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A reliability study of square wave bursting $\beta$-cells with noise
1. | Department of Dynamics and Control, Beihang University, Beijing, 100191, China |
2. | Department of Mathematics, The University of Texas at Arlington, Arlington, TX 76019, United States, United States |
3. | Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, United States |
References:
[1] |
J. C. Jonas, P. Gilon and J. C. Henquin, Temporal and quantitative correlation between insulin secretion and stably elevated or oscillatory cytoplasmic Ca2+ in mouse pancreatic $\beta$-cells, Diabetes, 47 (1998), 1266-1273.
doi: 10.2337/diabetes.47.8.1266. |
[2] |
P. Rorsman and G. Trube, Calcium and delayed potassium currents in mouse pancreatic $\beta$-cells under voltage clamp conditions, J. Physiol., 374 (1986), 531-550. |
[3] |
P. M. Dean and E. K. Matthews, Glucose-induced electrical activity in pancreatic islet cells, J. Physiol., 210 (1970), 255-264. |
[4] |
A. M. Scott, I. Atwater and E. Rojas, A method for the simultaneous measurement of insulin release and $\beta$-cell membrane potential in single mouse islets of Langerhans, Diabetologia., 21 (1981), 470-475.
doi: 10.1007/BF00257788. |
[5] |
F. M. Ashcroft and P. Rorsman, Electrophysiology of the pancreatic $\beta$-cell, Prog. Biophys. Mol. Biol., 54 (1989), 87-143.
doi: 10.1016/0079-6107(89)90013-8. |
[6] |
S. Intep and D. J. Higham, Zero, one and two-switch models of gene regulation, Discrete and Continuous Dynamical Systems-Series B, 14 (2010), 495-513.
doi: 10.3934/dcdsb.2010.14.495. |
[7] |
G. De Vries and A. Sherman, Channel sharing in pancreatic $\beta$-cell revisited: enhancement of emergent bursting by noise, J. Theor. Biol., 207 (2000), 513-530.
doi: 10.1006/jtbi.2000.2193. |
[8] |
M. I. Freidlin, Quasi-deterministic approximation, metastability and stochastic resonance, Phys. D, 137 (2000), 333-352.
doi: 10.1016/S0167-2789(99)00191-8. |
[9] |
L. Gammaitoni, P. Hänggi, P. Jung and F. Marchesoni, Stochastic resonance, Rev. Mod. Phys., 70 (1998), 223-287.
doi: 10.1103/RevModPhys.70.223. |
[10] |
T. Wellens, V. Shatokhin and A. Buchleitner, Stochastic resonance, Rep. Prog. Phys., 67 (2004), 45-105.
doi: 10.1088/0034-4885/67/1/R02. |
[11] |
A. Bar-Even, J. Paulsson, N. Maheshri, M. Carmi, E. O'Shea, Y. Pilpel and N. Barkai, Noise in protein expression scales with natural protein abundance, Nat Genet, 38 (2006), 636-643.
doi: 10.1038/ng1807. |
[12] |
J. R. Newman, S. Ghaemmaghami, J. Ihmels, D. K. Breslow, M. Noble, J. L. Derisi and J. S. Weissman, Single-cell proteomic analysis of S. cerevisiae reveals the architecture of biological noise, Nature, 441 (2006), 840-846.
doi: 10.1038/nature04785. |
[13] |
E. M. Ozbudak, M. Thattai, I. Kurtser, A. D. Grossman and A. van Oudenaarden, Regulation of noise in the expression of a single gene, Nat Genet, 31 (2002), 69-73.
doi: 10.1038/ng869. |
[14] |
G. M. Suel, R. P. Kulkarni, J. Dworkin, J. Garcia-Ojalvo and M. B. Elowitz, Tunability and noise dependence in differentiation dynamics, Science, 315 (2007), 1716-1719.
doi: 10.1126/science.1137455. |
[15] |
M. Turcotte, J. Garcia-Ojalvo and G. M. Süel, A genetic timer through noise-induced stabilization of an unstable state, PNAS, 105 (2008), 15732-15737.
doi: 10.1073/pnas.0806349105. |
[16] |
I. Atwater, L. Rosario and E. Rojas, Properties of the Ca-activated K+ channel in pancreatic beta-cells, Cell Calcium, 4 (1983), 451-461.
doi: 10.1016/0143-4160(83)90021-0. |
[17] |
T. R. Chay and H. S. Kang, Role of single-channel stochastic noise on bursting clusters of pancreatic $\beta$-cells, Biophys. J., 54 (1988), 427-435.
doi: 10.1016/S0006-3495(88)82976-X. |
[18] |
A. Sherman, J. Rinzel and J. Keizer, Emergence of organized bursting in clusters of pancreatic $\beta$-cells by channel sharing, Biophys. J., 54 (1988), 411-425.
doi: 10.1016/S0006-3495(88)82975-8. |
[19] |
M. Pedersen and M. Sørensen, The effect of noise on $\beta$-cell burst period, SIAM J. Appl. Math., 67 (2007), 530-542.
doi: 10.1137/060655663. |
[20] |
J. Su, J. Rubin and D. Terman, Effects of noise on elliptic bursters, Nonlinearity, 17 (2004), 133-157.
doi: 10.1088/0951-7715/17/1/009. |
[21] |
Z. F. Mainen and T. J. Sejnowski, Reliability of spike timing in neocortical neurons, Science, 268 (1995), 1503-1506.
doi: 10.1126/science.7770778. |
[22] |
R. D. Kumbhani, M. J. Nolt and L. A. Palmer, Precision, reliability, and information-theoretic analysis of visual thalamocortical neurons, J. Neurophysiol, 98 (2007), 2647-2663.
doi: 10.1152/jn.00900.2006. |
[23] |
S. Schreiber, J. M. Fellous, D. Whitmer, P. Tiesinga and T. J. Sejnowski, A new correlation-based measure of spike time reliability, Neurocomputing, 52-54 (2003), 925-931.
doi: 10.1016/S0925-2312(02)00838-X. |
[24] |
X. Hu, H. Jiang, C. G, C. Li and D. L. Sparks, Reliability of oculomotor command signals carried by individual neurons, PNAS, 104 (2007), 8137-8142.
doi: 10.1073/pnas.0702799104. |
[25] |
M. Pernarowski, Fast subsystem bifurcations in a slowly varying Lienard system exhibiting bursting, SIAM J. Appl. Math., 54 (1994), 814-832.
doi: 10.1137/S003613999223449X. |
[26] |
P. Fatt and B. Katz, Spontaneous subthreshold activity at motor nerve endings, J Physiol., 117 (1952), 109-128. |
[27] |
B. Ermentrout, "Simulating, Analyzing, and Animating Dynamical Sysems: A Guide to XPPAUT for Researchers and Students," Software Environ. Tools 14, SIAM, Philadelphia, 2002. |
[28] |
G. L. Gerstein and N. Y. Kiang, An approach to the quantitative analysis of electrophysiological data from single neurons, Biophys. J., 1 (1960), 15-28.
doi: 10.1016/S0006-3495(60)86872-5. |
[29] |
N. B. Rushforth, Behavioral and electrophysiological studies of hydra. I. Analysis of contraction pulse patterns, Biol. Bull., 140 (1971), 255-273.
doi: 10.2307/1540073. |
[30] |
H. Shimazaki and S. Shinomoto, A method for selecting the bin size of a time histogram, Neural Computation, 19 (2007), 1503-1527.
doi: 10.1162/neco.2007.19.6.1503. |
[31] |
L. G. Nowak, M. V. Sanchez-vives and D. A. McCormick, Influence of low and high frequency inputs on spike timing in visual cortical neurons, Cerebral Cortex, 7 (1997), 487-501.
doi: 10.1093/cercor/7.6.487. |
[32] |
R. J. Butera, Jr., J. Rinzel and J. C. Smith, Models of respiratory rhythm generation in the pre-Bötzinger complex. II. populations of coupled pacemaker neurons, J. Neurophysiol, 82 (1999), 398-415. |
[33] |
J. E. Rubin, Bursting induced by excitatory synaptic coupling in nonidentical conditional relaxation oscillators or square-wave bursters, Phys. Rev. E, 74 (2006), 021917.
doi: 10.1103/PhysRevE.74.021917. |
[34] |
R. Rodriguez and H. C. Tuckwell, Statistical properties of stochastic nonlinear dynamical models of single spiking neurons and neural networks, Phys. Rev. E, 54 (1996), 5585-5590.
doi: 10.1103/PhysRevE.54.5585. |
[35] |
S. Tanabe and K. Pakdaman, Dynamics of moments of FitzHugh-Nagumo neuronal models and stochastic bifurcations, Phys. Rev. E, 63 (2001), 031911.
doi: 10.1103/PhysRevE.63.031911. |
[36] |
M. G. Pedersen, A comment on noise enhanced bursting in pancreatic beta-cells, J. Theoret. Biol., 235 (2005), 1-3.
doi: 10.1016/j.jtbi.2005.01.025. |
[37] |
M. Frey and E. Simiu, Noise-induced chaos and phase space flux, Phys. D, 63 (1993), 321-340.
doi: 10.1016/0167-2789(93)90114-G. |
[38] |
N. Berglund and B. Gentz, "Stochastic Dynamic Bifurcations and Excitability in: Stochastic Methods in Neuroscience," Carlo Laing and Gabriel Lord (eds.), Oxford University Press, 2009. |
show all references
References:
[1] |
J. C. Jonas, P. Gilon and J. C. Henquin, Temporal and quantitative correlation between insulin secretion and stably elevated or oscillatory cytoplasmic Ca2+ in mouse pancreatic $\beta$-cells, Diabetes, 47 (1998), 1266-1273.
doi: 10.2337/diabetes.47.8.1266. |
[2] |
P. Rorsman and G. Trube, Calcium and delayed potassium currents in mouse pancreatic $\beta$-cells under voltage clamp conditions, J. Physiol., 374 (1986), 531-550. |
[3] |
P. M. Dean and E. K. Matthews, Glucose-induced electrical activity in pancreatic islet cells, J. Physiol., 210 (1970), 255-264. |
[4] |
A. M. Scott, I. Atwater and E. Rojas, A method for the simultaneous measurement of insulin release and $\beta$-cell membrane potential in single mouse islets of Langerhans, Diabetologia., 21 (1981), 470-475.
doi: 10.1007/BF00257788. |
[5] |
F. M. Ashcroft and P. Rorsman, Electrophysiology of the pancreatic $\beta$-cell, Prog. Biophys. Mol. Biol., 54 (1989), 87-143.
doi: 10.1016/0079-6107(89)90013-8. |
[6] |
S. Intep and D. J. Higham, Zero, one and two-switch models of gene regulation, Discrete and Continuous Dynamical Systems-Series B, 14 (2010), 495-513.
doi: 10.3934/dcdsb.2010.14.495. |
[7] |
G. De Vries and A. Sherman, Channel sharing in pancreatic $\beta$-cell revisited: enhancement of emergent bursting by noise, J. Theor. Biol., 207 (2000), 513-530.
doi: 10.1006/jtbi.2000.2193. |
[8] |
M. I. Freidlin, Quasi-deterministic approximation, metastability and stochastic resonance, Phys. D, 137 (2000), 333-352.
doi: 10.1016/S0167-2789(99)00191-8. |
[9] |
L. Gammaitoni, P. Hänggi, P. Jung and F. Marchesoni, Stochastic resonance, Rev. Mod. Phys., 70 (1998), 223-287.
doi: 10.1103/RevModPhys.70.223. |
[10] |
T. Wellens, V. Shatokhin and A. Buchleitner, Stochastic resonance, Rep. Prog. Phys., 67 (2004), 45-105.
doi: 10.1088/0034-4885/67/1/R02. |
[11] |
A. Bar-Even, J. Paulsson, N. Maheshri, M. Carmi, E. O'Shea, Y. Pilpel and N. Barkai, Noise in protein expression scales with natural protein abundance, Nat Genet, 38 (2006), 636-643.
doi: 10.1038/ng1807. |
[12] |
J. R. Newman, S. Ghaemmaghami, J. Ihmels, D. K. Breslow, M. Noble, J. L. Derisi and J. S. Weissman, Single-cell proteomic analysis of S. cerevisiae reveals the architecture of biological noise, Nature, 441 (2006), 840-846.
doi: 10.1038/nature04785. |
[13] |
E. M. Ozbudak, M. Thattai, I. Kurtser, A. D. Grossman and A. van Oudenaarden, Regulation of noise in the expression of a single gene, Nat Genet, 31 (2002), 69-73.
doi: 10.1038/ng869. |
[14] |
G. M. Suel, R. P. Kulkarni, J. Dworkin, J. Garcia-Ojalvo and M. B. Elowitz, Tunability and noise dependence in differentiation dynamics, Science, 315 (2007), 1716-1719.
doi: 10.1126/science.1137455. |
[15] |
M. Turcotte, J. Garcia-Ojalvo and G. M. Süel, A genetic timer through noise-induced stabilization of an unstable state, PNAS, 105 (2008), 15732-15737.
doi: 10.1073/pnas.0806349105. |
[16] |
I. Atwater, L. Rosario and E. Rojas, Properties of the Ca-activated K+ channel in pancreatic beta-cells, Cell Calcium, 4 (1983), 451-461.
doi: 10.1016/0143-4160(83)90021-0. |
[17] |
T. R. Chay and H. S. Kang, Role of single-channel stochastic noise on bursting clusters of pancreatic $\beta$-cells, Biophys. J., 54 (1988), 427-435.
doi: 10.1016/S0006-3495(88)82976-X. |
[18] |
A. Sherman, J. Rinzel and J. Keizer, Emergence of organized bursting in clusters of pancreatic $\beta$-cells by channel sharing, Biophys. J., 54 (1988), 411-425.
doi: 10.1016/S0006-3495(88)82975-8. |
[19] |
M. Pedersen and M. Sørensen, The effect of noise on $\beta$-cell burst period, SIAM J. Appl. Math., 67 (2007), 530-542.
doi: 10.1137/060655663. |
[20] |
J. Su, J. Rubin and D. Terman, Effects of noise on elliptic bursters, Nonlinearity, 17 (2004), 133-157.
doi: 10.1088/0951-7715/17/1/009. |
[21] |
Z. F. Mainen and T. J. Sejnowski, Reliability of spike timing in neocortical neurons, Science, 268 (1995), 1503-1506.
doi: 10.1126/science.7770778. |
[22] |
R. D. Kumbhani, M. J. Nolt and L. A. Palmer, Precision, reliability, and information-theoretic analysis of visual thalamocortical neurons, J. Neurophysiol, 98 (2007), 2647-2663.
doi: 10.1152/jn.00900.2006. |
[23] |
S. Schreiber, J. M. Fellous, D. Whitmer, P. Tiesinga and T. J. Sejnowski, A new correlation-based measure of spike time reliability, Neurocomputing, 52-54 (2003), 925-931.
doi: 10.1016/S0925-2312(02)00838-X. |
[24] |
X. Hu, H. Jiang, C. G, C. Li and D. L. Sparks, Reliability of oculomotor command signals carried by individual neurons, PNAS, 104 (2007), 8137-8142.
doi: 10.1073/pnas.0702799104. |
[25] |
M. Pernarowski, Fast subsystem bifurcations in a slowly varying Lienard system exhibiting bursting, SIAM J. Appl. Math., 54 (1994), 814-832.
doi: 10.1137/S003613999223449X. |
[26] |
P. Fatt and B. Katz, Spontaneous subthreshold activity at motor nerve endings, J Physiol., 117 (1952), 109-128. |
[27] |
B. Ermentrout, "Simulating, Analyzing, and Animating Dynamical Sysems: A Guide to XPPAUT for Researchers and Students," Software Environ. Tools 14, SIAM, Philadelphia, 2002. |
[28] |
G. L. Gerstein and N. Y. Kiang, An approach to the quantitative analysis of electrophysiological data from single neurons, Biophys. J., 1 (1960), 15-28.
doi: 10.1016/S0006-3495(60)86872-5. |
[29] |
N. B. Rushforth, Behavioral and electrophysiological studies of hydra. I. Analysis of contraction pulse patterns, Biol. Bull., 140 (1971), 255-273.
doi: 10.2307/1540073. |
[30] |
H. Shimazaki and S. Shinomoto, A method for selecting the bin size of a time histogram, Neural Computation, 19 (2007), 1503-1527.
doi: 10.1162/neco.2007.19.6.1503. |
[31] |
L. G. Nowak, M. V. Sanchez-vives and D. A. McCormick, Influence of low and high frequency inputs on spike timing in visual cortical neurons, Cerebral Cortex, 7 (1997), 487-501.
doi: 10.1093/cercor/7.6.487. |
[32] |
R. J. Butera, Jr., J. Rinzel and J. C. Smith, Models of respiratory rhythm generation in the pre-Bötzinger complex. II. populations of coupled pacemaker neurons, J. Neurophysiol, 82 (1999), 398-415. |
[33] |
J. E. Rubin, Bursting induced by excitatory synaptic coupling in nonidentical conditional relaxation oscillators or square-wave bursters, Phys. Rev. E, 74 (2006), 021917.
doi: 10.1103/PhysRevE.74.021917. |
[34] |
R. Rodriguez and H. C. Tuckwell, Statistical properties of stochastic nonlinear dynamical models of single spiking neurons and neural networks, Phys. Rev. E, 54 (1996), 5585-5590.
doi: 10.1103/PhysRevE.54.5585. |
[35] |
S. Tanabe and K. Pakdaman, Dynamics of moments of FitzHugh-Nagumo neuronal models and stochastic bifurcations, Phys. Rev. E, 63 (2001), 031911.
doi: 10.1103/PhysRevE.63.031911. |
[36] |
M. G. Pedersen, A comment on noise enhanced bursting in pancreatic beta-cells, J. Theoret. Biol., 235 (2005), 1-3.
doi: 10.1016/j.jtbi.2005.01.025. |
[37] |
M. Frey and E. Simiu, Noise-induced chaos and phase space flux, Phys. D, 63 (1993), 321-340.
doi: 10.1016/0167-2789(93)90114-G. |
[38] |
N. Berglund and B. Gentz, "Stochastic Dynamic Bifurcations and Excitability in: Stochastic Methods in Neuroscience," Carlo Laing and Gabriel Lord (eds.), Oxford University Press, 2009. |
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