Information-geometric measures for estimation of connection weight under correlated inputs

Estimation of neural connections from partially observed neural spikes

Plasticity is one of the most important properties of the nervous system, which enables animals to adjust their behavior to the ever-changing external environment. Changes in synaptic efficacy between neurons constitute one of the major mechanisms of plasticity. Therefore, estimation of neural connections is crucial for investigating information processing in the brain. Although many analysis methods have been proposed for this purpose, most of them suffer from one or all the following mathematical difficulties: (1) only partially observed neural activity is available; (2) correlations can include both direct and indirect pseudo-interactions; and (3) biological evidence that a neuron typically has only one type of connection (excitatory or inhibitory) should be considered. To overcome these difficulties, a novel probabilistic framework for estimating neural connections from partially observed spikes is proposed in this paper. First, based on the property of a sum of random variables, the proposed method estimates the influence of unobserved neurons on observed neurons and extracts only the correlations among observed neurons. Second, the relationship between pseudo-correlations and target connections is modeled by neural propagation in a multiplicative manner. Third, a novel information-theoretic framework is proposed for estimating neuron types. The proposed method was validated using spike data generated by artificial neural networks. In addition, it was applied to multi-unit data recorded from the CA1 area of a rat's hippocampus. The results confirmed that our estimates are consistent with previous reports. These findings indicate that the proposed method is useful for extracting crucial interactions in neural signals as well as in other multi-probed point process data.

Influence of external inputs and asymmetry of connections on information-geometric measures involving up to ten neuronal interactions

The investigation of neural interactions is crucial for understanding information processing in the brain. Recently an analysis method based on information geometry (IG) has gained increased attention, and the property of the pairwise IG measure has been studied extensively in relation to the two-neuron interaction. However, little is known about the property of IG measures involving more neuronal interactions. In this study, we systematically investigated the influence of external inputs and the asymmetry of connections on the IG measures in cases ranging from 1-neuron to 10-neuron interactions. First, the analytical relationship between the IG measures and external inputs was derived for a network of 10 neurons with uniform connections. Our results confirmed that the single and pairwise IG measures were good estimators of the mean background input and of the sum of the connection weights, respectively. For the IG measures involving 3 to 10 neuronal interactions, we found that the influence of external inputs was highly nonlinear. Second, by computer simulation, we extended our analytical results to asymmetric connections. For a network of 10 neurons, the simulation showed that the behavior of the IG measures in relation to external inputs was similar to the analytical solution obtained for a uniformly connected network. When the network size was increased to 1000 neurons, the influence of external inputs almost disappeared. This result suggests that all IG measures from 1-neuron to 10-neuron interactions are robust against the influence of external inputs. In addition, we investigated how the strength of asymmetry influenced the IG measures. Computer simulation of a 1000-neuron network showed that all the IG measures were robust against the modulation of the asymmetry of connections. Our results provide further support for an information-geometric approach and will provide useful insights when these IG measures are applied to real experimental spike data.

Long-term recordings improve the detection of weak excitatory-excitatory connections in rat prefrontal cortex

Characterization of synaptic connectivity is essential to understanding neural circuit dynamics. For extracellularly recorded spike trains, indirect evidence for connectivity can be inferred from short-latency peaks in the correlogram between two neurons. Despite their predominance in cortex, however, significant interactions between excitatory neurons (E) have been hard to detect because of their intrinsic weakness. By taking advantage of long duration recordings, up to 25 h, from rat prefrontal cortex, we found that 7.6% of the recorded pyramidal neurons are connected. This corresponds to ∼70% of the local E-E connection probability that has been reported by paired intracellular recordings (11.6%). This value is significantly higher than previous reports from extracellular recordings, but still a substantial underestimate. Our analysis showed that long recording times and strict significance thresholds are necessary to detect weak connections while avoiding false-positive results, but will likely still leave many excitatory connections undetected. In addition, we found that hyper-reciprocity of connections in prefrontal cortex that was shown previously by paired intracellular recordings was only present in short-distance, but not in long distance (∼300 micrometers or more) interactions. As hyper-reciprocity is restricted to local clusters, it might be a minicolumnar effect. Given the current surge of interest in very high-density neural spike recording (e.g., NIH BRAIN Project) it is of paramount importance that we have statistically reliable methods for estimating connectivity from cross-correlation analysis available. We provide an important step in this direction.

Information-geometric measures estimate neural interactions during oscillatory brain states

The characterization of functional network structures among multiple neurons is essential to understanding neural information processing. Information geometry (IG), a theory developed for investigating a space of probability distributions has recently been applied to spike-train analysis and has provided robust estimations of neural interactions. Although neural firing in the equilibrium state is often assumed in these studies, in reality, neural activity is non-stationary. The brain exhibits various oscillations depending on cognitive demands or when an animal is asleep. Therefore, the investigation of the IG measures during oscillatory network states is important for testing how the IG method can be applied to real neural data. Using model networks of binary neurons or more realistic spiking neurons, we studied how the single- and pairwise-IG measures were influenced by oscillatory neural activity. Two general oscillatory mechanisms, externally driven oscillations and internally induced oscillations, were considered. In both mechanisms, we found that the single-IG measure was linearly related to the magnitude of the external input, and that the pairwise-IG measure was linearly related to the sum of connection strengths between two neurons. We also observed that the pairwise-IG measure was not dependent on the oscillation frequency. These results are consistent with the previous findings that were obtained under the equilibrium conditions. Therefore, we demonstrate that the IG method provides useful insights into neural interactions under the oscillatory condition that can often be observed in the real brain.