Analysis of mechanism of conduction of nerve impulses during the relative refractory phase by a mathematical model of the giant squid axon

1972 ◽  
Vol 3 (4) ◽  
pp. 328-333
Author(s):  
E. N. Timin ◽  
B. I. Khodorov
Keyword(s):  
Mathematical Model ◽  
Squid Axon ◽  
Nerve Impulses ◽  
Giant Squid ◽  
Refractory Phase

Cl - channels in Chara

1982 ◽  
Vol 299 (1097) ◽  
pp. 435-445 ◽  
Keyword(s):  
Mathematical Model ◽  
Action Potential ◽  
Voltage Dependence ◽  
Quantitative Description ◽  
Chara Corallina ◽  
Squid Axon ◽  
Impedance Measurements ◽  
Time Constants ◽  
Effects Of Ph ◽  
Cl Channels

The action potential in the cells of the freshwater alga Chara corallina is slower than that in the nerve by about 1000-fold. The depolarization phase is brought on by the outflow of the Cl - ions. Voltage-clamp studies show that this Cl - current can be described by the Hodgkin-Huxley equations for the Na+ transient in the squid axon. The only change necessary to the form of the Hodgkin-Huxley equations is an introduction of a time delay between the stimulus and the onset of excitation. This mathematical model of the Chara action potential facilitates a quantitative description of the effects of pH and temperature. While a pH shift alters various Hodgkin-Huxley parameters, temperature change influences mainly the activation and inactivation time constants but leaves the voltage-dependence of these parameters unaffected. The delays in excitation are both temperature and potential dependent. In future some corrections to the Hodgkin-Huxley picture of the Chara action potential may be necessary, as recent impedance measurements suggest a change in the membrane capacitance at the time of excitation.

Technical advances in neuroscience

2015 ◽  
Author(s):  
Martin R. Turner ◽  
Matthew C. Kiernan ◽  
Kevin Talbot
Keyword(s):  
Nervous System ◽  
Brain Function ◽  
Genome Project ◽  
Resonance Imaging ◽  
Squid Axon ◽  
Giant Squid ◽  
Technological Advances ◽  
Technical Advances ◽  
The Brain ◽  
Molecular Framework

This chapter highlights key technological advances in neuroimaging, the understanding of impulse transmission, and the molecular biology of the nervous system that have underpinned our modern understanding of the brain, mind, and nervous system. Neuroimaging spans the sub-cellular and systems levels of neuroscience, beginning with electron microscopy and then, 50 years later, magnetic resonance imaging and increasingly sophisticated mathematical modelling of brain function. These developments have been interleaved with the improved understanding of neurotransmission, starting with the seminal observations made from giant squid axon recordings, which were translated into clinically useable tools through the application of electric current, and later with magnetic stimulation. It is during the last 50 years that a molecular framework for these concepts emerged, with the cloning of genes that began in Duchenne muscular dystrophy, paving the way for the wider human genome project.

scholarly journals A Mathematical Model for the Cardiac Action Potential Based on Slow Inactivation of Sodium Conductance

1968 ◽  
Vol 21 (1) ◽  
pp. 37 ◽  
Author(s):  
L Munk ◽  
E PGeorge
Keyword(s):  
Mathematical Model ◽  
Action Potential ◽  
Action Potentials ◽  
Sodium Current ◽  
Potassium Conductance ◽  
Slow Inactivation ◽  
Squid Axon ◽  
Purkinje Fibres ◽  
Cardiac Action ◽  
Potassium Conductances

A mathematical model for the action potential in Purkinje fibres is developed. It is based on voltage-clamp results which show that inactivation of sodium current in these muscles is much slower than in squid axon and that the latent rise in potassium conductance is not present. Both the sodium and the potassium conductances are represented as a sum of slow and fast components. This is incorporated in the suitably adjusted Hodgkin-Huxley model for the squid axon. It is shown that such a model can account satisfactorily for the shape of the action potentials in Purkinje fibres.

Burst Activity of the Buccal Ganglion of Aplysia Depilans

1972 ◽  
Vol 56 (3) ◽  
pp. 735-754
Author(s):  
R. M. ROSE_
Keyword(s):  
Mathematical Model ◽  
Burst Activity ◽  
Buccal Ganglion ◽  
Natural Stimulus ◽  
Nerve Impulses

1. The activity of the buccal ganglion of Aplysia depilans is manifested as regular and sequential bursts of nerve impulses. 2. Regularly firing bursts are seen in the absence of feeding movements. 3. Sequences of bursts lasting for several minutes have been recorded during feeding movements induced by a natural stimulus. 4. A feed-back system has been used to produce bursts in certain other cells synchronous with the regularly firing units. 5. During sequences of bursts there is an alternation of activity between the two groups of neurones. 6. One group is made up of four cells discharging synchronously but within different ranges of frequency. 7. A mathematical model of this activity will be presented in another paper.

scholarly journals The Hodgkin Huxley Model: Analysis of Dynamic Behavior of the Action Potential in the Giant Squid Axon

2020 ◽  
Vol V9 (05) ◽  
Author(s):  
S Suresh ◽  
V Bhavani ◽  
K Gopala Krishna ◽  
Ch Bhaskar Sri Sai, D U V V Siva Kumar ◽  
Keyword(s):  
Action Potential ◽  
Dynamic Behavior ◽  
Model Analysis ◽  
Squid Axon ◽  
Giant Squid

Mathematical model of hit phenomena and its application to movie advertisement

2008 ◽  
Author(s):  
Ishii Akira ◽  
Yoshida Narihiko ◽  
Hayashi Takafumi ◽  
Umemura Sanae ◽  
Nakagawa Takeshi
Keyword(s):  
Mathematical Model
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