key: cord-1040738-bwmkiyan
authors: Chatterjee, B.; Singh Sandhu, H.; Dixit, N. M.
title: The relative strength and timing of innate immune and CD8 T-cell responses underlie the heterogeneous outcomes of SARS-CoV-2 infection
date: 2021-06-21
journal: nan
DOI: 10.1101/2021.06.15.21258935
sha: 3e8c94af1be5a54a741b2cac05a1f112e4a6d162
doc_id: 1040738
cord_uid: bwmkiyan

SARS-CoV-2 infection results in highly heterogeneous outcomes, from cure without symptoms to acute respiratory distress and death. While immunological correlates of disease severity have been identified, how they act together to determine the outcomes is unknown. Here, using a new mathematical model of within-host SARS-CoV-2 infection, we analyze diverse clinical datasets and predict that a subtle interplay between innate and CD8 T-cell responses underlies disease heterogeneity. Our model considers essential features of these immune arms and immunopathology from cytokines and effector cells. Model predictions provided excellent fits to patient data and, by varying the strength and timing of the immune arms, quantitatively recapitulated viral load changes in mild, moderate, and severe disease, and death. Additionally, they explained several confounding observations, including viral recrudescence after symptom loss, prolonged viral positivity before cure, and mortality despite declining viral loads. Together, a robust conceptual understanding of COVID-19 outcomes emerges, bearing implications for interventions.

SARS-CoV-2 infection results in highly heterogeneous outcomes, from cure without symptoms to acute 19 respiratory distress and death. While immunological correlates of disease severity have been identified, 20

how they act together to determine the outcomes is unknown. Here, using a new mathematical model of 21

within-host SARS-CoV-2 infection, we analyze diverse clinical datasets and predict that a subtle interplay 22

between innate and CD8 T-cell responses underlies disease heterogeneity. Our model considers essential 23

features of these immune arms and immunopathology from cytokines and effector cells. Model 24

predictions provided excellent fits to patient data and, by varying the strength and timing of the immune 25 arms, quantitatively recapitulated viral load changes in mild, moderate, and severe disease, and death. 26

Additionally, they explained several confounding observations, including viral recrudescence after 27 symptom loss, prolonged viral positivity before cure, and mortality despite declining viral loads. 28

Together, a robust conceptual understanding of COVID-19 outcomes emerges, bearing implications for 29

interventions. 30 31 Teaser 32

Modeling explains how a subtle interplay between innate immune and CD8 T-cell responses determines 33 the severity of COVID-19. 34

Coronavirus disease 2019 (COVID-19), a respiratory infection caused by the severe acute respiratory 36 syndrome coronavirus 2 (SARS-CoV-2), evokes remarkably heterogeneous clinical outcomes (1, 2) . 37

While some individuals are cured without any symptoms, others suffer mild to moderate symptoms, and 38 yet others experience severe disease requiring hospitalization and intensive care, with a sizeable fraction 39 of the latter suffering death (1) (2) (3) . Several demographic correlates of disease severity, such as gender, co-40 morbidities, and age, have been identified (4). Further, immunological correlates of severe disease 41 outcomes, such as a subdued early innate immune response (5), and a late surge of proinflammatory 42 cytokines (6, 7) have also been reported. Yet, what determines this diversity of outcomes has remained an 43 outstanding question, challenging our understanding of infectious disease biology and, more immediately, 44

precluding optimal strategies for combating the raging COVID-19 pandemic. 45

While viral factors, including emerging mutations (8), may have a role in determining the outcomes, the 46 heterogeneous outcomes were reported in early studies (2, 3), before the majority of the clades of SARS-47

CoV-2 emerged (9), suggesting that the heterogeneity potentially originates from the variability in the 48 host immune responses to the infection (6). Rapidly accumulating evidence reinforces the role of the 49 immune response, particularly of the innate and the CD8 T-cell responses, in determining disease 50 outcomes: Soon after infection, an innate immune response is first mounted, involving the production of 51 cytokines, particularly type I and type III interferons, by virus-infected and immune cells (10). Interferons 52 work across viruses and, through autocrine and paracrine signaling mechanisms, can reduce viral 53 production from infected cells and render proximal target cells temporarily resistant to infection, 54

controlling disease progression (10, 11). With SARS-CoV-2, patients with mild disease had higher levels 55

of interferons in their upper respiratory airways than those with more severe disease, suggesting that 56 robust innate immune responses contribute to reduced severity of infection (5). 57

A few days into the infection, the adaptive immune response involving virus-specific effector CD8 T-58 cells is triggered. CD8 T-cells are thought to play a critical role in the clearance of SARS-CoV-2 (7): The 59

earlier the first detectable CD8 T-cell response, the shorter is the duration of the infection (12). CD8 T-60 cell numbers were higher in the bronchoalveolar lavage fluids of individuals with mild/moderate 61 symptoms than in those with severe infection (13). Clonal expansion of CD8 T-cells was compromised in 62 patients with severe symptoms (13, 14) . Infected individuals often suffer lymphopenia (15, 16), with the 63 extent of lymphopenia correlated with disease severity (15, 17) . Finally, the severity of the symptoms was 64

proportional to the level of exhaustion of CD8 T-cells (15, 17). Accordingly, a combination of the innate 65

and CD8 T-cell responses appears to drive viral clearance. 66

Once the disease is resolved, typically in 2-3 weeks, the cytokines and activated CD8 T-cell populations 67 decline and eventually fade away, leaving behind memory CD8 T-cells (7 infection in the unvaccinated is thought to be less significant than that of CD8 T-cells (7). Antibody titers 80 are higher in severely infected than in mildly infected individuals (7). Whereas a subset of antiviral 81

antibodies possibly contribute to the clearance of infection (28), autoantibodies, typically generated in 82 COVID-19 patients, against cytokines and cell surface and structural proteins of the host, may adversely 83 affect clinical outcomes (29). 84

Based on these observations, we hypothesized that the strength and the timing of the innate and the CD8 85

T-cell responses were the predominant factors responsible for the heterogeneous outcomes of SARS-86

CoV-2 infection. To test this hypothesis, we developed a mathematical model of within-host SARS-CoV-87 2 dynamics that incorporated the key features of the innate and the CD8 T-cell responses. We validated 88 the model against patient data and employed it to elucidate the interplay of the two immune arms in the 89 outcomes realized. 90

We considered an individual infected by SARS-CoV-2. We modeled disease progression in the individual 93 by following the time-evolution of the population of infected cells ( ), the strength of the effector CD8 T-94 cells ( ), the cytokine-mediated innate immune response ( ), and tissue damage ( ) ( Figure 1 ). We 95 considered the essential interactions between these entities (30) and constructed the following equations 96 to describe their time-evolution: 97

Here, the infected cells follow logistic growth (30), with a per capita growth rate 1 and carrying capacity 102

. This growth represents the infection of target cells by virions produced by infected cells (30). 103

is the maximum number of cells that can get infected, due to target cell or other limitations. The growth 104 rate 1 is assumed to be reduced by the innate immune response, , with the efficacy , due to 105

interferon-mediated protection of target cells and/or lowering of viral production from infected cells (10). 106

Effector cell-mediated killing of infected cells is captured by a mass action term with the second-order 107 rate constant 2 . The proliferation and exhaustion of CD8 T-cells are both triggered by infected cells at 108 maximal per capita rates 3 and 4 , respectively. and are the levels of infected cells at which the 109 proliferation and exhaustion rates are half-maximal, respectively. Following previous studies, we let 3 < 110 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted June 21, 2021. ; https://doi.org/10.1101/2021.06.15.21258935 doi: medRxiv preprint 4 and < , so that proliferation dominates at low antigen levels and exhaustion at high antigen 111 levels (30-32). The innate response, , is triggered by infected cells at the per capita rate 5 and is 112 depleted with the first-order rate constant 6 . To assess the severity of infection, we employ , which 113

represents the instantaneous tissue damage, with contributions from CD8 T-cell mediated killing of 114 infected cells, determined by , and from proinflammatory cytokines, represented by . Inflamed 115 tissue may recover with the first order rate constant . 116

Solving these equations would predict the time-course of the infection. We tested the model by applying 117

it to describe available patient data of viral load changes. 

A number of studies have reported viral load measurements during the course of SARS-CoV-2 infection 126 (33, 34). In most studies, measurements begin from the time of symptom onset because the time of 127 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted June 21, 2021. swabs are thought not to be the best correlates of disease outcome and severity (39). The sensitivity of 137 SARS-CoV-2 detection in sputum is substantially higher than in nasopharyngeal swabs (40). We 138 therefore employed data from the sputum samples in this study. We considered data from day zero to day 139 15 into the infection (supplementary text section A; supplementary tables S1-S3). Beyond two weeks, the 140 humoral response is mounted in most patients (7, 25), the role of which, as mentioned above, is poorly 141 understood (7). 142

We fit our model to the above viral load data, representing the dynamics of the infection and immune 143 responses in the respiratory tract. All patients in this dataset had mild symptoms, which waned by day 7 144

after the first virological test. The patients were of working age and otherwise healthy. In such patients, 145

markers of T-cell exhaustion are not significantly higher than healthy individuals and are markedly lower 146 than severely infected patients (15). Therefore, to facilitate more robust parameter estimation, we ignored 147

CD8 T-cell exhaustion in the present fits (by fixing 4 = 0). Furthermore, we assumed that the viral 148 population, , is in a pseudo-steady state with the infected cell population, so that ∝ . Since, the 149 dynamics of tissue damage ( ) is dependent on but does not affect the dynamics of infected cells ( ), CD8 150

T-cells ( ) and the cytokine mediated innate response ( ), in our model, we ignored for the present 151

fitting. This is further justified because the patients considered for fitting are mildly/moderately infected, 152

and are expected to suffer minimal tissue damage. Because the patients were all similar, we assumed that 153 would be similar in them and proportional to , the highest viral load reported across the 154 patients. We thus fit log 10 ( / ) calculated with our model to the normalized data of log 10 ( / ).

Our fits were not sensitive to (supplementary tables S4, S5). We allowed a delay following exposure 156

to account for the incubation period before viral replication can begin. We used a nonlinear mixed-effects 157 modelling approach for parameter estimation (41). Our model provided good fits to the data (figure 2, 158 first column of subplots) and yielded estimates of the parameters at the population-level (supplementary 159 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. observed in the patients. Patients 1, 2, 3, 4, and 14 had a single peak in viral load (or infected cell 186 numbers) followed by a decline of viral load leading to clearance (figure 2, second column of subplots). 187

Patients 7, 8 and 10, in contrast, had a second peak following the first. Our model predicted these distinct 188 patterns as arising from the temporal variation in the dynamics of the innate and CD8 T-cell responses. 189

The interactions between the innate response, , and infected cells, , in our model have signatures of the 190 classic predator-prey system (43) with the prey and the predator: In the absence of , grows. also 191 triggers , which in turn suppresses . declines in the absence of . These interactions, as with the 192 predator-prey system (43), predict oscillatory dynamics. Thus, following infection, grows, causing a rise 193 of in its wake. When rises sufficiently, it suppresses . When declines substantially, the production 194 of is diminished and declines. This allows to rise again and the cycle repeats. This cycle is broken 195 in our model by CD8 T-cells, . Viral clearance is not possible in our model without (supplementary 196 figure S1 ). When rises, it can suppress independently of , breaking the cycle and allowing to 197

dominate . Together, and can then clear the infection. In patients 7, 8, and 10, our best-fits predicted 198 an early innate immune response and a delayed CD8 T-cell response. The second peak was thus predicted 199 as a result of the above predator-prey oscillations that occurred before the CD8 T-cell response was 200 mounted. In patients 3, 4, and 14, a relatively early CD8 T-cell response was predicted, which precluded 201 the second peak. In patients 1 and 2, both the innate and CD8 T-cell responses were delayed, leaving little 202 time for the oscillations to arise in the 15 d period of our observations. We note that interpretations of the 203 multiple peaks in longitudinal viral load data have not been forthcoming (44). Our predictions offer a 204 plausible interpretation. 205

Third, the transient but robust innate immune response predicted (figure 2, third column of subplots) is 206 consistent with observations in mildly infected patients (45). Fourth, our prediction of the dynamics of the 207

CD8 T-cell response, where a gradual build-up is followed by a stationary phase (figure 2, fourth column) 208

is also consistent with observations. In mildly infected patients, SARS-CoV-2 specific T-cells were 209 detected as early as 2-5 days post symptom onset (12). This effector population remained stable or 210

increased for several months after clinical recovery (16, 46). 211

Our model thus fit the dynamics of infection in individuals showing mild symptoms and offered 212 explanations of disease progression patterns that had remained confounding. We examined next whether 213 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 21, 2021. ; https://doi.org/10.1101/2021.06.15.21258935 doi: medRxiv preprint the model could also describe more severely infected patients. For this, we varied different parameters in 214 our model and assessed the resulting dynamical features of the infection. 215

We reintroduced the CD8 T-cell exhaustion term, which we had ignored in the fits above because the 217 patients were mildly infected, and selected associated parameter estimates from previous studies (30). We 218 ensured that this did not affect our fits above (supplementary figure S2) . 219

Next, to estimate the severity of the disease, we also examined the dynamics of the instantaneous tissue 220 damage ( ). Typically, rose as the infection progressed and declined as it got resolved (supplementary 221 figure S3A , C). We reasoned that the severity of infection would be determined by the maximum tissue 222 damage suffered and the duration for which such damage lasted. Significant damage that is short-lived or 223 minimal damage that is long-lived may both be tolerable and lead to mild symptoms. We therefore 224 calculated the area under the curve (AUC) of , starting from when ascended above its half-maximal Associated immunopathology was nominal. These predictions were akin to asymptomatic and mild 246 infection scenarios. An early and robust effector T-cell response has been associated with milder 247

infections (12, 16, 46) . Here, in some cases with high 5 , a blip of the viral load was observed after an 248 initial phase of clearance. When 5 was decreased, marking a weaker innate response, the peak viral load 249 rose and immunopathology moderately increased. This was also observed when we decreased , which 250 lowered the efficacy with which the innate immune response inhibits the spread of the infection ( figure  251 3B). The latter trends associated with high 3 and low 5 have parallels to infected patients with robust 252

CD8 T-cell responses but impaired innate responses, such as those harboring mutations in the genes 253 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. observations of such clearance facilitated by cross-reactive effector T cells (12, 50). The outcomes were 299 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 21, 2021. 

In a recent study, patients were stratified by disease outcome and measurements of longitudinal viral load 304 from their saliva were fit using cubic splines, yielding ribbons of confidence intervals on viral loads for 305 each category (39). We digitized these ribbons and tested our model predictions against them (figure 4A-306 D, grey patches). The study reported data from symptom onset. We therefore added an estimated length 307 of the prodromal period to the timepoints in order to compare our model predictions. We set this length to 308 4.8 d from the German transmission chain data (37, 38) (supplementary table S2), which is also consistent 309 with other reported estimates (33). We estimated the viral load, , from our model predictions using the 310 pseudo-steady state approximation, ≈ / , where is the per capita rate of viral production from 311 infected cells and is the per capita rate of viral clearance. We set and to values estimated previously 312

(52) (supplementary text section A). 313 314 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. 

The ribbons of data are not amenable to fitting. We therefore varied parameters associated with the innate 327

and CD8 T-cell responses in our model to achieve dynamical profiles of viral load resembling the 328 ribbons. For the purpose of these simulations we ignored both the potential adverse and favorable effects 329 of antibodies. The ribbon for the non-hospitalized patients was associated with low viral loads (figure 330

4A). The peak viral load was approximately 10 6 copies of viral RNA. This relatively low peak viral load 331 could be captured by our model when the strength of the innate response was increased, which we 332 achieved by increasing 5 and/or (supplementary table S9). The duration of the infection was 333 dependent on the CD8 T-cell response. Strong CD8 T-cell stimulation, achieved with a low value of , 334 led to rapid clearance, whereas weaker stimulation, corresponding to a higher , allowed the infection to 335 remain for an extended period. We calculated the immunopathology associated with these simulations and 336

found it to be low (figure 4A, scale on the right; also see below). 337

The ribbon for patients eliciting moderate symptoms had a relatively higher viral load at the peak, 338

reaching approximately 10 8 copies of viral RNA ( figure 4B ). Parameters sufficiently close to the 339 population estimates above allowed us to capture the dynamics for these patients (supplementary table  340 S10). The associated immunopathology was considerably higher than the non-hospitalized patients. For 341 severely infected patients, the viral load peak was above 10 8 , reaching as high as 10 10 copies ( figure 4C ). 342

We achieved this high peak viral load by lowering the strength of the innate response (decreasing 5 343 and/or ; see supplementary table S11). The delayed clearance could be recapitulated by lowering CD8 344

T-cell stimulation (increasing and/or decreasing 3 ). The immunopathology was higher than those 345 calculated to capture the viral load dynamics in moderate patients (compare the scales in figure 4B and 346 4C). Lastly, for the deceased individuals, the peak viral load was similar to the severe patients. However, 347 the downward trend in the viral load after the peak seen with the severely infected patients was no longer 348 apparent ( figure 4D) . The viral load remained around 10 8 RNA copies till day 30 post-exposure. A much 349 weaker innate response (low ) and a weaker CD8 T-cell response (high ) could generate matching 350 profiles (supplementary table S12). The immunopathology for the deceased patients was consistently 351

higher than the severe patients, indicating that there might be an upper limit to the extent of 352 immunopathological tissue damage that lay somewhere between our estimates for severe and deceased 353 patients, and crossing which mortality would almost certainly result. 354

Our model thus recapitulated the trends in the viral load seen in patients with different severity of 355

infection. Furthermore, the model indicated that there should be a narrow range of immunopathology, 356

which acts as a threshold to determine the fatal outcomes in COVID-19 (figure 4D, scale on the right). 357 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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To assess whether variations in other model parameters could also achieve the above trends, we 358

performed a global sensitivity analysis of our parameters using one representative parameter combination 359

from each disease outcome category as reference (figure 4A-D, dashed curves; supplementary figures S9-360 S12; supplementary tables S9-S12). Specifically, we calculated how sensitive our measure of 361 immunopathology was to the parameters. We found that immunopathology was most sensitive to and 362 6 for non-hospitalized and moderately symptomatic patients (supplementary figures S9, S10). For 363 severely infected and deceased patients, , 3 and emerged as the important parameters 364

(supplementary figures S11, S12). These results reinforce our expectations above. In mild infections, the 365 innate immune response is strong and any variation in its strength would have the most influence on 366 disease severity. In more severe infections, the innate and adaptive responses are both involved and the 367 severity is therefore sensitive to variations in the strengths of both. 368

Model predictions thus successfully recapitulated the heterogeneous outcomes and the associated 369 dynamical patterns of SARS-CoV-2 infection. 370

The extreme heterogeneity in the outcomes of SARS-CoV-2 infection across infected individuals has 372 been puzzling. Here, using mathematical modeling and analysis of patient data, we predict that the 373 heterogeneity arises from the variations in the strength and the timing of the innate and the CD8 T-cell 374 responses across individuals. When both the innate and the CD8 T-cell arms are strong, asymptomatic or 375 mild infections result. When the CD8 T-cell arm is strong, clearance of the infection results. If the innate 376 arm is weak, the peak viral load can be large, resulting in higher immunopathology and moderate 377

symptoms. When the CD8 T-cell response is strong but delayed, a predator-prey type interaction between 378 the innate arm and the virus results, causing multiple peaks in viral load. These oscillations end when the 379

CD8 T-cell response is mounted, and clearance ensues. When the CD8 T-cell response is weak, but the 380 innate arm is strong, prolonged infection can result before clearance. When both the arms are weak, 381

severe infection including mortality follows. These predictions offer a conceptual understanding of the 382 heterogeneous outcomes of SARS-CoV-2 infection. They also offer a synthesis of the numerous 383 independent and seemingly disconnected clinical observations associated with the outcomes and present a 384 framework that may help tune interventions. 385

In the last year, several mathematical models of within-host SAR-CoV-2 dynamics have been developed 386

and have offered valuable insights (53). For instance, they have helped estimate the within-host basic 387

reproductive ratio (33, 34, 52) and assess the effects of drugs and vaccines (26, 27, 44, 54-57). Attempts 388

have also been made to capture the role of the immune system in disease progression and outcome (44, 389 55, 57-61). Available models, however, have either not been shown to fit longitudinal patient data or 390 have failed to describe the entire range of outcomes realized. To our knowledge, ours is the first study to 391 describe the outcomes realized comprehensively using a mathematical model that is consistent with 392 patient data. 393

Our model predictions help better understand known demographic correlates of disease severity and 394 mortality, such as gender, age and co-morbidities. In all these cases, as our predictions indicate, more 395

severe infections are associated with weaker CD8 T-cell responses and/or unregulated innate immune 396

responses. Male patients trigger higher levels of peripheral cytokine expression and elicit weaker CD8 T-397 cell responses than female patients (62), resulting in more frequent severity and mortality in males (43). 398 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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The increased mortality in the elderly is caused by immunosenescence, which is associated with 399 decreased proliferative capacity of lymphocytes and impaired functionality of innate immune cells (63). 400

Increased mortality is also associated with co-morbidities, such as type-2 diabetes (64), where 401 uncontrolled production of proinflammatory cytokines and inappropriate recruitment of lymphocytes is 402 observed (65). 403 is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 21, 2021. Study design. We constructed a mathematical model of within-host SARS-CoV-2 infection using 479 ordinary differential equations. Next, we utilized a nonlinear mixed-effects approach to fit the model to an 480

available clinical dataset and estimated model parameters (supplementary text, section A, B). The model 481 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The parameters were manually varied and the quality of the fits determined by visual inspection of the 502 simulation profile and the confidence interval ribbons. 503 Sensitivity analysis. We executed variance based global sensitivity analysis (VBGSA) on the models; the 504 details of the algorithm have been described elsewhere (94). We simultaneously varied the parameters up 505

to 5% above and below the population parameters in Monte Carlo simulations and calculated total effect 506 indices for the parameters (supplementary figures S9-S12). 507 508 Acknowledgments 509

We thank Pranesh Padmanabhan for insightful comments and Rajat Desikan for help with the Monolix 510 platform. BC is supported by the C. V. Raman postdoctoral fellowship at the Indian Institute of Science. 511

Conceptualization: BC, HSS, NMD 513

Methodology: BC, HSS 514

Investigation: BC, HSS 515

Visualization: BC, HSS 516

Supervision: NMD 517

Writing-original draft: BC, HSS 518

Writing-review & editing: BC, HSS, NMD 519 520 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted June 21, 2021. ; https://doi.org/10.1101/2021.06.15.21258935 doi: medRxiv preprint

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