Obesity increases genomic instability at DNA repeat-mediated endogenous mutation hotspots.

Obesity is associated with increased cancer risk, yet the underlying mechanisms remain elusive. Obesity-associated cancers involve disruptions in metabolic and cellular pathways, which can lead to genomic instability. Repetitive DNA sequences capable of adopting alternative DNA structures (e.

Selective sweeps in SARS-CoV-2 variant competition.

The main mathematical result in this paper is that change of variables in the ordinary differential equation (ODE) for the competition of two infections in a Susceptible-Infected-Removed (SIR) model shows that the fraction of cases due to the new variant satisfies the logistic differential equation, which models selective sweeps. Fitting the logistic to data from the Global Initiative on Sharing All Influenza Data (GISAID) shows that this correctly predicts the rapid turnover from one dominant variant to another. In addition, our fitting gives sensible estimates of the increase in infectivity.

Competitive exclusion in a model with seasonality: Three species cannot coexist in an ecosystem with two seasons.

Chan, Durrett, and Lanchier introduced a multitype contact process with temporal heterogeneity involving two species competing for space on the d-dimensional integer lattice. Time is divided into two seasons. They proved that there is an open set of the parameters for which both species can coexist when their dispersal range is sufficiently large.

Signatures of neutral evolution in exponentially growing tumors: A theoretical perspective.

Recent work of Sottoriva, Graham, and collaborators have led to the controversial claim that exponentially growing tumors have a site frequency spectrum that follows the 1/f law consistent with neutral evolution. This conclusion has been criticized based on data quality issues, statistical considerations, and simulation results. Here, we use rigorous mathematical arguments to investigate the site frequency spectrum in the two-type model of clonal evolution.

Controlling the spread of COVID-19 on college campuses.

This research was done during the DOMath program at Duke University from May 18 to July 10, 2020. At the time, Duke and other universities across the country were wrestling with the question of how to safely welcome students back to campus in the Fall. Because of this, our project focused on using mathematical models to evaluate strategies to suppress the spread of the virus on campus, specifically in dorms and in classrooms.

Integrating transcriptomics and bulk time course data into a mathematical framework to describe and predict therapeutic resistance in cancer.

A significant challenge in the field of biomedicine is the development of methods to integrate the multitude of dispersed data sets into comprehensive frameworks to be used to generate optimal clinical decisions. Recent technological advances in single cell analysis allow for high-dimensional molecular characterization of cells and populations, but to date, few mathematical models have attempted to integrate measurements from the single cell scale with other types of longitudinal data. Here, we present a framework that actionizes static outputs from a machine learning model and leverages these as measurements of state variables in a dynamic model of treatment response.

A facile technology for the high-throughput sequencing of the paired VH:VL and TCRβ:TCRα repertoires.

Natively paired sequencing (NPS) of B cell receptors [variable heavy (VH) and light (VL)] and T cell receptors (TCRb and TCRa) is essential for the understanding of adaptive immunity in health and disease. Despite many recent technical advances, determining the VH:VL or TCRb:a repertoire with high accuracy and throughput remains challenging. We discovered that the recently engineered xenopolymerase, RTX, is exceptionally resistant to cell lysate inhibition in single-cell emulsion droplets.

Determinants governing T cell receptor α/β-chain pairing in repertoire formation of identical twins.

The T cell repertoire in each individual includes T cell receptors (TCRs) of enormous sequence diversity through the pairing of diverse TCR α- and β-chains, each generated by somatic recombination of paralogous gene segments. Whether the TCR repertoire contributes to susceptibility to infectious or autoimmune diseases in concert with disease-associated major histocompatibility complex (MHC) polymorphisms is unknown. Due to a lack in high-throughput technologies to sequence TCR α-β pairs, current studies on whether the TCR repertoire is shaped by host genetics have so far relied only on single-chain analysis.

Extrapolating weak selection in evolutionary games.

This work is inspired by a 2013 paper from Arne Traulsen's lab at the Max Plank Institute for Evolutionary Biology (Wu et al. in PLoS Comput Biol 9:e1003381, 2013). They studied evolutionary games when the mutation rate is so small that each mutation goes to fixation before the next one occurs.

Persistence and reversal of plasmid-mediated antibiotic resistance.

In the absence of antibiotic-mediated selection, sensitive bacteria are expected to displace their resistant counterparts if resistance genes are costly. However, many resistance genes persist for long periods in the absence of antibiotics. Horizontal gene transfer (primarily conjugation) could explain this persistence, but it has been suggested that very high conjugation rates would be required.

Temporal profiles of avalanches on networks.

An avalanche or cascade occurs when one event causes one or more subsequent events, which in turn may cause further events in a chain reaction. Avalanching dynamics are studied in many disciplines, with a recent focus on average avalanche shapes, i.e.

Spatial evolutionary games with weak selection.

Recently, a rigorous mathematical theory has been developed for spatial games with weak selection, i.e., when the payoff differences between strategies are small.

Ordinary Differential Equation Models for Adoptive Immunotherapy.

Modified T cells that have been engineered to recognize the CD19 surface marker have recently been shown to be very successful at treating acute lymphocytic leukemias. Here, we explore four previous approaches that have used ordinary differential equations to model this type of therapy, compare their properties, and modify the models to address their deficiencies. Although the four models treat the workings of the immune system in slightly different ways, they all predict that adoptive immunotherapy can be successful to move a patient from the large tumor fixed point to an equilibrium with little or no tumor.

Genome assembly and geospatial phylogenomics of the bed bug Cimex lectularius.

The common bed bug (Cimex lectularius) has been a persistent pest of humans for thousands of years, yet the genetic basis of the bed bug's basic biology and adaptation to dense human environments is largely unknown. Here we report the assembly, annotation and phylogenetic mapping of the 697.9-Mb Cimex lectularius genome, with an N50 of 971 kb, using both long and short read technologies.

Outcomes of Active Surveillance for Ductal Carcinoma in Situ: A Computational Risk Analysis.

Background: Ductal carcinoma in situ (DCIS) is a noninvasive breast lesion with uncertain risk for invasive progression. Usual care (UC) for DCIS consists of treatment upon diagnosis, thus potentially overtreating patients with low propensity for progression. One strategy to reduce overtreatment is active surveillance (AS), whereby DCIS is treated only upon detection of invasive disease.

Estimating Tumor Growth Rates In Vivo.

In this paper, we develop methods for inferring tumor growth rates from the observation of tumor volumes at two time points. We fit power law, exponential, Gompertz, and Spratt’s generalized logistic model to five data sets. Though the data sets are small and there are biases due to the way the samples were ascertained, there is a clear sign of exponential growth for the breast and liver cancers, and a 2/3’s power law (surface growth) for the two neurological cancers.

Spatial Moran Models I. Stochastic Tunneling in the Neutral Case.

We consider a multistage cancer model in which cells are arranged in a -dimensional integer lattice. Starting with all wild-type cells, we prove results about the distribution of the first time when two neutral mutations have accumulated in some cell in dimensions ≥ 2, extending work done by Komarova [12] for = 1.

Spatial Moran models, II: cancer initiation in spatially structured tissue.

We study the accumulation and spread of advantageous mutations in a spatial stochastic model of cancer initiation on a lattice. The parameters of this general model can be tuned to study a variety of cancer types and genetic progression pathways. This investigation contributes to an understanding of how the selective advantage of cancer cells together with the rates of mutations driving cancer, impact the process and timing of carcinogenesis.

Assembly and diploid architecture of an individual human genome via single-molecule technologies.

We present the first comprehensive analysis of a diploid human genome that combines single-molecule sequencing with single-molecule genome maps. Our hybrid assembly markedly improves upon the contiguity observed from traditional shotgun sequencing approaches, with scaffold N50 values approaching 30 Mb, and we identified complex structural variants (SVs) missed by other high-throughput approaches. Furthermore, by combining Illumina short-read data with long reads, we phased both single-nucleotide variants and SVs, generating haplotypes with over 99% consistency with previous trio-based studies.

HPV clearance and the neglected role of stochasticity.

Clearance of anogenital and oropharyngeal HPV infections is attributed primarily to a successful adaptive immune response. To date, little attention has been paid to the potential role of stochastic cell dynamics in the time it takes to clear an HPV infection. In this study, we combine mechanistic mathematical models at the cellular level with epidemiological data at the population level to disentangle the respective roles of immune capacity and cell dynamics in the clearing mechanism.

Exact solution for a metapopulation version of Schelling's model.

In 1971, Schelling introduced a model in which families move if they have too many neighbors of the opposite type. In this paper, we will consider a metapopulation version of the model in which a city is divided into N neighborhoods, each of which has L houses. There are ρNL red families and ρNL blue families for some ρ < 1/2.

Chemical evolutionary games.

Inspired by the use of hybrid cellular automata in modeling cancer, we introduce a generalization of evolutionary games in which cells produce and absorb chemicals, and the chemical concentrations dictate the death rates of cells and their fitnesses. Our long term aim is to understand how the details of the interactions in a system with n species and m chemicals translate into the qualitative behavior of the system. Here, we study two simple 2×2 games with two chemicals and revisit the two and three species versions of the one chemical colicin system studied earlier by Durrett and Levin (1997).