Traditionally, it has been held that a central characteristic of stem cells is their ability to divide asymmetrically. Recent advances in inducible genetic labeling provided ample evidence that symmetric stem cell divisions play an important role in adult mammalian homeostasis. It is well understood that the two types of cell divisions differ in terms of the stem cells' flexibility to expand when needed. On the contrary, the implications of symmetric and asymmetric divisions for mutation accumulation are still poorly understood. In this paper we study a stochastic model of a renewing tissue, and address the optimization problem of tissue architecture in the context of mutant production. Specifically, we study the process of tumor suppressor gene inactivation which usually takes place as a consequence of two “hits”, and which is one of the most common patterns in carcinogenesis. We compare and contrast symmetric and asymmetric (and mixed) stem cell divisions, and focus on the rate at which double-hit mutants are generated. It turns out that symmetrically-dividing cells generate such mutants at a rate which is significantly lower than that of asymmetrically-dividing cells. This result holds whether single-hit (intermediate) mutants are disadvantageous, neutral, or advantageous. It is also independent on whether the carcinogenic double-hit mutants are produced only among the stem cells or also among more specialized cells. We argue that symmetric stem cell divisions in mammals could be an adaptation which helps delay the onset of cancers. We further investigate the question of the optimal fraction of stem cells in the tissue, and quantify the contribution of non-stem cells in mutant production. Our work provides a hypothesis to explain the observation that in mammalian cells, symmetric patterns of stem cell division seem to be very common.
Every colon cancer has its own unique characteristics, and therefore may respond differently to identical treatments. Here, we develop a data driven mathematical model for the interaction network of key components of immune microenvironment in colon cancer. We estimate the relative abundance of each immune cell from gene expression profiles of tumors, and group patients based on their immune patterns. Then we compare the tumor sensitivity and progression in each of these groups of patients, and observe differences in the patterns of tumor growth between the groups. For instance, in tumors with a smaller density of naive macrophages than activated macrophages, a higher activation rate of macrophages leads to an increase in cancer cell density, demonstrating a negative effect of macrophages. Other tumors however, exhibit an opposite trend, showing a positive effect of macrophages in controlling tumor size. Although the results indicate that for all patients the size of the tumor is sensitive to the parameters related to macrophages, such as their activation and death rate, this research demonstrates that no single biomarker could predict the dynamics of tumors.
The aim of this work is studying translating graphs by mean curvature flow in R 3 . We prove non-existence of complete translating graphs over bounded domains in R 2 . Furthermore, we show that there are only three types of complete translating graphs in R 3 ; entire graphs, graphs between two vertical planes, and graphs in one side of a plane. In the last two types, graphs are asymptotic to planes next to their boundaries. We also prove stability of translating graphs and then we obtain a pointwise curvature bound for translating graphs in R 3 .
As the immune system has a significant role in tumor progression, in this paper, we develop a data-driven mathematical model to study the interactions between immune cells and the osteosarcoma microenvironment. Osteosarcoma tumors are divided into three clusters based on their relative abundance of immune cells as estimated from their gene expression profiles. We then analyze the tumor progression and effects of the immune system on cancer growth in each cluster. Cluster 3, which had approximately the same number of naive and M2 macrophages, had the slowest tumor growth, and cluster 2, with the highest population of naive macrophages, had the highest cancer population at the steady states. We also found that the fastest growth of cancer occurred when the anti-tumor immune cells and cytokines, including dendritic cells, helper T cells, cytotoxic cells, and IFN-γ, switched from increasing to decreasing, while the dynamics of regulatory T cells switched from decreasing to increasing. Importantly, the most impactful immune parameters on the number of cancer and total cells were the activation and decay rates of the macrophages and regulatory T cells for all clusters. This work presents the first osteosarcoma progression model, which can be later extended to investigate the effectiveness of various osteosarcoma treatments.
One of the main challenges in machine learning (ML) is choosing an appropriate normalization method. Here, we examine the effect of various normalization methods on analyzing FPKM upper quartile (FPKM-UQ) RNA sequencing data sets. We collect the HTSeq-FPKM-UQ files of patients with colon adenocarcinoma from TCGA-COAD project. We compare three most common normalization methods: scaling, standardizing using z-score and vector normalization by visualizing the normalized data set and evaluating the performance of 12 supervised learning algorithms on the normalized data set. Additionally, for each of these normalization methods, we use two different normalization strategies: normalizing samples (files) or normalizing features (genes). Regardless of normalization methods, a support vector machine (SVM) model with the radial basis function kernel had the maximum accuracy (78%) in predicting the vital status of the patients. However, the fitting time of SVM depended on the normalization methods, and it reached its minimum fitting time when files were normalized to the unit length. Furthermore, among all 12 learning algorithms and 6 different normalization techniques, the Bernoulli naive Bayes model after standardizing files had the best performance in terms of maximizing the accuracy as well as minimizing the fitting time. We also investigated the effect of dimensionality reduction methods on the performance of the supervised ML algorithms. Reducing the dimension of the data set did not increase the maximum accuracy of 78%. However, it leaded to discovery of the 7SK RNA gene expression as a predictor of survival in patients with colon adenocarcinoma with accuracy of 78%.
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