Geometric mean of probability measures and geodesics of Fisher information metric

The space of all probability measures having positive density function on a connected compact smooth manifold $M$, denoted by $\mathcal{P}(M)$, carries the Fisher information metric $G$. We define the geometric mean of probability measures by the aid of which we investigate information geometry of $\mathcal{P}(M)$, equipped with $G$. We show that a geodesic segment joining arbitrary probability measures $\mu_1$ and $\mu_2$ is expressed by using the normalized geometric mean of its endpoints. As an application, we show that any two points of $\mathcal{P}(M)$ can be joined by a unique geodesic. Moreover, we prove that the function $\ell$ defined by $\ell(\mu_1, \mu_2):=2\arccos\int_M \sqrt{p_1\,p_2}\,d\lambda$, $\mu_i=p_i\,\lambda$, $i=1,2$ gives the Riemannian distance function on $\mathcal{P}(M)$. It is shown that geodesics are all minimal.Comment: 33 pages, 1 figur

STIMULATION OF ARITHMETIC SKILLS AND HEMODYNAMIC EFFECTS BY COFFEE-DRINKING : DOUBLE-BLIND ANALYSIS WITH DIFFERENT CONCENTRATIONS OF CAFFEINE

Effects of caffeine on arithmetic performance were investigated with 217 university students. A double-blind study for arithmetic skill test and hemodynamic effects was carried out after drinking caffeine-free or caffeine-containing (100, 180 and 250 mg) coffee. Eleven rounds of the arithmetic tests were performed ; first four rounds before, and subsequently seven rounds after coffee break. Each round consisted of three 1-min arithmetic tests. The arithmetic skill for each round was averaged. Simultaneously, heart rate and blood pressure once a round were also measured. The mean value of arithmetic skill at the 4th round (n=217) was 87.3±1.8/min.　The heart rate and mean blood pressure were 72.7±1.7 beats/min and 101.7±4.1 mmHg. As compared with caffeine-free group, caffeine at 100 mg significantly enhanced arithmetic skill for 60 to 90 min after coffee-drinking. The mean blood pressure was increased for 30 to 60 min after coffee-drinking (with caffeine 180 mg). But the ratio of arithmetic errors and heart rate were unaffected. At 250 mg, caffeine rather depressed arithmetic skill and blood pressure. These results indicate that caffeine (100 to 180 mg)-containing coffee drinking can enhance arithmetic skill and modulate hemodynamic actions, presumably resulting from stimulation of the central nervous system and cardiovascular system

DIRECT G PROTEIN GATING OF ACH-SENSITIVE K⁺ CHANNEL IN GUINEA-PIG ATRIAL CARDIOMYOCYTES : ANALYSIS BY INSIDE-OUT PATCH CLAMP MODE

Direct actions of guanosine 5'-triphosphate (GTP)-binding protein (G protein) on the K⁺ channel in isolated single atrial muscle cells from guinea-pig hearts were investigated. In cell-attached patch-clamp mode, ACh-sensitive K⁺ (K⁺ [ACh]) channels were stimulated by application of carbachol (10 μM). A unitary channel current identified by carbachol responsiveness was activated inwardly at the resting membrane potential, and was decreased with an increase in membrane potential. At 0 mV, the single-current was zero mV (the reversal potential). The extracellular and pipette solutions (140 mM KCl) were similar. It was a slope conductance of 44.7±3.5 pS (n=8) and an average open time at -80 mV of 1.4±0.3 msec (n=7). It had a strong inwardly-rectifier property at positive potentials. The response was blocked by the addition of atropine (1 μM) to the pipette solution. On switching from a cell-attached to an inside-out patch-clamp experiment (to avoid the influences of intracellular signal transductions), the activation of K⁺ [ACh] channels was gradually attenuated. Holding potential was -80 mV. But since other channels (i. e. ATP-sensitive K⁺ channel and inward-rectifying K^+ channel) still remained, the cell was transiently taken out from the bath solution (exposed to the air) to inactivate the channels. GTP (100 μM), which was applied by a concentration-clamp technique, activated the K⁺ [ACh] channels with the same characteristics within a moment of its application. The responses were reversible. These results indicate that G protein directly activates the K⁺ [ACh] channels on the atrial muscle cell membrane, independent of second messengers

MODULATIONS BY EXTERNAL PH ON ANODAL BREAK EXCITATION IN RABBIT SINO-ATRIAL NODAL CELLS

Effects of extracellular pH on anodal break excitation in rabbit sino-atrial (SA) nodal cells were investigated using the two-microelectrode voltage-clamp technique. The method of anodal break excitation was developed by Weidmann²⁸⁾，and is regarded as a measurement of the activity of the fast Na⁺ channel. Increasing external pH from 7.4 to 8.5 enhanced the maximum rate of depolarization by anodal break excitation，as compared with the values of control (at pH 7.4). In contrast，a decline of pH from 7.4 to 5.5 inhibited the maximum rate of depolarization，accompanied with depression in the activity. Acidification shifted the inactivation curves (h∞) of the fast Na⁺ current in the depolarizing direction，and alkalinization shifted it in the hyperpolarizing direction. These results suggest that proton would modulate the membrane surface charge of the SA nodal cells，resulting in alteration of the gating kinetics of ionic channels

PACEMAKER CURRENT (HYPERPOLARIZATION-ACTIVATED INWARD CURRENT) IN ISOLATED SINGLE PREGNANT RAT UTERINE MYOCYTES

Whole-cell patch clamp experiments were performed to examine the underlying currents to generate spontaneous activity in freshly isolated single longitudinal muscle cells of pregnant rat uterus (18-day gestation). Isolated single cells were spindle- or round-shaped (50-700 μm in length and 2-30 μm in diameter). The holding potential was -30 mV. Long-duration (3 sec) hyperpolarizing pulses were applied to -40 to -120 mV, in increments of 10 mV. Experiments were performed at room temperature (22℃). A　hyperpolarization-activated inward current (I_f) was produced. Current density at -120 mV was -1.03±0.31 pA/pF (n=5). The average capacitance was 64.3±2.3 pF (n=8). The threshold potential for activation of I_f was about -50 to -60 mV. The reversal potential was -18.6±2.1 mV (n=4). In the presence of Cs⁺ (3 mM), the I_f current at -120 mV was decreased by 76.5±2.1% (P<0.01, n=5). These results indicate that the Cs⁺⁻sensitive hyperpolarization-activated inward current is present in the longitudinal muscle cells of pregnant rat uterus. This I_f current may contribute somewhat to the electrogenesis of the spontaneous activity

Vascular Pharmacology of Mokuboito (Mu-Fang-Yi-Tang) and Its Constituents on the Smooth Muscle and the Endothelium in Rat Aorta

Pharmacological actions of Mokuboito and its constituents (Sinomenium acutum and sinomenine) on rat aorta were examined. Mokuboito and S. acutum at lower concentrations (0.03–1 mg ml−1) contracted the non-loaded aorta, but at higher concentrations (1–3 mg ml−1), reversed to dilate it. The vasoconstriction was blocked by phentolamine (10 μM). Sinomenine failed to exhibit the vasoconstriction. On the other hand, Mokuboito and S. acutum dilated the NE (5 μM)-induced vasoconstriction: at 3 mg ml−1, by 98.9 ± 2.5% (n = 6, P < 0.01) and 97.0 ± 4.8% (n = 6, P < 0.01). Vasorelaxation induced by Mokuboito and S. acutum was attenuated by indomethacin, L-NMMA and nicardipine. Propranolol decreased the vasorelaxation induced by Mokuboito, but not by S. acutum. Sinomenine also relaxed the constriction and at 100 μM, by 68.8 ± 5.1% (n = 7, P < 0.01). This vasorelaxation was attenuated by indomethacin, L-NMMA and nicardipine, and also by propranolol. Therefore, these results indicate that Mokuboito and its constituents exert both vasodilating actions mediated by endothelium-dependent mechanisms (PGI2 and NO from endothelium) and by endothelium-independent mechanisms (Ca2+ influx control on smooth muscle cells). Simultaneously, Mokuboito and S. acutum cause the vasoconstrictions mediated through α-adrenoceptor stimulation, but not sinomenine. Also, Mokuboito and sinomenine possess β-adrenoreceptor stimulating action, but not S. acutum

ENHANCEMENT OF ARITHMETIC SKILLS BY COFFEE-DRINKING : DOUBLE-BLIND STUDY FOR CAFFEINE-CONTAINING AND CAFFEINE-FREE COFFEES

Effects of caffeine on arithmetic performance were investigated with 99 university students. A double-blind study for arithmetic skill test was carried out, after drinking caffeine-free or caffeine-containing (180 mg) coffee. Eight rounds for the arithmetic tests were performed ; four rounds before, and four rounds after coffee break. Each round was 1-min arithmetic tests three times with 1-min intervals. The arithmetic skill and the ratio of arithmetic errors per each round were averaged. Simultaneously, heart rate was also measured. The mean values of arithmetic skill and the ratio of errors at the 4th round (n=99) were 81.4±1.7/min and 0.28±0.02%. The heart rate was 76.9±1.5 beats/min. Before and after coffee-drinking, arithmetic skill was enhanced, whereas the heart rate was significantly decreased. As compared with the caffeine-free group, caffeine significantly enhanced the arithmetic skill 45 and 60 min after coffee-drinking. But the ratio of arithmetic errors was not affected. The heart rate was significantly decreased only at 45 min later. These results indicate that caffeine (-containing coffee drinking) can enhance arithmetic skill and decrease the heart rate, presumably resulting from stimulation of the central nervous system

CARDIOPROTECTIVE ACTIONS OF ATP-SENSITIVE K⁺ CHANNEL OPENERS (CROMAKALIM, PINACIDIL AND NICORANDIL) IN CARDIAC PURKINJE FIBERS

Effects of ATP-dependent K⁺ channel openers on the action potentials and the contractile force in canine cardiac Purkinje fibers were examined. Cromakalim and pinacidil (0.3 to 10 μM), and nicorandil (0.3 to 1 mM) shortened both the 50% and 90% action potential durations (APD), and decreased the contractile force, in a concentration and frequency-dependent manner. These responses were reversible. The APD shortening and the negative inotropic effect induced by a switch of stimulation frequency (from 0.5 to 3 Hz) were potentiated by application of the openers. Other action potential parameters were unaffected, but the resting potential of relatively less negative voltage was hyperpolarized. These effects were potently antagonized by glibenclamide (a selective blocker of ATP-sensitive K⁺ channel). Under the calcium overload condition, the K⁺ channel openers abolished a delayed afterdepolarization and recovered the contractile force. These results suggest that the ATP-sensitive K⁺ channel openers increase the K⁺ conductance and simultaneously may possess cardioprotective actions to reduce the cellular Ca²⁺ level in calcium overloaded cells