Neocortical Pyramidal Cells Respond as Integrate-and-Fire Neurons to In Vivo–Like Input Currents

“A calcium-activated potassium current (IKCa) and, to a lesser degree, IM and IH, underlie spike-frequency adaptation, which is a common characteristic of pyramidal neurons (293, 619, 620, 650, 668, 793, 1027) and certain subclasses of inhibitory cells (499, 500).”

“A similar model of spike adaptation has been used in a study of contrast invariance of neurons in the visual cortex (Hansel and van Vreeswijk 2002), in neocortical rhythms (Fuhrmann et al. 2002), and in the response of neurons to in vivo-like currents (Rauch et al. 2003).”

“Recent studies comparing the response of neocortical pyramidal neurons with integrate-and-fire neurons have likewise concluded that the model provides a good description of observed responses (Rauch et al. 2003; Giugliano et al. 2004).”

“Recently, it was shown that an IF model can predict the mean rate of pyramidal cells recorded in in vitro experiments (Rauch et al. 2003) over a broad range of different time-dependent inputs.”

“I curve or transfer function, is well described, in the physiological range, by an expansive nonlinearity, both in vitro (Rauch et al., 2003) and in vivo (Anderson et al., 2000; Finn et al., 2007).”

“Despite its apparent simplicity, this model is capable of reproducing quantitatively the transfer function of neocortical pyramidal cells in presence of in vivo like noisy inputs [29].”

“Similar to previous work (Bryant and Segundo, 1976; Mainen and Sejnowski, 1995) we stimulated 24 neo-cortical pyramidal neurons in vitro with a time-dependent current while recording the neuronal membrane potential under patch clamp (Rauch et al., 2003).”

“, whereas cortical pyramidal neurons behave as nearly pure integrator”

“Given that the leaky integrate-andfire (IF) model is recovered from the EIF model in the limit T3 0, this empirical result goes some way in explaining the success of leaky IF models in predicting firing rates (Rauch et al. 2003) and spike times (Jolivet et al. 2006; Paninski et al. 2004).”

“The I&F neuron model is computationally simple (Tuckwell, 1988a; Gerstner & Kistler, 2002) while known to capture essential features of input integration and spiking dynamics in real neurons (Rauch et al., 2003).”

“In a finite network, the stable states become metastable due to fluctuations of neural activity similar to those typically observed in vivo (Shadlen and Newsome, 1994; Rauch et al., 2003; La Camera et al., 2006).”

“In this model the delay activity that decreases across the ISI results from slow firing rate adaptation, as observed in intracellular recordings in vitro; if a neuron is injected with strong currents, it will respond with spike trains of decreasing frequency and eventually will stop firing (Rauch et al., 2003).”

“%) of the experimentally measured frequencies were approximately given by ( f f )/2 with (Rauch et al. 2003) f 1 T 1 2 Nsp 14 (2) This formula corresponds, roughly, to a Poisson model for spike emission, corrected at low output rates: for large output rates the errors tend to be symmetrical and…”

“In order to reach a substantial predictive capability over a broad range of firing rates, some of us and others had to include dynamics in the threshold mimicking adaptation and/or refractoriness (Rauch et al. 2003; Jolivet et al. 2006b).”

“Chance et al. (2002) used K-gluconate, Rauch et al. (2003) used K-gluconate and high EGTA, and Shu et al. (2003) used sharp electrodes containing K-acetate.”

“Pyramidal neurons in the cortex have been widely reported to exhibit spike-frequency adaptation with timescales between 300 and 500 ms (Rauch et al., 2003).”

“(2002) as a realistic candidate for long lasting non-monotonic effects in current-to-rate response functions observed in vitro (Rauch et al., 2003) and associated with spike-frequency-mechanisms.”

“There is disagreement about whether it is possible to get exactly the same spike train statistics with a time-varying current compared with those that are obtained for a conductance drive (Rauch et al., 2003; Rudolph and Destexhe, 2003; Richardson, 2004).”

“Note that regular-spiking pyramidal cells show both type 1 properties as well as spike-frequency adaptation and thus can be modeled with integrate-and-fire models with adaptation current (Jolivet et al. 2008; Rauch et al. 2003), whereas fast-spiking interneurons display type 2 f–”

“Otherpipettesolutionswerereported notto alter significantly the response properties of the cells under very similar experimental conditions (Rauch et al. 2003).”

“There is a rich history of fitting neuron models to intracellular recordings of real neurons (Vanier and Bower 1999; Rauch et al. 2003; Keren et al. 2005; Achard and De Schutter 2006; Huys et al. 2006; Jolivet et al. 2006; Kobayashi and Shinomoto 2007; Druckmann et al. 2007; Badel et al. 2008; Kobayashi et al. 2009).”

“The effective-time-constant approximation is therefore relevant to experiment and provides a simple analytic base on which other pertinent biological details may be added.”

“These results confirm the previously reported observation that large variance changes are necessary to elicit a population firing rate response (Rauch et al., 2003, their Fig.”

“We have shown in a previous report that the LIF neuron with AHP adaptation can be fitted to the experimental response functions of rat pyramidal neurons under noisy current injection (Rauch et al., 2003).”

“In line with experimental evidence [93], the input-output transfer function in the absence of gliotransmission has a typical sigmoidal shape (black dots) which reflects the following: (i) gradual emergence of firing for low (>10Hz) fluctuating synaptic inputs; (ii) the progressive, quasi-linear increase of the firing…”

“As opposed to the previous report by Rauch et al. (2003), the passive properties and the corresponding best-fit effective parameters of the IF models showed a significant cross-correlation , both for the best-fit free search and the penalty search.”

“However, the frequency versus current (f-I) curve of cortical neurons is close to linear in the presence of noise (Rauch et al., 2003).”

“Some references of estimation of input parameters from ISI data are Brillinger (1988), Inoue et al. (1995), Shinomoto et al. (1999), Rauch et al. (2003), Paninski et al. (2004), Ditlevsen and Lansky (2005, 2006, 2007, 2008) and Ditlevsen and Ditlevsen (2008).”

“For purely illustrative purposes, we use in all figures as plausible values for cortical pyramidal cells I c = 0.2 nA, ν c = 10 Hz (Rauch et al., 2003).”

“Also in this case the response is linear, but the curve saturates for high values of input currents (as observed experimentally also in real neurons [40] ), thanks to the effect of refractory period circuit.”

“Benda and Herz, 2003; Rauch et al., 2003; Izhikevich, 2004), studies on the dynamic response properties are rare.”

“For example, Rauch et al. (2003) mention that they observed a divergence in the linear part of the f–”

“See, e.g. Rauch et al. (2003) for further elements in the context of experimental frameworks and Camera et al. (2008a,b) for a review.”

“conductance dynamics (exponential synapse; α-synapse, see Rall, 1967; synapse with two-state kinetics, see Destexhe, Mainen, & Sejnowski, 1994, 1998; computational models are described in appendix A). In all models, the parameters were adjusted to yield the same total conductance applied to the membrane for individual…”

“This model does not include adaptation effects, essential for fitting neural response dynamics of real cells (Rauch et al., 2002), limiting the increase in neural emission rates during sustained stimulation.”

“Such a function has been measured for cortical cells in vitro and turned out to be well described by the theoretical transfer function of both IF models [44].”

“Estimation methods from in vitro voltage recordings for known input were presented by Stevens and Zador (1998), Rauch et al. (2003) , Le Camera et al. (2004), Jolivet et al. (2006), Paninski et al. (2004).”

“The variable w describes the level of adaptation of the neuron and a represents the relevance of subthreshold adaptation.”

“Specifically, to account for a wide range of oscillation frequencies for presynaptic spike rates, ext is described by an Ornstein-Uhlenbeck (OU) process _ ext = ext ˝ ou + r 2 ˝ ou # ˘(t); (10) where ˝ ou denotes the correlation time, and # are the mean and standard deviation of the stationary normal distribution, i.e…”

“It can be noted that a more depolarized value for such a zero-flux condition has been suggested (Lansky and Lanska 1987; Rauch et al. 2003) as an approximation to the effects of the inhibitory synaptic-reversal potential.”

“Theoretical and experimental results show that the firing rate of an integrate-and-fire neuron is a monotonic function of the mean input currents [48], [49].”

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“Rauch et al. (2003) studied f-I curves of cortical pyramidal cells in the presence of noise.”

“Further, this leakiness potentially enables the neurons to process noisy signals in a noisy environment [30].”

“We fixed the correlation time to 3 ms in order to resemble fast excitatory and inhibitory synaptic inputs, and chose a standard deviation of 100 pA, which is in a similar range to what was used in other studies (Rauch et al., 2003; Arsiero et al., 2007; Thurley et al., 2008).”

“As integrate-and-fire neurons, pyramidal cells are not only sensitive to the rising slope and peak of the EPSP but also the duration and magnitude of the EPSP envelope (Shadlen and Newsome, 1994; Sakai et al., 1999; Rauch et al., 2003).”

“This can be seen as a type of gain control (Chance et al. 2002; Fellous et al. 2003; Rauch et al. 2003; Higgs et al. 2006; Arsiero et al. 2007; Lundstrom et al. 2008), whereby the strength of background fluctuations modulates the response to the mean.”

“…the neuronal input known; references using intracellular recordings are Clopath et al. (2007), Huys et al. (2006), Jolivet et al. (2004), Jolivet et al. (2006), La Camera et al. (2004), Paninski et al. (2005), Rauch et al. (2003) and references using spike times are Paninski et al. (2004, 2005).”

“A full statistical analysis of a model of sodium inactivation in the framework of integrate-and-fire models was introduced by Giugliano, La Camera, Rauch, Luescher and Fusi (2002) as a realistic candidate for long-lasting nonmonotonic effects in current-to-rate response functions observed in vitro ( Rauch, La Camera,…”

“In another approach, model parameters are estimated using solely the ISI statistics (Tuckwell and Richter, 1978; Inoue et al., 1995; Rauch et al., 2003; Camera et al., 2004; Shinomoto et al., 1999; Ditlevsen and Lansky, 2005, 2007; Mullowney and Iyengar, 2008).”

“A theory for networks of leaky integrate-and-fire (LIF) model neurons [27] is required, because this model has been shown to well approximate the properties of mammalian pyramidal neurons [28] and novel experimental techniques allow to reliably assess the temporal structure of correlations in the cortex [29].”

“Considering the stochastic diffusion models, the literature often makes reference to cortical neurons in vivo which are characterized by irregular spike sequences and many synaptic inputs with relatively small individual contributions to the membrane depolarization [22, 25, 28, 31–34].”

“The maximal output firing rates in figure are the maximal firing rates sustainable by the neurons Camera et al. 2006), pyramidal (PYR) neurons from SSC (Rauch et al. 2003) and mPFC (Arsiero et al. 2007), and dissociated cultures of rat neocortex (Giugliano et al. 2004).”

“…of background activity caused an expansive non-linearity in the IAF input-output curve within a physiologically relevant 1 up to 20 Hz range of firing, which has been reported previously for conductance-based IAF neurons (Fourcaud-Trocmé et al., 2003) and cortical neurons (Rauch et al., 2003).”

“…to white noise currents that share properties of in vivo activity, and Gaussian white noise provides a basic model for the distribution of total current inputs at the soma under conditions of intense synaptic bombardment (Mainen and Sejnowski, 1995; Destexhe et al., 2001; Rauch et al., 2003).”

“To include adaptation into previously non-adaptive models, a common approach is to modify the effective input by rescaling the external input with a function that depends on the mean neuronal firing rate in the past [15,43,44].”

“Furthermore, Rauch et al. (2003) showed that “neocortical pyramidal cells respond as integrate-and-fire neurons to in vivo-like currents.””

“The neural elements are exponential integrate-and-fire neurons, which capture experimentally observed neural response characteristics (Rauch et al ., 2003).”

“…or collection of multiple exponents, rather than a single exponent ( Thorson and Biederman-Thorson, 1974 ; Ulanovsky et al., 2004 ; Corrado et al., 2005 ; Fusi et al., 2007 ; Kording et al., 2007 ; Wark et al., 2009 ; Lundstrom et al., 2010 ; Rauch et al., 2003 ; Pozzorini et al., 2013 ).”

“…neuron is very idealized, therefore, a simulation of I&F neuronal networks can (usually) only offer a statistical understanding of a real physiological network, rather than a detailed neuron-by-neuron account of that network (Rauch et al., 2003; Fourcaud-Trocme et al., 2003; Geisler et al., 2005).”

“properties of neurons (Salinas and Sejnowski, 2000; Rauch et al., 2003) and captures the fundamental mechanisms of a physiological cell.”

“I curves can change considerably with the input (Chance et al., 2002; Rauch et al., 2003).”

“To obtain a meaningful estimation of the firing rate response we need long and stable recordings (Rauch et al. 2003; Köndgen et al. 2008).”

“The IF description of the spike emission process captures rather well the in vitro discharge dynamics of real, biological neurons ( Rauch et al., 2003 ).”

“As mentioned previously, with in-vivo-like current injection, the I & F neuronal model can capture well both the firing rate and sub-threshold dynamics of cortical neurons [30,31].”

“In vivo-like fluctuating currents were generated with a filtered Gaussian process and injected at the soma of L5 Pyr neurons of mouse SSC (see Materials and Methods).”

“Moreover, the current-based leaky integrate-and-fire neuron can reproduce in-vivo like activity (Rauch et al., 2003; Jolivet et al., 2006) and is analytically tractable, which enables the identification of mechanisms underlying specific network effects.”

“The integrate-and-fire neuron model [1] can efficiently be simulated [2,3] and well approximates the properties of mammalian neurons [4–6] and more detailed models [7].”

“Substantial effort has been made to develop simple models of excitatory and inhibitory spiking neurons, aiming to mimic the cortical activity (Gutkin and Ermentrout, 1998; Rauch et al., 2003; Jolivet et al., 2004, 2006; Shlizerman and Holmes, 2012).”

“Previously, three other mechanisms have been proposed for how gain changes can be achieved (Burkitt, 2001; Burkitt et al., 2003; Chance et al., 2002; Destexhe et al., 2001; Doiron et al., 2001; Fellous et al., 2003; Holt and Koch, 1997; Kuhn et al., 2004 ; Larkum et al., 2004; Mitchell and Silver, 2003; Murphy and Mil…”

“The first set consists of four rat neocortical pyramidal cells to which a protocol of in vivo like stimulation signals has been applied (Rauch et al. 2003; Destexhe et al. 2001).”

“We have chosen the above model because it provides a computationally tractable abstraction of neurosynaptic dynamics [40], but our general conclusions are not restricted to these specific dynamics.”

“…as was discussed in Kistler et al. (1997) and Fourcaud-Trocme et al. (2003), with appropriately chosen parameter values, versions of the IF model provide an excellent approximation of the HH model and even some experimental data (Carandini 1996; Rauch et al. 2003; Badel et al. 2008a, b).”

“This is known to affect the firing rate distributions in recurrent model networks (82; 83; 39), and generally lower the location of steady-states stable equilibria (Figs.”