Identification of connectivity in neural networks

Multivariate autoregressive modeling and granger causality analysis of multiple spike trains

Recent years have seen the emergence of microelectrode arrays and optical methods allowing simultaneous recording of spiking activity from populations of neurons in various parts of the nervous system. The analysis of multiple neural spike train data could benefit significantly from existing methods for multivariate time-series analysis which have proven to be very powerful in the modeling and analysis of continuous neural signals like EEG signals. However, those methods have not generally been well adapted to point processes. Here, we use our recent results on correlation distortions in multivariate Linear-Nonlinear-Poisson spiking neuron models to derive generalized Yule-Walker-type equations for fitting ''hidden" Multivariate Autoregressive models. We use this new framework to perform Granger causality analysis in order to extract the directed information flow pattern in networks of simulated spiking neurons. We discuss the relative merits and limitations of the new method.

Superlinear population encoding of dynamic hand trajectory in primary motor cortex

Neural activity in primary motor cortex (MI) is known to correlate with hand position and velocity. Previous descriptions of this tuning have (1) been linear in position or velocity, (2) depended only instantaneously on these signals, and/or (3) not incorporated the effects of interneuronal dependencies on firing rate. We show here that many MI cells encode a superlinear function of the full time-varying hand trajectory. Approximately 20% of MI cells carry information in the hand trajectory beyond just the position, velocity, and acceleration at a single time lag. Moreover, approximately one-third of MI cells encode the trajectory in a significantly superlinear manner; as one consequence, even small position changes can dramatically modulate the gain of the velocity tuning of MI cells, in agreement with recent psychophysical evidence. We introduce a compact nonlinear "preferred trajectory" model that predicts the complex structure of the spatiotemporal tuning functions described in previous work. Finally, observing the activity of neighboring cells in the MI network significantly increases the predictability of the firing rate of a single MI cell; however, we find interneuronal dependencies in MI to be much more locked to external kinematic parameters than those described recently in the hippocampus. Nevertheless, this neighbor activity is approximately as informative as the hand velocity, supporting the view that neural encoding in MI is best understood at a population level.

Synaptic connectivity in cultured hypothalamic neuronal networks

We have developed a novel approach to analyze the synaptic connectivity of spontaneously active networks of hypothalamic neurons in culture. Synaptic connections were identified by recording simultaneously from pairs of neurons using the whole cell configuration of the patch-clamp technique and testing for evoked postsynaptic current responses to electrical stimulation of one of the neurons. Excitatory and inhibitory responses were distinguished on the basis of their voltage and time dependence. The distribution of latencies between presynaptic stimulation and postsynaptic response showed multiple peaks at regular intervals, suggesting that responses via both monosynaptic and polysynaptic paths were recorded. The probability that an excitatory event is transmitted to another excitatory neuron and results in an above-threshold stimulation was found to be only one in three to four. This low value indicates that in addition to evoked synaptic responses other sources of excitatory drive must contribute to the spontaneous activity observed in these networks. The various types of synaptic connections (excitatory and inhibitory, monosynaptic, and polysynaptic) were counted, and the observations analyzed using a probabilistic model of the network structure. This analysis provides estimates for the ratio of inhibitory to excitatory neurons in the network (1:1.5) and for the ratio of postsynaptic cells receiving input from a single GABAergic or glutamatergic neuron (3:1). The total number of inhibitory synaptic connections was twice that of excitatory connections. Cell pairs mutually connected by an excitatory and an inhibitory synapse occurred significantly more often than predicted by a random process. These results suggests that the formation of neuronal networks in vitro is controlled by cellular mechanisms that favor inhibitory connections in general and specifically enhance the formation of reciprocal connections between pairs of excitatory and inhibitory neurons. These mechanisms may contribute to network formation and function in vivo.

Information theoretic analysis of action potential trains. II. Analysis of correlation among n neurons to deduce connection structure

We propose a cross-correlational method based on information theory, which produces a network connection structure to account for observed patterns of action potential activity in multi-unit recordings. Firing probabilities and conditional probabilities are estimated from the action potential trains of n neurons. Two-point mutual information (2pMI) and joint conditional mutual information (JCMI) are calculated by using the estimated probabilities, and then the n-point mutual information (npMI) is calculated. A significant peak of npMI indicates that each neuron is connected to all other neurons at specified time differences, either directly or indirectly. To distinguish between direct and indirect connection, the two-point m-joint conditional mutual information (2pJCMI) is calculated over the peak region for each pair of neurons. A minimum effective connection structure among the n neurons can be deduced in this manner. The procedure for deducing the connection structure for three- and n-neuron networks is described. We apply this method to action potential trains produced by simulated neural networks. Some limitations of the method are also discussed.

Chemical crosslinking studies of the isolated light-harvesting B800-850 complex of Chromatium minutissimum

The spatial relationship of polypeptides comprising the light-harvesting B800-850 complex of Chromatium minutissimum has been studied by means of chemical crosslinking of the isolated complex with cleavable, 1.2 nm-long dithiobis(succinimidyl propionate). The samples were analyzed by different types of electrophoresis and spectrophotometrically. No difference was shown between crosslinking of the B800-850 complex either solubilized or incorporated into proteoliposomes. It was found that two main polypeptides form only one type of heterodimer. The crosslinked complex was more thermostable. This crosslinkage restricted the conformational transitions causing the shift of the long wavelength band in the near infrared region. A structure of the complex is discussed.

Information theoretic analysis of action potential trains. I. Analysis of correlation between two neurons

A crosscorrelational method of action potential trains has been proposed, based on information theory. Two information theoretic quantities, mutual information and channel capacity, were calculated from a pair of action potential trains for detecting a crosscorrelation and estimating synaptic connectivity. The method was compared with conventional ones, using action potential trains obtained by the simulation of a neuron model. This method was shown to have the advantages to more easily find a weak but significant crosscorrelation and to give better estimation of synaptic connectivity independent of the firing probability of a presynaptic neuron.