Nonlinear mixed-effects modelling for single cell estimation: when, why, and how to use it.
BACKGROUND
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. 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.


RESULTS
Herein, 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.


CONCLUSIONS
When considering uninformative single-cell data, NLME yields more accurate parameter and noise estimates, compared to more traditional approaches, such as STS and JLH.
Department of Biomedical Engineering, Linköping University, Linköping, SE-58185, Sweden. markus.karlsson@liu.se.
Markus
M
Karlsson
Department of Biomedical Engineering, Linköping University, Linköping, SE-58185, Sweden. davidlarsivanjanzen88@gmail.com.|Department of Clinical and Experimental Medicine, Linköping University, Uppsala, SE-58185, Sweden. davidlarsivanjanzen88@gmail.com.|Current Address: Biomedical and Biological Systems Laboratory, School of Engineering, University of Warwick, Coventry, CV4 7AL, UK. davidlarsivanjanzen88@gmail.com.|Modeling and Simulation, AstraZeneca, Mölndal, Sweden. davidlarsivanjanzen88@gmail.com.|Department of Systems and Data Analysis, Fraunhofer-Chalmers Centre, Chalmers Science Park, Gothenburg, SE-412 88, Sweden. davidlarsivanjanzen88@gmail.com.
David L I
DL
Janzén
Instituto de Fisiología, Biología Molecular y Neurociencias, Consejo Nacional de Investigaciones Científicas y Técnicas and Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina. ludurrieu@gmail.com.
Lucia
L
Durrieu
Instituto de Fisiología, Biología Molecular y Neurociencias, Consejo Nacional de Investigaciones Científicas y Técnicas and Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina. alerner2@gmail.com.
Alejandro
A
Colman-Lerner
Pharmacometrics Group, Pharmaceutical Biosciences, Uppsala University, Uppsala, SE-75124, Sweden. Maria.Kjellsson@farmbio.uu.se.
Maria C
MC
Kjellsson
Department of Biomedical Engineering, Linköping University, Linköping, SE-58185, Sweden. gunnar.cedersund@liu.se.|Department of Clinical and Experimental Medicine, Linköping University, Uppsala, SE-58185, Sweden. gunnar.cedersund@liu.se.|IKE, Linköping University, Linköping, 58185, Sweden. gunnar.cedersund@liu.se.
Gunnar
G
Cedersund
D036681:Fluorescence Recovery After Photobleaching; D007700:Kinetics; D016014:Linear Models; D008954:Models, Biological; D017711:Nonlinear Dynamics; D059010:Single-Cell Analysis