Intrinsic variability of latency to first-spike. (English) Zbl 1266.92024
Summary: The assessment of the variability of neuronal spike timing is fundamental to gain understanding of latency coding. Based on recent mathematical results, we investigate theoretically the impact of channel noise on latency variability. For large numbers of ion channels, we derive the asymptotic distribution of latency, together with an explicit expression for its variance. Consequences in terms of information processing are studied with Fisher information in the C. Morris and H. Lecar model [Biophys. J. 35, No. 1, 193–213 (1081)]. A competition between sensitivity to input and precision is responsible for favoring two distinct regimes of latencies.
References:
| [1] | Adair RK (2003) Noise and stochastic resonance in voltage-gated ion channels. Biosystems 100(21): 12099–12104 |
| [2] | Arhem P, Blomberg C (2007) Ion channel density and threshold dynamics of repetitive firing in a cortical neuron model. Biosystems 89(1–3): 117–125 · doi:10.1016/j.biosystems.2006.03.015 |
| [3] | Berry MJ, Warland DK, Meister M (1997) The structure and precision of retinal spike trains. Proc Natl Acad Sci USA 94: 5411–5416 · doi:10.1073/pnas.94.10.5411 |
| [4] | Chase SM, Young ED (2008) Cues for sound localization are encoded in multiple aspects of spike trains in the inferior colliculus. J Neurophysiol 99: 1672–1682 · doi:10.1152/jn.00644.2007 |
| [5] | Chen Y, Yu L, Qin SM (2008) Detection of subthreshold pulses in neurons with channel noise. Phys Rev E 78: 51909 · doi:10.1103/PhysRevE.78.051909 |
| [6] | Chow CC, White JA (1996) Spontaneous action potentials due to channel fluctuations. Biophys J 71(6): 3013–3021 · doi:10.1016/S0006-3495(96)79494-8 |
| [7] | Colbert CM, Johnston D (1996) Axonal action-potential initiation and Na+ channel densities in the soma and axon initial segment of subicular pyramidal neurons. J. Neurosci 16(21): 6676–6686 |
| [8] | Colbert CM, Pan P (2002) Ion channel properties underlying axonal action potential initiation in pyramidal neurons. Nat Neurosci 5(6): 533–538 · doi:10.1038/nn0602-857 |
| [9] | Ethier SN, Kurtz TG (1986) Markov processes, characterization and convergence. John Wiley and Sons, Inc |
| [10] | Furukawa S, Middlebrooks JC (2002) Cortical representation of auditory space: information-bearing features of spike patterns. J Neurophysiol 87: 1749–1762 |
| [11] | Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. J Phys Chem 81(25): 2340–2361 · doi:10.1021/j100540a008 |
| [12] | Gollisch T, Meister M (2008) Rapid neural coding in the retina with relative spike latencies. Science 319(1): 1108–1111 · doi:10.1126/science.1149639 |
| [13] | Guyonneau R, VanRullen R, Thorpe SJ (2005) Spike times make sense. Trends Neurosci 28(1): 1–4 · doi:10.1016/j.tins.2004.10.010 |
| [14] | Heil P (2004) First-spike latency of auditory neurons revisited. Curr Opin Neurobiol 14: 461–467 · doi:10.1016/j.conb.2004.07.002 |
| [15] | Hille B (2001) Ion channels of excitable membranes. Sinauer, Sunderland, MA |
| [16] | Hodgkin AL (1948) The local electric changes associated with repetitive action in a non-medullated axon. J Physiol 107: 165–181 |
| [17] | Izhikevich EM (2007) Dynamical systems in neuroscience: the geometry of excitability and bursting. In: Computational neuroscience. MIT Press |
| [18] | Jenison RL, Reale RA (2003) Likelihood approaches to sensory coding in auditory cortex. Netw Comput Neural Syst 14: 83–102 |
| [19] | Johansson RS, Birznieks I (2004) First spikes in ensembles of human tactile afferents code complex spatial fingertip events. Nat Neurosci 7: 170–177 · doi:10.1038/nn1177 |
| [20] | Kiani R, Esteky H, Tanaka K (2005) Differences in onset latency of macaque inferotemporal neural responses to primate and non-primate faces. J Neurophysiol 94(2): 1587–1596 · doi:10.1152/jn.00540.2004 |
| [21] | Kjaer TW, Gawne TJ, Richmond BJ (1996) Latency: another potential code for feature binding in striate cortex. J Neurophysiol 76(2): 1356–1360 |
| [22] | Krishna BS (2002) A unified mechanism for spontaneous-rate and first-spike timing in the auditory nerve. J Comput Neurosci 13: 71–91 · doi:10.1023/A:1020116122533 |
| [23] | Lansky P, Musila M (1991) Variable initial depolarization in Stein’s neuronal model with synaptic reversal potentials. Biol Cybern 64: 285–291 · doi:10.1007/BF00199591 |
| [24] | Liberman MC (1978) Auditory-nerve response from cats raised in a low-noise chamber. J Acoust Soc Am 63(2): 442–455 · doi:10.1121/1.381736 |
| [25] | Manns D, Westecker ME (1983) Antidromic activation of spikes with bimodal and trimodal latencies in the olfactory bulb of rabbits. Brain Res 288(1–2): 119–130 · doi:10.1016/0006-8993(83)90086-0 |
| [26] | Mormann F, Kornblith S, Quian Quiroga R, Kraskov A, Cerf M, Fried I, Koch C (2008) Latency and selectivity of single neurons indicate hierarchical processing in the human medial temporal lobe. J Neurosci 28(36): 8865–8872 · doi:10.1523/JNEUROSCI.1640-08.2008 |
| [27] | Morris C, Lecar H (1981) Voltage oscillations in the barnacle giant muscle fiber. Biophys J 35(1): 193–213 · doi:10.1016/S0006-3495(81)84782-0 |
| [28] | Oser M, Uzuntarla M (2008) Effects of the network structure and coupling strength on the noise-induced response delay of a neuronal network. Phys Lett A 372: 4603–4609 · Zbl 1221.92024 · doi:10.1016/j.physleta.2008.05.003 |
| [29] | Pakdaman K, Thieullen M, Wainrib G (2009) Fluid limit theorems for stochastic hybrid systems with application to neuron models. J Appl Probab (accepted) · Zbl 1232.60019 |
| [30] | Pankratova EV, Polovinkin AV, Mosekilde E (2005) Resonant activation in a stochastic Hodgkin-Huxley model: Interplay between noise and suprathreshold driving effects. Eur Phys J B 45: 391–397 · doi:10.1140/epjb/e2005-00187-2 |
| [31] | Panzeri S, Petersen RS, Schultz SR, Lebedev M, Diamond ME (2001) The role of spike timing in the coding of stimulus location in rat somatosensory cortex. Neuron 29: 769–777 · doi:10.1016/S0896-6273(01)00251-3 |
| [32] | Reulen JPH (1984) Latency of visually evoked saccadic eye movements. Biol Cybern 50(4): 251–262 · doi:10.1007/BF00337075 |
| [33] | Rinzel J, Ermentrout GB (1989) Analysis of neural excitability and oscillations. In: Methods in neuronal modeling: from synapses to networks, MIT Press, Cambridge, MA, pp 135–169 |
| [34] | Rowat P (2007) Interspike interval statistics in the stochastic Hodgkin–Huxley model: coexistence of gamma frequency bursts and highly irregular firing. Neural Comput 19(5): 1215 · Zbl 1114.92017 · doi:10.1162/neco.2007.19.5.1215 |
| [35] | Ruggero MA (1992) Physiology and coding of sound in the auditory nerve. In: Popper AN, Fay RR (eds) The mammalian auditory pathway. Springer-Verlag, New York, pp 34–93 |
| [36] | Schneidman E, Freedman B, Segev I (1998) Ion channel stochasticity may be critical in determining the reliability and precision of spike timing. Neural Comput 10(7): 1679–1703 · doi:10.1162/089976698300017089 |
| [37] | Shuai JW, Jung P (2003) Optimal ion channel clustering for intracellular calcium signaling. Proc Natl Acad Sci 100(2): 506–512 · doi:10.1073/pnas.0236032100 |
| [38] | Skaugen E, Walloe L (1979) Firing behavior in a stochastic nerve membrane model based upon the Hodgkin–Huxley equations. Acta Physiol Scand 107(4): 343–363 · doi:10.1111/j.1748-1716.1979.tb06486.x |
| [39] | Tanabe S, Pakdaman K (2001) Noise-induced transitions in excitable neuron models. Biol Cybern 85: 269–280 · Zbl 1160.92320 · doi:10.1007/s004220100256 |
| [40] | Thorpe S, Fize D, Marlot C (1996) Speed of processing in the human visual system. Nature 381(6582): 520–522 · doi:10.1038/381520a0 |
| [41] | Tuckwell HC, Wan FYM (2005) Time to first spike in stochastic hodgkinhuxley systems. Physica A 351(2–4): 427–438 · doi:10.1016/j.physa.2004.11.059 |
| [42] | van Rossum MCW (2001) The transient precision of integrate and fire neurons: effect of background activity and noise. J Comput Neurosci 10: 303–311 · doi:10.1023/A:1011268215708 |
| [43] | van Rossum MCW, O’Brien BJ, Smith RG (2003) Effects of noise on the spike timing precision of retinal ganglion cells. J Neurophysiol 89: 2406–2419 · doi:10.1152/jn.01106.2002 |
| [44] | Van Rullen R (2003) Visual saliency and spike timing in the ventral visual pathway. J Physiol Paris 97(2-3): 365–377 · doi:10.1016/j.jphysparis.2003.09.010 |
| [45] | Verveen AA, Derksen HE (1965) Fluctuations in membrane potential of axons and the problem of coding. Biol Cybern 2(4): 153–160 |
| [46] | Wollner DA, Catterall WA (1986) Localization of sodium channels in axon hillocks and initial segments of retinal ganglion cells. Proc Natl Acad Sci USA 83(21): 8424–8428 · doi:10.1073/pnas.83.21.8424 |
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