"क्रिया विभव": अवतरणों में अंतर

{{Main|Quantitative models of the action potential}}

 

 

गणितीय और कम्प्यूटेशनल मॉडल ऐक्शन पोटेंशिअल को समझने के लिए आवश्यक हैं, और ऐसे पूर्वानुमान प्रस्तुत करते हैं जो कि प्रयोगात्मक डेटा के खिलाफ परीक्षण किया जा सकता है, एक सिद्धांत का एक कठोर परीक्षण प्रदान करना. इन मॉडलों में सबसे सही और सबसे महत्वपूर्ण होज्किन-हक्सले मॉडल) है जो चार साधारण अंतर समीकरण (ODEs) द्वारा ऐक्शन पोटेंशिअल का वर्णन करता है.<ref name="hodgkin_1952" /> हालांकि होज्किन-हक्सले मॉडल यथार्थवादी तंत्रिका मेम्ब्रेन का एक सरलीकरण हो सकता है क्योंकि यह प्रकृति में मौजूद है, इसकी जटिलता को प्रेरित किया है भी कई और अधिक मॉडल सरलीकृत मॉडल हैं, जैसे मॉरिस-लेकार<ref name="morris_1981">{{cite journal | author = Morris C, Lecar H | year = 1981 | title = Voltage oscillations in the barnacle giant muscle fiber | journal = Biophysical Journal | volume = 35 | pages = 193–213 | doi = 10.1016/S0006-3495(81)84782-0 | pmid = 7260316 | issue = 1 | pmc = 1327511}}</ref> और फिट्ज़ह्यू-नागुमो मॉडल,<ref name="fitzhugh">{{cite journal | author = FitzHugh R | year = 1961 | title = Impulses and physiological states in theoretical models of nerve membrane | journal = Biophysical Journal | volume = 1 | pages = 445–466 | doi = 10.1016/S0006-3495(61)86902-6 | pmid = 19431309 | issue = 6 | pmc = 1366333}}<br>* {{cite journal | author = Nagumo J, Arimoto S, Yoshizawa S | year = 1962 | title = An active pulse transmission line simulating nerve axon | journal = Proceedings of the IRE | volume = 50 | pages = 2061–2070 | doi = 10.1109/JRPROC.1962.288235}}</ref> जिनमें से दोनों में केवल दो युग्मित ODEs हैं. होज्किन-हक्सले और नागुमो मॉडल और उनके सम्बन्धियों, जैसे बोन्होफर-वैन डेर पोल मॉडल<ref name="bonhoeffer_vanderPol">{{cite journal | author = Bonhoeffer KF | year = 1948 | title = Activation of Passive Iron as a Model for the Excitation of Nerve | journal = J. Gen. Physiol. | volume = 32 | pages = 69–91 | doi = 10.1085/jgp.32.1.69 | pmid = 18885679 | issue = 1 | pmc = 2213747}}<br>* {{cite journal | author = Bonhoeffer KF | year = 1953 | title = Modelle der Nervenerregung | journal = Naturwissenschaften | volume = 40 | pages = 301–311 | doi = 10.1007/BF00632438}}<br>* {{cite journal | author = [[Balthasar van der Pol|van der Pol B]] | year = 1926 | title = On relaxation-oscillations | journal = Philosophical Magazine | volume = 2 | pages = 977–992}}<br>* {{cite journal | author = [[Balthasar van der Pol|van der Pol B]], van der Mark J | year = 1928 | title = The heartbeat considered as a relaxation oscillation, and an electrical model of the heart | journal = Philosophical Magazine | volume = 6 | pages = 763–775}}<br>* {{cite journal | author = [[Balthasar van der Pol|van der Pol B]], van der Mark J | year = 1929 | title = The heartbeat considered as a relaxation oscillation, and an electrical model of the heart | journal = Arch. Neerl. Physiol. | volume = 14 | pages = 418–443}}</ref> के गुणों का गणित के भीतर अच्छा अध्ययन किया गया है,<ref name="math_studies">{{cite book | author = Sato S, Fukai H, Nomura T, Doi S | year = 2005 | chapter = Bifurcation Analysis of the Hodgkin-Huxley Equations | title = Modeling in the Neurosciences: From Biological Systems to Neuromimetic Robotics | edition = 2nd | editor = Reeke GN, Poznanski RR, Lindsay KA, Rosenberg JR, Sporns O| publisher = CRC Press | location = Boca Raton | isbn = 978-0415328685 | pages = 459–478}}<br>* {{cite journal | author = Evans JW | year = 1972 | title = Nerve axon equations. I. Linear approximations | journal = Indiana U. Math. Journal | volume = 21 | pages = 877–885 | doi = 10.1512/iumj.1972.21.21071}}<br>* {{cite journal | author = Evans JW, Feroe J | year = 1977 | title = Local stability theory of the nerve impulse | journal = Math. Biosci. | volume = 37 | pages = 23–50 | doi = 10.1016/0025-5564(77)90076-1}}<br>* {{cite book | author = FitzHugh R | year = 1969 | chapter = Mathematical models of axcitation and propagation in nerve | title = Biological Engineering | editor = HP Schwann | publisher = McGraw-Hill | location = New York | pages = 1–85}}<br>* {{cite book | author = [[John Guckenheimer|Guckenheimer J]], [[Philip Holmes|Holmes P]] | year = 1986 | title = Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields | edition = 2nd printing, revised and corrected | publisher = Springer Verlag | location = New York | isbn = 0-387-90819-6| pages = 12–16}}</ref> अभिकलन <ref name="computational_studies">{{cite book | author = Nelson ME, Rinzel J| year= 1994|chapter= The Hodgkin-Huxley Model|title=The Book of GENESIS: Exploring Realistic Neural Models with the GEneral NEural SImulation System| editor= Bower J, Beeman D | publisher = Springer Verlag | location = New York|pages= 29–49 | chapterurl=http://www.genesis-sim.org/GENESIS/iBoG/iBoGpdf/chapt4.pdf}}<br>{{cite book | author = Rinzel J, Ermentrout GB | year = 1989 | chapter = Analysis of Neural Excitability and Oscillations | title = Methods in Neuronal Modeling: From Synapses to Networks | editor = [[Christof Koch|C. Koch]], I Segev | publisher = Bradford Book, The MIT Press | location = Cambridge, MA | isbn = 0-262-11133-0 | pages = 135–169}}</ref> और इलेक्ट्रॉनिक्स में भी.<ref name="keener_1983">{{cite journal | author = Keener JP | year = 1983 | title = Analogue circuitry for the van der Pol and FitzHugh-Nagumo equations | journal = IEEE Trans. on Systems, Man and Cybernetics | volume = 13 | pages = 1010–1014}}</ref> अधिक आधुनिक अनुसंधानों ने बड़े और एकीकृत प्रणालियों पर अधिक ध्यान केंद्रित किया है और जिसके तहत उन्होंने तंत्रिका प्रणाली के अन्य भागों के साथ ऐक्शन पोटेंशिअल को जोड़ा है (जैसे डेन्ड्राइट और सिनेप्सेस), और इस तरह शोध से अभिकलन तंत्रिका का अध्ययन कर सकते हैं<ref>{{cite book | author = [[Warren Sturgis McCulloch|McCulloch WS]] | year = 1988 | title = Embodiments of Mind | publisher = The MIT Press | location = Cambridge MA | isbn = 0-262-63114-8 | pages = 19–39, 46–66, 72–141}}<br>* {{cite book | title = Neurocomputing:Foundations of Research | editors = JA Anderson, E Rosenfeld | publisher = The MIT Press | location = Cambridge, MA | isbn = 0-262-01097-6 | pages = 15–41 | author = edited by James A. Anderson and Edward Rosenfeld. | year = 1988}}</ref> और सरल रिफ्लेक्स का भी, जैसे इस्केप रिफ्लेक्सेस जो सेन्ट्रल पैटर्न जनरेटर द्वारा नियंत्रित होता है.<ref name="cpg">{{cite book | author = Getting PA | year = 1989 | chapter = Reconstruction of Small Neural Networks | title = Methods in Neuronal Modeling: From Synapses to Networks | editor = [[Christof Koch|C Koch]] and I Segev | publisher = Bradford Book, The MIT Press | location = Cambridge, MA | isbn = 0-262-11133-0 | pages = 171–194}}</ref><ref name="pmid10713861">{{cite journal | author = Hooper SL | title = Central pattern generators | journal = Curr. Biol. | volume = 10 | issue = 5 | pages = R176 | year = 2000 | month = March | pmid = 10713861 | doi = 10.1016/S0960-9822(00)00367-5 | url = http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.133.3378&rep=rep1&type=pdf | issn = }}</ref>