Reconstruction of the input signal of the leaky integrate-and-fire neuronal model from its interspike intervals
Tóm tắt
Extracting the input signal of a neuron by analyzing its spike output is an important step toward understanding how external information is coded into discrete events of action potentials and how this information is exchanged between different neurons in the nervous system. Most of the existing methods analyze this decoding problem in a stochastic framework and use probabilistic metrics such as maximum-likelihood method to determine the parameters of the input signal assuming a leaky and integrate-and-fire (LIF) model. In this article, the input signal of the LIF model is considered as a combination of orthogonal basis functions. The coefficients of the basis functions are found by minimizing the norm of the observed spikes and those generated by the estimated signal. This approach gives rise to the deterministic reconstruction of the input signal and results in a simple matrix identity through which the coefficients of the basis functions and therefore the neuronal stimulus can be identified. The inherent noise of the neuron is considered as an additional factor in the membrane potential and is treated as the disturbance in the reconstruction algorithm. The performance of the proposed scheme is evaluated by numerical simulations, and it is shown that input signals with different characteristics can be well recovered by this algorithm.
Tài liệu tham khảo
Agarwal R, Sarma SV (2012) Performance limitations of relay neurons. Comput Biol 8:1–19
Bayly EJ (1968) Spectral analysis of pulse frequency modulation in the nervous systems. IEEE Trans Biomed Eng BME–15:257–265
Benedetto E, Sacerdote L (2013) On dependency properties of the ISIs generated by a two-compartment neuronal model. Biol Cybern 107(1):95–106
Bibbona E, Lansky P, Sacerdote L, Sirovich R (2008) Errors in estimation of the input signal for integrate and fire neuronal models. Phys Rev E 78(01):0119181–01191810
Bibbona E, Lansky P, Sirovich R (2010) Estimating input parameters from intracellular recordings in the Feller neuronal model. Phys Rev E 81(3):0319161–03191613
Breen BJ, Gerken WC, Butera RJ (2003) Hybrid integrate-and-fire model of a bursting neuron. Neural Comput 15:2843–2862
Bressloff PC (1995) Dynamics of a compartmental model integrate-and-fire neuron with somatic potential reset. Phys D Nonlinear Phenom 80(4):399–412
Brette R, Gerstner W (2005) Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. J Neurophysiol 94:3637–3642
Bruckstein AM, Morf M, Zeevi YY (1988) Demodulation methods for an adaptive neural encoder model. Biol Cybern 34:63–79
Brunel N, Nadal JP (1998) Mutual information, fisher information and population coding. Neural Comput 10(7):1731
Buonocore A, Caputo L, Pirozzi E, Ricciardi LM (2010) On a stochastic leaky integrate-and-fire neuronal model. Neural Comput 22:2558–2585
Burkitt AN (2006) A review of the integrate-and-fire neuron model: I. Homogenous synaptic input. Bioll Cybern 95:1–19
Cecchi GA, Sigman M, Alonso JM, Martínez L, Chialvo DR, Magnasco MO (2000) Noise in neurons is message dependent. PNAS 97(10):5557–5561
Ditlevsen S (2007) Parameters of stochastic diffusion processes estimated from observations of first-hitting times: application to the leaky integrate-and-fire neuronal model. Phys Rev E 76:041906
Dong Y, Mihalas S, Russell A, Etienne-Cummings R, Niebur E (2011) Estimating parameters of generalized integrate-and-fire neurons from the maximum likelihood of spike trains. Neural Comput 23:2833–2867
French AS, Holden AV (1971) Alias-free sampling of neuronal spike trains. Kybernetic 8:165–175
Gerstner W, Kistler WM (2002) Spiking neuron models. Cambridge University Press, Cambridge
Gerwinn S, Macke JH, Bethge M (2009) Bayesian population decoding of spiking neurons. Front Comput Neurosci 3:21. doi:10.3389/neuro.10.021
Gerwinn S, Macke JH, Bethge M (2011) Reconstructing stimuli from the spike times of leaky integrate and fire neurons. Front Neurosci 5:1–9
Gestri G (1971) Pulse frequency modulation in neural systems. Biophys J 11:98–109
Giraudo MT, Greenwood PE, Sacerdote L (2011) How sample paths of leaky integrate and fire models are influences by the presence of a firing threshold. Neural Comput 23(7):1743–1767
Inoue J, Sato S, Ricciardi L (1995) On the parameter estimation for diffusion models of single neuron’s activities. Biol Cybern 73:209–221
Iolov A, Ditlevsen S, Longtin A (2014) Fokker–Planck and Fortet equation-based parameter estimation for a leaky integrate-and-fire model with sinusoidal and stochastic forcing. J Math Neurosci 4(4):1–30. doi:10.1186/2190-8567-4-4
Izhikevich EM (2003) Simple model of spiking neurons. IEEE Trans Neural Netw 14:1569–1572
Jolivet R, Lewis TJ, Gerstner W (2004) Generalized integrate-and-fire models of neuronal activity approximate spike trains of a detailed model to a high degree of accuracy. J Neurophysiol 92:959–976
Jolivet R, Rauch A, Luscher HR, Gerstner W (2006) Predicting spike timing of neocortical pyramidal neurons by simple threshold models. J Comput Neurosci 21:35–49
Kim H, Shinomoto S (2012) Estimating nonstationary input signals from a single neuronal spike train. Phys Rev E 86:051903
Lansky P, Sanda P, He J (2006) The parameters of the stochastic leaky integrate-and-fire neuronal model. J Comput Neurosci 21:211– 223
Lansky P, Sacerdote L, Zucca C (2007) Optimum signal in a diffusion leaky integrate-and-fire neuronal model. Math Biosci 207:261–274
Lansky P, Sanda P, He J (2010) Effect of stimulation on the input parameters of stochastic leaky integrate-and-fire neuronal model. J Physiol 104:160–166
Lazar AA (2004) Time encoding with an integrate-and-fire neuron with a refractory period. Neurocomputing 58:53–58
Lazar AA, Pnevmatikakis EA (2008) Faithful representation of stimuli with a population of integrate-and-fire neurons. Neural Comput 20:2715–2744
Luenberger DG (1997) Optimization by vector space methods. Wiley, Hoboken
Mihalas S, Niebur E (2009) A generalized linear integrate-and-fire neural model produces diverse spiking behaviors. Neural Comput 21:704–718
Mullowney P, Iyengar S (2008) Parameter estimation for a leaky integrate-and-fire neuronal model from ISI data. J Comput Neurosci 24:179–194
Naud R, Gerstner W (2012) The performance (and limits) of simple neuron models: generalizations of the leaky integrate-and-fire model. In: Le Novere N (ed) Computational systems neurobiology. Springer, NewYork
Paninski L, Pillow JW, Simoncelli EP (2004) Maximum likelihood estimation of a stochastic integrate-and-fire neural encoding model. Neural Comput 16:2533–2561
Picchini U, Ditlevsen S, De Gaetano A, Lansky P (2008) Parameters of the diffusion leaky integrate-and-fire neuronal model for a slowly fluctuating signal. Neural Comput 20:2696–2714
Pillow JW, Ahmadian Y, Paninski L (2001) Model-based decoding, information estimation, and change-point detection techniques for multineuron spike trains. Neural Comput 23:1–45
Rudolph M, Destexhe A (2001) Correlation detection and resonance in neural systems with distributed noise sources. Phys Rev Lett 86:3662–3665
Rudolph M, Destexhe A (2006) Analytical integrate-and-fire neuron models with conductance-based dynamics for event-driven simulation strategies. Neural Comput 18:2146–2210
Sacerdote L, Giraudo NT (2013) Stochastic integrate and fire models: a review on mathematical methods and their applications. In: Bachar M (ed) Stochastic biomathematical models. Springer, NewYork
Sanderson AC (1980) Input–output analysis of an IPFM neural model: effects of spike regularity and record length, IEEE Trans. Biomed Eng BME–27:120–131
Seydnejad SR, Kitney RI (2001) Time-varying threshold integral pulse frequency modulation. IEEE Trans Biomed Eng 48:949–962
Seydnejad S (2008) Fixed threshold modeling of an adjustable threshold integrate-and-fire neuronal model. In: Proceedings of the 30th IEEE EMBS Conference, pp 2481–2484
Shimokawa T, Pakdaman K, Sato S (1999) Mean discharge frequency locking in the response of a noisy neuron model to subthreshold periodic stimulation. Phys Rev E 60:R33
Shlizerman E, Holmes P (2012) Neural dynamics, bifurcations, and firing rates in a quadratic integrate-and-fire model with a recovery variable. I: deterministic behavior. Neural Comput 24:2078–2118
Smith GD, Cox CL, Sherman SM, Rinzel J (2000) Fourier analysis of sinusoidally driven thalamocortical relay neurons and a minimal integrate-and-fire-or-burst model. J Neurophysiol 83:588–610
Stacey WC, Durand DM (2001) Synaptic noise improves detection of subthreshold signals in hippocampal CA1 neurons. J Neurophysiol 86:1104–1112