The effects of periodic and non-periodic inputs on the dynamics of a medial entorhinal cortex layer II stellate cell model

Various neuron types exhibit sub-threshold and firing frequency resonance in which the sub-threshold membrane potential or firing frequency responses to periodic inputs peak at a preferred frequency (or frequencies). Previous experimental work has shown that medial entorhinal cortex layer II stellate cells (SCs) exhibit sub-threshold and firing frequency resonance in the theta frequency band (4 - 10 Hz). In this thesis we seek to understand the biophysical and dynamic mechanism underlying these phenomena and how they are related. We studied the effects of sinusoidal current and synaptic conductance inputs at various frequencies, with and without noise, on the supra-threshold dynamics of a SC model. For current inputs, our results show that while the SC model exhibits a single frequency preference peak (in the theta frequency band) for low sinusoidal input levels, it exhibits three preferred frequency peaks for larger input levels. These additional peaks occur at frequencies that are roughly a multiple of the theta one. For synaptic conductance inputs, we observe an additional peak in the signal gain which occurs at a much higher frequency (in the high gamma frequency band). These findings depart from the linear prediction. The corresponding linearized model does not exhibit three preferred frequency peaks for current inputs and a much higher frequency for conductance inputs under the same conditions (such as parameters, noise, amplitude of inputs and maximal synaptic conductance) in the nonlinear model. Previous experimental work has shown high-frequency Poisson-distributed trains of combined excitatory and inhibitory conductance- and current-based synaptic inputs reduce amplitude of subthreshold oscillations of SCs. The second goal of this thesis is to investigate the mechanism underlying these phenomena in the context of the model. More specially, we studied the effects of both conductance- and current-based synaptic inputs at various maximal conductance values on a SC model. Our numerical simulations show that conductance-based synaptic inputs reduce the amplitude of SC\u27s subthreshold oscillations for low enough value of the maximal synaptic conductance value but amplify these oscillations at a higher range. These results are in contrast to the experimental results

The Mechanism of Abrupt Transition between Theta and Hyper-Excitable Spiking Activity in Medial Entorhinal Cortex Layer II Stellate Cells

Recent studies have shown that stellate cells (SCs) of the medial entorhinal cortex become hyper-excitable in animal models of temporal lobe epilepsy. These studies have also demonstrated the existence of recurrent connections among SCs, reduced levels of recurrent inhibition in epileptic networks as compared to control ones, and comparable levels of recurrent excitation among SCs in both network types. In this work, we investigate the biophysical and dynamic mechanism of generation of the fast time scale corresponding to hyper-excitable firing and the transition between theta and fast firing frequency activity in SCs. We show that recurrently connected minimal networks of SCs exhibit abrupt, threshold-like transition between theta and hyper-excitable firing frequencies as the result of small changes in the maximal synaptic (AMPAergic) conductance. The threshold required for this transition is modulated by synaptic inhibition. Similar abrupt transition between firing frequency regimes can be observed in single, self-coupled SCs, which represent a network of recurrently coupled neurons synchronized in phase, but not in synaptically isolated SCs as the result of changes in the levels of the tonic drive. Using dynamical systems tools (phase-space analysis), we explain the dynamic mechanism underlying the genesis of the fast time scale and the abrupt transition between firing frequency regimes, their dependence on the intrinsic SC's currents and synaptic excitation. This abrupt transition is mechanistically different from others observed in similar networks with different cell types. Most notably, there is no bistability involved. ‘In vitro’ experiments using single SCs self-coupled with dynamic clamp show the abrupt transition between firing frequency regimes, and demonstrate that our theoretical predictions are not an artifact of the model. In addition, these experiments show that high-frequency firing is burst-like with a duration modulated by an M-current

Cellular properties of the medial entorhinal cortex as possible mechanisms of spatial processing

Cells of the rodent medial entorhinal cortex (EC) possess cellular properties hypothesized to underlie the spatially periodic firing behaviors of 'grid cells' (GC) observed in vivo. Computational models have simulated experimental GC data, but a consensus as to what mechanism(s) generate GC properties has not been reached. Using whole cell patch-clamp and computational modeling techniques this thesis investigates resonance, rebound spiking and persistent spiking properties of medial EC cells to test potential mechanisms generating GC firing. The first experiment tested the voltage dependence of resonance frequency in layer II medial EC stellate cells. Some GC models use interference between velocity-controlled oscillators to generate GCs. These interference mechanisms work best with a linear relationship between voltage and resonance frequency. Experimental results showed resonance frequency decreased linearly with membrane potential depolarization, suggesting resonance properties could support the generation of GCs. Resonance appeared in medial EC but not lateral EC consistent with location of GCs. The second experiment tested predictions of a recent network model that generates GCs using medial EC stellate cell resonance and rebound spiking properties. Sinusoidal oscillations superimposed with hyperpolarizing currents were delivered to layer II stellate cells. Results showed that relative to the sinusoid, a limited phase range of hyperpolarizing inputs elicited rebound spikes, and the phase range of rebound spikes was even narrower. Tuning model parameters of the stellate cell population to match experimental rebound spiking properties resulted in GC spatial periodicity, suggesting resonance and rebound spiking are viable mechanisms for GC generation. The third experiment tested whether short duration current inputs can induce persistent firing and afterdepolarization in layer V pyramidal cells. During muscarinic acetylcholine receptor activation 1-2 second long current injections have been shown to induce persistent firing in EC principal cells. Persistent firing may underlie working memory performance and has been used to model GCs. However, input stimuli during working memory and navigation may be much shorter than 1-2 seconds. Data showed that input durations of 10, 50 and 100 ms could elicit persistent firing, and revealed time courses and amplitude of afterdepolarization that could contribute to GC firing or maintenance of working memory

Intrinsic electrophysiological properties of entorhinal cortex stellate cells and their contribution to grid cell firing fields

The medial entorhinal cortex (MEC) is an increasingly important focus for investigation of mechanisms for spatial representation. Grid cells found in layer II of the MEC are likely to be stellate cells, which form a major projection to the dentate gyrus. Entorhinal stellate cells are distinguished by distinct intrinsic electrophysiological properties, but how these properties contribute to representation of space is not yet clear. Here, we review the ionic conductances, synaptic, and excitable properties of stellate cells, and examine their implications for models of grid firing fields. We discuss why existing data are inconsistent with models of grid fields that require stellate cells to generate periodic oscillations. An alternative possibility is that the intrinsic electrophysiological properties of stellate cells are tuned specifically to control integration of synaptic input. We highlight recent evidence that the dorsal-ventral organization of synaptic integration by stellate cells, through differences in currents mediated by HCN and leak potassium channels, influences the corresponding organization of grid fields. Because accurate cellular data will be important for distinguishing mechanisms for generation of grid fields, we introduce new data comparing properties measured with whole-cell and perforated patch-clamp recordings. We find that clustered patterns of action potential firing and the action potential after-hyperpolarization (AHP) are particularly sensitive to recording condition. Nevertheless, with both methods, these properties, resting membrane properties and resonance follow a dorsal-ventral organization. Further investigation of the molecular basis for synaptic integration by stellate cells will be important for understanding mechanisms for generation of grid fields

Layer 3 Pyramidal Cells in the Medial Entorhinal Cortex Orchestrate Up-Down States and Entrain the Deep Layers Differentially

Up-down states (UDS) are synchronous cortical events of neuronal activity during non-REM sleep. The medial entorhinal cortex (MEC) exhibits robust UDS during natural sleep and under anesthesia. However, little is known about the generation and propagation of UDS-related activity in the MEC. Here, we dissect the circuitry underlying UDS generation and propagation across layers in the MEC using both in vivo and in vitro approaches. We provide evidence that layer 3 (L3) MEC is crucial in the generation and maintenance of UDS in the MEC. Furthermore, we find that the two sublayers of the L5 MEC participate differentially during UDS. Our findings show that L5b, which receives hippocampal output, is strongly innervated by UDS activity originating in L3 MEC. Our data suggest that L5b acts as a coincidence detector during information transfer between the hippocampus and the cortex and thereby plays an important role in memory encoding and consolidation

Biophysical foundation and function of depolarizing afterpotentials in principal cells of the medial entorhinal cortex

Neurons in layer II of the rodent medial entorhinal cortex (MEC) encode spatial information. One particular type, grid cells, tends to fire at specific spatial locations that form hexagonal lattices covering the explored environment. Within these firing fields grid cells frequently show short high-frequency spike sequences. Such bursts have received little attention but may contribute substantially to encoding spatial information. On the other hand, in vitro recordings of MEC principal cells have revealed that action potentials are followed by prominent depolarizing afterpotentials (DAP). Their biophysical foundation and function, however, are poorly understood. The objective of this study is to understand the mechanism behind the DAP by creating a biophysical realistic model of a stellate cell and to draw a connection between DAPs and burst firing in vivo. The developed single-compartment model reproduced the main electrophysi- ological characteristics of stellate cells in the MEC layer II, that are a DAP, sag, tonic firing in response to positive step currents and resonance. Using virtual blocking experiments, it was found that for the generation of the DAP only a NaP , KDR and leak current were necessary whereby the NaP current also exhibited a resurgent component. This suggests that for the generation of the DAP a balance between several currents is needed. In addition, the persistent and resurgent sodium current might play an important role. We analyzed the relevance of DAPs in vivo using whole-cell recordings of grid cells from Domnisoru et al. (2013). We found that around 20% of the cells exhibited a DAP. However, the percentage of cells was much lower than estimates from in vitro recordings. We showed that this is partly due to the quality of the recording as selecting APs from presumably good parts of the recording improved the visibility of DAPs. To investigate the relationship between DAPs and burst firing all cells were classified into bursty and non-bursty based on the spike-time autocorrelation. All cells with a DAP were bursty except the cell with the smallest DAP. Moreover, taking the mean of the spike-triggered average of the membrane potential for all bursty and non-bursty cells respectively showed a clear DAP for bursty but not for non-bursty cells. In summary, we found that the DAP can be realized in a single-compartment model by a NaP , KDR and leak current and provided evidence for the relevance of DAPs for burst firing in vivo

Mixed-mode Oscillations in Pyramidal Neurons Under Antiepileptic Drug Conditions

Subthreshold oscillations in combination with large-amplitude oscillations generate mixedmode oscillations (MMOs), which mediate various spatial and temporal cognition and memory processes and behavioral motor tasks. Although many studies have shown that canard theory is a reliable method to investigate the properties underlying the MMOs phenomena, the relationship between the results obtained by applying canard theory and conductancebased models of neurons and their electrophysiological mechanisms are still not well understood. The goal of this study was to apply canard theory to the conductance-based model of pyramidal neurons in layer V of the Entorhinal Cortex to investigate the properties of MMOs under antiepileptic drug conditions (i.e., when persistent sodium current is inhibited). We investigated not only the mathematical properties of MMOs in these neurons, but also the electrophysiological mechanisms that shape spike clustering. Our results show that pyramidal neurons can display two types of MMOs and the magnitude of the slow potassium current determines whether MMOs of type I or type II would emerge. Our results also indicate that slow potassium currents with large time constant have significant impact on generating the MMOs, as opposed to fast inward currents. Our results provide complete characterization of the subthreshold activities in MMOs in pyramidal neurons and provide explanation to experimental studies that showed MMOs of type I or type II in pyramidal neurons under antiepileptic drug conditions

Fluctuating Inhibitory Inputs Promote Reliable Spiking at Theta Frequencies in Hippocampal Interneurons

Theta-frequency (4–12 Hz) rhythms in the hippocampus play important roles in learning and memory. CA1 interneurons located at the stratum lacunosum-moleculare and radiatum junction (LM/RAD) are thought to contribute to hippocampal theta population activities by rhythmically pacing pyramidal cells with inhibitory postsynaptic potentials. This implies that LM/RAD cells need to fire reliably at theta frequencies in vivo. To determine whether this could occur, we use biophysically based LM/RAD model cells and apply different cholinergic and synaptic inputs to simulate in vivo-like network environments. We assess spike reliabilities and spiking frequencies, identifying biophysical properties and network conditions that best promote reliable theta spiking. We find that synaptic background activities that feature large inhibitory, but not excitatory, fluctuations are essential. This suggests that strong inhibitory input to these cells is vital for them to be able to contribute to population theta activities. Furthermore, we find that Type I-like oscillator models produced by augmented persistent sodium currents (INaP) or diminished A-type potassium currents (IA) enhance reliable spiking at lower theta frequencies. These Type I-like models are also the most responsive to large inhibitory fluctuations and can fire more reliably under such conditions. In previous work, we showed that INaP and IA are largely responsible for establishing LM/RAD cells’ subthreshold activities. Taken together with this study, we see that while both these currents are important for subthreshold theta fluctuations and reliable theta spiking, they contribute in different ways – INaP to reliable theta spiking and subthreshold activity generation, and IA to subthreshold activities at theta frequencies. This suggests that linking subthreshold and suprathreshold activities should be done with consideration of both in vivo contexts and biophysical specifics

Analysis of in vivo grid cell activity

The manner in which the brain encodes the position and movement of an animal as it navigates its environment has been a topic of intense study for decades. Interestingly, specific cell types have been identified that are thought to contribute to distinct aspects of spatial navigation. An important class, the so-called grid cells of the medial entorhinal cortex (MEC), fire spikes preferentially when the animal is near specific locations in its environment. For each grid cell, these locations form the vertices of a hexagonal lattice spanning the explored environment, which promoted the idea that the brain uses grid cells to measure the amount of distance travelled. On the other hand, many details about how the temporal firing behaviour of grid cells informs the brain about the animal's position and trajectory remain unclear. My thesis is based on two projects that address such issues of temporal coding in grid cells. In the first study we investigated grid cells based on spike-time autocorrelations and the existence of depolarizing afterpotentials (DAPs) following single spikes. Analyzing whole-cell data from mice running on virtual tracks, we found three different groups, "sparsely bursting cells", "bursty cells with depolarizing afterpotentials" and "bursty cells without depolarizing afterpotentials". Bursty cells with prominent DAPs were mostly stellate cells in Layer II of the MEC; their interspike intervals (ISIs) reflected DAP time-scales (5-10 ms). In contrast, neither the sparsely bursting pyramidal cells in Layer III, nor the high-frequency bursters in Layer II, showed a DAP. The ”bursty without DAP” cells had the earliest peaks in the ISI distributions, consistently around 4 ms. We hypothesized that these differences in the temporal characteristics could resemble differences on spatial coding. However, extracellular recordings from mice exploring real 2D arenas did not show strong differences in the tuning properties of the three cell groups. We next extended our analysis to non-grid principal cells in the MEC and found similar discharge characteristics. These findings suggest that depolarizing afterpotentials shape the temporal response characteristics of principal neurons in MEC with little effect on spatial properties. In the second study we asked whether grid cells encode the animal's current location or show some predictive behavior concerning the animal's future movement. We found that the grid cell firing rate is higher when the animal moves into a firing field of that neuron ("inbound" parts of the animal's trajectory) than when it travels in an outbound direction. We could eliminate this difference by shifting spikes ahead in time or in space along the momentary movement-direction or the head-direction vector or by a given distance along the trajectory. Optimal shifts ahead were around 170 ms and 2-3 cm, respectively. With these optimal forward shifts, we have shown that grid-cell activity indeed anticipates future movements. In short, in my thesis I have shown that DAPs influence burst firing characteristics of principal cells in the MEC and that grid cells exhibit anticipatory firing. Both findings add new aspects to the rich literature on the neural basis of spatial navigation