Information Processing in Single Cells and Small Networks: Insights from Compartmental Models

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1 Information Processing in Single Cells and Small Networks: Insights from Compartmental Models Panayiota Poirazi Institute of Molecular Biology and Biotechnology (IMBB), Foundation for Research and Technology-Hellas (FORTH), Vassilika VoutonP.O. Box 1385, Heraklion, Crete, GR GREECE Abstract. The goal of this paper is to present a set of predictions generated by detailed compartmental models regarding the ways in which information may be processed, encoded and propagated by single cells and neural assemblies. Towards this goal, I will review a number of modelling studies from our lab that investigate how single pyramidal neurons and small neural networks in different brain regions process incoming signals that are associated with learning and memory. I will first discuss the computational capabilities of individual pyramidal neurons in the hippocampus [1-3] and how these properties may allow a single cell to discriminate between different memories [4]. I will then present biophysical models of prefrontal layer V neurons and small networks that exhibit sustained activity under realistic synaptic stimulation and discuss their potential role in working memory [5]. Keywords: compartmental neuron models, learning and memory, information processing. PACS: 87.19Lb, , s, v, 87.10Ed, 87.16Mq, 87.16Vy, 87.18Sn INTRODUCTION Understanding how the brain works remains one of the most exciting and intricate challenges of modem biology. Despite the wealth of information that has accumulated during the past years regarding the molecular and biophysical mechanisms underlying neuronal activity, similar advances have yet to be made in understanding the rules that govern information processing and the relationship between structure and function of a neuron. Computational models provide a theoretical framework along with a technological platform for enhancing our understanding of nervous system functions. Certain tools are suitable for efficiently analysing and interpreting complex datasets, such as multi-channel recordings from hundreds of neurons, whereas others are used to simulate the activity of single cells, neural networks or systems of networks at various levels of abstraction. The development and apphcation of such modelling tools enable researchers to quantitatively investigate several hypotheses within interactive models of the systems under study. When used in conjunction with experimental techniques, these models facilitate hypothesis testing and help to identify key follow-up experiments. In this review, I will discuss a number of computational studies from our lab in which reahstic biophysical models are used to elucidate the computational tasks performed by single neurons and small networks. I will focus on neuron models that incorporate a significant level of detail and compare modelling predictions with experimental findings. METHODS The models presented here are all built and run within the NEURON simulation environment [6] and consist of multiple compartments each of which is represented as an electrical circuit, as depicted in Figure 1. They contain detailed representations of numerous biophysical mechanisms known to be present in these cells, such as ion channels, ion pumps and synaptic receptors. The morphology of our single neuron models is quite elaborated. CPl 108, Vol. 1, Computational Methods in Science and Engineering, Advances in Computational Science edited by G. Maroulis and T. E. Simos 2009 American Institute of Physics /09/$

2 similar to that of respective real cells, while the dendritic tree of neurons that are part of a network model is morphologically simplified. B dca Vafes FIGURE 1. The neuron as a multi-compartment model. A. The elaborated dendritic morphology of a pyramidal neuron is represented as a series of small electrical circuits. B. Biophysical mechanisms in each dendritic or spine compartment are modeled as resistance, source or capacitance units. RESULTS Whether incredibly simple as bipolar cells in the retina or immensely complex as Purkinje cells in the cerebellum [7], most neurons are composed of three major structural units: the dendrites, the soma (cell body) and the axon. For the past few decades, axons and dendrites were considered to be simple transmitting devices that communicate signals to and from the soma in which thresholded computations take place. As a result, neuronal cells were initially represented as spherical point neurons, consisting only of a cell body, and information transfer was thought to lie entirely in their average firing rates [8]. However, primarily computational and, more recently, physiological studies have shown that variations in morphology and ionic conductance composition of different neurons are there for a reason: to provide the cell with enhanced computational capabilities far outreaching those captured by a point neuron. Our work focuses on understanding these computational skills and providing a hnk between neural arithmetic and memory functions that can be performed either by individual cells or by small neural networks. Dendrites as Point Neurons, Neurons as Neural Networks It is now well established that dendrites of CAl pyramidal cells contain a large variety of voltage-dependent mechanisms, distributed non-uniformly throughout the dendritic tree, which heavily influence the cells' integrative behavior [9-16]. There is also evidence that elemental synaptic conductances may vary systematically as a function of dendritic location [17, 18] while dendritic K^ conductances can modify the excitability properties of apical dendrites in an activity-dependent manner, reveahng a new plasticity mechanism that takes place at the level of a small branch [19]. Many questions remain, however, regarding the contributions of these highly nonlinear membrane mechanisms to synaptic integration. To investigate the ways in which dendritic properties can influence the input-output function of hippocampal pyramidal neurons, we developed a vety detailed CAl pyramidal neuron model [1-3] that contained 17 types of ion channels -most of them distributed non-uniformly along the soma-dendritic axis- and 4 types of synaptic conductances. We first performed a number of validation studies in order to ensure that the model provides reasonable fits to a large variety of in vitro data bearing on the biophysical and integrative properties of hippocampal CAl pyramidal cells. The model was then used to investigate how dendrites integrate incoming signals that vaty both in their strength as well as their spatial location. We found that individual apical obhque dendrites of CAl pyramidal neurons act as independent 159

3 computational units that combine inputs using a sigmoidal activation function and that different branch outputs are linearly combined at the cell body. Both of these predictions were verified experimentally in a layer V pyramidal neuron [20] while a recent experimental study [21] confirmed that radial oblique dendrites of CAl pyramidal neurons function as single integrative compartments. As shown in Figure 6, layer V neocortical neurons summate linearly between-branch excitatory postsynaptic potentials (EPSPs) but implement a sigmoidal activation function for within-branch EPSPs (Fig 2B), similar to the model predictions (Fig 2A). Likewise, radial oblique dendrites of CAl pyramidal neurons combine synaptic inputs in a sigmoidal way (Fig 2C), as predicted by our model neuron (Fig 6A, red traces). In other words, thin dendritic branches seem capable of combining incoming signals according to a thresholding non-hnearity, much like a typical "point neuron." MODEL B EXPERIMENT (UyerV) EXPERIMEMT (CAl) ^'^ruiin b^aiich 1 Between hrflnctiea 4 0 S 10 1? Expected peak EPSP [mv] [1 OmV] 9*rA^^n iitiinctn^ti M ExpKted pw^ EPSP [mv] Expected pejk EPSP imvl FIGURE 2. Nonlinear dendritic computations in pyramidal neurons. A. Summation of paired, single-pulse inputs in the apical dendrites of our CAl pyramidal model cell. Simulations predict a sigmoidal modulation of combined excitatory postsynaptic potentials (EPSPs) within a branch (red symbols) and a linear summation of EPSPs between branches (green symbols). Red curves correspond to within-branch data for 3 individual dendrites. Due to differences in local vs. somatic responses, axis values for the red curves are scaled up by 10. B. Experimental verification of predicted summation rules in basal dendrites of a layer 5 pyramidal neuron. Single-pulse stimulation of synapses in different branches results in linear summation at the cell body (green squares). When y-amino butyric acid (GABA)ergic inhibition is blocked, the summation of within-branch EPSPs is modulated by a sigmoidal nonlinearity (all other symbols). Reproduced with permission from [20] C. Sequential single-pulse stimulation of individual spines within radial oblique dendrites of CAl pyramidal neurons using multi site two photon glutamate uncaging. The summation of somatic EPSPs generate in response to individual vs. combined stimulation of increasing number of synapses is highly nonlinear and closely resembles the model predictions shown in A (red traces). Reproduced with permission from [21]. If apical oblique dendrites are individually thresholded in CAl, layer V and most likely other classes of pyramidal neurons, the question that naturally arises is what advantage does this feature offer to the mammalian brain? To investigate the benefits of having compartmentalized, non-linear subunits we presented our model neuron with a large number of high-frequency input patterns varying in their spatio-temporal characteristics and recorded the model responses [22]. We found that the average firing rate of our detailed model cell in response to hundreds of different input patterns was accurately predicted by a two-layer neural network abstraction where individual obhque dendrites provided the 'hidden' nodes and the soma acted as the output layer (Figure 3). These findings suggested that the integrative properties of a highly complex, realistic model of a CAl pyramidal neuron containing more than 20 different membrane mechanisms could be described by a simple mathematical equation. Such a simplification is of great importance for future modelling efforts that try to understand the functionalities of large scale neuronal networks, since it allows the development of network models where each node (neuron) is modelled as a simplified two layer neural network instead of a full blown compartmental cell. 160

4 DifTused Clustered KX FIGURE 3. Modelling the model. A. Somatic model responses to high frequency synaptic stimulation (lasting 600ms) shown for 3 cases with 40 excitatory synapses distributed across the apical tree. In a fully dispersed case (left column), all 40 synapses were randomly assigned to the 37 terminal branches. In a fully concentrated case (right column), synapses were placed 8 to a branch on 5 randomly chosen branches. Mixed cases consisted of randomized assignments of 1, 2, 4, 6, or 8 synapses to varying numbers of terminal branches. Middle column shows a case with 2 groups each of 2 (blue) and 6 (yellow), plus 24 randomly dispersed synapses (green). Excitatory synapses were distributed at equally spaced intervals on each branch. A fixed set of 11 inhibitory synapses was used in all runs. Figure was adapted with permission from [22]. B. Schematic representation of a pyramidal neuron as a two-layer neural network. Radial Oblique dendrites provide the first layer of the network, each performing individually thresholded computations as shown in A and B. The outputs of this layer feed into the cell body, which constitutes the second layer of the network model. Model responses shown in A were fit by the abstract model shown in B, where U; were the number of excitatory inputs to each branch and a^ was the branch coefficient. Reproduced with permission from [23]. Encoding of Spatio-temporal Information with Bursts SLM - - Full/Diffused Temporal offset (ms) FIGURE 4. A. Schematic illustration of layer specific, asynchronous synaptic stimulation of synapses in the SR and SLM layer of the model cell. B. Model responses vary from bursting to spike blocking as a function of the delay (temporal offset) between the two stimulated pathways. If single pyramidal neurons can modify their firing rate according to the spatial arrangement of incoming signals, could such a property be used to encode and transmit information about these signals to the recipient cells? To investigate this hypothesis we used a refined version of our CAl model [24] where excitatory and inhibitory synaptic mechanisms were distributed according to detailed anatomical data for these cells [25]. We used a 161

5 previously published stimulation protocol [26] according to which synapses in the two primary pathways of the CAl region, namely the Stratum Radiatum (SR) and the Stratum Lacunosum Moleculare (SLM) layers, were stimulated with a delay raging from 0-450ms. The SLM pathway was always stimulated first as depicted in Figure 4A. According to the stimulation protocol, all synapses were stimulated 10 times at a frequency of IHz. However, each individual stimulus consisted of (a) a single supra-threshold pulse in the SR and (b) a sub-threshold 10-spike burst at loohz in the SLM. We found that as we varied the delay between the two stimulated pathways, the model response changed from bursting (short delays) to blockade of activity (long delays) in a sigmoidal-like way (Figure 4B). This modulation of excitability was attributed primarily to the NMDA (bursting) and GABAb (spike blocking) mechanisms since their blockade eliminated the respective enhancement and suppression effects [4]. These findings suggest that temporal information about incoming signals, such as the delay between the two stimulated pathways may be contained in the firing pattern of our model cell. Considering the results of [1, 3] whereby the spatial arrangement of synapses alone was shown to influence neuronal responses, we next sought to investigate whether the firing patterns of our model cell contain discriminatory information about both the temporal (delay) and spatial (arrangement) of incoming signals. To address this question we varied both the delay between the two stimulated pathways (from 0-160ms) and the distribution of synaptic contacts (randomly placed throughout each layer vs. clustered within a few branches) and recorded the timing of each spike in the model's response. We then calculated the inter-spike-intervals between successive spikes for both diffused and clustered arrangements and used them as input to a hierarchical clustering algorithm. We found that responses to clustered signals could be clearly discriminated from responses to diffused signals for delays from 0-120ms (Figure 5 A). Moreover, the time-to-first spike was shown to depend hnearly on the temporal offset for both arrangements while clustered signals resulted in significantly faster responses than diffused inputs across all delays from 0-lOOms (Figure 5B). These results show that our model cell can clearly discriminate between clustered and diffused signals, when it utilizes the succession of spikes and the latency for the initiation of the response. Taken together, these findings suggest that a single CAl pyramidal cell may be capable of encoding and transmitting spatio-temporal information about incoming signals to the recipient cell. -Dif.ieo B Clu120 to lu 100 :IJ80 I J.40 a. ILI.60 to 1.20 ^ lu.q C -ClLI.160 ^V -Dif120 -H -Clu140 -Dif.100 j-di ifo -I i-dif 8Q 4-Dif.60 lrdif.40 T-Dif20 leo OifTusect u Clustered eo 70 Temporal offset (ms) FIGURE 5. A. Hierarchical clustering of the average inter-spike-intervals between successive spikes in the model's response to input stimuli varying in both time and space. Model responses are grouped into separate clusters for diffused vs. clustered inputs for all temporal offsets below 120ms. For temporal offsets between ms the cell cannot clearly distinguish between clustered and diffused stimuli. B. Time-to-first-spike box plot for clustered and diffused stimuli. Clustered inputs accelerate dendritic integration and induce somatic responses significantly faster than diffused inputs, for all temporal offsets below 100ms. Modeling Working Memory in the Prefrontal Cortex: biophysical mechanisms underlying persistent activity Given that single pyramidal neurons can perform all sorts of complex computations, we next seek to correlate such computations with a more physiological measure of learning and memory such as working memory. Working 162

6 memory requires information to be held in the brain for short periods until the completion of a specific task, such as holding a phone number in mind until the number is actually dialed. Prefrontal cortex (PFC) is a brain area critically involved in working memory. PFC pyramidal neurons provide the necessary neural processing to establish the behavioral continuity over time by sustaining their firing rate throughout the delay period during working memory tasks [27, 28]. Although persistent activity in the PFC is well described, the underlying biophysical mechanisms have yet to be elucidated. The goal of this project is to delineate the role of synaptic (i.e. NMD A) and intrinsic (i.e. ICAN) mechanisms in the initiation and maintenance of persistent activity in a single PFC pyramidal neuron model. We use a detailed compartmental model of a layer V PFC pyramidal neuron which incorporates both structural properties and biophysical mechanisms. Specifically, our model neuron includes modehng equations for 14 types of ionic mechanisms, known to be present in these cells, as well as modehng equations for the regulation of intracellular calcium and potassium concentration [5]. Among these, a model for the calcium activated non-selective cation current (CAN conductance) is included, in order to simulate the experimentally induced Gq-coupled receptor activation in PFC pyramidal neurons and the presence of afterdepolarization. The model cell was first vahdated to ensure that it displays (a) proper I-V curves in response to step-pulse current injections and input resistance [29], (b) proper spike trains as well as proper backpropagating action potentials in the apical [30] and basal dendrites [31], (c) proper synaptic responses in the apical [32] and basal dendrites [33] and (d) proper sadp generation as a result of CAN conductance activation via current clamp or synaptic stimulation. The ratio of NMD A to AMPA currents was also adjusted to ensure that the basal dendrites exhibit proper NMDA spikes [31]. A Stimulation protocol B No CAN current With CAN current 20Hz stimulation SOsynapses gampa/gnmda ~ 1 gampa/gnmda ~ 3 AAjvUAWj ''IUUJ ^ 100ms JUUUUio* gampa/gnmda ~ 5 gampa/gnmda 10 FIGURE 6. Effect of CAN and NMDA conductances on persistent activity generation in the model cell. A. A total of 50 synapses in the basal dendrites of the model cell are stimulated for 500ms at 20 Hz. B. When CAN conductance is inactivated, the model cell responds with a train of spikes the frequency of which raises as the NMDA conductance increases. No activity is observed after the end of the stimulus. C. When the CAN conductance is activated, the response of the cell is much stronger leading to sustained activity for large NMDA conductances (blue, red, black). Note that the duration of the persistent activity increases along with the increase in the NMDA conductance. The vahdated model was then used to investigate the contribution of NMDA and CAN conductances to the emergence and maintenance of persistent activity. We used a simple stimulation protocol according to which a total of 50 excitatory synapses located in the basal dendrites of the model cell were stimulated for 500ms at a frequency of 20Hz. The model's response was recorded for a total of 10 seconds. As shown in Figure 6A, we found that the 163

7 NMDA conductance alone was not sufficient to induce persistent firing outlasting the duration of the stimulus. Gradual increases in the NMDA conductance were associated with respective increases in the model's firing frequency but in all cases firing stopped after the end of the stimulus. When the CAN conductance was activated (Figure 6B) the model responses became much stronger and activity beyond the duration of the stimulus was apparent for large NMDA conductances. Interestingly, the duration of the persistent firing was positively correlated with the NMDA conductance. These results suggest that the CAN current is necessary for the initiation of persistent firing while the NMDA current plays a modulatory role. B NMDA/AMPA=5 NMDA/AMPA=10 1 see NMD A/AM PA sadp(mv) J.-IO sadp (mv) FIGURE 7. Effect of NMDA conductance on persistent activity properties. A. The sadp is the voltage generated by the activation of the CAN conductance. The sadp needed for initiation of persistent firing decreases as the NMDA conductance increases. B. Contour maps showing the range of persistent activity durations. When the NMDA/AMPA conductance ratio is 5, persistent firing either lasts less than a second or more than 10 seconds. No intermediate durations were observed. When the NMDA conductance is doubled, persistent firing can last anywhere from 1-10 seconds. In both cases, duration probabilities were estimated over 50 trials where stimulated synapses were randomly placed in the basal dendrites. To further investigate the role of the NMDA current, we gradually decreased the CAN conductance for each one of the NMDA/AMPA conductance ratios (I, 3, 5, 10) and measured the least amount of CAN needed in order to have persistent firing. We estimated the CAN effect by measuring the resulting slow After-Depolarization-Potential (sadp). As shown in Figure 7A, the least amount of CAN activation that is needed to induce persistent firing decreases as a function of the NMDA/AMPA conductance ratio, suggesting that increased NMDA conductance lowers the amount of CAN current needed to induce persistent activity. Furthermore, the amount of NMDA current was also found to enhance the range of persistent activity duration. As shown in Figure 7B, for an NMDA/AMPA conductance ratio of 5, persistent firing either lasted less than a second or more than 10 seconds. No intermediate lengths were observed over 50 trials. However, when the NMDA conductance is doubled, persistent firing can last anywhere from I-IO seconds. In both cases, duration probabilities were estimated over 50 trials where stimulated synapses were randomly placed in the basal dendrites. Taken together, our findings suggest that (a) the CAN mechanism is necessary for inducing persistent activity in the PFC model cell, (b) synaptic stimulation, alone, using increasing conductance of the NMDA mechanism does not induce persistent activity, (c) in the presence of both mechanisms, the role of NMDA/AMPA is modulatory: it negatively regulates the amount of CAN needed for persistent activity generation and positively expands the range of persistent activity durations. Persistent Activity in a PFC Reverberating Microcircuit To investigate whether our conclusions regarding persistent activity at the single cell level also hold true in the case of a more reahstic network of PFC neurons, we reduced the morphology of the detailed model cell to 4 compartments (soma, basal dendrite, proximal apical and distal apical dendrite) and built a small reverberating microcircuit. The circuit, shown in Figure 8A, consisted of four pyramidal neurons and one intemeuron model and was connected with autapses, feedforward and feedback synapses as suggested by anatomical data [34]. The intemeuron model was taken from [35] and was shghtly modified so that its basic responses and membrane properties matched those of real layer V PFC intemeurons. 164

8 Initial stimulation Feedforward synapses Feedback synapses Autapses no CAN + CAN FIGURE 8. A. The reverberating microcircuit of PFC neurons. B. CAN conductance was found to enhance the probability of persistent activity generation in the model. The probability was computed for a total of 10 runs. To study the contribution of CAN and NMDA conductances in persistent activity properties in the network model, we used the following stimulation protocol: a total of 50 synapses were distributed in the proximal apical dendrites of each pyramidal neuron and were stimulated 10 times at a frequency of 20Hz. The experiment was repeated 10 times where we varied the precise timing of stimulation among the 50 synapses. NMDA/AMPA=5 + CAN conductance ISI(ms} ISI (ms) T [ FIGURE 9. Effect of CAN and NMDA mechanisms on persistent activity. Al, Bl, CI: Representative traces of neuronal firing during persistent activity when the NMDA/AMPA ratio is 5, 7 and 10, respectively. A2, B2, C2: ISI histograms of a total of 10 runs of persistent activity fitted with the gaussian function when the NMDA/AMPA ratio is 5, 7 and 10, respectively and the CAN conductance is not active. As the NMDA conductance increases, the ISIs distribution becomes narrower and shifts towards smaller values reflecting an increase in frequency and firing regularity. A3, B3, C3: ISI histograms of a total of 10 runs of persistent activity fitted with the gaussian function when the NMDA/AMPA ratio is 5, 7 and 10, respectively and the CAN conductance is active. Activation of the CAN conductance results in further enhancement of the model's firing frequency. 165

9 Using this protocol we found that in the microcircuit persistent activity could be induced in the absence of the CAN mechanism. However, as shown in Figure 8B, the probability for the emergence of persistent activity was greatly enhanced when the CAN current was activated. Furthermore, both NMDA and CAN currents modulated the firing frequency of the sustained activity. As shown in Figure 9, as the NMDA conductance increased, the frequency of persistent firing in the network also increased. Activation of the CAN conductance for different NMDA values had a similar effect whereby the firing frequency was further enhanced. Overall, our study suggests that for the emergence and maintenance of persistent mnemonic activity in layer V of the PFC, the interplay between subthreshold activity associated with the activation of the CAN mechanism, and reverberatory excitation associated with the NMDA mechanism is critical. CLOSING REMARKS In this paper, I presented a few projects from our lab that use detailed compartmental models of single cells and small networks to study information processing and its relation to learning and memory. One of the most important contributions of our work is that it challenges traditional views about the computational capabilities of single cells. For many years neuroscientists believed that the brain's transistor or fundamental processing unit was the neuron itself, which collects and processes incoming signals from neighbouring cells like a simple thresholded perceptron. We predicted, and others verified experimentally, that individual dendrites can do this same task enabhng the neuron itself to become a much more sophisticated computing machine. Our recent work further suggests that single cells may be capable of compacting different types of information about the network signals they receive and reliably transmitting them to their targets. We also predict that a delicate balance between single-cell and network dynamics may underhe the cellular correlate of short term memory. We hope that the insights gained from our modeling work will guide further experiments and open up new avenues for linking computational properties to behaviour, a major challenge for both modelhng and experimental studies of the future. ACKNOWLEDGMENTS This work was supported by the EMBO Young investigator Programme and a Marie Curie Individual Outgoing Fellowship, contract number: PEOPLE IOF-2I9622. REFERENCES 1. Poirazi, P., Brannon, T. and Mel, B.W., Arithmetic of Subthreshold Synaptic Summation in a Model CAl Pyramidal Cell Neuron, : p Poirazi, P., Brannon, T. and Mel, B.W., Online Supplement: About the Model Neuron, Poirazi, P., Brannon, T., and Mel, '8^N., Pyramidal Neuron as 2-Layer Neural Network. Neuron, : p Pissadaki, E.K., and Poirazi, P., Spatiotemporal encoding by a CAl pyramidal neuron model, in preparation. 5. Sidiropoulou, K., Papoutsi, A., and Poirazi, P., Biophysical mechanisms involved in initiating and maintaining persistent activity in PFC pyramidal neuron models, in preparation. 6. Hines, M., and Camevale, N., The NEURON simulation environment Neural Computation, : p Ramon y Cajal, S., Histologie du Systeme Nerveux de L'homme et des Vertebres Maloine. Vol. \ & , 1911, Paris. 8. McCuUoch, W., and Pitts, W., A logical calculus of the ideas immanent in nervous activity.. Bulletin of Mathematical Biophysics : p Magee, J., et al.. Electrical and calcium signaling in dendrites of hippocampalpyramidal neurons. Annu Rev Physiol, : p Hausser, M., N. Spruston, and G.J. Stuart, Diversity and dynamics of dendritic signaling. Science, (5492): p Reyes, A., Influence of dendritic conductances on the input-output properties of neurons. Annu Rev Neurosci, : p

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