Abstract
Influenza viruses cause a significant amount of morbidity and mortality. Understanding host immune control efficacy and how different factors influence acute lung injury and disease severity are critical. Here, we established the dynamical connections between viral loads, infected cells, CD8+ T cells, lung injury, and disease severity using an integrative model-experiment exchange. The model predicts that infection resolution is sensitive to CD8 expansion, that there is a critical T cell magnitude needed for efficient resolution, and that the rate of T cell-mediated clearance is dependent on infected cell density. We used whole lung histomorphometry to validate the model, which showed that the infected area matched the model-predicted infected cell dynamics, and that the resolved area paralleled the relative CD8 dynamics. Additional analysis revealed a nonlinear relation between disease severity (i.e., weight loss) and lung injury. These novel links between important pathogen kinetics and host pathology enhance our ability to forecast disease progression, potential complications, and therapeutic efficacy.
Introduction
Over 15 million respiratory infections and 200,000 hospitalizations result from influenza A viruses (IAVs) each year [1–4]. The incidence and severity of IAV infections increases when new strains emerge and/or when there is a lack of prior immunity. A robust immune response is crucial for resolving viral infections, but immune-mediated pathology can exacerbate disease [5–9]. High viral loads also play a role in disease progression [10], but these do not always correlate with the strength of the host response or with disease severity [11–14]. An understanding of how viral loads, host immune responses, and disease progression are related is critical to identify disease-specific markers that may help predict hospitalization or other complications.
During IAV infection, viral loads increase rapidly for the first 1-2 days of infection before reaching a peak (e.g., as in [13, 15–19]). In naïve hosts, viral loads then begin to decline, first slowly (< 1 log10 TCID50/d; 3–7 d) then rapidly (4 − 5 log10 TCID50/d; 7–9 d) [15]. We previously quantified this biphasic viral decline with a mathematical model, which indicated that the rate of infected cell clearance increases as the density of infected cells decreases [15]. The timing of the second, rapid viral decay phase coincides with the expansion of CD8+ T cells, which are the primary cell responsible for clearing infected cells and resolving the infection [20–24], and, to a lesser extent, neutralizing antibodies [21, 22, 24–26]. For the CD8+ T cell response, in particular, it remains unclear whether the efficacy of these cells is dictated by their own density [27, 28], infected cell density [29–31], or both [32]. While quantifying CD8+ T cell efficacy is difficult in vitro and in vivo, the question is ripe for in silico investigation. Indeed, several modeling studies have described CD8+ T cell-mediated infected cell clearance for various viral infections, including IAV, HIV, and LCMV (e.g., as in [17,27,29,32–38]). However, for IAV infections, nonlinearities in the efficiency of the CD8+ T cell response and the consequences on viral loads and host pathology have not yet been investigated in detail.
A better understanding of infected cell clearance may also yield insight into the damage induced to the lung during IAV infection. In general, widespread alveolar disease is observed in patients who succumb to the infection [39]. Further, hospitalized patients that died as a result from infection with the 2009 H1N1 influenza virus had large numbers of CD8+ T cells present in their lung tissue [7]. Large pulmonary populations of CD8+ T cells do contribute to lung injury by targeting IAV-infected cells (reviewed in [5]) in addition to ‘bystander damage’ to uninfected epithelial cells [40]. The accumulation of damage to the epithelium during IAV infection, either from virally-induced cell lysis or immune-mediated effects, is relatively understudied. This is in part due to the difficulty in measuring the dynamics of infected cells and in establishing how damage correlates to different host responses. Recent technological advances, including the use of reporter viruses [41–44] and lung histomorphometry [12, 45–47], have provided an opportunity to acquire these types of measurements. However, even with these techniques, quantitative data over the course of infection is not currently available. Having data such as these should help reconcile potential nonlinearities in infected cell clearance and provide insight into the accumulated lung damage, which we hypothesize is a marker of disease severity.
In general, measures of disease severity do not seem to be directly correlated to viral loads or to specific immunological components. In humans infected with IAV, viral loads typically increase prior to the onset of systemic symptoms, which peak around 2–3 d post-infection (pi) [18,48,49]. Respiratory symptoms often last longer and can remain following viral clearance [48]. In the murine model, weight loss is used as an indicator of disease progression and severity, where greater weight loss corresponds to more severe disease [50–52]. Animal weights typically drop slowly in the first several days during an IAV infection and more rapidly as the infection begins to resolve [19, 53]. This is unlike viral load dynamics in these animals, which increase rapidly during the first 0–3 d pi then remain relatively constant prior to resolution [15]. Because weight loss often occurs following resolution of the infection, immune-mediated pathology is thought to play a role [5, 52, 54–56]. Host and pathogen factors, such as age, viral proteins, and inoculum size, can also influence disease progression [13, 14, 57, 58]. While the causes of IAV-associated disease and mortality remain elusive, this gap in knowledge impairs our ability to effectively predict, understand, and treat the disease.
To gain deeper insight into the dynamics of viral resolution and investigate the connection between viral loads and disease severity, we simultaneously measured viral loads and CD8+ T cells daily from the lungs of BALB/cJ mice infected with influenza A/Puerto Rico/8/34 (H1N1) (PR8). We then developed a model that describes their kinetics to explore the mechanisms and dynamics of CD8+ T cell influx and their efficiency in removing virus-infected cells. The model verified our previous results that infected cells are cleared in a density-dependent manner. We further determined that infection duration is dependent on the magnitude of CD8+ T cells rather than their efficacy. Exploring these findings through quantitative whole lung histomorphometry corroborated the model-predicted infected cell dynamics and the direct relation between infected cell clearance and CD8+ T cell expansion. In addition, these data revealed a nonlinear connection between disease severity, as measured by weight loss, and the amount of the lung impacted by the infection. The data, model, and analyses provide a robust quantification of the density-dependent nature of CD8+ T cell-mediated clearance, and the critical connections between these cells and the dynamics of viral loads, infected cells, lung injury, and disease severity.
Results
Virus and CD8+ T cell kinetics
In animals infected with 75 TCID50 PR8, virus rapidly infects cells or is cleared within 4 h pi (Figure 1). Virus then increases exponentially and peaks after ∼2 d pi. Following the peak, virus enters a biphasic decline. In the first phase (2–6 d pi), virus decays slowly and at a relatively constant rate (0.2 log10 TCID50/d) [15]. In the second phase (7–8 d pi), virus is cleared rapidly with a loss of 4 − 5 log10 TCID50 in 1–2 d (average of −3.8 log10 TCID50/d) [15]. CD8+ T cells remain at their baseline level from 0–2 d pi before they infiltrate the lung tissue and increase slightly at 2–3 d pi. The population briefly contracts (3–5 d pi) before expanding rapidly (6–8 d pi). This expansion corresponds to the second viral decay phase. Sixty percent of mice clear the infection by 8 d pi, and the other forty percent by 9 d pi. CD8+ T cells decline following viral clearance (8–10 d pi), but do not return to their baseline level. These cells then increase again slightly from 10–12 d pi.
Viral kinetic model with CD8+ T cell-mediated clearance
We previously described the viral load kinetics and biphasic decline using a density-dependent (DD) model in Equations (S7)–(S10) (Supplementary Information) [15], which assumes that the rate of infected cell clearance increases as the density of infected cells decreases (i.e., δd(I2) = δd/(Kδ + I2)). Because the rapid decay of virus is thought to be due to the clearance of infected cells by CD8+ T cells, we developed a model that describes the dynamics of these cells and their efficiency in resolving the infection (Equations (1)–(6); Figure 1A). The model includes equations for effector (E, denoted CD8E) and memory (EM, denoted CD8M) CD8+ T cells, and two mechanisms of infected cell clearance. During the first viral decay phase (2–6 d pi), the rate of infected cell clearance by unspecified mechanisms is relatively constant (δ). During the rapid, second viral decay phase (7–8 d pi), CD8E-mediated infected cell clearance occurs at a rate that increases as the density of infected cells decreases . Excluding this density dependence entirely resulted in a significant and premature decline in viral loads, which disagreed with the experimental data. We also tested whether the density dependence could be included in the CD8+ T cell expansion rate rather than in the infected cell clearance rate (see Equations (S1)–(S6)) as other models have done (e.g., as in [59–61]). This modification yielded a close fit to the viral load and CD8+ T cell data at 6–10 d pi but not at other time points (Figure S1). However, the viral load data was slightly underestimated at 7 d pi and the rapid decline between 7–8 d pi. Thus, retaining the density-dependence in the rate of infected cell clearance most accurately captured the entire dataset. Although memory CD8+ T cells are not the focus here, it was necessary to include the CD8M population because CD8+ T cells are at a significantly higher level at 10–12 d pi than at 0 d pi (Figure 1B). The model includes terms for CD8E infiltration (ξI2/(KE + E)), which accounts for the initial increase at 2–3 d pi, and for CD8E expansion (ηEI2(t − τE)), which accounts for the larger increase between 5–8 d pi. To capture the contraction of CD8+ T cells between these times (3–5 d pi), it was necessary to assume that CD8E infiltration is reduced by their own population (i.e., ξ(E) = ξ/(KE + E)). In both terms, the increase is proportional to the number of infected cells. Fitting the model simultaneously to viral loads and CD8+ T cells from the lungs of infected animals illustrated the accuracy of the model (Figure 1B). The resulting parameter values, 95% confidence intervals (CIs), ensembles, and histograms are given in Table 1 and in Figures 2 and S2–S3.
Plotting the model ensembles revealed a correlation between the two infected cell clearance parameters (δ and δE; Figure 2B), which represent the efficacy of the non-specific immune response and the CD8+ T cell response, respectively. Performing a sensitivity analysis showed that the viral load dynamics do not change substantially when these parameters are increased or decreased. However, decreasing the rate of non-specific infected cell clearance (i.e., lower δ) resulted in a significant increase in the number of CD8E due to the small increase in the number of infected cells (Figures S4-S5). Even with a larger CD8E population, recovery was delayed by only ∼ 0.1 d. Given the correlation between δ and δE (Figure 2B), a more efficient CD8E response (i.e., higher δE) may be able to overcome this short delay in resolution. The lack of sensitivity to changes in the infected cell clearance parameters is in contrast to the DD model, where the viral dynamics were most sensitive to perturbations in δd (Figure S4) [15], which encompasses multiple processes. With CD8+ T cells explicitly included in the model, the infection duration was most sensitive to changes in the rate of CD8E expansion (η) (Figures S4, S5; discussed in more detail below).
Examining the parameter ensembles and sensitivity analysis also yielded insight into how other model parameters affect the CD8+ T cell response. The rates of CD8E expansion (η) and clearance (dE) were slightly correlated, indicating a balance between these two processes (Figure 2C). This correlation and the sensitivity of η produced model dynamics that were also sensitive to changes in the CD8E clearance rate (dE) (Figure S6). As expected, the rates of CD8M generation (ζ) and CD8E clearance (dE) were correlated (Figure 2C). It has been estimated that approximately 5–10% of effector CD8+ T cells survive to become a long-lasting memory population [62]. Despite the inability to distinguish between CD8E and CD8M in the data, the model predicts that 17% of CD8E transitioned to the memory class by 15 d pi. Additional insight into the regulation of the CD8+ T cell response, results from the model fitting, and a comparison of the DD model and the CD8+ T cell model are included in the Supporting Information.
Density-dependent infected cell clearance
To gain further insight into the nonlinear dynamics of CD8+ T cell-mediated infected cell clearance, we plotted the clearance rate as a function of infected cells (I2) and CD8E (E) (Figure 3). This confirmed that there is minimal contribution from CD8E-mediated clearance to viral load kinetics or infected cell kinetics prior to 7 d pi (Figure 3A–C, markers a–b). At the initiation of the second decay phase (7 d pi), the clearance rate is δE(I2, E) = 3.5/d (Figure 3A–B, marker c). As the infected cell density declines towards the half-saturation constant , the clearance rate increases rapidly to a maximum of 4830/d (Figure 3A–C, markers d–g). The model predicts that there are 6 × 105 infected cells remaining at 7 d pi, which can be eliminated by CD8E in 6.7 h.
To explore how recovery time is altered by varying CD8E levels, we examined the resulting dynamics from increasing or decreasing the rate of CD8E expansion (η). When η was increased by 50%, the CD8E population increased by a substantial 670% (Figure S5). However, this was insufficient to significantly shorten the infection (8.4 d versus 7.8 d). The infection duration can be reduced if CD8E expansion began earlier (i.e., smaller τE; Figure S6). Although recovery is not significantly expedited by a larger CD8E population, the infection is dramatically prolonged if these cells are depleted (Figures 3D–E and S5). This in silico analysis revealed a bifurcation in recovery time, such that the infection is either resolved within ∼15 d pi or may last up to ∼45 d if CD8E are below a critical magnitude required to resolve the infection (Figure 3D–E). The critical number of total CD8+ T cells needed for successful viral clearance was CD8, which was 39.2% of the maximum number of CD8+ T cells obtained from the best-fit solution (i.e., Êmax = 1.9 × 106 CD8). This corresponds to 17% of CD8E (i.e., CD8E; Figure 3D–E). The model analysis indicated that decreasing the total number of CD8+ T cells by as little as 0.1% from this critical level (i.e., 39.2% to 39.1%) lengthen the infection from 15 d pi to 25 d pi (Figure 3D).
Lung injury dynamics
To investigate the dynamics of infected cells, we quantified these cells and the progression and resolution of the lung injury using serial whole lung histomorphometry (Figure 4A). Antigen-positive areas of the lung (“active” lesions) were first detectable at 2 d pi (Figure 4A–B), which coincides with the peak in viral loads. The infected area continued to increase in a nonlinear manner until 6 d pi, whereas viral loads remained high until 7 d pi (Figure 1B). At this time, resolution of the infection began and the infected area declined at a rate of ∼28.7%/d between 6–7 d pi (Figure S7A). Few to no infected cells were present at 8 d pi (Figure 4A). Correspondingly, virus was undetectable in most animals by 8 d pi (Figure 1B). Because the percent active lesion is a reflection of the influenza-positive cells, we examined whether the CD8+ T cell model accurately predicted these dynamics. In the model, the accumulated infection is defined by the cumulative area under the curve (CAUC) of the productively infected cells (I2). Plotting the percent active lesion against the CAUC of I2 shows that the model accurately reflects the cumulative infected cell dynamics and, thus, the infection progression within the lung (Figure 4B). Plotting the CAUC of I2 for all parameter sets in the 95% CIs further illustrates the accuracy by showing that the heterogeneity in the histomorphometry data is captured (Figure 4B), which is larger than the heterogeneity in viral loads (Figure 1B).
Antigen-negative, previously-infected or damaged areas of the lung (“inactive” lesions) are evident beginning at 5 d pi (Figure 4A,C). This resolution of the infection continued from 5–8 d pi, causing a 14.6%/d increase in the area of inactive lesions (Figure S7B). Following this, healing of the injured lung is apparent as the inactive lesioned areas decline (−14.5%/d from 9–10 d pi; Figures 4C and S7B). These dynamics parallel the CD8+ T cell dynamics (Figure 1B). Fitting a line to the CD8+ T cell data from 5–8 d pi indicated that the influx rate is 4.7 × 105 cells/d (Figure S7C). Thus, the model estimates that every 100,000 CD8+ T cells clear ∼ 3.1% of the lung. During the CD8+ T cell contraction phase (8–10 d pi; Figure 1B), a similar linear regression analysis suggested that these cells decline at a rate of ∼ 3.3 × 105 CD8/d (Figure S7C). Similar to the relation discussed above, the dynamics of the damaged areas of the lung corresponded precisely to the dynamics of the percent maximum CD8E (i.e., E/Emax) in the model (Figure 4C). Further, adding the predicted dynamics for the active and inactive lesions agrees with the dynamics of the total percent lesion (Figure S8).
Weight loss predicts area of lung injured
To monitor disease progression, weight loss was measured daily throughout the course of infection (Figure 4D). During the first 5 d pi, animals gradually lost ∼4% of their initial weight. This was followed by a sharper drop (8%) at 6 d pi. Animal weights increased slightly at 7 d pi (∼6%) before reaching peak weight loss (10–14%) at 8 d pi. Following virus resolution, the animals’ weights began to restore as the inactive lesions resolved (9–10 d pi; Figure 4D). We hypothesized that these weight loss dynamics may reflect the area of the lung impacted by the infection. Indeed, plotting weight loss together with the percent total (active and inactive) lesioned area of the lung revealed the similarity in their dynamics (Figure 4D-E). To further quantify their relationship, we plotted the percent weight loss against the percent total lesioned area and observed a nonlinear relation. Thus, we fit the saturating function to these data, where L is the percent total lesioned area, W is percent weight loss, lmax is the maximum rate of the interaction, Kw is the half-saturation constant, and n is the Hill coefficient. This function provided a close fit to the data (R2 = 0.9; Figure 4E) with best-fit parameters lmax=39.7% total lesioned area, Kw=2.6% weight loss, and n = 5.2.
Discussion
Influenza A virus infections pose a significant threat to human health, and it is crucial to understand how the virus spreads within the respiratory tract, how specific immune responses contribute to infection control, and how these relate to disease progression. Although it has been difficult to directly relate these features, we circumvented the challenge by pairing comprehensive experimental data with robust mathematical models and analyses. Our iterative model-driven experiment approach [63, 64] revealed important dynamic relations between virus, infected cells, CD8+ T cells, lung damage, and weight loss (Figure 5). Identifying these nonlinear connections allows for more accurate interpretations of viral infection data and significant improvement in our ability to predict disease severity, the likelihood of complications, and therapeutic efficacy.
Our histomorphometric data provided the first quantification of the spread of influenza virus infection within the lung and the dynamics of lung injury. These data allowed us to validate our model’s predicted infected cell dynamics and provide support that their density impacts the rate at which they are cleared by effector CD8+ T cells (CD8E) (Figure 4). Interestingly, CD8+ T cell dynamics can be mostly replicated when assuming the density dependence lies within their expansion (Figure S1). Discriminating between these mechanisms is difficult in vivo, but the ability of the model in Equations (1)–(6) to capture the entire time course of CD8E dynamics is compelling. Regardless of the mechanism, we first detected this density-dependence in a model that excluded specific immune responses (i.e., Equations (S7)–(S10)) [15]. That model was a mathematically elegant way to capture the nonlinearity in the viral load decline, but it could not distinguish between different mechanisms of viral clearance. Here, we verified that the second viral clearance phase reflects CD8+ T cell-mediated clearance, determined that their efficiency increases as more infected cells are removed, and identified the critical level needed for a timely recovery (Figure 3).
Several factors may contribute to the density-dependent change in the rate of CD8E-mediated clearance. One possibility is that the slowed rate of clearance at high infected cell densities is due to a “handling time” effect, which represents the time required for an immune cell to remove an infected cell (e.g., as in [15, 27, 32, 65–68]). When CD8E interact with infected cells, a complex is formed for ∼20–40 min [35, 69–72]. Because CD8E could not interact with other infected cells during this time, the global rate of infected cell clearance would be lowest when infected cells outnumber CD8E. In addition, contact by a single CD8E may be insufficient to remove an infected cell [31]. Infected cell clearance is more frequently observed after interactions with multiple CD8E, with an average of 3.9 contact events either serially or simultaneously [31]. Thus, the high density of infected cells early in the infection reduces the probability that a single virus-infected cell would be targeted a sufficient number times to induce cell death. However, as CD8E accumulate and the density of infected cells decreases (Figure 3A), the probability of simultaneous interactions will increase. This should reduce the handling time required to remove of an infected cell and, thus, result in a higher efficiency. While this is a likely explanation, it is possible that spatial limitations also contribute, such that a high infected cell density may hinder CD8+ T cells from reaching infected cells on the interior of the infected tissue. Crowding of immune cells at the periphery of infected lesions has been observed in other infections (e.g., in tuberculosis granulomas [73, 74]) and has been suggested in agent-based models of influenza virus infection [75].
The new knowledge about how the infection spreads throughout the lung also uncovered a novel connection between the percent weight loss of an infected animal (i.e., disease severity) and the percent total area of the lung injured during the virus infection (Figure 4D–E). This discovery is significant because it suggests that disease severity is linked to the extent of lung injury, which we showed is directly connected to infected cell and CD8E kinetics (Figure 4B–C) and indirectly connected to viral load kinetics (Figure 5). Other studies utilizing histomorphometry data, although not quantitatively, corroborate the relationship between weight loss and lung involvement during IAV infection [12]. For example, animals treated with antivirals in various conditions (single or combination therapy and in immunocompetent or immunosuppressed hosts) demonstrated that, although viral loads are not always significantly reduced, the antiviral-induced reductions in weight loss corresponded to decreased infected areas of the lung [12, 45]. Examining the lung injury kinetics and its connection with weight loss in various infection settings (e.g., high versus low dose, different ages or sex, under therapy, other strains or viruses, etc.) and how innate responses contribute to the lung injury should improve our predictive capabilities. This may be particularly helpful in understanding the exacerbated morbidity and mortality in elderly individuals, where there is typically lower viral loads compared to adults coupled with increased weight loss, symptoms, and/or mortality within animal models [13, 14].
The nonlinear relations derived from the lung injury analysis (Figures 4–5) further provide a way to interpret and utilize weight loss data, which is the most readily available type of data and commonly used as a measure of disease severity in infection models. These results demonstrate significant potential for weight loss data to be used, analyzed, and interpreted within both modeling and experimental studies. In our data and others’, there is a spike in weight loss, symptom score, and/or inflammation at ∼6 d pi [53, 57, 76, 77] (Figure 4D). Our data suggests that this may be due to CD8E infiltration and activity while the infection continues to spread. The subsequent increase in animal weights starting at 7 d pi is concurrent with the decline in infected lesions (Figure 4). Utilizing this observation and the function describing the correlation between the percent lung lesion and weight loss (L(W); Figure 4E), the kinetics of the active and inactive lesioned areas can be directly estimated from weight loss data (Figure 5). Taking this one step further, the dynamics of the CAUC of the productively infected cells (I2) and the relative CD8E can be obtained. Finally, the CD8+ T cell model (Equations (1)–(6)) can be employed to estimate the viral load and CD8+ T cell dynamics (Figure 5). These connections can be reversed to estimate disease severity (i.e., weight loss) from viral load data.
The model’s 95% CI predictions of the lesioned area nicely captured the heterogeneity in the data (Figures 4 and S8), which is remarkable given the minimal variability in the virus and CD8+ T cell data and model fit (Figure 1B). The differential heterogeneity suggests that small changes to viral loads can induce a significant changes in disease severity. Indeed, this has been observed when antivirals are administered [78–83] or when host responses are modified [84–86]. It may also indicate that viral loads are not a reliable measure of infection severity. This knowledge should also aid future studies seeking to estimate therapeutic efficacy or the effects of immune modulation. There was a slight over-estimation of the inactive lesion early in the infection (1–5 d pi, dark gray shading; Figure 4). This may suggest that the CD8+ T cells present during this time do not have effector capabilities or are not virus-specific (Figure 4C). These cells could also be tissue resident T cells and/or T cells circulating in the blood.
Weight loss increases following infection resolution (8–9 d pi), which is likely attributed to CD8+ T cell-mediated pathology (Figure 4C). This is supported by other studies that suggest a large number of CD8+ T cells poses a risk of acute lung tissue injury [5–9]. According to our model predictions, excessive CD8+ T cell numbers may augment disease progression yet do not improve recovery time (Figure S5). Instead, an earlier onset of CD8E proliferation (i.e., smaller τE) would be required to significantly shorten the infection (Figure S6). This aligns with evidence that hosts with adaptive immune responses primed by vaccine or prior infection recover more rapidly [87, 88]. While higher CD8+ T cell numbers have little impact on viral kinetics, the model agrees with clinical and experimental studies from a wide range of host species that impaired CD8+ T cell responses can prolong an IAV infection [17, 22, 26, 89–91]. That is, virus can persist for up to several weeks if CD8+ T cell-mediated clearance is unsuccessful (Figure 3; [26,92,93]). The bifurcation in recovery time revealed by the model suggests that this may occur when the number of effector CD8+ T cells are less than 2.3×105 CD8E (Figure 3D–E). This number is expected to vary depending on parameters like the rate of virus replication and the infected cell lifespan, which has been noted in another modeling study that detailed similar bifurcation behavior [94]. Although some previously published models also suggested delayed resolution with depleted CD8+ T cell responses [17, 36, 37, 95], this bifurcation has not been observed and their estimated delays in recovery do not amount to the long-lasting infections in immunodeficient patients [26, 92, 93]. Further, although one model is able to match viral load kinetics in the absence of B cells or T cells [36], the result was contingent on the continuous abundance of susceptible cells that was caused by a reversion of an interferon-induced refractory state, which is not supported by experimental data [96]. Including innate responses or antibodies in our model may affect the parameter values, the predicted CD8+ T cell threshold value, and/or the critical number of CD8+ T cells required for recovery, but the close fit of the model and estimation of the lung lesions suggests that the qualitative results would not change.
In addition to illuminating the connections between virus spread, virus clearance, the associated pathology, and the severity of disease, the histomorphometric data validated the model’s infected cell dynamics (Figure 4B). The dynamics of susceptible and infected cells throughout the infection and the accuracy of the target cell limited approximation used within influenza viral kinetic models have been questioned for several years [64,97–102]. The ability of the model to accurately predict the histomorphometry data corroborates the use of this approximation, which assumes a limited number of available target cells and describes their decline by infection only. Although the slowing of virus spread is likely more dynamic and involves immune-mediated mechanisms, more complex dynamics are unnecessary to describe the data. Further, the model and data agree that there are few infected cells during the time when viral loads are growing most rapidly (0–2 d pi; Figures 1B and 4B). We previously used this information to derive approximations for the model and gain deeper insight into how each parameter influences the kinetics [103], which has helped numerous studies interpret their results [15, 17, 104, 105]. The data also supports the model’s hypothesis that that there is minimal clearance of infected cells prior to CD8E infiltration (Figure 3A–B). The knowledge of the model’s accuracy and of the spatial spread throughout the lung should aid investigation into the mechanisms that limit virus growth during the early stages of the infection.
Employing targeted model-driven experimental designs to examine and validate theoretical predictions like the ones presented here is pivotal to elucidating the mechanisms of infection spread and clearance [63, 64]. Examining other infections (e.g., coronaviruses) and modifications to the dynamics (e.g., high dose or antiviral therapy) will help refine the dynamical link between virus, host immune responses, and disease severity and identify its generalizability. Determining the factors that influence disease severity/weight loss is vital to understanding the disproportionate mortality in at-risk populations (e.g., elderly) and to improve therapeutic design. This is particularly important because current antivirals alleviate symptoms but do not effectively lower viral loads [78–83]. The predictive capabilities of validated models like the one here should prove useful in forecasting infection dynamics for a variety of scenarios. These tools and analyses provide a more meaningful interpretation of infection data, new ways to interpret weight loss data, and a deeper understanding of the progression and resolution of the disease, which will undoubtedly aid our ability to effectively combat influenza.
Methods and Materials
Ethics statement
All experimental procedures were performed under protocol O2A-020 approved by the Animal Care and Use Committee at St. Jude Children’s Research Hospital under relevant institutional and American Veterinary Medical Association (AVMA) guidelines and were performed in a biosafety level 2 facility that is accredited by the American Association for Laboratory Animal Science (AALAS).
Mice
Adult (6 week old) female BALB/cJ mice were obtained from Jackson Laboratories (Bar Harbor, ME). Mice were housed in groups of 5 mice in high-temperature 31.2cm × 23.5cm × 15.2cm polycarbonate cages with isolator lids. Rooms used for housing mice were maintained on a 12:12-hour light:dark cycle at 22 ± 2°C with 50% humidity in the biosafety level 2 facility at St. Jude Children’s Research Hospital (Memphis, TN). Prior to inclusion in the experiments, mice were allowed at least 7 d to acclimate to the animal facility such that they were 7 weeks old at the time of infection. Laboratory Autoclavable Rodent Diet (PMI Nutrition International, St. Louis, MO) and autoclaved water were available ad libitum. All experiments were performed under an approved protocol and in accordance with the guidelines set forth by the Animal Care and Use Committee at St. Jude Children’s Research Hospital.
Infectious agents
All experiments were done using the mouse adapted influenza A/Puerto Rico/8/34 (H1N1) (PR8).
Infection experiments
The viral infectious dose (TCID50) was determined by interpolation using the method of Reed and Muench [106] using serial dilutions of virus on Madin-Darby canine kidney (MDCK) cells (obtained from Dr. Jonathan McCullers). Mice were intranasally inoculated with 75 TCID50 PR8 diluted in 100µl of sterile PBS. Mice were weighed at the onset of infection and each subsequent day to monitor illness and mortality. Mice were euthanized if they became moribund or lost 30% of their starting body weight. For viral load and CD8+ T cell quantification, experiments were repeated three times to ensure reproducibility and two complete experiments (10 animals per time point) were used for these studies. Histomorphometry was performed on five animals per time point.
Lung harvesting for viral and cellular dynamics
Mice were euthanized by CO2 asphyxiation. Lungs were aseptically harvested, washed three times in PBS, and placed in 500µl sterile PBS. Whole lungs were digested with collagenase (1mg/ml, Sigma C0130), and physically homogenized by syringe plunger against a 40µm cell strainer. Cell suspensions were centrifuged at 4°C, 500xg for 7 min. The supernatants were used to determine the viral titers (TCID50) by serial dilutions on MDCK monolayers. Following red blood cell lysis, cells were washed in MACS buffer (PBS, 0.1M EDTA, 0.01M HEPES, 5mM EDTA and 5% heat-inactivated FBS). Cells were then counted with trypan blue exclusion using a Cell Countess System (Invitrogen, Grand Island, NY) and prepared for flow cytometric analysis as indicated below.
Lung titers
For each animal, viral titers were obtained using serial dilutions on MDCK monolayers and normalized to the total volume of lung homogenate supernatant. The resulting viral loads are shown in Figure 1B and were previously published and utilized for calibration of the density-dependent model (Equations (S7)–(S10) (Supplementary Information)) [15].
Flow cytometric analysis
Flow cytometry (LSRII Fortessa; Becton Dickinson, San Jose, CA) was performed on the cell pellets after incubation with 200µl of a 1:2 dilution of Fc block (human-γ globulin) on ice for 30 min, followed by surface marker staining with anti-mouse antibodies: CD11c (eFluor450, eBioscience), CD11b (Alexa700, BD Biosciences), Ly6G (PerCp-Cy5.5, Biolegend), Ly6C (APC, eBioscience), F4/80 (PE, eBioscience), CD3e (PE-Cy7, BD Biosciences or BV785, Biolegend), CD4 (PE-Cy5, BD Biosciences), CD8α (BV605, BD Biosciences), DX5 (APC-Cy7, Biolegend or APC-e780, Affymetrix, Inc) and MHC-II (FITC, eBioscience). The data were analyzed using FlowJo 10.4.2 (Tree Star, Ashland, OR) where viable cells were gated from a forward scatter/side scatter plot and singlet inclusion. Following neutrophil (Ly6Ghi) and subsequent macrophage (CD11chiF4/80hi) exclusion, CD8+ T cells were gated as CD3e+CD8α+CD4−DX5−. The absolute numbers of CD8+ T cells was calculated based on viable events analyzed by flow cytometry as related to the total number of viable cells per sample. We chose to use the kinetics of the total number of CD8+ T cells rather than virus-specific CD8+ T cells because virus-specific subsets often have varying dynamics (e.g., as in [13]) and would complicate the model and potentially skew the results. The gating strategy is shown in Figure S9.
Lung histomorphometry and immunohistochemistry
The lungs from IAV infected mice were fixed via intratracheal infusion and then immersion in 10% buffered formalin solution. Tissues were paraffin embedded, sectioned, and stained for influenza virus using a primary goat polyclonal antibody (US Biological, Swampscott, MA) against influenza A, USSR (H1N1) at 1:1000 and a secondary biotinylated donkey anti-goat antibody (sc-2042; Santa Cruz Biotechnology, Santa Cruz, CA) at 1:200 on tissue sections subjected to antigen retrieval for 30 minutes at 98°C. The extent of virus spread was quantified by capturing digital images of whole-lung sections stained for viral antigen using an Aperio ScanScope XT Slide Scanner (Aperio Technologies, Vista, CA) then manually outlining defined fields. Alveolar areas containing virus antigen-positive pneumocytes were highlighted in red (defined as “active” infection), whereas lesioned areas containing minimal or no virus antigen-positive debris were highlighted in green (defined as “inactive” infection). Lesions containing a mix of virus antigen-positive and antigen-negative pneumocytes were highlighted in orange (defined as “mixed” infection). The percentage of each defined lung field was calculated using the Aperio ImageScope software. Representative images and quantitative analyses of viral spread and lung pathology during IAV infection are shown in Figure 4A–C.
CD8+ T cell model
To examine the contribution of CD8+ T cells to the biphasic viral load decay, we expanded the density-dependent (DD) model (Equations (S7)–(S10) (Supplementary Information)) to include two mechanisms of infected cell clearance (non-specific clearance (δ) and CD8+ T cell-mediated clearance (δE(I2, E))) and two CD8+ T cell populations: effector (E, denoted CD8E) and memory (EM, denoted CD8M) CD8+ T cells. The model is given by Equations (1)–(6).
In this model, target cells become infected with virus at rate βV per day. Once infected, cells enter an eclipse phase (I1) before transitioning at rate k per day to a productively-infected state (I2). These infected cells produce virus at rate p mathrmTCID50 per infected cell per day, and virus is cleared at rate c per day. Virus-producing infected cells (I2) are cleared by non-specific mechanisms (e.g., apoptosis and/or innate immune responses) at a constant rate δ per day. Innate immune responses were excluded from the model because the viral load data is linear during the time where they act (2–7 d pi) and, thus, additional equations cannot improve the fit. Productively infected cells are cleared by CD8E at rate per day, where the rate of infected cell clearance is per day and is the half-saturation constant. The CD8E-mediated clearance rate (δE(I2, E)) is dependent on the density of infected cells and is similar to the infected cell clearance term in the DD model (see Equation (S9)) [15]. Similar density-dependent forms have also been used in models that describe the CD8+ T cell response to other virus infections [32, 34, 65]. Models that exclude this density-dependence were examined, but these models resulted in a poor fit to the data. This is due in part to the infiltration of CD8+ T cells from 3–5 d pi (Figure 1). We did examine a model that excluded these dynamics and included CD8+ T cell expansion as a density-dependent function (e.g., ηEI2(t − τE)/(KI + I2)) while keeping a linear rate of CD8-mediated infected cell clearance (δEEI2) (Equations (S1)–(S6); Figure S1). This model was adapted from other published models [60, 61, 107] and can produce similar dynamics from 6-10 d pi, but there is less experimental support for this model.
The model assumes that CD8E infiltrate the lung proportional to infected cells at rate ξ(E) = ξ/(KE + E) CD8E per cell per day, which is down-regulated by the CD8E already present in the lung. The associated half-saturation constant is KE. Similar terms for CD8E regulation have been used in modeling HIV infections [34, 108] and in models that examined CD8+ T cell proliferation mechanisms [109]. In our model, CD8E expansion occurs at rate η per infected cell per day with time delay τE. This term accounts for local CD8E proliferation in the lung [110,111] and migration of CD8E from secondary lymphoid organs [20,112–114]. The delay may signify the time it takes CD8E to become activated by antigen presenting cells, differentiate, proliferate, and/or migrate to the infection site. The lung CD8E population declines due to cell death and/or emigration at rate dE per day. These cells transition to CD8M (EM) at rate ζ CD8M per CD8E per day after τM days. The model schematic and fit to the viral load and CD8+ T cell data are in Figure 1.
Parameter estimation
Given a parameter set θ, the cost C(θ) was minimized across parameter ranges using an Adaptive Simulated Annealing (ASA) global optimization algorithm [15] to compare experimental and predicted values of log10 TCID50/lung virus (V) and of log10 total CD8+ T cells/lung (Ê = E + EM + Ê0, where Ê0 is the initial number of CD8+ T cells at 0 d pi). The cost function is defined by where (ti, vi,j) is the viral load data, (ti, ei,j) is the CD8+ T cell data, and V (θ, ti) and Ê(θ, ti) are the corresponding model predictions. Here, sE = (vmax − vmin)/(emax − emin) is a scaling factor, and γi = Ji+1Ji−1 where Ji is the number of observations at time ti. Errors of the log10 data were assumed to be normally distributed. To explore and visualize the regions of parameters consistent with the model, we fit Equations (1)–(6) to 2000 bootstrap replicates of the data. If the fit was within χ2 = 0.05 of the best-fit and the CD8 derivative was not a statistical outlier as determined by the function isoutlier, then the bootstrap was considered successful [15, 104, 115]. For each best-fit estimate, we provide 95% confidence intervals (CI) obtained from the bootstrap replicates (Table 1). All calculations were performed in Python using the simanneal package [116] followed by a L-BFGS-B [117,118] deterministic minimization through SciPy’s minimize function. SciPy integrate.ode using lsoda and PyDDE [119] were used as the ODE and DDE solvers.
Estimated parameters included the rates of virus infection (β), virus production (p), virus clearance (c), eclipse phase transition (k), non-specific infected cell clearance (δ), CD8E-mediated infected cell clearance (δE), half-saturation constants ( and KE), CD8E infiltration (ξ), CD8E expansion (η), delay in CD8E expansion (τE), CD8E clearance (dE), CD8M generation (ζ), delay in CD8M generation (τM), and the baseline number of CD8+ T cells (Ê0). Bounds were placed on the parameters to constrain them to physically realistic values. Because biological estimates are not available for all parameters, ranges were set reasonably large based on preliminary results and previous estimates [15]. The rate of infection (β) was allowed to vary between , and the rate of virus production (p) between 10−1 −103 TCID50 cell−1 d−1. Bounds for the virus clearance rate (c) were 1 d−1 (t1/2 = 16.7 h) and 103 d−1 (t1/2 = 1 min). To insure biological feasibility, the lower and upper bounds for the eclipse phase transition rate (k) were 4 − 6 d−1 as done previously [15].
The rate of non-specific infected cell clearance (δ) was given limits of 0.05 − 1 d−1. The CD8E-mediated infected cell clearance rate (δE) varied between 0.01 − 2 cells , and the associated half-saturation constant was bounded between 102 − 106 cells. The upper bound of δE was chosen to maintain the convergence of δ to nonzero values. Bounds for the rate of CD8E infiltration (ξ) were , and bounds for the half-saturation constant (KE) were 103 − 106 CD8E. The CD8E expansion rate (η) varied between 10−8 − 10−6 cell−1 d−1, and the delay in CD8E expansion (τE) between 2–6 d. The rate of CD8E clearance (dE) had limits of 0.05 − 2 d−1. The rate of CD8M generation (ζ) varied between , and the delay in CD8M generation (τM) varied between 3–4 d. Larger bounds were examined for this parameter, however, the parameter is non-identifiable and a small range was required for convergence. Bounds for the baseline number of CD8+ T cells (Ê0) were set to the upper and lower values of the data at 0 d pi (3.0 ×105 −5.3 ×105 CD8).
The initial number of target cells (T (0)) was set to 107 cells [15,104,115]. The initial number of infected cells I1(0) was set to 75 cells to reflect an initial dose of 75 TCID50 [15]. We previously found that estimating I1(0), fixing V (0) = 75 TCID50, or estimating V (0) did not improve the fit and could not be statistically justified [15]. The initial number of productively infected cells (I2(0)), the initial free virus (V (0)), and the initial number of CD8E (E(0)) and CD8M (EM (0)) were set to 0.
Linear regression
The function polyfit in MATLAB was used to perform linear regression on the percent active lesioned area, the percent inactive lesioned area, and the CD8+ T cells during the expansion phase (5–8 d pi) and the contraction phase (9–10 d pi). Linear fits are shown in Figure S7.
Area under the curve
The function cumtrapz in MATLAB was used to estimate the cumulative area under the curve (CAUC) of the infected cells (I2) for the best-fit model solution.
Acknowledgments
This work was supported by NIH grant AI100946, AI125324, and AI139088 and ALSAC. We thank Alan Perelson for his helpful comments, and Robert Michael for technical assistance.
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