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Caravagna2010 - Tumour suppression by immune system

ABSTRACT: Tumour suppression by immune system through stochastic oscillations GiulioCaravagnaa Albertod’Onofriob PaoloMilazzoa RobertoBarbutia https://doi.org/10.1016/j.jtbi.2010.05.013 Abstract The well-known Kirschner–Panetta model for tumour–immune System interplay [Kirschner, D., Panetta, J.C., 1998. Modelling immunotherapy of the tumour–immune interaction. J. Math. Biol. 37 (3), 235–252] reproduces a number of features of this essential interaction, but it excludes the possibility of tumour suppression by the immune system in the absence of therapy. Here we present a hybrid–stochastic version of that model. In this new framework, we show that in reality the model is also able to reproduce the suppression, through stochastic extinction after the first spike of an oscillation.

SUBMITTER: Mohammad Umer Sharif Shohan

PROVIDER: BIOMD0000000912 | BioModels | 2020-01-20

REPOSITORIES: BioModels

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Tumour suppression by immune system through stochastic oscillations.

Caravagna Giulio G d'Onofrio Alberto A Milazzo Paolo P Barbuti Roberto R

Journal of theoretical biology 20100516 3

The well-known Kirschner-Panetta model for tumour-immune System interplay [Kirschner, D., Panetta, J.C., 1998. Modelling immunotherapy of the tumour-immune interaction. J. Math. Biol. 37 (3), 235-252] reproduces a number of features of this essential interaction, but it excludes the possibility of tumour suppression by the immune system in the absence of therapy. Here we present a hybrid-stochastic version of that model. In this new framework, we show that in reality the model is also able to re ...[more]

PMID: 20580640

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Project description:This mathematical model of T cell-tumour interactions considering the roles of T cell competition and stochastic extinction events in CAR T cell therapy is described by the publication: Kimmel GJ, Locke FL, Altrock PM. "The roles of T cell competition and stochastic extinction events in chimeric antigen receptor T cell therapy." Proc Biol Sci. 2021 Mar 31;288(1947):20210229. doi: 10.1098/rspb.2021.0229 Comment: Reproduction of Fig. 2(a) and (b) was simulated by using the fitted model parameter set given in Table 1 of the manuscript's Supplementary Material, however substituting the values of r_N and rho_C for those stated in Table 1 of the publication manuscript, i.e. r_N = 0.17 and rho_C = 0.0251. Abstract: Chimeric antigen receptor (CAR) T cell therapy is a remarkably effective immunotherapy that relies on in vivo expansion of engineered CAR T cells, after lymphodepletion (LD) by chemotherapy. The quantitative laws underlying this expansion and subsequent tumour eradication remain unknown. We develop a mathematical model of T cell–tumour cell interactions and demonstrate that expansion can be explained by immune reconstitution dynamics after LD and competition among T cells. CAR T cells rapidly grow and engage tumour cells but experience an emerging growth rate disadvantage compared to normal T cells. Since tumour eradication is deterministically unstable in our model, we define cure as a stochastic event, which, even when likely, can occur at variable times. However, we show that variability in timing is largely determined by patient variability. While cure events impacted by these fluctuations occur early and are narrowly distributed, progression events occur late and are more widely distributed in time. We parameterized our model using population-level CAR T cell and tumour data over time and compare our predictions with progression-free survival rates. We find that therapy could be improved by optimizing the tumour-killing rate and the CAR T cells' ability to adapt, as quantified by their carrying capacity. Our tumour extinction model can be leveraged to examine why therapy works in some patients but not others, and to better understand the interplay of deterministic and stochastic effects on outcomes. For example, our model implies that LD before a second CAR T injection is necessary.

Project description:This ordinary differential equation model is the Panetta-Kirschner model of tumor-immune interactions is described in the publication: Cappuccio A, Castiglione F, Piccoli B." Determination of the optimal therapeutic protocols in cancer immunotherapy." Math Biosci. 2007 Sep;209(1):1-13. doi: 10.1016/j.mbs.2007.02.009. Comment: The model represented in Equations 1-3 is the Panetta-Kirschner model and was used to reproduce Fig. 1. N.B.: Labelling of Fig. 1 graphs in manuscript mismatches with simulation results - CTL and tumor cell plots swapped. Abstract: Cancer immunotherapy aims at eliciting an immune system response against the tumor. However, it is often characterized by toxic side-effects. Limiting the tumor growth and, concurrently, avoiding the toxicity of a drug, is the problem of protocol design. We formulate this question as an optimization problem and derive an algorithm for its solution. Unlike the standard optimal control approach, the algorithm simulates impulse-like drug administrations. It relies on an exact computation of the gradient of the cost function with respect to any protocol by means of the variational equations, that can be solved in parallel with the system. In comparison with previous versions of this method [F. Castiglione, B. Piccoli, Optimal control in a model of dendritic cell transfection cancer immunotherapy, Bull. Math. Biol. 68 (2006) 255-274; B. Piccoli, F. Castiglione, Optimal vaccine scheduling in cancer immunotherapy, Physica A. 370 (2) (2007) 672-680], we optimize both the timing and the dosage of each administration and introduce a penalty term to avoid clustering of subsequent injections, a requirement consistent with the clinical practice. In addition, we implement the optimization scheme to simulate the case of multi-therapies. The procedure works for any ODE system describing the pharmacokinetics and pharmacodynamics of an arbitrary number of therapeutic agents. In this work, it was tested for a well known model of the tumor-immune system interaction [D. Kirschner, J.C. Panetta, Modeling immunotherapy of tumor-immune interaction, J. Math. Biol. 37 (1998) 235-252]. Exploring three immunotherapeutic scenarios (CTL therapy, IL-2 therapy and combined therapy), we display the stability and efficacy of the optimization method, obtaining protocols that are successful compromises between various clinical requirements.

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Caravagna2010 - Tumour suppression by immune system

Publications

Tumour suppression by immune system through stochastic oscillations.

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