Numerical Estimation of the Asymptotic Behaviour of Solid Partitions of an Integer

The number of solid partitions of a positive integer is an unsolved problem in combinatorial number theory. In this paper, solid partitions are studied numerically by the method of exact enumeration for integers up to 50 and by Monte Carlo simulations using Wang-Landau sampling method for integers up to 8000. It is shown that, for large n, ln[p(n)]/n^(3/4) = 1.79 \pm 0.01, where p(n) is the number of solid partitions of the integer n. This result strongly suggests that the MacMahon conjecture for solid partitions, though not exact, could still give the correct leading asymptotic behaviour.Comment: 6 pages, 4 figures, revtex

Landscape of somatic mutations in 560 breast cancer whole-genome sequences.

We analysed whole-genome sequences of 560 breast cancers to advance understanding of the driver mutations conferring clonal advantage and the mutational processes generating somatic mutations. We found that 93 protein-coding cancer genes carried probable driver mutations. Some non-coding regions exhibited high mutation frequencies, but most have distinctive structural features probably causing elevated mutation rates and do not contain driver mutations. Mutational signature analysis was extended to genome rearrangements and revealed twelve base substitution and six rearrangement signatures. Three rearrangement signatures, characterized by tandem duplications or deletions, appear associated with defective homologous-recombination-based DNA repair: one with deficient BRCA1 function, another with deficient BRCA1 or BRCA2 function, the cause of the third is unknown. This analysis of all classes of somatic mutation across exons, introns and intergenic regions highlights the repertoire of cancer genes and mutational processes operating, and progresses towards a comprehensive account of the somatic genetic basis of breast cancer

Retrospective evaluation of whole exome and genome mutation calls in 746 cancer samples

Funder: NCI U24CA211006Abstract: The Cancer Genome Atlas (TCGA) and International Cancer Genome Consortium (ICGC) curated consensus somatic mutation calls using whole exome sequencing (WES) and whole genome sequencing (WGS), respectively. Here, as part of the ICGC/TCGA Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium, which aggregated whole genome sequencing data from 2,658 cancers across 38 tumour types, we compare WES and WGS side-by-side from 746 TCGA samples, finding that ~80% of mutations overlap in covered exonic regions. We estimate that low variant allele fraction (VAF < 15%) and clonal heterogeneity contribute up to 68% of private WGS mutations and 71% of private WES mutations. We observe that ~30% of private WGS mutations trace to mutations identified by a single variant caller in WES consensus efforts. WGS captures both ~50% more variation in exonic regions and un-observed mutations in loci with variable GC-content. Together, our analysis highlights technological divergences between two reproducible somatic variant detection efforts

Contrasting the impact of cytotoxic and cytostatic drug therapies on tumour progression

A tumour grows when the total division (birth) rate of its cells exceeds their total mortality (death) rate. The capability for uncontrolled growth within the host tissue is acquired via the accumulation of driver mutations which enable the tumour to progress through various hallmarks of cancer. We present a mathematical model of the penultimate stage in such a progression. We assume the tumour has reached the limit of its present growth potential due to cell competition that either results in total birth rate reduction or death rate increase. The tumour can then progress to the final stage by either seeding a metastasis or acquiring a driver mutation. We influence the ensuing evolutionary dynamics by cytotoxic (increasing death rate) or cytostatic (decreasing birth rate) therapy while keeping the effect of the therapy on net growth reduction constant. Comparing the treatments head to head we derive conditions for choosing optimal therapy. We quantify how the choice and the related gain of optimal therapy depends on driver mutation, metastasis, intrinsic cell birth and death rates, and the details of cell competition. We show that detailed understanding of the cell population dynamics could be exploited in choosing the right mode of treatment with substantial therapy gains. Author summary Cells and organisms evolve to better survive in their environments and to adapt to new challenges. Such dynamics manifest in a particularly problematic way with the evolution of drug resistance, which is increasingly recognized as a key challenge for global health. Thus, developing therapy paradigms that factor in evolutionary dynamics is an important goal. Using a minimal mathematical model of a cancer cell population we contrast cytotoxic (increasing death rate) and cytostatic (decreasing birth rate) treatments while keeping the effect of the therapy on the net growth reduction constant. We then quantify how the choice and the related gain of optimal therapy depends on driver mutation, metastasis, intrinsic cell birth and death rates and the details of cell competition. Most importantly, we identify specific cell population dynamics under which a certain treatment could be significantly better than the alternative.Peer reviewe

The prognostic role of tumor budding and tumor-stroma ratio in pulmonary metastasis of colorectal carcinoma

Abstract Objective: To evaluate the prognostic value of tumor budding and tumor-stroma ratio (TSR) in resected pulmonary metastases of colorectal carcinoma (CRC). Methods: In total, 106 pulmonary metastasectomies were performed to 74 patients in two study hospitals during 2000–2020. All relevant clinical data were retrospectively collected. Tumor budding based on the International Tumor Budding Consensus Conference recommendations and TSR in the first resected pulmonary metastases and primary tumors were evaluated from diagnostic hematoxylin-eosin-stained histopathological slides. Results: 60 patients (85.7%) had low tumor budding (≤5 buds/field) and 10 patients (14.3%) had high tumor budding (>5 buds/field) in their first pulmonary metastases of CRC. 5-year overall survival rates of pulmonary metastasectomy in low and high total tumor budding were 28.3% and 37.3% (p = 0.387), respectively. 19 patients (27.1%) had low TSR and 51 patients (72.9%) had high TSR. The 5-year overall survival rates were 32.9% in low and 28.6% in high TSR of first pulmonary metastases (p = 0.746). Tumor budding and TSR did not provide prognostic value in Cox multivariate analysis. Tumor budding and TSR in resected pulmonary metastases were not associated with those of the primary tumor. Conclusion: Tumor budding and TSR in the resected pulmonary metastases of CRC showed no statistically significant prognostic value, however, additional well-powered confirmatory studies are needed

A community effort to create standards for evaluating tumor subclonal reconstruction

Tumor DNA sequencing data can be interpreted by computational methods that analyze genomic heterogeneity to infer evolutionary dynamics. A growing number of studies have used these approaches to link cancer evolution with clinical progression and response to therapy. Although the inference of tumor phylogenies is rapidly becoming standard practice in cancer genome analyses, standards for evaluating them are lacking. To address this need, we systematically assess methods for reconstructing tumor subclonality. First, we elucidate the main algorithmic problems in subclonal reconstruction and develop quantitative metrics for evaluating them. Then we simulate realistic tumor genomes that harbor all known clonal and subclonal mutation types and processes. Finally, we benchmark 580 tumor reconstructions, varying tumor read depth, tumor type and somatic variant detection. Our analysis provides a baseline for the establishment of gold-standard methods to analyze tumor heterogeneity

A community effort to create standards for evaluating tumor subclonal reconstruction

Methods for reconstructing tumor evolution are benchmarked in the DREAM Somatic Mutation Calling Tumour Heterogeneity Challenge. Tumor DNA sequencing data can be interpreted by computational methods that analyze genomic heterogeneity to infer evolutionary dynamics. A growing number of studies have used these approaches to link cancer evolution with clinical progression and response to therapy. Although the inference of tumor phylogenies is rapidly becoming standard practice in cancer genome analyses, standards for evaluating them are lacking. To address this need, we systematically assess methods for reconstructing tumor subclonality. First, we elucidate the main algorithmic problems in subclonal reconstruction and develop quantitative metrics for evaluating them. Then we simulate realistic tumor genomes that harbor all known clonal and subclonal mutation types and processes. Finally, we benchmark 580 tumor reconstructions, varying tumor read depth, tumor type and somatic variant detection. Our analysis provides a baseline for the establishment of gold-standard methods to analyze tumor heterogeneity