A mathematical model of the nerve impulse at the molecular level

1970 ◽  
Vol 7 (3-4) ◽  
pp. 313-328 ◽  
Author(s):  
Douglas Kenneth McIlroy
Keyword(s):  
Mathematical Model ◽  
Molecular Level ◽  
Nerve Impulse

scholarly journals The study of chaotic and regular regimes of the fractal oscillators FitzHugh-Nagumo

2018 ◽  
Vol 62 ◽  
pp. 02017 ◽  
Author(s):  
Olga Lipko ◽  
Roman Parovik
Keyword(s):  
Mathematical Model ◽  
Lyapunov Exponents ◽  
Nerve Impulse ◽  
Chaotic Attractors ◽  
Control Parameters ◽  
Schmidt Orthogonalization ◽  
Non Local ◽  
Explicit Finite Difference ◽  
Maximum Lyapunov Exponents ◽  
Orthogonalization Procedure

In this paper we study the conditions for the existence of chaotic and regular oscillatory regimes of the hereditary oscillator FitzHugh-Nagumo (FHN), a mathematical model for the propagation of a nerve impulse in a membrane. To achieve this goal, using the non-local explicit finite-difference scheme and Wolf’s algorithm with the Gram-Schmidt orthogonalization procedure and the spectra of the maximum Lyapunov exponents were also constructed depending on the values of the control parameters of the model of the FHN. The results of the calculations showed that there are spectra of maximum Lyapunov exponents both with positive values and with negative values. The results of the calculations were also confirmed with the help of oscillograms and phase trajectories, which indicates the possibility of the existence of both chaotic attractors and limit cycles.

Neuroscience

1991 ◽  
Vol 159 (6) ◽  
pp. 891-893
Author(s):  
Paul J. Harrison
Keyword(s):  
Clinical Practice ◽  
Linkage Analysis ◽  
Theoretical Basis ◽  
Molecular Level ◽  
Second Messengers ◽  
Nerve Impulse ◽  
The Past ◽  
Considerable Debate ◽  
Near Future

Neuroscience, encouraged by the advent of approaches at the molecular level, is finally beginning to play an important part in the theoretical basis of psychiatry. Although its immediate effect on clinical practice remains limited, this too is likely to change within the near future. Psychiatrists, and Membership candidates in particular, are now expected to be au fait with everything from conduction of the nerve impulse to second messengers and linkage analysis. Unfortunately, the complexity and breadth of the underlying science is expanding at an ever-increasing rate, making it difficult to keep up to date with advances. The following are offered as readable overviews of the neuroscientific areas especially relevant to psychiatry, with an emphasis on publications or editions produced within the past three years, since the rate of progress renders most texts rapidly redundant. The broader question of how all this neuroscience is going to alter psychiatry – for better or worse – has also attracted considerable debate, if few conclusions (e.g. Pardes, 1986; Detre, 1987).

Evaluation of a mathematical model analysing the relation between intradental nerve impulse activity and perceived pain in man

1986 ◽  
Vol 19 (3-4) ◽  
pp. 261-277 ◽  
Author(s):  
Uno G.H. Fors ◽  
Michael L. Ahlquist ◽  
Lennart G.A. Edwall ◽  
Glenn A.T. Haegerstam
Keyword(s):  
Mathematical Model ◽  
Impulse Activity ◽  
Nerve Impulse ◽  
Perceived Pain

scholarly journals The phyllotaxis of the aortic valve

2019 ◽  
Vol 89 (3) ◽  
Author(s):  
Marco Moscarelli ◽  
Ruggero De Paulis
Keyword(s):  
Mathematical Model ◽  
Coronary Artery ◽  
Aortic Valve ◽  
Human Body ◽  
Fractal Geometry ◽  
Heart Valves ◽  
Molecular Level ◽  
Golden Ratio ◽  
Fibonacci Sequence ◽  
Sun Exposure

Biological systems ubiquitously and inevitably exhibit stochasticity in traits from the molecular level to the multicellular and morphological level. However, there are several examples of natural events that might be described in mathematical terms. Plants grow in a structured and geometric way to maximize their sun exposure for photosynthesis while reducing the stress. The ‘Fibonacci sequence’ and its ‘golden ratio’ are considered a mathematical regularity and model that is one of the corner-stone of the ‘phyllotaxis’, the part of the botany that studies how plants branch. Nevertheless, we currently do not know if such mathematical model can be applied to humans. Different authors have hypothesized that ‘fractal’ might be identified along with the ‘golden-ratio’ in the human body (coronary artery, heart valves etc.). The aortic valve and the aortic root might represent an interesting model of human fractal geometry, where the phyllotactic rules can be reasonably applied, and where deviation from normality might results in dysfunction. However, in the absence of scientific validations, such report represents only the authors’ perceptions of a beautiful shape.

Preparatory Procedures for Electron Microscopic Analysis at the Molecular Level of Resolution

1978 ◽  
Vol 36 (3) ◽  
pp. 516-520
Author(s):  
F.J. Sjostrand
Keyword(s):  
Electron Microscope ◽  
Molecular Level ◽  
Microscopic Analysis ◽  
Resolving Power ◽  
Cellular Structures ◽  
Electron Microscopic ◽  
Systematic Analysis ◽  
Technical Developments ◽  
Thin Sectioning ◽  
Obvious Reason

In the 1940's and 1950's electron microscopy conferences were attended with everybody interested in learning about the latest technical developments for one very obvious reason. There was the electron microscope with its outstanding performance but nobody could make very much use of it because we were lacking proper techniques to prepare biological specimens. The development of the thin sectioning technique with its perfectioning in 1952 changed the situation and systematic analysis of the structure of cells could now be pursued. Since then electron microscopists have in general become satisfied with the level of resolution at which cellular structures can be analyzed when applying this technique. There has been little interest in trying to push the limit of resolution closer to that determined by the resolving power of the electron microscope.

XRF and PIXE Analysis of light and Dark Adapted Ocular Tissue

1982 ◽  
Vol 40 ◽  
pp. 190-191
Author(s):  
B. J. Panessa ◽  
H. W. Kraner ◽  
J. B. Warren ◽  
K. W. Jones
Keyword(s):  
Trace Metals ◽  
Pigment Epithelium ◽  
Nerve Impulse ◽  
Light Response ◽  
Ocular Tissue ◽  
Emission Spectrometry ◽  
Retinol Dehydrogenase ◽  
Pixe Analysis ◽  
X Ray ◽  
Optimal Function

During photoexcitation the retina requires specific electrolytes and trace metals for optimal function (Na, Mg, Cl, K, Ca, S, P, Cu and Zn). According to Hagins (1981), photoexcitation and generation of a nerve impulse involves the movement of Ca from the rhodopsin-ladened membranes of the rod outer segment (ROS) to the plasmalemma, which in turn decreases the in-flow of Na into the photoreceptor, resulting in hyperpolarization. In toad isolated retinas, the presence of Ba has been found to increase the amplitude and prolong the delay of the light response (Brown and Flaming, 1978). Trace metals such as Cu, Zn and Se are essential for the activity of the metalloenzymes of the retina and retina pigment epithelium (RPE) (i.e. carbonic anhydrase, retinol dehydrogenase, tyrosinase, glutathione peroxidase, superoxide dismutase...). Therefore the content and fluctuations of these elements in the retina and choroid are of fundamental importance for the maintenance of vision. This paper presents elemental data from light and dark adapted frog ocular tissues examined by electron beam induced x-ray microanalysis, x-ray fluorescence spectrometry (XRF) and proton induced x-ray emission spectrometry (PIXE).

RNA polymerase: Preparation and structural analysis of helical polymers

1984 ◽  
Vol 42 ◽  
pp. 152-153
Author(s):  
E. Loren Buhle ◽  
Pamela Rew ◽  
Ueli Aebi
Keyword(s):  
Structural Analysis ◽  
Rna Polymerase ◽  
Molecular Level ◽  
X Ray Diffraction ◽  
Helical Polymers ◽  
X Ray ◽  
E Coli ◽  
The Past ◽  
Ordered Arrays ◽  
Low Ionic Strength

While DNA-dependent RNA polymerase represents one of the key enzymes involved in transcription and ultimately in gene expression in procaryotic and eucaryotic cells, little progress has been made towards elucidation of its 3-D structure at the molecular level over the past few years. This is mainly because to date no 3-D crystals suitable for X-ray diffraction analysis have been obtained with this rather large (MW ~500 kd) multi-subunit (α2ββ'ζ). As an alternative, we have been trying to form ordered arrays of RNA polymerase from E. coli suitable for structural analysis in the electron microscope combined with image processing. Here we report about helical polymers induced from holoenzyme (α2ββ'ζ) at low ionic strength with 5-7 mM MnCl2 (see Fig. 1a). The presence of the ζ-subunit (MW 86 kd) is required to form these polymers, since the core enzyme (α2ββ') does fail to assemble into such structures under these conditions.

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