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Finally, we show how GTE can be applied to the analysis of real neurons and demonstrate the properties of network of dissociated, cultured neurons. We find a rich, non-random topology characterized by an elevated mean clustering coefficient and long-range connectivity profiles. Thus GTE is a promising method for the reconstruction of network connectivities, especially when taking into account its generality due to the model-free approach.

We analyzed single unit recordings in area MT from macaque monkeys performing an attentional task. They were presented a stimulus made out of two moving random-dot-patterns (RDP) within the receptive field of the recorded MT cell. In one experiment the two RDPs were spatially separated, in another they were overlapping at the same location. Attention was directed to a fixation spot or to only one of the two RDPs. The angle between the two RDPs was kept fixed at 120 degrees so that covarying the motion directions provided tuning curves with two peaks. Using a combination of model-based and model-free approaches we found a variety of non-multiplicative effects, including significant differences between the two experimental conditions, underlying the integration of two stimuli and attentional modulation, such as changes in peak position and shape. In order to understand these effects we explore multi-areal network models with multiple coupled rings, in which functional interactions between hypercolumns of area MT and lower hierarchical order, like V1, are taken into account. We derive a parameterization of a high-dimensional manifold representing possible coupling mechanisms which is constrained by data from the two experiments we analyzed. This allows the identification of qualitative correlation patterns between local and inter-areal functional interactions and attentional spotlight mechanisms in our modeling framework.

Cortical neurons and, particularly, inhibitory interneurons display a large diversity of morphological, synaptic, electrophysiological, and molecular properties, as well as diverse embryonic origins. Various authors have proposed alternative classification schemes that rely on the concomitant observation of several multimodal features. However, a broad variability is generally observed even among cells that are grouped into a same class. Furthermore, the attribution of specific neurons to a single defined class is often difficult, because individual properties vary in a highly graded fashion, suggestive of continua of features between types. Going beyond the description of representative traits of distinct classes, we focus here on the analysis of atypical cells[1]. We introduce a novel paradigm for neuronal type classification, assuming explicitly the existence of a structured continuum of diversity. Our approach, grounded on the theory of fuzzy sets[2], identifies a small optimal number of model archetypes[3]. At the same time, it quantifies the degree of similarity between these archetypes and each considered neuron. This allows highlighting archetypal cells, which bear a clear similarity to a single model archetype, and edge cells, which manifest a convergence of traits from multiple archetypes. A ready-to-use software package allowing classification of neuronal data with standard tools (MATLAB, Python, ...) via this fuzzy clustering approach without the need for a reimplementation of the algorithmic aspects is in preparation.

Calcium imaging has become a standard technique for the measurement of the activity of a population of cultured neurons. Typically these recordings are slow compared to the cell dynamics and display a low signal-to-noise ratio, but they allow for the simultaneous recording of hundreds of neurons. We are interested in reconstructing an approximation of the structural connectivity of a culture of neurons. This would allow for characterization of the bulk properties of these networks, such as the dependence of connection probability of two nodes on the distance between them, the degree distribution or the clustering coefficient, which are currently inaccessible with single-cell or even typical multi-electrode techniques. In order to benchmark our connectivity inference methods, we first study simulations of fluorescence signals and examine established methods of inferring the topology. It turns out that we can improve on these methods if we turn to measures from information theory, which do not rely on a linearity assumption. Because we are interested in directed networks, our measure of choice is Transfer Entropy [1,2]. It turns out that we can achieve a high quality of the reconstruction if we allow for novel extensions of this measure. Specifically, we need to take into account the ability of the network to display different dynamical states (fig. ​(fig.1).1). We need to focus on phases of activity where the dynamics in the network are dominated by direct monosynaptic interactions, and where therefore the effective connectivity corresponds closely to the structural connectivity. Additionally, we need to correct for the slow acquisition rate of the recording by allowing for instantaneous interactions between nodes in addition to interactions from different image frames. Figure 1 The averaged fluorescence signal of the nodes in our network (A) reveals the existence of quiet phases and network spikes, which is then represented in the histogram over time (B). The effective connectivity calculated from the data points when the averaged ... We demonstrate post-processing improvements of the reconstruction using the Data Processing Inequality that are only possible in the case of information theoretical measures. These methods, already applied with success in the reconstruction of gene regulatory networks [3], help to discriminate indirect from direct interactions. We then apply our algorithm to real data from large cultures of hippocampal neurons in vitro stained with Fluo-4 AM dye. We probe and quantify the distance-dependent probability of connection and other topological properties of the reconstructed network, finding deviations from a random topology. Finally we point out and quantify which experimental parameters would be most relevant for an improved reconstruction using our method.