Fig 1.
Challenges regarding the identification of the interaction between different components of a biological system.
(A) Time-resolved measurements for the concentrations of different biological components and factors lead to the question on their dynamical interactions. Out of a global model considering all possible interactions and processes for the different factors within the system (B) one needs to identify the (sub-)model that best explains the experimental data (C). FAMoS provides a computational method that uses a sophisticated way to search the total model space for the most appropriate (sub-)model.
Fig 2.
(A) Based on a given (sub-)model of the global model, FAMoS works by creating and testing neighbouring models against experimental data. Thereby, the algorithm distinguishes between three main methods for exploring the model space including (a) forward search, in which a parameter that was not considered in the previous model is additionally considered, (b) backward elimination, in which a parameter of the current model is deleted from the analysis, and (c) swap search, in which two parameters out of pre-defined parameter sets are exchanged. (B) Starting with a pre-defined model and method, FAMoS creates the neighbouring models and compares their ability to describe the experimental data, with the methods and/or models dynamically updated at the end of each iteration. The algorithm finally returns the model that was found to best explain the experimental data.
Fig 3.
(A) Importance of critical parameters sets. In the shown example, model state B is assumed to be achieved initially only from either state A or C. Therefore, the corresponding connections μAB and μCB are defined as a critical parameter set. Only models containing at least one of the parameters are evaluated. (B) Definition of swap parameter sets: The transition from A to B, μAB, as well as a multiplication within B, ρB, are structurally similar parameters that can explain an increase in model state B and define a swap parameter set, i.e., parameters can be replaced against each other for model testing.
Fig 4.
Evaluation of a 4-compartment model using FAMoS.
(A) The global model containing all possible interactions between and within the 4 different compartments considering multiplication and transition processes. (B) Simulated data for the dynamics of the different components using a sub-model as shown on the right (true model). The different crosses indicate the mean over 10 independent measurements at each time point for each compartment (see Methods for model parameterization). (C) Evaluation of all possible models of (A) against the simulated data with the 5000 best models ranked according to their AICc-values. (D) Sketch of a single FAMoS run starting with a specified model and showing the convergence towards the final selected model over time. Individual iterations indicate the changes in the selected models after each iteration by adding (red), removal (green) or swapping (blue) of individual parameters. (E) Comparing the performance of FAMoS with and without using the swap search-method based on a total of 65.535 runs, i.e., starting FAMoS with every possible (sub-)model of the global model shown in (A).
Fig 5.
Assessing cell proliferation dynamics by dye dilution experiments within different culture conditions.
(A) Representative plot for PKH-distribution and separation for cellular subsets according to the number of divisions 7 days after the transfer of the cells. (B) Distribution for CD4+ and CD8+ T cells according to the number of divisions either in 2D suspension (left column) or 3D ex vivo collagen cultures (right column) at 2 and 7 days post transfer of the cells. (C) Schematic representation of the proliferation dynamics. Cells are assumed to proliferate or die with division dependent proliferation (ρ) and death rates (δ), respectively.
Fig 6.
Assessing cell proliferation dynamics of CD4+ T cells by dye-dilution experiments within different culture conditions.
(A) Akaike weights for the individual parameters based on all 8669 model evaluations within the 5 independent FAMoS runs performed for the analysis of the CD4+ T cells. Parameters selected within the final model (depicted by 2 out of 5 runs) are shown in black, non-selected parameters in orange. A representative FAMoS run is shown in S2 Fig. (B) Determined model structures and parameter estimates for the generation-dependent proliferation (ρ) and death rates (δ), as well as adaptation time periods (τ) for CD4+ T cells within suspension (blue) and collagen (red). Points indicate best parameter estimates obtained for each rate with shaded areas defining the corresponding 95%-confidence intervals obtained by profile-likelihood analyses (see Table 1 and S3 Fig). (C) Observed (grey) and predicted distribution of cell populations for CD4+ T cells using the determined model structure and the best parameter estimates obtained for each condition (blue = suspension, red = collagen).
Table 1.
Estimated generation dependent proliferation and death rates.
The table shows the best estimates for the generation dependent proliferation, ρ, and death rates, δ (both in ×10−2h−1), as well as the length of the adaptation phase (in h) for both CD4+ and CD8+ T cells based on the cell proliferation data and dependent on the culture condition. Numbers in brackets denote 95%-confidence intervals obtained by profile likelihood analysis (upper bound of 1 indicates unidentifiability). Estimates are obtained for the best model identified by FAMoS for each cell type indicating influences of the environment on cell proliferation. In addition, standard deviation of the data, (in ×10−3), was estimated with
and
. A visualization of the estimates can be found in Fig 6B and Panel B in S5 Fig.