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Defining informative priors for ensemble modeling in systems biology


Ensemble modeling in molecular systems biology requires the reproducible translation of kinetic parameter data into informative probability distributions (priors), as well as approaches that sample parameters from these distributions without violating the thermodynamic consistency of the overall model. Although a number of pioneering frameworks for ensemble modeling have been published, the issue of generating informative priors has not yet been addressed. Here, we present a protocol that aims to fill this gap. This protocol discusses the collection of parameter values from a diverse range of sources (literature, databases and experiments), assessment of their plausibility, and creation of log-normal probability distributions that can be used as informative priors in ensemble modeling. Furthermore, the protocol enables sampling from the generated distributions while maintaining thermodynamic consistency. Once all parameter values have been retrieved from literature and databases, the protocol can be implemented within ~5–10 min per parameter. The aim of this protocol is to facilitate the design and use of informative distributions for ensemble modeling, especially in fields such as synthetic biology and systems medicine.

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Fig. 1: Workflow of the protocol from parameter collection to generation of probability distributions and confirmation of thermodynamic consistency for interconnected parameters.
Fig. 2: Calculation of the weighted median of two unitless parameter values (modes), 103 and 106 (log-transformed to 6.9078 and 13.82, respectively), with varying weights and uncertainty.
Fig. 3
Fig. 4
Fig. 5: Estimated probability distributions for parameters KD1 and \(k_1^ -\), plotted on a log scale.
Fig. 6: The bivariate distribution for parameters k1 and kon1 and the two marginal distributions.


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We thank F. Del Carratore and the Synthetic Biology Research Centre for Synthetic Biology of Fine and Speciality Chemicals (SYNBIOCHEM) for providing technical support. This work received funding from the UK Biotechnology and Biological Sciences Research Council (BB/M000354/1, BB/M017702/1 (R.B.)) and the European Union’s Horizon 2020 Research and Innovation Programme (grant agreement no. 720793, the H2020 TOPCAPI project (R.B.)).

Author information

Authors and Affiliations



A.T. designed and developed the mathematical strategy and the MATLAB functions of the protocol and wrote the manuscript. A.H. designed the first step of the protocol, concerning the criteria of the assignment of weights; performed tests with diverse case studies; and provided feedback for the improvement of the protocol and the manuscript. M.U. tested the protocol and provided insightful advice on the improvement of the manuscript and the computational functions. R.B. supervised the project and wrote the manuscript.

Corresponding author

Correspondence to Rainer Breitling.

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The authors declare that they have no competing interests as defined by Nature Research, or other interests that might be perceived to influence the results and/or discussion reported in this paper.

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Related links

Key references using this protocol

1. Achcar, F. et al. PLOS Comput. Biol. 8, e1002352 (2012):

2. Achcar, F., Barrett, M. P. & Breitling, R. FEBS J. 280, 4640–4651 (2013):

3. Tsigkinopoulou, A., Baker, S. M. & Breitling, R. Trends Biotechnol. 35, 518–529 (2017):

Integrated supplementary information

Supplementary Figure 1 Properties of the standard normal and log-normal distributions (μ = 0 and σ = 1).

For the normal distribution, the standard deviation (σ) is additive, and 68.27% of the probability density are contained within the confidence interval [μ−σ, μ+σ]. For the log-normal distribution, the geometric standard deviation is multiplicative and describes a confidence interval around the geometric mean of the distribution, which contains 68.27% of the probability density. The Spread (or multiplicative standard deviation) describes the confidence interval around the mode of the distribution, which contains this fraction of the density. The geometric standard deviation and the Spread are equally valid ways to describe our uncertainty about a parameter, and each has its advantages for some applications. For the protocol, the main advantage in using the Mode and the Spread is the fact that the Spread is symmetric around the most likely value (mode), in the same way as the standard deviation of a normal distribution (i.e., the probability density at each endpoint of the interval is identical). This is not the case for the geometric standard deviation, as shown in the figure. As a result, is more intuitive to specify and communicate our uncertainty about a parameter by using the confidence interval around the mode, rather than that around the median. As can be seen in the figure, the most likely parameter values might not even be included in the confidence interval around the median, which is clearly undesirable when specifying the range of plausible values.

Supplementary Figure 2 Schematic representation of the model.

Blue arrows correspond to the maintenance of the ATP/ADP ratio by direct assignment (in combination with reaction 13), rather than by differential equations, in the published model. Likewise, the cytosolic glycerol levels are kept at zero by direct assignment, corresponding to rapid export of glycerol.

Supplementary Figure 3 Effect of reducing TPI on the steady-state flux of glucose, pyruvate and glycerol.

Replicated results matching Fig. 3b of the published model (Helfert et al,. Biochem. J. (2001)).

Supplementary Figure 4 Plots of the initial priors (red lines) and the samples from the final distributions (green histograms), along with the P values of the K-S test.

For the parameter Km+ the adjusted distribution is also included (blue line).

Supplementary Figure 5

Pairwise correlations between the sampled parameter values.

Supplementary information

Supplementary Text and Figures

Supplementary Figures 1–5, Supplementary Software 1–7, Supplementary Results 1 and 2, and Supplementary Tables 1–7

Supplementary Software 8

Supplementary Software scripts

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Tsigkinopoulou, A., Hawari, A., Uttley, M. et al. Defining informative priors for ensemble modeling in systems biology. Nat Protoc 13, 2643–2663 (2018).

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