Modelling the effects of lymph node swelling on T-cell response

Swelling of the lymph nodes is commonly observed during the adaptive immune response, yet its impacts on T cell trafficking and subsequent immune response are not well known. To better understand the effect of macro-scale alterations in the lymph node, we developed an agent-based model of the lymph node paracortex, describing T cell trafficking and response to antigen-presenting dendritic cells alongside swelling-induced changes in T cell recruitment and egress, and regulation of expression of egress-modulating T cell receptor Sphingosine-1-phosphate receptor-1. Validation of the model was achieved with in-silico replication of a range of published in-vivo and cell culture experiments. Analysis of CD4 and CD8 effector T cell response under varying swelling conditions showed that paracortical swelling aided initial T cell activation but could inhibit subsequent effector CD8 T cell production if swelling occurs too early in the T cell proliferative phase. A global sensitivity analysis revealed that the effects of some parameters switch from aiding to inhibiting T cell response over a ten day response period. Furthermore, temporarily extending retention of newly differentiated effector T cells, mediated by Sphingosine-1-phosphate receptor-1 expression, mitigated some of the effects of early paracortical swelling. These results

The lymphatic system is a converging network of organs and lymphatic vessels (LVs) 2 that maintains fluid balance in the body and also delivers crucial antigen information to 3 lymph nodes (LNs) for initiation of adaptive immunity. A successful immune response 4 relies not only on the interaction of different immune cell types, but also on the 5 maintenance of an appropriate physical environment in the LNs to facilitate those 6 interactions. LNs contain specific compartments populated by T cells (TCs), B cells, Sphingosine-1-Phosphate (S1P) and chemokine signalling axes. After entering the LNs, 51 TCs initially express S1P 1 r at very low levels but begin re-expressing S1P 1 r after 2 hours 52 [31,32]. TCs exit the LNs by probing and subsequently entering cortical sinuses in the 53 paracortex or the interface with the medulla, aided by chemotaxis as both destinations 54 contain higher S1P concentrations ( Fig 1A) [33,34]. During inflammation, TC S1P 1 r 55 expression is reciprocally regulated by CD69, an early TC activation marker that can be 56 up-regulated in TCs by the presence of inflammatory mediators, contributing to the 57 initial decrease in TC egress and later retention of activated TCs [35]. The exploration of potential roles for swelling of LNs in adaptive immunity is limited 59 by the range of possible experiments in which parts of the process could be modulated, 60 and the ability to track relevant outcomes in real time. Mathematical models can help 61 fill these knowledge gaps, and suggest new experiments that target specific mechanisms 62 and measure outcomes at specific time points. Modelling cell populations with partial 63 differential equations is computationally expensive and typically involves assuming 64 uniform cell responses to stimuli. Within Agent Based Models (ABMs), cells are that each grid compartment represents, while maintaining entry and exit areas defined 97 as a percentage of the outer radius (Fig 2A,G). 98

Fig 2.
Grouping the parameters of the model. Model geometry, TC initialisation, DC initialisation and T cell movement are not varied in the sensitivity analysis. TC movement parameters were varied in preliminary trials before being fixed. Reference sources for all parameters are available in S2 File.

TC recruitment 99
Under baseline conditions, TC recruitment rate was specified as 2000 TCs/hour, naive 100 TC transit time (T res ) as 6-24 hours and the TC-to-compartment ratio was assumed 101 constant (see S1.1). In accordance with images depicting HEV location, 90% of TCs 102 enter at 'HEV entry' compartments designated as the inner half of the paracortical 103 radius [48]. These grids also correspond to the blood vessel volume (V B ), which changes 104 in proportion to overall paracortical volume change [4,45]. Remaining TCs enter via the 105 SCS interface at compartments adjacent to the afferent half of the external surface. To 106 allow blood vessel volume (V B ) changes to contribute to TC recruitment rate, TC influx 107 is made proportional to normalised blood vessel volumeV B (normalised with respect to 108 the pre-stimulus value). Acute recruitment changes due to inflammation-induced 109 signalling cascades at the HEVs are represented by incorporating an inflammatory 110 index, (I f ), triggered by antigenic presence (sum of MHC thresholds to trigger (T1) and 111 cap (T2) recruitment) (2). TC influx is therefore : TC egress and S1P 1 r expression 115 The relative expression of S1P 1 r (SP) is varied from 0.01 (egress inhibition) to 1 proportional to MHC presented, while losing stimulation at rate λ S (Fig 2C), similarly 143 to the methods of [37,41,57] TCs, memory TCs, effector TCs exited and memory TCs exited) from day 3 to 13, 176 assuming monotonic relationships [60].

178
The relationship between initial proportion of cognate TCs and subsequent effector TC 179 production has been studied in-vitro by applying antigen to pools of TCs with known 180 starting cognate frequencies [59,61]. To compare the model behaviour, the initial CD8 + TCs present compared to similar experiments [32,65].

196
The model produces realistic baseline TC motility and response 197 to agDCs

198
The average TC velocity (n=200) was 13.1µm/min and reached 24µm/min (Fig 4D), in mice [70]. The mean TC paracortex transit time was 13.1 hours (n=16,000), ranging 203 from 20 minutes to >60 hours (Fig 4C), in-line with observations that 74% of 204 CD4 + TCs and 64% of CD8 + TCs transit the murine LNs within a day [71]. hours after initial agDCs entry, and by day 11 had returned to within 15% of 209 pre-stimulus values (Fig 5A), in-line with temporal responses observed in-vivo [9,14,72]. 210 The appearance of activated, effector, and memory TCs began at 16-24 hours, day 3.5 211 and day 5 post-agDC entry, respectively, in agreement with cell-culture models and 212 in-vivo observations [73,74]. Effector CD4 + TCs appeared 1-1.5 hours before CD8 + 213 effector TCs (Fig 5A,B). As observed in studies using cell culture, the peak population 214 of cognate CD8 + TCs was an order of magnitude higher than that of CD4 + TCs 215 ( Fig 5C) [75]. The contraction phase began at day 7 and continued through day 11. The 216 increase in TC egress rate peaked a day later than the increase in TC entry rate 217 ( Fig 5D), corresponding well with in-vivo observations of delayed increase in TC egress 218 and TC recruitment dynamics [10,76]. Memory TCs (black line in B) began to appear at 5 days and 25% of the peak number of memory TCs remained at the end of the simulation. Cognate CD4 + TCs (Green line in C) began to proliferate extensively at day 2.2, compared to cognate CD8 + TCs (purple line C) that began to proliferate at day 4 and reached numbers 10x more than cognate CD4 + TCs. D. TC entry rate increased 2x due to detection of antigenic stimulus whilst TC egress rate declined between day 1 and 2, then increased 3x by day 4.
When the proportion of initially cognate TCs, F cog , was increased from 7e-5 to This compares well with results observed when transgenic DT-sensitive agDCs were 240 injected into murine LNs, then eliminated by injecting DT 1 or 12 hours later, which 241 resulted in a 93% and 85% decrease in CD8 + TC magnitude respectively when 242 compared to no-elimination (S4 FigA) [64].

243
Abrogating S1P 1 r down-regulation after antigenic stimulus detection in-silico, 244 reduced the number of activated TCs in the paracortex by 60%, 72% and 81% at 245 V max =1.2 ,2.0 and 2.5 ( Figure S5D). This was a smaller reduction than observed during 246 in-vivo experiments when activated TCs maintaining S1P 1 r expression were transferred 247 to LNs, resulting in 90% less activated TC retention in the LNs 15 hours later compared 248 to control mice (S5 FigA) [32]. The in-silico reduction was, however, greater than the 249 40% reduction in activated TCs found with constitutive TC expression of S1P 1 r in-vivo 250 post-immunisation (S5 FigB) [65]. The in-silico total number of CD4 + and CD8 + abrogated (S5 FigE,F). This is similar to the 27% and 5% of control response recorded 253 with constitutive inhibition of S1P 1 r expression in-vivo (S5 FigC) [65].
Paracortical swelling consistently aids TC activation but not 255 effector TC production 256 When maximal swelling (V max ) was varied from 1 to 2.8, activated TC number 257 positively correlated with V max (p<10 −5 ) doubling in number (Fig 7A). However, total 258 number of effector TCs negatively correlated with V max (p<10 −4 ) and decreased by 259 15% (Fig 7B). Neither the number of effector TCs that exited by day 10, nor total and contacts whereas at V max =1.2, there was no significant correlation (Fig 8A,B). correlated with cognate TC contacts as V max increased (p=0.002) (Fig 8D). Up to V max =1.8, the number of effector TCs present increased with contacts ( Fig 8E)  Varying the ease of swelling influences resulting TC populations. 284 In some cases, varying the required number of T cells present to reach half the maximal 285 swelling, (T mid ), counteracted the effect of varying maximal swelling of LNs on effector 286 TC production. When simulations were carried out with a lower or higher T mid of 8e4 287 or 12e4, and a small (V max =1.2) or large (V max =2.5) maximal swelling, a similar 288 number of effector TCs were produced with a low T mid and low V max compared to with 289 a high T mid and high V max (Fig 9C). The difference in effector TC response appeared 290 to be due to cognate CD8 + TC behaviour, as there was no significant difference in 291 cognate CD4 + TCs numbers with T mid =8e4 or 12e4 at either V max =1.2 or 2.5 292 (Fig 9D,E). With a lower T mid of 8e4, paracortex swelling began one day earlier than 293 with T mid =12e4 (Fig 9A). Most TCs were activated with a low T mid and high V max , 294 however at least 40% more activated TCs were recorded when V max was high compared 295 to when V max was low regardless of T mid (Fig 9B). Further simulations varying T mid with a wider maximal swelling range confirmed that the number of activated TCs 297 increased with expansion, but at every value of V max , correlated negatively with T mid 298 (Fig 10A), which suggests that earlier swelling, whether induced by larger T mid or 299 V max , aids initial TC activation.   Fig 10D). Production of cognate CD4 + TCs may be aided by a lower T mid and earlier 306 expansion, as at a lower V max , increasing T mid showed a trend towards less cognate 307 CD4 + TCs leaving the paracortex, although this did not reach significance (at V max =1, 308 p=0.08 and at V max =1.5, p=0.051) (Fig 10F). However, at larger swelling no benefit is 309 gained by varying T mid as total cognate CD4 + TC numbers increased with V max 310 regardless of T mid value. Therefore, the increased effector TC number with high T mid 311 and V max is mainly due to CD8 + TCs, with the number of cognate CD8 + TCs that 312 exited paracortex correlating positively with T mid (p=<0.05) at a high V max (Fig 10E). 313 TC and DC contacts were consistent with the earlier results (Fig 8C) that at a larger paracortical expansion, with each value of T mid , the overall number of cognate TCs contacted was less than when the same value of T mid was applied with a smaller 316 paracortical expansion (Fig 10B,C). However, at the larger maximal swelling value of 317 2.5, as T mid increased, the DCs contacted more cognate TCs. At V max = 2, no 318 correlation between contacts and overall cognate TC number occurred (S7 FigA), but a 319 positive correlation was observed between contacts and effector TCs produced 320 (p<10 −3 ), CD8 + TCs produced (p=0.03) and CD8 + exited (p=0.027) (Fig 10D,E) V max (Fig 10G). TC activation was also 40% higher than the value at V max =1.0, but 327 less than the 120% increase at V max =2.6 (S7 FigB). In contrast, no correlation was TC activation and effector TC production ( Table 1,2 and S1 Table). However, when paracortical expansion was allowed, a positive correlation was observed in the first week 343 only. The effect of V max also reversed between weeks one and two, positively correlating 344 June 15, 2020 16/37 to activated TCs in the paracortex up to day 4 and 6 (p<0.05) but negatively correlating from day 6 (p<10 −6 ) with activated TCs, effector TCs present and effector 346 TCs exited (Table 1 and 2, S1 Table-S3 Table). Another example of a parameter that 347 changed TC dynamics is the duration of DC entry (DC in ). Reducing DC in while 348 maintaining the number of entering DCs activates TCs earlier, whereas increasing it 349 facilitates sustained but slower TC activation (Table 1). An additional sensitivity 350 analysis increasing the upper-range of S1P 1 r down-regulation on activated TCs (SP act ), 351 from 0.4 to 0.8, eliminated the correlation between V max and effector TCs (Table 3).

With Swelling Parameter Day2
Day 3 Day 4 Day 5 Day 6 M ax N T F cog + + + + + + + + + + + + The average TC to grid compartment ratio fluctuated within realistic levels in most 360 simulations (0.6-1.3 in a volume equivalent to 1.75 TCs) (Fig 11A) resulted in a significant difference in effector TC production at V max = 1.0 and V max = 367 1.4, but no overall trend was observed (Fig 11B). However, when TCs were permitted to 368 re-enter HEVs with a low probability (P e2 ), in a fixed-volume paracortex, the TC to Regardless of permitted maximal swelling, down-regulating S1P 1 r on early effector TC 377 to less than 80% of naïve TC expression (SP Early <0.8) produced a sustained increase 378 in total TCs, despite the action only directly affecting the small subset of early effector 379 TCs (Fig 12A). Reducing SP early to 0.4 doubled the total number of effectors TCs, 380 whilst SP early =<0.1 increased the number of effector TCs that left the node by day 10 381 by 3-fold (Fig 12G). The number of effector TCs that exited continued to increase as most effector TCs were produced at the smallest value of SP early and largest maximal 384 swelling ( Fig 12G). When analysing the TC sub-populations, the number of both CD4 + 385 and CD8 + effector TCs that exited the paracortex by day 10 increased 3-4 fold with 386 SP early < 0.1 (Fig 12H,I). No further increase in CD8 + TCs exited was observed when 387 SP early was decreased to 0.05. was decreased from 0.8 to 0.1 (Fig 12J). However, when SP early was >=0.1, at larger 393 values of V max (>=2.0), despite less DCs and cognate TCs contact, the same number or 394 more effectors TCs exited than at smaller swellings. Other changes with a lowered 395 SP early of <=1 included an increase in TC egress rate that was sustained for two days 396 longer, and at V max <2.0, a doubling of TC egress rate from days 1-5, compared to 397 simulations with V max =>2 (Fig 12B,D). By day 6 to 8, TC egress rate was similar 398 between values of V max . Despite increase in TC egress the TC to grid-compartment 399 ratio also increased with SP early <=0.1 therefore TC egress did not exceed TC 400 production (Fig 12.C,E). However, the TC to grid-compartment ratio was highest at 401 lower values of V max and SP early <0.1, but this parameter combination did not produce 402 the most effector TCs, suggesting the balance between retention and increase is key for 403 efficient TC production.

Discussion
In this work we aimed to better understand the role of lymph node swelling and other 406 adaptive immune processes in the formation of TC responses. Our study builds on 407 methods used in previous work that confirmed the ability of ABMs to predict immune 408 cell behaviours [37,[39][40][41]43]. Model validation was accomplished by comparing 409 predictions to a range of published experiments, and robustness was confirmed by 410 multiple parameter variation analyses. By varying paracortical swelling and S1P 1 r 411 expression, we showed that paracortical swelling aids TC activation, but early swelling 412 can impair effector TC response. However, temporary retention of newly differentiated 413 TCs influences the overall effector TC response more than swelling, providing a 414 mechanism to overcome swelling-induced impairment.

415
A key finding from our study was the strong influence of S1P 1 r down-regulation on 416 newly differentiated effector TCs on the number of effector TCs produced during 417 immune response (Fig 12). Our study focused on the effect of temporary 418 down-regulation of S1P 1 r on effector TCs that can amplify overall response, whereas 419 previous studies have focused on the inhibitory effects of permanent S1P 1 r 420 down-regulation. Induction and maintenance of S1P 1 r down-regulation on all TCs 421 present is the mechanism of the recently developed multiple sclerosis drug Fingolipid, to 422 prevent effector TCs migrating to the brain and participating in autoimmune 423 response [77]. Inhibition of S1P 1 r expression on effector TCs only has also been carried 424 out in-vivo [24]. However, temporary down-regulation on selectively newly differentiated 425 TCs may prove technically difficult, suggesting identification of alternative means of 426 retention is desirable.

427
Another key finding was that the initial 5 days of paracortical swelling facilitates the 428 retention of activated TCs in the LNs (Fig 7A). Both TC recruitment and TC egress 429 increase with swelling (Fig 7E,F) and therefore overall TC trafficking rate is increased, 430 yet activated TCs are retained due to S1P 1 r down-regulation. When S1P 1 r-mediated 431 retention is removed, depleted activation is observed in-silico and in-vivo (S5 Fig) and 432 our simulations show that swelling no longer aids activation. Additionally, increased TC 433 recruitment with HEV growth that accompanies swelling allows more cognate TCs to 434 enter, an effect that is amplified when activated TCs proliferate. TC activation did not 435 June 15, 2020 21/37 appear to be constrained by DC and TC interaction during these simulations, as the mean number of cognate TCs a DC interacted with decreased with swelling, despite the 437 increased space for TC migration and access (Fig 8C). 438 Thirdly, our results suggest that swelling of LNs too early can negatively impact TC 439 response, by reducing the total number of effector TCs and the number of exiting 440 effector CD8 + TCs (Fig 10). Conversely, delaying swelling (increasing T mid ) can result 441 in just as many, if not more effector TC exiting the paracortex by day 10, as long as  (Table 1-3). 448 We also observed that early swelling hindered the CD8 + effector TC response more 449 than CD4 + TCs, potentially due to the later and longer duration of simulated CD8 + 450 TC proliferation [78]. Earlier proliferation of CD4 + TCs in the model may mean that a 451 point of exponential proliferation is reached such that further proliferation is However, this discrepancy may be because the 40% figure was recorded after accounting 487 for reduced naive TCs homing to the LN due to the lack of S1P 1 r expression, prior to 488 possible TC activation that was subsequently also affected.

489
A limitation of the model is that paracortical expansion is dependent only on TC initial inhibition of stromal cell proliferation by increased secretion of IFN type 1 [79]. 496 The delayed increase in volume in response to TC number then reflects the switch in elasticity of FRC network [9,80]. Furthermore, TC numbers are impacted by retention, 500 but the effects of regulation of TC expression of chemokine-receptor CCR7 and the role 501 of chemo-attraction in locating and retaining TCs in the paracortex was omitted [50].

502
When both CCR7 and S1P 1 r expression on TCs was inhibited in-vivo, the TCs 503 migrated to the edges of the paracortex, due to the loss of chemo-attraction deep within 504 the paracortex, but could not exit due to lack of S1P 1 r expression. Accordingly, 505 inclusion of S1P 1 r down-regulation was prioritised over CCR7 but the identified strong 506 influence of retention suggests future models should include a wider range of retentive 507 influences [24].

508
In future iterations of the model, inclusion of additional factors such as lymph flow 509 and pressure alterations (along with fluid exchange with nodal blood vessels), could also 510 significantly improve the representation of swelling, and thus TC egress and retention. 511 It has long been known that changes in hydrostatic and oncotic pressure differences 512 across nodal blood vessel walls can reverse the net fluid exchange [81,82]. Afferent 513 lymphatic flow to the LNs also increases with immune response. Therefore, a key next 514 step is to couple the ABM to a computational flow models while resident DCs in the 515 LNs could also be added and the maximal permitted swelling increased to confirm the 516 observed trends. Changes in proliferation and differentiation continued after the initial stimulus was no 546 longer present. TC recruitment and TC egress changes also accompanied the response. 547 Results in-silico showed an overall increase in response with increasing F cog (n=8).

551
Simulations using a wider range of F cog values (C,D) confirmed no. of total cognate 552 CD4 + TCs and CD8 + TCs increased linearly with F cog . E. Mice were infected with 553 VSV-M45 or VSV-ova with starting precursor CD8 + frequencies of 7e-5,8e-5 and 13e-5 554 respectively. The peak number of resulting TCs as a percent of overall CD8 + TCs present is shown.F. Simulations using the same F cog in-silico showed a similar 556 increasing trend with similar increase rate.  Table. Parameters that significantly affected memory TCs number in 604 the paracortex. Data is only shown from day 5 to day 12 post-stimuli, as they are not 605 produced in the first few days. At day 5, V max still showed some positive correlation 606 with memory TCs present but by day 7 shows a negative correlation.

607
S3 Table. Parameters that significantly affected the number of memory 608 TCs exited in the paracortex from day 5 to day 12 post-stimuli.