Modelling vasopressin synthesis and storage dynamics during prolonged osmotic 1 challenge and recovery based on activity dependent upregulation of mRNA 2 transcription 3

11 12 Hypothalamic vasopressin neurons are neuroendocrine cells which form part of the 13 homeostatic systems that maintain osmotic pressure. In response to synaptic inputs 14 encoding osmotic pressure and changes in plasma volume, they generate spike 15 triggered secretion of peptide hormone vasopressin from axonal terminals in the 16 posterior pituitary. The thousands of neurons’ secretory signals generate a summed 17 plasma vasopressin signal acting at the kidneys to regulate water loss. Vasopressin is 18 synthesised in cell bodies, packaged into vesicles, and transported to large stores in 19 the pituitary terminals. Supported by activity-dependent upregulation of synthesis and 20 transport, these stores can maintain a secretion response for several days of elevated 21 osmotic pressure, tested by dehydration or salt loading. However, despite upregulated 22 synthesis, stores gradually decline during sustained challenge, followed by a slow 23 recovery. With no evidence of a store encoding feedback signal, previous modelling 24 explained these synthesis dynamics based on activity-dependent upregulation of 25 transcription and mRNA content. Here this model is adapted and integrated into our 26 existing spiking and secretion model to generate a neuronal population model, able to 27 simulate the secretion, store depletion, and replenishment, response to sustained 28 osmotic challenge, matching the dynamics observed experimentally and making 29 functional predictions for the cell body mechanisms.

nuclei of the hypothalamus, in response to input signals that encode osmotic pressure 37 and plasma volume, synthesise and secrete the antidiuretic hormone vasopressin. 38 Vasopressin in its antidiuretic role is a core element of the homeostatic system that 39 maintains osmotic pressure (water/salt balance), signalling the kidneys to regulate 40 how much water is retained. Acting as a heterogeneous population, these neurons are 41 able to maintain a constantly functioning physiological signal over lifelong periods of 42 time. To sustain such a signal the system must be both very robust and efficient. It 43 must also be able to respond rapidly to large changes in demand. 44 Vasopressin is synthesised in the neuronal cell bodies and packaged into large 45 dense core vesicles that are transported down the axons to the posterior pituitary, 46 where the vesicles are stored in axon swellings and terminals that form larger reserve 47 and smaller releasable pools. We have previously modelled the spiking and secretion 48 mechanisms of these neurons (MacGregor and Leng, 2012, including the 49 dynamics of these pools. Here we build and integrate with our existing model, a 50 quantitative model of the synthesis mechanisms, to better understand how the 51 properties of these neurons relate to their function on long timescales. 52 In normal (basal) conditions mammals drink and ingest sodium (in the diet) 53 intermittently, but constantly lose water through respiration and perspiration. Under 54 homeostatic regulation, osmotic pressure fluctuates around a 'set point'; increases 55 above this will be corrected by increased sodium excretion in urine, by increased 56 thirst, and to compensate lack of availability or intermittent ingestion of water, by 57 secreting vasopressin to concentrate the urine and minimise water loss. Falling below 58 this set point occurs less commonly, when excess water has been consumed, or salt 59 has been lost. Both tonic signalling and a response to perturbations must be 60 maintained, and accordingly there is an almost continuous depletion of the pituitary 61 vasopressin stores, which must be replenished by the synthesis, packaging, and 62 transport of new vasopressin vesicles. 63 In conscious, normally hydrated rats, as in humans, the basal vasopressin 64 plasma concentration is ~1 pg/ml (Robertson, Shelton and Athar, 1976;Verbalis, 65 Baldwin and Robinson, 1986) and maximal antidiuresis is observed at a concentration 66 the amount of synthesis per unit of mRNA. 135 The pathway between osmotic stimulus and transcription is still uncertain. The 136 major candidate is a pathway via cyclic AMP (Carter and Murphy, 1989;Sladek et 137 al., 1996;Wong et al., 2003) that acts to drive the CREB3L1 transcription promoter 138 (Greenwood et al., 2015). There is also evidence for a glutamate-NMDA receptor-139 Ca 2+ entry driven pathway (Lake, Corrêa and Müller, 2019). Here we are using a very 140 simple representation to predict the necessary dynamics rather than any detailed 141 modelling of the mechanisms. 142 Our objective here was to integrate, adapt and extend the Pittsburgh model 143 into our existing integrated spiking and secretion model in order to fully simulate the 144 pathway from osmotic signal to plasma hormone signal. The challenge we identified 145 when testing the secretion model (MacGregor and  is that heterogeneity, 146 which brings essential benefits to producing a robust signal response, results in widely 147 varying rates of secretion and store depletion across the population. The synthesis 148 mechanism must be able to cope with varied demand not only as a population but also 149 between individual neurons. 150 The new synthesis modelling has been kept as simple and general as possible, 151 and should be capable of being adapted to other neuroendocrine cells, but is still able 152 to produce strong quantitative as well as qualitative matches to the experimental data 153 on synthesis rates, mRNA content, and depletion and repletion of vasopressin stores 154 during prolonged osmotic challenge and recovery. However, in designing and fitting 155 to match experimental data that shows a cycle of depletion and recovery during and 156 after an osmotic challenge, the synthesis model is essentially constrained to fail at the 157 task of matching supply to demand. By attempting to fix this in the model we explore 158 why the stores get depleted; what are the limiting mechanisms, and why these limits 159 might be necessary. To set targets for fitting and testing the model, an extensive literature survey 166 was used to gather multiple types of physiological data recorded in rats during a 167 prolonged osmotic challenge and the following recovery. This extends the examples 168 of (Fitzsimmons et al., 1992) where they compared multiple sources measuring the 169 depletion and recovery of pituitary vasopressin stores. The data used here (Figure 1 The osmotic stimulus protocols vary between using dehydration (water 185 deprivation) and salt loading (high Na drinking water) to raise osmolarity. In all the 186 measurements except for plasma vasopressin these two protocols appear to produce an 187 equivalent response (

The Spiking and Secretion Models 214
The spiking model used to generate the results here uses parameters (Table 1)  215 chosen to simulate a typical magnocellular vasopressin neuron, based on detailed fits 216 to in vivo recordings (MacGregor and Leng, 2012). As the synaptic input rate is 217 increased, spiking shifts from silence to irregular spiking, phasic patterned spiking 218 (long bursts and silences), increasing burst durations, and eventually continuous 219 spiking. Figure   between the transcription rate and depletion due to translation and synthesis. The rate 252 of synthesis is directly proportional to the mRNA content (m). The secretion rate and 253 plasma concentration driven by the single phasic neuron are noisy but sustain steady 254 levels until the reserve store is depleted. The releasable pool (which is refilled from 255 the reserve) buffers the secretion response to maintain a steady rate until the reserve 256 store is very heavily depleted. With no synthesis, the store fully depletes and plasma 257 concentration falls to zero. With synthesis, the rate is insufficient to match the highly 258 stimulated secretion rate and the store is still depleted, though at a slower rate. When 259 it is depleted, secretion and plasma concentration is sustained, at a level purely 260 dependent on the upregulated synthesis rate. We would not expect to observe this in 261 the heterogeneous population in vivo, but this is what we would predict in a 262 homogeneous population, assuming a sustained osmotic stimulus.

269
For illustration, rather than physiological simulation, the model here is initialised with a full 270 store and zero stimulus, switching at time 0 to a sustained highly osmotic input signal.

271
Transcription drives the accumulation of mRNA content, which in turn determines the rate of Maícas-Royo, Leng and MacGregor, 2018). Coupled to the plasma model, this allows 280 the prediction of the rates of secretion that correspond to plasma concentrations 281 observed in vivo. In basal normo-osmotic conditions rat plasma vasopressin in vivo is 282 ~ 1 pg/ml. In highly stimulated hyper-osmotic conditions plasma vasopressin in vivo 283 rises to around 20 pg/ml. The left panels of Figure 4 show the single neuron model 284 sustaining a mean 1 pg/ml plasma concentration with input rate Ire = 252 Hz. The 285 initial value for mRNA content (m = 15), was set using an initial test to find its stable 286 value at this input rate. The first target for tuning the synthesis model parameters was 287 for synthesis to match secretion in basal conditions, in order to sustain a stable reserve 288 store. The reserve store plot shows this achieved by reducing the synthesis rate (sr = 289 0.65) compared to the final heterogeneous model parameter (sr = 1.1), which produces 290 a small rise in the store, with synthesis exceeding secretion. 291 292

Simulating Sustained Osmotic Challenge and Recovery 293
The second target for tuning the model was to match the experimental data 294 measuring vasopressin store content in rats during a five day osmotic challenge (no 295 water access, or salt loading using high Na + drinking water) and the following 296 recovery ( Figure 1). Experiments measuring osmolarity (or equivalent plasma Na + ) 297 and plasma vasopressin during similar protocols (Walters and Hatton, 1974;298 Nordmann, 1985;Yue et al., 2008) suggest that the osmotic stimulus rises mostly 299 linearly during the challenge for at least the first three days before levelling off at 300 sustained high levels, and rapidly recovering after the challenge period. We simplified 301 this by using a linear ramp in the input rate to simulate the prolonged osmotic 302 challenge, illustrated in the right hand panels of Figure 4. The initial input rate 252 Hz 303 was ramped to 640 Hz over 5 days and then returned to 252 Hz, targeted to match the 304 store depletion observed in the experimental data. 305 The transcription rate mostly tracks the osmotic stimulus. The stores decline in 306 content to ~ 25% before slowly recovering following the challenge, matching the 307 experimental data and the results with the original Pittsburgh synthesis model. The 308 mRNA content shows a more non-linear increase, and decline during the recovery 309 period, as it sustains elevated synthesis rates to replenish the stores. However, the 310 reduced synthesis rate (sr = 0.65) used to match secretion at basal levels ( Figure 4 left) 311   show a population store that falls to ~ 25 % during the 5 day challenge and 404 replenishes to almost full over the 15 day recovery period, very similar to the 405 experimental data in rats. A notable difference however is that the model's store using 406 the linear ramp (black) protocol shows a slower initial decline. The match was 407 improved by using a more non-linear ramp (red) in the osmotic input signal, 408 producing a more rapid initial increase that gradually slows. Experimental evidence 409 for the ramp in osmotic input and plasma vasopressin is variable and limited by 410 temporally sparse measurements but suggests something that lies between these two. 411 The model was further modified (blue) by adding a 24 h delay between the synthesis 412 rate and the store fill rate representing the slow transport of new vesicles from the cell 413 body to the pituitary stores, thought to take up to 24 h depending on osmotic status 414 (Russell, Brownstein and Gainer, 1981). The delay more closely matches the 415 depletion observed experimentally, but its effect is modulatory, and not sufficient to 416 explain store depletion alone. 417 418

What Limits the Synthesis Response? 419
The current model matches the limited upregulation of synthesis, and 420 depletion of stores, observed in the experimental data. Changes to the model, 421 attempting to improve this response, were tested to predict which mechanisms might 422 be responsible for this limited ability to match secretion demand (Figure 7). Two 423 methods were found which were able to produce a much faster upregulation of 424 synthesis while maintaining the ability to function in basal and stimulated states 425 without under-or over-filling the stores. The first method (red in Figure 7) accelerates 426 the upregulation of transcription. This required three parameter changes, increasing 427 the rate of transcription but also compensating the increased amount so that only the 428 speed of the response was changed (kT 0.33 to 3.3, sbasal 0.7 to 7, sr 1.1 to 0.11). The 429 produces a much faster increase in the mRNA store and corresponding synthesis rate, 430 resulting in a much smaller vasopressin store depletion. However it also predicts a 431 much larger increase in mRNA than is observed experimentally (20-fold compared to 432 ~5 to 8-fold). The second method (blue in Figure 7) increases the rate of translation 433  Rather than the mechanism necessarily being Ca 2+ -dependent, the necessary 500 assumption here is that transcription closely tracks spike activity. This helps the 501 model to maintain a tracking between the synthesis and secretion rates without any 502 cross-communication. If transcription was more directly driven by synaptic input then 503 the complexities of phasic firing would disrupt this tracking. 504 Where the model's behaviour becomes more complex is in the dynamics of 505 stores in a heterogeneous population. Heterogeneous activity levels would be 506 expected to present a big challenge to maintaining the tracking between synthesis and 507 secretion rates and it was surprising how robust the heterogeneous population proved 508 to be. This is partly because heterogeneity as well as adding complexity, also removes 509 some by linearising the relationship between the input and output signals. However, 510 there is some variation across the heterogenous population in how well stores are 511 maintained, suggesting that a statically heterogeneous population will gradually 512 diverge in store content. The simple model tested here puts no limits on the mRNA 513 content or vasopressin stores in individual neurons. These limits are likely to exist in 514 some form and would act to reduce the divergence between neurons, but it does 515 nevertheless seem likely that a static heterogeneous population would struggle to 516 maintain function over long periods. Thus the model here has developed a tool to 517 further examine rather than solve the problem of store divergence identified in the 518 previous work (MacGregor and . 519 The alternative is dynamic or regulated heterogeneity. Here we refer to our 520 neurons as a population, connected only at their functional input and output signals. 521 However vasopressin neurons have the ability to communicate through dendritic 522 release of various signals including vasopressin, and potentially act as a network. 523 There is evidence that these signals act to modulate the activity of neighbouring 524 neurons (Gouzènes et al., 1998) and it has been proposed that the network might act 525 to cycle activity levels (Scott and Brown, 2010), letting rested neurons replace those 526 that have been more active and become depleted. Such a mechanism would also 527 contribute to the lifetime robustness of the system by compensating for lost neurons. 528 The question for this that arises from the work here is what measure would regulate 529 the dendritic signals? For the same reasons that synthesis rates are not thought to be 530 directly coupled to secretion (distant and distributed stores), it would be difficult to 531 directly measure store depletion. Do the stores available for dendritic release deplete 532 sufficiently in parallel to the peripheral stores? Could elements of the synthesis 533 mechanism also regulate dendritic signalling? 534 One of the main limitations in interpreting the results here is the highly 535 simplified simulation of the prolonged osmotic challenge. The linear ramp is based on 536 experimental data measuring vasopressin concentrations, osmotic pressure, and/or 537 plasma Na + which show mostly linear increases with time during an osmotic 538 challenge over at least three days. After three days however, these increases tend to 539 slow, probably as the high sustained vasopressin output, and regulation of other 540 elements involved in osmotic homeostasis, such as salt excretion, achieve some sort 541 of new equilibrium. There is also evidence of this in the data measuring store content, 542 where the rate of depletion appears to fall towards the latter part of the challenge. We 543 began addressing this here in the model using a non-linear input ramp, but a much 544 better approach in terms of gaining understanding would be to integrate the neural 545 population model into a simple system model of osmotic homeostasis, providing 546 feedback between the vasopressin output and the osmotic input signal. 547 Another assumption here is the simple linear encoding between osmotic seconds. This is modelled here using an integrate-and-fire based model (MacGregor 573 and Leng, 2012) modified to include a set of activity-dependent potentials that 574 modulate excitability to shape spike patterning and generate an emergent bistability, 575 matching the observed phasic firing and detailed spike patterning measured using 576 analysis such as the inter-spike interval (ISI) histogram and hazard function (Sabatier 577 et al., 2004). Importantly the model also matches the changes in the phasic spiking 578 that occur in response to a changing input signal. 579 The excitability modulating potentials include a hyperpolarising afterpotential 580 (HAP), a fast depolarising afterpotential (DAP), and a slow after hyperpolarisation 581 (AHP). Each of these is modelled using a single variable that is step incremented with 582 each spike and decays exponentially. This simple form has proven sufficient to 583 produce close quantitative matches to experimentally measured spike patterning and 584 is used here for the activity dependent elements of the model. 585 The phasic firing mechanism uses a slow DAP based on a Ca 2+ inactivated 586 hyperpolarising K + leak current VL (i.e. an activity-dependent depolarisation generated 587 by switching off a hyperpolarisation). This is modulated by two opposing step-and-588 decay variables representing spike generated Ca 2+ entry, and dendritic dynorphin 589 release, which slowly accumulates to oppose the action of Ca 2+ and reactivate the K + 590 leak current, eventually terminating a burst and sustaining the period of inter-burst 591 silence. 592 With more detail in (MacGregor and Leng, 2012;Maícas Royo et al., 2016), 593 the spiking model is summarised by: 594 where V is the membrane potential, Vrest is the resting potential, and Vsyn is the 598 summed synaptic input signal described below. AHPslow is the renamed AHP of 599 (MacGregor and Leng, 2012) to distinguish it from the medium AHP of (Maícas 600 Royo et al., 2016). The default parameters are given in Table 1. 601 602 603   ~51s. This matches the estimate of (Ginsburg and Heller, 1953) but is shorter than 663 other estimates of 120s (Czaczkes and Kleeman, 1964). 664 As well as adding the plasma model we also refitted the existing vasopressin 665 secretion model (MacGregor and    Table 2. To simulate a transport delay between synthesis and 729 the store, s in this equation was replaced sdelay, using the recorded value for s from an 730 earlier timestep. 731 732