Our focus in this study was to analyze the effect of differences in mean membrane potential on the resonant frequency of neurons in entorhinal cortex. The effect of membrane potential on resonant frequency was measured from neurons at different positions along the D/V and M/L axis in layer II of medial and lateral EC, respectively.
shows photographs of horizontal () and coronal () sections along the D/V and M/L axis of medial and lateral EC, respectively. Two magnifications are shown in order to show cell location within layer II of the slice as well as morphological detail. Cells of medial EC had radiating dendrites in all directions resembling the morphology of stellate cells (Alonso and Klink, 1993
), while cells of lateral EC had dendrites extending horizontally across layer II and vertically into layer I, resembling the morphology of fan cells (Tahvildari and Alonso, 2005
). To better describe the coverage of medial and lateral EC, shows the estimated recording sites of medial (n=53 of 87) and lateral (n=43 of 43) EC cells from horizontal and coronal sections, respectively. Our recording sites tended to stay within 2 mm of the caudo-medial tip of the medial EC and within the dorsolateral band (close to the rhinal sulcus) of lateral EC.
Fig. 1 Anatomy and morphology in layer II cells of medial and lateral EC. (A–H) Panels in the left and right columns correspond to photomicrographs taken from medial EC in horizontal sections and lateral EC in coronal sections, respectively. In each (more ...)
Fig. 2 Slice orientation and anatomical location of recording sites in medial and lateral EC. (A–B) A whole brain schematic depicting relative positions of the hippocampal formation and surrounding parahippocampal regions, as well as horizontal and coronal (more ...)
shows recordings of membrane potential from neurons in medial and lateral EC. Insets show a closer look at subthreshold voltage traces. In both medial and lateral EC, subthreshold membrane potential oscillations appeared between clusters of action potentials (, asterisk). Subsequent current steps to values beyond threshold increased the duration and the number of spikes within a cluster, generating a train of action potentials (, arrowhead). Cluster firing was defined as in previous studies (Klink and Alonso, 1993
; Fransen et al., 2004) as cells displaying clear groups of spikes, often doublets or triplets, in which spiking events were separated by periods of subthreshold oscillations. There was a large difference between the responses of medial and lateral EC cells to nine successive 50 pA hyperpolarizing step currents. All medial EC cells showed large sag potentials in response to hyperpolarizing current steps (see for individual traces and for the mean sag across the population), while cells of lateral EC showed much smaller sag potentials at all hyperpolarization levels (). Cells in medial EC showed rebound depolarization and spiking (, asterisk) after hyperpolarizing current injection.
Fig. 3 Physiological properties differ between cells of medial and lateral EC. (A–F) Panels in the left and right columns correspond to data from a single cell in medial EC and lateral EC (coronal), respectively. (A) As the holding current is gradually (more ...)
After examining cellular responses to depolarizing and hyperpolarizing current steps, ZAP stimuli were delivered at various membrane potentials in order to measure the resonant frequencies of each cell. Consistent with previous studies, we found from these experiments that along the dorsal to ventral axis of medial EC, cells showed a gradient in the resonant frequencies near resting potential such that higher frequencies were found in more dorsal regions and lower frequencies in more ventral regions. depict recordings with holding potentials of −65 mV from three medial and three lateral EC cells, respectively. In the medial EC, the resonant frequency decreased as a function of distance from the dorsal surface of the brain (A: 3.6 mm, 7.81 Hz; B: 5.0 mm, 6.16 Hz; and C: 6.7 mm, 3.97 Hz). However, in lateral EC, the resonant frequency was almost always under 2 Hz, regardless of the distance from the rhinal sulcus (coronal, D: 0.56 mm, 1.26 Hz; E: 0.92 mm, 0.88 Hz; and F: 1.81 mm, 0.76 Hz) or the dorsal surface of the brain (horizontal).
Fig. 4 Resonant frequency decreases along the dorsal to ventral axis of medial EC. (A–F) ZAP stimuli (not shown) were set to appropriate amplitudes that ensured subthreshold membrane potential dynamics. For each recording, the cell’s membrane (more ...)
Since ZAPs were delivered at different membrane potentials, analyses of resonant frequency by D/V position were done in 2 mV voltage bins according to the cell’s membrane potential in each recording. show plots of resonant frequency as a function of D/V position for five different voltage bins of medial EC cells as well as resultant r2 values for linear fits to the data (A, −56.5 to −54.5 mV, r2 =0.00908; B, −60.5 to −58.5 mV, r2 = 0.595; C, −62.5 to −60.5 mV, r2 = 0.299; D, −64.5 to −62.5 mV, r2 = 0.353; E, −70.5 to −68.5 mV, r2 = 0.0246). At voltages near the resting membrane potential (), the resonant frequency clearly decreased along the D/V axis in the medial EC. However, at membrane potentials away from rest, slopes flattened out, suggesting the relationship between resonant frequency and membrane potential is weaker at these voltages. Unlike medial EC cells, show that the lateral EC cells lacked resonant properties regardless of their anatomical position in both horizontal (F–J) and coronal (K–O) sections.
Fig. 5 The medial EC population shows a clear decrease of the resonant frequency along the D/V axis at membrane potentials near resting potential. (A–J) Resonant frequencies, recorded from horizontal sections, are plotted as a function of D/V distance (more ...)
An important result from the ZAP analyses was the inverse linear relationship found between membrane potential and resonant frequency in all cells of the medial EC. show that as the membrane potential becomes more depolarized the resonant frequency decreases, or stated another way, as the membrane potential becomes more hyperpolarized, the resonant frequency increases (A: −62 mV, 3.387 Hz; B: −67 mV, 4.792 Hz; and C: −72 mV, 6.042 Hz). The linear relationship between resonant frequency and membrane potential between −70 and −55 mV can be seen in the plots for three individual medial entorhinal neurons in dorsal medial regions in and in ventral medial regions in . The linear relationship in this membrane potential range was seen in every cell of the medial EC (see later figures). In contrast, in the lateral EC, almost all cells showed resonant frequencies of less than 2 Hz across all membrane potentials. Three examples of this are shown in . Only a few cells in lateral EC showed resonant frequencies above 2 Hz, and those that did had frequencies that were always below 3 Hz. E. Examples of the resonant frequency at different membrane potentials in individual dorsal and ventral lateral EC neurons are shown in .
Fig. 6 Resonant frequency decreases with membrane potential depolarization in medial EC. (A–F) ZAP stimuli were set to appropriate amplitudes that ensured subthreshold membrane potential dynamics. For each recording, the cell’s membrane potential (more ...)
We simulated the inverse linear relationship between membrane potential and resonant frequency by constructing a biophysical model of layer II medial EC stellate cells. We performed simulations with various holding currents in order to systematically test the effect of mean membrane potential on the resonant frequency. In , example voltage and impedance traces are shown for four mean membrane potentials, while shows the voltage dependence of the H-current channel activation, inverse time constant, and the resonant frequency. At more hyperpolarized membrane potentials, the H current activation and inverse time constant are large, leading to higher resonant frequencies. As the model cell becomes more depolarized, activation of the H-current and its inverse time constant decrease, resulting in lower resonant frequencies. It is important to note that at membrane potentials between −55 to −70 mV the simulations gave an approximately linear relationship with a negative slope. This result is in agreement with what was found experimentally. At more hyperpolarized membrane potentials (−70 to −85 mV) tested in the biophysical model, the activation of the H-current approaches its maximum, causing the resonant frequency to approach an asymptotic level.
Fig. 7 Biophysical model of medial EC cells displays relationship between increase in membrane potential and decrease in resonant frequency. (A–D) Simulated membrane potential trace (top), impedance, and impedance curve fits (bottom) at 4 different membrane (more ...)
We then checked to see if this same phenomenon of approach to an asymptotic level occurred in vitro, by measuring the resonant frequency at more hyperpolarized levels (−55 to −80 mV, n=17) and (−60 to −90 mV, n=7) in layer II medial EC cells. The results of these experiments () show that at membrane potentials below −70 mV, the resonant frequency approaches an asymptotic value, suggesting saturation to a maximum resonant frequency. also highlights some other important findings of this study. Controls recorded at different time points ten minutes apart show that the resonant frequency was very stable () and we found the resonant frequency does not show hysteresis (). We measured the voltage dependence of resonance in four different ways. First, as was done for all other cells, the resonant frequency was measured from hyperpolarized to depolarized membrane potentials. This was usually done without returning the membrane potential to rest between individual holding potentials. However, in cells shown in , we stepped to rest before each step in the depolarized direction. We also reversed the voltage direction in which we measured the resonant frequency, so as to start at −55 mV and end at −80 mV. Additionally, we measured the resonant frequency at randomly chosen voltages. In all cases (n=14 cells) the voltage direction did not appreciably alter the voltage dependence of the resonant frequency. To ensure our results were not influenced by the use of different amplitudes of the ZAP stimulus, we held medial EC cells (n=6) at three different potentials (−65, −70, and −75 mV) and measured the resonant frequency with 40, 80, 120, and 200 pA peak-to-peak amplitude ZAP stimuli at each potential. In all six cells we found that the resonant frequency was very similar at a given potential, regardless of the ZAP amplitude used. Examples from two cells are shown in . The correlation between the presence of the H-current and resonant properties prompted experiments where the H current blocker, ZD7288, was applied to medial EC cells. These experiments abolished both the sag potential (not shown) and the resonant properties (, n = 3) in medial EC cells. In addition, the firing properties of the medial EC cells became very similar to those in the lateral EC, and stopped showing firing of spikes in clusters.
Fig. 8 The resonant frequency in medial EC approaches an asymptotic value at membrane potentials below −70 mV, does not display hysteresis, and is not affected by the amplitude of the ZAP stimulus. (A–B) The resonant frequency shown at more hyperpolarized (more ...)
Fig. 9 ZD7288 abolishes resonance properties in medial EC. (A–C) The resonant frequency was measured in three membrane potential directions (A, B: −55 to −80 mV, circles; −80 to −55 mV, triangles; random membrane potentials, (more ...)
We then pooled the medial EC data measuring the resonant frequency from −55 to −70 mV and from −55 to −80 mV. The finding of higher resonant frequencies in dorsal medial EC compared to ventral medial EC still held true (). In addition, across the population the dorsal cells showed more of an asymptotic approach to a maximum across membrane potentials compared to the ventral population. Lastly we investigated how the slope of resonance versus membrane potential (Hz/mV) changes for individual cells along the D/V axis of the medial EC. For all cells (n=87) we looked at the slope of resonant frequency versus membrane potential computed across the full range of membrane potentials from −80 to −55 mV () and a more limited range from −70 to −55 mV (). In both analyses, the difference in slope of resonance frequency versus membrane potential showed an apparent negative trend along the D/V axis, but this trend did not reach statistical significance ().
Fig. 10 Population data showing resonant frequencies at all membrane potentials in dorsal medial EC compared to ventral EC. (A–B) Cells in the dorsal medial EC (A, n=48) show higher frequencies compared to ventral medial EC cells (B, n=31) and a clearer (more ...)