INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Spike-frequency adaptation (SFA) is the decrease in instantaneous discharge rate during a sustained current injection and is a specialized feature of many types of neurons. SFA has been observed in neurons of various systems from several species, including non mammalian ones such as the crayfish stretch receptor (Michaelis and Chaplain 1975). In mammals, SFA has been observed in rodent motoneurons (Granit et al. 1963; Sawczuk et al. 1995), hippocampal CA1 pyramidal cells (Lancester and Nicoll 1987; Madison and Nicoll 1984), and pyramidal cells of the piriform cortex (Barkai and Hasselmo 1994). In the neocortex of rodents, SFA has been identified in most pyramidal neurons, in particular those that have been traditionally classified as regular spiking cells, but in some bursting neurons as well (Connors and Gutnick 1990; Mason and Larkman 1990; McCormick et al. 1985). SFA has also been identified in neurons of other mammalian systems, including the rabbit CA1 and CA3 pyramidal neurons (Moyer et al. 1996; Thompson et al. 1996), cat motoneurons (Granit et al. 1963; Kernell and Monster 1982) and layer V neurons of the sensorimotor cortex recorded in vitro (Schwindt et al. 1988; Stafstrom et al. 1984), neurons of cat visual cortex in vivo (Ahmed et al. 1998), and even regular spiking cells of the human neocortex (Avoli and Olivier 1989; Foehring et al. 1991; Lorenzon and Foehring 1992).

The biophysical mechanisms underlying SFA are not yet established. SFA has most commonly been linked to the phenomena of afterhyperpolarization (AHP), found to follow current-induced repetitive firing (Madison and Nicoll 1984; Schwindt et al. 1988). AHP is an action-potential-dependent hyperpolarized potential that markedly summates with successive spikes. Because the build-up of AHP with successive spikes is relatively slow, its effects on discharge frequency are greater at later inter-spike intervals (Madison and Nicoll 1984). The ionic mechanisms underlying AHPs and their functions have been studied in neurons from several species, such as the cat (Schwindt et al. 1988; Stafstrom et al. 1984), guinea pig (Connors et al. 1982; McCormick et al. 1985), and rat (Madison and Nicoll 1984), and have been suggested to be largely produced by Ca²⁺-activated slow K⁺ currents (Connors et al. 1982; Hotson and Prince 1980; Madison and Nicoll 1984; Schwindt et al. 1988). In slices of human cortical tissue, AHP was observed, and the currents underlying the medium and slow AHPs were shown to influence the interspike interval during repetitive firing and to produce SFA (Avoli et al. 1994; Lorenzon and Foehring 1992). Other ionic currents that have been suggested to contribute to the development of SFA include the M-current (I_M), which is a slow-activating noninactivating voltage-sensitive potassium current (Madison and Nicoll 1984; McCormick et al. 1993), and the slow Na inactivation (Michaelis and Chaplain 1975; Schwindt and Crill 1982).

The functional significance of SFA is not clear either. Some possible roles of SFA have been suggested. These include the phenomena of forward masking and selective attention (Liu and Wang 2001; Wang 1998). In forward masking, when two or more inputs are presented sequentially in time, the neuronal response to the first input inhibits responses to subsequent inputs by activating I_AHP with a delay. In selective attention, in the presence of two or more inputs, the adaptation process can selectively suppress the neuronal responses to weaker inputs so that the response to the strongest input "pops-out" in time.

In this work, we studied the significance of SFA in modulating the input-output properties of a neocortical neuron embedded in a noisy environment. In particular, the response properties of an adapting neuron to oscillatory inputs suggest a role for SFA in the synchronization of neuronal assemblies. Previous results suggested a role for adaptation in stabilizing synchroneous behavior (Crook et al. 1998; van Vreeswijk and Hansel 2001). Here we show that by knowing the characteristics of SFA in individual neurons of the population, it is possible to predict the frequency of oscillations for which synchronization could occur, i.e., the frequency of possible spontaneously emerging population rhythms.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Experimental

Slice preparation and recording procedures as in Markram et al. (1997). Briefly, Wistar rats (13-15 days) were rapidly decapitated, and neocortical slices (sagittal; 300 mm thick) were sectioned (DSK, Microslicer, Japan). Neurons in the somatosensory cortex were identified using IR-DIC video-microscopy (Zeiss Axioplan, fitted with [mult]40-W/0.75 NA objective; Zeiss, Oberkochen, Germany), and patch-clamp recordings were obtained. Recorded neurons were selected up to 120 µm below the surface of the slice and separated from each other by up to 150 µm. Experiments were performed at 32-34°C with extracellular solution that contained (in mM) 125 NaCl, 2.5 KCl, 25 glucose, 25 NaHCO₃, 1.25 NaH2PO₄, 1.5 mM CaCl₂, and 1.5 mM MgCl₂. Somatic whole cell recordings (10-20 M access resistance) were obtained, and signals were amplified using Axoclamp-2B amplifiers (Axon Instruments), captured on the computer using pulse control (by Dr. R. Bookman and colleagues, Miami University), and analyzed in programs written in Igor (Igor Wavemetrics, Lake Oswego, OR). Pipettes solution contained (in mM) 100 K-gluconate, 20 KCl, 4 ATP-Mg, 10 phosphocreatine, 0.3 GTP, 10 HEPES, and 0.5% biocytin (pH 7.3, 310 mOsm).

Modeling

Two models are used in this study. The first is an integrate-and-fire model of a spiking adapting neuron, used for detailed simulations. The second is a mean firing-rate model of an adapting neuron.

INTEGRATE-AND-FIRE MODEL OF AN ADAPTING NEURON. To simulate the spiking behavior of a pyramidal neuron exhibiting SFA, we consider a model of an adapting neuron, based on the classical leaky integrate-and-fire model of a neuron (Tuckwell 1988). The model for an adapting neuron takes into account an additional hyperpolarizing potassium current, referred to as the adaptation current (Treves 1993).

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MEAN FIRING RATE MODEL OF AN ADAPTING NEURON. To enable analytical calculations, a simplified model was constructed to simulate the mean instantaneous firing rate of an adapting neuron under noisy conditions, averaged over many repetitions of the same input. The model is based on two differential equations for the mean firing rate of the neuron and for the mean adaptation current, and a third analytical equation that translates mean voltages into mean firing rates.

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SIMULATIONS OF NETWORKS COMPOSED OF ADAPTING NEURONS. We consider small networks of only a few neurons, with manually designed architecture of connections as well as large scale randomly connected networks. The activity of the networks, composed of adapting neurons, is simulated using the detailed integrate-and-fire model formulated in Eqs. 1 and 5. All neurons can be driven by an externally injected current (Iext) as well as by synaptic current (Isyn), which is induced by the activity of the presynaptic neurons. For each simulated neuron, once a spike occurs, a synaptic current is activated in all of its postsynaptic targets. Synaptic currents (EPSCs) are simulated by the difference of two exponentials, multiplied by the synaptic strength, J

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where ₁ and ₂ are the rise and decay time constants of EPSCs and V_syn is the synaptic reversal potential in use.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Response properties: comparison between experiments and models

To compare the performance of the model neuron with that of real neurons, similar current injections were applied to both model neurons and also to several layer II-IV pyramidal neurons, whose voltage responses were recorded in slice preparations of rat somatosensory cortex. Under in vivo conditions, however, a neocortical neuron is exposed to the background activity of its presynaptic neurons and thus experiences noisy input currents (Softky and Koch 1993). This study, therefore focuses on the the response of an adapting neuron to various noisy current injections.

RESPONSE TO NOISELESS STEP CURRENTS. The response of the neurons to noiseless step currents was used primarily to compare the response of the model neuron to that of real neocortical neurons and to extract realistic model parameters for subsequent analysis. In Fig. 1A, we show the typical response of an adapting neuron to a constant current injection. It can be seen that the interval between subsequent spikes in the train is increasing.

View larger version (25K): [in this window] [in a new window]   Fig. 1. The response of adapting neurons to noiseless step current injections. A: the voltage response of a model neuron to a non noisy current. Parameters: M = 58 ms, Rin = 0.2 G, k = 10(G)1, N = 230 ms, and  = 0.02. Amplitude of injected current: 210 pA. B: inter-spike interval (ISI) curves for a layer IV pyramidal cell and for the model neuron, whose parameters were chosen to fit the ISI curve of the real neuron.

RESPONSE TO NOISY STEP CURRENTS. Under in vivo conditions, where spontaneous activity of presynaptic neurons causes strong background fluctuations in the membrane potential, non noisy step currents represent unrealistic inputs to a neocortical neuron. We therefore explored the behavior of the adapting neuron in response to a fluctuating input.

View larger version (49K): [in this window] [in a new window]   Fig. 2. The response of adapting neurons to noisy step current injections. The injected current had a mean of 130 pA and I = 43.5 pA. A: voltage response of a model adapting neuron. Parameters as in Fig. 1 with M = 4 ms. B: response of a model adapting neuron. Poststimulus time histogram (PSTH) is computed for 500 different realizations of the noisy current injection. In each trial, the noise realization was different. Parameters: M = 6 ms, Rin = 0.2 G, k = 12(G)1, N = 214 ms, and  = 0.014. Amplitude of the current injected is 130 pA, and the chosen bin size is 4 ms. , the response of the mean firing rate model of an adapting neuron for the same model parameters, with e = 6 ms. C: PSTH obtained from experimental traces recorded in vitro from a layer IV pyramidal neuron for the same injection protocol. PSTH computed for 107 different realizations of the noisy current. Bin size as in B.

RESPONSE TO NOISY OSCILLATORY CURRENTS. The response of the model neuron to oscillatory currents of the form I(t) = I₀ + I₁ sin(2ft), with white noise, was examined. An example of an adapting neuron's response to such an injected current is illustrated in Fig. 3A (the initial transient is not shown). Note that the oscillatory response has the same frequency as that of the injected current. However, in the presented example, the phase of the response is advanced relative to that of the current by almost 40°.

View larger version (36K): [in this window] [in a new window]   Fig. 3. The response of model adapting neurons to oscillatory current injections. A: PSTH of a model adapting neuron computed in response to injected current with an oscillatory mean (top) and added white noise. Frequency of oscillations: 4 Hz. White line indicates the solution of the corresponding mean firing rate model, with e = 10 ms. Model parameters: M = 40 ms, Rin = 0.2 G, k = 25(G)1, N = 80 ms, and  = 0.05. The oscillatory current had a mean of 1,000 pA, and 50-pA amplitude oscillations, I = 53 pA. B: the phase shift of the firing rate relative to the phase of the current injected, plotted as a function of the frequency of oscillations. Phase shift was determined according to the phase of the vector sum of the phases of all the spikes emitted over all the trials. Arrow indicates the preferred frequency of the neuron, for which the phase shift of the firing rate, relative to the phase of the input current, is 0.

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View larger version (20K): [in this window] [in a new window]   Fig. 4. The effect of changing the degree of adaptation on the preferred frequency of a model neuron. A: the phase shift of the firing rate relative to the phase of the current injected, for different degrees of adaptation, simulated by varying k (all the other parameters as in Fig. 3). Results obtained from simulations of the detailed integrate-and-fire model of an adapting neuron, with k = 0.15, 5, 10, 15, 20, and 25 µS. B: the dependence of the preferred frequency upon k. Data points are extracted from the curves in A.

View larger version (30K): [in this window] [in a new window]   Fig. 5. The response of neocortical adapting neurons to oscillatory current injections. A: the PSTH of a neocortical adapting pyramidal neuron to an oscillatory current injection of 10 Hz (left) and 20 Hz (right). PSTH constructed from the response of the neuron to 200 cycles of the input current. The neuron is denoted Cell 2 in B. Bin size used for the histogram is 2 ms. Solid line is overlaid to indicate the time course of the average input current. B: the phase shift of the firing rate relative to the phase of the current injected, obtained from 3 middle layer pyramidal neurons. Mean value of oscillatory current was 300 pA, and the amplitude of oscillations was 60 pA. Average firing rates of the neurons were 11.8, 15.7, and 19 Hz.

View larger version (24K): [in this window] [in a new window]   Fig. 6. Dependence of the phase-frequency curves on DC level (I0) and amplitude of oscillations (I1). A: the effect of changing the DC level (200-600 pA) of the oscillatory current on the phase-frequency curves. Amplitude of oscillations is kept constant (75 pA). B: the effect of changing the amplitude of oscillations (70,100,130,160, and190 pA) of the injected current on the phase-frequency curves. I0 is kept constant (600 pA). Results obtained from simulations of the detailed integrate-and-fire model of an adapting neuron. Model parameters of the neuron are as in Fig. 3. In both A and B I was set to 32 pA.

Emergence of population rhythms in networks of adapting neurons

To study the implications of the preferred frequency on synchronization in neural networks, small networks of model neurons, driven by an external oscillatory input, were considered. Synchronous oscillations of discharge rate are achieved if all neurons exhibit the same phase shift of discharge, relative to the external input current, for a given modulation frequency.

In Fig. 7, results are presented for a network of four identical neurons, in which one neuron receives an oscillatory external input and the others receive a constant current injection (DC shift) to keep them firing at the same mean discharge rate. Because the neurons are identical, they all have the same phase-frequency curve relative to their own input current (Fig. 7A). We therefore expected the neurons to synchronize at their preferred frequency. However, synchronization was achieved at a lower frequency than the "preferred frequency" of the neurons (Fig. 7). The neurons synchronize at a frequency in which they all produce a phase shift that exactly opposes the phase shift caused by the synaptic delay at that frequency. We denote this frequency as the corrected preferred frequency and suggest the following method to determine its value. For a given frequency of input current, the phase shift of each neuronal element relative to its own input and the phase of the synaptic delay is determined. The "corrected" phase shift (Fig. 7B) is obtained by adding the phase of the synaptic delay to the phase shift of the response. The frequency for which the `corrected' phase shift is zero is the frequency of current injection for which the neurons will exhibit synchronization. This can be seen in Fig. 7C, where at the corrected preferred frequency, the phase shift of the rate response relative to the externally injected current is shown to be equal for all neurons. We therefore expect that the corrected preferred frequency will determine the rhythms in neocortical networks.

View larger version (25K): [in this window] [in a new window]   Fig. 7. Implication of preferred frequency for synchronized network oscillations: small network. A network of 4 identical neurons, with asymmetric connectivity is simulated. External current is injected to one neuron only. A: the phase-frequency curves for each of the neurons relative to their inputs. Inset: network connectivity. B: the phase-frequency curves for each of the neurons relative to their inputs, considering the phase of synaptic delay (see RESULTS). C: the phase-frequency curves for each of the neurons relative to the phase of the external current injected. Synchronization of discharge rates is achieved at the frequency where the curves meet. Note that this is the same frequency as the corrected preferred frequency of the neurons. Parameters of the neurons are as in Fig. 3. The injected oscillatory current had a mean of 300 pA and amplitude of oscillation (I1) was 75 pA. I set to 32 pA. Synaptic parameters were 1 = 1 ms, 2 = 6.5 ms, and Vsyn = 60 mV. The synaptic strength, J, was set to 1 pA. Under these conditions, the magnitude of oscillations in the mean synaptic current, seen by each neuron, is of the same order of magnitude as I1. The mean firing rate of the neurons is 53 Hz.

This prediction was tested in a large, randomly connected, homogenous network of 200 identical adapting neurons, each receiving an uncorrelated noisy current injection with a constant mean, to induce spontaneous firing (Fig. 8). Under conditions in which the average firing rate of the neurons was well above zero at all times, a synchronized oscillatory spiking activity appeared spontaneously in the network, for sufficiently strong synaptic connectivity. Note that no external oscillatory current was injected to any of the neurons in the network, and therefore the population rhythm is an emergent property of the network. In the presented example (Fig. 8, A and B), the frequency of the synchronized oscillations is 6.64 Hz. The frequency of the population rhythm remains constant over time. However, the amplitude of modulation in the average population histogram slowly waxes and wanes. This is expected because each neuron in the population experiences a slightly different input current due to random connectivity and noisy current injection, and therefore the frequency of oscillations in subgroups of neurons may be slightly different, resulting in beats of the activity. The input current that each neuron in the population receives is a combination of the externally injected current, as well as the synaptic current. The mean input current (I₀) and the amplitude of the oscillations of the input current (I₁) that a representative neuron of the population received on average in the simulation were determined. This was used to construct the corrected phase-frequency curve for a single neuron in the homogenous network, taking into account the phase of the synaptic delay at each of the input frequencies (Fig. 8C). The corrected preferred frequency of the neuron was determined as 6.7 Hz. From this result, as well as from simulation results of similar networks with different model parameters, we conclude that the frequency of the emerging population rhythm in a large network is indeed predicted by the corrected preferred frequency of the single neurons.

View larger version (37K): [in this window] [in a new window]   Fig. 8. Implication of preferred frequency for synchronized network oscillations: large network. A network of 200 adapting neurons is simulated. Each neuron receives inputs from 50 other randomly chosen neurons. All neurons receive a noisy DC current of 200 pA, with I = 32 pA. A: the raster plot of a homogenous network of adapting neurons. The activity of 1 of every 3 neurons is shown. Model parameters: M = 40 ms, Rin = 0.2 G, k = 20(G)1, N = 80 ms, and  = 0.05. Synaptic parameters were 1 = 1 ms, 2 = 6.5 ms, and Vsyn = 60 mV. The synaptic strength, J, was set to 0.0615 pA. B: the population histogram of the homogenous network whose activity is shown in A. Bin size of histogram is 5 ms. A population rhythm emerges with a frequency of 6.64 Hz. C: the corrected phase-frequency curve of a single adapting neuron of the population, considering the phase of synaptic delay that the neuron experiences. I0 = 253 pA and I1 = 12.5 pA were determined according to the mean input current to which the neuron was exposed in the simulation of A and B. The corrected preferred frequency of the neuron is 6.7 Hz. Curve was constructed according to simulations of the detailed integrate-and-fire model of an adapting neuron. D: the population histogram of a heterogeneous network. All neurons are identical, except for k which is normally distributed around 20(G)1, with SD = 2(G)1. Bin size as in B. Population rhythm is still obtained and at the same frequency as in B.

Exploration of various homogenous populations revealed that the frequency of the population rhythm is indeed lower for networks composed of neurons with smaller _k, as predicted by Eq. 10. The degree of synchronization was found to increase when _k decreases down to a certain value (results not shown). This result can be explained by the fact that for any _k, there exists a minimal synaptic strength, J_c(_k), which is required in order for network oscillations to emerge; below this critical synaptic strength, the network has a steady state solution with no oscillations. The larger J is relative to J_c(_k), the larger are the amplitudes of the emergent population rhythm. Because J_c(_k) is positively related to _k, then decreasing _k results in a decreased J_c(_k), and therefore if J is kept unchanged, this would indeed result in higher degrees of synchronization.

It could be argued that it is not realistic to assume that a neocortical network consists of identical neurons. Rather, it is more plausible that the parameters of the neurons are randomly distributed across the population. We therefore explored the effect of having a heterogeneous population of adapting neurons whose parameters are all identical, except that _k is normally distributed around a certain value. The results (Fig. 8D) indicate that the emergence of the population rhythm is a robust phenomenon that is not sensitive to the exact parameters of the neurons in the population. In fact, the frequency of the rhythm did not change and is the same as the one predicted by the preferred frequency of a single neuron with the average parameters of the population (Fig. 8C). Interestingly, the heterogeneous population actually becomes more synchronized than the corresponding homogeneous population (compare to Fig. 8A). This may be explained by the fact the population is composed, among others, of neurons with small _k, which may act to enhance synchronization.

If the strength of the connections is increased, the network can switch to a different regime of activity. This regime is characterized by synchronous bursts of firing across the network, with zero activity between the bursts, and was recently studied in noiseless networks of adapting neurons (van Vreeswijk and Hansel 2001).

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Spike-frequency adaptation in neocortical pyramidal neurons was examined using the whole cell patch-clamp technique and phenomenological models of neuronal activity. Noisy current was injected to reproduce the irregular firing typically observed under in vivo conditions (Softky and Koch 1993). Spike-frequency adaptation was shown to play an important role in shaping the response of a neocortical neuron to such noisy stimuli. A detailed model was used to simulate the spiking response of the neocortical pyramidal neuron as well as a simplified model that captures its response in terms of the instantaneous average discharge rate.

In the intact brain a neuron is embedded in large, spontaneously active networks. It is therefore generally assumed that a neuron in vivo experiences noisy inputs due to the background activity of its presynaptic neurons. We simulate this background activity by adding white noise to the injected stimuli. The response of a neuron under such conditions, was quantified by computing the poststimulus time histogram (PSTH) of the neuron and thus reflects mean firing rate characteristics only.

The study of the output of a model adapting neuron exposed to oscillatory inputs revealed a dependence of the firing rate response on the frequency of stimulation. Low-frequency modulated inputs produced a phase advance of the output response relative to the input current, whereas high-frequency modulated stimuli induced a phase delay of the response. A special frequency was observed, referred to as the preferred frequency of stimulation, for which the phase delay of neuron's activity relative to the input is zero. The prediction of such phase-frequency curves was confirmed by recordings of neocortical pyramidal neurons. Additional experimental support for the existence of the predicted phase-frequency curves is obtained from the firing rate responses of thalamic relay neurons in the cat's lateral geniculate nucleus (Smith et al. 2000) and of regular spiking neurons in the guinea pig visual cortex (Carandini et al. 1996), both recorded in brain-slice preparations. The latter study also supports the predicted dependence of the phase-frequency curves of neocortical neurons on the DC level of current injection, I₀ (see also Kamondi et al. 1998 for low-frequency modulation).

Recently, it was shown that the response of nonadapting integrate-and-fire neurons to noisy oscillatory currents is also sensitive to the statistical properties of the noise (Brunel et al. 2001; Rudolph and Destexhe 2001). In particular, if the noise is low-pass filtered, e.g., due to the finite duration of synaptic currents, the dynamics of the firing rate becomes very fast for high-frequency oscillations. Hence, the phase of the delay approaches zero even in the absence of an adapting mechanism. However, for realistic values of parameters, this deviation of behavior from the white noise case occurs at frequencies that are significantly above the range we focus on in this study.

The significance of the preferred frequency of an adapting neuron for the emergence of synchronous population rhythms in the neocortex was investigated. The study of small networks, composed of only four neurons, one of which was stimulated by an externally oscillatory noisy current, suggested that the neurons may synchronize at a corrected preferred frequency, which takes into account the phase of the synaptic delay. This prediction was tested in recurrent networks of 200 adapting neurons with no externally oscillatory current injection. Nevertheless an oscillatory synchronized population activity spontaneously emerged. We found that the frequency of the population rhythm was indeed predicted by the corrected preferred frequency of single neurons. We conclude that the frequency of population rhythms can be predicted by the parameters of single neocortical neurons.

According to the model analysis, the preferred frequency depends on the parameters of adaptation and thus can be adjusted by neuromodulators, such as ACh (Tang et al. 1997), that affect the degree of adaptation of pyramidal neurons. High concentrations of neuromodulators can result in the shut off of adaptation currents and hence in the abolishment of population rhythms. Adaptation could therefore be one of the crucial factors in setting the frequency of population rhythms in the neocortex. Indeed, in Sanchez-Vives and McCormick (2000), it is suggested that the slow oscillations in the neocortex are generated through a recurrent network of excitatory connections and that the periodicity is affected largely by the time course of the outward currents generating the slow AHP of pyramidal and spiny stellate cells. Moreover, it has been shown that the low-frequency oscillations are indeed suppressed by a variety of neurotransmitters, including ACh and norepinephrine (NE), presumably through the reduction of specialized K⁺ conductances, such as that underlying the AHP currents (Steriade et al. 1993). Faster rhythms are possibly determined by other mechanisms, which depend on the activity of inhibitory interneurons, and could therefore be less sensitive to the effect of neuromodulators (Brunel 2000; Tsodyks et al. 1997; Wilson and Cowan 1972).

In addition to the expected significance of adaptation in determining possible frequencies for neocortical population rhythms, theoretical models have also suggested that the phase-relation of spike occurrence relative to the population cycle may be capable of carrying sensory information (e.g., Buzsáki and Chrobak 1995; Hopfield 1995; Kamondi et al. 1998; Laurent 1996; Lisman and Idiart 1995; Tsodyks et al. 1996). Experimental support for such "phase coding" has been specifically demonstrated by the phenomenon of spike phase precession observed in CA1 pyramidal "place cells" (O'Keefe and Recce 1993; Skaggs et al. 1996). These place cells undergo progressive phase precession during the time that the rat crosses the place field of the cell. In this sense, the phase shift of the spike discharge relative to the theta population cycle encodes the rat's position in space. It has been suggested (Kamondi et al. 1998) that this phase precession is explained by increasing depolarization due to increased excitation by afferents in the center of the field, causing the cells to fire progressively earlier during the theta cycle. Such a dependence of the phase on the DC level (I₀) for low-frequency modulated inputs is in accordance with our observations. In the context of `phase-coding' of sensory information, adaptation might have a role in enriching the coding language, by adding negative phase shifts to the vocabulary of the code.