Biology subjects

Altrock, P. M.

Publications and source records attributed to Altrock, P. M..

5 recordsLinked to original sources

bioRxiv2018

Leveraging single cell RNA sequencing experiments to model intra-tumor heterogeneity

PURPOSEMany cancers can be treated with targeted therapy. Almost inevitably, tumors develop resistance to targeted therapy, either from preexistence or by evolving new genotypes and traits. Intra-tumor heterogeneity serves as a reservoir for resistance, which often occurs due to selection of minor cellular sub-clones. On the level of gene expression, the clonal heterogeneity can only be revealed by high-dimensional single cell methods. We propose to use a general diversity index (GDI) to quantify heterogeneity on multiple scales and relate it to disease evolution.\n\nMETHODSWe focused on individual patient samples probed with single cell RNA sequencing to describe heterogeneity. We developed a pipeline to analyze single cell data, via sample normalization, clustering and mathematical interpretation using a generalized diversity measure, and exemplify the utility of this platform using single cell data.\n\nRESULTSWe focused on three sources of RNA sequencing data: two healthy bone marrow (BM) samples, two acute myeloid leukemia (AML) patients, each sampled before and after BM transplant (BMT), four samples of pre-sorted lineages, and six lung carcinoma patients with multi-region sampling. While healthy/normal samples scored low in diversity overall, GDI further quantified in which respect these samples differed. While a widely used Shannon diversity index sometimes reveals less differences, GDI exhibits differences in the number of potential key drivers or clonal richness. Comparing pre and post BMT AML samples did not reveal differences in heterogeneity, although they can be very different biologically.\n\nCONCLUSIONGDI can quantify cellular heterogeneity changes across a wide spectrum, even when standard measures, such as the Shannon index, do not. Our approach offers wide applications to quantify heterogeneity across samples and conditions.

cancer biology↗

bioRxiv2018

Finite size effects in diffusive public goods games

A particular challenge in the co-evolutionary dynamics of growing populations is to determine the effects of population assortment on growth advantage of cooperative traits. Here we study the coevolution of cooperators that are public good producers and consumers, and free riders that are only public good consumers. Using an individual-based model and its continuum limit we show that the differential growth rate between producers and free-riders depends on the spatial Fourier decomposition of their respective densities. Further, we derive a finite-size correction, which scales as the cell size, which accurately describes the dynamics of a randomly assorted population. Using this result we are also able to derive an effective benefit to cost relation, which provides a criterion that relates the parameters of the model (e.g. diffusion constant of the public good, decay rate and cost) to the long-term persistence of cooperation. Our findings provide a powerful tool for the analysis of diffusive public goods games, and can explain commonly observed patterns of cooperation, rather than the tragedy of the commons, based on the derived finite-size correction.

ecology↗

bioRxiv2018

Neighborhood size-effects in nonlinear public goods games

Ecological and evolutionary dynamics can be strongly affected by population assortment and frequency-dependent selection. In growing populations, a particular challenge is to disentangle global ecological effects from local frequency-dependent effects. Here we implement a logistic growth and death model on the global scale, coupled to frequency-dependent growth rates influenced by a public goods game between cooperators and defectors. For each individual, the public good is only effective within a neighborhood of other individuals, and the public good-growth rate relationship can be nonlinear. At low numbers of cooperators, increases of public good accumulate synergistically; at high numbers, increases in public good only provide diminishing returns-the inflection point of this pattern is given by the strength of frequency-dependent selection in relation to the background fitness effect. We observed complex critical behavior in the evolutionary dynamics equilibria, determined by the relative magnitude of frequency-dependent to constant (background) growth benefits. We predict neighborhood-size-driven state changes, hysteresis between polymorphic and monomorphic equilibria, and observed that type-dependent differences in neighborhood sizes can destabilize monomorphic cooperative states but increase coexistence of cooperators and defectors. Stochastic neighborhood size fluctuations also led to coexistence and could stabilize the purely cooperative equilibrium. Our results quantify the role of assortment through neighborhood-size effects and nonlinearity of the gains function in eco-evolutionary dynamics, which is relevant for a variety of microbial and cellular public goods games.

ecology↗

bioRxiv2017

A computational model of MGUS progression to Multiple Myeloma identifies optimum screening strategies and their effects on mortality

Recent advances uncovered therapeutic interventions that might reduce the risk of progression of premalignant diagnoses, such as from Monoclonal Gammopathy of Undetermined Significance (MGUS) to multiple myeloma (MM). It remains unclear how to best screen populations at risk and how to evaluate the ability of these interventions to reduce disease prevalence and mortality at the population level. To address these questions, we developed a computational modeling framework. We used individual-based computational modeling of MGUS incidence and progression across a population of diverse individuals, to determine best screening strategies in terms of screening start, intervals, and risk-group specificity. Inputs were life tables, MGUS incidence and baseline MM survival. We measured MM-specific mortality and MM prevalence following MGUS detection from simulations and mathematical precition modeling. We showed that our framework is applicable to a wide spectrum of screening and intervention scenarios, including variation of the baseline MGUS to MM progression rate and evolving MGUS, in which progression increases over time. Given the currently available progression risk-point estimate of 61% risk, starting screening at age 55 and follow-up screening every 6yrs reduced total MM prevalence by 19%. The same reduction could be achieved with starting age 65 and follow-up every 2yrs. A 40% progression risk reduction per MGUS patient per year would reduce MM-specific mortality by 40%. Generally, age of screening onset and frequency impact disease prevalence, progression risk reduction impacts both prevalence and disease-specific mortality, and screeenign would generally be favorable in high-risk individuals. Screening efforts should focus on specifically identified groups of high lifetime risk of MGUS, for which screening benefits can be significant. Screening low-risk MGUS individuals would require improved preventions.

epidemiology↗

bioRxiv2017

Extinction Times In Tumor Public Goods Games

Cancer evolution and progression are shaped by cellular interactions and Darwinian selection. Evolutionary game theory incorporates both of these principles, and has been proposed as a framework to understand tumor cell population dynamics. A cornerstone of evolutionary dynamics is the replicator equation, which describes changes in the relative abundance of different cell types, and is able to predict evolutionary equilibria. Typically, the replicator equation focuses on differences in relative fitness. We here show that this framework might not be sufficient under all circumstances, as it neglects important aspects of population growth. Standard replicator dynamics might miss critical differences in the time it takes to reach an equilibrium, as this time also depends on cellular turnover in growing but bounded populations. As the system reaches a stable manifold, the time to reach equilibrium depends on cellular death and birth rates. These rates shape the timescales, in particular in co-evolutionary dynamics of growth factor producers and free-riders. Replicator dynamics might be an appropriate framework only when birth and death rates are of similar magnitude. Otherwise, population growth effects cannot be neglected when predicting the time to reach an equilibrium, and cell type specific rates have to be accounted for explicitly.

cancer biology↗