
C. Statistical methods

Aim.
Creating essential statistical methodology to compare modelgenerated data with experimental data on neuronal morphology and network connectivity. Relevance. Quantitative analysis of 3D neuronal geometries is needed for comparing modelgenerated morphologies with cortical neurons, and for determining how neuronal morphology influences synaptic connectivity (project A). Further, quantitative analysis is required to translate connectivity formation in project A into effective rules necessary for project B. With the advance of multielectrode recording techniques, spike trains can be recorded simultaneously from many neurons in a network. The timing relations in these spike trains are strongly determined by synaptic connectivity. Therefore, it is a ‘reverse engineering’ challenge to extract from multielectrode recordings the connectivity pattern of the underlying neuronal network. This approach will be used to compare modelgenerated network connectivity (project B) with connectivity in developing cultures of cortical neuronal networks (Van Pelt data; [53,54]). 7 Background. Many metrical and topological measures exist for the statistical comparison of axonal/dendritic branching patterns [43]. However, statistical measures for characterizing the 3D structure of neuronal morphologies are largely lacking. Here, we will develop such methods, by means of averaged 3D neuronal fields. This methodology will be used for defining connectivity between two neurons (as in [40]) on the basis of overlap functions of their 3D neuronal fields. To analyze timing relationships between pairs of spike trains and to estimate network connectivity, some studies [23,38] used conditional firing probabilities and crosscovariance measures. However, propagation of activity in a neuronal network is the result of interactions between many neurons, so that a multidimensional rather than a pairwise comparison approach is called for [7]. In our previous CLS program, we created a modelbased Bayesian method to derive underlying connectivity from the spatiotemporal patterns of firing in multielectrode recordings [30]. Project C will build on these highly promising approaches and will increase their efficiency for large data sets. Approach. Existing measures of neuronal shapes will be used and extended for 3D geometry with measures for the radial and angular extensiveness of neuronal arborizations. We will describe the 3D geometry of an ‘averaged neuron’ of a particular type by its 3D morphodensity field (morphofield), representing the spatial distribution of ‘neuronal mass’ (e.g., neuronal length or neuronal volume). New statistical methodology is needed to compare, for example, morphofields of modeled neurons with those of cortical neurons. The morphofield description will also be used for defining the connectivity between two neurons (as a function of cell type, cell body distance, and orientation) on the basis of the volume integral of their morphofield overlap, and applied in projects A and B. To derive network connectivity from multiple spike train data, we will first apply existing methods based on conditional firing probabilities [23] and crosscovariances [38]. Next, because activity propagation occurs between groups of neurons rather than between pairs, multivariate techniques [26], such as multivariate autoregressive models (MAR), will be evaluated for making more accurate inferences on network connectivity. Markov models have also been used for analyzing multielectrode spike trains [29,4], but these were not primarily designed to derive connectivity. We will evaluate whether these approaches can be used to make connectivity inferences. In our previous CLS program, we have already made a promising start with modelbased Markovian models, in which all possible simultaneous firing patterns of the individual neurons are the states of the Markov state space, where the parameter estimation is done by a Bayesian approach [30]. However, this model needs to be made more efficient, e.g., by using more effective signal integration schemes. If time allows, we will also evaluate whether our methods for deriving connectivity can be made applicable to field potential data instead of spike trains. Research Questions and Validation. Quantitative analysis of 3D neuronal morphologies will be applied and validated on our modelgenerated data (project A) and on neuronal morphologies from the data sets mentioned under project A. Our methods to infer connectivity will be applied and validated on the unique data sets we have (Van Pelt; [53,54]) on activity patterns in developing cultures of cortical neuronal networks. An important test case for connectivity inference is provided by the model from project B, because there both the activity patterns and the underlying connectivity are exactly known. If extension of our methods to field potential data is feasible, we will validate our methods also on inhouse data sets on activity and connectivity in cortical brain slices from mouse strains with different cognitive abilities (Brussaard).
