Fig 1.
(a) We first consider an experimental dataset (dataset A) to be explained. (b) Additional information from various sources (datasets B) is collected to build feasible window constraints. (c) By incorporating these constraints into the cost function, (d) we transform the cost function landscape to enhance the search for the global minimum.
Fig 2.
Building feasible window constraints.
Panels (a)-(d) show the four synthetic datasets (B1-B4) with different frequencies, replicates, and deviation. Panel (e) shows the datasets merged in a normalized space, where the grid shows the number of vertical cells determined by clustering the X3 value and the number of horizontal cells is determined by clustering the time dataset. The feasible windows are chosen according to the maximum number of points between cells in the same column.
Fig 3.
Dynamics of cycle Lotka-Volterra model for the two different approaches.
A comprehensive comparison of model predictions for two approaches: the standard quantitative approach (purple) and using our CrossLabFit approach (turquoise). In the panel of plots, each column represents the variables X1 and X3. The first row shows the results of the standard approach results using synthetic data with log-normal noise, highlighted by red circles. The last row integrates feasible window constraints for X3. The ground truth is denoted by a solid red line, contrasted with a color-coded solid line and shaded area showing the median and confidence interval, respectively, of the simulations obtained by estimating parameters using nonparametric bootstrapping, for each approach.
Fig 4.
Parameter distribution and likelihood profiles for cycle Lotka-Volterra model.
Panel (a) shows violin plots illustrating the variability and density of the estimated parameters a2, a3, a6, and a7 derived from 1000 bootstrap resamples across the two data integration strategies. The width of each violin indicates the sample density at different values, with a red line marking the ground truth. Dashed lines within each violin represent the median and interquartile range. Panels (b)-(e) show likelihood profiles for four parameters in the Lotka-Volterra model (a2, a3, a6, and a7), comparing two data integration strategies (standard and CrossLabFit approach) against the ground truth to assess parameter identifiability. These panels plot against parameter values, indicating that minima closer to the ground truth represent more accurate estimates.
Fig 5.
Building feasible window constraints for CD8+ T cell dynamic.
The data were normalized using the minimum and maximum values of each dataset. The plot shows the data from the four sources and the feasible window constraints formed by a grid, where the number of vertical cells is determined by clustering the CD8+ T cell data and the number of horizontal cells is determined by clustering the days dataset. The windows were chosen according to the maximum number of points between cells in the same column.
Fig 6.
Dynamics of influenza model for the two different approaches.
A comprehensive comparison of influenza model predictions for two approaches: the standard quantitative approach (purple) and using our CrossLabFit approach (turquoise). In the panel of plots, each column shows the viral dynamics V (panels (a) and (c)) and T cell dynamic T (panels (b) and (d)). The first row shows standard approach results using viral load data, highlighted by red circles. The last row integrates feasible window constraints for T. Color-coded solid line and shaded area illustrate the median and confidence interval, respectively, of the simulations obtained by estimating parameters using nonparametric bootstrapping, for each approach.
Fig 7.
Parameter distribution and likelihood profiles for influenza model.
Panel (a) shows violin plots illustrating the variability and density of the estimated parameters β, , p, and r derived from 1000 bootstrap resamples across the two data integration strategies. The width of each violin indicates the sample density at different values. Dashed lines within each violin represent the median and interquartile range. Panels (b)-(e) show likelihood profiles for four parameters in the influenza model (β,
, p, and r), comparing two data integration strategies ( the standard and our CrossLabFit approaches) to assess parameter identifiability. The stars indicate the median values from the parameter distributions obtained via bootstrapping, with colors corresponding to the respective approach.
Table 1.
Comparison of estimated parameters for the influenza A model in mouse lungs.
Values are median and 95% confidence interval from bootstrapped estimates.
Table 2.
Parameters for the three Lotka-Volterra models used to generate synthetic data.
Table 3.
Parameter values for the influenza model.