scholarly journals Damped oscillations of the probability of random events followed by absolute refractory period: exact analytical results

2022 ◽  
Vol 155 ◽  
pp. 111695
Author(s):  
A.V. Paraskevov ◽  
A.S. Minkin
Keyword(s):  
Refractory Period ◽  
Absolute Refractory Period ◽  
Damped Oscillations ◽  
Analytical Results ◽  
Random Events

scholarly journals Damped oscillations of the probability of random events followed by absolute refractory period

2019 ◽  
Author(s):  
A.V. Paraskevov ◽  
A.S. Minkin
Keyword(s):  
Analytical Calculation ◽  
Analytical Description ◽  
Initial Condition ◽  
Absolute Refractory Period ◽  
Damping Coefficients ◽  
Event Probability ◽  
Damped Oscillations ◽  
Bernoulli Scheme ◽  
Random Events ◽  
Refractory State

AbstractMany events are followed by an absolute refractory state, when for some time after the event a repetition of a similar event is impossible. If uniform events, each of which is followed by the same period of absolute refractoriness, occur randomly, as in the Bernoulli scheme, then the event probability as a function of time can exhibit damped transient oscillations caused by a specific initial condition. Here we give an exact analytical description of the oscillations, with a focus on application within neuroscience. The resulting formulas stand out for their relative simplicity, enabling analytical calculation of the damping coefficients for the second and third peaks of the event probability.

Respiration-dependent Movements of the Column of Stylidium gvaminifolium

1981 ◽  
Vol 8 (1) ◽  
pp. 45 ◽  
Author(s):  
G.P Findlay ◽  
N Findlay
Keyword(s):  
Refractory Period ◽  
Angular Displacement ◽  
Metabolic Energy ◽  
Original Position ◽  
Firing Process ◽  
Mechanical Stimuli ◽  
Anaerobic Conditions ◽  
Absolute Refractory Period ◽  
Refractory Periods ◽  
Graded Responses

The column of the trigger plant, Stylidium graminifolium, when fully set responds to mechanical stimuli by flipping through an angle of about 4 radians in a fast firing movement lasting about 15-30 ms, and then slowly resetting to its original position in about 400 s. After resetting there is an absolute refractory period of about 500 s during which no further response to stimuli can be initiated, followed by a relative refractory period when graded responses increasing in rate and magnitude with time can be obtained. The resetting movement and the process, occurring during the refractory period, allowing subsequent firing to occur, are inhibited when the air surrounding the column is replaced by nitrogen. The firing movement, however, is not affected by these anaerobic conditions. Thus the firing movement is caused by passive physical forces, rapidly utilizing potential energy from a store built up during the previous resetting and refractory periods. Removal of the labellum, which the column touches when set, causes the column to oscillate with amplitude of about 3-3.5 radians and period of 1-2 ks. When the column is held at a constant angular displacement it develops an oscillatory torque with similar period. These oscillations are inhibited at all stages of the cycle by anaerobic conditions. It appears that the oscillatory behaviour is not a slowed-down firing process followed by normal resetting, but is linked throughout the cycle to the metabolic energy supply.

scholarly journals Inotropic Effects of Trains of Impulses Applied during the Contraction of Cardiac Muscle

1960 ◽  
Vol 44 (2) ◽  
pp. 415-432 ◽  
Author(s):  
A. J. Brady ◽  
B. C. Abbott ◽  
W. F. H. M. Mommaerts
Keyword(s):  
Cell Membrane ◽  
Cardiac Muscle ◽  
Direct Effect ◽  
Refractory Period ◽  
Muscle Preparation ◽  
Inotropic Effects ◽  
Absolute Refractory Period ◽  
The Absolute ◽  
Stimulation Of

The application of a train of supramaximal stimuli during the absolute refractory period of a cardiac muscle preparation has two effects: a depression of the contraction during which it is applied, and a large potentiation of subsequent contractions. The former is ascribed to a direct effect upon the cell membrane, and is an indication of the continued control of the contractile event by this membrane. The latter is explained as a sudden liberation of norepinephrine by a stimulation of embedded nerve elements, which norepinephrine then distributes itself through the tissue and finally diffuses away.

UNIT ACTIVITY IN THE PARAVENTRICULAR NUCLEUS OF FEMALE RATS AT DIFFERENT STAGES OF THE REPRODUCTIVE CYCLE AND AFTER OVARIECTOMY, WITH OR WITHOUT OESTROGEN OR PROGESTERONE TREATMENT

1973 ◽  
Vol 59 (3) ◽  
pp. 545-558 ◽  
Author(s):  
H. NEGORO ◽  
S. VISESSUWAN ◽  
R. C. HOLLAND
Keyword(s):  
Firing Rate ◽  
Paraventricular Nucleus ◽  
Reproductive Cycle ◽  
Refractory Period ◽  
Full Term ◽  
Ovariectomized Rats ◽  
Oestrogen Treatment ◽  
Absolute Refractory Period ◽  
Firing Rates ◽  
The Mean

SUMMARY Spontaneous firing rates were determined from extracellular recordings made from 878 antidromically identified units in the paraventricular nucleus (PVN) during the reproductive cycle of the female rat and in analytical experiments. In the latter, rats were ovariectomized and subsequently received either no treatment or oestrogen and/or progesterone. Among rats at metoestrus, dioestrus, mid-pregnancy and in ovariectomized progesterone-treated groups there was no significant difference in the firing rates. However, they were significantly lower than the rates recorded during pro-oestrus, oestrus, full-term pregnancy, the day of parturition, during lactation and in ovariectomized, oestrogen-treated rats. In spayed rats the mean firing rate was significantly lower than at pro-oestrus, oestrus, fullterm pregnancy, the 24 h period after parturition, during lactation and after oestrogen treatment. When progesterone was given subcutaneously to oestrogenized rats, the PVN activity, increased by oestrogen, was significantly depressed 4 h after administration. By 8 h the firing rate had completely recovered. The frequency distribution of the firing rates in pro-oestrus and oestrus showed an approximately normal distribution while those in metoestrus and dioestrus and mid-pregnancy had a Poisson distribution. At full term there were two peaks: one in the range of 3–5 spikes/s and the other less than one spike/s. The distribution was approximately normal on the day of parturition and subsequently the pattern became irregular. In ovariectomized rats and those treated with progesterone it was of a Poisson type while there was a distinct shift to higher frequencies after oestrogen treatment. The mean absolute refractory period, measured for each unit, varied and appears to be dependent on hormonal conditions. It was short in oestrus and long in dioestrus and mid-pregnancy. Oestrogen treatment significantly shortened the absolute refractory period of ovariectomized rats.

scholarly journals On The Excitation of Crustacean Muscle

1936 ◽  
Vol 13 (1) ◽  
pp. 111-130
Author(s):  
C. F. A. PANTIN
Keyword(s):  
Refractory Period ◽  
Motor Nerve ◽  
Carcinus Maenas ◽  
Motor Units ◽  
Repetitive Stimulation ◽  
Muscle Fibres ◽  
Absolute Refractory Period ◽  
Excitable System ◽  
Crustacean Muscle ◽  
The Absolute

1. The response of certain limb muscles in Carcinus maenas to stimuli of different frequencies and intensities has been analysed. The precautions necessary to obtain reproducible results in crustacean muscle are recorded. The material must be fresh; the duration of stimulation short; and each individual shock must be less than the true chronaxie, to prevent multiple excitation of the nerve. 2. A single stimulus produces a microscopic response or none at all. A succession of shocks, however, causes a contraction, the rate of which increases with the frequency, till this reaches the high values of 300-400 shocks per sec. The rate of contraction varies absolutely continuously with the frequency from 300 per sec. down to the microscopic response observed at less than 10 per sec. The rate of contraction increases very rapidly indeed between frequencies of 50 and 200 per sec, so that this range includes almost all rates of contraction. 3. The limiting frequency of 300-400 per sec. is close to the refractory period. For pairs of stimuli, the absolute refractory period is about 1σ at 18° C. This is followed by a relative refractory phase and sometimes by a supernormal phase. The excitability has returned to normal after about 4σ. In repetitive stimulation the absolute refractory period lengthens. 4. With stimuli of increasing intensity, the responses of both flexor and extensor muscles show first a threshold for excitation of the motor nerve, and, at a higher intensity, a threshold for inhibition. At very high intensities (10-20 times the true threshold) large contractions may be obtained owing to repetitive excitation. 5. With suitable precautions it can be shown that between the threshold of excitation and the threshold of inhibition there is great independence between the response and the intensity of the stimulus. The system behaves as a single excitable system and possibly in some cases a single axon supplies the entire muscle. 6. The chronaxie of the nerve to single shocks and to repetitive stimulation is of the order of 0.2-0.4σ. Single shocks of high intensity give multiple excitation, and the thresholds for this simulate a chronaxie curve. False chronaxies up to 30σ can be obtained in this way. 7. There is no evidence of a double excitable system in the muscles of the walking leg of Carcinus such as has sometimes been recorded in crustacean claws. There is no doubling of intensity-duration or refractory period curves. 8. All the effects observed are explicable in terms of neuromuscular facilitation. The response is governed entirely by the frequency and number of stimuli. Each shock in a series brings more and more muscle fibres into action. With increasing frequency of stimulation, not only are there more contraction increments in a given time, but the increment following each shock is larger. 9. At low and moderate frequencies the rate of development of tension is governed by the rate at which impulses reach the muscle. At the highest frequencies a limit is set to the rate of contraction by the physical properties of the muscle. 10. There is a close analogy between the neuromuscular mechanism disclosed here and the neuromuscular mechanism of the Coelenterata. In both there is a tendency for an entire effector to behave as a single system in which the response is governed by the number and frequency of impulses received by the muscle. This system is distinguished sharply from that of vertebrate skeletal muscle in which gradation of response is brought about through the multiplicity of motor units.

scholarly journals The Responses of Heteroxenia (Alcyonaria) to Stimulation and to some Inorganic Ions

1956 ◽  
Vol 33 (3) ◽  
pp. 604-614
Author(s):  
G. A. HORRIDGE
Keyword(s):  
Refractory Period ◽  
Inorganic Ions ◽  
The Other ◽  
Conducting System ◽  
Magnesium Ions ◽  
Absolute Refractory Period ◽  
Potassium Sodium ◽  
Sodium Calcium ◽  
Calcium And Magnesium ◽  
Calcium And Magnesium Ions

1. In Heteroxenia there are two distinct kinds of response; one is the unco-ordinated rhythm of the autozooids; the other is the maintained spasm which is co-ordinated over the colony. 2. The absolute refractory period of the conducting system which co-ordinates the spasm of the colony is found to be 0.08 sec. 3. The actions of excesses of potassium, sodium, calcium and magnesium ions suggest that the rhythm resembles that of Scyphozoa. 4. The organization and overlap of the two conducting systems in the autozooid disk recall the scyphozoan pattern of two nerve nets. However, in Heteroxenia there is little evidence of interaction between the two systems.

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