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.