Katie A. Ferguson

Experimentally constrained CA1 fast-firing parvalbumin-positive interneuron network models exhibit sharp transitions into coherent high frequency rhythms.

The coupling of high frequency oscillations (HFOs; >100 Hz) and theta oscillations (3–12 Hz) in the CA1 region of rats increases during REM sleep, indicating that it may play a role in memory processing. However, it is unclear whether the CA1 region itself is capable of providing major contributions to the generation of HFOs, or if they are strictly driven through input projections. Parvalbumin-positive (PV+) interneurons may play an essential role in these oscillations due to their extensive connections with neighboring pyramidal cells, and their characteristic fast-spiking. Thus, we created mathematical network models to investigate the conditions under which networks of CA1 fast-spiking PV+ interneurons are capable of producing high frequency population rhythms. We used whole-cell patch clamp recordings of fast-spiking, PV+ cells in the CA1 region of an intact hippocampal preparation in vitro to derive cellular properties, from which we constrained an Izhikevich-type model. Novel, biologically constrained network models were constructed with these individual cell models, and we investigated networks across a range of experimentally determined excitatory inputs and inhibitory synaptic strengths. For each network, we determined network frequency and coherence. Network simulations produce coherent firing at high frequencies (>90 Hz) for parameter ranges in which PV-PV inhibitory synaptic conductances are necessarily small and external excitatory inputs are relatively large. Interestingly, our networks produce sharp transitions between random and coherent firing, and this sharpness is lost when connectivity is increased beyond biological estimates. Our work suggests that CA1 networks may be designed with mechanisms for quickly gating in and out of high frequency coherent population rhythms, which may be essential in the generation of nested theta/high frequency rhythms.

Excitatory Inputs Determine Phase-Locking Strength and Spike-Timing of CA1 Stratum Oriens/Alveus Parvalbumin and Somatostatin Interneurons during Intrinsically Generated Hippocampal Theta Rhythm.

Theta oscillations are essential for learning and memory, and their generation requires GABAergic interneurons. To better understand how theta is generated, we explored how parvalbumin (PV) and somatostatin (SOM) interneurons in CA1 stratum oriens/alveus fire during hippocampal theta and investigated synaptic mechanisms underlying their behavior. Combining the use of transgenic mice to visually identify PV and SOM interneurons and the intact hippocampal preparation that can generate theta oscillations in vitro without cholinergic agonists, we performed simultaneous field and whole-cell recordings. We found that PV interneurons uniformly fire strongly phase-locked to theta, whereas SOM neurons are more heterogeneous with only a proportion of cells displaying tight phase-locking. Differences in phase-locking strength could be explained by disparity in excitatory inputs received; PV neurons received significantly larger EPSCs compared with SOM neurons, and the degree of phase-locking in SOM neurons was significantly correlated with the size of EPSCs. In contrast, IPSC amplitude did not differ between cell types. We determined that the local CA1 rhythm plays a more dominant role in driving CA1 interneuron firing than afferent inputs from the CA3. Last, we show that PV and strongly phase-locked SOM neurons fire near the peak of CA1 theta, under the tight control of excitatory inputs that arise at a specific phase of each theta cycle. These results reveal a fundamental mechanism of neuronal phase-locking and highlight an important role of excitation from the local network in governing firing behavior during rhythmic network states. SIGNIFICANCE STATEMENT Rhythmic activity in the theta range (3–12 Hz) is important for proper functioning of the hippocampus, a brain area essential for learning and memory. To understand how theta rhythm is generated, we investigated how two types of inhibitory neurons, those that express parvalbumin and somatostatin, fire action potentials during theta in an in vitro preparation of the mouse hippocampus. We found that the amount of excitatory input they receive from the local network determines how closely their spikes follow the network theta rhythm. Our findings reveal an important role of local excitatory input in driving inhibitory neuron firing during rhythmic states and may have implications for diseases, such as epilepsy and Alzheimers disease, which affect the hippocampus and related areas.

Examining the limits of cellular adaptation bursting mechanisms in biologically-based excitatory networks of the hippocampus

Determining the biological details and mechanisms that are essential for the generation of population rhythms in the mammalian brain is a challenging problem. This problem cannot be addressed either by experimental or computational studies in isolation. Here we show that computational models that are carefully linked with experiment provide insight into this problem. Using the experimental context of a whole hippocampus preparation in vitro that spontaneously expresses theta frequency (3–12 Hz) population bursts in the CA1 region, we create excitatory network models to examine whether cellular adaptation bursting mechanisms could critically contribute to the generation of this rhythm. We use biologically-based cellular models of CA1 pyramidal cells and network sizes and connectivities that correspond to the experimental context. By expanding our mean field analyses to networks with heterogeneity and non all-to-all coupling, we allow closer correspondence with experiment, and use these analyses to greatly extend the range of parameter values that are explored. We find that our model excitatory networks can produce theta frequency population bursts in a robust fashion.Thus, even though our networks are limited by not including inhibition at present, our results indicate that cellular adaptation in pyramidal cells could be an important aspect for the occurrence of theta frequency population bursting in the hippocampus. These models serve as a starting framework for the inclusion of inhibitory cells and for the consideration of additional experimental features not captured in our present network models.

Network models provide insights into how oriens-lacunosum-moleculare and bistratified cell interactions influence the power of local hippocampal CA1 theta oscillations.

Hippocampal theta is a 4–12 Hz rhythm associated with episodic memory, and although it has been studied extensively, the cellular mechanisms underlying its generation are unclear. The complex interactions between different interneuron types, such as those between oriens–lacunosum-moleculare (OLM) interneurons and bistratified cells (BiCs), make their contribution to network rhythms difficult to determine experimentally. We created network models that are tied to experimental work at both cellular and network levels to explore how these interneuron interactions affect the power of local oscillations. Our cellular models were constrained with properties from patch clamp recordings in the CA1 region of an intact hippocampus preparation in vitro. Our network models are composed of three different types of interneurons: parvalbumin-positive (PV+) basket and axo-axonic cells (BC/AACs), PV+ BiCs, and somatostatin-positive OLM cells. Also included is a spatially extended pyramidal cell model to allow for a simplified local field potential representation, as well as experimentally-constrained, theta frequency synaptic inputs to the interneurons. The network size, connectivity, and synaptic properties were constrained with experimental data. To determine how the interactions between OLM cells and BiCs could affect local theta power, we explored how the number of OLM-BiC connections and connection strength affected local theta power. We found that our models operate in regimes that could be distinguished by whether OLM cells minimally or strongly affected the power of network theta oscillations due to balances that, respectively, allow compensatory effects or not. Inactivation of OLM cells could result in no change or even an increase in theta power. We predict that the dis-inhibitory effect of OLM cells to BiCs to pyramidal cell interactions plays a critical role in the resulting power of network theta oscillations. Overall, our network models reveal a dynamic interplay between different classes of interneurons in influencing local theta power.

Simple, biologically-constrained CA1 pyramidal cell models using an intact, whole hippocampus context.

The hippocampus is a heavily studied brain structure due to its involvement in learning and memory. Detailed models of excitatory, pyramidal cells in hippocampus have been developed using a range of experimental data. These models have been used to help us understand, for example, the effects of synaptic integration and voltage gated channel densities and distributions on cellular responses. However, these cellular outputs need to be considered from the perspective of the networks in which they are embedded. Using modeling approaches, if cellular representations are too detailed, it quickly becomes computationally unwieldy to explore large network simulations. Thus, simple models are preferable, but at the same time they need to have a clear, experimental basis so as to allow physiologically based understandings to emerge. In this article, we describe the development of simple models of CA1 pyramidal cells, as derived in a well-defined experimental context of an intact, whole hippocampus preparation expressing population oscillations. These models are based on the intrinsic properties and frequency-current profiles of CA1 pyramidal cells, and can be used to build, fully examine, and analyze large networks.

Combining Theory, Model, and Experiment to Explain How Intrinsic Theta Rhythms Are Generated in an In Vitro Whole Hippocampus Preparation without Oscillatory Inputs

Abstract Scientists have observed local field potential theta rhythms (3–12 Hz) in the hippocampus for decades, but understanding the mechanisms underlying their generation is complicated by their diversity in pharmacological and frequency profiles. In addition, interactions with other brain structures and oscillatory drives to the hippocampus during distinct brain states has made it difficult to identify hippocampus-specific properties directly involved in theta generation. To overcome this, we develop cellular-based network models using a whole hippocampus in vitro preparation that spontaneously generates theta rhythms. Building on theoretical and computational analyses, we find that spike frequency adaptation and postinhibitory rebound constitute a basis for theta generation in large, minimally connected CA1 pyramidal (PYR) cell network models with fast-firing parvalbumin-positive (PV+) inhibitory cells. Sparse firing of PYR cells and large excitatory currents onto PV+ cells are present as in experiments. The particular theta frequency is more controlled by PYR-to-PV+ cell interactions rather than PV+-to-PYR cell interactions. We identify two scenarios by which theta rhythms can emerge, and they can be differentiated by the ratio of excitatory to inhibitory currents to PV+ cells, but not to PYR cells. Only one of the scenarios is consistent with data from the whole hippocampus preparation, which leads to the prediction that the connection probability from PV+ to PYR cells needs to be larger than from PYR to PV+ cells. Our models can serve as a platform on which to build and develop an understanding of in vivo theta generation.

Mean field analysis gives accurate predictions of the behaviour of large networks of sparsely coupled and heterogeneous neurons

Large networks of integrate-and-fire (IF) model neurons are often used to simulate and study the behaviour of biologically realistic networks. However, to fully study the large network behaviour requires an exploration of large regions of a multidimensional parameter space. Such exploration is generally not feasible with large network models, due to the computational time required to simulate a network with biologically significant size. To circumvent these difficulties we use a mean-field approach, based on the work of [1]. We consider a sparsely coupled, excitatory network of 10,000 Izhikevich model neurons [2], with Destexhe-type synapses [3]. The cellular models were fit to hippocampal CA1 pyramidal neurons and have heterogeneous applied currents with a normal distribution. We derived a mean-field system for the network which consists of differential equations for the mean of the adaptation current and the synaptic conductance. As CA1 is an area that displays prominent theta oscillations [4], we used the mean-field system to study how the frequency of bursting depends on various model parameters. Figure ​Figure1A1A shows an example study. These studies were successful in guiding numerical simulations of the large network. When parameter values determined from the mean-field analysis are used in a large network simulation, bursting of the predicted frequency occurs (Figure ​(Figure1B1B). Figure 1 A. Mean-field prediction of the bursting frequency as a function of the unitary synaptic conductance and the mean applied current. B. Simulation of a network of 10,000 neurons with unitary conductance 0.058 nS and mean current 250 pA, showing an oscillation ...

Experimentally constrained network model of hippocampal fast-firing parvalbumin-positive interneurons

Our PV+ interneurons are represented with an Izhikevich-type model [2], and involve parameter values that are designed to approximate the cell’ si ntrinsic properties. To determine these parameters, spike characteristics and passive properties were extracted from wholecell patch clamp recordings of PV+ interneurons in the CA1 region of an intact hippocampal preparation in vitro. Our network model is composed of these individual PV+ cell models, and the network size, architecture, and synaptic properties are chosen to be consistent with those found in the literature. Recordings during emergent network oscillations [3] provided us with information about realistic firing rates and synaptic activity of PV+ interneurons. These firing rates, used in combination with the cell’s intrinsic frequency-current profile, provided physiological constraints on the amount of synaptic current the PV+ cells receive during these spontaneous network oscillations. Under voltage clamp, excitatory post-synaptic current peaks are used in our model as an upper bound on the range of synaptic input. We used this network model to determine whether coherent rhythms could be produced within experimental constraints. Our model produced intrinsic properties and spiking behaviors which approximated the experimentally determined membrane capacitance, resting membrane potential, threshold potential, spike width, spike peak potential, peak after-hyperpolarizing potential, and amount of adaptation. Model parameters were determined such that the slope of the model’s frequency-current profile and the model rheobase current were within the range of our experimental data. As such, we have produced a network model of PV+ interneurons that has direct links to cellular characteristics with model parameters that have clear biological interpretations. In addition, network simulations of our PV+ interneuron model produced coherent gamma output. Since the firing properties and network architecture of PV+ interneurons puts them in an ideal position to influence network activity, this cell type will likely remain a focus of experimentalists and modelers alike. A model such as ours, with clear links to biology, may be used as a platform to investigate the role of these fast-firing PV+ interneurons in network oscillations and behaviour.

Network models provide insight into how oriens-lacunosum-moleculare (OLM) and bistratified cell (BSC) interactions influence local CA1 theta rhythms

Although hippocampal theta, a 4-12 Hz rhythm associated with episodic memory, has been studied extensively, the cellular mechanisms underlying its generation are unclear. OLM cells have been considered pacemakers of local CA1 theta [1], but recent experimental work has disputed this role [2]. The complex interactions that OLM cells have with other cell types, such as bistratified cells (BSCs) [3], make their contribution to network rhythms difficult to determine experimentally. One can address this issue using mathematical network models, which allow one to explore the contribution of specific cell populations and network connectivity in a simplified setting, and make predictions to guide further experimental work. Thus, we created a network model that is tied to experimental work on both the cellular and network level, and explored how cell interactions affect the power of local oscillations. We derived cellular properties from patch clamp recordings of fast-spiking parvalbumin-positive (PV+) interneurons – likely comprising basket cells (BCs), axo-axonic cells (AACs), and BSCs – and of somatostatin-positive putative OLM cells in the CA1 region of an intact hippocampus in vitro, and used these properties to constrain Izhikevich-type models of BCs/AACs, BSCs, and OLM interneurons. We constructed our network model with these individual cell models, and constrained network size, connectivity, and synaptic properties with experimental data. Experimental excitatory postsynaptic currents (EPSCs) recorded during endogenous CA1 theta oscillations were used to drive the various cell model populations, and we used a simple local field potential (LFP) model to integrate the effects of cell firing. To determine how the interactions between OLM cells and BSCs affect local theta rhythms, we explored how specific features of the network affected model LFP power. In addition, we simulated optogenetic experiments by silencing the OLM cell model population during the network rhythm. Spike characteristics and firing behaviors in our network models approximated those determined experimentally. Our models distinguish between regimes in which OLM cells minimally or strongly affect the power of network oscillations, and predict that the dis-inhibitory effect of OLM cells on BSC to pyramidal cell interactions plays a critical role in the power of network theta oscillations. When OLM to BSC model connections are not too strong, the OLM cells’ direct influence on pyramidal cells balances with its indirect dis-inhibitory effect (through the BSCs). In this case, when the OLM cell population is silenced, there is a compensatory effect on network power, and thus minimal change in power. However, when these OLM to BSC connections are stronger, the dis-inhibition of pyramidal cells does not balance with their direct influence, and thus silencing OLM cells has a stronger effect. This does not change when we consider various distributions of strengths in which the cell populations affect the LFP. Thus, our network models are able to make particular predictions that can be tested with optogenetics.

Basket cell contributions to the generation of theta rhythms in model hippocampal CA1 networks

Theta oscillations are one of the most prominent and well-studied clocking mechanisms detected in the mammalian brain. Recorded from the hippocampus during R.E.M. sleep and exploratory behavior, these 3-12 Hz rhythms are thought to play a lead role in spatial navigation, episodic memory, and the timing of place cell firing [1]. Although these oscillations have been heavily studied, the mechanism(s) responsible for the generation of these rhythms remains unknown. A popular theory hypothesizes that pacemaker neurons in the medial septum drive hippocampal rhythms [1] , but recent research shows that in an intact hippocampus preparation in vitro, the CA1 hippocampal region possesses the necessary circuitry to generate intrinsic theta rhythms [2]. To determine the mechanism(s) underlying the generation of these CA1 hippocampal theta rhythms, we created a mathematical network model. Our mathematical network model is composed of four types of cells: pyramidal cells, fast-spiking parvalbumin-positive basket cells (PV+BCs), slow-spiking cholecystokinin-positive basket cells (CCK+BCs), and oriens – lacunosum-moleculare (O-LM) interneurons. Each cell type is represented by a single-compartment, conductance-based model, and intrahippocampal connections among the chosen cell types are modeled based on experimental data of known connectivities. In addition, intracellular data recorded from the CA1 region of the intact hippocampus in vitro was used in combination with mathematical extraction techniques [3,4] to determine the balance of synaptic excitation and inhibition in individual cell types during the theta rhythm. Thus, experimental recordings, data analysis, and modeling were combined to generate an understanding of the mechanism(s) involved in the CA1 hippocampal theta rhythm. Our network model produces robust theta rhythms and cellular phase relationships in accordance with the experimental data. Interestingly, we find that inhibitory input imposed on pyramidal cells from the PV+BCs is a critical component in the production of these theta rhythms because the existence of the rhythm is most sensitive to these inhibitory conductances. This finding is surprising, as research has focused on the role of PV+BCs in faster gamma rhythms (20-100 Hz). In addition, we extracted mean synaptic conductance values from intracellular recordings of PV+BC and somatostatin-expressing (putative O-LM) interneuron activity. These synaptic values indicate that from the quiescent relative to the active state of the CA1 theta rhythm, the PV+BCs undergo a more significant reduction in inhibition than the putative O-LM interneurons. Optogenetics will be used to test predictions about the role of individual interneuron types in the generation of CA1 hippocampal theta rhythms.