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Register a new userA multi-phenotypic cancer model with cell plasticity
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The conventional cancer stem cell (CSC) theory indicates a hierarchy of CSCs and non-stem cancer cells (NSCCs), that is, CSCs can differentiate into NSCCs but not vice versa. However, an alternative paradigm of CSC theory with reversible cell plasticity among cancer cells has received much attention very recently. Here we present a generalized multi-phenotypic cancer model by integrating cell plasticity with the conventional hierarchical structure of cancer cells. We prove that under very weak assumption, the nonlinear dynamics of multi-phenotypic proportions in our model has only one stable steady state and no stable limit cycle. This result theoretically explains the phenotypic equilibrium phenomena reported in various cancer cell lines. Furthermore, according to the transient analysis of our model, it is found that cancer cell plasticity plays an essential role in maintaining the phenotypic diversity in cancer especially during the transient dynamics. Two biological examples with experimental data show that the phenotypic
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The phenotypic plasticity of cancer cells has received special attention in recent years. Even though related models have been widely studied in terms of mathematical properties, a thorough statistical analysis on parameter estimation and model selection is still very lacking. In this study, we present a Bayesian approach on the relative frequencies of cancer stem cells (CSCs). Both Gibbs sampling and Metropolis-Hastings (MH) algorithm are used to perform point and interval estimations of cell-state transition rates between CSCs and non-CSCs. Extensive simulations demonstrate the validity of our model and algorithm. By applying this method to a published data on SW620 colon cancer cell line, the model selection favors the phenotypic plasticity model, relative to conventional hierarchical model of cancer cells. Moreover, it is found that the initial state of CSCs after cell sorting significantly influences the occurrence of phenotypic plasticity.
The paradigm of phenotypic plasticity indicates reversible relations of different cancer cell phenotypes, which extends the cellular hierarchy proposed by the classical cancer stem cell (CSC) theory. Since it is still question able if the phenotypic plasticity is a crucial improvement to the hierarchical model or just a minor extension to it, it is worthwhile to explore the dynamic behavior characterizing the reversible phenotypic plasticity. In this study we compare the hierarchical model and the reversible model in predicting the cell-state dynamics observed in biological experiments. Our results show that the hierarchical model shows significant disadvantages over the reversible model in describing both long-term stability (phenotypic equilibrium) and short-term transient dynamics (overshoot) of cancer cells. In a very specific case in which the total growth of population due to each cell type is identical, the hierarchical model predicts neither phenotypic equilibrium nor overshoot, whereas thereversible model succeeds in predicting both of them. Even though the performance of the hierarchical model can be improved by relaxing the specific assumption, its prediction to the phenotypic equilibrium strongly depends on a precondition that may be unrealistic in biological experiments, and it also fails to capture the overshoot of CSCs. By comparison, it is more likely for the reversible model to correctly describe the stability of the phenotypic mixture and various types of overshoot behavior.
Following antigen stimulation, the net outcomes of a T cell response are shaped by integrated signals from both positive co-stimulatory and negative regulatory molecules. Recently, the blockade of negative regulatory molecules (i.e. immune checkpoint signals) demonstrates therapeutic effects in treatment of human cancer, but only in a fraction of cancer patients. Since this therapy is aimed to enhance T cell responses to cancers, here we devised a conceptual model by integrating both positive and negative signals in addition to antigen stimulation. A digital range of adjustment of each signal is formulated in our model for prediction of a final T cell response. This model allows us to evaluate strategies in order to enhance antitumor T cell responses. Our model provides a rational combination strategy for maximizing the therapeutic effects of cancer immunotherapy.
Studying the development of malignant tumours, it is important to know and predict the proportions of different cell types in tissue samples. Knowing the expected temporal evolution of the proportion of normal tissue cells, compared to stem-like and non-stem like cancer cells, gives an indication about the progression of the disease and indicates the expected response to interventions with drugs. Such processes have been modeled using Markov processes. An essential step for the simulation of such models is then the determination of state transition probabilities. We here consider the experimentally more realistic scenario in which the measurement of cell population sizes is noisy, leading to a particular hidden Markov model. In this context, randomness in measurement is related to noisy measurements, which are used for the estimation of the transition probability matrix. Randomness in sampling, on the other hand, is here related to the error in estimating the state probability from small cell populations. Using aggregated data of fluorescence-activated cell sorting (FACS) measurement, we develop a minimum mean square error estimator (MMSE) and maximum likelihood (ML) estimator and formulate two problems to find the minimum number of required samples and measurements to guarantee the accuracy of predicted population sizes using a transition probability matrix estimated from noisy data. We analyze the properties of two estimators for different noise distributions and prove an optimal solution for Gaussian distributions with the MMSE. Our numerical results show, that for noisy measurements the convergence mechanism of transition probabilities and steady states differ widely from the real values if one uses the standard deterministic approach in which measurements are assumed to be noise free.
The polarisation of cells and tissues is fundamental for tissue morphogenesis during biological development and regeneration. A deeper understanding of biological polarity pattern formation can be gained from the consideration of pattern reorganisation in response to an opposing instructive cue, which we here consider by example of experimentally inducible body axis
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