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Sustainable research on computational models of neuronal networks requires published models to be understandable, reproducible, and extendable. Missing details or ambiguities about mathematical concepts and assumptions, algorithmic implementations, or parameterizations hinder progress. Such flaws are unfortunately frequent and one reason is a lack of readily applicable standards and tools for model description. Our work aims to advance complete and concise descriptions of network connectivity but also to guide the implementation of connection routines in simulation software and neuromorphic hardware systems. We first review models made available by the computational neuroscience community in the repositories ModelDB and Open Source Brain, and investigate the corresponding connectivity structures and their descriptions in both manuscript and code. The review comprises the connectivity of networks with diverse levels of neuroanatomical detail and exposes how connectivity is abstracted in existing description languages and simulator interfaces. We find that a substantial proportion of the published descriptions of connectivity is ambiguous. Based on this review, we derive a set of connectivity concepts for deterministically and probabilistically connected networks and also address networks embedded in metric space. Beside these mathematical and textual guidelines, we propose a unified graphical notation for network diagrams to facilitate an intuitive understanding of network properties. Examples of representative network models demonstrate the practical use of the ideas. We hope that the proposed standardizations will contribute to unambiguous descriptions and reproducible implementations of neuronal network connectivity in computational neuroscience.

Modern electrophysiological recordings simultaneously capture single-unit spiking activities of hundreds of neurons spread across large cortical distances. Yet, this parallel activity is often confined to relatively low-dimensional manifolds. This implies strong coordination also among neurons that are most likely not even connected. Here, we combine in vivo recordings with network models and theory to characterize the nature of mesoscopic coordination patterns in macaque motor cortex and to expose their origin: We find that heterogeneity in local connectivity supports network states with complex long-range cooperation between neurons that arises from multi-synaptic, short-range connections. Our theory explains the experimentally observed spatial organization of covariances in resting state recordings as well as the behaviorally related modulation of covariance patterns during a reach-to-grasp task. The ubiquity of heterogeneity in local cortical circuits suggests that the brain uses the described mechanism to flexibly adapt neuronal coordination to momentary demands.

Male moths aiming to locate pheromone-releasing females rely on stimulus-adapted search maneuvers complicated by a discontinuous distribution of pheromone patches. They alternate sequences of upwind surge when perceiving the pheromone and cross-or downwind casting when the odor is lost. We compare four search strategies: three reactive versus one cognitive. The former consist of pre-programmed movement sequences triggered by pheromone detections while the latter uses Bayesian inference to build spatial probability maps. Based on the analysis of triphasic responses of antennal lobe neurons (On, inhibition, Off), we propose three reactive strategies. One combines upwind surge (representing the On response to a pheromone detection) and spiral casting, only. The other two additionally include crosswind (zigzag) casting representing the Off phase. As cognitive strategy we use the infotaxis algorithm which was developed for searching in a turbulent medium. Detection events in the electroantennogram of a moth attached to a robot indirectly control this cyborg, depending on the strategy in use. The recorded trajectories are analyzed with regard to success rates, efficiency, and other features. In addition, we qualitatively compare our robotic trajectories to behavioral search paths. Reactive searching is more efficient (yielding shorter trajectories) for higher pheromone doses whereas cognitive searching works better for lower doses. With respect to our experimental conditions (2 m from starting position to pheromone source), reactive searching with crosswind zigzag yields the shortest trajectories (for comparable success rates). Assuming that the neuronal Off response represents a short-term memory, zigzagging is an efficient movement to relocate a recently lost pheromone plume. Accordingly, such reactive strategies offer an interesting alternative to complex cognitive searching.

Insects and robots searching for odour sources in turbulent plumes face the same problem: the random nature of mixing causes fluctuations and intermittency in perception. Pheromone-tracking male moths appear to deal with discontinuous flows of information by surging upwind, upon sensing a pheromone patch, and casting crosswind, upon losing the plume. Using a combination of neurophysiological recordings, computational modelling and experiments with a cyborg, we propose a neuronal mechanism that promotes a behavioural switch between surge and casting. We show how multiphasic On/Off pheromone-sensitive neurons may guide action selection based on signalling presence or loss of the pheromone. A Hodgkin-Huxley-type neuron model with a small-conductance calcium-activated potassium (SK) channel reproduces physiological On/Off responses. Using this model as a command neuron and the antennae of tethered moths as pheromone sensors, we demonstrate the efficiency of multiphasic patterning in driving a robotic searcher toward the source. Taken together, our results suggest that multiphasic On/Off responses may mediate olfactory navigation and that SK channels may account for these responses.

Most current studies of neuronal activity dynamics in cortex are based on network models with completely random wiring. Such models are chosen for mathematical convenience, rather than biological grounds, and additionally reflect the notorious lack of knowledge about the neuroanatomical microstructure. Here, we describe some families of new, more realistic network models and explore some of their properties. Specifically, we consider spatially embedded networks and impose specific distance-dependent connectivity profiles. Each of these network models can cover the range from purely local to completely random connectivity, controlled by a single parameter. Stochastic graph theory is then used to describe and analyze the structure and the topology of these networks.

Insects and robots searching for odour sources in turbulent plumes face the same problem: the random nature of mixing causes fluctuations and intermittency in perception. Pheromone-tracking male moths appear to deal with discontinuous flows of information by surging upwind, upon sensing a pheromone patch, and casting crosswind, upon losing the plume. Using a combination of neurophysiological recordings, computational modelling and experiments with a cyborg, we propose a neuronal mechanism that promotes a behavioural switch between surge and casting. We show how multiphasic On/Off pheromone-sensitive neurons may guide action selection based on signalling presence or loss of the pheromone. A Hodgkin-Huxley-type neuron model with a small-conductance calcium-activated potassium (SK) channel reproduces physiological On/Off responses. Using this model as a command neuron and the antennae of tethered moths as pheromone sensors, we demonstrate the efficiency of multiphasic patterning in driving a robotic searcher toward the source. Taken together, our results suggest that multiphasic On/Off responses may mediate olfactory navigation and that SK channels may account for these responses.

Male moths aiming to locate pheromone-releasing females rely on stimulus-adapted search maneuvers complicated by a discontinuous distribution of pheromone patches. They alternate sequences of upwind surge when perceiving the pheromone and cross- or downwind casting when the odor is lost. We compare four search strategies: three reactive versus one cognitive. The former consist of pre-programmed movement sequences triggered by pheromone detections while the latter uses Bayesian inference to build spatial probability maps. Based on the analysis of triphasic responses of antennal lobe neurons (On, inhibition, Off), we propose three reactive strategies. One combines upwind surge (representing the On response to a pheromone detection) and spiral casting, only. The other two additionally include crosswind (zigzag) casting representing the Off phase. As cognitive strategy we use the infotaxis algorithm which was developed for searching in a turbulent medium. Detection events in the electroantennogram of a moth attached to a robot indirectly control this cyborg, depending on the strategy in use. The recorded trajectories are analyzed with regard to success rates, efficiency, and other features. In addition, we qualitatively compare our robotic trajectories to behavioral search paths. Reactive searching is more efficient (yielding shorter trajectories) for higher pheromone doses whereas cognitive searching works better for lower doses. With respect to our experimental conditions (2 m from starting position to pheromone source), reactive searching with crosswind zigzag yields the shortest trajectories (for comparable success rates). Assuming that the neuronal Off response represents a short-term memory, zigzagging is an efficient movement to relocate a recently lost pheromone plume. Accordingly, such reactive strategies offer an interesting alternative to complex cognitive searching.

Most studies on the dynamics of recurrent cortical networks are either based on purely random wiring or neighborhood couplings. Neuronal cortical connectivity, however, shows a complex spatial pattern composed of local and remote patchy connections. We ask to what extent such geometric traits influence the \"idle\" dynamics of two-dimensional (2d) cortical network models composed of conductance-based integrate-and-fire (iaf) neurons. In contrast to the typical 1 mm(2) used in most studies, we employ an enlarged spatial set-up of 25 mm(2) to provide for long-range connections. Our models range from purely random to distance-dependent connectivities including patchy projections, i.e., spatially clustered synapses. Analyzing the characteristic measures for synchronicity and regularity in neuronal spiking, we explore and compare the phase spaces and activity patterns of our simulation results. Depending on the input parameters, different dynamical states appear, similar to the known synchronous regular \"SR\" or asynchronous irregular \"AI\" firing in random networks. Our structured networks, however, exhibit shifted and sharper transitions, as well as more complex activity patterns. Distance-dependent connectivity structures induce a spatio-temporal spread of activity, e.g., propagating waves, that random networks cannot account for. Spatially and temporally restricted activity injections reveal that a high amount of local coupling induces rather unstable AI dynamics. We find that the amount of local versus long-range connections is an important parameter, whereas the structurally advantageous wiring cost optimization of patchy networks has little bearing on the phase space.