Interplay between somatic and dendritic inhibition promotes the emergence and stabilization of place fields

During exploration of novel environments, place fields are rapidly formed in hippocampal CA1 neurons. Place cell firing rate increases in early stages of exploration of novel environments but returns to baseline levels in familiar environments. However, although similar in amplitude and width, place fields in familiar environments are more stable than in novel environments. We propose a computational model of the hippocampal CA1 network, which describes the formation, the dynamics and the stabilization of place fields. We show that although somatic disinhibition is sufficient to form place cells, dendritic inhibition along with synaptic plasticity is necessary for stabilization. Our model suggests that place cell stability is due to large excitatory synaptic weights and large dendritic inhibition. We show that the interplay between somatic and dendritic inhibition balances the increased excitatory weights, so that place cells return to their baseline firing rate after exploration. Our model suggests that different types of interneurons are essential to unravel the mechanisms underlying place field plasticity. Finally, we predict that artificial induced dendritic events can shift place fields even after place field stabilization.


Introduction
The hippocampus encodes spatial representations. A subset of hippocampal pyramidal cells-23 called place cells-fire action potentials when the animal is in a specific location within the environ-24 ment, the place fields [O'Keefe and Dostrovsky, 1971,O'Keefe, 1976,O'keefe and Nadel, 1978 son and McNaughton, 1993]. How these place fields are formed is not clear yet. In particular, imental data open up puzzling questions: 27 Subthreshold responses of silent cells, when recorded at the soma, are not place-tuned [Epsztein 28 et al., 2011]. If a spatially uniform current is applied to silent cells, however, these cells start to 29 produce place-tuned activity [Lee et al., 2012]. This transition from silent to place cell is abrupt. This 30 result suggests that silent cells receive place-tuned inputs but there is no signature of those inputs at 31 the soma. How can silent cells become place cell despite the fact that their subthreshold response 32 is untuned? 33 There is increasing evidence suggesting that place fields are not formed from scratch [Cacucci 34 et al., 2007, Dragoi and Tonegawa, 2011, Dragoi and Tonegawa, 2013, Dragoi and Tonegawa, 2014 2 Results

79
In all simulations, we model CA1 pyramidal neurons as two-compartment, rate-based neurons 80 (figure 1). The neurons have non-linear dendritic units to account for dendritic spikes (figure 1). We 81 assume that place-tuned inputs are projected onto dendrites of all CA1 cells and the propagation of 82 inputs from dendrites to soma is gated by somatic depolarization (figure 1). For the sake of simplic-83 ity, synaptic plasticity depends on presynaptic activity and the postsynaptic dendritic activation only 84 (figure 1, see methods for details). Finally, exploration of novel environments has been shown to 85 modulate CA1 interneuron activity in an interneuron-type-specific manner [Sheffield et al., 2017]. In 86 our model, we hypothesize the existence of a novelty signal and we assume that interneuron activity 87 is modulated by this novelty signal (figure 1, see methods). In particular, dendrite-targeting inhibi-88 tion is decreased in novel environments and slowing returns to baseline. Conversely, soma-targeting 89 inhibition is increased in novel environments followed by a slow decay to baseline. 90 2.1 Somatic disinhibition is sufficient to turn silents cell into place cells 91 We first investigate how silent cells can be transiently turned into place cells through the injec-92 tion of a spatially uniform current. We simulate 10 input neurons, which could be thought of as from dendrites to soma is gated by somatic depolarization.
2.2 Dendritic disinhibition and synaptic plasticity allows silent cells to turn into stable place cells 110 Using our model, we next investigate whether there is an alternative mechanism underlying place 111 field formation of originally silent cells. As before, we simulate 10 input neurons projecting onto one 122 Therefore, our model suggests that the combination of dendritic-activity-dependent synaptic plastic-123 ity and novelty-modulated interneuron activity can turn silent cells into place cells. Interestingly, 124 dendritic activity in simulated CA1 neurons precedes and predicts place field development in silent 125 cells in our model, consistent with the experimental findings of Sheffield et al. [Sheffield et al., 2017]. 126 2.3 Interplay between somatic and dendritic inhibition balances increased ex-127 citatory synaptic weights so that place cells firing rate returns to baseline 128 We then study neurons in our model that are already place cells in a novel environment. As 129 before, our model consists of a CA1 cell receiving place-tuned inputs. But here, the synaptic weights Thus the dendritic inhibition is higher, resulting in a lower activation of the dendritic compartment  We next investigate whether place fields in familiar environments are more stable than at the 147 beginning of the exploration phase in novel environments-despite both having the same amplitude 148 and tuning width. In order to do that, we assume that the place field can be affected by three sources of 149 noise: (i) noise on the place fields of presynaptic neurons, (ii) noise on the firing rates of presynaptic 150 neurons, or (iii) noise on synaptic weights, accounting e.g. for synaptic turnover or synaptic failure 151 (figure 4A). In all three cases, we compare the effect of noise on place fields at the beginning of 152 exploration (figure 4, blue curves) to its effect on place fields at the end of exploration (figure 4, 153 orange curves; see methods). In case (i), we assume that the amplitudes of presynaptic place fields are 154 not all the same. Instead, we multiply each place field by a random number whose variance increases 155 with the noise amplitude (see methods). Of course, the more noise we impose, the less stable place 156 cells are (figure 4A). However, the noise on presynaptic place fields is more effective at destabilizing 157 place cells in the first lap of exploration compared to at the end of exploration (figure 4A), suggesting 158 that place cells become more stable. In case (ii), we assume that all presynaptic place fields have 159 the same amplitude but input neurons can also fire at any time with probability p. This probability 160 increases linearly with noise amplitude. Again, place fields at the final lap are more stable than initial 161 place fields (figure 4B). In case (iii), we change synaptic weights by random amounts whose variance 162 is proportional to the noise amplitude. This source of noise also affects initial place fields more 163 than it does to final place fields ( figure 4C). In all three cases, the stabilization of place fields results 164 from increased synaptic weights and higher dendritic inhibition (figure 3F). Therefore, place fields in 165 familiar environments are more stable to noise than place fields at the beginning of novel environment 166 exploration, consistent with experimental observations [Cohen et al., 2017].

167
In order to investigate the role of each component of the network in stabilizing place fields, we 168 artificially modify the final state of the network while keeping the neuron's place field unchanged. We

175
In summary, strong synaptic connections are relatively less affected by noise on synaptic weights, 176 whereas higher dendritic inhibition cancels out-of-field fluctuations being transmitted from presynap-177 tic neurons. 178 We next investigate whether dendritic nonlinearity can contribute to stable place field develop-179 ment. In our model, when inputs are strong enough, they can induce dendritic spikes, which in turn 180 lead to strong potentiation. As such, dendritic spikes-or dendritic nonlinearities-might form a 181 mechanism for reliably selecting presynaptic inputs. To test this hypothesis, we simulate our model 182 with initially uniform synaptic weights and no novelty signal. We then compare it with an alternative 183 model where dendrites do not have a nonlinearity but can reach the same maximum level of activ-  figure 2D). Contrarily, neurons with dendritic nonlinearity consistently develop stable place fields.
188 Therefore, our model suggests that dendritic nonlinearities might contribute to place field develop-  Using our model, we next explore whether it is possible to perturb or change single CA1 place 192 fields. We simulate a single neuron receiving place-tuned input such that one of its input synapses is 193 stronger than the remaining connections. We assume that the animal is exploring a novel environment.
As such, interneuron activity is modulated by a novelty signal that decays over time (figure 5A, see 195 methods). The stronger synaptic weight leads to the activation of our neuron, which leads to the 196 strengthening of that synaptic weight. This positive feedback loop leads to the development of a 197 strong place field (figure 5B). 198 We then test whether we can shift the tuning of the place field towards a new location by artificially 199 activating CA1 neurons. In order to do that, we simulate the network until the novelty signal is in the case where there is remaining dendritic activity. This dendritic activity allows for plasticity, 210 and therefore for the re-emergence of a place field (supplementary figure 3). Altogether, our model 211 predicts that, if induced over enough laps, artificial dendritic activity can shift place field location.

212
The size of the induction region might affect the efficacy to shift place field location. To investigate 213 this, we increase the induction area to twice its original size. In this case, the induction over three 214 laps is enough to remove the initial place field, but not enough to induce the formation of a new 215 one (figure 5E). Induction over 30 laps-which is enough to induce the development of a new place 216 field for a small induction area-is not enough to promote the development of a new place field 217 (figure 5F). The larger the induction area, the easier it is to remove the initial place tuning (figure 5G).

218
Nevertheless, a large induction area leads to a competition between inputs within that area. Because 219 of that, our model predicts that, surprisingly, the larger the induction region, the more induction laps 220 are needed to induce the development of new receptive fields (figure 5H). 221 We next compare the induction of place field shift in novel and familiar environments. We hy-222 pothesize that in novel environments, place fields should be more plastic and, therefore, it should be 223 easier to induce a shift in place field location. In order to test this, we induce dendritic activity on the 224 second lap. As shown above, the induction protocol in familiar environments has to be applied over 225 several laps to successfully induce place field shift. In novel environments conversely, applying the 226 induction protocol over a few laps is enough to induce the development of a new place field. Indeed, 227 the induction of dendritic activity over 1-2 laps is sufficient to shift place field location (figure 5I-J).

228
As initially hypothesized, our model indicates that we need fewer induction laps to induce place field we induce dendritic activity within a region far from the peak of the neuron's place field. Since the 238 modulation of inhibition is applied over the entire environment, there is an increase in both within-239 field and out-of-field firing rate. Accordingly, the shift in place field location is harder than in the 240 case without manipulation of inhibition (figure 5K). We conclude that, surprisingly, resetting inhi-241 bition to novel environment levels is not enough to make place fields plastic again. Indeed, overall 242 manipulation of inhibition reinforces stable place fields by increasing within-field activity.

243
In summary, our model suggests that single-cell place fields can be shifted under the induction 244 of dendritic activity. Our model predicts that small induction areas are more efficient to induce the 245 development of new place fields. Induction in novel environments is also more efficient than in 246 familiar ones. Counter-intuitively, resetting novel environment level of inhibition represses place 247 field plasticity. We propose a model of the hippocampal CA1 place cells in which interneuron activity is mod-250 ulated by novelty in an interneuron-type-dependent manner. Using our simulations, we identify the 251 potential mechanisms underlying the evolution of place fields and the transition from silent to place 252 cells in novel environments. During the initial stages of exploration of novel environments, dendritetargeting inhibition is reduced whereas soma-targeting inhibition is increased. The reduction in den-254 dritic inhibition opens a window for plasticity, leading to the formation and stabilization of receptive 255 fields. We then show that place fields are more stable in familiar environments than in novel envi-256 ronments. Our simulations suggest that this extra stability is due to stronger synaptic weights and 257 increased dendritic inhibition. Our model makes predictions on how to perturb place fields by den-258 dritic activation. In our model, dendritic activation can shift place field location. We predict that this 259 shift is easier if the dendritic activity is induced only within a small region of the environment. We 260 also predict that it is easier to induce place field shift in novel than in familiar environments. Our 261 model, albeit simple, provides a mechanism for several features of the CA1 network and provides 262 testable predictions.

263
The modulation of interneuron activity during exploration of novel environments is thought to be can also be responsible for controlling plasticity at CA1 pyramidal neurons.

279
Place cell firing rate has been shown to increase rapidly following exposure to novel environ-280 ments [Frank et al., 2004, Cohen et al., 2017. As suggested by Cohen et al. [Cohen et al., 2017], 281 this increase is associated with increased excitatory inputs onto CA1 pyramidal cells in our model.

282
Through exploration, pyramidal cell firing rate returns to baseline levels in familiar environments.

283
This later reduction in place cell firing rate has been suggested to be associated with a reduction in  al., 1996, Kentros et al., 1998, Cacucci et al., 2007. The increase in dendritic inhibition in familiar 294 environments in our model induces a reduction in dendritic events and, thus, a reduction in plasticity-295 induced changes in place fields. Additionally, the combination of weak out-of-field inputs and strong 296 dendritic inhibition leads to higher robustness to noise. Overall, place fields stabilize following the   We use two-compartment, rate-based neuron models. Each neuron is modeled as two compart-315 ments: one representing the soma and another representing the dendrites. The dendritic compart-316 ment's activity, r dend , is determined by where τ 0 is a time constant, R i is the firing rate of neuron i in the presynaptic layer, w i is the synaptic 318 weight from a neuron in the presynaptic layer, I dend is the input from dendrite-targeting interneurons- where I soma is the input from soma-targeting interneurons-simulating PV+ interneuron inputs-and 329 N th is the threshold for somatic activation.
where η ex is the learning rate of excitatory connections, η homeo is the learning rate of the homeostatic 337 term, and θ homeo is a target homeostatic constant. The simulated CA1 neurons receive feedforward input from N pre neurons. These input neurons 340 are tuned to specific locations and their firing rates span over the entire environment. All the place 341 fields of input neurons have the same tuning width, σ pre , and the same amplitude, A pre . We assume 342 that the animal explores an annular track of length L with speed v. The firing rate of an input neuron 343 with place field centered at p 0 is where p is the animal's position, and d is the distance, along the track, between the animal's position 345 and the center of the place field.

Novelty signal
When simulating the exploration of a novel environment, we assume that the interneuron activity 348 changes over time and is interneuron-type specific. We define a quantity, named novelty signal, that where I ∞ is the inhibitory activity in familiar environments, and I 0 is the initial inhibitory activity in 353 novel environments. The initial level of dendritic inhibition is assumed to be lower than its level in 354 familiar environments, I 0 dend < I ∞ dend . The initial level of somatic inhibition is assumed to be higher 355 than its level in familiar environments, I 0 soma > I ∞ soma . rescale this place field such that its peak is set to 1; (5) we change the state of the network by adding 362 noise to it (see below); (6) we repeat (2)-(4); (7) we calculate the absolute distance between the two 363 rescaled receptive fields; (8) we repeat (6)-(7) N noise times and take an average over all samples (sup-364 plementary figure 5). To measure the effect of noise in familiar environments, we follow the same 365 steps but using the state of the network at the beginning of the last lap (lap 50) in step (1).

366
We assume that place fields can be affected by three sources of noise: (i) noise at presynaptic place 367 fields, (ii) noise at presynaptic firing rates, and (iii) noise at synaptic weights. In case (i), we multiply    1996). Impaired hippocampal representation of space in ca1-specific nmdar1 knockout mice.    , input synaptic weights are weak, dendritic inhibition is low and somatic inhibition is high. During the final lap (right, orange), some input synaptic weights are strong, dendritic inhibition is high and somatic inhibition is low. Therefore, although place field amplitude and width are the same in the first and last lap (D blue and orange), the network is in a different state. Effect of noise on place fields for the first (blue) and last (orange) laps of exploration. (A) Destabilization of place fields by noise on presynaptic place fields. We measure the change on postsynaptic place field following changes on presynaptic place field amplitudes (see methods). (B) Destabilization of place fields by noise on presynaptic firing rates. We measure the change on postsynaptic place field following the addition of a noisy input to presynaptic neurons (see methods). (C) Destabilization of place fields by noise on synaptic weights. We measure the change in postsynaptic place field following changes on synaptic weights (see methods). For all three sources of noise (A-C), the effect of the noise over place fields is higher in the first lap than in the last lap. . Red curve shows the evolution of the novelty signal over laps. The novelty signal resetting leads to a reduction in dendritic inhibition across the whole track. Therefore, the in-field activity increases, leading to the reinforcement of the initial place field.