Takuma Tanaka

Recurrent infomax generates cell assemblies, neuronal avalanches, and simple cell-like selectivity

Recently multineuronal recording has allowed us to observe patterned firings, synchronization, oscillation, and global state transitions in the recurrent networks of central nervous systems. We propose a learning algorithm based on the process of information maximization in a recurrent network, which we call recurrent infomax (RI). RI maximizes information retention and thereby minimizes information loss through time in a network. We find that feeding in external inputs consisting of information obtained from photographs of natural scenes into an RI-based model of a recurrent network results in the appearance of Gabor-like selectivity quite similar to that existing in simple cells of the primary visual cortex. We find that without external input, this network exhibits cell assemblylike and synfire chainlike spontaneous activity as well as a critical neuronal avalanche. In addition, we find that RI embeds externally input temporal firing patterns to the network so that it spontaneously reproduces these patterns after learning. RI provides a simple framework to explain a wide range of phenomena observed in in vivo and in vitro neuronal networks, and it will provide a novel understanding of experimental results for multineuronal activity and plasticity from an information-theoretic point of view.

Parvalbumin-producing cortical interneurons receive inhibitory inputs on proximal portions and cortical excitatory inputs on distal dendrites.

To examine inputs to parvalbumin (PV)‐producing interneurons, we generated transgenic mice expressing somatodendritic membrane‐targeted green fluorescent protein specifically in the interneurons, and completely visualized their dendrites and somata. Using immunolabeling for vesicular glutamate transporter (VGluT)1, VGluT2, and vesicular GABA transporter, we found that VGluT1‐positive terminals made contacts 4‐ and 3.1‐fold more frequently with PV‐producing interneurons than VGluT2‐positive and GABAergic terminals, respectively, in the primary somatosensory cortex. Even in layer 4, where VGluT2‐positive terminals were most densely distributed, VGluT1‐positive inputs to PV‐producing interneurons were 2.4‐fold more frequent than VGluT2‐positive inputs. Furthermore, although GABAergic inputs to PV‐producing interneurons were as numerous as VGluT2‐positive inputs in most cortical layers, GABAergic inputs clearly preferred the proximal dendrites and somata of the interneurons, indicating that the sites of GABAergic inputs were more optimized than those of VGluT2‐positive inputs. Simulation analysis with a PV‐producing interneuron model compatible with the present morphological data revealed a plausible reason for this observation, by showing that GABAergic and glutamatergic postsynaptic potentials evoked by inputs to distal dendrites were attenuated to 60 and 87%, respectively, of those evoked by somatic inputs. As VGluT1‐positive and VGluT2‐positive axon terminals were presumed to be cortical and thalamic glutamatergic inputs, respectively, cortical excitatory inputs to PV‐producing interneurons outnumbered the thalamic excitatory and intrinsic inhibitory inputs more than two‐fold in any cortical layer. Although thalamic inputs are known to evoke about two‐fold larger unitary excitatory postsynaptic potentials than cortical ones, the present results suggest that cortical inputs control PV‐producing interneurons at least as strongly as thalamic inputs.

Enhanced desensitization followed by unusual resensitization in GABAA receptors in phospholipase C-related catalytically inactive protein-1/2 double-knockout mice

Phospholipase C-related catalytically inactive proteins (PRIP-1/2) are previously reported to be involved in the membrane trafficking of GABAA receptor (GABAAR) and the regulation of intracellular Ca2+ stores. GABAAR-mediated currents can be regulated by the intracellular Ca2+. However, in PRIP-1/2 double-knockout (PRIP-DKO) mice, it remains unclear whether the kinetic properties of GABAARs are modulated by the altered regulation of intracellular Ca2+ stores. Here, we investigated whether GABAAR currents (IGABA) evoked by GABA puff in layer 3 (L3) pyramidal cells (PCs) of the barrel cortex are altered in PRIP-DKO mice. The deletion of PRIP-1/2 enhanced the desensitization of IGABA but induced a hump-like tail current (tail-I) at the GABA puff offset. IGABA and the hump-like tail-I were suppressed by GABAAR antagonists. The enhanced desensitization of IGABA and the hump-like tail-I in PRIP-DKO PCs were mediated by increases in the intracellular Ca2+ concentration and were largely abolished by a calcineurin inhibitor and ruthenium red. Calcium imaging revealed that Ca2+-induced Ca2+ release (CICR) and subsequent store-operated Ca2+ entry (SOCE) are more potent in PRIP-DKO PCs than in wild-type PCs. A mathematical model revealed that a slowdown of GABA-unbinding rate and an acceleration of fast desensitization rate by enhancing its GABA concentration dependency are involved in the generation of hump-like tail-Is. These results suggest that in L3 PCs of the barrel cortex in PRIP-DKO mice, the increased calcineurin activity due to the potentiated CICR and SOCE enhances the desensitization of GABAARs and slows the GABA-unbinding rate, resulting in their unusual resensitization following removal of GABA.

Replicating receptive fields of simple and complex cells in primary visual cortex in a neuronal network model with temporal and population sparseness and reliability

We propose a new principle for replicating receptive field properties of neurons in the primary visual cortex. We derive a learning rule for a feedforward network, which maintains a low firing rate for the output neurons (resulting in temporal sparseness) and allows only a small subset of the neurons in the network to fire at any given time (resulting in population sparseness). Our learning rule also sets the firing rates of the output neurons at each time step to near-maximum or near-minimum levels, resulting in neuronal reliability. The learning rule is simple enough to be written in spatially and temporally local forms. After the learning stage is performed using input image patches of natural scenes, output neurons in the model network are found to exhibit simple-cell-like receptive field properties. When the output of these simple-cell-like neurons are input to another model layer using the same learning rule, the second-layer output neurons after learning become less sensitive to the phase of gratings than the simple-cell-like input neurons. In particular, some of the second-layer output neurons become completely phase invariant, owing to the convergence of the connections from first-layer neurons with similar orientation selectivity to second-layer neurons in the model network. We examine the parameter dependencies of the receptive field properties of the model neurons after learning and discuss their biological implications. We also show that the localized learning rule is consistent with experimental results concerning neuronal plasticity and can replicate the receptive fields of simple and complex cells.

Multistable attractors in a network of phase oscillators with three-body interactions.

Three-body interactions have been found in physics, biology, and sociology. To investigate their effect on dynamical systems, as a first step, we study numerically and theoretically a system of phase oscillators with a three-body interaction. As a result, an infinite number of multistable synchronized states appear above a critical coupling strength, while a stable incoherent state always exists for any coupling strength. Owing to the infinite multistability, the degree of synchrony in an asymptotic state can vary continuously within some range depending on the initial phase pattern.

Information maximization principle explains the emergence of complex cell-like neurons

We propose models and a method to qualitatively explain the receptive field properties of complex cells in the primary visual cortex. We apply a learning method based on the information maximization principle in a feedforward network, which comprises an input layer of image patches, simple cell-like first-output-layer neurons, and second-output-layer neurons (Model 1). The information maximization results in the emergence of the complex cell-like receptive field properties in the second-output-layer neurons. After learning, second-output-layer neurons receive connection weights having the same size from two first-output-layer neurons with sign-inverted receptive fields. The second-output-layer neurons replicate the phase invariance and iso-orientation suppression. Furthermore, on the basis of these results, we examine a simplified model showing the emergence of complex cell-like receptive fields (Model 2). We show that after learning, the output neurons of this model exhibit iso-orientation suppression, cross-orientation facilitation, and end stopping, which are similar to those found in complex cells. These properties of model neurons suggest that complex cells in the primary visual cortex become selective to features composed of edges to increase the variability of the output.

Solvable model of the collective motion of heterogeneous particles interacting on a sphere

I propose a model of mutually interacting particles on an M-dimensional unit sphere. I derive the dynamics of the particles by extending the dynamics of the Kuramoto–Sakaguchi model. The dynamics include a natural-frequency matrix, which determines the motion of a particle with no external force, and an external force vector. The position (state variable) of a particle at a given time is obtained by the projection transformation of the initial position of the particle. The same projection transformation gives the position of the particles with the same natural-frequency matrix. I show that the motion of the center of mass of an infinite number of heterogeneous particles whose natural-frequency matrices are obtained from a class of multivariate Lorentz distribution is given by an M-dimensional ordinary differential equation in closed form. This result is an extension of the Ott–Antonsen theory.

A mathematical model of negative covariability of inter-columnar excitatory synaptic actions caused by presynaptic inhibition.

We previously showed that a positive covariability between intracortical excitatory synaptic actions onto the two layer three pyramidal cells (PCs) located in mutually adjacent columns is changed into a negative covariability by column‐wise presynaptic inhibition of intracortical inputs, implicated as a basis for the desynchronization of inter‐columnar synaptic actions. Here we investigated how the inter‐columnar desynchronization is modulated by the strength of presynaptic inhibition or other factors, by using a mathematical model. Based on our previous findings on the paired‐pulse depression (PPD) of intracortical excitatory postsynaptic currents (EPSCs) evoked in PCs located in the stimulated home column (HC) but no PPD in PCs located in the adjacent column (AC), a mathematical model of synaptic connections between PCs and inhibitory interneurons was constructed. When the paired‐pulse ratio (PPR) was decreased beyond 0.80, the correlation coefficient between the two second EPSC amplitudes in the paired PCs located in the HC and AC and that in the paired PCs located in the same HC exhibited opposite changes, and reached a global negative maximum and local positive maximum, respectively, at almost the same PPR (0.40). At this PPR, the desynchronization between the two cell assemblies in mutually adjacent columns would be maximized. These positive and negative covariabilities were not produced without background oscillatory synchronization across columns and were enhanced by increasing the synchronization magnitude, indicating that the synchronization leads to the desynchronization. We propose that a slow oscillatory synchronization across columns may emerge following the liberation from the column‐wise presynaptic inhibition of inter‐columnar synaptic inputs.

Projection patterns of corticofugal neurons associated with vibrissa movement

Abstract Rodents actively whisk their vibrissae, which, when they come in contact with surrounding objects, enables rodents to gather spatial information about the environment. Cortical motor command of whisking is crucial for the control of vibrissa movement. Using awake and head-fixed rats, we investigated the correlations between axonal projection patterns and firing properties in identified layer 5 neurons in the motor cortex, which are associated with vibrissa movement. We found that cortical neurons that sent axons to the brainstem fired preferentially during large-amplitude vibrissa movements and that corticocallosal neurons exhibited a high firing rate during small vibrissa movements or during a quiet state. The differences between these two corticofugal circuits may be related to the mechanisms of motor-associated information processing.

Inhibition of GluR Current in Microvilli of Sensory Neurons via Na+-Microdomain Coupling Among GluR, HCN Channel, and Na+/K+ Pump

Glutamatergic dendritic EPSPs evoked in cortical pyramidal neurons are depressed by activation of hyperpolarization-activated cyclic nucleotide-gated (HCN) channels expressed in dendritic spines. This depression has been attributed to shunting effects of HCN current (Ih) on input resistance or Ih deactivation. Primary sensory neurons in the rat mesencephalic trigeminal nucleus (MTN) have the somata covered by spine-like microvilli that express HCN channels. In rat MTN neurons, we demonstrated that Ih enhancement apparently diminished the glutamate receptor (GluR) current (IGluR) evoked by puff application of glutamate/AMPA and enhanced a transient outward current following IGluR (OT-IGluR). This suggests that some outward current opposes inward IGluR. The IGluR inhibition displayed a U-shaped voltage-dependence with a minimal inhibition around the resting membrane potential, suggesting that simple shunting effects or deactivation of Ih cannot explain the U-shaped voltage-dependence. Confocal imaging of Na+ revealed that GluR activation caused an accumulation of Na+ in the microvilli, which can cause a negative shift of the reversal potential for Ih (Eh). Taken together, it was suggested that IGluR evoked in MTN neurons is opposed by a transient decrease or increase in standing inward or outward Ih, respectively, both of which can be caused by negative shifts of Eh, as consistent with the U-shaped voltage-dependence of the IGluR inhibition and the OT-IGluR generation. An electron-microscopic immunohistochemical study revealed the colocalization of HCN channels and glutamatergic synapses in microvilli of MTN neurons, which would provide a morphological basis for the functional interaction between HCN and GluR channels. Mathematical modeling eliminated the possibilities of the involvements of Ih deactivation and/or shunting effect and supported the negative shift of Eh which causes the U-shaped voltage-dependent inhibition of IGluR.