Identification of synaptic connections in neural ensembles by graphical models (original) (raw)

Partial correlation analysis for the identification of synaptic connections

Biological Cybernetics, 2003

In this paper, we investigate the use of partial correlation analysis for the identification of functional neural connectivity from simultaneously recorded neural spike trains. Partial correlation analysis allows one to distinguish between direct and indirect connectivities by removing the portion of the relationship between two neural spike trains that can be attributed to linear relationships with recorded spike trains from other neurons. As an alternative to the common frequency domain approach based on the partial spectral coherence we propose a new statistic in the time domain. The new scaled partial covariance density provides additional information on the direction and the type, excitatory or inhibitory, of the connectivities. In simulation studies, we investigated the power and limitations of the new statistic. The simulations show that the detectability of various connectivity patterns depends on various parameters such as connectivity strength and background activity. In particular, the detectability decreases with the number of neurons included in the analysis and increases with the recording time. Further, we show that the method can also be used to detect multiple direct connectivities between two neurons. Finally, the methods of this paper are illustrated by an application to neurophysiological data from spinal dorsal horn neurons.

Using partial directed coherence to describe neuronal ensemble interactions

Journal of Neuroscience Methods, 1999

This paper illustrates the use of the recently introduced method of partial directed coherence in approaching how interactions among neural structures change over short time spans that characterize well defined behavioral states. Central to the method is its use of multivariate time series modelling in conjunction with the concept of Granger causality. Simulated neural network models were used to illustrate the technique's power and limitations when dealing with neural spiking data. This was followed by the analysis of multi-unit activity data illustrating dynamical change in the interaction of thalamo-cortical structures in a behaving rat.

Nonlinear Modeling of Causal Interrelationships in Neuronal Ensembles

IEEE Transactions on Neural Systems and Rehabilitation Engineering, 2000

The increasing availability of multiunit recordings gives new urgency to the need for effective analysis of "multidimensional" time-series data that are derived from the recorded activity of neuronal ensembles in the form of multiple sequences of action potentials-treated mathematically as point-processes and computationally as spike-trains. Whether in conditions of spontaneous activity or under conditions of external stimulation, the objective is the identification and quantification of possible causal links among the neurons generating the observed binary signals. A multiple-input/ multiple-output (MIMO) modeling methodology is presented that can be used to quantify the neuronal dynamics of causal interrelationships in neuronal ensembles using spike-train data recorded from individual neurons. These causal interrelationships are modeled as transformations of spiketrains recorded from a set of neurons designated as the "inputs" into spike-trains recorded from another set of neurons designated as the "outputs." The MIMO model is composed of a set of multiinput/single-output (MISO) modules, one for each output. Each module is the cascade of a MISO Volterra model and a threshold operator generating the output spikes. The Laguerre expansion approach is used to estimate the Volterra kernels of each MISO module from the respective inputoutput data using the least-squares method. The predictive performance of the model is evaluated with the use of the receiver operating characteristic (ROC) curve, from which the optimum threshold is also selected. The Mann-Whitney statistic is used to select the significant inputs for each output by examining the statistical significance of improvements in the predictive accuracy of the model when the respective inputs is included. Illustrative examples are presented for a simulated system and for an actual application using multiunit data recordings from the hippocampus of a behaving rat.

An Application of Directed Information to Infer Synaptic Connectivity

Anais de XXXIV Simpósio Brasileiro de Telecomunicações, 2016

This paper introduces a review on directed information and its application as a causality measure among two stochastic processes. Jiao's method for estimating directed information from data, using the context tree weighting algorithm is described and then used to infer synaptic connectivity from simulated neurons, from their neural spike trains only. It is observed that positive values of directed information estimates correctly predicted synaptic connections.

Reconstructing Cortical Networks: Case of Directed Graphs with High Level of Reciprocity

Bolyai Society Mathematical Studies, 2008

The problem of prediction of yet uncharted connections in the large scale network of the cerebral cortex is addressed. Our approach was determined by the fact that the cortical network is highly reciprocal although directed, i.e. the input and output connection patterns of vertices are slightly different. In order to solve the problem of predicting missing connections in the cerebral cortex, we propose a probabilistic method, where vertices are grouped into two clusters based on their outgoing and incoming edges, and the probability of a connection is determined by the cluster affiliations of the vertices involved. Our approach allows accounting for differences in the incoming and outgoing connections, and is free from assumptions about graph properties. The method is general and applicable to any network for which the connectional structure is mapped to a sufficient extent. Our method allows the reconstruction of the original visual cortical network with high accuracy, which was confirmed after comparisons with previous results. For the first time, the effect of extension of the visual cortex was also examined on graph reconstruction after complementing it with the subnetwork of the sensori-

Identification of connectivity in neural networks

Biophysical Journal, 1990

Analytical and experimental pressions derived can be used with stimulus-related correlations. Finally, methods are provided for estimating nonstationary or stationary records, we illustrate the use and interpretation synaptic connectivities from simultaand can be readily extended from pairof the analytical expressions on simuneous recordings of multiple neurons. wise to multineuron estimates. Furtherlated spike trains and neural networks, The results are based on detailed, yet more, we show analytically how the and give explicit confidence measures flexible neuron models in which spike estimates are improved as more neuon the estimates. trains are modeled as general doubly rons are sampled, and derive the stochastic point processes. The ex-appropriate normalizations to eliminate D;ot , I Dp .

Partial Directed Coherence and the Inference of Structural Connectivity among Spiking Neurons

2002

This paper presents a summary of the recently introduced concept of partial directed coherence. We discuss its application to the connectivity inference of networks composed of integrate-and-fire neurons, whose signals require the process of reconstruction via kernels prior to analysis. Some specific results of the effect of different reconstruction parameters are presented via Monte Carlo simulations.

Correlational Strength and Computational Algebra of Synaptic Connections Between Neurons

Nips, 1987

Intracellular recordings in spinal cord motoneurons and cerebral cortex neurons have provided new evidence on the correlational strength of monosynaptic connections, and the relation between the shapes of postsynaptic potentials and the associated increased firing probability. In these cells, excitatory postsynaptic potentials (EPSPs) produce crosscorrelogram peaks which resemble in large part the derivative of the EPSP. Additional synaptic noise broadens the peak, but the peak area-i.e., the number of above-chance firings triggered per EPSP-remains proportional to the EPSP amplitude. A typical EPSP of 100 ~v triggers about .01 firings per EPSP. The consequences of these data for information processing by polysynaptic connections is discussed. The effects of sequential polysynaptic links can be calculated by convolving the effects of the underlying monosynaptic connections. The net effect of parallel pathways is the sum of the individual contributions.

Computational approaches to neuronal network analysis

Philosophical Transactions of the Royal Society B: Biological Sciences, 2010

Computational modelling is an approach to neuronal network analysis that can complement experimental approaches. Construction of useful neuron and network models is often complicated by a variety of factors and unknowns, most notably the considerable variability of cellular and synaptic properties and electrical activity characteristics found even in relatively 'simple' networks of identifiable neurons. This chapter discusses the consequences of biological variability for network modelling and analysis, describes a way to embrace variability through ensemble modelling and summarizes recent findings obtained experimentally and through ensemble modelling.