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The activity and distribution of Piezo1 molecules, along with the maturity and strength of focal adhesions (FAs), serve as critical factors influencing cell mechanosensing. Notably, migrating epithelial cells and mesenchymal-like cancer cells exhibit significantly different behaviors regarding these elements. In cancer cells, Piezo1 molecules are distributed uniformly, while in epithelial cells, their distribution is heterogeneous. In epithelial cells, Piezo1 molecules tend to group around FAs, a phenomenon that is enhanced by actomyosin contractility. However, a reduction in contractility results in a more uniform distribution of Piezo1 molecules. The expression and activity levels of Piezo1 molecules are markedly higher in cancer cells compared to epithelial cells. The activity of Piezo1 molecules correlates with the intracellular calcium concentration. Despite the extensive experimental studies on the properties of migrating epithelial and mesenchymal-like cancer cells, the physical explanations remain lacking. The primary objective of this theoretical study is to explore: (i) the inhomogeneous distribution of Piezo1 molecules in epithelial cells in relation to the Marangoni eff

Cold atmospheric plasma (CAP) has shown its promising application in cancer treatment both in vitro and in vivo. However, the anti-cancer mechanism is still largely unknown. CAP may kill cancer cells via triggering the rise of intracellular ROS, DNA damage, mitochondrial damage, or cellular membrane damage. While, the specific vulnerability of cancer cells to CAP has been observed, the underlying mechanism of such cell-based specific vulnerability to CAP is completely unknown. Here, through the comparison of CAP treatment and H2O2 treatment on 10 different cancer cell lines in vitro, we observed that the H2O2 consumption speed by cancer cells was strongly correlated to the cytotoxicity of CAP treatment on cancer cells. Cancer cells that clear extracellular H2O2 more quickly are more resistant to the cytotoxicity of CAP treatment. This finding strongly indicates that the anti-oxidant system in cancer cells play a key role in the specific vulnerability of cancer cells to CAP treatment in vitro.

Although a good comprehension of how cancer cells collectively migrate by following molecular rules which influence the state of cell-cell adhesion contacts has been generated, the impact of collective migration on cellular rearrangement from subcellular to supracellular level remains less understood. Thus, considering collective cell migration (CCM) of cancer mesenchymal cells on one side and healthy epithelial cells on the other during the fusion of two cell aggregates could result in a powerful tool in order to address the contribution of structural changes at subcellular level which influence the cellular rearrangements and help to understand this important, but still controversial topic. While healthy epithelial cells undergo volumetric cell rearrangement driven by the tissue surface tension, which results in a collision of opposite directed velocity front near the contact point between two cell aggregates, mesenchymal cells follow quite different scenario. These cells are capable of reducing the surface tension and undergo surface cell rearrangement. The main goal of this contribution is to discuss the origin of surface activity of cancer cells by accounting for the crosstalk

Cancer is increasingly perceived as a systems-level, network phenomenon. The major trend of malignant transformation can be described as a two-phase process, where an initial increase of network plasticity is followed by a decrease of plasticity at late stages of tumor development. The fluctuating intensity of stress factors, like hypoxia, inflammation and the either cooperative or hostile interactions of tumor inter-cellular networks, all increase the adaptation potential of cancer cells. This may lead to the bypass of cellular senescence, and to the development of cancer stem cells. We propose that the central tenet of cancer stem cell definition lies exactly in the indefinability of cancer stem cells. Actual properties of cancer stem cells depend on the individual "stress-history" of the given tumor. Cancer stem cells are characterized by an extremely large evolvability (i.e. a capacity to generate heritable phenotypic variation), which corresponds well with the defining hallmarks of cancer stem cells: the possession of the capacity to self-renew and to repeatedly re-build the heterogeneous lineages of cancer cells that comprise a tumor in new environments. Cancer stem cells rep

Stem cells have the potential to produce lineages of non-stem cell populations (differentiated cells) via a ubiquitous hierarchal division scheme. Differentiation of a stem cell into (partially) differentiated cells can happen either symmetrically or asymmetrically. The selection dynamics of a mutant cancer stem cell should be investigated in the light of a stem cell proliferation hierarchy and presence of a non-stem cell population. By constructing a three-compartment Moran-type model composed of normal stem cells, mutant (cancer) stem cells and differentiated cells, we derive the replicator dynamics of stem cell frequencies where asymmetric differentiation and differentiated cell death rates are included in the model. We determine how these new factors change the conditions for a successful mutant invasion and discuss the variation on the steady state fraction of the population as different model parameters are changed. By including the phenotypic plasticity/dedifferentiation, in which a progenitor/differentiated cell can transform back into a cancer stem cell, we show that the effective fitness of mutant stem cells is not only determined by their proliferation and death rates bu

Asymmetric partition of fate determinants during cell division is a hallmark of cell differentiation. Recent work suggested that such a mechanism is hijacked by cancer cells to increase both their phenotypic heterogeneity and plasticity and in turn their fitness. To quantify fluctuations in the partitioning of cellular elements, imaging-based approaches are used, whose accuracy is limited by the difficulty of detecting cell divisions. Our work addresses this gap proposing a general method based on high-throughput flow cytometry measurements coupled with a theoretical framework. We applied our method to a panel of both normal and cancerous human colon cells, showing that different kinds of colon adenocarcinoma cells display very distinct extents of fluctuations in their cytoplasm partition, explained by an asymmetric division of their size. To test the accuracy of our population-level protocol, we directly measure the inherited fractions of cellular elements from extensive time-lapses of live-cell laser scanning microscopy, finding excellent agreement across the cell types. Ultimately, our flow cytometry-based method promises to be accurate and easily applicable to a wide range of b

We consider the decision making by mammalian cells, looking them as dynamic systems with rhythms. We calculate the effective dimension of the cell division model of the healthy mammalian cells consistent with the data: it is described via a four dimensional dynamic system. We assume that the cell's decision making property is strongly affected by the cells rhythms, their causal relations, and by the correlation between internal states of different cells in tissue. There is a strong correlation between the states of different healthy cells (verified partially experimentally), and we assume that there is no such a correlation between internal states of the healthy and cancer cells. The origins of the cancer are just the disruption of this correlation (self-identification of the cells) and the change of the causal relations between the Circadian and cell cycle rhythms. Assuming the Gaussian channel version of the cell-cell communications and a key role of public goods for the cancer cells, we get a strong correlation between the states of different cancer cells.

Glucose is a primary energy source for cancer cells. Several lines of evidence support the idea that monocarboxylate transporters, such as MCT1, elicit metabolic reprogramming of cancer cells in glucose-poor environments, allowing them to reuse lactate, a byproduct of glucose metabolism, as an alternative energy source with serious consequences for disease progression. We employ a synergistic experimental and mathematical modelling approach to explore the evolutionary processes at the root of cancer cell adaptation to glucose deprivation, with particular focus on the mechanisms underlying the increase in MCT1 expression observed in glucose-deprived aggressive cancer cells. Data from in vitro experiments on breast cancer cells are used to inform and calibrate a mathematical model that comprises a partial integro-differential equation for the dynamics of a population of cancer cells structured by the level of MCT1 expression. Analytical and numerical results of this model suggest that environment-induced changes in MCT1 expression mediated by lactate-associated signalling pathways enable a prompt adaptive response of glucose-deprived cancer cells, whilst fluctuations in MCT1 expressi

Predictive modeling of the evolutionary dynamics of cancer is a challenge issue in computational cancer biology. In this paper, we propose a general mathematical model framework for the evolutionary dynamics of cancer with plasticity and heterogeneity in cancer cells. Cancer is a group of diseases involving abnormal cell growth, during which abnormal regulations in stem cell regeneration are essential for the dynamics of cancer development. In general, the dynamics of stem cell regeneration can be simplified as a $\mathrm{G_0}$ phase cell cycle model, which lead to a delay differentiation equation. When cell heterogeneity and plasticity are considered, we establish a differential-integral equation based on the random transition of epigenetic states of stem cells during cell division. The proposed model highlights cell heterogeneity and plasticity, and connects the heterogeneity with cell-to-cell variance in cellular behaviors, e.g. proliferation, apoptosis, and differentiation/senescence, and can be extended to include gene mutation-induced tumor development. Hybrid computations models are developed based on the mathematical model framework, and are applied to the process of inflam

Heterogeneity in the size distribution of cancer cell populations has been recently linked to drug resistance and invasiveness. However, despite many progresses have been made in understanding how such heterogeneous size distributions arise in fast-proliferating cell types -like bacteria and yeast-, comprehensive investigations on cancer cell populations are still lacking mainly due to the difficulties of monitoring the proliferation of the time scales typical of mammalian cells. From a reductionist cell dynamics point of view, the strategies allowing size homeostasis are roughly grouped into three classes, \emph{i.e.} timer, sizer, or adder. These strategies are empirically distinguishable given the phenomenological measurable relationship between the cell size at birth and at division, which requires following the proliferation at the single-cell level. Here, we show how it is possible to infer the growth regime and division strategy of leukemia cell populations using live cell fluorescence labeling and flow cytometry in combination with a quantitative analytical model where both cell growth and division rates depend on powers of the cell size. Using our novel approach, we found

Cancer cell migration between different body parts is the driving force behind cancer metastasis, which is the main cause of mortality of patients. Migration of cancer cells often proceeds by penetration through narrow cavities in locally stiff, yet flexible tissues. In our previous work, we developed a model for cell geometry evolution during invasion, which we extend here to investigate whether leader and follower (cancer) cells that only interact mechanically can benefit from sequential transmigration through narrow micro-channels and cavities. We consider two cases of cells sequentially migrating through a flexible channel: leader and follower cells being closely adjacent or distant. Using Wilcoxon's signed-rank test on the data collected from Monte Carlo simulations, we conclude that the modelled transmigration speed for the follower cell is significantly larger than for the leader cell when cells are distant, i.e. follower cells transmigrate after the leader has completed the crossing. Furthermore, it appears that there exists an optimum with respect to the width of the channel such that cell moves fastest. On the other hand, in the case of closely adjacent cells, effectively

Cancer cells exhibit increased motility and proliferation, which are instrumental in the formation of tumours and metastases. These pathological changes can be traced back to malfunctions of cellular signalling pathways, and calcium signalling plays a prominent role in these. We formulate a new model for cancer cell movement which for the first time explicitly accounts for the dependence of cell proliferation and cell-cell adhesion on calcium. At the heart of our work is a non-linear, integro-differential (non-local) equation for cancer cell movement, accounting for cell diffusion, advection and proliferation. We also employ an established model of cellular calcium signalling with a rich dynamical repertoire that includes experimentally observed periodic wave trains and solitary pulses. The cancer cell density exhibits travelling fronts and complex spatial patterns arising from an adhesion-driven instability (ADI). We show how the different calcium signals and variations in the strengths of cell-cell attraction and repulsion shape the emergent cellular aggregation patterns, which are a key component of the metastatic process. Performing a linear stability analysis, we identify para

Mammalian cells are restricted from proliferating indefinitely. Telomeres at the end of each chromosome are shortened at cell division and, when they reach a critical length, the cell will enter permanent cell cycle arrest - a state known as senescence. This mechanism is thought to be tumor suppressing, as it helps prevent precancerous cells from dividing uncontrollably. Stem cells express the enzyme telomerase, which elongates the telomeres, thereby postponing senescence. However, unlike germ cells and most types of cancer cells, stem cells only express telomerase at levels insufficient to fully maintain the length of their telomeres leading to a slow decline in proliferation potential. It is not yet fully understood how this decline influences the risk of cancer and the longevity of the organism. We here develop a stochastic model to explore the role of telomere dynamics in relation to both senescence and cancer. The model describes the accumulation of cancerous mutations in a multicellular organism and creates a coherent theoretical framework for interpreting the results of several recent experiments on telomerase regulation. We demonstrate that the longest average cancer free l

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 conversions from NCSSs to CSCs greatly contribute to the transient growth of CSCs proportion shortly after the drastic reduction of it. In particular, an inter

Cancer stem cells have been shown to be critical to the development of a variety of solid cancers. The precise interplay mechanisms between cancer stem cells and the rest of a tissue are still not elucidated. To shed light on the interactions between stem and non-stem cancer cell populations we develop a two-population mathematical model, which is suitable to describe tumorsphere growth. Both interspecific and intraspecific interactions, mediated by the microenvironment, are included. We show that there is a tipping point, characterized by a transcritical bifurcation, where a purely non-stem cell attractor is replaced by a new attractor that contains both stem and differentiated cancer cells. The model is then applied to describe the outcome of a recent experiment. This description reveals that, while the intraspecific interactions are inhibitory, the interspecific interactions stimulate growth. This can be understood in terms of stem cells needing differentiated cells to reinforce their niches, and phenotypic plasticity favoring the de-differentiation of differentiated cells into cancer stem cells. We posit that this is a consequence of the deregulation of the quorum sensing that

Cancer stem cells are controlled by developmental networks that are often topologically indistinguishable from normal, healthy stem cells. The question is why cancer stem cells can be both phenotypically distinct and have morphological effects so different from normal stem cells. The difference between cancer stem cells and normal stem cells lies not in differences their network architecture, but rather in the spatial-temporal locality of their activation in the genome and the resulting expression in the body. The metastatic potential cancer stem cells is not based primarily on their network divergence from normal stem cells, but on non-network based genetic changes that enable the evolution of gene-based phenotypic properties of the cell that permit its escape and travel to other parts of the body. Stem cell network theory allows the precise prediction of stem cell behavioral dynamics and a mathematical description of stem cell proliferation for both normal and cancer stem cells. It indicates that the best therapeutic approach is to tackle the highest order stem cells first, otherwise spontaneous remission of so called cured cancers will always be a danger. Stem cell networks poin

Current methods for capturing circulating tumor cells (CTCs) are based on the overexpression of cytokeratin (CK) or epithelial cell-adhesion molecule (EpCAM) on cancer cells. However, during the process of metastasis, tumor cells undergo epithelial to mesenchymal transition (EMT) that can lead to the loss of CK/EpCAM expression. Therefore, it is vital to develop a capturing technique independent of CK/EpCAM expression on the cancer cell. To develop this technique, it is important to identify common secondary oncogenic markers overexpressed on tumor cells before and after EMT. We analyzed the biomarker expression levels in tumor cells, before and after EMT, and found two common proteins human epidermal growth factor receptor 2 (Her2) and epidermal growth factor receptor (EGFR) whose levels remained unaffected. So, we synthesized immunomagnetic iron nanocubes covalently conjugated with antibodies of Her2 or EGFR to capture cancer cells irrespective of the EMT status. The nanocubes showed high specificity (6 to 9 fold) in isolating the cancer cells of interest from a mixture of cells spiked in serum. We characterized the captured cells for identifying their EMT status. Thus, we believ

In this review, we discuss recent advances on the plasticity of cancer stem cells and highlight their relevance to understand the metastatic process and to guide therapeutic interventions. Recent results suggest that the strict hierarchical structure of cancer cell populations advocated by the cancer stem cell model must be reconsidered since the depletion of cancer stem cells leads the other tumor cells to switch back into the cancer stem cell phenotype. This plasticity has important implications for metastasis since migrating cells do not need to be cancer stem cells in order to seed a metastasis. We also discuss the important role of the immune system and the microenvironment in modulating phenotypic switching and suggest possible avenues to exploit our understanding of this process to develop an effective strategy for precision medicine.

The identification of cancer stem cells in vivo and in vitro relies on specific surface markers that should allow to sort cancer cells in phenotypically distinct subpopulations. Experiments report that sorted cancer cell populations after some time tend to express again all the original markers, leading to the hypothesis of phenotypic switching, according to which cancer cells can transform stochastically into cancer stem cells. Here we explore an alternative explanation based on the hypothesis that markers are not perfect and are thus unable to identify all cancer stem cells. Our analysis is based on a mathematical model for cancer cell proliferation that takes into account phenotypic switching, imperfect markers and error in the sorting process. Our conclusion is that the observation of reversible expression of surface markers after sorting does not provide sufficient evidence in support of phenotypic switching.