The frequency response of the action of light on the membrane potential ofNitella

Summary Cells ofNitella flexilis were illuminated with light of sinusoidally modulated intensity at frequencies between 0.1 and 64 cycles/min and the frequency response of the changes of the membrane potential caused by light were measured. A band-pass characteristic was found which is known from similar investigations inAcetabularia. The slope of the frequency response was of the 1/f²-type. This slope and the band-pass characteristic lead to the conclusion that three poles and one zero are comprised in the network function of the action of light on the membrane potential. It is discussed which models regarding the mechanism of the action of light on the membrane potential account for the frequency response measured.

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Zusammenfassung Der Frequenzgang der Lichtwirkung auf das Membranpotential vonNitella.Internodienzellen der AlgeNitella flexilis wurden mit sinusförmig moduliertem Licht im Frequenzbereich von 0,1 bis 64 Schwingungen/min beleuchtet und der Frequenzgang der durch das Licht verursachten Änderungen der Membranspannung gemessen. Es trat eine Bandpaßcharakteristik auf, die jedoch nicht im Deteil untersucht wurde, da sie schon von Messungen anAcetabularia bekannt ist. Das Interesse lag auf der hochfrequenten Flanke. Es wurde gefunden, daß die Asymptote mit 1/f² abfällt. Aus der Bandpaßcharakteristik und der Flankensteilheit ist zu entnehmen, daß die Netzwerkfunktion der Lichtwirkung auf das Membranpotential im untersuchten Frequenzbereich 3 Polstellen und eine Nullstelle enthält. Es wird diskutiert, welche Schlüsse daraus über den Mechanismus der Lichtwirkung zu ziehen sind.

     

Dependence of the threshold of sinusoidal grating displacement on its spatial frequency characteristics

The threshold of detection of sinusoidal grating displacement was studied under conditions of the absence of apparent movement. It was shown that the threshold rises with the pattern size and depends on the number of grating cycles at a constant stimulus magnitude. The stimulus size in 2–3 periods is optimal for its localization. The results suggest that objects in the visual field are localized by mechanisms tuned to a certain spatial frequency and selective to a certain image size. The size of the analyzed part of the visual field requires respective frequency tuning of the mechanism.     

The dependence of impulse propagation speed on firing frequency, dispersion, for the Hodgkin-Huxley model.

Propagation speed of an impulse is influenced by previous activity. A pulse following its predecessor too closely may travel more slowly than a solitary pulse. In contrast, for some range of interspike intervals, a pulse may travel faster than normal because of a possible superexcitable phase of its predecessor's wake. Thus, in general, pulse speeds and interspike intervals will not remain constant during propagation. We consider these issues for the Hodgkin-Huxley cable equations. First, the relation between speed and frequency or interspike interval, the dispersion relation, is computed for particular solutions, steadily propagating periodic wave trains. For each frequency, omega, below some maximum frequency, omega max, we find two such solutions, one fast and one slow. The latter are likely unstable as a computational example illustrates. The solitary pulse is obtained in the limit as omega tends to zero. At high frequency, speed drops significantly below the solitary pulse speed; for 6.3 degrees C, the drop at omega max is greater than 60%. For an intermediate range of frequencies, supernormal speeds are found and these are correlated with oscillatory swings in sub- and superexcitability in the return to rest of an impulse. Qualitative consequences of the dispersion relation are illustrated with several different computed pulse train responses of the full cable equations for repetitively applied current pulses. Moreover, changes in pulse speed and interspike interval during propagation are predicted quantitatively by a simple kinematic approximation which applies the dispersion relation, instantaneously, to individual pulses. One example shows how interspike time intervals can be distorted during propagation from a ratio of 2:1 at input to 6:5 at a distance of 6.5 cm.     

A nonlinear cascade model for action potential encoding in an insect sensory neuron.

Action potential encoding in the cockroach tactile spine neuron can be represented as a single-input single-output nonlinear dynamic process. We have used a new functional expansion method to characterize the nonlinear behavior of the neural encoder. This method, which yields similar kernels to the Wiener method, is more accurate than the latter and is efficient enough to obtain reasonable kernels in less than 15 min using a personal computer. The input stimulus was band-limited white Gaussian noise and the output consisted of the resulting train of action potentials, which were unitized to give binary values. The kernels and the system input-output signals were used to identify a model for encoding comprising a cascade of dynamic linear, static nonlinear, and dynamic linear components. The two dynamic linear components had repeatable and distinctive forms with the first being low-pass and the second being high-pass. The static nonlinearity was fitted with a fifth-order polynomial function over several input amplitude ranges and had the form of a half-wave rectifier. The complete model gave a good approximation to the output of the neuron when both were subjected to the same novel white noise input signal.     

The estimation of the frequency response function of a mechanoreceptor

Widespread use has been made of linear systems theory to describe the input-output relations of receptors. The frequency response function of an insect mechanoreceptor, the tactile spine of the cockroach, has been estimated by using deterministic inputs (sines and step functions), deterministic inputs added to a stochastic, auxiliary signal (band-limited white noise), and a stochastic input alone. When a stochastic input is used, spectral analysis provides methods for estimating the coherence function as well as the frequency response function. The coherence function of the tactile spine is low, suggesting that the linear frequency response function is not a good characterization of the input-output relation of the receptor. Two non-linearities, rectification and phase-locking are described. Rectification can reduce the absolute value of the frequency response measured using sine waves of all frequencies without changing its form. Phase-locking changes the form of the frequency response function at high frequencies. Use of a stochastic auxiliary signal linearizes the input-output relations of the receptor in the sense that the cycle histograms obtained with sinusoidal inputs are more sinusoidal and the form of the frequency response function agrees with that predicted from the step response over a wider range of frequencies.     

Simulations of the cardiac action potential based on the Hodgkin-Huxley kinetics with the use of Microsoft Excel spreadsheets

The purpose of this study was to develop a method to simulate the cardiac action potential using a Microsoft Excel spreadsheet. The mathematical model contained voltage-gated ionic currents that were modeled using either Beeler-Reuter (B-R) or Luo-Rudy (L-R) phase 1 kinetics. The simulation protocol involves the use of in-cell formulas directly typed into a spreadsheet. The capability of spreadsheet iteration was used in these simulations. It does not require any prior knowledge of computer programming, although the use of the macro language can speed up the calculation. The normal configuration of the cardiac ventricular action potential can be well simulated in the B-R model that is defined by four individual ionic currents, each representing the diffusion of ions through channels in the membrane. The contribution of Na+ inward current to the rate of depolarization is reproduced in this model. After removal of Na+ current from the model, a constant current stimulus elicits an oscillatory change in membrane potential. In the L-R phase 1 model where six types of ionic currents were defined, the effect of extracellular K+ concentration on changes both in the time course of repolarization and in the time-independent K+ current can be demonstrated, when the solutions are implemented in Excel. Using the simulation protocols described here, the users can readily study and graphically display the underlying properties of ionic currents to see how changes in these properties determine the behavior of the heart cell. The method employed in these simulation protocols may also be extended or modified to other biological simulation programs.     

Effects of transient receptor potential-like current on the firing pattern of action potentials in the Hodgkin-Huxley neuron during exposure to sinusoidal external voltage

Transient receptor potential vanilloid-1 (TRPV1) channels play a role in several inflammatory and nociceptive processes. Previous work showed that magnetic electrical field-induced antinociceptive [corrected] action is mediated by activation of capsaicin-sensitive sensory afferents. In this study, a modified Hodgkin-Huxley model, in which TRP-like current (ITRP) was incorporated, was implemented to predict the firing behavior of action potentials (APs), as the model neuron was exposed to sinusoidal changes in externally-applied voltage. When model neuron is exposed to low-frequency sinusoidal voltage, increased maximal conductance of ITRP can enhance repetitive bursts of APs accompanied by a shortening of inter-spike interval (ISI) in AP firing. The change in ISIs with number of interval is periodic with the phase-locking. In addition, increased maximal conductance of ITRP can abolish chaotic pattern of AP firing in model neuron during exposure to high-frequency voltage. The ISI pattern is converted from irregular to constant, as maximal conductance of ITRP is increased under such high-frequency voltage. Our simulation results suggest that modulation of TRP-like channels functionally expressed in small-diameter peripheral sensory neurons should be an important mechanism through which it can contribute to the firing pattern of APs.     

Sinusoidal voltage clamp of the Hodgkin-Huxley model.

A voltage clamp consisting of a sinusoidal voltage of amplitude V1 and frequency f, superimposed on a steady voltage level V0, is applied to the Hodgkin-Huxley model of the squid giant axon membrane. The steady-state response is a current composed of sinusoidal components of frequencies O, f, 2f, 3f,... The frequencies greater than f arise from the nonlinearity of the membrane. The total current is described by a power series in V1; each coefficient of this series is composed of current components for one or more frequencies. For different frequencies one can derive higher-order generalized admittances characterizing the nonlinear as well as the linear properties of the membrane. Formulas for the generalized admittances are derived from the Hodgkin-Huxley equations for frequencies up to 3f, using a perturbation technique. Some of the resulting theoretical curves are compared with experimental results, with good qualitative agreement.     

Dependence of the nerve pulse generation threshold on the ability of forming an input signal based on the Hodgkin-Huxley model]

Different methods of definition of the threshold of the action potential (AP) generation were considered. It was established that the threshold defined as a difference between the critical value of the membrane depolarization and the resting potential was practically independent of the value and duration of an input signal which was given as a stepped function. It was shown that the critical values of the membrane depolarization could be defined by the point of bend, as well as by the point of maximum of the curve curvature on the frontal part of AP.     

Parametric resonance and amplification in excitable membranes. The Hodgkin-Huxley model

It has previously been shown by different investigators that the excitable membrane shows a resonant sensitivity to periodic external perturbations, but its Q-factor is, as a rule, low. The present paper analyses the possible ways of increasing the membrane Q, using a model of the Hodgkin-Huxley type. It is found, in particular, that it can be increased considerably by modulating periodically the membrane capacitance or the activation and inactivation rate constants of ionic channels, with a frequency of about 2 fo (fo being the fundamental frequency of damped oscillations in the membrane), the extent of modulation not exceeding the critical value 2/Q. In this case, a significant parametric amplification of the membrane current takes place. If the modulation coefficient is above 2/Q, the membrane can display a parametric resonance that causes stable self-oscillations in the potential with a frequency approximately fo. The conditions for the realization of parametric amplification and resonance in biological membranes are discussed.     

Conditions of appearance of local response and action potential in a simple mathematical model of nerve

A simple mathematical model of a nerve fibre is proposed. According to the model the current-voltage relation for the peak Na-current is represented as a broken line. It is shown that within the potential range, where the differential (slope) Na-conductance isnegative but its absolutevalue is smaller than the membrane conductance, the fibre gives a subthreshold local response. Within the range, where differential Na-conductance is negative and has absolute value larger than the membrane conductance, the action potential arises, the rise being independent on the strength of the stimulus and conditioned only by the membrane parameters. A simple formula is obtained which describes the relation between the strength of the threshold stimulus, I, and its duration, t₀. There are two parameters in this formula, which can be measured independently: the time constant of the membrane and the lag-period in the Na-current. Insertion of these parameters into the formula allows one to construct a theoretical I-t₀ curve in good agreement with experiment.     

The response of the seated human to sinusoidal vibration and impact

Low back pain has been shown to occur more frequently among vehicle drivers than in representative control groups. Thus the response of the human to vibration and impact is of interest. This study investigated the response of the spine to both impact and sinusoidal excitation in either a relaxed or erect seated posture. The sinusoidal testing apparatus used was a resonating system consisting of two parallel wooden beams, simply supported, and the impact testing apparatus a bearing-guided, spring-suspended platform, struck from below. Ten subjects (5 males, 5 females) were evaluated using both methods. Transfer functions were compared at 2-4 Hz, 4-8 Hz and 8-16 Hz intervals using a sign test. Although in 24 comparisons of either test method (vibration or impact) or posture (erect or relaxed) where eleven showed differences significant at the p less than .05 level, only 2 out of 24 comparisons were the differences distinct enough to be significant (at the p less than .01 level). Both of these latter differences were due to test method while the subjects were sitting erect. In those instances where there were no significant differences due to test method, the impact method may be a viable replacement for the vibration test method. Where the levels of significance are higher (p less than .01 or p less than .05), further study of the magnitude of the differences is indicated and may reveal further insight into the seated individual as a system.