Existence and stability of periodic travelling wave solutions to Nagumo's nerve equation

Summary Nagumo's nerve conduction equation has a one-parameter family of spatially periodic travelling wave solutions. First, we prove the existence of these solutions by using a topological method. (There are some exceptional cases in which this method cannot be applied in showing the existence.) A periodic travelling wave solution corresponds to a closed orbit of a third-order dynamical system. The Poincaré index of the closed orbit is determined as a direct consequence of the proof of the existence. Second, we prove that the periodic travelling wave solution is unstable if the Poincaré index of the corresponding closed orbit is + 1. By using this result, together with the result of the author's previous paper, it is concluded that the slow periodic travelling wave solutions are always unstable. Third, we consider the stability of the fast periodic travelling wave solutions. We denote by L(c) the spatial period of the travelling wave solution with the propagation speed c. It is shown that the fast solution is unstable if its period is close to L_min, the minimum of L(c).     

Comparison of renal ornithine transcarbamylase activities within different chicken breeds

Comparisons were made of the renal ornithine transcarbamylase (OTC) activities within different groups of chickens including Japanese native breeds. OTC activities varied markedly within these groups. The Cochin Bantam breed and White Leghorn B line had an especially high activity, about 400 units/g of kidney, in contrast to two Japanese native breeds, Japanese Game (white variety) and Banshuu Gashiwa, and the California Gray breed, which showed a very low activity, the values being almost undetectable. In crossing experiments using the California Gray breed as a tester strain, Cochin Bantam OTC represents a simple autosomal incompletely dominant trait similar to the White Leghorn B line OTC. Kinetic studies using partially purified OTC preparations from the White Leghorn B line and Cochin Bantam breed revealed that both enzymes were identical for a variety of enzymic characteristics. In light of these results, the physiological significance of chick kidney OTC is discussed.     

The effect of dexamethasone on the functioning of C3 receptor sites on the surfaces of human fibroblasts

The presence of C₃ receptor sites on the cell surfaces of WI-38 fibroblasts was reported in a previous paper. Here the effect of dexamethasone sodium sulfate of C₃ receptor site function was studied. The incubation of WI-38 fibroblasts with dexamethasone sodium sulfate produces the biphasic mode of action, i.e., the growth-stimulating phase with low doses (90–230 μg/ml) and the growth-inhibiting phase with high doses (450–900 μg/ml). The function of C₃ receptor sites on WI-38 fibroblasts seems to be very stable and cannot be suppressed by the pretreatment of WI-38 fibroblasts with dexamethasone in high concentrations, where the cell growth is inhibited.     

Metabolism of 1alpha-hydroxyvitamin D3 to 1alpha, 25-dihydroxyvitamin D3 in perfused rat liver.

The metabolism of 1α-hydroxyvitamin D₃ (1α-OH-D₃) was studied in rat liver perfused with [³H]-1α-OH-D₃. [³H]-1α-OH-D₃ was converted very rapidly to a more polar metabolite, which was identified as 1α,25-dihydroxy-vitamin D₃ [1α,25-(OH)₂-D₃] by co-chromatography with synthetic 1α,25-(OH)₂-D₃ as well as by gas chromatography-mass spectrometry. [³H]-1α,25-(OH)₂-D₃ appeared in the perfusate as early as 20 min after addition of [³H]-1α-OH-D₃, and its level in the perfusate increased linearly for at least 120 min. These data strongly indicate that 1α-OH-D₃ is metabolized to 1α,25-(OH)₂-D₃, which exerts biological effects on bone and intestine.     

Properties of the conversion of an enzyme-ATP complex to a phosphorylated intermediate in the reaction of Na+-K+-dependent ATPase1.

Previously, we proposed the following reaction machanism for the transport ATPase (EC 3.6.1.3) reaction in the presence of high concentrations of Mg2+ and Na+:(see article). Some kinetic and thermodynamic properties of steps 3 and 4 were investigated, and the following results were obtained. 1. When the reaction was started by adding ATP to the enzyme in the presence of 50 mM Na+ and 0.5 mM K+ or in the presence of 50mM Na+ and 0.5mM Rb+, the amount of E ADP P increased with time and maintained a constant level after reaching a maximum. We could not observe the initial burst of EP formation, which was observed by Post er al. in the presence of 8 mM Na+ and 0.01 mM Rb+. 2. The existence of quasi-equilibrium between E2ATP and E ADP P in the presence of low concentrations of Na+ was suggested by the fact that the values of the reciprocal of the equilibrium constant, K3 of step 3 obtained by the following three methods were almost the same. a) The value of 1+K3 was estimated from the ratio of vo/[EP] to kd, where vo is the rate of ATP hydrolysis in the steady state, [EP] the concentration of EP, and kd the first-order rate constant of EP disappearance after stopping EP formation. b) This value was also calculated from the ratio of the amount of P1 liberated to that of decrease in EP after stopping EP formation. c) The value of K3 was also calculated from the initial rapid decrease in EP on adding K+ and EDTA, assuming that the rapid decrease was due to a shift of the equilibrium toward E2ATP on adding K+. For example, the value of K3 with 10mM NaCL and 0.5mM KCL was 7--11. Although ATP formation due to a shift of the equilibrium toward E2ATP by a K+ jump in the presence of a low concentration of Na+ was observed at 0 degrees, the amount of ATP formed by a K+ jump at 15 degrees was less than the value expected from the shift of the equilibrium. 3. The values of delta H degrees and delta S degrees of step 3 were estimated in the presence of a sufficient amount of Na+ and in the absence of K+. They were +4--+5 kcal mole minus 1 and +15--+16 entropy units mole minus1, respectively. On the basis of kinetic studies of the elementary steps and the overall reaction of Na+-K+-dependent ATPase [EC 3.6.1.3], we (1--4) showed that a phosphorylated intermediate, EP, is formed via two kinds of enzyme-substrate complex, E1ATP and E2ATP, that the EP is in K+-dependent quasi-equilibrium with E2ATP, and that in the presence of high concentration of Mg2+, EP is in a high-energy state and contains bound ADP, E ADP P.(see article).     

C3b and c3d receptor sites on human fibroblasts derived from several human tissues.

The C3b and C3d receptor sites on one cell line of human diploid fibroblasts (WI-38) were reported in previous papers [3, 4]. In this paper we describe that C3b and C3d receptor sites can also be detected in fibroblast cell lines derived from other human tissues. We consider that C3b and C3d receptors are normally found on the cell surfaces of all human fibroblasts.     

Induced pluripotent stem cell‐derived myeloid cells expressing OX40 ligand amplify antigen‐specific T cells in advanced melanoma

Immune checkpoint inhibitors improved the survival rate of patients with unresectable melanoma. However, some patients do not respond, and variable immune‐related adverse events have been reported. Therefore, more effective and antigen‐specific immune therapies are urgently needed. We previously reported the efficacy of an immune cell therapy with immortalized myeloid cells derived from induced pluripotent stem cells (iPS‐ML). In this study, we generated OX40L‐overexpressing iPS‐ML (iPS‐ML‐Zsgreen‐OX40L) and investigated their characteristics and in vivo efficacy against mouse melanoma. We found that iPS‐ML‐Zsgreen‐OX40L suppressed the progression of B16‐BL6 melanoma, and prolonged survival of mice with ovalbumin (OVA)‐expressing B16 melanoma (MO4). The number of antigen‐specific CD8⁺ T cells was higher in spleen cells treated with OVA peptide‐pulsed iPS‐ML‐Zsgreen‐OX40L than in those without OX40L. The OVA peptide‐pulsed iPS‐ML‐Zsgreen‐OX40L significantly increased the number of tumor‐infiltrating T lymphocytes (TILs) in MO4 tumor. Flow cytometry showed decreased regulatory T cells but increased effector and effector memory T cells among the TILs. Although we plan to use allogeneic iPS‐ML in the clinical applications, iPS‐ML showed the tumorgenicity in the syngeneic mice model. Incorporating the suicide gene is necessary to ensure the safety in the future study. Collectively, these results indicate that iPS‐ML‐Zsgreen‐OX40L therapy might be a new method for antigen‐specific cancer immunotherapy.