Fig 1.
Multiple data on T cell response from COVID-19 patients with different symptoms.
a. The percentage of naïve CD4+ T cells over CD4+ T cells. b. The percentage of naïve CD8+ T cells over CD8+ T cells. c. Counts of CD4+ T cells. d. Counts of CD8+ T cells. a-d include healthy control (HC: n = 50), moderate (n = 117) and severe (n = 40) patients from Yale New Haven Hospital (Dataset 4). e. The percentage of Tim-3 expression on CD4+ T cells. f. The percentage of Tim-3 on CD8+ T cells. e-f include healthy control (HC: n = 6), mild (n = 29) and severe (n = 12) patients from the Fifth Medical Center of PLA General Hospital of China (Dataset 2). g. The distribution of Tim-3 expression levels in CD4+ T/Treg cells. h. The distribution of Tim-3 expression levels in cytotoxic T lymphocytes (CTLs). g-h include moderate (n = 8) and critical (n = 13) patients from Charité-Universitätsmedizin Berlin and University Hospital Leipzig (Dataset 5). Significance was determined by two-sided, Wilcoxon rank-sum test.
Fig 2.
Framework of multiscale model of SARS-CoV-2 infection.
Intracellular: The S protein of SARS-CoV-2 binds to receptor proteins (ACE2, NRP1) on the cell surface. Viral dynamics within a target cell are considered, which include (1) the release of RNA of SARS-CoV-2, (2) virus-activated IFN expression, (3) positive feedback of IFNs, (4) activation of AVPs by IFNs, (5) natural depletion of IFNs, (6) inhibition of the virus by AVPs, (7) viral RNA replication, (8) protein synthesis, assembly of novel SARS-CoV-2 and budding into the extracellular environment, (9) natural degradation of AVPs, and (10) degradation of viral RNA. The progeny viruses leave the target cell by budding and further infect additional susceptible cells. Intercellular: The status of target cells is divided into uninfected and infected. There is a supplied source of normal cells that will be transformed into infected cells if they are infected by the virus. The infected cell is identified and cleaned by effector T cells. With respect to cellular communication, T cells mediate the immune response to SARS-CoV-2. PRRs on the cell surface sense SARS-CoV-2 and activate the immune response. Immune cells secrete cytokines, such as IL-6, IL-10, IFN-γ, etc., and activate naïve T cells. The activated T cells undergo differentiation and proliferation, and emerge as effector T cells. Activated T cells and effector T cells clear the infected cells and secrete cytokines. Some of cytokines (pro-inflammatory cytokines) induce chronic inflammation, dysfunction of the immune response, and exhaustion of the effector T cells, which contribute to disease progression. Organism: The population size of infected cells dictates the progression and severity of COVID-19. The progression of COVID-19 is divided to two phases, symptomatic and asymptomatic. Furthermore, the severity of symptomatic patients is primarily divided into mild-moderate and severe.
Table 1.
Summary of key parameters, biological significance, effects, and available clinical and/or experimental evidence.
Fig 3.
Progression dynamics in response to SARS-CoV-2 infection without considering T cell exhaustion (ρ = 0).
a. Time course of the ratio of infected cells (RIC) (out of 200 independent runs). The black dashed line is the threshold between the asymptomatic and symptomatic state. b. Comparison of incubation periods between simulations and real data in COVID-19. The black line shows the cumulative probability obtained from default values in Table A in S1 Text (out of 200 independent runs). The orange dots represent real data of incubation periods from Dataset 1. c. Two simulated trajectories were developed for the symptomatic and asymptomatic states (red and blue lines, respectively). (i)-(vi) respectively for the ratio of infected cells (RIC), extracellular virus concentration (Xex), intracellular virus concentration per cell (Xin), infected rate of susceptible cells, cytokine levels ([Cytokines]), and effector T cell counts ([Teffector]). Other parameters were assigned default values shown in Table A in S1 Text.
Fig 4.
Disease evolution dynamics from asymptomatic and symptomatic states in response to SARS-CoV-2 infection without considering T cell exhaustion (ρ = 0).
a. The percentage of cases (out of 200 independent runs) that developed into a state and the distribution of incubation period (TIP) for various IC50 values of viral replication (K1) and IFN response rate (λ2) after infection. b. The distribution of symptomatic frequency. The color column indicates the percentage of symptomatic cases (out of 100 individual runs) when K1 varies 40–50 and λ2 varies 0.2–0.4. c. The distribution (fraction of individual) of RIC at six different time points. The black dashed lines show the threshold separating asymptomatic and symptomatic states. Different color lines correspond to the IC50 of viral replication (K1) and interferon response rate (λ2). Other parameters were given default values as shown in Table A in S1 Text.
Fig 5.
Bimorphism of patient symptoms.
a. Distribution of RIC on day 30 after SARS-CoV-2 infection. b. Scatterplot of varied parameters and RIC on day 30. c. Distribution of the severity of COVID-19 patients. The color column shows RIC at day 30 when K4 varies between 40 and 150 and ρ varies within [0, 3 × 10−3]. The black dashed line shows the threshold between mild-moderate and severe cases. Other parameters assigned the default values shown in Table A in S1 Text.
Fig 6.
Bifurcation of parameter K4 and ρ for RIC, [Cytokines] and [Teffector] on day 30 after infection.
a-c for parameter K4 when the value of ρ is taken as 0.0025. d-f for parameter ρ when the value of K4 is taken as 84. Red solid circles and blue squares represent severe and mild-moderate cases, respectively. The other parameters are default and are shown in Table A in S1 Text. The gray region indicates a bistable status for mild-moderate and severe cases.
Fig 7.
Dynamics of COVID-19 in response to a scarcity of naïve T cells and a mild exhaustion of T cells (ρ = 0.0005) (out of 100 individual runs).
a. Time course of the average ratio of infected cells. b. Time course of average cytokines. c. Time course of average effector T cells. Red and blue lines indicate different levels of naïve T cells with ([T0] = 105 cells/ml) and ([T0] = 2 × 105 cells/ml), respectively. The error bar indicates standard deviation. Other parameters were assigned default values as shown in Table A in S1 Text.
Fig 8.
Comparison of the simulated efficacy for different treatment strategies in moderate and severe cases.
a and b are the simulated efficacy of eight treatment strategies for moderate patients (ρ = 0.0005) and severe patients (ρ = 0.0025), respectively. Different colors correspond to treatment strategies. The table below the histogram shows the detailed values of the quadruple (ε1, ε2, ε3, ε4). “-” indicates that corresponding values are 0. Other parameters were given default values as shown in Table A in S1 Text.
Fig 9.
Therapeutic efficacy of united treatments for moderate and severe cases.
a-f are combination of treatments for moderate cases. g-l are combination of treatments for severe cases. The dotted lines indicate half maximal efficacy. The colored bar is the therapeutic coefficient.
Fig 10.
Schematic diagram for the multi-scale modeling of SARS-CoV-2 infection.
a. Susceptible cells in normal tissue are infected by SARS-CoV-2. b. Cell states vary from normal to infected. Each normal cell becomes an infected cell with a probability of , and the infected cell spreads virus to the microenvironment and further infect other susceptible cells. c. The T cell response is triggered by infected cells that secrete cytokines (such as ILs, TNFs, IFNs, etc.). Naïve T cells are activated by cytokines and produce effector T cells to clear infected cells. Meanwhile, the above Eqs (1)–(17) represent the multi-scale model in the current study. This model includes viral dynamics, IFN response, and T cell response after SARS-CoV-2 infection. The viral dynamics and IFN response are coupled through the indexes of infected cells, and the T cell response and cytokines are connected by the number of infected cells. Cytokines are produced by both infected cells and effector T cells, promoting T cell exhaustion. Infected cells are removed with a probability of η(t) × dt. If an infected cell is cleared, a normal cell is generated to keep the total number of target cells unchanged. d. Normal tissue develops into abnormal tissue, and the severity is measured by the ratio of infected cells in the tissue.