Mathematical analysis identifies the optimal treatment strategy for epidermal growth factor receptor-mutated non-small cell lung cancer.

Introduction: In Asians, more than half of non-small cell lung cancers (NSCLC) are induced by epidermal growth factor receptor (EGFR) mutations. Although patients carrying EGFR driver mutations display a good initial response to EGFR-Tyrosine Kinase Inhibitors (EGFR-TKIs), additional mutations provoke drug resistance. Hence, predicting tumor dynamics before treatment initiation and formulating a reasonable treatment schedule is an urgent challenge. Methods: To overcome this problem, we constructed a mathematical model based on clinical observations and investigated the optimal schedules for EGFR-TKI therapy. Results: Based on published data on cell growth rates under different drugs, we found that using osimertinib that are efficient for secondary resistant cells as the first-line drug is beneficial in monotherapy, which is consistent with published clinical statistical data. Moreover, we identified the existence of a suitable drug-switching time; that is, changing drugs too early or too late was not helpful. Furthermore, we demonstrate that osimertinib combined with erlotinib or gefitinib as first-line treatment, has the potential for clinical application. Finally, we examined the relationship between the initial ratio of resistant cells and final cell number under different treatment conditions, and summarized it into a therapy suggestion map. By performing parameter sensitivity analysis, we identified the condition where　osimertinib-first therapy was recommended as the optimal treatment option. Discussion: This study for the first time theoretically showed the optimal treatment strategies based on the known information in NSCLC. Our framework can be applied to other types of cancer in the future.

Subclonal accumulation of immune escape mechanisms in microsatellite instability-high colorectal cancers.

BACKGROUND: Intratumor heterogeneity (ITH) in microsatellite instability-high (MSI-H) colorectal cancer (CRC) has been poorly studied. We aimed to clarify how the ITH of MSI-H CRCs is generated in cancer evolution and how immune selective pressure affects ITH. METHODS: We reanalyzed public whole-exome sequencing data on 246 MSI-H CRCs. In addition, we performed a multi-region analysis from 6 MSI-H CRCs. To verify the process of subclonal immune escape accumulation, a novel computational model of cancer evolution under immune pressure was developed. RESULTS: Our analysis presented the enrichment of functional genomic alterations in antigen-presentation machinery (APM). Associative analysis of neoantigens indicated the generation of immune escape mechanisms via HLA alterations. Multiregion analysis revealed the clonal acquisition of driver mutations and subclonal accumulation of APM defects in MSI-H CRCs. Examination of variant allele frequencies demonstrated that subclonal mutations tend to be subjected to selective sweep. Computational simulations of tumour progression with the interaction of immune cells successfully verified the subclonal accumulation of immune escape mutations and suggested the efficacy of early initiation of an immune checkpoint inhibitor (ICI) -based treatment. CONCLUSIONS: Our results demonstrate the heterogeneous acquisition of immune escape mechanisms in MSI-H CRCs by Darwinian selection, providing novel insights into ICI-based treatment strategies.

Computational modeling of locoregional recurrence with spatial structure identifies tissue-specific carcinogenic profiles.

Introduction: Local and regional recurrence after surgical intervention is a significant problem in cancer management. The multistage theory of carcinogenesis precisely places the presence of histologically normal but mutated premalignant lesions surrounding the tumor - field cancerization, as a significant cause of cancer recurrence. The relationship between tissue dynamics, cancer initiation and cancer recurrence in multistage carcinogenesis is not well known. Methods: This study constructs a computational model for cancer initiation and recurrence by combining the Moran and branching processes in which cells requires 3 or more mutations to become malignant. In addition, a spatial structure-setting is included in the model to account for positional relativity in cell turnover towards malignant transformation. The model consists of a population of normal cells with no mutation; several populations of premalignant cells with varying number of mutations and a population of malignant cells. The model computes a stage of cancer detection and surgery to eliminate malignant cells but spares premalignant cells and then estimates the time for malignant cells to re-emerge. Results: We report the cellular conditions that give rise to different patterns of cancer initiation and the conditions favoring a shorter cancer recurrence by analyzing premalignant cell types at the time of surgery. In addition, the model is fitted to disease-free clinical data of 8,957 patients in 27 different cancer types; From this fitting, we estimate the turnover rate per month, relative fitness of premalignant cells, growth rate and death rate of cancer cells in each cancer type. Discussion: Our study provides insights into how to identify patients who are likely to have a shorter recurrence and where to target the therapeutic intervention.

HLA Class I Analysis Provides Insight Into the Genetic and Epigenetic Background of Immune Evasion in Colorectal Cancer With High Microsatellite Instability.

BACKGROUND & AIMS: A detailed understanding of antitumor immunity is essential for optimal cancer immune therapy. Although defective mutations in the B2M and HLA-ABC genes, which encode molecules essential for antigen presentation, have been reported in several studies, the effects of these defects on tumor immunity have not been quantitatively evaluated. METHODS: Mutations in HLA-ABC genes were analyzed in 114 microsatellite instability-high colorectal cancers using a long-read sequencer. The data were further analyzed in combination with whole-exome sequencing, transcriptome sequencing, DNA methylation array, and immunohistochemistry data. RESULTS: We detected 101 truncating mutations in 57 tumors (50%) and loss of 61 alleles in 21 tumors (18%). Based on the integrated analysis that enabled the immunologic subclassification of microsatellite instability-high colorectal cancers, we identified a subtype of tumors in which lymphocyte infiltration was reduced, partly due to reduced expression of HLA-ABC genes in the absence of apparent genetic alterations. Survival time of patients with such tumors was shorter than in patients with other tumor types. Paradoxically, tumor mutation burden was highest in the subtype, suggesting that the immunogenic effect of accumulating mutations was counterbalanced by mutations that weakened immunoreactivity. Various genetic and epigenetic alterations, including frameshift mutations in RFX5 and promoter methylation of PSMB8 and HLA-A, converged on reduced expression of HLA-ABC genes. CONCLUSIONS: Our detailed immunogenomic analysis provides information that will facilitate the improvement and development of cancer immunotherapy.

Pan-cancer methylome analysis for cancer diagnosis and classification of cancer cell of origin.

The accurate and early diagnosis and classification of cancer origin from either tissue or liquid biopsy is crucial for selecting the appropriate treatment and reducing cancer-related mortality. Here, we established the CAncer Cell-of-Origin (CACO) methylation panel using the methylation data of the 28 types of cancer in The Cancer Genome Atlas (7950 patients and 707 normal controls) as well as healthy whole blood samples (95 subjects). We showed that the CACO methylation panel had high diagnostic potential with high sensitivity and specificity in the discovery (maximum AUC = 0.998) and validation (maximum AUC = 1.000) cohorts. Moreover, we confirmed that the CACO methylation panel could identify the cancer cell type of origin using the methylation profile from liquid as well as tissue biopsy, including primary, metastatic, and multiregional cancer samples and cancer of unknown primary, independent of the methylation analysis platform and specimen preparation method. Together, the CACO methylation panel can be a powerful tool for the classification and diagnosis of cancer.

Mathematical Modeling of Locoregional Recurrence Caused by Premalignant Lesions Formed Before Initial Treatment.

Locoregional recurrence after surgery is a major unresolved issue in cancer treatment. Premalignant lesions are considered a cause of cancer recurrence. A study showed that premalignant lesions surrounding the primary tumor drove a high local cancer recurrence rate after surgery in head and neck cancer. Based on the multistage theory of carcinogenesis, cells harboring an intermediate number of mutations are not cancer cells yet but have a higher risk of becoming cancer than normal cells. This study constructed a mathematical model for cancer initiation and recurrence by combining the Moran and branching processes in which cells require two specific mutations to become malignant. There are three populations in this model: (i) normal cells with no mutation, (ii) premalignant cells with one mutation, and (iii) cancer cells with two mutations. The total number of healthy tissue is kept constant to represent homeostasis, and there is a rare chance of mutation every time a cell divides. If a cancer cell with two mutations arises, the cancer population proliferates, violating the homeostatic balance of the tissue. Once the number of cancer cells reaches a certain size, we conduct computational resection and remove the cancer cell population, keeping the ratio of normal and premalignant cells in the tissue unchanged. After surgery, we considered tissue dynamics and eventually observed the second appearance of cancer cells as recurrence. Consequently, we computationally revealed the conditions where the time to recurrence became short by parameter sensitivity analysis. Particularly, when the premalignant cells' fitness is higher than normal cells, the proportion of premalignant cells becomes large after the surgical resection. Moreover, the mathematical model was fitted to clinical data on disease-free survival of 1,087 patients in 23 cancer types from the TCGA database. Finally, parameter values of tissue dynamics are estimated for each cancer type, where the likelihood of recurrence can be elucidated. Thus, our approach provides insights into the concept to identify the patients likely to experience recurrence as early as possible.

Mathematical Modeling and Mutational Analysis Reveal Optimal Therapy to Prevent Malignant Transformation in Grade II IDH-Mutant Gliomas.

Isocitrate dehydrogenase-mutant low-grade gliomas (IDHmut-LGG) grow slowly but frequently undergo malignant transformation, which eventually leads to premature death. Chemotherapy and radiotherapy treatments prolong survival, but can also induce genetic (or epigenetic) alterations involved in transformation. Here, we developed a mathematical model of tumor progression based on serial tumor volume data and treatment history of 276 IDHmut-LGGs classified by chromosome 1p/19q codeletion (IDHmut/1p19qcodel and IDHmut/1p19qnoncodel) and performed genome-wide mutational analyses, including targeted sequencing and longitudinal whole-exome sequencing data. These analyses showed that tumor mutational burden correlated positively with malignant transformation rate, and chemotherapy and radiotherapy significantly suppressed tumor growth but increased malignant transformation rate per cell by 1.8 to 2.8 times compared with before treatment. This model revealed that prompt adjuvant chemoradiotherapy prolonged malignant transformation-free survival in small IDHmut-LGGs (≤ 50 cm3). Furthermore, optimal treatment differed according to genetic alterations for large IDHmut-LGGs (> 50 cm3); adjuvant therapies delayed malignant transformation in IDHmut/1p19qnoncodel but often accelerated it in IDHmut/1p19qcodel. Notably, PI3K mutation was not associated with malignant transformation but increased net postoperative proliferation rate and decreased malignant transformation-free survival, prompting the need for adjuvant therapy in IDHmut/1p19qcodel. Overall, this model uncovered therapeutic strategies that could prevent malignant transformation and, consequently, improve overall survival in patients with IDHmut-LGGs. SIGNIFICANCE: A mathematical model successfully estimates malignant transformation-free survival and reveals a link between genetic alterations and progression, identifying precision medicine approaches for optimal treatment of IDH-mutant low-grade gliomas.

A CDC7 inhibitor sensitizes DNA-damaging chemotherapies by suppressing homologous recombination repair to delay DNA damage recovery.

Cell division cycle 7 (CDC7), a serine/threonine kinase, plays important roles in DNA replication. We developed a highly specific CDC7 inhibitor, TAK-931, as a clinical cancer therapeutic agent. This study aimed to identify the potential combination partners of TAK-931 for guiding its clinical development strategies. Unbiased high-throughput chemical screening revealed that the highest synergistic antiproliferative effects observed were the combinations of DNA-damaging agents with TAK-931. Functional phosphoproteomic analysis demonstrated that TAK-931 suppressed homologous recombination repair activity, delayed recovery from double-strand breaks, and led to accumulation of DNA damages in the combination. Whole-genome small interfering RNA library screening identified sensitivity-modulating molecules, which propose the experimentally predicted target cancer types for the combination, including pancreatic, esophageal, ovarian, and breast cancers. The efficacy of combination therapy in these cancer types was preclinically confirmed in the corresponding primary-derived xenograft models. Thus, our findings would be helpful to guide the future clinical strategies for TAK-931.

Combination treatment with a PI3K/Akt/mTOR pathway inhibitor overcomes resistance to anti-HER2 therapy in PIK3CA-mutant HER2-positive breast cancer cells.

Amplification and/or overexpression of human epidermal growth factor receptor 2 (HER2) are observed in 15-20% of breast cancers (HER2+ breast cancers), and anti-HER2 therapies have significantly improved prognosis of patients with HER2+ breast cancer. One resistance mechanism to anti-HER2 therapies is constitutive activation of the phosphoinositide 3-kinase (PI3K) pathway. Combination therapy with small-molecule inhibitors of AKT and HER2 was conducted in HER2+ breast cancer cell lines with or without PIK3CA mutations, which lead to constitutive activation of the PI3K pathway. PIK3CA mutations played important roles in resistance to single-agent anti-HER2 therapy in breast cancer cell lines. Combination therapy of a HER2 inhibitor and an AKT inhibitor, as well as other PI3K pathway inhibitors, could overcome the therapeutic limitations associated with single-agent anti-HER2 treatment in PIK3CA-mutant HER2+ breast cancer cell lines. Furthermore, expression of phosphorylated 4E-binding protein 1 (p4EBP1) following the treatment correlated with the antiproliferative activities of the combination, suggesting that p4EBP1 may have potential as a prognostic and/or efficacy-linking biomarkers for these combination therapies in patients with HER2+ breast cancer. These findings highlight potential clinical strategies using combination therapy to overcome the limitations associated with single-agent anti-HER2 therapies in patients with HER2+ breast cancer.

Liganded T3 receptor ß2 inhibits the positive feedback autoregulation of the gene for GATA2, a transcription factor critical for thyrotropin production.

The serum concentration of thyrotropin (thyroid stimulating hormone, TSH) is drastically reduced by small increase in the levels of thyroid hormones (T3 and its prohormone, T4); however, the mechanism underlying this relationship is unknown. TSH consists of the chorionic gonadotropin α (CGA) and the ß chain (TSHß). The expression of both peptides is induced by the transcription factor GATA2, a determinant of the thyrotroph and gonadotroph differentiation in the pituitary. We previously reported that the liganded T3 receptor (TR) inhibits transactivation activity of GATA2 via a tethering mechanism and proposed that this mechanism, but not binding of TR with a negative T3-responsive element, is the basis for the T3-dependent inhibition of the TSHß and CGA genes. Multiple GATA-responsive elements (GATA-REs) also exist within the GATA2 gene itself and mediate the positive feedback autoregulation of this gene. To elucidate the effect of T3 on this non-linear regulation, we fused the GATA-REs at -3.9 kb or +9.5 kb of the GATA2 gene with the chloramphenicol acetyltransferase reporter gene harbored in its 1S-promoter. These constructs were co-transfected with the expression plasmids for GATA2 and the pituitary specific TR, TRß2, into kidney-derived CV1 cells. We found that liganded TRß2 represses the GATA2-induced transactivation of these reporter genes. Multi-dimensional input function theory revealed that liganded TRß2 functions as a classical transcriptional repressor. Then, we investigated the effect of T3 on the endogenous expression of GATA2 protein and mRNA in the gonadotroph-derived LßT2 cells. In this cell line, T3 reduced GATA2 protein independently of the ubiquitin proteasome system. GATA2 mRNA was drastically suppressed by T3, the concentration of which corresponds to moderate hypothyroidism and euthyroidism. These results suggest that liganded TRß2 inhibits the positive feedback autoregulation of the GATA2 gene; moreover this mechanism plays an important role in the potent reduction of TSH production by T3.

Metastatic seeding of human colon cancer cell clusters expressing the hybrid epithelial/mesenchymal state.

Emerging evidence supports the theory that tumor cell clusters efficiently metastasize to distant organs. However, the roles of epithelial-to-mesenchymal transition (EMT) in metastasizing tumor cell clusters have not yet been fully elucidated. To investigate this issue, tumor fragments were dissected from 40 colorectal cancer (CRC) patients and implanted subcutaneously into immunodeficient mice. We observed that tumors developed from the tumor fragments obtained from 28 of the 40 CRC patients. The tumors were then dissociated into cell suspensions to be orthotopically injected into secondary mice. The tumors from 13 of the 28 patients progressed. Furthermore, metastases formed spontaneously in the liver and lungs from the tumor fragments obtained from 8 of these 13 patients. Moreover, employing a mathematical analysis, we showed that tumor cell clusters seeded these metastases significantly more often than did single tumor cells. Membrane E-cadherin- and nuclear ZEB1-positive tumor cells indicating the hybrid epithelial/mesenchymal state were also detected in primary tumors of various CRC patients, and in the corresponding patient-derived xenografts (PDXs) and circulating tumor cell clusters in the bloodstreams of mice. In contrast, ZEB1 staining was barely detectable in the patient-matched liver metastases presumably developing through mesenchymal-to-epithelial transition. Inhibition of E-cadherin or ZEB1 expression by shRNA notably prevented the PDX-derived tumor organoids from colonizing the liver, when injected intrasplenically into mice, indicating E-cadherin and ZEB1 expressions to be required for their metastatic colonization. Taken together, these findings suggest that the epithelial/mesenchymal state mediates metastatic seeding of human CRC cell clusters into distant organs.

Multifocal origin of occupational cholangiocarcinoma revealed by comparison of multilesion mutational profiles.

Recently identified occupational cholangiocarcinoma among printing workers is characterized by chronic bile duct injuries and precancerous or early cancerous lesions at multiple sites of the bile ducts. These observations suggested the potential multifocal carcinogenesis of the disease. We performed whole-exome analysis of multiple lesions, including the invasive carcinomas and precancerous lesions of four occupational cholangiocarcinoma cases. A much higher mutation burden was observed in both the invasive carcinomas (mean 76.3/Mb) and precancerous lesions (mean 71.8/Mb) than in non-occupational cholangiocarcinomas (mean 1.6/Mb). Most somatic mutations identified in 11 of 16 lesions did not overlap with each other. In contrast, a unique trinucleotide mutational signature of GpCpY to GpTpY was shared among the lesions. These results suggest that most of these lesions are multiclonal in origin and that common mutagenic processes, which may be induced by exposure to haloalkanes or their metabolites, generated somatic mutations at different sites of the bile ducts. A similarly high mutation rate had already been identified in the precancerous lesions, implying an increased potential for carcinogenesis throughout the biliary tree. These genomic features support the importance of ongoing close follow-up of the patients as a group at high risk of recurrence.

Computational modeling of pancreatic cancer patients receiving FOLFIRINOX and gemcitabine-based therapies identifies optimum intervention strategies.

Pancreatic ductal adenocarcinoma (PDAC) exhibits a variety of phenotypes with regard to disease progression and treatment response. This variability complicates clinical decision-making despite the improvement of survival due to the recent introduction of FOLFIRINOX (FFX) and nab-paclitaxel. Questions remain as to the timing and sequence of therapies and the role of radiotherapy for unresectable PDAC. Here we developed a computational analysis platform to investigate the dynamics of growth, metastasis and treatment response to FFX, gemcitabine (GEM), and GEM+nab-paclitaxel. Our approach was informed using data of 1,089 patients treated at the Massachusetts General Hospital and validated using an independent cohort from Osaka Medical College. Our framework establishes a logistic growth pattern of PDAC and defines the Local Advancement Index (LAI), which determines the eventual primary tumor size and predicts the number of metastases. We found that a smaller LAI leads to a larger metastatic burden. Furthermore, our analyses ascertain that i) radiotherapy after induction chemotherapy improves survival in cases receiving induction FFX or with larger LAI, ii) neoadjuvant chemotherapy improves survival in cases with resectable PDAC, and iii) temporary cessations of chemotherapies do not impact overall survival, which supports the feasibility of treatment holidays for patients with FFX-associated adverse effects. Our findings inform clinical decision-making for PDAC patients and allow for the rational design of clinical strategies using FFX, GEM, GEM+nab-paclitaxel, neoadjuvant chemotherapy, and radiation.

Stochastic Evolution of Pancreatic Cancer Metastases During Logistic Clonal Expansion.

Despite recent progress in diagnostic and multimodal treatment approaches, most cancer deaths are still caused by metastatic spread and the subsequent growth of tumor cells in sites distant from the primary organ. So far, few quantitative studies are available that allow for the estimation of metastatic parameters and the evaluation of alternative treatment strategies. Most computational studies have focused on situations in which the tumor cell population expands exponentially over time; however, tumors may eventually be subject to resource and space limitations so that their growth patterns deviate from exponential growth to adhere to density-dependent growth models. In this study, we developed a stochastic evolutionary model of cancer progression that considers alterations in metastasis-related genes and intercellular growth competition leading to density effects described by logistic growth. Using this stochastic model, we derived analytical approximations for the time between the initiation of tumorigenesis and diagnosis, the expected number of metastatic sites, the total number of metastatic cells, the size of the primary tumor, and survival. Furthermore, we investigated the effects of drug administration and surgical resection on these quantities and predicted outcomes for different treatment regimens. Parameter values used in the analysis were estimated from data obtained from a pancreatic cancer rapid autopsy program. Our theoretical approach allows for flexible modeling of metastatic progression dynamics.

Mathematical modeling identifies optimum lapatinib dosing schedules for the treatment of glioblastoma patients.

Human primary glioblastomas (GBM) often harbor mutations within the epidermal growth factor receptor (EGFR). Treatment of EGFR-mutant GBM cell lines with the EGFR/HER2 tyrosine kinase inhibitor lapatinib can effectively induce cell death in these models. However, EGFR inhibitors have shown little efficacy in the clinic, partly because of inappropriate dosing. Here, we developed a computational approach to model the in vitro cellular dynamics of the EGFR-mutant cell line SF268 in response to different lapatinib concentrations and dosing schedules. We then used this approach to identify an effective treatment strategy within the clinical toxicity limits of lapatinib, and developed a partial differential equation modeling approach to study the in vivo GBM treatment response by taking into account the heterogeneous and diffusive nature of the disease. Despite the inability of lapatinib to induce tumor regressions with a continuous daily schedule, our modeling approach consistently predicts that continuous dosing remains the best clinically feasible strategy for slowing down tumor growth and lowering overall tumor burden, compared to pulsatile schedules currently known to be tolerated, even when considering drug resistance, reduced lapatinib tumor concentrations due to the blood brain barrier, and the phenotypic switch from proliferative to migratory cell phenotypes that occurs in hypoxic microenvironments. Our mathematical modeling and statistical analysis platform provides a rational method for comparing treatment schedules in search for optimal dosing strategies for glioblastoma and other cancer types.

Correction: Integrated Multiregional Analysis Proposing a New Model of Colorectal Cancer Evolution.

[This corrects the article DOI: 10.1371/journal.pgen.1005778.].

Personalized Management of Pancreatic Ductal Adenocarcinoma Patients through Computational Modeling.

Phenotypic diversity in pancreatic ductal adenocarcinoma (PDAC) results in a variety of treatment responses. Rapid autopsy studies have revealed a subgroup of PDAC patients with a lower propensity to develop metastatic disease, challenging the common perception that all patients die of widely metastatic disease, but questions remain about root causes of this difference and the potential impact on treatment strategies. In this study, we addressed these questions through the development of a mathematical model of PDAC progression that incorporates the major alteration status of specific genes with predictive utility. The model successfully reproduced clinical outcomes regarding metastatic patterns and the genetic alteration status of patients from two independent cohorts from the United States and Japan. Using this model, we defined a candidate predictive signature in patients with low metastatic propensity. If a primary tumor contained a small fraction of cells with KRAS and additional alterations to CDKN2A, TP53, or SMAD4 genes, the patient was likely to exhibit low metastatic propensity. By using this predictive signature, we computationally simulated a set of clinical trials to model whether this subgroup would benefit from locally intensive therapies such as surgery or radiation therapy. The largest overall survival benefit resulted from complete resection, followed by adjuvant chemoradiation therapy and salvage therapies for isolated recurrence. While requiring prospective validation in a clinical trial, our results suggest a new tool to help personalize care in PDAC patients in seeking the most effective therapeutic modality for each individual. Cancer Res; 77(12); 3325-35. ©2017 AACR.

Prediction of postoperative liver regeneration from clinical information using a data-led mathematical model.

Although the capacity of the liver to recover its size after resection has enabled extensive liver resection, post-hepatectomy liver failure remains one of the most lethal complications of liver resection. Therefore, it is clinically important to discover reliable predictive factors after resection. In this study, we established a novel mathematical framework which described post-hepatectomy liver regeneration in each patient by incorporating quantitative clinical data. Using the model fitting to the liver volumes in series of computed tomography of 123 patients, we estimated liver regeneration rates. From the estimation, we found patients were divided into two groups: i) patients restored the liver to its original size (Group 1, n = 99); and ii) patients experienced a significant reduction in size (Group 2, n = 24). From discriminant analysis in 103 patients with full clinical variables, the prognosis of patients in terms of liver recovery was successfully predicted in 85-90% of patients. We further validated the accuracy of our model prediction using a validation cohort (prediction = 84-87%, n = 39). Our interdisciplinary approach provides qualitative and quantitative insights into the dynamics of liver regeneration. A key strength is to provide better prediction in patients who had been judged as acceptable for resection by current pragmatic criteria.

Integrated Multiregional Analysis Proposing a New Model of Colorectal Cancer Evolution.

Understanding intratumor heterogeneity is clinically important because it could cause therapeutic failure by fostering evolutionary adaptation. To this end, we profiled the genome and epigenome in multiple regions within each of nine colorectal tumors. Extensive intertumor heterogeneity is observed, from which we inferred the evolutionary history of the tumors. First, clonally shared alterations appeared, in which C>T transitions at CpG site and CpG island hypermethylation were relatively enriched. Correlation between mutation counts and patients' ages suggests that the early-acquired alterations resulted from aging. In the late phase, a parental clone was branched into numerous subclones. Known driver alterations were observed frequently in the early-acquired alterations, but rarely in the late-acquired alterations. Consistently, our computational simulation of the branching evolution suggests that extensive intratumor heterogeneity could be generated by neutral evolution. Collectively, we propose a new model of colorectal cancer evolution, which is useful for understanding and confronting this heterogeneous disease.

The evolution of tumor metastasis during clonal expansion with alterations in metastasis driver genes.

Metastasis is a leading cause of cancer-related deaths. Carcinoma generally initiates at a specific organ as a primary tumor, but eventually metastasizes and forms tumor sites in other organs. In this report, we developed a mathematical model of cancer progression with alterations in metastasis-related genes. In cases in which tumor cells acquire metastatic ability through two steps of genetic alterations, we derive formulas for the probability, the expected number, and the distribution of the number of metastases. Moreover, we investigate practical pancreatic cancer disease progression in cases in which both one and two steps of genetic alterations are responsible for metastatic formation. Importantly, we derive a mathematical formula for the survival outcome validated using clinical data as well as direct simulations. Our model provides theoretical insights into how invisible metastases distribute upon diagnosis with respect to growth rates, (epi)genetic alteration rates, metastatic rate, and detection size. Prediction of survival outcome using the formula is of clinical importance in terms of determining therapeutic strategies.