Mathematical model of colorectal cancer initiation

Selective sweep probabilities in spatially expanding populations

Evolution during range expansions shapes biological systems from microbial communities and tumours up to invasive species. A fundamental question is whether, when a beneficial mutation arises during a range expansion, it will evade clonal interference and sweep through the population to fixation. However, most theoretical investigations of range expansions have been confined to regimes in which selective sweeps are effectively impossible, while studies of selective sweeps have either assumed constant population size or have ignored spatial structure. Here we use mathematical modelling and analysis to investigate selective sweep probabilities in the alternative yet biologically relevant scenario in which mutants can outcompete and displace a slowly spreading wildtype. Assuming constant radial expansion speed, we derive probability distributions for the arrival time and location of the first surviving mutant and hence find surprisingly simple approximate and exact expressions for selective sweep probabilities in one, two and three dimensions, which are independent of mutation rate. Namely, the selective sweep probability is approximately 1 - c w t / c m d , where c w t and c m are the wildtype and mutant radial expansion speeds, and d the spatial dimension. Using agent-based simulations, we show that our analytical results accurately predict selective sweep frequencies in the two-dimensional spatial Moran process. We further compare our results with those obtained for alternative growth laws. Parameterizing our model for human tumours, we find that selective sweeps are predicted to be rare except during very early solid tumour growth, thus providing a general, pan-cancer explanation for findings from recent sequencing studies.

Colorectal cancer initiation: Understanding early-stage disease for intervention

How tumors arise or the cause of precancerous lesions is a fundamental question in cancer biology. It is generally accepted that tumors originate from normal cells that undergo uncontrolled proliferation owing to genetic alterations. At the onset of adenoma formation, cancer driver mutations confer clonal growth advantage, enabling mutant cells to outcompete and eliminate the surrounding healthy cells. Hence, the development of precancerous lesions is not only attributed to the expansion of pre-malignant clones, but also relies on the relative fitness of mutated cells compared to the neighboring cells. Colorectal cancer (CRC) is an excellent model to investigate cancer origin as it follows a stereotypical process from mutant cell hyperplasia to adenoma formation and progression. Here, we review the evolving understanding of colonic tumor development, focusing on how cell intrinsic and extrinsic factors impact cell competition and the "clone war" between cancer-initiating cells and normal stem cells. We also discuss the promises and limitations of targeting cell competitiveness in cancer prevention and early intervention. The field of tumor initiation is currently in its infancy, elucidating the adenoma origin is crucial for designing effective prevention strategies and early treatments before cancer becomes incurable.

Synergistic epistasis among cancer drivers can rescue early tumors from the accumulation of deleterious passengers

Epistasis among driver mutations is pervasive and explains relevant features of cancer, such as differential therapy response and convergence towards well-characterized molecular subtypes. Furthermore, a growing body of evidence suggests that tumor development could be hampered by the accumulation of slightly deleterious passenger mutations. In this work, we combined empirical epistasis networks, computer simulations, and mathematical models to explore how synergistic interactions among driver mutations affect cancer progression under the burden of slightly deleterious passengers. We found that epistasis plays a crucial role in tumor development by promoting the transformation of precancerous clones into rapidly growing tumors through a process that is analogous to evolutionary rescue. The triggering of epistasis-driven rescue is strongly dependent on the intensity of epistasis and could be a key rate-limiting step in many tumors, contributing to their unpredictability. As a result, central genes in cancer epistasis networks appear as key intervention targets for cancer therapy.

The role of Akkermansia muciniphila in colorectal cancer: A double-edged sword of treatment or disease progression?

Colorectal cancer (CRC) is the second most cancer-related death worldwide. In recent years, probiotics have been used to reduce the potential risks of CRC and tumors with various mechanisms. Different bacteria have been suggested to play different roles in the progression, prevention, or treatment of CRC. Akkermansia muciniphila is considered a next-generation probiotic for preventing and treating some diseases. Therefore, in this review article, we aimed to describe and discuss different mechanisms of A. muciniphila as an intestinal microbiota or probiotic in CRC. Some studies suggested that the abundance of A. muciniphila was higher or increased in CRC patients compared to healthy individuals. However, the decreased abundance of A. muciniphila was associated with severe symptoms of CRC, indicating that A. muciniphila did not play a role in the development of CRC. In addition, A. muciniphila administration elevates gene expression of proliferation-associated molecules such as S100A9, Dbf4, and Snrpd1, or markers for cell proliferation. Some other studies suggested that inflammation and tumorigenesis in the intestine might promoted by A. muciniphila. Overall, the role of A. muciniphila in CRC development or inhibition is still unclear and controversial. Various methods of bacterial supplementation, such as viability, bacterial number, and abundance, could all influence the colonization effect of A. muciniphila administration and CRC progression. Overall, A. mucinipila has been revealed to modulate the therapeutic potential of immune checkpoint inhibitors. Preliminary human data propose that oral consumption of A. muciniphila is safe, but its efficacy needs to be confirmed in more human clinical studies.

Evolving copy number gains promote tumor expansion and bolster mutational diversification

The timing and fitness effect of somatic copy number alterations (SCNA) in cancer evolution remains poorly understood. Here we present a framework to determine the timing of a clonal SCNA that encompasses multiple gains. This involves calculating the proportion of time from its last gain to the onset of population expansion (lead time) as well as the proportion of time prior to its first gain (initiation time). Our method capitalizes on the observation that a genomic segment, while in a specific copy number (CN) state, accumulates point mutations proportionally to its CN. Analyzing 184 whole genome sequenced samples from 75 patients across five tumor types, we commonly observe late gains following early initiating events, occurring just before the clonal expansion relevant to the sampling. These include gains acquired after genome doubling in more than 60% of cases. Notably, mathematical modeling suggests that late clonal gains may contain final-expansion drivers. Lastly, SCNAs bolster mutational diversification between subpopulations, exacerbating the circle of proliferation and increasing heterogeneity.

Modeling cancer progression: an integrated workflow extending data-driven kinetic models to bio-mechanical PDE models

Computational modeling of cancer can help unveil dynamics and interactions that are hard to replicate experimentally. Thanks to the advancement in cancer databases and data analysis technologies, these models have become more robust than ever. There are many mathematical models which investigate cancer through different approaches, from sub-cellular to tissue scale, and from treatment to diagnostic points of view. In this study, we lay out a step-by-step methodology for a data-driven mechanistic model of the tumor microenvironment. We discuss data acquisition strategies, data preparation, parameter estimation, and sensitivity analysis techniques. Furthermore, we propose a possible approach to extend mechanistic ordinary differential equation models to PDE models coupled with mechanical growth. The workflow discussed in this article can help understand the complex temporal and spatial interactions between cells and cytokines in the tumor microenvironment and their effect on tumor growth.

Mathematical modeling the gene mechanism of colorectal cancer and the effect of radiation exposure

Cancer is the result of continuous accumulation of gene mutations in normal cells. The number of mutations is different in different types of cancer and even in different patients with the same type of cancer. Therefore, studying all possible numbers of gene mutations in malignant cells is of great value for the understanding of tumorigenesis and the treatment of cancer. To this end, we applied a stochastic mathematical model considering the clonal expansion of any premalignant cells with different mutations to analyze the number of gene mutations in colorectal cancer. The age-specific colorectal cancer incidence rates from the Surveillance, Epidemiology and End Results (SEER) registry in the United States and the Life Span Study (LSS) in Nagasaki and Hiroshima, Japan are chosen to test the reasonableness of the model. Our fitting results indicate that the transformation from normal cells to malignant cells may undergo two to five driver mutations for colorectal cancer patients without radiation-exposed environment, two to four driver mutations for colorectal cancer patients with low level radiation-exposure, and two to three driver mutations for colorectal cancer patients with high level radiation-exposure. Furthermore, the net growth rate of the mutated cells with radiation-exposure was is higher than that of the mutated cells without radiation-exposure for the models with two to five driver mutations. These results suggest that radiation environment may affect the clonal expansion of cells and significantly affect the development of tumors.

Stochastic model for cell population dynamics quantifies homeostasis in colonic crypts and its disruption in early tumorigenesis

The questions of how healthy colonic crypts maintain their size, and how homeostasis is disrupted by driver mutations, are central to understanding colorectal tumorigenesis. We propose a three-type stochastic branching process, which accounts for stem, transit-amplifying (TA) and fully differentiated (FD) cells, to model the dynamics of cell populations residing in colonic crypts. Our model is simple in its formulation, allowing us to estimate all but one of the model parameters from the literature. Fitting the single remaining parameter, we find that model results agree well with data from healthy human colonic crypts, capturing the considerable variance in population sizes observed experimentally. Importantly, our model predicts a steady-state population in healthy colonic crypts for relevant parameter values. We show that APC and KRAS mutations, the most significant early alterations leading to colorectal cancer, result in increased steady-state populations in mutated crypts, in agreement with experimental results. Finally, our model predicts a simple condition for unbounded growth of cells in a crypt, corresponding to colorectal malignancy. This is predicted to occur when the division rate of TA cells exceeds their differentiation rate, with implications for therapeutic cancer prevention strategies.

A Poisson distribution-based general model of cancer rates and a cancer risk-dependent theory of aging

This article presents a formula for modeling the lifetime incidence of cancer in humans. The formula utilizes a Poisson distribution-based "np" model to predict cancer incidence, with "n" representing the effective number of cell turnover and "p" representing the probability of single-cell transformation. The model accurately predicts the observed incidence of cancer in humans when a reduction in cell turnover due to aging is taken into account. The model also suggests that cancer development is ultimately inevitable. The article proposes a theory of aging based on this concept, called the "np" theory. According to this theory, an organism maintains its order by balancing cellular entropy through continuous proliferation. However, cellular "information entropy" in the form of accumulated DNA mutations increases irreversibly over time, restricting the total number of cells an organism can generate throughout its lifetime. When cell division slows down and fails to compensate for the increased entropy in the system, aging occurs. Essentially, aging is the phenomenon of running out of predetermined cell resources. Different species have evolved separate strategies to utilize their limited cell resources throughout their life cycle.

Oncogene-like addiction to aneuploidy in human cancers

Most cancers exhibit aneuploidy, but its functional significance in tumor development is controversial. Here, we describe ReDACT (Restoring Disomy in Aneuploid cells using CRISPR Targeting), a set of chromosome engineering tools that allow us to eliminate specific aneuploidies from cancer genomes. Using ReDACT, we created a panel of isogenic cells that have or lack common aneuploidies, and we demonstrate that trisomy of chromosome 1q is required for malignant growth in cancers harboring this alteration. Mechanistically, gaining chromosome 1q increases the expression of MDM4 and suppresses p53 signaling, and we show that TP53 mutations are mutually exclusive with 1q aneuploidy in human cancers. Thus, tumor cells can be dependent on specific aneuploidies, raising the possibility that these "aneuploidy addictions" could be targeted as a therapeutic strategy.

A computational model for the cancer field effect

Introduction

The Cancer Field Effect describes an area of pre-cancerous cells that results from continued exposure to carcinogens. Cells in the cancer field can easily develop into cancer. Removal of the main tumor mass might leave the cancer field behind, increasing risk of recurrence.

Methods

The model we propose for the cancer field effect is a hybrid cellular automaton (CA), which includes a multi-layer perceptron (MLP) to compute the effects of the carcinogens on the gene expression of the genes related to cancer development. We use carcinogen interactions that are typically associated with smoking and alcohol consumption and their effect on cancer fields of the tongue.

Results

Using simulations we support the understanding that tobacco smoking is a potent carcinogen, which can be reinforced by alcohol consumption. The effect of alcohol alone is significantly less than the effect of tobacco. We further observe that pairing tumor excision with field removal delays recurrence compared to tumor excision alone. We track cell lineages and find that, in most cases, a polyclonal field develops, where the number of distinct cell lineages decreases over time as some lineages become dominant over others. Finally, we find tumor masses rarely form via monoclonal origin.

Mathematical modeling the order of driver gene mutations in colorectal cancer

Tumor heterogeneity is a large obstacle for cancer study and treatment. Different cancer patients may involve different combinations of gene mutations or the distinct regulatory pathways for inducing the progression of tumor. Investigating the pathways of gene mutations which can cause the formation of tumor can provide a basis for the personalized treatment of cancer. Studies suggested that KRAS, APC and TP53 are the most significant driver genes for colorectal cancer. However, it is still an open issue regarding the detailed mutation order of these genes in the development of colorectal cancer. For this purpose, we analyze the mathematical model considering all orders of mutations in oncogene, KRAS and tumor suppressor genes, APC and TP53, and fit it on data describing the incidence rates of colorectal cancer at different age from the Surveillance Epidemiology and End Results registry in the United States for the year 1973-2013. The specific orders that can induce the development of colorectal cancer are identified by the model fitting. The fitting results indicate that the mutation order with KRAS → APC → TP53, APC → TP53 → KRAS and APC → KRAS → TP53 explain the age-specific risk of colorectal cancer with very well. Furthermore, eleven pathways of gene mutations can be accepted for the mutation order of genes with KRAS → APC → TP53, APC → TP53 → KRAS and APC → KRAS → TP53, and the alternation of APC acts as the initiating or promoting event in the colorectal cancer. The estimated mutation rates of cells in the different pathways demonstrate that genetic instability must exist in colorectal cancer with alterations of genes, KRAS, APC and TP53.

Waiting times in a branching process model of colorectal cancer initiation

We study a multi-stage model for the development of colorectal cancer from initially healthy tissue. The model incorporates a complex sequence of driver gene alterations, some of which result in immediate growth advantage, while others have initially neutral effects. We derive analytic estimates for the sizes of premalignant subpopulations, and use these results to compute the waiting times to premalignant and malignant genotypes. This work contributes to the quantitative understanding of colorectal tumor evolution and the lifetime risk of colorectal cancer.

Phenotypic heterogeneity analysis of APC-mutant colon cancer by proteomics and phosphoproteomics identifies RAI14 as a key prognostic determinant in East Asians and Westerners

Adenomatous polyposis coli (APC) is an important tumor suppressor and is mostly linked to the regulation of the WNT/β-catenin signaling pathway. APC mutation has been identified as an early event in more than 80% of sporadic colorectal cancers (CRCs). Moreover, prognostic differences are observed in CRC patients with APC mutations. Although previous genomics studies have investigated the roles of concomitant gene mutations in determining the phenotypic heterogeneity of APC-mutant tumors, valuable prognostic determinants for APC-mutant CRC patients are still lacking. Based on the proteome and phosphoproteome data, we classified APC-mutant colon cancer patients and revealed genomic, proteomic and phosphoproteomic heterogeneity in APC-mutant tumors. More importantly, we identified RAI14 as a key prognostic determinant for APC-mutant but not APC-wildtype colon cancer patients. The heterogeneity and the significance of prognostic biomarkers in APC-mutant tumors were further validated in the Clinical Proteomic Tumor Analysis Consortium (CPTAC) colon cancer cohort. In addition, we found that colon cancer patients with high expression of RAI14 were less responsive to chemotherapy. Knockdown of RAI14 in cell lines led to reduced cell migration and changes in epithelial-mesenchymal transition (EMT)-related markers. Mechanistically, knockdown of RAI14 remodeled the phosphoproteome associated with cell adhesion, which might affect EMT marker expression and promote F-actin degradation. Collectively, this work describes the phenotypic heterogeneity of APC-mutant tumors and identifies RAI14 as an important prognostic determinant for APC-mutant colon cancer patients. The prognostic utility of RAI14 in APC-mutant colon cancer will provide early warning and increase the chance of successful treatment.

Metabolism and Colorectal Cancer

Reprogrammed metabolism is a hallmark of colorectal cancer (CRC). CRC cells are geared toward rapid proliferation, requiring nutrients and the removal of cellular waste in nutrient-poor environments. Intestinal stem cells (ISCs), the primary cell of origin for CRCs, must adapt their metabolism along the adenoma-carcinoma sequence to the unique features of their complex microenvironment that include interactions with intestinal epithelial cells, immune cells, stromal cells, commensal microbes, and dietary components. Emerging evidence implicates modifiable risk factors related to the environment, such as diet, as important in CRC pathogenesis. Here, we focus on describing the metabolism of ISCs, diets that influence CRC initiation, CRC genetics and metabolism, and the tumor microenvironment. The mechanistic links between environmental factors, metabolic adaptations, and the tumor microenvironment in enhancing or supporting CRC tumorigenesis are becoming better understood. Thus, greater knowledge of CRC metabolism holds promise for improved prevention and treatment.

Oncogene-like addiction to aneuploidy in human cancers

Most cancers exhibit aneuploidy, but its functional significance in tumor development is controversial. Here, we describe ReDACT (Restoring Disomy in Aneuploid cells using CRISPR Targeting), a set of chromosome engineering tools that allow us to eliminate specific aneuploidies from cancer genomes. Using ReDACT, we created a panel of isogenic cells that have or lack common aneuploidies, and we demonstrate that trisomy of chromosome 1q is required for malignant growth in cancers harboring this alteration. Mechanistically, gaining chromosome 1q increases the expression of MDM4 and suppresses TP53 signaling, and we show that TP53 mutations are mutually-exclusive with 1q aneuploidy in human cancers. Thus, specific aneuploidies play essential roles in tumorigenesis, raising the possibility that targeting these "aneuploidy addictions" could represent a novel approach for cancer treatment.

Literature review of imaging, pathological diagnosis, and outcomes of metachronous lung and pancreatic metastasis of cecal cancer

Background

Pancreatic metastasis from colorectal cancer is extremely rare. Here, we report a case of colorectal cancer with lung and pancreatic metastasis and analyze the histopathology, immunohistochemistry, and next-generation sequencing (NGS) to generate a differential diagnosis and treatment of metastatic colon cancer.

Case presentation

AC1

A 78-year-old man was admitted because of a recently elevated carcinoembryonic antigen. This patient had undergone laparoscopic right hemicolectomy for cecal cancer IIA (T3N0M0) 5 years before admission, and thoracoscopic left upper lung wedge resection for primary colon cancer lung metastasis 2 years before admission. At that time, the patient was thought to have pancreatic metastasis from colon cancer. He underwent laparoscopic distal pancreatectomy (combined with splenectomy). Postoperative pathology revealed colon cancer metastasis. We performed NGS on tumor samples at three loci and found colon cancer's most common oncogenic driver genes (KRAS, APC, and TP53). One month after surgery, the patient was given capecitabine for six cycles of chemotherapy. At present, no high adverse reactions have been reported.

Discussion

For patients with pancreatic space-occupying, such as a previous history of colorectal cancer, and recent carcinoembryonic antigen elevation, we should highly suspect pancreatic metastatic colorectal cancer. NGS is an essential auxiliary for identifying metastatic tumors. Surgery combined with postoperative chemotherapy is an effective treatment.

Optimal pathways control fixation of multiple mutations during cancer initiation

Cancer starts after initially healthy tissue cells accumulate several specific mutations or other genetic alterations. The dynamics of tumor formation is a very complex phenomenon due to multiple involved biochemical and biophysical processes. It leads to a very large number of possible pathways on the road to final fixation of all mutations that marks the beginning of the cancer, complicating the understanding of microscopic mechanisms of tumor formation. We present a new theoretical framework of analyzing the cancer initiation dynamics by exploring the properties of effective free-energy landscape of the process. It is argued that although there are many possible pathways for the fixation of all mutations in the system, there are only a few dominating pathways on the road to tumor formation. The theoretical approach is explicitly tested in the system with only two mutations using analytical calculations and Monte Carlo computer simulations. Excellent agreement with theoretical predictions is found for a large range of parameters, supporting our hypothesis and allowing us to better understand the mechanisms of cancer initiation. Our theoretical approach clarifies some important aspects of microscopic processes that lead to tumor formation.

Multiscale modeling of collective cell migration elucidates the mechanism underlying tumor-stromal interactions in different spatiotemporal scales

Metastasis is the pathogenic spread of cancer cells from a primary tumor to a secondary site which happens at the late stages of cancer. It is caused by a variety of biological, chemical, and physical processes, such as molecular interactions, intercellular communications, and tissue-level activities. Complex interactions of cancer cells with their microenvironment components such as cancer associated fibroblasts (CAFs) and extracellular matrix (ECM) cause them to adopt an invasive phenotype that promotes tumor growth and migration. This paper presents a multiscale model for integrating a wide range of time and space interactions at the molecular, cellular, and tissue levels in a three-dimensional domain. The modeling procedure starts with presenting nonlinear dynamics of cancer cells and CAFs using ordinary differential equations based on TGFβ, CXCL12, and LIF signaling pathways. Unknown kinetic parameters in these models are estimated using hybrid unscented Kalman filter and the models are validated using experimental data. Then, the principal role of CAFs on metastasis is revealed by spatial-temporal modeling of circulating signals throughout the TME. At this stage, the model has evolved into a coupled ODE-PDE system that is capable of determining cancer cells' status in one of the quiescent, proliferating or migratory conditions due to certain metastasis factors and ECM characteristics. At the tissue level, we consider a force-based framework to model the cancer cell proliferation and migration as the final step towards cancer cell metastasis. The ability of the multiscale model to depict cancer cells' behavior in different levels of modeling is confirmed by comparing its outputs with the results of RT PCR and wound scratch assay techniques. Performance evaluation of the model indicates that the proposed multiscale model can pave the way for improving the efficiency of therapeutic methods in metastasis prevention.

A mechanistic mathematical model of initiation and malignant transformation in sporadic vestibular schwannoma

BACKGROUND

A vestibular schwannoma (VS) is a relatively rare, benign tumour of the eighth cranial nerve, often involving alterations to the gene NF2. Previous mathematical models of schwannoma incidence have not attempted to account for alterations in specific genes, and could not distinguish between nonsense mutations and loss of heterozygosity (LOH).

METHODS

Here, we present a mechanistic approach to modelling initiation and malignant transformation in schwannoma. Each parameter is associated with a specific gene or mechanism operative in Schwann cells, and can be determined by combining incidence data with empirical frequencies of pathogenic variants and LOH.

RESULTS

This results in new estimates for the base-pair mutation rate u = 4.48 × 10^-10 and the rate of LOH = 2.03 × 10^-6/yr in Schwann cells. In addition to new parameter estimates, we extend the approach to estimate the risk of both spontaneous and radiation-induced malignant transformation.

DISCUSSION

We conclude that radiotherapy is likely to have a negligible excess risk of malignancy for sporadic VS, with a possible exception of rapidly growing tumours.

Modeling age-specific incidence of colon cancer via niche competition

Cancer development is a multistep process often starting with a single cell in which a number of epigenetic and genetic alterations have accumulated thus transforming it into a tumor cell. The progeny of such a single benign tumor cell expands in the tissue and can at some point progress to malignant tumor cells until a detectable tumor is formed. The dynamics from the early phase of a single cell to a detectable tumor with billions of tumor cells are complex and still not fully resolved, not even for the well-known prototype of multistage carcinogenesis, the adenoma-adenocarcinoma sequence of colorectal cancer. Mathematical models of such carcinogenesis are frequently tested and calibrated based on reported age-specific incidence rates of cancer, but they usually require calibration of four or more parameters due to the wide range of processes these models aim to reflect. We present a cell-based model, which focuses on the competition between wild-type and tumor cells in colonic crypts, with which we are able reproduce epidemiological incidence rates of colon cancer. Additionally, the fraction of cancerous tumors with precancerous lesions predicted by the model agree with clinical estimates. The correspondence between model and reported data suggests that the fate of tumor development is majorly determined by the early phase of tumor growth and progression long before a tumor becomes detectable. Due to the focus on the early phase of tumor development, the model has only a single fit parameter, the time scale set by an effective replacement rate of stem cells in the crypt. We find this effective rate to be considerable smaller than the actual replacement rate, which implies that the time scale is limited by the processes succeeding clonal conversion of crypts.

Cancer development is a multistep process often starting with a single cell turning into a tumor cell whose progeny growths via clonal expansion into a macroscopic tumor with billions of cells. While experimental insight exists on the cellular scale and cancer registries provide statistics on detectable tumors, the complex dynamics leading from the microscopic cellular scale to a macroscopic tumor is still not fully resolved. Models of cancer biology are commonly used to explain incidence rates but usually require the fit of several biological parameters due to the complexity of the incorporated processes. We employ a cell-based model based on the competition in colonic crypts, to reproduce epidemiological age-specific incidence rates of colon cancer. Due to the focus on the early stage of tumor development, only the time scale in the model has to be calibrated. The agreement between theoretical prediction and epidemiological observation suggests that the fate of tumor development is dominated by the early phase of tumor development long before a tumor becomes detectable.

Mathematical Perspectives in the Variable Texture Products Cutting Process

The methods utilized to construct and identify the mathematical equation that characterizes the cutting of items with varied textures are presented in this work. Using laboratory equipment, the cutting process was carried out experimentally. The cutting energy was calculated based on the experimental results. The energy required to perform this process is directly influenced by the textural characteristics of the products used, as per the analysis of the experimental results obtained after the cutting process (density, humidity, products with or without peel). The gathered information was used to develop a general equation that would properly describe the process. Table Curve 3D software was used to create mathematical equations that define the relationship between input parameters, the type of product being cut, cutting speed, and output parameters, i.e., cutting energy. The equations that have the same correlation coefficient were discovered using the working methodology; it was specifically designed for this purpose.

The role of spatial structures of tissues in cancer initiation dynamics

It is widely believed that biological tissues evolved to lower the risks of cancer development. One of the specific ways to minimize the chances of tumor formation comes from proper spatial organization of tissues. However, the microscopic mechanisms of underlying processes remain not fully understood. We present a theoretical investigation on the role of spatial structures in cancer initiation dynamics. In our approach, the dynamics of single mutation fixations are analyzed using analytical calculations and computer simulations by mapping them to Moran processes on graphs with different connectivity that mimic various spatial structures. It is found that while the fixation probability is not affected by modifying the spatial structures of the tissues, the fixation times can change dramatically. The slowest dynamics is observed in "quasi-one-dimensional" structures, while the fastest dynamics is observed in "quasi-three-dimensional" structures. Theoretical calculations also suggest that there is a critical value of the degree of graph connectivity, which mimics the spatial dimension of the tissue structure, above which the spatial structure of the tissue has no effect on the mutation fixation dynamics. An effective discrete-state stochastic model of cancer initiation is utilized to explain our theoretical results and predictions. Our theoretical analysis clarifies some important aspects on the role of the tissue spatial structures in the cancer initiation processes.

New Insights into Bile Acids Related Signaling Pathways in the Onset of Colorectal Cancer

Colorectal cancer (CRC) ranks as the second among the causes of tumor death worldwide, with an estimation of 1.9 million new cases in 2020 and more than 900,000 deaths. This rate might increase by 60% over the next 10 years. These data are unacceptable considering that CRC could be successfully treated if diagnosed in the early stages. A high-fat diet promotes the hepatic synthesis of bile acids (BAs) increasing their delivery to the colonic lumen and numerous scientific reports correlate BAs, especially secondary BAs, with CRC incidence. We reviewed the physicochemical and biological characteristics of BAs, focusing on the major pathways involved in CRC risk and progression. We specifically pointed out the role of BAs as signaling molecules and the tangled relationships among their nuclear and membrane receptors with the big bang of molecular and cellular events that trigger CRC occurrence.

Genome-wide analysis of mRNA and microRNA expression in colorectal cancer and adjacent normal mucosa

mRNA expression varies in human cancers. Such altered mRNA expression is negatively regulated by the expression of microRNAs (miRNAs), which play an important role in human tumorigenesis. According to this theory, inverse mRNA/miRNA expression may be a direct driver of cancer development, and certain genetic events may occur prior to the development of any discernible histological abnormalities. We examined the inverse expression between mRNAs and their corresponding miRNAs in colorectal cancer (CRC) and adjacent normal mucosa and performed pathway analysis to identify mRNA/miRNA networks. The cancer samples were divided into first (20 cases) and second (24 cases) cohorts, and 48 samples were obtained from two sections of the normal mucosa adjacent to the tumors from the second cohort. We investigated mRNAs with commonly altered expression in CRC and adjacent normal mucosa using isolated cancer glands and normal crypts from the first cohort, compared with that of distal normal crypts, using an array-based method. As a result, significant inverse correlations between CEACAM1 and miRNA-7114-5p and between AK1 and miRNA-6780-5p were found in CRC and adjacent normal mucosa. We validated these correlations in the second cohort using RT-PCR. To confirm these findings, transfection and immunohistochemical assays were also performed, which verified the inverse correlation between CEACAM1 and miRNA-7114-5p. Our findings suggest that the inverse correlations between the CEACAM1/miRNA-7114-5p and possibly AK1/miRNA-6780-5p pairs play an important role in early CRC development, and may help identify potential molecular targets for early detection of CRC.

Extraction of Mathematical Correlations Applied in the Aerodynamic Separation of Solid Particles

This article describes the methodology used to identify the mathematical equation that describes the correlations between the input and output parameters of an experiment. As a technological process, aerodynamic separation was chosen to represent the behavior of a solid particle within an ascending vertical airflow. The experimental data were used to identify two parameters, namely the average linear velocity and the angular velocity. The Table Curve 3D program was used to develop a mathematical equation describing the dependence between the input parameters (the shape and size of the solid particle, as well as the velocity of the airflow) and the monitored parameters. A pyramid-type analysis (following a filtering system, a general equation was determined from a large number of equations that characterize an experimental set mathematically) was designed in order to determine a single mathematical equation that describes the correlation between the input variables and those obtained as accurately as possible. The determination of the mathematical equation started with the number of equations generated by the Table Curve 3D program; then, the equations with a correlation coefficient greater than 0.85 were chosen; and finally, the common equations were identified. Respecting the working methodology, one equation was identified, which has for the average linear velocity, a correlation coefficient r2 of between 0.88–0.99 and 0.86–0.99 for the angular velocity.

Aspirin's effect on kinetic parameters of cells contributes to its role in reducing incidence of advanced colorectal adenomas, shown by a multiscale computational study

Aspirin intake has been shown to lead to significant protection against colorectal cancer, for example with an up to twofold reduction in colorectal adenoma incidence rates at higher doses. The mechanisms contributing to protection are not yet fully understood. While aspirin is an anti-inflammatory drug and can thus influence the tumor microenvironment, in vitro and in vivo experiments have recently shown that aspirin can also have a direct effect on cellular kinetics and fitness. It reduces the rate of tumor cell division and increases the rate of cell death. The question arises whether such changes in cellular fitness are sufficient to significantly contribute to the epidemiologically observed protection. To investigate this, we constructed a class of mathematical models of in vivo evolution of advanced adenomas, parameterized it with available estimates, and calculated population level incidence. Fitting the predictions to age incidence data revealed that only a model that included colonic crypt competition can account for the observed age-incidence curve. This model was then used to predict modified incidence patterns if cellular kinetics were altered as a result of aspirin treatment. We found that changes in cellular fitness that were within the experimentally observed ranges could reduce advanced adenoma incidence by a sufficient amount to account for age incidence data in aspirin-treated patient cohorts. While the mechanisms that contribute to the protective effect of aspirin are likely complex and multi-factorial, our study demonstrates that direct aspirin-induced changes of tumor cell fitness can significantly contribute to epidemiologically observed reduced incidence patterns.

Quantification of the Selective Advantage of Driver Mutations Is Dependent on the Underlying Model and Stage of Tumor Evolution

Measuring the selective fitness advantages provided by driver mutations has the potential to facilitate a precise quantitative understanding of cancer evolution. However, accurately measuring the selective advantage of driver mutations has remained a challenge in the field. Early studies reported small selective advantages of drivers, on the order of 1%, whereas newer studies report much larger selective advantages, as high as 1,200%. In this article, we argue that the calculated selective advantages of cancer drivers are dependent on the underlying mathematical model and stage of cancer evolution and that comparisons of numerical values of selective advantage without regard for the underlying model and stage can lead to spurious conclusions.

Risk of lung cancer due to external environmental factor and epidemiological data analysis

Lung cancer is a cancer with the fastest growth in the incidence and mortality all over the world, which is an extremely serious threat to human's life and health. Evidences reveal that external environmental factors are the key drivers of lung cancer, such as smoking, radiation exposure and so on. Therefore, it is urgent to explain the mechanism of lung cancer risk due to external environmental factors experimentally and theoretically. However, it is still an open issue regarding how external environment factors affect lung cancer risk. In this paper, we summarize the main mathematical models involved the gene mutations for cancers, and review the application of the models to analyze the mechanism of lung cancer and the risk of lung cancer due to external environmental exposure. In addition, we apply the model described and the epidemiological data to analyze the influence of external environmental factors on lung cancer risk. The result indicates that radiation can cause significantly an increase in the mutation rate of cells, in particular the mutation in stability gene that leads to genomic instability. These studies not only can offer insights into the relationship between external environmental factors and human lung cancer risk, but also can provide theoretical guidance for the prevention and control of lung cancer.

Modeling the Th17 and Tregs Paradigm: Implications for Cancer Immunotherapy

CD4 + T cell differentiation is governed by gene regulatory and metabolic networks, with both networks being highly interconnected and able to adapt to external stimuli. Th17 and Tregs differentiation networks play a critical role in cancer, and their balance is affected by the tumor microenvironment (TME). Factors from the TME mediate recruitment and expansion of Th17 cells, but these cells can act with pro or anti-tumor immunity. Tregs cells are also involved in tumor development and progression by inhibiting antitumor immunity and promoting immunoevasion. Due to the complexity of the underlying molecular pathways, the modeling of biological systems has emerged as a promising solution for better understanding both CD4 + T cell differentiation and cancer cell behavior. In this review, we present a context-dependent vision of CD4 + T cell transcriptomic and metabolic network adaptability. We then discuss CD4 + T cell knowledge-based models to extract the regulatory elements of Th17 and Tregs differentiation in multiple CD4 + T cell levels. We highlight the importance of complementing these models with data from omics technologies such as transcriptomics and metabolomics, in order to better delineate existing Th17 and Tregs bifurcation mechanisms. We were able to recompilate promising regulatory components and mechanisms of Th17 and Tregs differentiation under normal conditions, which we then connected with biological evidence in the context of the TME to better understand CD4 + T cell behavior in cancer. From the integration of mechanistic models with omics data, the transcriptomic and metabolomic reprograming of Th17 and Tregs cells can be predicted in new models with potential clinical applications, with special relevance to cancer immunotherapy.

Mathematical modeling of multiple pathways in colorectal carcinogenesis using dynamical systems with Kronecker structure

Like many other types of cancer, colorectal cancer (CRC) develops through multiple pathways of carcinogenesis. This is also true for colorectal carcinogenesis in Lynch syndrome (LS), the most common inherited CRC syndrome. However, a comprehensive understanding of the distribution of these pathways of carcinogenesis, which allows for tailored clinical treatment and even prevention, is still lacking. We suggest a linear dynamical system modeling the evolution of different pathways of colorectal carcinogenesis based on the involved driver mutations. The model consists of different components accounting for independent and dependent mutational processes. We define the driver gene mutation graphs and combine them using the Cartesian graph product. This leads to matrix components built by the Kronecker sum and product of the adjacency matrices of the gene mutation graphs enabling a thorough mathematical analysis and medical interpretation. Using the Kronecker structure, we developed a mathematical model which we applied exemplarily to the three pathways of colorectal carcinogenesis in LS. Beside a pathogenic germline variant in one of the DNA mismatch repair (MMR) genes, driver mutations in APC, CTNNB1, KRAS and TP53 are considered. We exemplarily incorporate mutational dependencies, such as increased point mutation rates after MMR deficiency, and based on recent experimental data, biallelic somatic CTNNB1 mutations as common drivers of LS-associated CRCs. With the model and parameter choice, we obtained simulation results that are in concordance with clinical observations. These include the evolution of MMR-deficient crypts as early precursors in LS carcinogenesis and the influence of variants in MMR genes thereon. The proportions of MMR-deficient and MMR-proficient APC-inactivated crypts as first measure for the distribution among the pathways in LS-associated colorectal carcinogenesis are compatible with clinical observations. The approach provides a modular framework for modeling multiple pathways of carcinogenesis yielding promising results in concordance with clinical observations in LS CRCs.

Superlinear growth reveals the Allee effect in tumors

Integrating experimental data into ecological models plays a central role in understanding biological mechanisms that drive tumor progression where such knowledge can be used to develop new therapeutic strategies. While the current studies emphasize the role of competition among tumor cells, they fail to explain recently observed superlinear growth dynamics across human tumors. Here we study tumor growth dynamics by developing a model that incorporates evolutionary dynamics inside tumors with tumor-microenvironment interactions. Our results reveal that tumor cells' ability to manipulate the environment and induce angiogenesis drives superlinear growth-a process compatible with the Allee effect. In light of this understanding, our model suggests that, for high-risk tumors that have a higher growth rate, suppressing angiogenesis can be the appropriate therapeutic intervention.