Computational and Mathematical Methods in Medicine

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1. E. D. Adrian and Y. Zotterman, “The impulses produced by sensory nerve endings—part 2. The response of a single end organ,” Journal of Physiology, vol. 61, pp. 151–171, 1926. View at Google Scholar
2. W. Bialek, F. Rieke, R. R. de Ruyter van Steveninck, and D. Warland, “Reading a neural code,” Science, vol. 252, no. 5014, pp. 1854–1857, 1991. View at Google Scholar · View at Scopus
3. M. N. Shadlen and W. T. Newsome, “The variable discharge of cortical neurons: implications for connectivity, computation, and information coding,” Journal of Neuroscience, vol. 18, no. 10, pp. 3870–3896, 1998. View at Google Scholar · View at Scopus
4. M. Carandini, “Amplification of trial-to-trial response variability by neurons in visual cortex,” PLoS Biology, vol. 2, no. 9, article E264, 2004. View at Publisher · View at Google Scholar · View at Scopus
5. D. MacKay and W. McCulloch, “The limiting information capacity of a neuronal link,” Bulletin of Mathematical Biophysics, vol. 14, no. 2, pp. 127–135, 1952. View at Publisher · View at Google Scholar · View at Scopus
6. B. N. Lundstrom and A. L. Fairhall, “Decoding stimulus variance from a distributional neural code of interspike intervals,” Journal of Neuroscience, vol. 26, no. 35, pp. 9030–9037, 2006. View at Publisher · View at Google Scholar · View at Scopus
7. R. Rieke, D. Warland, R. de Ruyter van Steveninck, and W. Bialek, Spikes: Exploring the Neural Code, Massachusetts Institute of Technology Press, Cambridge, Mass, USA, 1997.
8. W. Bair and C. Koch, “Temporal precision of spike trains in extrastriate cortex of the behaving macaque monkey,” Neural Computation, vol. 8, no. 6, pp. 1185–1202, 1996. View at Google Scholar · View at Scopus
9. R. C. de Charms and A. Zador, “Neural representation and the cortical code,” Annual Review of Neuroscience, vol. 23, pp. 613–647, 2000. View at Publisher · View at Google Scholar · View at Scopus
10. B. Gutkin, G. B. Ermentrout, and M. Rudolph, “Spike generating dynamics and the conditions for spike-time precision in cortical neurons,” Journal of Computational Neuroscience, vol. 15, no. 1, pp. 91–103, 2003. View at Publisher · View at Google Scholar · View at Scopus
11. J. Kretzberg, M. Egelhaaf, and A. K. Warzecha, “Membrane potential fluctuations determine the precision of spike timing and synchronous activity: a model study,” Journal of Computational Neuroscience, vol. 10, no. 1, pp. 79–97, 2001. View at Publisher · View at Google Scholar · View at Scopus
12. L. Cathala, S. Brickley, S. Cull-Candy, and M. Farrant, “Maturation of EPSCs and intrinsic membrane properties enhances precision at a cerebellar synapse,” Journal of Neuroscience, vol. 23, no. 14, pp. 6074–6085, 2003. View at Google Scholar · View at Scopus
13. M. C. van Rossum, B. J. O'Brien, and R. G. Smith, “Effects of noise on the spike timing precision of retinal ganglion cells,” Journal of Neurophysiology, vol. 89, no. 5, pp. 2406–2419, 2003. View at Publisher · View at Google Scholar · View at Scopus
14. K. Diba, C. Koch, and I. Segev, “Spike propagation in dendrites with stochastic ion channels,” Journal of Computational Neuroscience, vol. 20, no. 1, pp. 77–84, 2006. View at Publisher · View at Google Scholar · View at Scopus
15. S. E. Street and P. B. Manis, “Action potential timing precision in dorsal cochlear nucleus pyramidal cells,” Journal of Neurophysiology, vol. 97, no. 6, pp. 4162–4172, 2007. View at Publisher · View at Google Scholar · View at Scopus
16. V. J. Uzzell and E. J. Chichilnisky, “Precision of spike trains in primate retinal ganglion cells,” Journal of Neurophysiology, vol. 92, no. 2, pp. 780–789, 2004. View at Publisher · View at Google Scholar · View at Scopus
17. E. Arabzadeh, S. Panzeri, and M. E. Diamond, “Deciphering the spike train of a sensory neuron: counts and temporal patterns in the rat whisker pathway,” Journal of Neuroscience, vol. 26, no. 36, pp. 9216–9226, 2006. View at Publisher · View at Google Scholar · View at Scopus
18. R. C. Liu, S. Tzonev, S. Rebrik, and K. D. Miller, “Variability and information in a neural code of the cat lateral geniculate nucleus,” Journal of Neurophysiology, vol. 86, no. 6, pp. 2789–2806, 2001. View at Google Scholar · View at Scopus
19. R. A. DiCaprio, C. P. Billimoria, and B. C. Ludwar, “Information rate and spike-timing precision of proprioceptive afferents,” Journal of Neurophysiology, vol. 98, no. 3, pp. 1706–1717, 2007. View at Publisher · View at Google Scholar · View at Scopus
20. A. Rokem, S. Watzl, T. Gollisch, M. Stemmler, A. V. Herz, and I. Samengo, “Spike-timing precision underlies the coding efficiency of auditory receptor neurons,” Journal of Neurophysiology, vol. 95, no. 4, pp. 2541–2552, 2006. View at Publisher · View at Google Scholar · View at Scopus
21. J. A. Simmons, N. Neretti, N. Intrator, R. A. Altes, M. J. Ferragamo, and M. I. Sanderson, “Delay accuracy in bat sonar is related to the reciprocal of normalized echo bandwidth, or Q,” Proceedings of the National Academy of Sciences of the United States of America, vol. 101, no. 10, pp. 3638–3643, 2004. View at Publisher · View at Google Scholar · View at Scopus
22. M. I. Sanderson and J. A. Simmons, “Target representation of naturalistic echolocation sequences in single unit responses from the inferior colliculus of big brown bats,” Journal of the Acoustical Society of America, vol. 118, no. 5, pp. 3352–3361, 2005. View at Publisher · View at Google Scholar · View at Scopus
23. D. A. Butts, C. Weng, J. Jin et al., “Temporal precision in the neural code and the timescales of natural vision,” Nature, vol. 449, no. 7158, pp. 92–95, 2007. View at Publisher · View at Google Scholar · View at Scopus
24. A. A. Faisal, L. P. J. Selen, and D. M. Wolpert, “Noise in the nervous system,” Nature Reviews Neuroscience, vol. 9, no. 4, pp. 292–303, 2008. View at Publisher · View at Google Scholar · View at Scopus
25. M. Frerking, J. Schulte, S. P. Wiebe, and U. Stäubli, “Spike timing in CA3 pyramidal cells during behavior: implications for synaptic transmission,” Journal of Neurophysiology, vol. 94, no. 2, pp. 1528–1540, 2005. View at Publisher · View at Google Scholar · View at Scopus
26. J. M. Fellous, M. Rudolph, A. Destexhe, and T. J. Sejnowski, “Synaptic background noise controls the input/output characteristics of single cells in an in vitro model of in vivo activity,” Neuroscience, vol. 122, no. 3, pp. 811–829, 2003. View at Publisher · View at Google Scholar · View at Scopus
27. V. M. Rodriguez-Molina, A. Aertsen, and D. H. Heck, “Spike timing and reliability in cortical pyramidal neurons: effects of EPSC kinetics, input synchronization and background noise on spike timing,” PLoS ONE, vol. 2, no. 3, article no. E319, 2007. View at Publisher · View at Google Scholar · View at Scopus
28. D. Paré, E. Shink, H. Gaudreau, A. Destexhe, and E. J. Lang, “Impact of spontaneous synaptic activity on the resting properties of cat neocortical pyramidal neurons in vivo,” Journal of Neurophysiology, vol. 79, no. 3, pp. 1450–1460, 1998. View at Google Scholar · View at Scopus
29. J. M. Bekkers and C. F. Stevens, “Quantal analysis of EPSCs recorded from small numbers of synapses in hippocampal cultures,” Journal of Neurophysiology, vol. 73, no. 3, pp. 1145–1156, 1995. View at Google Scholar · View at Scopus
30. V. N. Murthy, T. J. Sejnowski, and C. F. Stevens, “Heterogeneous release properties of visualized individual hippocampal synapses,” Neuron, vol. 18, no. 4, pp. 599–612, 1997. View at Google Scholar · View at Scopus
31. J. M. Bekkers, G. Richerson, and C. F. Stevens, “Origin of variability in quantal size in cultured hippocampal neurons and hippocampal slices,” Proceedings of the National Academy of Sciences of the United States of America, vol. 87, no. 14, pp. 5359–5362, 1990. View at Publisher · View at Google Scholar · View at Scopus
32. G. Liu, S. Choi, and R. W. Tsien, “Variability of neurotransmitter concentration and nonsaturation of postsynaptic AMPA receptors at synapses in hippocampal cultures and slices,” Neuron, vol. 22, no. 2, pp. 395–409, 1999. View at Google Scholar · View at Scopus
33. L. J. Defelice, Introduction to Membrane Noise, Plenum Press, New York, NY, USA, 1981.
34. J. A. White, J. T. Rubinstein, and A. R. Kay, “Channel noise in neurons,” Trends in Neurosciences, vol. 23, no. 3, pp. 131–137, 2000. View at Publisher · View at Google Scholar · View at Scopus
35. E. Schneidman, B. Freedman, and I. Segev, “Ion channel stochasticity may be critical in determining the reliability and precision of spike timing,” Neural Computation, vol. 10, no. 7, pp. 1679–1703, 1998. View at Google Scholar · View at Scopus
36. R. C. Cannon, C. O'Donnell, and M. F. Nolan, “Stochastic ion channel gating in dendritic neurons: morphology dependence and probabilistic synaptic activation of dendritic spikes,” PLoS Computational Biology, vol. 6, no. 8, Article ID E1000886, 2010. View at Publisher · View at Google Scholar · View at Scopus
37. E. Kuriscak, S. Trojan, and Z. Wünsch, “Model of spike propagation reliability along the myelinated axon corrupted by axonal intrinsic noise sources,” Physiological Research, vol. 51, no. 3, pp. 205–215, 2002. View at Google Scholar · View at Scopus
38. A. A. Faisal and S. B. Laughlin, “Stochastic simulations on the reliability of action potential propagation in thin axons,” PLoS Computational Biology, vol. 3, no. 5, article E79, 2007. View at Publisher · View at Google Scholar · View at Scopus
39. A. Manwani and C. Koch, “Detecting and estimating signals in noisy cable structures, I: neuronal noise sources,” Neural Computation, vol. 11, no. 8, pp. 1797–1829, 1999. View at Google Scholar
40. I. Oren, E. O. Mann, O. Paulsen, and N. Hájos, “Synaptic currents in anatomically identified CA3 neurons during hippocampal gamma oscillations in vitro,” Journal of Neuroscience, vol. 26, no. 39, pp. 9923–9934, 2006. View at Publisher · View at Google Scholar
41. J. J. Lawrence, Z. M. Grinspan, J. M. Statland, and C. J. McBain, “Muscarinic receptor activation tunes mouse stratum oriens interneurones to amplify spike reliability,” Journal of Physiology, vol. 571, no. 3, pp. 555–562, 2006. View at Publisher · View at Google Scholar · View at Scopus
42. K. Vervaeke, H. Hu, L. J. Graham, and J. F. Storm, “Contrasting effects of the persistent Na⁺ current on neuronal excitability and spike timing,” Neuron, vol. 49, no. 2, pp. 257–270, 2006. View at Publisher · View at Google Scholar · View at Scopus
43. C. Koch, Biophysics of Computation: Information Processing in Single Neurons, Oxford University Press, New York, NY, USA, 1999.
44. J. M. Bower and C. Koch, “Experimentalists and modelers: can we all just get along?” Trends in Neurosciences, vol. 15, no. 11, pp. 458–461, 1992. View at Google Scholar · View at Scopus
45. J. M. Bower and D. Beeman, The Book of GENESIS: Exploring Realistic Neural Models with the General Neural Simulation System, Springer, New York, NY, USA, 1995.
46. R. D. Traub, J. G. Jefferys, R. Miles, M. A. Whittington, and K. Tóth, “A branching dendritic model of a rodent CA3 pyramidal neurone,” Journal of Physiology, vol. 481, no. 1, pp. 79–95, 1994. View at Google Scholar · View at Scopus
47. E. D. Menschik and L. H. Finkel, “Neuromodulatory control of hippocampal function: towards a model of Alzheimer's disease,” Artificial Intelligence in Medicine, vol. 13, no. 1-2, pp. 99–121, 1998. View at Publisher · View at Google Scholar · View at Scopus
48. A. Kapur, R. A. Pearce, W. W. Lytton, and L. B. Haberly, “GABA(A)-mediated IPSCs in piriform cortex have fast and slow components with different properties and locations on pyramidal cells,” Journal of Neurophysiology, vol. 78, no. 5, pp. 2531–2545, 1997. View at Google Scholar · View at Scopus
49. M. Rapp, Y. Yarom, and I. Segev, “Modeling back propagating action potential in weakly excitable dendrites of neocortical pyramidal cells,” Proceedings of the National Academy of Sciences of the United States of America, vol. 93, no. 21, pp. 11985–11990, 1996. View at Publisher · View at Google Scholar · View at Scopus
50. S. Bertrand and J. C. Lacaille, “Unitary synaptic currents between lacunosum-moleculare interneurones and pyramidal cells in rat hippocampus,” Journal of Physiology, vol. 532, no. 2, pp. 369–384, 2001. View at Publisher · View at Google Scholar · View at Scopus
51. R. E. Fisher, R. Gray, and D. Johnston, “Properties and distribution of single voltage-gated calcium channels in adult hippocampal neurons,” Journal of Neurophysiology, vol. 64, no. 1, pp. 91–104, 1990. View at Google Scholar · View at Scopus
52. J. C. Magee and D. Johnston, “Characterization of single voltage-gated Na⁺ and Ca²⁺ channels in apical dendrites of rat CA1 pyramidal neurons,” Journal of Physiology, vol. 487, no. 1, pp. 67–90, 1995. View at Google Scholar · View at Scopus
53. J. Kang, J. R. Huguenard, and D. A. Prince, “Voltage-gated potassium channels activated during action potentials in layer V neocortical pyramidal neurons,” Journal of Neurophysiology, vol. 83, no. 1, pp. 70–80, 2000. View at Google Scholar · View at Scopus
54. P. A. Lima and N. V. Marrion, “Mechanisms underlying activation of the slow AHP in rat hippocampal neurons,” Brain Research, vol. 1150, no. 1, pp. 74–82, 2007. View at Publisher · View at Google Scholar · View at Scopus
55. B. Lancaster, R. A. Nicoll, and D. J. Perkel, “Calcium activates two types of potassium channels in rat hippocampal neurons in culture,” Journal of Neuroscience, vol. 11, no. 1, pp. 23–30, 1991. View at Google Scholar · View at Scopus
56. X. Chen and D. Johnston, “Properties of single voltage-dependent K⁺ channels in dendrites of CA1 pyramidal neurones of rat hippocampus,” Journal of Physiology, vol. 559, no. 1, pp. 187–203, 2004. View at Publisher · View at Google Scholar · View at Scopus
57. D. Linaro, M. Storace, and M. Giugliano, “Accurate and fast simulation of channel noise in conductance-based model neurons by diffusion approximation,” PLoS Computational Biology, vol. 2, no. 3, article e1001102, 17 pages, 2011. View at Google Scholar
58. B. Hille, Ionic Channels of Excitable Membranes, Sinauer Associates, Sunderland, Mass, USA, 2nd edition, 1992.
59. A. D. Coop, H. Cornelis, and F. Santamaria, “Dendritic excitability modulates dendritic information processing in a Purkinje cell model,” Frontiers in Computational Neuroscience, vol. 4, pp. 1–10, 2010. View at Google Scholar
60. A. L. Hodgkin and A. F. Huxley, “A quantitative description of membrane current and its application to conduction and excitation in nerve,” Journal of Physiology, vol. 117, no. 4, pp. 500–544, 1952. View at Google Scholar · View at Scopus
61. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN: The Art of Scientific Computing, Cambridge University Press, New York, NY, USA, 1992.
62. R. J. MacGregor, Neural and Brain Modeling, Academic Press, New York, NY, USA, 1987.
63. R. Halas and M. Jukl, “On Beck's coloring of posets,” Discrete Mathematics, vol. 309, no. 13, pp. 4584–4589, 2009. View at Publisher · View at Google Scholar · View at Scopus
64. W. S. Cleveland, “Robust locally weighted regression and smoothing scatterplots,” Journal of the American Statistical Association, vol. 74, no. 368, pp. 829–836, 1995. View at Google Scholar
65. A. K. McAllister and C. F. Stevens, “Nonsaturation of AMPA and NMDA receptors at hippocampal synapses,” Proceedings of the National Academy of Sciences of the United States of America, vol. 97, no. 11, pp. 6173–6178, 2000. View at Publisher · View at Google Scholar · View at Scopus
66. S. Nurse and J. C. Lacaille, “Late maturation of GABA(B) synaptic transmission in area CA1 of the rat hippocampus,” Neuropharmacology, vol. 38, no. 11, pp. 1733–1742, 1999. View at Publisher · View at Google Scholar · View at Scopus
67. E. Hanse and B. Gustafsson, “Quantal variability at glutamatergic synapses in area CA1 of the rat neonatal hippocampus,” Journal of Physiology, vol. 531, no. 2, pp. 467–480, 2001. View at Publisher · View at Google Scholar · View at Scopus
68. Z. F. Mainen and T. J. Sejnowski, “Reliability of spike timing in neocortical neurons,” Science, vol. 268, no. 5216, pp. 1503–1506, 1995. View at Google Scholar · View at Scopus
69. G. T. Buracas, A. M. Zador, M. R. DeWeese, and T. D. Albright, “Efficient discrimination of temporal patterns by motion-sensitive neurons in primate visual cortex,” Neuron, vol. 20, no. 5, pp. 959–969, 1998. View at Publisher · View at Google Scholar · View at Scopus
70. Y. Prut, E. Vaadia, H. Bergman, I. Haalman, H. Slovin, and M. Abeles, “Spatiotemporal structure of cortical activity: properties and behavioral relevance,” Journal of Neurophysiology, vol. 79, no. 6, pp. 2857–2874, 1998. View at Google Scholar · View at Scopus
71. M. N. Shadlen and W. T. Newsome, “Noise, neural codes and cortical organization,” Current Opinion in Neurobiology, vol. 4, no. 4, pp. 569–579, 1994. View at Publisher · View at Google Scholar · View at Scopus
72. G. Buzsaki and J. J. Chrobak, “Temporal structure in spatially organized neuronal ensembles: a role for interneuronal networks,” Current Opinion in Neurobiology, vol. 5, no. 4, pp. 504–510, 1995. View at Publisher · View at Google Scholar · View at Scopus
73. B. J. Richmond, M. W. Oram, and M. C. Wiener, “Response features determining spike times,” Neural Plasticity, vol. 6, no. 4, pp. 133–145, 1999. View at Publisher · View at Google Scholar · View at Scopus
74. T. Weiss, R. W. Veh, and U. Heinemann, “Dopamine depresses cholinergic oscillatory network activity in rat hippocampus,” European Journal of Neuroscience, vol. 18, no. 9, pp. 2573–2580, 2003. View at Publisher · View at Google Scholar · View at Scopus
75. J. E. Mikkonen, J. Huttunen, and M. Penttonen, “Contribution of a single CA3 neuron to network synchrony,” NeuroImage, vol. 31, no. 3, pp. 1222–1227, 2006. View at Publisher · View at Google Scholar · View at Scopus
76. J. A. White, M. I. Banks, R. A. Pearce, and N. J. Kopell, “Networks of interneurons with fast and slow gamma-aminobutyric acid type A (GABA(A)) kinetics provide substrate for mixed gamma-theta rhythm,” Proceedings of the National Academy of Sciences of the United States of America, vol. 97, no. 14, pp. 8128–8133, 2000. View at Publisher · View at Google Scholar · View at Scopus
77. N. Axmacher and R. Miles, “Intrinsic cellular currents and the temporal precision of EPSP-action potential coupling in CA1 pyramidal cells,” Journal of Physiology, vol. 555, no. 3, pp. 713–725, 2004. View at Publisher · View at Google Scholar · View at Scopus
78. Y. Yang, M. R. DeWeese, G. H. Otazu, and A. M. Zador, “Millisecond-scale differences in neural activity in auditory cortex can drive decisions,” Nature Neuroscience, vol. 11, no. 11, pp. 1262–1263, 2008. View at Publisher · View at Google Scholar · View at Scopus
79. P. Maršálek, “Coincidence detection in the Hodgkin-Huxley equations,” BioSystems, vol. 58, no. 1–3, pp. 83–91, 2000. View at Publisher · View at Google Scholar
80. T. M. Hospedales, M. C. van Rossum, B. P. Graham, and M. B. Dutia, “Implications of noise and neural heterogeneity for vestibulo-ocular reflex fidelity,” Neural Computation, vol. 20, no. 3, pp. 756–778, 2008. View at Publisher · View at Google Scholar · View at Scopus
81. A. Saarinen, M. L. Linne, and O. Yli-Harja, “Stochastic differential equation model for cerebellar granule cell excitability,” PLoS Computational Biology, vol. 4, no. 2, Article ID E1000004, 2008. View at Publisher · View at Google Scholar · View at Scopus