GunningErhardtWearing2014

Main file includes case reports, demographic rates, and IPUMS census microdata (large). R scripts are included to read in data. See README for more details

Optimizing homeostatic cell renewal in hierarchical tissues

<div><p>In order to maintain homeostasis, mature cells removed from the top compartment of hierarchical tissues have to be replenished by means of differentiation and self-renewal events happening in the more primitive compartments. As each cell division is associated with a risk of mutation, cell division patterns have to be optimized, in order to minimize or delay the risk of malignancy generation. Here we study this optimization problem, focusing on the role of division tree length, that is, the number of layers of cells activated in response to the loss of terminally differentiated cells, which is related to the balance between differentiation and self-renewal events in the compartments. Using both analytical methods and stochastic simulations in a metapopulation-style model, we find that shorter division trees are advantageous if the objective is to minimize the total number of one-hit mutants in the cell population. Longer division trees on the other hand minimize the accumulation of two-hit mutants, which is a more likely evolutionary goal given the key role played by tumor suppressor genes in cancer initiation. While division tree length is the most important property determining mutant accumulation, we also find that increasing the size of primitive compartments helps to delay two-hit mutant generation.</p></div

Supplementary Figures and Tables from Evidence of cryptic incidence in childhood diseases

Persistence and extinction are key processes in infectious disease dynamics that, due to incomplete reporting, are seldom directly observable. For fully immunizing diseases, reporting probabilities can be readily estimated from demographic records and case reports. Yet reporting probabilities are not sufficient to unambiguously reconstruct disease incidence from case reports. Here, we focus on disease presence (i.e. marginal probability of non-zero incidence), which provides an upper bound on the marginal probability of disease extinction. We examine measles and pertussis in pre-vaccine era U.S. cities, and describe a conserved scaling relationship between population size, reporting probability and observed presence (i.e. non-zero case reports). We use this relationship to estimate disease presence given perfect reporting, and define cryptic presence as the difference between estimated and observed presence. We estimate that, in early twentieth century U.S. cities, pertussis presence was higher than measles presence across a range of population sizes, and that cryptic presence was common in small cities with imperfect reporting. While the methods employed here are specific to fully immunizing diseases, our results suggest that cryptic incidence deserves careful attention, particularly in diseases with low case counts, poor reporting and longer infectious periods

Comparison between the average number of mutants from 100 stochastic simulations without replacement and the number of mutants predicted by the ODE approximation.

<p>(a) Comparing the number of mutants for a high value of the proliferation probability, <i>v</i> = 0.9. (b) Comparing the number of mutants when the proliferation probability is small, <i>v</i> = 0.1. Solid lines correspond to the number of mutants in compartment <i>C</i>_<i>i</i>, <i>i</i> = 1, …, 3, predicted by the ODE approximation and dashed lines correspond to the mean number of mutants in compartment <i>C</i>_<i>i</i> from the stochastic simulations. We assume <i>n</i> = 3, a mutation rate of <i>u</i> = 10⁻³, and the compartment sizes are <i>N</i>₀ = 1063, <i>N</i>₁ = 10⁴, <i>N</i>₂ = 10⁵, <i>N</i>₃ = 10⁶.</p

Mean number of mutants from 1000 stochastic simulations.

<p>We compare two arrangements of the compartment sizes for <i>n</i> = 3: constant from <i>C</i>₀ to <i>C</i>₃ (<i>N</i>₀ = 65, <i>N</i>₁ = 65, <i>N</i>₂ = 65, <i>N</i>₃ = 65) and increasing from <i>C</i>₀ to <i>C</i>₃ (<i>N</i>₀ = 20, <i>N</i>₁ = 40, <i>N</i>₂ = 80, <i>N</i>₃ = 120). (a) The mean number of mutants produced in compartments <i>C</i>₁, <i>C</i>₂ and <i>C</i>₃ for <i>v</i> = 0.9. Note that no mutants were produced in compartment <i>C</i>₀ over the time scale shown. (b) The mean number of mutants produced in compartments <i>C</i>₀, <i>C</i>₁, <i>C</i>₂ and <i>C</i>₃ for <i>v</i> = 0.1. (c) The mean of the total number of mutants comparing both architectures for <i>v</i> = 0.9 (blue line) and <i>v</i> = 0.1 (green line). For all panels, solid lines correspond to constant architecture and dashed lines to increasing architecture. In these simulations <i>u</i> = 0.001.</p

Chikungunya Viral Fitness Measures within the Vector and Subsequent Transmission Potential

<div><p>Given the recent emergence of chikungunya in the Americas, the accuracy of forecasting and prediction of chikungunya transmission potential in the U.S. requires urgent assessment. The La Reunion-associated sub-lineage of chikungunya (with a valine substitution in the envelope protein) was shown to increase viral fitness in the secondary vector, <i>Ae. albopictus</i>. Subsequently, a majority of experimental and modeling efforts focused on this combination of a sub-lineage of the East-Central-South African genotype (ECSA-V) – <i>Ae. albopictus</i>, despite the Asian genotype being the etiologic agent of recent chikungunya outbreaks world-wide. We explore a collection of data to investigate relative transmission efficiencies of the three major genotypes/sub-lineages of chikungunya and found difference in the extrinsic incubation periods to be largely overstated. However, there is strong evidence supporting the role of <i>Ae. albopictus</i> in the expansion of chikungunya that our R0 calculations cannot attribute to fitness increases in one vector over another. This suggests other ecological factors associated with the <i>Ae. albopictus-</i>ECSA-V cycle may drive transmission intensity differences. With the apparent bias in literature, however, we are less prepared to evaluate transmission where <i>Ae. aegypti</i> plays a significant role. Holistic investigations of CHIKV transmission cycle(s) will allow for more complete assessment of transmission risk in areas affected by either or both competent vectors.</p></div

Distribution of the generation times to second mutation from 5000 stochastic simulations.

<p>We consider two arrangements of the compartment sizes for <i>n</i> = 3: constant from <i>C</i>₀ to <i>C</i>₃ (<i>N</i>₀ = 65, <i>N</i>₁ = 65, <i>N</i>₂ = 65, <i>N</i>₃ = 65) and increasing from <i>C</i>₀ to <i>C</i>₃ (<i>N</i>₀ = 20, <i>N</i>₁ = 40, <i>N</i>₂ = 80, <i>N</i>₃ = 120). (a) The time to observe a second mutant for both architectures and a high value of the self-renewal probability, <i>v</i> = 0.9. The mean time for constant and increasing architectures is 3.33 and 3.39 respectively; the <i>p</i>-value obtained by two-tailed <i>t</i>-test is <i>p</i> = 0.078, indicating that the means are different only at the 10% level (size effect is 0.04). (b) The time to observe a second mutant for both architectures and a small value of the self-renewal probability, <i>v</i> = 0.1. The mean time for constant and increasing architectures is 3.67 and 3.60 respectively; the <i>p</i>-value is <i>p</i> ≪ 0.001, indicating that the means are different; the effect size is 0.16. (c) and (d) The time to observe a second mutant for a constant and increasing architecture, respectively, for small and high <i>v</i>. In these simulations <i>u</i> = 0.001, and the effect size is 0.68 and 0.46 respectively.</p

Properties of division trees as a function of <i>v</i>, the probability of self-renewal in compartments 1, …, <i>n</i> − 1.

<p>(a) Mean tree length, defined as the mean number of compartments involved in the division trees. (b) Mean division position. For an individual tree, sequence <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005967#pcbi.1005967.e005" target="_blank">(1)</a>, this is defined as ; plotted is the expectation of this quantity across all the trees. In this example, <i>n</i> = 4.</p

Schematics showing key concepts of the paper.

<p>(a) Two types of symmetric divisions: self-renewals and differentiations. Each circle represents a cell, and <i>i</i> denotes the <i>i</i>th compartment, while <i>i</i> + 1 denotes the (<i>i</i> + 1)th compartment. Panels (b) and (c) demonstrate the division chains that replenish 8 differentiated cells eliminated from the top compartment. Dead cells are denoted by X’s and arrows show divisions. Cells are arranged in horizontal layers corresponding to compartments. Only the dividing cells are shown (for example, there may be more than 4 cells in the second to top compartment in panel (b)). In (b), the dead cells are replaced by a longer division tree, and in (c) by four shorter division trees.</p

The role of the self-renewal rate on mutant generation and mutant dynamics (the analytical approach).

<p>(a) The probability of generating a mutant in each of the compartments for 6 different values of <i>v</i>: <i>v</i> = 0, 0.05, 0.1, 0.4, 0.7, 1. (b) The expected number of mutants produced from a single mutant cell in the absence of further de-novo mutations, plotted as a function of time for three different values of <i>v</i>. (c,d) The expected dynamics of mutants generated in different compartments at <i>t</i> = 0, in the absence of new mutations, for (c) <i>v</i> = 0.1 and (d) <i>v</i> = 0.5. Other parameters are: <i>n</i> = 4, and the compartment sizes are, from <i>C</i>₀ to <i>C</i>_<i>n</i>: 40, 80, 120, 160, 200.</p