We conducted a systematic review of published experimental data on T cell trafficking in mouse. Carefully curated datasets were used for model calibration and validation. In total, data from three preclinical studies that included 30 experimental measurements were used for the estimation of model parameters (i.e., 25 values of mean T-cell concentrations in time for different tissues, and 5 values for steady-state concentrations of endogenous T cells). Three additional studies, providing 24 experimental timepoint measurements were used for independent cross-validation. A multistep approach was implemented for model development, as shown in Figure 1A .

Parameters of endogenous T cell recirculation were estimated based on experimental data describing T cell concentrations under non-inflammatory conditions and under steady-state physiological conditions in mouse tissues (28, 29). The estimated maximal rate of homeostatic T cell proliferation in the spleen was verified against data in mice which underwent thymectomy (30). Parameters of exogenously administered T cell recirculation were estimated based on murine experimental data from Khot et al. (15). In that study, autologous Cr⁵¹-labeled spleen T cells were injected intravenously, and radioactivity levels (per gram of tissue) were measured in various organs. To incorporate these data into the model, we parameterized T cell concentrations using Equation S4 (see Supplementary Material ). Area-under-the-curve (AUC) estimates show that exogenously administered cells quickly transfer from blood and lung (AUC=(0.089 ± 0.057)* 10 8   and (2.26 ± 0.54)* 10 8 cells/ml), to then accumulate in liver and lymph nodes (AUC=(6.75 ± 2.21)* 10 8   and (1.62 ± 0.60)* 10 8 cells/ml), to ultimately home to the spleen (AUC= (30.65 ± 11.37)* 10 8 cells/ml).

Experimental data describing T cell kinetics following an intravenous administration of Zr⁸⁹-labeled T/CAR-T cells in mouse were used for an external cross-validation of the model. In those experiments, radioactivity detection was performed via positron-emission tomography (PET) for various types and doses of T cells as follows: (i) infusion of labeled T cells in a dose of 20.0* 10 6 cells (31); (ii) infusion of CAR-T cells in doses of 1.90-, 7.10-, and 16.8* 10 6 cells (16); and (iii) infusion of CAR-T cells in a dose of 1.00* 10 6 cells (32).

To capture the kinetics and inter-organ recirculation of endogenous and exogenously administered T cells, we developed a physiologically-based compartmental model of T cell migration, formulated with a system of sixteen ODEs. The model scheme is presented in Figure 1B . It includes 6 compartments corresponding to the following organs: blood, lungs, spleen, liver, ‘regional LNs’ and ‘generalized LNs’ (the latter representing secondary lymphoid structures). One of the main assumptions in our model relates to the independent circulation of endogenous vs. exogenous T cells in the various organs. Also, we assumed that exogenously administered and endogenous T cells displayed identical rates of organ-to-blood migration. For other model parameters, we considered quantitative differences in parameter values, given that experimental settings of exogenous cell product manufacturing resulted in variously modified T cells. Firstly, we assumed different rates of migration to the spleen, lung and LNs, for endogenous vs. exogenously administered T cells. Secondly, we assumed that the migratory behavior of exogenously administered T cells would not depend on disease status (i.e., identical T cell distribution patterns in healthy vs. tumor-bearing mice, in non-tumor organs). Thirdly, we assumed that exogenously administered T cells undergo degradation in the lungs [via phagocytosis by alveolar macrophages, based on a model by Zhu et al. (33)] and in blood – thereby accounting for all apoptotic processes in the whole organism.

Importantly, we did not include any proliferation potential of exogenous T cells in the model, since we did not consider the mechanisms required to stimulate antigen-specific proliferation (including exogenous T cell activation and interactions with antigen-presenting cells) in the present study.

Model equations were formulated using the following phenomenological view on T cell systemic and tissue dynamics. Endogenous T cells are produced in the thymus and migrate to blood (model parameter V_{inf_thymus} ) and various organs. The rate of homeostatic T cell proliferation in the spleen was described using a Michaelis-Menten like equation. The corresponding EC₅₀ value for homeostatic proliferation in the spleen was estimated as the degree of T cell depletion in the mouse spleen following irradiation, upon which proliferating T cells were observed (34). T cells can migrate from blood to tissues and back. For lung and liver compartments, the model considered T cell trafficking to lymph nodes through afferent lymphatic vessels. The rate of T cell migration from LNs to blood was assumed to be the same as the rate of T cell migration through the thoracic duct. Small distal LNs were represented in the model by a regional LN compartment, with T cells being transported from there to a generalized LN compartment via efferent lymphatic vessels.

Overall, intravenously administered T cells were set to follow the same migration patterns as endogenous T cells (see Figure 1B ). However, characteristic residence times were observed for exogenously administered T cells, in specific organs such as the spleen and the liver (10, 35). Various mechanistic explanations have been put forward to explain these observations; e.g., Ganusov and Tomura proposed that a tight network of sinusoids in liver and spleen may slow down cell migration at supra-high T cell numbers (20). An alternative biological explanation is that the rate of T cell migration may well be heterogeneous and dependent on morphological aspects of the spleen, e.g., the white pulp, red pulp, and marginal zones (22). To integrate these biophysical features into the model, we included additional variables representing the exogenous T cell abundance in the spleen, liver and LNs compartments ( T e x _ d e l _ s p l e e n , T e x _ d e l _ l i v e r ,   T e x _ d e l _ l n , T e x _ d e l _ r e g l n ,   respectively). Exogenously administered T cells were set to migrate out of blood and the lungs according to the following clearance processes: systemic apoptosis in blood and degradation by alveolar macrophages in lungs.

The parameters of the model of the model are listed in Table 1 . Overall, the system of equations was formulated as follows:

The first equation describes the influx of endogenous T cells from the thymus to the blood compartment (first term: V i n f _ t h y m u s ). T cell migration from blood ( T b l o o d ) to all other compartments (lungs, spleen, liver, generalized LNs and regional LNs with rate constants of, respectively, µ₁₂ , µ₁₃ , µ₁₄ , µ₁₅ , µ₁₆ ) is described by the second term. The selective transition of CCR7⁺ T cells to LNs is taken into account by multiplying the rate of T cell migration from blood to LN compartments (regional and generalized) by f_ccr7 , and the transfer rate to non-lymphoid organs, where non-naive T cells migrate to, by (1-f_ccr7). The next five terms in Equation 1 describe T cell migration from, respectively, lungs, liver, spleen, generalized LNs and regional LNs, to blood. The last term of Equation 1 represents the rate of T cell death via apoptosis.

Equation 2 describes the rate of change of exogenously administered T cell abundance in blood, T_{ex_blood} , following the infusion. This rate is determined by the balance of the rates of cell transitions from blood to lungs, liver, spleen, generalized LNs and regional LNs, and back to blood. The last term in Equation 2 depicts the apoptotic rate of exogenously administered T cells.

Equation 3 describes the rate of change of T cell levels in the lungs. The three terms in Equation 3 represent the kinetics of T cell transition from blood to lungs, from lungs to blood, and from lungs to the generalized LN compartment.

According to Equation 4, exogenously administered T cells migrate to the lungs, and back, via the same route as endogenous T cells. They degrade in the lungs, according to the last term in Equation 4. This T cell degradation feature was taken from the model by Zhu et al. (33).

Equation 5 is similar to Equation 3; it describes the rates of T cell migration from blood to liver and back, and T cell flow within afferent lymphatics to LNs.

Equation 6 represents the migration of exogenously administered T cells from blood to liver and the migration from liver to blood and LNs. The last two terms describe the transitions of exogenously administered T cells through a ‘delay-causing’ compartment within the liver. The rates of T cell inflow and outflow via the delay compartment in Equation 7 are assumed to be linear.

The spleen is a lymphoid organ; we considered T cell homeostatic proliferation, as described by the last term of Equation 8.

Equation 9 depicts processes which affect exogenously administered T cell numbers in the spleen: migration from blood to spleen, and back. To reproduce T cell kinetics in the spleen, another delay compartment was introduced. The last two terms of Equation 9 represent rates of exogenously administered T cell transitions to the delay compartment and back.

Equation 10 describes the transition of exogenously administered T cells within the spleen to the delay compartment and back.

The inflow of CCR7⁺ T cells from blood to LNs through HEVs was taken into account in the first terms of Equations 11, 14 (exogenously administered T cells) and of Equations 12, 13 (endogenous T cells). The first three terms in Equations 11, 12 are similar; they represent the inflow of T cells from blood and the transition of T cells from non-lymphoid organs (liver and lung, respectively). The last terms in these two equations describe the rate of T cell inflow via efferent lymphatics to the generalized LNs. Equation 11 also includes delay-related terms, to capture cell accumulation in the LNs, as shown in previous research (19, 20). The first two terms in Equations 13, 14 represent rates of T cell inflow from blood - through HEVs - to regional LNs and migration via efferent lymphatics to the generalized LNs compartment. For exogenously administered T cells in the regional LN compartment, we also considered cell accumulation via a delay compartment, as described by the last two terms of Equation 14.

Equations 15, 16 represent the dynamics of exogenously administered T cells in the delay compartments for, respectively, the generalized and regional LNs.

Overall, the model includes 30 parameters which are summarized in Table 1 . Some parameters were assumed to differ between endogenous vs. exogenously administered T cells (e.g., rate constants for migration from blood to spleen and generalized and regional LNs). Parameters which are in common were sub-divided into three groups: a) those verified against data describing steady-state levels of CD3⁺ T cells in mouse tissues (28, 29); b) those estimated based on half-lives of T cells in various organs (19); and c) those estimated using additional experimental data. The last group included parameters for endogenous T cell homeostatic proliferation, which were estimated using data in irradiated mice, and parameters for exogenously administered T cells, which were adjusted against experimental data on exogenously administered T cell kinetics in different tissues (15).

A nonlinear fixed-effect modeling approach was used for the calibration of model parameters with a log-normal distribution assumed for the experimental data. The following log-likelihood cost (LLC) function was maximized to find an optimal set for the fitted parameter values:

where θ ^ is the vector of parameter estimates for the model being considered, y represents the observed data, and p ( y ; θ ^ )   is the probability density function of the observed data given the parameter estimates. The model with the highest value of L L y ( θ ^ ) was selected as the model of choice.

In addition, relative standard errors (RSE) for model parameters θ ^ and the residual error model were estimated. For all parameters, RSE values lower than 50% were a prerequisite for model selection.

Weighted residuals (WRES) were calculated as the normalized difference between observations and their expected values:

where   V is the variance-covariance matrix of y , and E(y) is the mathematical expectation of the model solutions obtained using parameters θ ^ perturbed by a random value sampled from the residual error model.

The Monolix software, version 2020R1, was used for fixed-effects modeling, while data visualisation and forward simulations were performed in the R software, version 4.0.2 (R-project, www.r-project.org). Model sensitivity analyses were performed using the “sensitivity” R package; model simulations were performed using the “RsSimulx” R package; visualization of model solutions was performed using “ggplot2” and “tidyverse” R packages.

We used a sequential approach to curate and integrate all available quantitative information into the model (see the flowchart in Figure 1A ).

In a first stage, we calibrated parameters pertaining to endogenous T cell migration (V_{inf_thymus} , µ₁₂, µ₁₃ , µ₁₄ , µ₁₅ , µ₂₅ , µ₄₅ , µ₁₆ ), based on data describing the steady-state levels of T cells in various compartments. In addition, we determined a ratio between rates of T cell migration through HEVs (V_{blood_ln} ) vs. afferent lymphatics (V_{lung_ln} , V_{liver_ln} ), based on the knowledge that only ∼10% of T cells migrate to lymph nodes via afferent lymphatics (6). The rate constants for T cell migration from various tissues to blood (µ₂₁, µ₃₁, µ₄₁, µ₆₁ ) were calculated using estimates of cellular half-lives provided by Ganusov and Tomura (20). The parameter value for µ₅₁ was calculated as the rate of T cell flux to the thoracic duct. As shown in Figure 2F , the model consistently described the experimental data, i.e., endogenous T cells would accumulate in lymphoid organs at concentrations of 1.57* 10 8   cells/ml in the spleen and 3.36* 10 8   cells/ml in LNs, whereas T cell levels in blood and lungs at steady-state were significantly lower (1.70*10⁶ cells/ml and 4.22* 10 6 cells/ml, respectively); and liver exhibited the lowest level of T cell infiltration (∼4.20* 10 5 cells/ml).

In a second stage of model calibration, we fixed all parameters for endogenous T cells, all rate constants for exogenous T cell migration from organs to blood (assumed to be the same as for the endogenous cell migration), as well as the parameter that characterizes the rate of T cell apoptosis. We then estimated parameters µ_13ex, µ_12ex, µ_15ex, µ_16ex and parameters describing the delay in T cell migration into liver, spleen and LNs (k_del3, k_del4, k_del5, k_del6 ) using experimental data on exogenously administered T cell kinetics (15). Since parameters k_del3, k_del5, k_del6 represent the rate constants for the accumulation of cells in lymphoid organs, we assumed the same value for these three parameters. The resultant calibrated model consistently described available experimental data ( Figures 2A–E ). In particular, the model adequately reproduced the fast T cell elimination from blood ( Figure 2A ) and the comparably rapid transitory kinetics in the highly vascularized lungs ( Figure 2B ), as well as the slower kinetics in the spleen (with the peak value C_max of ∼12.6*10⁶ cells/ml at 9 hrs) and the liver (C_max of ∼3.4*10⁶ cells/ml at 8 hrs) ( Figure 2E ). The model also satisfactorily described the cellular kinetics in the regional LN compartment, with a C_max of 0.5*10⁶ cells/ml at 45.5 hrs post administration ( Figure 2D ). Goodness-of-fit plots ( Figure 3 ) provide further support for an adequate description of the experimental data by the model. In particular, the moderate over-estimation of C_max in blood holds for only some of the reported blood measurements (squares on Figure 3A ), with weighted residuals (WRES) lying within a [−2, +2] range ( Figure 3B ).

It is worth noting that, initially, we had considered a model structure featuring only one lumped LN compartment, i.e., without any regional LN compartment ( Supplementary Figure 1 , Supplementary Material ). The corresponding model could not describe the available experimental LN data for exogenously administered T cells, yet it adequately captured the cellular dynamics in tissues other than LNs ( Supplementary Figure 2 , Supplementary Material ).

To validate the model and assess its predictive power, we performed simulations of external data which had not been used in the model calibration process. In particular, the model was validated against experimental data in mice which received infusions of radiolabeled T cells or CAR-T cells, in doses of 1.0*10⁶, 1.9*10⁶, 7.1*10⁶, or 16.8*10⁶ cells per animal (16, 31, 32). Due to the different methods used for T cell labeling, with corresponding differing detections and units of radioactivity in a region of interest (ROI) in the experimental studies, we adjusted the data using a scaling coefficient, ω, in Equation 17 as follows:

An averaged calibration coefficient value of 2.7 was determined for ω, although there are several reasons for significant variability across studies due to the characteristics of the various experiments (See Section 5, Supplementary Material ).

As shown in Figure 4A , the model adequately described experimental data for doses of 1.9*10⁶ and 7.1*10⁶ CAR-T cells. However, it slightly over-predicted peak levels following doses of 1.0*10⁶ and 1.9*10⁶ (C_max values of 0.6*10⁶ and 1.1*10⁶ cells/ml predicted by the model vs. observed C_max values of 0.3*10⁶ and 0.5*10⁶ cells/ml, respectively). At the same time, T cell levels at later timepoints, following a dose of 16.8*10⁶ cells were under-estimated, with a predicted value C_max of 1.02*10⁷ cells/ml vs. a higher C_max of 1.50*10⁷ cells/ml observed in the experimental data. These differences between observed and model-predicted values may have been caused by uncertainties related to the calibration of the radioactivity labeling data. Since the actual calibration curves for the various experimental settings were not available, we applied an empirical approach to map the data onto a uniform scale, which may have introduced an additional bias. To further validate the model, we also used external data on exogenous T cell levels in the spleen, under various doses (13). The linear dependence between T cell counts in the spleen and the administered doses was successfully reproduced by the model, for this external set of experimental data ( Figure 4B ).

Two types of sensitivity analyses were conducted: a global sensitivity analysis for parameters and variables describing endogenous T cell homeostasis, and a local sensitivity analysis for those describing exogenously administered T cell numbers and accumulation.

The Partial Rank Correlation Coefficient (PRCC) method was used to perform the global sensitivity assessment of the model (47). Model parameters were sampled using a Latin hypercube sampling (LHS) procedure. 5000 sets of parameters were sampled for single estimation of PRCC. The procedure was repeated 200 times to estimate standard errors. The lower and upper bounds of the parameters were assumed to be determined by values corresponding to a two-fold change from steady-state T cell concentrations. Model solutions were computed over a large time window (up to 80,000 hrs), to ensure steady-state conditions. Under such a setting, the PRCC may characterize the relative importance or effect of a parameter, along with its positive/negative correlation mode, vs. model output variability.

As shown in Figure 5 , the PRCC coefficients for the rate constants of T cell migration from blood to spleen and back (µ₁₃ and µ₃₁ ) were about 4-times higher in terms of their impact on steady-state levels of T cells in spleen vs. blood. A similar relationship was found for the lungs (see Supplementary Figure 3 in the Supplementary Material ): the rate constants of migration from blood to the lungs and back (µ₁₂ and µ₂₁ ) were more important for the lungs than for blood, with corresponding PRCC coefficients about 10-times higher. According to this sensitivity analysis, the key systemic parameters with comparable impact on T cell homeostasis in all compartments were V_{inf_thymus} and k_{_apo} . Parameters of homeostatic proliferation Vmax_pro and EC50_pro were also important for T cell levels in all compartments.

Although the sensitivity analysis predicted rather low PRCC coefficients for T cell inflow rate parameters from the lungs and liver to the LNs via afferent lymphatic vessels (µ₂₅ and µ₄₅ ), in relation to T cell levels in the blood and the spleen, it revealed that these processes were essential in driving T cell levels in the organs themselves. This is demonstrated by the 5x higher values of the corresponding PRCC coefficients for the lungs and liver vs. other compartments (excluding LNs for µ₂₅ ), which highlights the importance of considering the model’s sensitivity to the lymphatic system parameters. The T cell inflow constant from lungs to LNs, µ₂₅ , carried significance for homeostasis in the lung and LNs, as shown in Supplementary Figures 3A, C of the Supplementary Material . Also, it should be noted that the parameter f c c r 7 was predicted to play a minor influence on T cell homeostasis in blood and spleen, while the levels of T cells in liver, the lungs, and both regional and generalized LN compartments appeared to be more sensitive to f c c r 7 .

To estimate the impact of kinetic parameters on exogenously administered T cell dynamics, a local sensitivity analysis was conducted. Parameter values were varied in the following way: decreased by 50% or increased by 100% from their best-fit estimates (i.e., two-fold changes). Figure 6 shows the sensitivity profiles for exogenous T cell in blood (A), spleen (B), liver (C) and regional LN (D). Supplementary Figure 6 in the Supplementary Material presents the dependence of the total number of exogenous T cells vs. time, which was calculated as the sum of T cell numbers in all compartments. For all compartments excluding blood, the most important parameters were the rate constants of T cell inflow from blood to organ: changes in µ_13ex, µ₁₄ and µ_16ex resulted in proportional changes of the AUC in spleen, liver, and regional LNs, respectively. The same behavior was shown to hold for the lungs (see Supplementary Figure 4A in the Supplementary Material ).

For the generalized LN compartment (see Figure S4B ), the most important parameter was the T cell inflow rate from organ to blood (µ₅₁ ). Interestingly, the rate constant of T cell transition to the lungs, µ_12ex , was significant with respect to all variables, including the level of T cells in blood. This rate relates to the change in the fraction of total exogenous T cells trafficking to the lungs, where a relatively high level of T cell degradation is set in the model ( Supplementary Figure 6B ), red and grey curves, Supplementary Material ). Also, an increase in the rate constant, k_del3 , which describes the T cell transition rate to the delay compartment in the spleen, resulted in a stronger accumulation of exogenous T lymphocytes in the delay compartment and a higher AUC in the spleen ( Figure 6B ). The same sensitivity pattern was observed for other delay compartments: increases in k_del4, k_del5 and, to a lesser degree, in k_del6 resulted in higher T-cell AUC values in the liver as well as in the generalized LN and regional LN compartments. On the contrary, increases in k_off parameters resulted in a faster migration to, and exit from the corresponding compartments and, as a consequence, in lower AUC values (as shown for k_off3 , k_off4 , k_off6 in Figures 6B–D ), respectively). The rate constant capturing the inflow of cells to the regional LN compartment and the delay-related parameter for that compartment (µ_16ex , k_del6 ) were important only within this compartment; inflow rate constants and delay parameters in all other compartments had a low impact on T cell AUC values. We also explored the importance of these parameters with respect to their effects on C_max values ( Supplementary Figure 5 , Supplementary Material ) and obtained similar results. Except for parameters µ_12ex, µ_13ex, µ_14, µ_16ex , which were the most important parameters determining C_max in the corresponding compartments, the inflow rates from blood to other compartments were more significant than the rate constants reflecting transitions to delay compartments. For example, for the value of C_max in the spleen, the rate constants of T cell inflow to the lungs and liver (µ_12ex , µ₁₄ ) were more significant than k_del3 , k_off3 .

Overall, these kinetic behaviors reflect the inter-dependence of T cell levels in various organ and tissue compartments, which are inherently linked in a continuous flow-like system such as the whole organism.

Model simulations were conducted to investigate the effects of specific factors such as exogenous T cell dose and CCR7 expression levels, on T cell kinetics and distribution. To explore more specifically the dose dependency on cellular kinetics, we performed the following numerical experiments representing intravenously administered T cells at doses of 1.0, 3.0, 5.0, 10, 20, 50, or 100 million cells per mouse ( Figure 7 ). Low doses of 1.0, 3.0, 5.0 or 10 million T cells resulted in C_max values in blood of, respectively: {0.46, 1.40, 2.30, 4.65}*10⁶ cells/ml. High doses of 20, 50, or 100 million T cells resulted in C_max values of, respectively, {9.30, 23.3, 46.5}*10⁶ cells/ml. Consequently, there is a linear relationship between the dose of adoptively transferred cells and T cell concentrations in the spleen (see Figure 4B , 72 hr post-infusion timepoint), which is observed experimentally and predicted by the calibrated model. A similar relationship was revealed in other compartments (see Figures 7B–F ). We also simulated T cell concentration in the generalized LN compartment ( Figure 7F ) and found a linear dependence between the dose and the accumulation of lymphocytes in this compartment.

In order to investigate distribution effects of CCR7 expression levels on exogenously administered T cells, the parameter f_{ccr7_ex} was varied over a range of 0.1 to 0.9 ( Figure 8 ). As summarized in Table 2 , a change in f_{ccr7_ex} from 0.1 to 0.3 did not significantly affect the exogenous cell AUC in spleen and blood (respectively, {9.91,11.09,12.59}*10⁸; and {0.11, 0.12, 0.14}*10⁸ cells/ml). A further increase in CCR7 expression levels (with increasing f_{ccr7_ex} values of 0.7, 0.8, 0.9) led to a higher accumulation of T cells in spleen and blood, with AUC levels of {27.52, 39.1, 67.38}*10⁸ in the spleen and {0.26, 0.36,0.61}*10⁸ in blood ( Figure 8C ). Interestingly, this non-linear relationship is not observed in the liver and lung compartments, where the effects of varying CCR7 expression levels were less pronounced. Indeed, there were only minor differences in kinetics, whether low (0.1 to 0.5) or high (0.7 to 0.9) values of f_{ccr7_ex} were tested ( Figures 8B, D ). The C_max value in non-lymphoid organs, reflective of the distribution phase, was inversely related to f_{ccr7_ex} : it increased from 2.63*10⁶ up to 4.01*10⁶ cells/ml for the liver, and from 7.67*10⁶ to 31.3*10⁶ cells/ml for the lungs, with decreasing values of f_{ccr7_ex} (from 0.9 to 0.1). However, during the elimination phase, higher C_max values led to a slightly lower trough concentrations in the lungs at 360 hrs, with trough cell levels decreasing from 7.7*10⁴ to 7.5*10⁴ cells/ml. Therefore, the lowest value of C_max (f_{ccr7_ex} = 0.9) led to the highest trough level of T cells in the lungs, although the difference was rather modest.

This observed non-linearity in cell kinetics also led to significant differences in the biodistribution coefficient, BC ( Table 2 ). An increase in f_{ccr7_ex} resulted in an increase in BC in the regional LN compartment, yet in a reduced T cell concentration relatively to blood in the generalized LN compartment (with a lower BC value in LNs). BC in non-lymphoid organs was also diminished; an increase in f c c r 7 _ e x   resulted in a higher BC in the spleen compartment. Interestingly, the AUC value appeared to change faster in blood vs. LNs.

To illustrate key differences in the kinetic behavior of exogenous vs. endogenous T cell populations, we performed simulations which simultaneously tracked the kinetics of these two T cell populations. Concentrations of endogenous T cells were at steady-state in each compartment (see Figure 2F and Supplementary Figure 7 , dark red lines, Supplementary Material ). Since exogenous T cells were administered in high numbers, their kinetics appeared as temporary ‘perturbations’ in T cell numbers in various compartments, with higher or lower exposures depending on the presence of delay compartments (see Figures 2A–E ) and Supplementary Figure 7 , dark red lines, Supplementary Material ). However, even the largest dose of exogenously administered T cells would not exceed ∼1% of the total lymphocyte count in mouse; exogenous T cells would therefore not be expected to significantly perturb the dynamics of endogenous T cells.