[1]
|
D. M. Quinn, A. S. Balasubremanian, B. P. Doctor and P. Taylor, “Enzymes of the Cholinestrase Family,” Plenum Press, London, 1995.
|
[2]
|
S. Tucek, “Acetylcholine Synthesis in Neurons,” Chapman and Hall, London, 1978.
|
[3]
|
C. A. Guyton, “Medical Physiology,” 7th Edition, W. B. Saunders Company, Philadelphia, 1986.
|
[4]
|
T. E. Barman, “Enzyme Handbook,” Vol. 1, Springer-Verlage, New York, 1969.
|
[5]
|
R. R. Llinás, “The Squid Giant Synapse: A Model for Chemical Transmission,” Oxford University Press, London, 1999.
|
[6]
|
http://www.biology.ucsd.edu/classes/bibc102.WI99/neuro/Neurotransmitter. html
|
[7]
|
H. Soreq and H. Zakut, “Human Cholinsterases and Anticholinesterases,” Academic Press, San Diego, 1993.
|
[8]
|
A. L. Koch, “The pH in the Neighborhood of Membranes Generating a Protomotive Force,” Journal of Theoretical Biology, Vol. 120, No. 1, 1986, pp. 73-84.
|
[9]
|
R. Friboulet, A. David and D. Thomas, “Excitability Memory and Oscillation in Artificial Acetylcholinesterase Membranes,” Journal of Membrane Science, Vol. 8, No. 33, 1981, pp. 33-39. doi:10.1016/S0376-7388(00)82137-7
|
[10]
|
J. L. Hindmarsh and R. M. Rose, “A Model of Neuronal Bursting Using Three Coupled First Order Differential Equations,” Proceedings of the Royal Society, Vol. 221, No. 1222, 1984, pp. 87-102. doi:10.1098/rspb.1984.0024
|
[11]
|
J. L. Hindmarsh and R. M. Rose, “A Model of the Nerve Impulse Using Two First-Order Differential Equations,” Nature, Vol. 296, No. 5853, 1982, pp. 162-164.
doi:10.1038/296162a0
|
[12]
|
R. Fitzhugh, “Impulses and Physiological States in Theoretical Models of Nerve Membranes,” Biophysical Journal, Vol. 1, No. 6, 1985, pp. 445-466.
doi:10.1016/S0006-3495(61)86902-6
|
[13]
|
A. V. Holden and Y. S. Fan, “Crisis-Induced Chaos in the Rose-Hindmarsh Model for Neuronal Activity,” Chaos, Solitons and Fractals, Vol. 2, No. 6, 1992, pp. 583-595.
doi:10.1016/0960-0779(92)90055-R
|
[14]
|
A. V. Holden and Y. S. Fan, “From Simple to Complex Oscillatory Behaviour via Intermittent Chaos in the Rose-Hindmarsh Model for Neuronal Activity,” Chaos, Solitons and Fractals, Vol. 2, No. 4, 1992, pp. 349-369.
doi:10.1016/0960-0779(92)90012-C
|
[15]
|
A. V. Holden and Y. S. Fan, “From Simple to Simple Bursting Oscillatory Behaviour via Chaos in the Rose-Hindmarsh Model for Neuronal Activity,” Chaos, Solitons and Fractals, Vol. 2, No. 3, 1992, pp. 221-236.
doi:10.1016/0960-0779(92)90032-I
|
[16]
|
Y. S. Fan and A. V. Holden, “Bifurcation, Bursting, Chaos and Crisis in the Rose-Hindmarsh Model for Neuronal Activity,” Chaos, Solitons and Fractals, Vol. 3, No. 4, 1993, pp. 439-449.
doi:10.1016/0960-0779(93)90029-Z
|
[17]
|
G. Ibrahim, O. Saleh, I. H. Mustafa, A. H. El Ahwany and S. S. E. H. El Nashaie, “Modeling Peiodic and Aperiodic Behavior of Acetylcholine Hydrolysis,” International Review of Chemical Engineering, Vol. 2, No. 6, 2010, pp. 19-33.
|
[18]
|
G. Ibrahim and S. S. E. H. Elnashaie, “Hyperchaos in Acetylcholinesterase Enzyme Systems,” Chaos, Solitons and Fractals, Vol. 8, No. 12, 1997, pp. 1997-2007.
|
[19]
|
I. H. Mustafa, G. Ibrahim, A. Elkamel, S. S. E. H. Elnashaie and P. Chen, “Non-Linear Feedback Modeling and Bifurcation of the Acetylcholine Neurocycle and Its Relation to Alzheimer’s and Parkinson’s Diseases,” Chemical Engineering Science, Vol. 64, No. 1, 2009, pp. 69-90. doi:10.1016/j.ces.2008.09.009
|
[20]
|
I. H. Mustafa, A. Elkamel, G. Ibrahim, P. Chen and S. S. E. H. Elnashaie, “Effect of Choline and Acetate Substrates on Bifurcation and Chaotic Behavior of Acetylcholine Neurocycle and Alzheimer’s and Parkinson’s Diseases,” Chemical Engineering Science, Vol. 64, No. 9, 2009, pp. 2096-2112. doi:10.1016/j.ces.2009.01.027
|
[21]
|
I. H. Mustafa, A. Elkamel, P. Chen, G. Ibrahim and S. S. E. H. Elnashaie, “Effect of Cholineacetyltransferase Activity and Choline Recycle Ratio on Diffusion-Reaction Modelling, Bifurcation and Chaotic Behavior of Acetylcholine Neurocycle and Their Relation to Alzheimer’s and Parkinson’s Diseases,” Chemical Engineering Science, Vol. 68, No. 1, 2012, pp. 19-35.
doi:10.1016/j.ces.2011.08.012
|
[22]
|
P. Garhyan, A. M. Botero and S. S. E. H. Elnashaie, “Complex Bifurcation/Chaotic Behavior of Acetylcholinesterase and Cholineacetyltransferase Enzymes System,” Applied Mathematical Modelling, Vol. 30, 2006, pp. 824-853.
|
[23]
|
L. B. Hersh and M. Peet, “Re-Evaluation of the Kinetic Mechanism of the Choline Acetyltransferase Reaction,” The Journal of Biological Chemistry, Vol. 252, No. 14, 1977, pp. 4796-4802.
|
[24]
|
E. J. Doedel, A. R. Champneys, T. F. Fairgrieve, Y. A. Kuznetsov, B. Sandstede and X. J. Wang, “AUTO97: Continuation and Bifurcation Software for Ordinary Differential Equations,” Department of Computer Science, Concordia University, Montreal, 1997.
|
[25]
|
S. S. E. H. Elnashaie, G. Ibrahim and F. A. Teymour, “Chaotic Behavior of an Acetylcholinesterase Enzyme System,” Chaos, Solitons and Fractals, Vol. 5, No. 6, 1995, pp. 933-954. doi:10.1016/0960-0779(94)00205-5
|
[26]
|
S. Karel and H. Milan, “Biotechnological Aspects of Membrane Function,” Critical Reviews in Biotechnology, Vol. 17, No. 2, 1997, pp. 69-86.
doi:10.3109/07388559709146607
|
[27]
|
M. Obara, M. Szeliga and J. Albrecht, “Regulation of pH in the Mammalian Central Nervous System under Normal and Pathological Conditions: Facts and Hypotheses,” Neurochemistry International, Vol. 52, No. 6, 2008, pp. 905-919. doi:10.1016/j.neuint.2007.10.015
|
[28]
|
J. Antosdiewicz, J. A. McCammon and M. K. Gilson, “Prediction of pH-Dependent Properties of Proteins,” Journal of Molecular Biology, Vol. 238, No. 3, 1994, pp. 415-436.
doi:10.1006/jmbi.1994.1301
|
[29]
|
D. M. Michaelson and I. Angel, “Determination of Delta pH in Cholinergic Synaptic Vesicles: Its Effect on Storage and Release of Acetylcholine,” Life Sciences, Vol. 27, No. 1, 1980, pp. 39-44.
doi:10.1016/0024-3205(80)90017-X
|
[30]
|
H. H. Fuldner and H. Stadler, “31P-NMR Analysis of Synaptic Vesicles, Status of ATP and Internal pH,” European Journal of Biochemistry, Vol. 121, No. 3, 1982, pp. 519-524. doi:10.1111/j.1432-1033.1982.tb05817.x
|
[31]
|
R. Ahdu-Hacohen, D. Duridanova, H. Meiri and R. Rahamimoff, “Hydrogen Ions Control Synaptic Vesicle Ion Channel Activity in Torpedo Electromotor Neurons,” Journal of Physiology, Vol. 556, No. 2, 2004, pp. 347-352.
|
[32]
|
S. M. Parsons, “Transport Mechanisms in Acetylcholine and Monoamine Storage,” The FASEB Journal, Vol. 14, No. 15, 2000, pp. 2423-2434. doi:10.1096/fj.00-0203rev
|
[33]
|
S. Heven, X. H. Li and G. P. Michael, “Energization of Plant Cell Membranes by H+-Pumping ATPases: Regulation and Biosynthesis,” The Plant Cell, Vol. 11, No. 4, 1999, pp. 677-689.
|
[34]
|
A. L. Koch, “The pH in the Neighborhood of Membranes Generating a Protomotive Force,” Journal of Theoretical Biology, Vol. 120, No. 1, 1986, pp. 73-84.
doi:10.1016/S0022-5193(86)80018-2
|
[35]
|
C. Rae, R. Scott, C. H. Thompson, I. Dumughn, G. Kemp, P. Styles, I. M. Tracey and G. K. Radda, “Is Brain pH a Biochemical Marker of IQ?” Proceedings of the Royal Society, Vol. 263, No. 1373, 1996, pp. 1061-1064.
doi:10.1098/rspb.1996.0156
|
[36]
|
A. Zauner and J. P. Muizelaar, “Brain Metabolism and Cerebral Blood Flow,” In: P. Reilly and R. Bullock, Eds., Head Injury: Pathophysiology and Management of Severe Closed Injury, Chapman and Hall, London, 1997.
|
[37]
|
I. Wessler, E. Roth, S. Schwarze, W. Weikel, F. Bittinger, C. J. Kirkpatrick and H. Kilbindger, “Release of Non-Neural Acetylcholine from the Human Placenta: Difference to Neural Acetylcholine,” Naunyn-Schmiedeberg’s Archives of Pharmacology, Vol. 364, No. 3, 2001, pp. 205-212. doi:10.1007/s002100100445
|
[38]
|
S. Kysela and J. Torok, “Histamine H1-Receptor Antagonists do not Prevent the Appearance of Endothelium-Dependant Relaxation to Acetylcholine in Rat Pulmonary Artery,” Physiological Research, Vol. 45, No. 4, 1996, pp. 345-350.
|
[39]
|
R. R. Chay and J. Rinzel, “Bursting, Beating and Chaos in an Excitable Membrane Model,” Biophysical Journal, Vol. 47, No. 3, 1985, pp. 357-366.
doi:10.1016/S0006-3495(85)83926-6
|
[40]
|
W. F. Boron and E. L. Boulpaep, “Medical Physiology,” W.B. Saunders, Philadelphia, 2002.
|
[41]
|
P. Constable, “A Simplified Strong Ion Model for Acid-Base Equilibria: Application to Horse Plasma,” Journal of Applied Physiology, Vol. 83, No. 1, 1997, pp. 297-311.
|
[42]
|
K. A. Gossett, D. D. French, B. Cleghorn and G. E. Church, “Effect of Acute Acidemia on Blood Biochemical Variables in Healthy Ponies,” American Journal of Veterinary Research, Vol. 51, No. 9, 1990, pp. 1375-1379.
|
[43]
|
L. P. Sil’nikov, “A Contribution to the Problem of the Structure of an Extended Neighbourhood of a Structurally Stable Equilibrium of Saddle-Focus Type,” Mathematics of the USSR-Sbornik, Vol. 10, No. 1, 1970, pp. 91-102.
doi:10.1070/SM1970v010n01ABEH001588
|
[44]
|
O. E. Rossler, J. L. Hudsun and R. Rossler, “Homoclinic Hyperchaos—An Explicit Example,” Physica D: Nonlinear Phenomena, Vol. 62, No. 1-4, 1993, pp. 80-86.
|
[45]
|
C. Javier, I. A. García and J. Sorolla, “Resolution of the Poincaré Problem and Nonexistence of Algebraic Limit Cycles in Family (I) of Chinese Classification,” Chaos, Solitons & Fractals, Vol. 24, No. 2, 2005, pp. 491-499.
doi:10.1016/j.chaos.2004.06.076
|
[46]
|
S. Wiggins, “Introduction to Applied Nonlinear Dynamical Systems and Chaos,” Springer-Velag, New York, 1990.
|
[47]
|
J. Guckenheimer and P. Hohns, “Nonlinear Oscillations, Dynamical Systems and Bifurcntion of Vector Fields,” Springer, New York, 1983.
|
[48]
|
M. Franaszek, “Long-Lived Periodic Transients,” Acta Physica Polonica B, Vol. 22, No. 9, 1991.
|
[49]
|
P. Fatt and B. Katz, “Spontaneous Sub Threshold Activity at Motor Nerve Endings,” The Journal of Physiology, Vol. 117, No. 1, 1952, pp. 109-128.
|
[50]
|
M. R. Bennett, “The Origin of Gaussian Distributions of Synaptic Potentials,” Progress in Neurobiology, Vol. 46, No. 4, 1995, pp. 331-350.
doi:10.1016/0301-0082(94)00061-L
|
[51]
|
Y. Dunant and M. Israel, “Neurotransmitter Release at Rapid Synapses,” Biochimie, Vol. 82, No. 4, 2000, pp. 289-302. doi:10.1016/S0300-9084(00)00194-2
|
[52]
|
M. C. Rosales-Hernandez, J. E. Mendieta-Wejebe, J. Correa-Basurto, J. I. Vazques-Alcantara, E. Terres-Rojas and J. Trujillo-Ferrara, “Catalytic Activity of Acetylcholinesterase Immobilized on Mesoporous Molecular Sieves,” International Journal of Biological Macromolecules, Vol. 40, No. 5, 2007, pp. 444-448.
doi:10.1016/j.ijbiomac.2006.11.004
|
[53]
|
F. H. White, D. A. Thompson and K. Cohari, “Ultra Structural Morphometry of Gap Junctions during Differentiation of Stratified Squamous Epithelium,” Journal of Cell Science, Vol. 69, 1984, pp. 67-85.
|
[54]
|
W. Van Der Kloot, J. Molgo, R. Cameron and C. Colasante, “Vesicle Size and Transmitter Release at the Frog Neuromuscular Junction When Quantal Acetylcholine Content Is Increased or Decreased,” Journal of Physiology, Vol. 541, 2002, pp. 385-393.
doi:10.1113/jphysiol.2001.014407
|
[55]
|
L. P. Sartchenko and D. A. Rusakov, “The Optimal Height of Synaptic Cleft,” Proceedings of the National Academy of Sciences of the USA, Vol. 104, No. 6, 2007, pp. 1823-1828. doi:10.1073/pnas.0606636104
|
[56]
|
A. L. Hodgkin, “The Local Electric Changes Associated with Repetitive Action in a Non-Medulated Axon,” Journal of Physiology, Vol. 107, 1948, pp. 165-181.
|
[57]
|
J. D. Murray, “Mathematical Biology,” Springer, New York, 1990.
|
[58]
|
D. R. Clother and J. Brindley, “Excitability of an Age-Structured Plankton Ecosystem,” Journal of Mathematical Biology, Vol. 39, No. 5, 1999, pp. 377-420.
doi:10.1007/s002850050172
|
[59]
|
A. Zhabotinsky and A. Zaikin, “Concentration Wave Propagation in Two-Dimensional Liquid-Phase Self-Oscillating System,” Nature, Vol. 225, 1970, pp. 535-537.
|
[60]
|
E. M. Izhikevich, “Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting,” MIT Press, Cambridge, 2007.
|