A Discrete Time Model for the Analysis of Medium-Throughput C. elegans Growth Data

BACKGROUND: As part of a program to predict the toxicity of environmental agents on human health using alternative methods, several in vivo high- and medium-throughput assays are being developed that use C. elegans as a model organism. C. elegans-based toxicological assays utilize the COPAS Biosort flow sorting system that can rapidly measure size, extinction (EXT) and time-of-flight (TOF), of individual nematodes. The use of this technology requires the development of mathematical and statistical tools to properly analyze the large volumes of biological data. METHODOLOGY/PRINCIPAL FINDINGS: Findings A Markov model was developed that predicts the growth of populations of C. elegans. The model was developed using observations from a 60 h growth study in which five cohorts of 300 nematodes each were aspirated and measured every 12 h. Frequency distributions of log(EXT) measurements that were made when loading C. elegans L1 larvae into 96 well plates (t = 0 h) were used by the model to predict the frequency distributions of the same set of nematodes when measured at 12 h intervals. The model prediction coincided well with the biological observations confirming the validity of the model. The model was also applied to log(TOF) measurements following an adaptation. The adaptation accounted for variability in TOF measurements associated with potential curling or shortening of the nematodes as they passed through the flow cell of the Biosort. By providing accurate estimates of frequencies of EXT or TOF measurements following varying growth periods, the model was able to estimate growth rates. Best model fits showed that C. elegans did not grow at a constant exponential rate. Growth was best described with three different rates. Microscopic observations indicated that the points where the growth rates changed corresponded to specific developmental events: the L1/L2 molt and the start of oogenesis in young adult C. elegans. CONCLUSIONS: Quantitative analysis of COPAS Biosort measurements of C. elegans growth has been hampered by the lack of a mathematical model. In addition, extraneous matter and the inability to assign specific measurements to specific nematodes made it difficult to estimate growth rates. The present model addresses these problems through a population-based Markov model

Application of a Mathematical Model to Describe the Effects of Chlorpyrifos on Caenorhabditis elegans Development

The nematode Caenorhabditis elegans is being assessed as an alternative model organism as part of an interagency effort to develop better means to test potentially toxic substances. As part of this effort, assays that use the COPAS Biosort flow sorting technology to record optical measurements (time of flight (TOF) and extinction (EXT)) of individual nematodes under various chemical exposure conditions are being developed. A mathematical model has been created that uses Biosort data to quantitatively and qualitatively describe C. elegans growth, and link changes in growth rates to biological events. Chlorpyrifos, an organophosphate pesticide known to cause developmental delays and malformations in mammals, was used as a model toxicant to test the applicability of the growth model for in vivo toxicological testing.L1 larval nematodes were exposed to a range of sub-lethal chlorpyrifos concentrations (0-75 microM) and measured every 12 h. In the absence of toxicant, C. elegans matured from L1s to gravid adults by 60 h. A mathematical model was used to estimate nematode size distributions at various times. Mathematical modeling of the distributions allowed the number of measured nematodes and log(EXT) and log(TOF) growth rates to be estimated. The model revealed three distinct growth phases. The points at which estimated growth rates changed (change points) were constant across the ten chlorpyrifos concentrations. Concentration response curves with respect to several model-estimated quantities (numbers of measured nematodes, mean log(TOF) and log(EXT), growth rates, and time to reach change points) showed a significant decrease in C. elegans growth with increasing chlorpyrifos concentration.Effects of chlorpyrifos on C. elegans growth and development were mathematically modeled. Statistical tests confirmed a significant concentration effect on several model endpoints. This confirmed that chlorpyrifos affects C. elegans development in a concentration dependent manner. The most noticeable effect on growth occurred during early larval stages: L2 and L3. This study supports the utility of the C. elegans growth assay and mathematical modeling in determining the effects of potentially toxic substances in an alternative model organism using high-throughput technologies

"Phenomenal Conservatism" - Ch 2 of Seemings and Epistemic Justification

In this chapter I introduce and analyse the tenets of phenomenal conservatism, and discuss the problem of the nature of appearances. After that, I review the asserted epistemic merits phenomenal conservatism and the principal arguments adduced in support of it. Finally, I survey objections to phenomenal conservatism and responses by its advocates. Some of these objections will be scrutinised and appraised in the next chapters