A computational grid-to-place-cell transformation model indicates a synaptic driver of place cell impairment in early-stage Alzheimer’s Disease

Alzheimer’s Disease (AD) is characterized by progressive neurodegeneration and cognitive impairment. Synaptic dysfunction is an established early symptom, which correlates strongly with cognitive decline, and is hypothesised to mediate the diverse neuronal network abnormalities observed in AD. However, how synaptic dysfunction contributes to network pathology and cognitive impairment in AD remains elusive. Here, we present a grid-cell-to-place-cell transformation model of long-term CA1 place cell dynamics to interrogate the effect of synaptic loss on network function and environmental representation. Synapse loss modelled after experimental observations in the APP/PS1 mouse model was found to induce firing rate alterations and place cell abnormalities that have previously been observed in AD mouse models, including enlarged place fields and lower across-session stability of place fields. Our results support the hypothesis that synaptic dysfunction underlies cognitive deficits, and demonstrate how impaired environmental representation may arise in the early stages of AD. We further propose that dysfunction of excitatory and inhibitory inputs to CA1 pyramidal cells may cause distinct impairments in place cell function, namely reduced stability and place map resolution.

content is reduced [38]. 67 The model we present here is to our knowledge the first grid-cell-to-place-cell 68 transformation model able to recapitulate the dynamics of CA1 place cell behaviour 69 over long timescales, including long-term persistent place fields and stable place cell 70 density [39][40][41][42][43]. Our modeling results provide strong support for the hypothesis that 71 synaptic dysfunction drives cognitive impairment in early AD by disturbing the firing 72 homeostasis of cortico-hippocampal circuits [15,44,45]. We further predict that 73 excitatory and inhibitory synaptic dysfunction have distinct effects on place cell 74 function in AD, suggesting a direction for future experimental work. 75

76
To study the effect of AD-related synapse loss on hippocampal place coding, we 77 simulated a population of CA1 pyramidal cells, which received excitatory input from 78 grid cells and inhibitory feedback from interneurons, beginning from the model of Acker 79 et al. [28]. Place cell function was analysed in a 1 m linear environment, with cells 80 characterised by their firing rates within each 1 cm bin along the track. The model was 81 constrained to parameters that reproduced key characteristics of long-term CA1 place 82 coding (see Methods). We then analysed and contrasted the effect of progressive 83 excitatory and inhibitory synapse loss on network function to examine whether 84 AD-related synapse loss may induce impairments in place cell function. 85 Key requirements for long-term stability of CA1 place cell 86 dynamics 87 In order to simulate place cell function over time, we implemented a 88 grid-cell-to-place-cell transformation model previously described by Acker et al. [28]. In 89 line with the recently established mean synapse lifetime of only 10 days in CA1 [46,47], 90 the model employed daily synapse turnover and demonstrated that Hebbian plasticity is 91 sufficient to stabilize place fields, suggesting that memory can persist in the correlation 92 structure of a dynamic network [48]. Improved feedback inhibition and synaptic plasticity 103 Interneuron-mediated feedback involved inhibition of pyramidal cells with firing rates 104 below a given fraction of the highest firing rate. However, cell activities were compared 105 across the entire track, whereas interneuron-mediated feedback is hypothesised to be 106 precisely temporally coordinated, generating gamma-frequency rhythms [50,51]. To 107 better approximate this, feedback inhibition was restricted to individual bins along the 108 track, which promoted firing in positions of low general activity with otherwise low constraints on synaptic weights and weight change, however, these approaches 114 diminished stability, causing strongly fluctuating place cell numbers with no long-term 115 stable cells. 116 To introduce additional homeostatic constraints, Hebbian learning was replaced by 117 the Bienenstock-Cooper-Munro (BCM) learning rule [52]. BCM learning relies on basic 118 Hebbian principles but incorporates a dynamic threshold for weight change that 119 depends on recent postsynaptic activity and enables bidirectional modification of 120 synapse strength. Consequently, high firing rates increase the threshold for potentiation 121 and may result in synaptic depression instead, thus increasing competition. Under BCM 122 learning, the rate of novel place field formation increased slightly, but not sufficiently, to 123 balance place field loss.

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Unsuccessful strategies to stabilize place field density 125 As most forms of synaptic homeostasis observed experimentally operate over hours or 126 days [53,54], the rate of homeostasis was reduced. Multiplicative synaptic scaling does 127 not allow for the homeostasis rate to be adjusted, so subtractive normalization was 128 implemented. Under subtractive normalization, all synapses converging onto a neuron 129 are changed by the same magnitude to keep the total synaptic input fixed, rather than 130 weight adjustments being proportional to individual strength [55], thereby generating 131 more competition [56]. Here, the sum of weights converging onto each cell rarely 132 stabilized at the homeostatic point, as this would have required negative weights, yet the 133 subtractive decay term was not sufficient to effectively limit growth of relatively stronger 134 weights. Thus, subtractive normalization did not elicit the desired weight stabilization. 135 Incorporation of multiple enclosures was motivated by theories that place fields from 136 different enclosures may 'mix' in familiar environments [57]. Running sessions in novel 137 environments, represented by distinct grid cell arrangements [34], induced new place 138 fields that were retained in the familiar environment through their effects on synaptic 139 weights. However, continuous introduction of new enclosures was required to prevent 140 stabilization at a specific subset of place cells, but still resulted in a general decline with 141 occasional spikes in place cell number. These spikes were likely mediated by close 142 correspondence of the novel and familiar grid inputs, facilitating rapid place field 143 formation. 144 It has also been proposed that the co-existence of more and less stable stimulus 145 responses may result from a diversity in synaptic plasticity [58]. Indeed, applying 146 diverse learning rates across cells resulted in more place field formation than the BCM 147 rule alone, however, again, it was not sufficiently high for stabilization. Furthermore, 148 there was a stronger afferent synaptic strength divide, such that cells with slow 149 plasticity were generally outcompeted.

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Stable place cell density through improved connectivity 151 The CA1 network was scaled according to relative cell and synapse numbers in the rat 152 [59] (Fig 2A), as there was less extensive data available for the mouse. Layer III of the 153 EC is estimated to consist of 250,000 principal cells, 80% of which are spatially tuned 154 [60,61]. Using estimated CA1 population sizes [59], this gives a pyramidal to grid cell 155 ratio of 1.5575:1 and a pyramidal cell to interneuron ratio of 8:1. Due to the vast 156 diversity and incomplete functional characterisation of interneurons, a single As a result of lower excitatory synaptic density, pyramidal cell firing rates were lower 160 but remained stable. The mean firing rate over 365 days was 0.52 Hz, with a range of 161 0-8.23 Hz, which corresponds closely to mean firing rates detected previously in CA1 162 place cells in vivo [62][63][64][65]. Interestingly, the network reproduced the stable place cell 163 density observed experimentally, with cells dynamically losing and gaining place fields 164 (Fig 2B-C). On average, 61% of cells were active each day, 72% of which formed 165 significant place fields. Place field width ranged between 5 − 40 cm with a mean width 166 of 12.6 cm ( Fig 2D). As some cells fired throughout most of the track but there were no 167 place fields of intermediate width (Fig 2D), cells with firing fields of > 50 cm were not 168 classified as place cells. The probability of recurrence of place cells with place fields that have drifted less 173 than 5 cm between any two sessions, a measure of how likely it is for a cell to retain its 174 place field, decreased from 98% and 51.9% for sessions 5 and 30 days apart, respectively, 175 to 32% and 17.2% in the new model (Fig 2B). At stable place cell density, this indicates 176 increased variability in the place cell ensemble.

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At sufficient network size, determined to be approximately 5,000 grid cells and 7,788 178 pyramidal cells, the general features of the model are robust to cell number changes.

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The general features are also robust to the choice of inhibition model, although using 183 an 'E%-max' inhibition model, in which cells whose firing rate is within 10% of the most 184 excited cell escape inhibition, as opposed to a 'winner-takes-all' model, increases the 185 proportion of place cells due to lower competition (winner-takes-all: mean ± SEM 186 = 29.0% ± 0.2%; E%-max: 43.8% ± 0.1%). The 'E%-max' model was used here as it 187 accounts for feedback delay [66].  Synaptic scaling led to a compensatory increase in the mean and range of synaptic 199 weights (Fig 4B), which likely mediated the relatively small reduction and increased 200 variability of mean firing rates.

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The proportion of place cells decreased (Fig 4A), while the remaining cells retained a 202 constant place field width (mean ± SEM = 12.6 ± 0.02 cm). The reduced number of 203 place cells may have slightly diminished coverage of the environment. In addition, the 204 probability of recurrence of active cells and place cells between sessions 20 days apart, 205 declined over time (Fig 4C-E), indicating lower stability. Although the proportion of place cells increased, the fraction of active cells that form 222 significant place fields decreased from 92.5% to 85.7% between days 20-360. This is 223 likely linked to increased activity, as the proportion of cells with multiple place fields 224 (mean ± SEM days 200-360: wildtype = 2.9% ± 0.09%; IN-PC loss: 3.6% ± 0.1%), 225 which did not classify as place cells, and cells that were active throughout most of the 226 track ( Fig 5D) increased over time.

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In addition to more place field formation, the mean place field width slightly 228 increased (Fig 5B-D), indicating a reduced place map resolution.  (Fig 3D). 236 In addition to a progressive increase in the proportion of highly active cells (Fig 3D), 237 more frequent changes in the firing rate could be observed (Fig 6). For instance, in the 238 wildtype just under half of all silent cells remained silent across sessions 20 days apart, 239 while this was only true for a third of cells in the synapse loss model. Nevertheless, 240 activity shifts were mostly gradual in both models, as exemplified by most new highly 241 active cells coming from the pool of 'intermediately active' cells ( Fig 6). The proportion of place cells remained constant over time (mean ± SEM 243 = 43.5% ± 0.01%) (Fig 7A), despite increased activity. There was a gradual increase in 244 mean place field width (day 20: mean ± SEM = 12.7 ± 0.1 cm; day 360: 245 13.8 ± 0.1 cm) (Fig 7B) comparable to the inhibitory synapse loss model (day 360: 246 13.7 ± 0.1 cm). Furthermore, there was more variability and abnormal place field sizes 247 (Fig 7B), likely mediated by a lack of inhibition in conjunction with lower excitatory 248 input.

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As in the excitatory synapse loss model, the recurrence probability of place cells was 250 gradually reduced (Fig 7C-E). Place cell density was maintained by a slight increase in 251 new place cells (mean ± SEM for days 40-360: 18.8% ± 0.1%, wildtype: 252 17.8% ± 0.1%) (Fig. 7A).  To increase place field formation, interneuron-mediated feedback on more plausible 265 timescales and BCM learning were implemented. While Hebbian plasticity is dominantly 266 used in place cell models, the BCM rule has also been shown to support place coding 267 [71,72]. However, to enable temporal competition using the BCM rule, the rate of 268 synaptic change must be substantially slower than the rate of input presentation, which 269 requires extensive environmental sampling [52]. In contrast, computational modelling 270 suggests fast synaptic changes are required to generate place fields at a realistic 271 timescale [73]. This implies that place coding may involve a learning scheme other than 272 the BCM rule, or multiple learning schemes depending on the input. Alternatively, de 273 Almeida et al. [27] have proposed that place field formation may not rely on synaptic 274 plasticity, except for refinements and long-term stability. They demonstrated place field 275 formation in a grid-cell-to-place-cell model without learning, consistent with close to 276 normal CA1 place coding during exploration in mice with non-functional 277 N-methyl-D-aspartate-receptors (NMDARs), despite exhibiting an NMDAR-dependent 278 form of long-term potentiation [74]. Furthermore, features of BCM learning have been 279 observed in the hippocampus, most notably a dynamic postsynaptic-activity-dependent 280 threshold for synaptic strengthening [75,76]. As such, BCM-like learning remains a 281 plausible alternative to Hebbian learning and has successfully produced the desired 282 grid-cell-to-place-cell transformation at the timescale considered here.

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Place cell density was stabilized using a more biologically plausible connectivity, 284 thereby facilitating more realistic feedback inhibition and more dynamic grid cell input 285 through lower synaptic density.

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Our model also incorporated synaptic scaling, for which underlying biophysical 287 mechanisms have been identified, including activity-dependent modulation of glutamate 288 receptor expression [77]. While homeostatic mechanisms operate at a slower timescale 289 in vivo, modelling studies commonly speed up homeostasis to stabilize Hebbian learning 290 [78][79][80]. The mechanisms underlying this temporal contradiction between Hebbian 291 plasticity and homeostasis remain unclear, however, proposed explanations include a yet 292 unidentified rapid compensatory process [78].

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In mice, it has been reported that 31% of CA1 pyramidal cells are active, while 20% 294 form significant place fields in an environment [43]. While comparisons are difficult due 295 to differences in experimental setup and the possibility of missing silent cells in in vivo 296 recordings, our model, with 61.0% active cells and 43.8% place cells, likely involves a 297 higher proportion of place cells than is observed in vivo, even compared to rat estimates 298 [81,82]. As the fraction of active cells and place cells decreased with increasing cell 299 numbers, this may be due to the small network size.

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Place map stability, with a recurrence probability of place cells of 32% and 17% for 301 sessions 5 and 30 days apart, respectively, is comparable to experimental values of 25% 302 October 8, 2020 14/29 and 15% [43]. As observed in vivo, the recurrence probability was found to only be 303 moderately time dependent.

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The mean place field size of 12.6 cm was relatively small, with reported lengths in 305 1m linear tracks ranging between 20 − 25 cm [43,83]. Place fields are generally smaller 306 in computational models [28,29,84] and it has been argued that grid cell inputs may 307 not be sufficient to produce realistic field sizes without additional input from weakly 308 spatially-modulated cells or recurrent connections among CA3 place cells [85]. In some 309 studies, place field size has been increased by adjusting the grid scale [29,84]. Thus, 310 there are multiple strategies that may enable more realistic place field sizes, however, 311 such discrepancies in spatial scale are unlikely to significantly affect the network 312 properties [29]. 313 Ziv et al. [43] have found that place cells generally maintain identical place fields in 314 vivo, whereas our model exhibited a high level of remapping, prompting strict positional 315 constraints on place fields considered 'identical' across sessions. The proportion of new 316 cells within the place cell ensemble increased with cell number (7,788 pyramidal cells: and in AD patients [67,68]. Despite synaptic scaling, the median firing rate decreased 323 and there was more firing variability. The decreased activity may have also impacted 324 interneuron function by lowering the inhibition threshold, thereby providing an 325 additional buffer for the firing rate. Lower mean firing rates in combination with some 326 highly active neurons have also been observed in the CA1 region of 3xTg and APP/PS1 327 mice, in which this was accompanied by lower entropy, a measure of firing pattern 328 diversity, indicating reduced coding capacity [86,87].

329
There was a lower proportion of place cells compared to the wildtype, which has also 330 been observed in 6-months-old APP/PS1 and APP-KI mice [23,24]. Our model also 331 suggests that excitatory synapse loss could mediate reduced stability of place maps. As 332 reduced stability coincides with spatial memory impairments in APP-KI and 3xTg mice 333 [23,87], which also exhibit synaptic abnormalities [88,89] but have normal place field 334 sizes [23,87], it may be a key mechanism contributing to memory deficits in AD.

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Inhibitory synapse loss may link hyperactivity to reduced map 336 resolution 337 As interneurons play a key role in the spatiotemporal control of neuronal activity 338 [15,90], disturbances of which correlate strongly with cognitive deficits [24,91,92], the 339 'GABAergic hypothesis', which suggests impaired inhibition may be a critical link 340 between the diverse dysfunctions occurring in AD, has gained popularity in recent years 341 [15].

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The increase in firing rate, proportion of highly active cells and cells that were active 343 throughout the whole track is consistent with the hyperactivity observed in CA1 in vivo 344 [93]. Place fields were larger and showed increased variability compared to the wildtype, 345 as has been observed in Tg2576 and APP/TTA mice in conjunction with lower spatial 346 information content [22,25]. Increased place cell number and place field size indicate a 347 lower resolution place map, as hypothesised to occur in experimental models [25].
Excitatory and inhibitory synapse loss may distinctly contribute 349 to network dysregulation 350 Korzhova et al. [94] recently identified a progressive increase in activity of 351 intermediately active cells as the primary source of highly active neurons in the cortex 352 of APP/PS1 mice, which was also observed in our model, supporting their hypothesis 353 that network pathology may stem from stable aberrant activity of single cells.

354
When both excitatory and inhibitory synapses were affected, the resolution and 355 stability of the place map were significantly diminished, accompanied by increased 356 neuronal activity. This combination of dysfunctions has also been detected in an APP 357 transgenic model [25], and in a mouse model overexpressing synaptojanin-1 (Synj1), a 358 regulator of synaptic function, which has been implicated in AD [95,96]. This provides 359 further support for synaptic dysfunction underlying place cell abnormalities and suggests 360 that both excitatory and inhibitory synaptic dysfunction contribute to place cell 361 dysfunction in AD and produce distinct impairments in environmental representation. 362 Implications for future work 363 The causative link established here between synaptic dysfunction and cognitive 364 impairments is in line with current theories implicating impaired functional connectivity 365 as the major driver of AD pathogenesis [15,19,45].

366
Based on our findings, we predict that hyperactivity in CA1 should coincide with 367 place cell abnormalities and spatial impairments. Furthermore, we hypothesise that 368 impaired spatiotemporal control of pyramidal cell firing by interneurons may be a major 369 contributor to abnormal place field size. Similarly, decay of excitatory EC inputs may 370 underlie reduced ensemble stability. An experimental study employing EC lesions 371 supports our finding that place map stability is reduced in the absence of such inputs, 372 however they also reported increased place field sizes [97]. Recent evidence suggests 373 pyramidal cells in EC layer II also directly innervate CA1 interneurons and that 374 synapses between these populations are selectively lost in Tg2576-APPswe mice [98].

375
The Tg2576-APPswe model had enlarged place fields, which could be rescued by 376 optogenetic activation of the EC-interneuron synapses. As such, place field enlargement 377 in response to EC lesions may have been mediated by impaired interneuron function.

378
The relative contribution of excitatory and inhibitory synapse dysfunction in AD is 379 still unclear but may enable the identification of new therapeutic targets. Due to the 380 high inter-connectivity within the hippocampal circuit, addressing this question 381 experimentally requires precise silencing of synaptic transmission, however silencing 382 with the required spatiotemporal control is challenging, potentially limiting the 383 feasibility of such experiments [99].

384
Potential extensions to the model 385 A biophysical model would enable examination of other interesting network properties 386 observed in AD, such as hypersynchrony [100]. The model could also be further 387 improved by including synaptic weights, synaptic homeostasis and an explicit firing rate 388 for the interneurons, ideally also accounting for the diversity of interneuron types in 389 CA1. Homeostatic inhibitory mechanisms, including altered receptor levels and 390 GABAergic synaptic sprouting have been reported in vivo [101,102]. Furthermore, it 391 would be interesting to extend the model to incorporate place cell remapping, as this 392 has been found to be impaired in AD [23].

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A general limitation of grid-cell-to-place-cell feedforward networks is recent evidence 394 for place-cell-to-grid-cell feedback, including the disappearance of grid cell firing in 395 response to place cell inactivation, although the function of this feedback remains 396 unclear [103]. Furthermore, recent experimental findings have challenged the view that 397 grid cells are the major determinant of place field formation, including the formation of 398 place fields after grid cell disruption [97,104] and the earlier emergence of place cell 399 firing during rat development [105,106]. Input from subcortical structures, the pre-and 400 parasubiculum and CA3 have all been found to contribute to the spatial tuning of CA1 401 place fields [30,[107][108][109]. Spatial input from CA3, for instance, is essential for rapid 402 contextual learning in novel environments, temporal coding at the population level and 403 memory retrieval [38,110]. In light of this evidence, Bush et al. [30] have proposed that 404 place cell firing is determined by a variety of sensory inputs, with grid cells providing 405 complementary self-motion-derived input to support precise navigation. However, the 406 relative contribution of different cell populations to CA1 place coding remains subject 407 to active research and may even be dynamic, varying with condition or state [111].

408
While synaptic loss has been found to occur prior to the formation of amyloid 409 plaques [112], plaque proximity-dependent loss has been reported in mouse models 410 [113][114][115]. As such, it would also be interesting to explore the effect of concentrated 411 areas of synaptic loss. In addition, shrinking cell population sizes, affecting interneurons 412 as early as 6-to-12-months of age, have been detected in vivo [70,[116][117][118], and may 413 contribute to network dysfunction.
414 Overall, our model shows that synapse loss in CA1 is sufficient to generate the 415 network abnormalities observed in experimental models and AD patients, including 416 hyperactivity [93,100]. Furthermore, the resulting network abnormalities were shown to 417 induce place cell dysfunction, which has been hypothesised to underlie spatial memory 418 impairment in AD. Thus, our model shows synapse loss is sufficient to drive progressive 419 network dysfunction and impaired spatial representation.

421
Grid cell simulation 422 We simulated a 1 metre linear track, with cells characterized by their firing rate in each 423 1 cm bin. Grid cells were simulated as described by Blair et al. [119] (Eq 1), such that 424 their firing rate varied in a hexagonal grid with orientation, phase and offset randomly 425 chosen from a uniform distribution, where x j (p, λ, θ, c) is the firing rate of grid cell j at position p with inter-vertex spacing 427 λ, angular offset θ and spatial phase c. λ varies between 30 − 100 cm, c ranges between 428 0 − 100 cm and θ ranges between 0 − 60°. '·' indicates the dot product operator. θ k is 429 given by (cos (θ k ), sin (θ k )), such that the cosine function gives a pattern of alternating 430 maxima and minima in direction θ k . The hexagonal grid is generated by the sum of Pyramidal cell simulation 435 Pyramidal cell activity was modelled as the sum of excitatory grid cell inputs [27], where y i (p) is the firing rate of pyramidal cell i at position p in Hz, x (p) is the vector 437 of firing rates of all grid cells that project to pyramidal cell i, at position p, and w i is 438 the vector of synaptic weights converging onto pyramidal cell i.

440
The initial weight w ij (s) of a synapse between grid cell j and pyramidal cell i was 441 assumed to vary with synaptic area s ranging between 0 − 0.2 µm 2 , as described by de 442 Almeida et al. [27], The probability density of the synaptic area of excitatory synapses onto granule cells in 444 the model is given by [27] 445 with A = 100.7, B = 0.002, σ 1 = 0.022 µm 2 , σ 2 = 0.018 µm 2 , and σ 3 = 0.15 µm 2 , as 446 determined by Trommald and Hulleberg [120]. therefore fire earlier within each cycle [28]. Two modes of inhibition were employed, as 456 specified: in the 'winner-takes-all' mode, only the most excited cell escaped inhibition, 457 while in the 'E%-max' mode, cells were inhibited if their firing rate was not within some 458 fraction of the excitation of the most excited cell [27]. E% was approximated to 459 account for feedback delay, determined by the ratio of the membrane time constant to 460 the time lag between a cell spiking and the incidence of feedback inhibition, which 461 approximately gives E% = 10% [66].

462
The feedback inhibition mechanism initially compared pyramidal cell firing rates 463 across the entire track. As specified in the Results section, the feedback inhibition cycle 464 was shortened by incorporating position-specific inhibition within each bin along the 465 track.

466
Thus, a pyramidal cell was inhibited when the condition was satisfied, where y i (p) is the the firing rate of pyramidal cell i at position p, k  information from all pyramidal cells and projecting to a single cell each.

478
Where specified in the Results section, the network architecture was updated to fit 479 experimental data on relative cell and synapse numbers in CA1 [59]. The network 480 architecture was scaled to 5,000 grid cells, such that there were 7,788 pyramidal cells Where specified, synaptic weights w ij between grid cell j and pyramidal cell i were 486 updated once a day using Hebbian learning, where x j (p) is the firing rate of grid cell j at position p, y i (p) is the firing rate of place 488 cell i at position p, and η = 0.003 is the learning rate [28].

BCM learning 490
Where specified, synaptic weights were instead updated once a day according to the 491 BCM rule [52], 492 dw ij dt = x j (p) φ (y i (p) , ξ) , where ξ = (ȳ i y0 ) if φ (y, ξ) ≥ l φ (y, ξ) , otherwise. (8) Homeostatic mechanisms 495 Multiplicative scaling was applied to synaptic weights after each update by dividing by 496 the sum of all weights converging onto each pyramidal cell and multiplying by the 497 expected sum of synaptic strengths [121]. This value corresponded to the expected 498 value of the sum of n random draws from the empirical distribution of weights, where n 499 is the number of synapses converging onto each cell.

500
Where specified, subtractive normalization was instead applied after Hebbian 501 learning [122] 502 where θ homeo = 50 and η homeo is the homeostatic learning rate, set to 0.1 of the 503 Hebbian learning rate to mimic the relative temporal timescale of Hebbian plasticity 504 and homeostatic mechanisms in the hippocampus [78].

505
Synapse turnover 506 Synapses were turned over once a day to achieve a mean synapse lifetime τ of 10 days 507 [46]. The number of synapses replaced per cell was derived using the exponential decay 508 model 509 where N (t) and N 0 are the number of synapses on day t and 0, respectively, and the 510 number of synapses replaced per cell corresponds to N 0 − N (t). Naive synapses received 511 random weights from the synaptic strength distribution. In the scaled model, 512 interneuron-to-pyramidal-cell connections were turned over at the same rate.

514
Loss of grid-cell-to-pyramidal-cell synapses and interneuron-to-pyramidal-cell synapses 515 were implemented individually and in combination, as specified, to analyze the effects of 516 excitatory and inhibitory synapse loss on place cell function.

517
Interneuron-to-pyramidal-cell synapse loss due to axonal loss in the APP/PS1 model 518 [69] was implemented by eliminating a fraction of randomly chosen synapses each day 519 using the quadratic regression for the change in the number of synapses ∆S(T ) at 520 timepoint T months from the first running session, 521 ∆S(T ) = −0.0532T 2 − 2.2179T.

524
Place field analysis 525 A significant place field was defined as a single continuous region of 5 − 50 cm (see 526 Results section), in which the cell's firing rate was within 20% of the its maximum firing 527 rate during the running session [28]. For calculating the probability of recurrence of a 528 place cell, a place field was deemed to have been maintained across sessions if the