Olav Stetter

Model-free reconstruction of excitatory neuronal connectivity from calcium imaging signals.

A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically infeasible, even in simpler systems like dissociated neuronal cultures. We introduce an improved algorithmic approach based on Transfer Entropy to reconstruct structural connectivity from network activity monitored through calcium imaging. We focus in this study on the inference of excitatory synaptic links. Based on information theory, our method requires no prior assumptions on the statistics of neuronal firing and neuronal connections. The performance of our algorithm is benchmarked on surrogate time series of calcium fluorescence generated by the simulated dynamics of a network with known ground-truth topology. We find that the functional network topology revealed by Transfer Entropy depends qualitatively on the time-dependent dynamic state of the network (bursting or non-bursting). Thus by conditioning with respect to the global mean activity, we improve the performance of our method. This allows us to focus the analysis to specific dynamical regimes of the network in which the inferred functional connectivity is shaped by monosynaptic excitatory connections, rather than by collective synchrony. Our method can discriminate between actual causal influences between neurons and spurious non-causal correlations due to light scattering artifacts, which inherently affect the quality of fluorescence imaging. Compared to other reconstruction strategies such as cross-correlation or Granger Causality methods, our method based on improved Transfer Entropy is remarkably more accurate. In particular, it provides a good estimation of the excitatory network clustering coefficient, allowing for discrimination between weakly and strongly clustered topologies. Finally, we demonstrate the applicability of our method to analyses of real recordings of in vitro disinhibited cortical cultures where we suggest that excitatory connections are characterized by an elevated level of clustering compared to a random graph (although not extreme) and can be markedly non-local.

Transfer Entropy Reconstruction and Labeling of Neuronal Connections from Simulated Calcium Imaging

Neuronal dynamics are fundamentally constrained by the underlying structural network architecture, yet much of the details of this synaptic connectivity are still unknown even in neuronal cultures in vitro. Here we extend a previous approach based on information theory, the Generalized Transfer Entropy, to the reconstruction of connectivity of simulated neuronal networks of both excitatory and inhibitory neurons. We show that, due to the model-free nature of the developed measure, both kinds of connections can be reliably inferred if the average firing rate between synchronous burst events exceeds a small minimum frequency. Furthermore, we suggest, based on systematic simulations, that even lower spontaneous inter-burst rates could be raised to meet the requirements of our reconstruction algorithm by applying a weak spatially homogeneous stimulation to the entire network. By combining multiple recordings of the same in silico network before and after pharmacologically blocking inhibitory synaptic transmission, we show then how it becomes possible to infer with high confidence the excitatory or inhibitory nature of each individual neuron.

Leaders of neuronal cultures in a quorum percolation model.

We present a theoretical framework using quorum percolation for describing the initiation of activity in a neural culture. The cultures are modeled as random graphs, whose nodes are excitatory neurons with kin inputs and kout outputs, and whose input degrees kin = k obey given distribution functions pk. We examine the firing activity of the population of neurons according to their input degree (k) classes and calculate for each class its firing probability Φk(t) as a function of t. The probability of a node to fire is found to be determined by its in-degree k, and the first-to-fire neurons are those that have a high k. A small minority of high-k-classes may be called “Leaders,” as they form an interconnected sub-network that consistently fires much before the rest of the culture. Once initiated, the activity spreads from the Leaders to the less connected majority of the culture. We then use the distribution of in-degree of the Leaders to study the growth rate of the number of neurons active in a burst, which was experimentally measured to be initially exponential. We find that this kind of growth rate is best described by a population that has an in-degree distribution that is a Gaussian centered around k = 75 with width σ = 31 for the majority of the neurons, but also has a power law tail with exponent −2 for 10% of the population. Neurons in the tail may have as many as k = 4,700 inputs. We explore and discuss the correspondence between the degree distribution and a dynamic neuronal threshold, showing that from the functional point of view, structure and elementary dynamics are interchangeable. We discuss possible geometric origins of this distribution, and comment on the importance of size, or of having a large number of neurons, in the culture.

Design of the first neuronal connectomics challenge: From imaging to connectivity

We are organizing a challenge to reverse engineer the structure of neuronal networks from patterns of activity recorded with calcium fluorescence imaging. Unraveling the brain structure at the neuronal level at a large scale is an important step in brain science, with many ramifications in the comprehension of animal and human intelligence and learning capabilities, as well as understanding and curing neuronal diseases and injuries. However, uncovering the anatomy of the brain by disentangling the neural wiring with its very fine and intertwined dendrites and axons, making both local and far reaching synapses, is a very arduous task: traditional methods of axonal tracing are tedious, difficult, and time consuming. This challenge proposes to approach the problem from a different angle, by reconstructing the effective connectivity of a neuronal network from observations of neuronal activity of thousands of neurons, which can be obtained with state-of-the-art fluorescence calcium imaging. To evaluate the effectiveness of proposed algorithms, we will use data obtained with a realistic simulator of real neurons for which we have ground truth of the neuronal connections. We produced simulated calcium imaging data, taking into account a model of fluorescence and light scattering. The task of the participants is to reconstruct a network of 1000 neurons from time series of neuronal activities obtained with this model. This challenge is part of the official selection of the WCCI 2014 competition program.

Network reconstruction from calcium imaging data of spontaneously bursting neuronal activity

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.

State-dependent network reconstruction from calcium imaging signals

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.