemble. There is growing experimental evidence that the local circuits of cerebral cortex are far from the simplest random model, according to which connections appear independently with a fixed probability. This evidence is based on a set of observed features that have been collectively called the "nonrandomness" of the cortical circuitry. In this thesis we have explored to what extent several alternative architectures (clustered networks, networks with distance-dependent connectivity and networks that exhibit a given in/out-degree distribution) could be compatible with the reported nonrandom features. We showed that all these structural models can explain the experimental observations, which implies that these nonrandom properties do not provide much information about the underlying organization. This is mainly due to the fact that real data are collected from sparse neuronal samples due to experimental limitations. We sought a local measure that can nevertheless help to distinguish between different alternatives, and we found it in the "sample degree correlation" (SDC), or the correlation coefficient between in- and out-degrees in small groups of neurons. The analysis of the SDC in real data suggests that cortical microcircuits are heterogeneous in structure and possibly shaped through a mixture of distance-dependent and non-symmetrical organizational principles. We finally explored some of the dynamical consequences of imposing a heterogeneous structure in models of neuronal activity. This heterogeneity appears through an arbitrary joint in/out-degree distribution in the entire network. By means of both mean-field approximations and spectral analysis, we demonstrate that broad and positively correlated degree distributions can have an important effect on neuronal dynamics, which suggests that this particular type of structural heterogeneity might allow for richer network computations as compared to standard random models.L'estructura té un paper fonamental a l'hora de determinar els tipus d'operacions que els circuits neuronals poden dur a terme. Entendre les lleis que defineixen la connectivitat de les xarxes del cervell i les seves implicacions en la dinàmica neuronal és, per tant, un pas important en la comprensió del funcionament d'aquestes xarxes. Els circuits locals del còrtex, que es creu suporten les computacions essencials i bàsiques de la funció cerebral, estan organitzats de manera altament ordenada i estereotipada, i aquesta arquitectura, en termes molt generals, s'ha conservat al llarg de les diferents espècies, de les diverses àrees cerebrals i dels individus. Una bona manera de representar matemàticament aquesta família de xarxes és mitjançant models definits per una sèrie de lleis de connectivitat que inclouen un cert grau d'aleatorietat. Les lleis reflecteixen el patró estructural comú, mentre que l'aleatorietat ha de ser interpretada com la variabilitat quan es comparen diferents xarxes del conjunt. Cada vegada hi ha més evidència experimental que els circuits locals del còrtex estan lluny del model aleatori més simple, segons el qual les connexions apareixen de manera independent amb una probabilitat fixada. Aquesta troballa es fonamenta en un conjunt d'observacions a les quals ens referim col·lectivament com la ?no aleatorietat? dels circuits corticals. En aquesta tesi hem explorat fins a quin punt diverses arquitectures alternatives (xarxes amb agrupació, xarxes amb connectivitat dependent de la distància i xarxes definides a través d'una certa distribució de graus d'entrada i de sortida) podrien ser compatibles amb les propietats de no aleatorietat. Hem mostrat que tots els models estructurals alternatius que havíem proposat poden explicar les observacions esmentades, per tant aquestes propietats no aporten gaire informació sobre el tipus d'organització subjacent. Això es deu principalment al fet que les dades reals provenen d'anàlisis molt restringides, en les quals l'estructura s'estudia a partir de mostres locals formades per poques neurones. Vam buscar un estadístic local que permetés, malgrat aquestes dificultats, distingir entre les diverses estructures alternatives, i l'hem trobat en el coeficient de correlació entre els graus d'entrada i de sortida en mostres petites, que hem anomenat "sample degree correlation" (SDC) en anglès. L'anàlisi d'aquesta mesura en dades reals suggereix que els microcircuits corticals tenen una configuració heterogènia -en el sentit que semblen diferir dels models simples proposats- i estan modelats possiblement per factors dependents de la distància física entre neurones però també per principis addicionals que actuen de manera no simètrica. Finalment, hem estudiat algunes de les conseqüències dinàmiques d'imposar una estructura heterogènia en models d'activitat neuronal. Aquesta heterogeneïtat apareix en els nostres models a través de la distribució conjunta de graus d'entrada i de sortida a la xarxa completa. Fent ús d'aproximacions de camp mitjà i de l'anàlisi espectral, hem mostrat que les distribucions de grau amb elevada variància i correlació positiva poden tenir un efecte rellevant en la dinàmica neuronal, fet que suggereix que aquest tipus d'heterogeneïtat estructural podria facilitar uns modes de computació més rics en comparació dels models aleatoris estàndard.Postprint (published version