Cluster synchronization in an ensemble of neurons interacting through chemical synapses

In networks of periodically firing spiking neurons that are interconnected with chemical synapses, we analyze cluster state, where an ensemble of neurons are subdivided into a few clusters, in each of which neurons exhibit perfect synchronization. To clarify stability of cluster state, we decompose linear stability of the solution into two types of stabilities: stability of mean state and stabilities of clusters. Computing Floquet matrices for these stabilities, we clarify the total stability of cluster state for any types of neurons and any strength of interactions even if the size of networks is infinitely large. First, we apply this stability analysis to investigating synchronization in the large ensemble of integrate-and-fire (IF) neurons. In one-cluster state we find the change of stability of a cluster, which elucidates that in-phase synchronization of IF neurons occurs with only inhibitory synapses. Then, we investigate entrainment of two clusters of IF neurons with different excitability. IF neurons with fast decaying synapses show the low entrainment capability, which is explained by a pitchfork bifurcation appearing in two-cluster state with change of synapse decay time constant. Second, we analyze one-cluster state of Hodgkin-Huxley (HH) neurons and discuss the difference in synchronization properties between IF neurons and HH neurons.Comment: Notation for Jacobi matrix is changed. Accepted for publication in Phys. Rev.

Chaos synchronization in gap-junction-coupled neurons

Depending on temperature the modified Hodgkin-Huxley (MHH) equations exhibit a variety of dynamical behavior including intrinsic chaotic firing. We analyze synchronization in a large ensemble of MHH neurons that are interconnected with gap junctions. By evaluating tangential Lyapunov exponents we clarify whether synchronous state of neurons is chaotic or periodic. Then, we evaluate transversal Lyapunov exponents to elucidate if this synchronous state is stable against infinitesimal perturbations. Our analysis elucidates that with weak gap junctions, stability of synchronization of MHH neurons shows rather complicated change with temperature. We, however, find that with strong gap junctions, synchronous state is stable over the wide range of temperature irrespective of whether synchronous state is chaotic or periodic. It turns out that strong gap junctions realize the robust synchronization mechanism, which well explains synchronization in interneurons in the real nervous system.Comment: Accepted for publication in Phys. Rev.

resection of oligometastases from CRC

A 74-year-old woman underwent right hemicolectomy and partial ileal resection for ascending colon cancer with synchronous peritoneal metastasis. Histopathological examination showed moderately differentiated adenocarcinoma with mucinous component, pT4b N3 M1, and Stage IV. Postoperative chemotherapy comprising 36 courses of mFOLFOX6 with bevacizumab was administered. Twenty-two months after the surgery, computed tomography (CT) revealed a 20 mm nodular lesion adjacent to the gastric wall, and laparoscopic resection of the nodule was performed. Thirty-nine months after the second surgery, CT showed a 24 mm nodular lesion involving the liver parenchyma, and partial hepatectomy involving the nodule was performed. Histopathological examination of the nodules resected by the second and third surgeries showed the same features as the primary ascending colon cancer. The nodules were diagnosed as metachronous peritoneal metastases. The patient followed up without chemotherapy after the second and third surgery, showed no recurrence for 26 months after the third surgery. Fortunately, more than 7 years have passed since the primary tumor resection. Hence, surgical resection for synchronous and repeated metachronous peritoneal oligometastases from colon cancer can offer long-term survival

Linear stability analysis of retrieval state in associative memory neural networks of spiking neurons

We study associative memory neural networks of the Hodgkin-Huxley type of spiking neurons in which multiple periodic spatio-temporal patterns of spike timing are memorized as limit-cycle-type attractors. In encoding the spatio-temporal patterns, we assume the spike-timing-dependent synaptic plasticity with the asymmetric time window. Analysis for periodic solution of retrieval state reveals that if the area of the negative part of the time window is equivalent to the positive part, then crosstalk among encoded patterns vanishes. Phase transition due to the loss of the stability of periodic solution is observed when we assume fast alpha-function for direct interaction among neurons. In order to evaluate the critical point of this phase transition, we employ Floquet theory in which the stability problem of the infinite number of spiking neurons interacting with alpha-function is reduced into the eigenvalue problem with the finite size of matrix. Numerical integration of the single-body dynamics yields the explicit value of the matrix, which enables us to determine the critical point of the phase transition with a high degree of precision.Comment: Accepted for publication in Phys. Rev.

Neutrophil S100A9 supports M2 macrophage niche formation in granulomas

慢性炎症「肉芽腫」における好中球の新しい炎症制御系の解明 --M2マクロファージの新たな誘導メカニズム解明--. 京都大学プレスリリース. 2023-02-17.In search of inflammatory Achilles heel. 京都大学プレスリリース. 2023-03-10.Mycobacterium infection gives rise to granulomas predominantly composed of inflammatory M1-like macrophages, with bacteria-permissive M2 macrophages also detected in deep granulomas. Our histological analysis of Mycobacterium bovis bacillus Calmette-Guerin-elicited granulomas in guinea pigs revealed that S100A9-expressing neutrophils bordered a unique M2 niche within the inner circle of concentrically multilayered granulomas. We evaluated the effect of S100A9 on macrophage M2 polarization based on guinea pig studies. S100A9-deficient mouse neutrophils abrogated M2 polarization, which was critically dependent on COX-2 signaling in neutrophils. Mechanistic evidence suggested that nuclear S100A9 interacts with C/EBPβ, which cooperatively activates the Cox-2 promoter and amplifies prostaglandin E2 production, followed by M2 polarization in proximal macrophages. Because the M2 populations in guinea pig granulomas were abolished via treatment with celecoxib, a selective COX-2 inhibitor, we propose the S100A9/Cox-2 axis as a major pathway driving M2 niche formation in granulomas

Topological Dislocations and Mixed State of Charge Density Waves

We discuss the possibility of the ``mixed state'' in incommensurate charge density waves with three-dimensional order. It is shown that the mixed state can be created by applying an electric field perpendicular to the chains. This state consists of topological dislocations induced by the external field and is therefore similar to the mixed states of superfluids (type-II superconductor or liquid Helium II). However, the peculiar coupling of charge density waves with the electric field strongly modifies the nature of the mixed state compared to the conventional superfluids. The field and temperature dependence of the properties of the mixed state are studied, and some experimental aspects are discussed.Comment: 10 pages, Revtex format, no figures, to appear in Phys. Rev. Let

Oscillator neural network model with distributed native frequencies

We study associative memory of an oscillator neural network with distributed native frequencies. The model is based on the use of the Hebb learning rule with random patterns ($\xi_i^{\mu}=\pm 1$), and the distribution function of native frequencies is assumed to be symmetric with respect to its average. Although the system with an extensive number of stored patterns is not allowed to get entirely synchronized, long time behaviors of the macroscopic order parameters describing partial synchronization phenomena can be obtained by discarding the contribution from the desynchronized part of the system. The oscillator network is shown to work as associative memory accompanied by synchronized oscillations. A phase diagram representing properties of memory retrieval is presented in terms of the parameters characterizing the native frequency distribution. Our analytical calculations based on the self-consistent signal-to-noise analysis are shown to be in excellent agreement with numerical simulations, confirming the validity of our theoretical treatment.Comment: 9 pages, revtex, 6 postscript figures, to be published in J. Phys.