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Neurotransmitter concentrations in the presence of neural switching in one dimension
1. | Department of Mathematics, University of Utah, Salt Lake City, UT 84112, United States |
2. | Department of Mathematics, The Ohio State University, Columbus, OH 43210, United States |
3. | Department of Mathematics, Duke University, Durham, NC 27708, United States |
References:
[1] |
C. W. Atcherley, K. M. Wood, K. L. Parent, P. Hashemi and M. L. Heien, The coaction of tonic and phasic dopamine dynamics, Chem. Commun., 51 (2015), 2235-2238.
doi: 10.1039/C4CC06165A. |
[2] |
P. Blandina, J. Goldfarb, B. Craddock-Royal and J. P. Green, Release of endogenous dopamine by stimulation of 5-hydroxytryptamine3 receptors in rat striatum, J. Pharmacol. Exper. Therap., 251 (1989), 803-809. |
[3] |
N. Bonhomme, P. Duerwaerdere, M. Moal and U. Spampinato, Evidence for 5-HT4 receptor subtype involvement in the enhancement of striatal dopamine release induced by serotonin: A microdialysis study in the halothane-anesthetized rat, Neuropharmacology, 34 (1995), 269-279.
doi: 10.1016/0028-3908(94)00145-I. |
[4] |
P. C. Bressloff and S. D. Lawley, Escape from a potential well with a randomly switching boundary, J. Phys. A, 48 (2015), 225001, 25pp, URL http://dx.doi.org/10.1088/1751-8113/48/22/225001.
doi: 10.1088/1751-8113/48/22/225001. |
[5] |
P. C. Bressloff and S. D. Lawley, Escape from subcellular domains with randomly switching boundaries, Multiscale Model. Simul., 13 (2015), 1420-1445, URL http://dx.doi.org/10.1137/15M1019258.
doi: 10.1137/15M1019258. |
[6] |
D. J. Brooks, Dopamine agonists: their role in the treatment of Parkinson's disease, J. Neurol. Neurosurg Psychiatry, 68 (2000), 685-689.
doi: 10.1136/jnnp.68.6.685. |
[7] |
H. Crauel, Random point attractors versus random set attractors, J. London Math. Soc. (2), 63 (2001), 413-427, URL http://dx.doi.org/10.1017/S0024610700001915.
doi: 10.1017/S0024610700001915. |
[8] |
L. C. Daws, W. Koek and N. C. Mitchell, Revisiting serotonin reuptake inhibitors and the therapeutic effects of "uptake 2'' in psychiatric disorders, ACS Chem. Neurosci., 4 (2013), 16-21. |
[9] |
L. Daws, S. Montenez, W. Owens, G. Gould, A. Frazer, G. Toney and G. Gerhardt, Transport mechanisms governing serotonin clearance in vivo revealed by high speed chronoamperometry, J Neurosci Meth, 143 (2005), 49-62.
doi: 10.1016/j.jneumeth.2004.09.011. |
[10] |
R. Feldman, J. Meyer and L. Quenzer, Principles of Neuropharmacology, Sinauer Associates, Inc, Sunderland, MA., 1997. |
[11] |
K. Fuxe, A. B. Dahlstrom, G. Jonsson, D. Marcellino, M. Guescini, M. Dam, P. Manger and L. Agnati, The discovery of central monoamine neurons gave volume transmission to the wired brain, Prog. Neurobiol., 90 (2010), 82-100.
doi: 10.1016/j.pneurobio.2009.10.012. |
[12] |
M. Hajos, S. E. Gartside, A. E. P. Villa and T. Sharp, Evidence for a repetitive (burst) firing pattern in a sub-population of 5-hydroxytryptamine neurons in the dorsal and median raphe nuclei of the rat, Neuroscience, 69 (1995), 189-197.
doi: 10.1016/0306-4522(95)00227-A. |
[13] |
E. Kandel, J. Schwartz, T. Jessell, S. Siegelbaum and A. Hudspeth, Principles of Neural Science, 5th edition, McGraw-Hill Education / Medical, 2012. |
[14] |
S. D. Lawley, Boundary value problems for statistics of diffusion in a randomly switching environment: PDE and SDE perspectives, SIAM J. Appl. Dyn. Syst., 15 (2016), 1410-1433, URL http://dx.doi.org/10.1137/15M1038426.
doi: 10.1137/15M1038426. |
[15] |
S. D. Lawley and J. P. Keener, A new derivation of Robin boundary conditions through homogenization of a stochastically switching boundary, SIAM J. Appl. Dyn. Syst., 14 (2015), 1845-1867, URL http://dx.doi.org/10.1137/15M1015182.
doi: 10.1137/15M1015182. |
[16] |
S. D. Lawley, J. C. Mattingly and M. C. Reed, Stochastic switching in infinite dimensions with applications to random parabolic PDE, SIAM Journal on Mathematical Analysis, 47 (2015), 3035-3063, URL http://dx.doi.org/10.1137/140976716.
doi: 10.1137/140976716. |
[17] |
J. C. Mattingly, Ergodicity of $2$D Navier-Stokes equations with random forcing and large viscosity, Comm. Math. Phys., 206 (1999), 273-288, URL http://dx.doi.org/10.1007/s002200050706.
doi: 10.1007/s002200050706. |
[18] |
T. Pasik and P. Pasik, Serotonergic afferents in the monkey neostriatum, Acta Biol Acad Sci Hung, 33 (1982), 277-288. |
[19] |
M. Reed, H. F. Nijhout and J. Best, Projecting biochemistry over long distances, Math. Model. Nat. Phenom., 9 (2014), 133-138.
doi: 10.1051/mmnp/20149109. |
[20] |
B. Schmalfuß, A random fixed point theorem based on Lyapunov exponents, Random Comput. Dynam., 4 (1996), 257-268. |
[21] |
J.-J. Soghomonian, G. Doucet and L. Descarries, Serotonin innervation in adult rat neostriatum i. quantified regional distribution, Brain Research, 425 (1987), 85-100.
doi: 10.1016/0006-8993(87)90486-0. |
[22] |
L. Tao and C. Nicholson, Diffusion of albumins in rat cortical slices and relevance to volume transmission, Neuroscience, 75 (1996), 839-847.
doi: 10.1016/0306-4522(96)00303-X. |
[23] | |
[24] |
K. M. Wood, A. Zeqja, H. F. Nijhout, M. C. Reed, J. A. Best and P. Hashemi, Voltametric and mathematical evidence for dual transport mediation of serotonin clearance in vivo, J. Neurochem., 130 (2014), 351-359. |
show all references
References:
[1] |
C. W. Atcherley, K. M. Wood, K. L. Parent, P. Hashemi and M. L. Heien, The coaction of tonic and phasic dopamine dynamics, Chem. Commun., 51 (2015), 2235-2238.
doi: 10.1039/C4CC06165A. |
[2] |
P. Blandina, J. Goldfarb, B. Craddock-Royal and J. P. Green, Release of endogenous dopamine by stimulation of 5-hydroxytryptamine3 receptors in rat striatum, J. Pharmacol. Exper. Therap., 251 (1989), 803-809. |
[3] |
N. Bonhomme, P. Duerwaerdere, M. Moal and U. Spampinato, Evidence for 5-HT4 receptor subtype involvement in the enhancement of striatal dopamine release induced by serotonin: A microdialysis study in the halothane-anesthetized rat, Neuropharmacology, 34 (1995), 269-279.
doi: 10.1016/0028-3908(94)00145-I. |
[4] |
P. C. Bressloff and S. D. Lawley, Escape from a potential well with a randomly switching boundary, J. Phys. A, 48 (2015), 225001, 25pp, URL http://dx.doi.org/10.1088/1751-8113/48/22/225001.
doi: 10.1088/1751-8113/48/22/225001. |
[5] |
P. C. Bressloff and S. D. Lawley, Escape from subcellular domains with randomly switching boundaries, Multiscale Model. Simul., 13 (2015), 1420-1445, URL http://dx.doi.org/10.1137/15M1019258.
doi: 10.1137/15M1019258. |
[6] |
D. J. Brooks, Dopamine agonists: their role in the treatment of Parkinson's disease, J. Neurol. Neurosurg Psychiatry, 68 (2000), 685-689.
doi: 10.1136/jnnp.68.6.685. |
[7] |
H. Crauel, Random point attractors versus random set attractors, J. London Math. Soc. (2), 63 (2001), 413-427, URL http://dx.doi.org/10.1017/S0024610700001915.
doi: 10.1017/S0024610700001915. |
[8] |
L. C. Daws, W. Koek and N. C. Mitchell, Revisiting serotonin reuptake inhibitors and the therapeutic effects of "uptake 2'' in psychiatric disorders, ACS Chem. Neurosci., 4 (2013), 16-21. |
[9] |
L. Daws, S. Montenez, W. Owens, G. Gould, A. Frazer, G. Toney and G. Gerhardt, Transport mechanisms governing serotonin clearance in vivo revealed by high speed chronoamperometry, J Neurosci Meth, 143 (2005), 49-62.
doi: 10.1016/j.jneumeth.2004.09.011. |
[10] |
R. Feldman, J. Meyer and L. Quenzer, Principles of Neuropharmacology, Sinauer Associates, Inc, Sunderland, MA., 1997. |
[11] |
K. Fuxe, A. B. Dahlstrom, G. Jonsson, D. Marcellino, M. Guescini, M. Dam, P. Manger and L. Agnati, The discovery of central monoamine neurons gave volume transmission to the wired brain, Prog. Neurobiol., 90 (2010), 82-100.
doi: 10.1016/j.pneurobio.2009.10.012. |
[12] |
M. Hajos, S. E. Gartside, A. E. P. Villa and T. Sharp, Evidence for a repetitive (burst) firing pattern in a sub-population of 5-hydroxytryptamine neurons in the dorsal and median raphe nuclei of the rat, Neuroscience, 69 (1995), 189-197.
doi: 10.1016/0306-4522(95)00227-A. |
[13] |
E. Kandel, J. Schwartz, T. Jessell, S. Siegelbaum and A. Hudspeth, Principles of Neural Science, 5th edition, McGraw-Hill Education / Medical, 2012. |
[14] |
S. D. Lawley, Boundary value problems for statistics of diffusion in a randomly switching environment: PDE and SDE perspectives, SIAM J. Appl. Dyn. Syst., 15 (2016), 1410-1433, URL http://dx.doi.org/10.1137/15M1038426.
doi: 10.1137/15M1038426. |
[15] |
S. D. Lawley and J. P. Keener, A new derivation of Robin boundary conditions through homogenization of a stochastically switching boundary, SIAM J. Appl. Dyn. Syst., 14 (2015), 1845-1867, URL http://dx.doi.org/10.1137/15M1015182.
doi: 10.1137/15M1015182. |
[16] |
S. D. Lawley, J. C. Mattingly and M. C. Reed, Stochastic switching in infinite dimensions with applications to random parabolic PDE, SIAM Journal on Mathematical Analysis, 47 (2015), 3035-3063, URL http://dx.doi.org/10.1137/140976716.
doi: 10.1137/140976716. |
[17] |
J. C. Mattingly, Ergodicity of $2$D Navier-Stokes equations with random forcing and large viscosity, Comm. Math. Phys., 206 (1999), 273-288, URL http://dx.doi.org/10.1007/s002200050706.
doi: 10.1007/s002200050706. |
[18] |
T. Pasik and P. Pasik, Serotonergic afferents in the monkey neostriatum, Acta Biol Acad Sci Hung, 33 (1982), 277-288. |
[19] |
M. Reed, H. F. Nijhout and J. Best, Projecting biochemistry over long distances, Math. Model. Nat. Phenom., 9 (2014), 133-138.
doi: 10.1051/mmnp/20149109. |
[20] |
B. Schmalfuß, A random fixed point theorem based on Lyapunov exponents, Random Comput. Dynam., 4 (1996), 257-268. |
[21] |
J.-J. Soghomonian, G. Doucet and L. Descarries, Serotonin innervation in adult rat neostriatum i. quantified regional distribution, Brain Research, 425 (1987), 85-100.
doi: 10.1016/0006-8993(87)90486-0. |
[22] |
L. Tao and C. Nicholson, Diffusion of albumins in rat cortical slices and relevance to volume transmission, Neuroscience, 75 (1996), 839-847.
doi: 10.1016/0306-4522(96)00303-X. |
[23] | |
[24] |
K. M. Wood, A. Zeqja, H. F. Nijhout, M. C. Reed, J. A. Best and P. Hashemi, Voltametric and mathematical evidence for dual transport mediation of serotonin clearance in vivo, J. Neurochem., 130 (2014), 351-359. |
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