Abstract
BackgroundStudies of cell-to-cell variation have in recent years grown in interest, due to improved bioanalytical techniques which facilitates determination of small changes with high uncertainty. Like much high-quality data, single-cell data is best analysed using a systems biology approach. The most common systems biology approach to single-cell data is the standard two-stage (STS) approach. In STS, data from each cell is analysed in a separate sub-problem, meaning that only data from the same cell is used to calculate the parameter values within that cell. Because only parts of the data are considered, problems with parameter unidentifiability are exaggerated in STS. In contrast, a related approach to data analysis has been developed for the studies of patient-to-patient variations. This approach, called nonlinear mixed-effects modelling (NLME), makes use of all data, when estimating the patient-specific parameters. NLME would therefore be advantageous compared to STS also for the study of cell-to-cell variation. However, no such systematic evaluation of the two approaches exists.ResultsHerein, such a systematic comparison between STS and NLME has been performed. Different examples, both linear and nonlinear, and both simulated and real experimental data, have been examined. With informative data, there is no significant difference in the results for either parameter or noise estimation. However, when data becomes uninformative, NLME is significantly superior to STS. These results hold independently of whether the loss of information is due to a low signal-to-noise ratio, too few data points, or a bad input signal. The improvement is shown to come from both the consideration of a joint likelihood (JLH) function, describing all parameters and data, and from an a priori postulated form of the population parameters. Finally, we provide a small tutorial that shows how to use NLME for single-cell analysis, using the free and user-friendly software Monolix.ConclusionsWhen considering uninformative single-cell data, NLME yields more accurate parameter and noise estimates, compared to more traditional approaches, such as STS and JLH.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-015-0203-x) contains supplementary material, which is available to authorized users.
Highlights
Studies of cell-to-cell variation have in recent years grown in interest, due to improved bioanalytical techniques which facilitates determination of small changes with high uncertainty
Linear model: nonlinear mixed-effects modelling (NLME) is advantageous in cases of low-quality data We generated fluorescent recovery after photo-bleaching (FRAP) data structured like the real experimental data (Methods) but with known true kinetic parameters, in order to determine whether there is a difference between standard two-stage (STS)’s and NLME’s ability to estimate the true parameters in a system (Fig. 2)
NLME were given the true form of the kinetic parameter distributions among the cell population
Summary
Studies of cell-to-cell variation have in recent years grown in interest, due to improved bioanalytical techniques which facilitates determination of small changes with high uncertainty. The most straightforward analysis of such data is to fit an exponential curve to the data, and evaluate the value of the exponent [4] (Fig. 1b) The limitation of such an approach is that the exponent does not correspond to the velocity of any specific mechanism, but to a phenomenological description lumping many sub-processes together. PDE-based models are usually utilized for forward-simulation, i.e. where simulations of different scenarios are performed, but where the model is assumed as known Another important type of modelling is known as reversed-engineering, in which parameters with mechanistic interpretation are estimated based on the data, and where conclusions can be drawn regarding mechanisms in the biological system [6,7,8,9] (Fig. 1d)
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