Rate of excitation propagation in a reduced Hodgkins-Huxley model. II. Slow relaxation of the sodium current]

The influence of sodium current activation on the value of nerve excitation conduction velocity is investigated on the basis of Hodgkin-Huxley model. The potassium activation and sodium inactivation are considered as slow processes which do not develop to an appreciable extent in the region of conduction velocity formation. The system of equations was derived and solved analytically after neglecting the dependency of sodium relaxation time on potential; the approximation of steady-state sodium activation was also used with the help of Hevyside function. The algebraic equation for conduction velocity was obtained; its solution has a simple analytical form in two limits of rapid and slow sodium current relaxation. The comparison with the experimental data has shown that at not very high temperatures the slow (compared to the potential dynamics) sodium current relaxation approximation is more appropriate. The dependency of impulse velocity on capacitance and conductance of the fiber was analyzed.     

Impulse photoconductivity of solutions of ohlorophyll and its analogs. III. Photoconductivity of hexanol solutions of chlorophyll a in the presence of n-benzoquinone. Kinetic and temperature measurements]

It is shown that an increase deltasigma of electroconductivity of chlorophyll "a" (Chlalpha) solution in hexanole in the presence of n-benzoquinone (Q) under impulse illumination of solution is proportional to flash intensity: deltasigma=1(0,99+/-0,07). Dependence deltasigma on solution temperature is of an exponential character with the activation energy Esigma=0,30+/-0,01 ev. In the temperature range studied (248--298 degrees K) the ratio between the recombination velocity constant and the mobility of ion-radicals Chlalpha+ and Q-(Kp/mu) is shown to be equal (8+/-1)X 10(-8) cm-v. The activation energy for the dissociation of coulomb pair (Chlalpha+Q-) into free ion-radicals Epiapproximately0,1 ev is evaluated. The value of total mobility of negative and positive ion-radicals is calculated from the date obtained and literature ones: mu=(1,0+/-0,2)X10(-5) cm2/v-sec.     

ON THE THEORY OF NERVOUS CONDUCTION

Assuming that the propagation of the nervous impulse consists in the excitation of adjacent regions of the nerve by the action current of the already excited region, exact equations for the velocity of such a propagation are established and integrated. The result depends on the assumptions which we make about the laws of excitation. If Hoorweg''s law is accepted, it is found that the velocity of propagation decreases exponentially with time, and that there is a limiting distance which the impulse will travel and which cannot be exceeded. If however a set of equations proposed by L. Lapique is assumed to govern the process of excitation, we find that the velocity of propagation asymptotically reaches a constant value.     

Electrophysiological evidence for ammonium as a substitute for potassium in activating the sodium pump in a crayfish sensory neuron

Electrophysiological studies were performed on slowly adapting cells of the crayfish (Astacus astacus) stretch receptor to examine some aspects of the operation of the sodium pump. Intracellular sodium activity (aiNa) and pH (pHi) were measured with liquid ion exchanger microelectrodes and the effects of NH3/NH+4 were observed. In cells in which the sodium pump was inhibited by K+-free solution, NH+4 induced a decrease of aiNa that can be explained only in Na+ extrusion is assumed. pHi measurements provide indirect evidence that NH+4 was taken up at the same time as Na+ was extruded. Ouabain blocks the operation of the sodium pump in the presence of K+ and NH+4. This result suggests that the ammonium-mediated decrease in aiNa in K+-free solution was caused by activation of the sodium pump. The results obtained by electrophysiological methods in a living cell are qualitatively in good agreement when compared with biochemical investigations on assays of crustacean Na+-K+ ATPase.     

The role of succinic acid in neuron reaction to synaptic activation

It has been shown on Retzius neuron of the leech that after preintroduction of sodium succinate the reaction to synaptic stimulation expressed in increased frequency of the impulse activity proceeds more intensively than in the norm. In connection with the fact that against the background of succinate effect reaction to acetylcholine increases it is suggested that this very mediator is responsible for slower decrease of the impulse activity frequency at synaptic activation.     

Semiconduction as the mechanism of the cytochrome oxidase reaction. Low activation energy of semiconduction measured for cytochrome oxidase protein. Solid state theory of cytochrome oxidase predicts observed kinetic peculiarities.

Cytochrome oxidase protein has a measured activation energy of semiconduction much smaller than that of other proteins, falling within the range of the activation energy of the cytochrome oxidase reaction in solution. Many kinetic peculiarities of the cytochrome oxidase reaction difficult to explain by mass-action theories are easily accounted for if semiconduction is assumed to be the controlling mechanism.     

The nerve impulse in the axon — a new theory

The Classical Theory of function in the nervous system postulates that the nerve impulse is the result of a sequential reversal of the membrane potential due to an increased permeability of the membrane, first to sodium ions, then to potassium ions. The new theory presents a bio-physical model which depicts the nerve impulse as an event involving the motions of electrons and waves, and their interactions with sodium and potassium atoms and ions. The velocity of the nerve impulse (the most important parameter of nerve function) is determined by the product of two constants: c = the speed of light, which is a constant for all nerves; k =a constant for each nerve and is believed to be a specific property of nerve matter related in some way to the atomic process. The theory proposes that the nerve impulse in the axon is dualistic in nature (particles and waves play equally significant roles). The dualistic nature accounts for the three most fundamental characteristics of conduction of the nerve impulse: periodicity (conduction of a nerve impulse over long distances with constant velocity and form); non-summing (two nerve impulses cannot be in the same place at the same time); quantum nature of each nerve impulse — i.e., the unit message of the nerve impulse is an indivisible unit.     

Activation process of pepsinogen.

The activation process of pepsinogen was analyzed by a combination of computer simulation and experiment. In order to investigate in detail the behavior of the basic schemes proposed in the previous study, further computer simulations were conducted. Some experiments were performed based on the information obtained. The changes in the UV difference spectrum in the early stage was measured by the stopped-flow technique and the conversion of pepsinogen to pepsin [EC 3.4.23.1] was followed by sodium dodecyl sulfate-polyacrylamide gel electrophoresis. Furthermore, on the basis of the experimental results, the most reasonable scheme was selected and modified. As a result, a scheme for the activation process of pepsinogen was obtained (Scheme 8). On the basis of the above analyses, it was assumed that the first step and the third step are pH-dependent based on the change in the UV spectrum, that the second step is a nonlinear reaction containing a looped reaction with a dimeric intermediate (in this step, peptide fragments are released and pepsinogen is converted to a pepsin-like molecule), and that the third step is an equilibrium reaction involving proton binding.     

Gating current harmonics. IV. Dynamic properties of secondary activation kinetics in sodium channel gating.

The kinetics for sodium channel gating appear to involve three coupled processes: (a) "primary" activation, (b) "secondary" activation, and (c) inactivation. Gating current data obtained in dynamic steady states with sinusoidal voltage-clamp were analyzed to give further details about the secondary activation process in sodium channel gating. Unlike primary activation and inactivation, the secondary activation kinetics involve physical processes that become defined when the data are analyzed as a function of the sinusoid frequency in addition to mean membrane potential. The effects of these processes are described, and a physical interpretation is presented.     

A model of pulsatile flow in a uniform deformable vessel.

Simulations of blood flow in natural and artificial conduits usually require large computers for numerical solution of the Navier-Stokes equations. Often, physical insight into the fluid dynamics is lost when the solution is purely numerical. An alternative to solving the most general form of the Navier-Stokes equations is described here, wherein a functional form of the solution is assumed in order to simplify the required computations. The assumed forms for the axial pressure gradient and velocity profile are chosen such that conservation of mass is satisfied for fully established pulsatile flow in a straight, deformable vessel. The resulting equations are cast in finite-difference form and solved explicitly. Results for the limiting cases of rigid wall and zero applied pressure are found to be in good agreement with analytical solutions. Comparison with the experimental results of Klanchar et al. [Circ. Res. 66, 1624-1635 (1990]) also shows good agreement. Application of the model to realistic physiological parameter values provides insight as to the influence of the pulsatile nature of the flow field on wall shear development in the presence of a moving wall boundary. Specifically, the model illustrates the dependence of flow rate and shear rate on the amplitude of the vessel wall motion and the phase difference between the applied pressure difference and the oscillations of the vessel radius. The present model can serve as a useful tool for experimentalists interested in quantifying the magnitude and character of velocity profiles and shearing forces in natural and artificial biologic conduits.     

An analytical solution countercurrent heat transfer between parallel vessels with a linear axial temperature gradient

Presented in this paper is a solution for countercurrent heat exchange between two parallel vessels embedded in an infinite medium with a linear temperature gradient along the axes of the vessels. The velocity profile within the vessel is assumed to be parabolic. This solution describes the temperature field within the vessels, as well as in the tissue, and establishes that the intravessel temperature is not uniform, as is generally assumed to be the case. An explicit expression for the intervessel thermal resistance based on the difference between cup-mixed mean temperatures is derived.     

THE EFFECT OF ACETATE BUFFER MIXTURES,ACETIC ACID,AND SODIUM ACETATE,ON THE PROTOPLASM,AS INFLUENCING THE RATE OF PENETRATION OF CRESYL BLUE INTO THE VACUOLE OF NITELLA

When living cells of Nitella are exposed to a solution of sodium acetate and are then placed in a solution of brilliant cresyl blue made up with a borate buffer mixture at pH 7.85, a decrease in the rate of penetration of dye is found, without any change in the pH value of the sap. It is assumed that this inhibiting effect is caused by the action of sodium on the protoplasm. This effect is not manifest if the dye solution is made up with phosphate buffer mixture at pH 7.85. It is assumed that this is due to the presence of a greater concentration of base cations in the phosphate buffer mixture. In the case of cells previously exposed to solutions of acetic acid the rate of penetration of dye decreases with the lowering of the pH value of the sap. This inhibiting effect is assumed to be due chiefly to the action of acetic acid on the protoplasm, provided the pH value of the external acetic acid is not so low as to involve an inhibiting effect on the protoplasm by hydrogen ions as well. It is assumed that the acetic acid either has a specific effect on the protoplasm or enters as undissociated molecules and by subsequent dissociation lowers the pH value of the protoplasm. With acetate buffer mixture the inhibiting effect is due to the action of sodium and acetic acid on the protoplasm. The inhibiting effect of acetic acid and acetate buffer mixture is manifested whether the dye solution is made up with borate or phosphate buffer mixture at pH 7.85. It is assumed that acetic acid in the vacuole serves as a reservoir so that during the experiment the inhibiting effect still persists.     

Multiple site optical recording of transmembrane voltage (MSORTV) in patterned growth heart cell cultures: assessing electrical behavior, with microsecond resolution, on a cellular and subcellular scale.

We have applied multiple site optical recording of transmembrane voltage (MSORTV) to patterned growth cultures of heart cells to analyze the effect of geometry per se on impulse propagation in excitable tissue, with cellular and subcellular resolution. Extensive dye screening led to the choice of di-8-ANEPPS as the most suitable voltage-sensitive dye for this application; it is internalized slowly and permits optical recording with signal-to-noise ratios as high as 40:1 (measured peak-to-peak) and average fractional fluorescence changes of 15% per 100 mV. Using a x 100 objective and a fast data acquisition system, we could resolve impulse propagation on a microscopic scale (15 microns) with high temporal resolution (uncertainty of +/- 5 microseconds). We could observe the decrease in conduction velocity of an impulse propagating along a narrow cell strand as it enters a region of abrupt expansion, and we could explain this phenomenon in terms of the micro-architecture of the tissue. In contrast with the elongated and aligned cells forming the narrow strands, the cells forming the expansions were aligned at random and presented 2.5 times as many cell-to-cell appositions per unit length. If the decrease in conduction velocity results entirely from this increased number of cell-to-cell boundaries per unit length, the mean activation delay introduced by each boundary can be estimated to be 70 microseconds. Using this novel experimental system, we could also demonstrate the electrical coupling of fibroblasts and endotheloid cells to myocytes in culture.     

ENZYMES IN ONTOGENESIS (ORTHOPTERA) : XIII. ACTIVATION OF PROTYROSINASE AND THE OXIDATION OF ASCORBIC ACID

1. Protyrosinase from the egg of the grasshopper, Melanoplus differentialis, can be activated by excess sodium oleate or Aerosol. 2. The 3:4 quinone products of the reaction of activated protyrosinase with tyramine or tyrosine will oxidize ascorbic acid to dehydroascorbic acid. 3. The velocity of this latter oxidation of ascorbic acid increases with the amount of tyramine or tyrosine. 4. The oxidation of ascorbic acid by the tyramine-tyrosinase reaction delays the time of appearance of a red color associated with an indole quinone intermediary product in the formation of melanin. 5. Protyrosinase, in itself, and in the presence of tyrosinase substrates does not bring about the oxidation of ascorbic acid. 6. A naturally occurring substrate in a preparation of protyrosinase, sufficient to cause the oxidation of ascorbic acid, can be removed by dialysis against a 0.9 per cent sodium chloride solution. 7. Dialysis against such a solution does not change the properties of protyrosinase; the inactive enzyme must still be activated before it will catalyze the oxidation of tyramine or tyrosine. 8. When the natural substrate, tyrosine, or tyramine is absent, activation of protyrosinase does not result in the oxidation of ascorbic acid.     

The Role of Calcium Ions in Modulation of Impulse Activity of the Isolated Muscle Spindle of the Frog Rana temporaria

The effect of various concentrations of Ca⁺² and Mg⁺² as well as of calcium channel blockers verapamil and nifedipin on impulse activity of frog isolated muscle spindles was studied. Removal of Ca ions from the external Ringer solution was established to increase spontaneous and evoked activity of the muscle spindle. A 4- and 8-fold increase of Ca⁺² concentration produces inhibition and complete cessation of the spontaneous and evoked activity in the muscle spindle. Replacement of Ca⁺² by Mg⁺² is observed to cause no statistically significant change of the spontaneous activity of the isolated muscle spindle; at the same time, at the dynamic spindle extension, the impulse activity rate at the dynamic and static phases of the response rises. Nifedipin and verapamil, blockers of Ca⁺² channels, suppress impulse activity both in norm and on the background of increased impulse activity evoked by removal of Ca⁺² from the external solution. An increase of muscle spindle impulse activity after the removal of Ca⁺² from the external solution is accounted for by transformation of calcium channels of the muscle spindle sensory endings into selective sodium channels.     

Activation of human quadriceps femoris during isometric, concentric, and eccentric contractions.

Maximal and submaximal activation level of the right knee-extensor muscle group were studied during isometric and slow isokinetic muscular contractions in eight male subjects. The activation level was quantified by means of the twitch interpolation technique. A single electrical impulse was delivered, whatever the contraction mode, on the femoral nerve at a constant 50 degrees knee flexion (0 degrees = full extension). Concentric, eccentric (both at 20 degrees /s velocity), and isometric voluntary activation levels were then calculated. The mean activation levels during maximal eccentric and maximal concentric contractions were 88.3 and 89.7%, respectively, and were significantly lower (P < 0.05) with respect to maximal isometric contractions (95.2%). The relationship between voluntary activation levels and submaximal torques was linearly fitted (P < 0.01): comparison of slopes indicated lower activation levels during submaximal eccentric compared with isometric or concentric contractions. It is concluded that reduced neural drive is present during 20 degrees /s maximal concentric and both maximal and submaximal eccentric contractions. These results indicate a voluntary activation dependency on both tension levels and type of muscular actions in the human knee-extensor muscle group.     

Temporal stability of solitary impulse solutions of a nerve equation

We study a differential equation that models nerve impulse transmission. The nonlinearity is simplified to be piecewise linear in order to allow explicit solution. In general, two solitary impulse solutions are exhibited. The temporal stability of these solutions is analyzed by a technique that identifies the number of unstable modes. These results extend the results of Rinzel and Keller (1973, Biophys. J. 13:1313) by showing that the slower unstable solution has only one unstable mode, and that the fast solution, as conjectured, has no unstable modes and is therefore stable.     

Pulsatile blood flow effects on temperature distribution and heat transfer in rigid vessels

The effect of blood velocity pulsations on bioheat transfer is studied. A simple model of a straight rigid blood vessel with unsteady periodic flow is considered. A numerical solution that considers the fully coupled Navier-Stokes and energy equations is used for the simulations. The influence of the pulsation rate on the temperature distribution and energy transport is studied for four typical vessel sizes: aorta, large arteries, terminal arterial branches, and arterioles. The results show that: the pulsating axial velocity produces a pulsating temperature distribution; reversal of flow occurs in the aorta and in large vessels, which produces significant time variation in the temperature profile. Change of the pulsation rate yields a change of the energy transport between the vessel wall and fluid for the large vessels. For the thermally important terminal arteries (0.04-1 mm), velocity pulsations have a small influence on temperature distribution and on the energy transport out of the vessels (8 percent for the Womersley number corresponding to a normal heart rate). Given that there is a small difference between the time-averaged unsteady heat flux due to a pulsating blood velocity and an assumed nonpulsating blood velocity, it is reasonable to assume a nonpulsating blood velocity for the purposes of estimating bioheat transfer.     

Plasma Approach to Describing the Electric Dynamics of a Neuron

The electric excitation of a neuron is interpreted as the formation of a nonlinear solitary ion acoustic wave of the charge density of sodium and hydrogen ions in an electrolytic intracellular fluid, which is treated as a dense plasma. It is shown that such a wave can be described by the coupled sine-Gordon and Korteweg-de Vries equations, having a solution in the form of a soliton whose internal vibrational structure is described by the Fermi-Pasta-Ulam spectrum. It is concluded that a nerve impulse can be interpreted as a low-frequency solitary wave of the charge density of sodium ions with a trapped high-frequency charge density wave of protons.     

Steady-state kinetic investigation of specific anion effects on the catalytic activity of yeast glutathione reductase

The catalytic activity of yeast glutathione reduetase at pH 7.6 is sensitive to the sodium phosphate buffer concentration and the presence of monovalent sodium salts in the assay medium. Low concentrations of sodium phosphate activate and high concentrations inhibit enzymatic activity. The optimal concentration is at about 0.06 m sodium phosphate. In the presence of 0.06 m sodium phosphate, addition of a variety of monovalent sodium salts results in inhibition of enzymatic activity, the inhibition being competitive with respect to NADPH and noncompetitive with respect to oxidized glutathione. At suboptimal concentrations of sodium phosphate, addition of monovalent sodium salts activates enzymatic activity. In addition, at suboptimal sodium phosphate concentration Lineweaver-Burk plots of initial velocity at constant NADPH concentration with oxidized glutathione as the variable substrate are nonlinear, being concave down. The nonlinear behavior can be eliminated by addition of 0.1 m sodium chloride. It is concluded that there are at least two specific anion binding sites at or near the enzyme active site. The anion inhibition is explained in terms of an ordered sequential mechanism for glutathione reduetase. The anion activation is analyzed in terms of a change of reaction pathway, the reactive enzyme species being dependent upon the oxidized glutathione concentration.