A study of the accuracy of moment-closure approximations for stochastic chemical kinetics J. Chem. Phys. 136, 154105 (2012) Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs. C 2015 AIP Publishing LLC.[http://dx

Models describing the process of stem-cell differentiation are plentiful, and may offer insights into the underlying mechanisms and experimentally observed behaviour. Waddington’s epigenetic landscape has been providing a conceptual framework for differentiation processes since its inception. It also allows, however, for detailed mathematical and quantitative analyses, as the landscape can, at least in principle, be related to mathematical models of dynamical systems. Here we focus on a set of dynamical systems features that are intimately linked to cell differentiation, by considering exemplar dynamical models that capture important aspects of stem cell differentiation dynamics. These models allow us to map the paths that cells take through gene expression space as they move from one fate to another, e.g. from a stem-cell to a more specialized cell type. Our analysis highlights the role of the transition state (TS) that separates distinct cell fates, and how the nature of the TS changes as the underlying landscape changes—change that can be induced by e.g. cellular signaling. We demonstrate that models for stem cell differentiation may be interpreted in terms of either a static or transitory landscape. For the static case the TS represents a particular transcriptional profile that all cells approach during differentiation. Alternatively, the TS may refer to the commonly observed period of heterogeneity as cells undergo stochastic transitions.

Cancers accumulate mutations that lead to neoantigens, novel peptides that elicit an immune response, and consequently undergo evolutionary selection. Here we establish how the clonal structure of neoantigens in a growing cancer is shaped by negative selection, by constructing a mathematical model of neoantigen evolution. The model predicts that, without immune escape, tumour neoantigens are either clonal or absent from large subclones, and hyper-mutated tumours can only establish following the evolution of immune evasion. Strong negative selection on neoantigens leads to an increased number of neutrally-evolving tumours, as a consequence of selective pressure for immune escape. The clone size distribution under negative selection is effectivelyneutral, and becomes more neutral-like under stronger negative selection. These results are consistent with the analysis of neoantigen clone sizes and immune escape in exome and RNA sequencing data from colon, stomach and endometrial cancers. 4 RESULTS Mathematical model of tumour growth predicts distinct antigen-hot and -cold tumoursWe created a mathematical model of neoantigen evolution during tumour growth, based on a stochastic branching process (Figure 1a and Methods). At each step, tumour cells of lineage i produced two surviving offspring at birth rate b=1 per unit time or died with death rate determined by the strength of negative selection against the cumulative antigenicity of neoantigens in the lineage. Neoantigens accumulated at rate µ per cell per division, and had antigenicity s drawn from a pre-specified distribution. s can be interpreted as the effectiveness of immune predation against an antigen: s=0 indicates no selection pressure (neutral evolution), and s<0 strong negative selection (following ref 34 ). Tumour growth was simulated until the tumour reached a predefined population size (approximating a clinically detectable size) or until a sufficiently long time elapsed without tumour establishment (corresponding to no cancer formation within a person's lifetime).We first examined the temporal neoantigen burden in simulated tumours. We defined the 'antigen score' of a tumour as the proportion of tumour cells carrying cumulative antigenicity ≥ ! . Tumours simulated with identical parameters separated into two distinct groups: 'antigen-hot' and 'antigen-cold'. Antigen-hot tumours had an antigen score close to 1, corresponding to every tumour cell in the population being highly antigenic, whereas in antigen-cold tumours the majority of cells lacked immunogenic mutations (Figure 1b&c). The proportion of antigen-hot tumours depended on the selection strength (Figure S1a): increased negative selection for neoantigens decreased the probability of observing antigen-hot tumours. In antigen-cold tumours, the proportion of neoantigen-carrying cells also decreased inversely with negative selection.

Genetic and epigenetic variation, together with transcriptional plasticity, contribute to intratumour heterogeneity1. The interplay of these biological processes and their respective contributions to tumour evolution remain unknown. Here we show that intratumour genetic ancestry only infrequently affects gene expression traits and subclonal evolution in colorectal cancer (CRC). Using spatially resolved paired whole-genome and transcriptome sequencing, we find that the majority of intratumour variation in gene expression is not strongly heritable but rather ‘plastic’. Somatic expression quantitative trait loci analysis identified a number of putative genetic controls of expression by cis-acting coding and non-coding mutations, the majority of which were clonal within a tumour, alongside frequent structural alterations. Consistently, computational inference on the spatial patterning of tumour phylogenies finds that a considerable proportion of CRCs did not show evidence of subclonal selection, with only a subset of putative genetic drivers associated with subclone expansions. Spatial intermixing of clones is common, with some tumours growing exponentially and others only at the periphery. Together, our data suggest that most genetic intratumour variation in CRC has no major phenotypic consequence and that transcriptional plasticity is, instead, widespread within a tumour.

Next generation sequencing has yielded an unparalleled means of quickly determining the molecular make-up of patient tumors. In conjunction with emerging, effective immunotherapeutics for a number of cancers, this rapid data generation necessitates a paired high-throughput means of predicting and assessing neoantigens from tumor variants that may stimulate immune response. Here we offer NeoPredPipe (Neoantigen Prediction Pipeline) as a contiguous means of predicting putative neoantigens and their corresponding recognition potentials for both single and multi-region tumor samples. NeoPredPipe is able to quickly provide summary information for researchers, and clinicians alike, on neoantigen burdens while providing high-level insights into tumor heterogeneity given somatic mutation calls and, optionally, patient HLA haplotypes. Given an example dataset we show how NeoPredPipe is able to rapidly provide insights into neoantigen heterogeneity, burden, and immune stimulation potential. Through the integration of widely adopted tools for neoantigen discovery NeoPredPipe offers a contiguous means of processing single and multi-region sequence data. NeoPredPipe is user-friendly and adaptable for high-throughput performance. NeoPredPipe is freely available at https://github.com/MathOnco/NeoPredPipe. 109 approach also highlights regions with neoantigen loads different from their closest 110 neighbors, such as Region61 and Region62 of Carcinoma 7. Therefore the analysis can 111 inform future experimental and bioinformatic investigations of samples allowing for new 112 evolutionary and mechanistic insights into tumor development, evolution, and 113 progression. 114 Conclusions 115 We present NeoPredPipe, an efficient, high-throughput, and user-friendly pipeline for 116 neoantigen prediction and interrogation for single and multi-region tumor VCF files. By 117 tying together commonly utilized bioinformatics toolsets and integrating recent 118 advances in neoantigen assessment, NeoPredPipe yields concise information typically 119 required by researchers and clinicians. Through user options based on computational 120 limitations the pipeline is scalable and customizable for individual research questions.121

Colorectal malignancies are a leading cause of cancer-related death1 and have undergone extensive genomic study2,3. However, DNA mutations alone do not fully explain malignant transformation4–7. Here we investigate the co-evolution of the genome and epigenome of colorectal tumours at single-clone resolution using spatial multi-omic profiling of individual glands. We collected 1,370 samples from 30 primary cancers and 8 concomitant adenomas and generated 1,207 chromatin accessibility profiles, 527 whole genomes and 297 whole transcriptomes. We found positive selection for DNA mutations in chromatin modifier genes and recurrent somatic chromatin accessibility alterations, including in regulatory regions of cancer driver genes that were otherwise devoid of genetic mutations. Genome-wide alterations in accessibility for transcription factor binding involved CTCF, downregulation of interferon and increased accessibility for SOX and HOX transcription factor families, suggesting the involvement of developmental genes during tumourigenesis. Somatic chromatin accessibility alterations were heritable and distinguished adenomas from cancers. Mutational signature analysis showed that the epigenome in turn influences the accumulation of DNA mutations. This study provides a map of genetic and epigenetic tumour heterogeneity, with fundamental implications for understanding colorectal cancer biology.

Background Next generation sequencing has yielded an unparalleled means of quickly determining the molecular make-up of patient tumors. In conjunction with emerging, effective immunotherapeutics for a number of cancers, this rapid data generation necessitates a paired high-throughput means of predicting and assessing neoantigens from tumor variants that may stimulate immune response. Results Here we offer N eo P red P ipe (Neoantigen Prediction Pipeline) as a contiguous means of predicting putative neoantigens and their corresponding recognition potentials for both single and multi-region tumor samples. NeoPredPipe is able to quickly provide summary information for researchers, and clinicians alike, on predicted neoantigen burdens while providing high-level insights into tumor heterogeneity given somatic mutation calls and, optionally, patient HLA haplotypes. Given an example dataset we show how NeoPredPipe is able to rapidly provide insights into neoantigen heterogeneity, burden, and immune stimulation potential. Conclusions Through the integration of widely adopted tools for neoantigen discovery NeoPredPipe offers a contiguous means of processing single and multi-region sequence data. NeoPredPipe is user-friendly and adaptable for high-throughput performance. NeoPredPipe is freely available at https://github.com/MathOnco/NeoPredPipe .

Cancer evolution is driven by the acquisition of somatic mutations that provide cells with a beneficial phenotype in a changing microenvironment. However, mutations that give rise to neoantigens, novel cancer-specific peptides that elicit an immune response, are likely to be disadvantageous. Here we show how the clonal structure and immunogenotype of growing tumours is shaped by negative selection in response to neoantigenic mutations. We construct a mathematical model of neoantigen evolution in a growing tumour, and verify the model using genomic sequencing data. The model predicts that, in the absence of active immune escape mechanisms, tumours either evolve clonal neoantigens (antigen-'hot'), or have no clonally-expanded neoantigens at all (antigen-'cold'), whereas antigen-'warm' tumours (with high frequency subclonal neoantigens) form only following the evolution of immune evasion. Counterintuitively, strong negative selection for neoantigens during tumour formation leads to an increased number of antigen-warm or -hot tumours, as a consequence of selective pressure for immune escape. Further, we show that the clone size distribution under negative selection is effectively-neutral, and moreover, that stronger negative selection paradoxically leads to more neutral-like dynamics. Analysis of antigen clone sizes and immune escape in colorectal cancer exome sequencing data confirms these results.Overall, we provide and verify a mathematical framework to understand the evolutionary dynamics and clonality of neoantigens in human cancers that may inform patientspecific immunotherapy decision-making.