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In previous theoretical research, we inferred that cancer stem cells (CSCs), the cells that presumably drive tumor growth and resistance to conventional cancer treatments, are not uniformly distributed in the bulk of a tumorsphere. To confirm this theoretical prediction, we cultivated tumorspheres enriched in CSCs, and performed immunofluorecent detection of the stemness marker SOX2 using a confocal microscope. In this article, we present a method developed to process the images that reconstruct the amount and location of the CSCs in the tumorspheres. Its advantage is the use of a statistical criterion to classify the cells in stem and differentiated instead of setting an arbitrary threshold. From the analysis of the results of the methods using graph theory and computational modeling, we concluded that the distribution of Cancer Stem Cells in an experimental tumorsphere is non-homogeneous. This method is independent of the tumorsphere assay being useful for analyzing images in which several different kinds of cells are stained with different markers., Comment: 14 pages, 6 figures, 2 tables

The growth of many solid tumors has been found to be driven by chemo- and radiotherapy-resistant cancer stem cells (CSCs). A suitable therapeutic avenue in these cases may involve the use of a differentiating agent (DA) to force the differentiation of the CSCs and of conventional therapies to eliminate the remaining differentiated cancer cells (DCCs). To describe the effects of a DA that reprograms CSCs into DCCs, we adapt a differential equation model developed to investigate tumorspheres, which are assumed to consist of jointly evolving CSC and DCC populations. We analyze the mathematical properties of the model, finding the equilibria and their stability. We also present numerical solutions and phase diagrams to describe the system evolution and the therapy effects, denoting the DA strength by a parameter \(a_{dif}\).To obtain realistic predictions, we choose the other model parameters to be those determined previously from fits to various experimental datasets. These datasets characterize the progression of the tumor under various culture conditions. Typically, for small values of \(a_{dif}\) the tumor evolves towards a final state that contains a CSC fraction, but a strong therapy leads to the suppression of this phenotype. Nonetheless, different external conditions lead to very diverse behaviors. For some environmental conditions, the model predicts a threshold not only in the therapy strength, but also in its starting time, an early beginning being potentially crucial. In summary, our model shows how the effects of a DA depend critically not only on the dosage and timing of the drug application, but also on the tumor nature and its environment., Comment: 21 pages, 10 figures (17 images)

Using geometrical arguments it is shown that Cancer Stem Cells (CSC) must be confined inside solid tumors under natural situations. Aided by an agent-based model and percolation theory, the probability for a CSC to be at the border of a colony is estimated. This probability is estimated as a function of the CSCs self-renewal probability $p_s$, i.e. the chance that an CSC become non-differentiate after mitosis. In the most common situations, $p_s$ is small and CSCs are mostly destined to produce differentiated cells at a very low rate. The results presented here show that CSCs form a small core in the center of the cancer cell colony, becoming quiescent due to the lack of space to proliferate, which stabilizes their population size. This result provides a simple explanation for the CSC niche size that dispenses with the need of quorum sensing or other proposed signalling mechanisms. It is also supports the hypothesis that metastases are likely to start at the very beginning of the tumoral development.

We study a minimal cognitive flocking model, which assumes that the moving entities navigate using exclusively the available instantaneous visual information. The model consists of active particles, with no memory, that interact by a short-ranged, position-based, attractive force that acts inside a vision cone (VC) and lack velocity-velocity alignment. We show that this active system can exhibit -- due to the VC that breaks Newton's third law -- various complex, large-scale, self-organized patterns. Depending on parameter values, we observe the emergence of aggregates or milling-like patterns, the formation of moving -- locally polar -- files with particles at the front of these structures acting as effective leaders, and the self-organization of particles into macroscopic nematic structures leading to long-ranged nematic order. Combining simulations and non-linear field equations, we show that position-based active models, as the one analyzed here, represent a new class of active systems fundamentally different from other active systems, including velocity-alignment-based flocking systems. The reported results are of prime importance in the study, interpretation, and modeling of collective motion patterns in living and non-living active systems.

The classic Vicsek model [Phys.Rev.Lett. {\bf75},1226(1995)] is studied in the regime of very low noise intensities, which is shown to be characterized by a cluster (MC) that contains a macroscopic fraction of the system particles. It is shown that the well-known power-law behavior of the cluster size distribution loses its cutoff becoming bimodal at very low noise intensities: A peak develops for larger sizes to settle the emergence of the MC. The average cluster number m*, is introduced as a parameter that properly describes this change, i.e. a line in the noise-speed phase portrait can be identified to separates both regimes. The average largest cluster parameter also develops large fluctuations at a non zero critical noise. Finite size scaling analysis is performed to show that a phase transition to a macroscopic cluster is taking place. Consistency of the results with the literature is also checked and commented upon.

Tumor growth is often the result of the simultaneous development of two or more cancer cell populations. Their interaction between them characterizes the system evolution. To obtain information about these interactions we apply the recently developed vector universality (VUN) formalism to various instances of competition between tumor populations. The formalism allows us: (a) to quantify the growth mechanisms of a HeLa cell colony, describing the phenotype switching responsible for its fast expansion, (b) to reliably reconstruct the evolution of the necrotic and viable fractions in both in vitro and in vivo tumors using data for the time dependences of the total masses, and (c) to show how the shedding of cells leading to subspheroid formation is beneficial to both the spheroid and subspheroid populations, suggesting that shedding is a strong positive influence on cancer dissemination.