Optimal cancer evasion in a dynamic immune microenvironment generates diverse post-escape tumor antigenicity profiles

  1. Jason T George
  2. Herbert Levine

  • Curated by eLife

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    eLife assessment

    This study presents a valuable mathematical model for the adaptive dynamics of cancer evolution in response to immune recognition. The mathematical analysis is rigorous and convincing, and overall the framework presented could be used in the future as a solid base for analytically tracking tumor evasion strategies. However additional discussion is needed to clarify certain gaps between the theory and cancer evolution in real systems. The work will be of interest to evolutionary cancer biologists and potentially it may also have implications for the design of clinical interventions.

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Abstract

The failure of cancer treatments, including immunotherapy, continues to be a major obstacle in preventing durable remission. This failure often results from tumor evolution, both genotypic and phenotypic, away from sensitive cell states. Here, we propose a mathematical framework for studying the dynamics of adaptive immune evasion that tracks the number of tumor-associated antigens available for immune targeting. We solve for the unique optimal cancer evasion strategy using stochastic dynamic programming and demonstrate that this policy results in increased cancer evasion rates compared to a passive, fixed strategy. Our foundational model relates the likelihood and temporal dynamics of cancer evasion to features of the immune microenvironment, where tumor immunogenicity reflects a balance between cancer adaptation and host recognition. In contrast with a passive strategy, optimally adaptive evaders navigating varying selective environments result in substantially heterogeneous post-escape tumor antigenicity, giving rise to immunogenically hot and cold tumors.

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  1. Version published to 10.7554/elife.82786 on eLife
  2. eLife

    Author Response

    Reviewer #2 (Public Review):

    The manuscript "Optimal Cancer Evasion in a Dynamic Immune Microenvironment Generates Diverse Post-Escape Tumor Antigenicity Profiles" by George and Levine describes TEAL - a mathematical model for the dynamics of cancer evolution in response to immune recognition. The authors consider a process in which tumor cells from one clone are characterized by a set of neoantigens that may be recognized by the immune system with a certain probability. In response to the recognition, the tumor may adapt to evade immune recognition, by effective removal of recognizable neoantigens. The authors characterize the statistics of this adaptive process, considering, in particular, the evasion probability parameter, and a possibility of an adaptive strategy when this parameter is optimized in each step of the evolution. The dynamics of the latter process are solved with a dynamic programming approach. In the optimal case, the model captures the tradeoff between a cancer population's need for adaptability in hostile immune microenvironments and the cost of such adaptability to that population. Additionally, immune recognition of neoantigens is incorporated. These two factors, antitumor vs pro-tumor IME as quantified by the Beta penalty term, and the level of immune recognition as quantified by the rate q, form the basis of a characterization of tumors as 'hot' or 'cold'.

    I think this framework is a valuable attempt to formally characterize the processes and conditions that result in immunologically hot vs cold tumors. The model and the analytical work are sound and potentially interesting to a major audience. However, certain points require clarification for evaluation of the relevance of the model:

    1. Tumor clonality

    My main concern is about the lack of representation of the evolutionary process in the model and that the heterogeneity of the tumor is just glossed over.

    The single mention of the problem occurs in Section 2, p2: "Our focus is on a clonal population, recognizing that subclonal TAA distributions in this model may be studied by considering independent processes in parallel for each clone."

    I don't think this assumption resolves the impact of tumor heterogeneity on the immune evasion process. Furthermore, I would claim that the process depicted in Fig 1A is very rare and that cancers rarely lose recognizable neoantigens - typically it would be realized via subclonal evolution, with an already present cancer clone without the neoantigens picking up. Similarly, the adaptation of a tumor clone is an evolutionary process - supposedly the subclones that manage to escape recognition via genetic or epigenetic changes are the ones that persist. It is not clear what the authors assume about the heterogeneity of the adapting/adapted population between different generations, n->(n+1). Is the implicit assumption that the n+1 generation is again clonal, i.e. that the fitness advantage of the resulting subclone was such that the remaining clones were eliminated? Or does the model just focuses on the fittest subclone? A discussion on whether these considerations are relevant to the result would clarify the relevance of the result.

    We thank the reviewer for these helpful clarifying points. Empirical evidence in lung cancer exists for genomic changes manifesting as lost neoantigens in treatment-resistant clones (and Anagnostou et al. Cancer Discovery 2017) showed that those lost antigens were also shown to generate functional immune responses). Similar results for melanoma have also been shown (Verdegaal et al. Nature 2016), with loss of neoantigens associated with reactivity in TILs. Recent observations (Jaeger et al. Clinical Cancer Research 2020) even show that mutated peptides may be hid by protein stabilization, in addition to reduced expression patterns. We however do wish to clarify that our model implicitly equates antigen loss and the progression of a subpopulation currently adapted to evade immune targeting – either by direct pruning of the fittest subclone or by stochastic emergence and subsequent growth of a new one lacking the targeted antigens – as equivalent.

    Because we for foundational understanding studied the case where a single clonal signature was tracked in time, we under-explained the implementation of such a model in more complicated cases. As mentioned previously, the next most complicated scenario involves a heterogeneous population of cancer cells with disjoint neoantigen profiles. In this case, a parallel process can be studied wherein the effects of recognition in one environment are decoupled from the other (relevant to, for example, spatially distinct sub-populations). This description however misses the case where such disparate populations evolve to express shared antigens, or in the case where there are both clonal and subclonal antigen targets. Here, our model can still be applied in parallel to study distinct clones but requires additional structure. Namely, in this case we would need to incorporate non-trivial coupling between the possible recognition/selection against certain antigens shared across clones. For example, control of a population with clonal antigens {a,b} but having unique subclones having either antigens {w,x} or {y,z} could be considered by studying the process in parallel, and control in the next periods would require recognition/selection against either 1) at least one of {w,x} and at least one of {y,z}, or 2) at least one of {a,b}. In this more general framework, the arrival of new subclones with distinct features from the parent clone in question could also be incorporated and studied across time periods. This strategy of subdividing more complicated evolutionary structures has now been further elaborated on in the Methods section, and we have expounded these points in the discussion (see additions given under Editor Comment 2).

    1. Time scales

    Section 2, p2: "We assume henceforth that the recognition-evasion pair consists of the T cell repertoire of the adaptive immune system and a cancer cell population, recognizable by a minimal collection of s_n TAAs present on the surface of cancer cells in sufficient abundance for recognition to occur over some time interval n.".

    How do the results depend on the duration of interval n? The duration should be long enough to allow for recognition and, up to some limiting duration, proportional to the TAA recognition probability q. However, it should not be so long that the state of the system can change significantly. A clarification on this point is needed.

    We agree with the reviewer that these points should be elaborated upon when discussing the time interval. Very briefly, we opted for a discrete-time model tracking a cancer population under selective immune pressure. In order for 𝒒 to represent the total recognition probability of an immune system against a particular TAA, the time interval πš«π’ in question is a coarse-grained feature representing the time between the earliest chance that the adaptive immune system may identify a cancer clone and the latest point after which such a recognition event would no longer be able to prevent cancer escape. This time period may vary substantially across cancer subtypes and depends on the cancer per-cell division rate, for example (George, Levine. Can Res 2020). As the reviewer pointed out, in implementing such a model there is an asymmetric risk to considering πš«π’ too large, as the future state of the system may not be well-reflected by the simple loss and addition of new TAAs. On the other hand, considering small time intervals πš«π’, while possible, would require the incorporation of additional intermediate states ending in neither cancer elimination nor cancer escape.

    We have clarified the points that the reviewer has brought up by adding them to the discussion section: In this discrete-time evolutionary model, the intertemporal period considered represents the time period between the earliest moment that the adaptive immune system may identify a cancer clone and the latest point after which such a recognition event would no longer be able to prevent cancer escape (George, Levine. Can Res 2020). This effectively gives 𝒒 a probabilistic representation for the total rate of opportunity to recognize a given TAA during cancer progression. Implementing this model in cancer subtype-specific contexts thus requires a consideration of the per-cell division rates, for example.

    Reviewer #3 (Public Review):

    Cancer cell populations co-evolve under the pressure exerted by the recognition of tumor-associated antigens by the adaptive immune system. Here, George and Levine analyze how cancers could dynamically adapt the rate of tumor-associated antigen loss to optimize their probability of escape. This is an interesting hypothesis that if confirmed experimentally could potentially inform treatments. The authors analyze mathematically how such optimally adapting tumors gain and lose tumorassociated antigens over time. By simplifying the complex interplay of immune recognition and tumor evolution in a toy model, the authors are able to study questions of practical interest analytically or through stochastic simulations. They show how different model parameters relating to the tumor microenvironment and immune surveillance lead to different dynamics of tumor immunogenicity, and more immunologically hot or cold tumors.

    Simple models are important because they allow an exhaustive study of dynamical regimes for different parameters, such as has been done elegantly in this study. However, in this quest for simplification, the authors have not considered biological features that are likely to be of importance for understanding the process of cancer immune co-evolution in generality: tumor heterogeneity and immune recognition that only stochastically results in cancer elimination. In this sense, this paper might be seen as the opening act in a series of more sophisticated models, and the authors discuss avenues towards such further developments.

    We share the reviewer’s credence in foundational modeling for comprehensive predictions on available dynamical behavior for the important problem at hand. The reviewer also correctly points out that that future model refinement will be needed to further develop the foundational model developed in this work. In an attempt to illustrate one of the more reasonable generalizations, which is to include nontrivial sub-clonal heterogeneity in tumor antigens, we now describe how one would go about enhancing the existing model to address this, which has been added to the Methods and Discussion sections (see additions given under Editor Comment 2).

  3. eLife

    eLife assessment

    This study presents a valuable mathematical model for the adaptive dynamics of cancer evolution in response to immune recognition. The mathematical analysis is rigorous and convincing, and overall the framework presented could be used in the future as a solid base for analytically tracking tumor evasion strategies. However additional discussion is needed to clarify certain gaps between the theory and cancer evolution in real systems. The work will be of interest to evolutionary cancer biologists and potentially it may also have implications for the design of clinical interventions.

  4. eLife

    Reviewer #1 (Public Review):

    George and Levine present in their manuscript a mathematical framework describing the evolution of tumor cells under immune surveillance. The adaptive immune system recognizes tumor associate antigens (TAAs) to eliminate the cancer cells, while the tumor evades it through an evolutionary process of clonal selection. Their framework describes how the TAAs are gained and lost from the tumor, as a discreet time-stochastic process. The authors construct and parametrize their model to fit different known regimes of tumor and its microenvironment and explore the consequences of different tumor behaviors. Specifically, they suggest that tumor cells might sense the action of the immune system and adapt their escape probability.

    The mathematical analysis is clear and is an impressive attempt to find governing principles behind a complicated and messy process. While the model cannot give specific predictions at this point, it facilitates understanding real-world observations, like high and low mutation tumors. As such it can motivate further modeling of more realistic situations. In its current form, however, the manuscript is difficult to follow, with the many mathematical details and regimes confounding the message. Also, since the model simplifies the clonal nature of the evolution processes considerably, in its current form it has limited capability to make predictions or be more than supporting evidence to empirically known observations.

  5. eLife

    Reviewer #2 (Public Review):

    The manuscript "Optimal Cancer Evasion in a Dynamic Immune Microenvironment Generates Diverse Post-Escape Tumor Antigenicity Profiles" by George and Levine describes TEAL - a mathematical model for the dynamics of cancer evolution in response to immune recognition. The authors consider a process in which tumor cells from one clone are characterized by a set of neoantigens that may be recognized by the immune system with a certain probability. In response to the recognition, the tumor may adapt to evade immune recognition, by effective removal of recognizable neoantigens. The authors characterize the statistics of this adaptive process, considering, in particular, the evasion probability parameter, and a possibility of an adaptive strategy when this parameter is optimized in each step of the evolution. The dynamics of the latter process are solved with a dynamic programming approach. In the optimal case, the model captures the tradeoff between a cancer population's need for adaptability in hostile immune microenvironments and the cost of such adaptability to that population. Additionally, immune recognition of neoantigens is incorporated. These two factors, anti-tumor vs pro-tumor IME as quantified by the Beta penalty term, and the level of immune recognition as quantified by the rate q, form the basis of a characterization of tumors as 'hot' or 'cold'.

    I think this framework is a valuable attempt to formally characterize the processes and conditions that result in immunologically hot vs cold tumors. The model and the analytical work are sound and potentially interesting to a major audience. However, certain points require clarification for evaluation of the relevance of the model:

    1. Tumor clonality

    My main concern is about the lack of representation of the evolutionary process in the model and that the heterogeneity of the tumor is just glossed over.

    The single mention of the problem occurs in Section 2, p2: "Our focus is on a clonal population, recognizing that subclonal TAA distributions in this model may be studied by considering independent processes in parallel for each clone."

    I don't think this assumption resolves the impact of tumor heterogeneity on the immune evasion process. Furthermore, I would claim that the process depicted in Fig 1A is very rare and that cancers rarely lose recognizable neoantigens - typically it would be realized via subclonal evolution, with an already present cancer clone without the neoantigens picking up. Similarly, the adaptation of a tumor clone is an evolutionary process - supposedly the subclones that manage to escape recognition via genetic or epigenetic changes are the ones that persist. It is not clear what the authors assume about the heterogeneity of the adapting/adapted population between different generations, n->(n+1). Is the implicit assumption that the n+1 generation is again clonal, i.e. that the fitness advantage of the resulting subclone was such that the remaining clones were eliminated? Or does the model just focuses on the fittest subclone? A discussion on whether these considerations are relevant to the result would clarify the relevance of the result.

    1. Time scales

    Section 2, p2: "We assume henceforth that the recognition-evasion pair consists of the T cell repertoire of the adaptive immune system and a cancer cell population, recognizable by a minimal collection of s_n TAAs present on the surface of cancer cells in sufficient abundance for recognition to occur over some time interval n.".

    How do the results depend on the duration of interval n? The duration should be long enough to allow for recognition and, up to some limiting duration, proportional to the TAA recognition probability q. However, it should not be so long that the state of the system can change significantly. A clarification on this point is needed.

  6. eLife

    Reviewer #3 (Public Review):

    Cancer cell populations co-evolve under the pressure exerted by the recognition of tumor-associated antigens by the adaptive immune system. Here, George and Levine analyze how cancers could dynamically adapt the rate of tumor-associated antigen loss to optimize their probability of escape. This is an interesting hypothesis that if confirmed experimentally could potentially inform treatments. The authors analyze mathematically how such optimally adapting tumors gain and lose tumor-associated antigens over time. By simplifying the complex interplay of immune recognition and tumor evolution in a toy model, the authors are able to study questions of practical interest analytically or through stochastic simulations. They show how different model parameters relating to the tumor microenvironment and immune surveillance lead to different dynamics of tumor immunogenicity, and more immunologically hot or cold tumors.

    Simple models are important because they allow an exhaustive study of dynamical regimes for different parameters, such as has been done elegantly in this study. However, in this quest for simplification, the authors have not considered biological features that are likely to be of importance for understanding the process of cancer immune co-evolution in generality: tumor heterogeneity and immune recognition that only stochastically results in cancer elimination. In this sense, this paper might be seen as the opening act in a series of more sophisticated models, and the authors discuss avenues towards such further developments.

  7. Version published to 10.1101/2022.08.03.502723v1 on bioRxiv