Clonal stochasticity in early NK cell response to mouse cytomegalovirus is generated by mature subsets of varying proliferative ability

Reviewer #1 (Public review):

Summary:

The objective of this study was to infer the population dynamics (rates of differentiation, division, and loss) and lineage relationships of clonally expanding NK cell subsets during an acute immune response.

Strengths:

A rich dataset and thorough analysis of a particular class of stochastic models.

Weaknesses:

The stochastic models used are quite simple; each population is considered homogeneous with first-order rates of division, death, and differentiation. In Markov process models such as these, there is no dependence of cellular behavior on its history of divisions. In recent years models of clonal expansion and diversification, in the settings of T and B cells, have progressed beyond this picture. So I was a little surprised that there was no mention of the literature exploring the role of replicative history in differentiation (e.g. Bresser Nat Imm 2022), nor of the notion of family 'division destinies' (either in division number or the time spent proliferating, as described by the Cyton and Cyton2 models developed by Hodgkin and collaborators; e.g. Heinzel Nat Imm 2017). The emerging view is that variability in clone (family) size may arise predominantly from the signals delivered at activation, which dictate each precursor's subsequent degree of expansion, rather than from the fluctuations deriving from division and death modeled as Poisson processes.

As you pointed out, the Gerlach and Buchholz Science papers showed evidence for highly skewed distributions of family sizes and correlations between family size and phenotypic composition. Is it possible that your observed correlations could arise if the propensity for immature CD27+ cells to differentiate into mature CD27- cells increases with division number? The relative frequency of the two populations would then also be impacted by differences in the division rates of each subset - one would need to explore this. But depending on the dependence of the differentiation rate on division number, there may be parameter regimes (and time points) at which the more differentiated cells can predominate within large clones even if they divide more slowly than their immature precursors. One might not then be able to rule out the two-state model. I would like to see a discussion or rebuttal of these issues.

Reviewer #2 (Public review):

Summary:

Wethington et al. investigated the mechanistic principles underlying antigen-specific proliferation and memory formation in mouse natural killer (NK) cells following exposure to mouse cytomegalovirus (MCMV), a phenomenon predominantly associated with CD8+ T cells. Using a rigorous stochastic modeling approach, the authors aimed to develop a quantitative model of NK cell clonal dynamics during MCMV infection.

Initially, they proposed a two-state linear model to explain the composition of NK cell clones originating from a single immature Ly49+CD27+ NK cell at 8 days post-infection (dpi). Through stochastic simulations and analytical investigations, they demonstrated that a variant of the two-state model incorporating NK cell death could explain the observed negative correlation between NK clone sizes at 8 dpi and the percentage of immature (CD27+) NK cells (Page 8, Figure 1e, Supplementary Text 1). However, this two-state model failed to accurately reproduce the first (mean) and second (variance and covariance) moments of the measured CD27+ and CD27- NK cell populations within clones at 8 dpi (Figure 1g).

To address this limitation, the authors increased the model's complexity by introducing an intermediate maturation state, resulting in a three-stage model with the transition scheme: CD27+Ly6C- → CD27-Ly6C- → CD27-Ly6C+. This three-stage model quantitatively fits the first and second moments under two key constraints: (i) immature CD27+ NK cells exhibit faster proliferation than CD27- NK cells, and (ii) there is a negative correlation (upper bound: -0.2) between clone size and the fraction of CD27+ cells. The model predicted a high proliferation rate for the intermediate stage and a high death rate for the mature CD27-Ly6C+ cells.

Using NK cell reporter mice data from Adams et al. (2021), which tracked CD27+/- cell population dynamics following tamoxifen treatment, the authors validated the three-stage model. This dataset allowed discrimination between NK cells originating from the bone marrow and those pre-existing in peripheral blood at the onset of infection. To test the prediction that mature CD27- NK cells have a higher death rate, the authors measured Ly49H+ NK cell viability in the mice spleen at different time points post-MCMV infection. Experimental data confirmed that mature (CD27-) NK cells exhibited lower viability compared to immature (CD27+) NK cells during the expansion phase (days 4-8 post-infection).

Further mathematical analyses using a variant of the three-stage model supported the hypothesis that the higher death rate of mature CD27- cells contributes to a larger proportion of CD27- cells in the dead cell compartment, as introduced in the new variant model.

Altogether, the authors proposed a three-stage quantitative model of antigen-specific expansion and maturation of naïve Ly49H+ NK cells in mice. This model delineates a maturation trajectory: (i) CD27+Ly6C- (immature) → (ii) CD27-Ly6C- (mature I) → (iii) CD27-Ly6C+ (mature II). The findings highlight the highly proliferative nature of the mature I (CD27-Ly6C-) phenotype and the increased cell death rate characteristic of the mature II (CD27-Ly6C+) phenotype.

Strengths:

By designing models capable of explaining correlations, first and second moments, and employing analytical investigations, stochastic simulations, and model selection, the authors identified the key processes underlying antigen-specific expansion and maturation of NK cells. This model distinguishes the processes of antigen-specific expansion, contraction, and memory formation in NK cells from those observed in CD8+ T cells. Understanding these differences is crucial not only for elucidating the distinct biology of NK cells compared to CD8+ T cells but also for advancing the development of NK cell therapies currently under investigation.

Weaknesses:

The conclusions of this paper are largely supported by the available data. However, a comparative analysis of model predictions with more recent works in the field would be desirable. Moreover, certain aspects of the simulations, parameter inference, and modeling require further clarification and expansion, as outlined below:

(1) Initial Conditions and Grassmann Data: The Grassmann data is used solely as a constraint, while the simulated values of CD27+/CD27- cells could have been directly fitted to the Grassmann data, which assumes a 1:1 ratio of CD27+/CD27- at t = 0. This approach would allow for an alternative initial condition rather than starting from a single CD27+ cell, potentially improving model applicability.

(2) Correlation Coefficients in the Three-State Model: Although the parameter scan of the three-state model (Figure 2) demonstrates the potential for achieving negative correlations between colony size and the fraction of CD27+ cells, the authors did not present the calculated correlation coefficients using the estimated parameter values from fitting the three-state model to the data. Including these simulations would provide additional insight into the parameter space that supports negative correlations and further validate the model.

(3) Viability Dynamics and Adaptive Response: The authors measured the time evolution of CD27+/- dynamics and viability over 30 days post-infection (Figure 4). It would be valuable to test whether the three-state model can reproduce the adaptive response of CD27- cells to MCMV infection, particularly the observed drop in CD27- viability at 5 dpi (prior to the 8 dpi used in the study) and its subsequent rebound at 8 dpi. Reproducing this aspect of the experiment is critical to determine whether the model can simultaneously explain viability dynamics and moment dynamics. Furthermore, this analysis could enable sensitivity analysis of CD27- viability with respect to various model parameters.

Author response:

Public Reviews:

Reviewer #1 (Public review):

Summary:

The objective of this study was to infer the population dynamics (rates of differentiation, division, and loss) and lineage relationships of clonally expanding NK cell subsets during an acute immune response.

Strengths:

A rich dataset and thorough analysis of a particular class of stochastic models.

Weaknesses:

The stochastic models used are quite simple; each population is considered homogeneous with first-order rates of division, death, and differentiation. In Markov process models such as these, there is no dependence of cellular behavior on its history of divisions. In recent years models of clonal expansion and diversification, in the settings of T and B cells, have progressed beyond this picture. So I was a little surprised that there was no mention of the literature exploring the role of replicative history in differentiation (e.g. Bresser Nat Imm 2022), nor of the notion of family 'division destinies' (either in division number or the time spent proliferating, as described by the Cyton and Cyton2 models developed by Hodgkin and collaborators; e.g. Heinzel Nat Imm 2017). The emerging view is that variability in clone (family) size may arise predominantly from the signals delivered at activation, which dictate each precursor's subsequent degree of expansion, rather than from the fluctuations deriving from division and death modeled as Poisson processes.

As you pointed out, the Gerlach and Buchholz Science papers showed evidence for highly skewed distributions of family sizes and correlations between family size and phenotypic composition. Is it possible that your observed correlations could arise if the propensity for immature CD27+ cells to differentiate into mature CD27- cells increases with division number? The relative frequency of the two populations would then also be impacted by differences in the division rates of each subset - one would need to explore this. But depending on the dependence of the differentiation rate on division number, there may be parameter regimes (and time points) at which the more differentiated cells can predominate within large clones even if they divide more slowly than their immature precursors. One might not then be able to rule out the two-state model. I would like to see a discussion or rebuttal of these issues.

We thank the reviewer for the insightful comment. We are currently in the process of developing alternate models based on the above comment and the references (Bresser Nat Imm 2022 and Heinzel Nat Imm 2017). We plan to include the results from the analysis in the revised version.

Reviewer #2 (Public review):

Summary:

Wethington et al. investigated the mechanistic principles underlying antigen-specific proliferation and memory formation in mouse natural killer (NK) cells following exposure to mouse cytomegalovirus (MCMV), a phenomenon predominantly associated with CD8+ T cells. Using a rigorous stochastic modeling approach, the authors aimed to develop a quantitative model of NK cell clonal dynamics during MCMV infection.

Initially, they proposed a two-state linear model to explain the composition of NK cell clones originating from a single immature Ly49+CD27+ NK cell at 8 days post-infection (dpi). Through stochastic simulations and analytical investigations, they demonstrated that a variant of the two-state model incorporating NK cell death could explain the observed negative correlation between NK clone sizes at 8 dpi and the percentage of immature (CD27+) NK cells (Page 8, Figure 1e, Supplementary Text 1). However, this two-state model failed to accurately reproduce the first (mean) and second (variance and covariance) moments of the measured CD27+ and CD27- NK cell populations within clones at 8 dpi (Figure 1g).

To address this limitation, the authors increased the model's complexity by introducing an intermediate maturation state, resulting in a three-stage model with the transition scheme: CD27+Ly6C- → CD27-Ly6C- → CD27-Ly6C+. This three-stage model quantitatively fits the first and second moments under two key constraints: (i) immature CD27+ NK cells exhibit faster proliferation than CD27- NK cells, and (ii) there is a negative correlation (upper bound: -0.2) between clone size and the fraction of CD27+ cells. The model predicted a high proliferation rate for the intermediate stage and a high death rate for the mature CD27-Ly6C+ cells.

Using NK cell reporter mice data from Adams et al. (2021), which tracked CD27+/- cell population dynamics following tamoxifen treatment, the authors validated the three-stage model. This dataset allowed discrimination between NK cells originating from the bone marrow and those pre-existing in peripheral blood at the onset of infection. To test the prediction that mature CD27- NK cells have a higher death rate, the authors measured Ly49H+ NK cell viability in the mice spleen at different time points post-MCMV infection. Experimental data confirmed that mature (CD27-) NK cells exhibited lower viability compared to immature (CD27+) NK cells during the expansion phase (days 4-8 post-infection).

Further mathematical analyses using a variant of the three-stage model supported the hypothesis that the higher death rate of mature CD27- cells contributes to a larger proportion of CD27- cells in the dead cell compartment, as introduced in the new variant model.

Altogether, the authors proposed a three-stage quantitative model of antigen-specific expansion and maturation of naïve Ly49H+ NK cells in mice. This model delineates a maturation trajectory: (i) CD27+Ly6C- (immature) → (ii) CD27-Ly6C- (mature I) → (iii) CD27-Ly6C+ (mature II). The findings highlight the highly proliferative nature of the mature I (CD27-Ly6C-) phenotype and the increased cell death rate characteristic of the mature II (CD27-Ly6C+) phenotype.

Strengths:

By designing models capable of explaining correlations, first and second moments, and employing analytical investigations, stochastic simulations, and model selection, the authors identified the key processes underlying antigen-specific expansion and maturation of NK cells. This model distinguishes the processes of antigen-specific expansion, contraction, and memory formation in NK cells from those observed in CD8+ T cells. Understanding these differences is crucial not only for elucidating the distinct biology of NK cells compared to CD8+ T cells but also for advancing the development of NK cell therapies currently under investigation.

Weaknesses:

The conclusions of this paper are largely supported by the available data. However, a comparative analysis of model predictions with more recent works in the field would be desirable. Moreover, certain aspects of the simulations, parameter inference, and modeling require further clarification and expansion, as outlined below:

(1) Initial Conditions and Grassmann Data: The Grassmann data is used solely as a constraint, while the simulated values of CD27+/CD27- cells could have been directly fitted to the Grassmann data, which assumes a 1:1 ratio of CD27+/CD27- at t = 0. This approach would allow for an alternative initial condition rather than starting from a single CD27+ cell, potentially improving model applicability.

We thank the reviewer for this comment. We are working on performing the above analysis and plan to include results from the analysis in the revised manuscript.

(2) Correlation Coefficients in the Three-State Model: Although the parameter scan of the three-state model (Figure 2) demonstrates the potential for achieving negative correlations between colony size and the fraction of CD27+ cells, the authors did not present the calculated correlation coefficients using the estimated parameter values from fitting the three-state model to the data. Including these simulations would provide additional insight into the parameter space that supports negative correlations and further validate the model.

We will include the above calculation in the revised manuscript.

(3) Viability Dynamics and Adaptive Response: The authors measured the time evolution of CD27+/- dynamics and viability over 30 days post-infection (Figure 4). It would be valuable to test whether the three-state model can reproduce the adaptive response of CD27- cells to MCMV infection, particularly the observed drop in CD27- viability at 5 dpi (prior to the 8 dpi used in the study) and its subsequent rebound at 8 dpi. Reproducing this aspect of the experiment is critical to determine whether the model can simultaneously explain viability dynamics and moment dynamics. Furthermore, this analysis could enable sensitivity analysis of CD27- viability with respect to various model parameters.

We will include some discussion of potential mechanisms of cell viability in this experiment.