Mathematical modelling of cancer stem cell-targeted immunotherapy

Dynamics of an Antitumour Model with Pulsed Radioimmunotherapy

In this paper, an antitumour model for characterising radiotherapy and immunotherapy processes at different fixed times is proposed. The global attractiveness of the positive periodic solution for each corresponding subsystem is proved with the integral inequality technique. Then, based on the differentiability of the solutions with respect to the initial values, the eigenvalues of the Jacobian matrix at a fixed point corresponding to the tumour-free periodic solution are determined, resulting in a sufficient condition for local stability. The solutions to the ordinary differential equations are compared, the threshold condition for the global attractiveness of the tumour-free periodic solution is provided in terms of an indicator $R_0$ , and the permanence of a system with at least one tumour-present periodic solution is investigated. Furthermore, the effects of the death rate, effector cell injection dosage, therapeutic period, and effector cell activation rate on indicator $R_0$ are determined through numerical simulations, and the results indicate that radioimmunotherapy is more effective than either radiotherapy or immunotherapy alone.

Optimal control model of tumor treatment in the context of cancer stem cell

We consider cancer cytotoxic drugs as an optimal control problem to stabilize a heterogeneous tumor by attacking not the most abundant cancer cells, but those that are crucial in the tumor ecosystem. We propose a mathematical cancer stem cell model that translates the hierarchy and heterogeneity of cancer cell types by including highly structured tumorigenic cancer stem cells that yield low differentiated cancer cells. With respect to the optimal control problem, under a certain admissibility hypothesis, the optimal controls of our problem are bang-bang controls. These control treatments can retain the entire tumor in the neighborhood of an equilibrium. We simulate the bang-bang control numerically and demonstrate that the optimal drug scheduling should be administered continuously over long periods with short rest periods. Moreover, our simulations indicate that combining multidrug therapies and monotherapies is more efficient for heterogeneous tumors than using each one separately.

"Double hit" strategy: Removal of sialic acid from the dendritic cell surface and loading with CD44+/CD24-/low cell lysate inhibits tumor growth and metastasis by targeting breast cancer stem cells

Cancer stem cells (CSCs), which represent the root cause of resistance to conventional treatments, recurrence, and metastasis, constitute the critical point of failure in cancer treatments. Targeting CSCs with dendritic cell (DC)-based vaccines have been an effective strategy, but sialic acids on the surface of DCs limit the interaction with loaded antigens. We hypothesized that removal of sialic acid moieties on immature DCs (iDCs) could significantly affect DC-CSC-antigen loading, thereby leading to DC maturation and improving immune recognition and activity. The lysate of CD44⁺/CD24^-/low breast CSCs (BCSCs) was pulsed with sialidase-treated DCs to obtain mature dendritic cells (mDCs). The roles of cytoskeletal elements in antigen uptake and dendritic cell maturation were determined by immunofluorescence staining, flow cytometry, and cytokine measurement, respectively. To test the efficacy of the vaccine in vivo, CSCs tumor-bearing mice were immunized with iDC or mDC. Pulsing DCs with antigen increased the expression levels of actin, gelsolin, talin, WASp, and Arp2, especially in podosome-like regions. Compared with iDCs, mDCs expressed high levels of CD40, CD80, CD86 costimulatory molecules and increased IL-12 production. Vaccination with mDC: i) increased CD8+ and CD4 + T-cell numbers, ii) prevented tumor growth with anti-mitotic activity and apoptotic induction, iii) suppressed metastasis by decreasing Snail, Slug, and Twist expressions. This study reveals for the first time that sialic acid removal and loading with CSC antigens induces significant molecular, morphological, and functional changes in DCs and that this new DC identity may be considered for future combined immunotherapy strategies against breast tumors.

An integrative model of cancer cell differentiation with immunotherapy. Phys Biol 2021;18. [PMID: 34633296 DOI: 10.1088/1478-3975/ac2e72] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

In order to improve cancer treatments, cancer cell differentiation and immunotherapy are the subjects of several studies in different branches of interdisciplinary sciences. In this work, we develop a new population model that integrates other complementary ones, thus emphasizing the relationship between cancer cells at different differentiation stages and the main immune system cells. For this new system, specific ranges were found where transdifferentiation of differentiated cancer cells can occur. In addition, a specific therapy against cancer stem cells was analysed by simulating cytotoxic cell vaccines. In reference to the latter, the different combinations of parameters that optimize it were studied.

Higher order solitary solutions to the meta-model of diffusively coupled Lotka-Volterra systems

A meta-model of diffusively coupled Lotka-Volterra systems used to model various biomedical phenomena is considered in this paper. Necessary and sufficient conditions for the existence of nth order solitary solutions are derived via a modified inverse balancing technique. It is shown that as the highest possible solitary solution order n is increased, the number of nonzero solution parameter values remains constant for solitary solutions of order n > 3 . Analytical and computational experiments are used to illustrate the obtained results.

A minimal model of T cell avidity may identify subtherapeutic vaccine schedules

T cells protect the body from cancer by recognising tumour-associated antigens. Recognising these antigens depends on multiple factors, one of which is T cell avidity, i.e., the total interaction strength between a T cell and a cancer cell. While both high- and low-avidity T cells can kill cancer cells, durable anti-cancer immune responses require the selection of high-avidity T cells. Previous experimentation with anti-cancer vaccines, however, has shown that most vaccines elicit low-avidity T cells. Optimising vaccine schedules may remedy this by preferentially selecting high-avidity T cells. Here, we use mathematical modelling to develop a simple, phenomenological model of avidity selection that may identify vaccine schedules that disproportionately favour low-avidity T cells. We calibrate our model to our prior, more complex model, and then validate it against several experimental data sets. We find that the sensitivity of the model's parameters change with vaccine dosage, which allows us to use a patient's data and clinical history to screen for suitable vaccine strategies.

Understanding the effect of measurement time on drug characterization

In order to determine correct dosage of chemotherapy drugs, the effect of the drug must be properly quantified. There are two important values that characterize the effect of the drug: εmax is the maximum possible effect of a drug, and IC50 is the drug concentration where the effect diminishes by half. There is currently a problem with the way these values are measured because they are time-dependent measurements. We use mathematical models to determine how the εmax and IC50 values depend on measurement time and model choice. Seven ordinary differential equation models (ODE) are used for the mathematical analysis; the exponential, Mendelsohn, logistic, linear, surface, Bertalanffy, and Gompertz models. We use the models to simulate tumor growth in the presence and absence of treatment with a known IC50 and εmax. Using traditional methods, we then calculate the IC50 and εmax values over fifty days to show the time-dependence of these values for all seven mathematical models. The general trend found is that the measured IC50 value decreases and the measured εmax increases with increasing measurement day for most mathematical models. Unfortunately, the measured values of IC50 and εmax rarely matched the values used to generate the data. Our results show that there is no optimal measurement time since models predict that IC50 estimates become more accurate at later measurement times while εmax is more accurate at early measurement times.