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.

Neurons in sensory systems convey information about physical stimuli in their spike trains. In vitro, single neurons respond precisely and reliably to the repeated injection of the same fluctuating current, producing regions of elevated firing rate, termed events. Analysis of these spike trains reveals that multiple distinct spike patterns can be identified as trial-to-trial correlations between spike times (Fellous, Tiesinga, Thomas, & Sejnowski, 2004 ). Finding events in data with realistic spiking statistics is challenging because events belonging to different spike patterns may overlap. We propose a method for finding spiking events that uses contextual information to disambiguate which pattern a trial belongs to. The procedure can be applied to spike trains of the same neuron across multiple trials to detect and separate responses obtained during different brain states. The procedure can also be applied to spike trains from multiple simultaneously recorded neurons in order to identify volleys of near-synchronous activity or to distinguish between excitatory and inhibitory neurons. The procedure was tested using artificial data as well as recordings in vitro in response to fluctuating current waveforms.

Information geometry has been suggested to provide a powerful tool for analyzing multineuronal spike trains. Among several advantages of this approach, a significant property is the close link between information-geometric measures and neural network architectures. Previous modeling studies established that the first- and second-order information-geometric measures corresponded to the number of external inputs and the connection strengths of the network, respectively. This relationship was, however, limited to a symmetrically connected network, and the number of neurons used in the parameter estimation of the log-linear model needed to be known. Recently, simulation studies of biophysical model neurons have suggested that information geometry can estimate the relative change of connection strengths and external inputs even with asymmetric connections. Inspired by these studies, we analytically investigated the link between the information-geometric measures and the neural network structure with asymmetrically connected networks of N neurons. We focused on the information-geometric measures of orders one and two, which can be derived from the two-neuron log-linear model, because unlike higher-order measures, they can be easily estimated experimentally. Considering the equilibrium state of a network of binary model neurons that obey stochastic dynamics, we analytically showed that the corrected first- and second-order information-geometric measures provided robust and consistent approximation of the external inputs and connection strengths, respectively. These results suggest that information-geometric measures provide useful insights into the neural network architecture and that they will contribute to the study of system-level neuroscience.

Computational modeling of neural substrates provides an excellent theoretical framework for the understanding of the computational roles of neuromodulation. In this review, we illustrate, with a large number of modeling studies, the specific computations performed by neuromodulation in the context of various neural models of invertebrate and vertebrate preparations. We base our characterization of neuromodulations on their computational and functional roles rather than on anatomical or chemical criteria. We review the main framework in which neuromodulation has been studied theoretically (central pattern generation and oscillations, sensory processing, memory and information integration). Finally, we present a detailed mathematical overview of how neuromodulation has been implemented at the single cell and network levels in modeling studies. Overall, neuromodulation is found to increase and control computational complexity.