Fig. 4: Comparison between theoretical results and empirical data.
From: Metabolic coordination and phase transitions in spatially distributed multi-cellular systems
Snapshots of lactate gradient and single-cell fluxes from (a) experimental frames of ref. 31 (at intervals of 1 hour) and (b) from CBM simulations performed by sampling (13) with parameters βG and βO that, at each time step, provide the maximum likelihood reconstruction of the empirical average lactate flux. See Supplementary Method 8 for details. Comparison between empirical (line: mean value, shaded region: standard error from jackknife resampling) and theoretical (error bars; black: fit, red: predictions) flux values as a function of time for (c) mean lactate flux, (d) standard deviation of single cell lactate flux and (e) nearest-neighbor correlations. The errors on the inferred quantities were calculated from the errors on the inferred values of βG and βO. f Mean-field phase diagram with the critical lines and the inferred values of βO and βG (markers with error bars) colored according to the time stamp for the 36 frames of the experimental dataset. For details on how the errors were estimated, see Supplementary Method 8. g Same as (f ), but in the plane (\(\langle {u}_{{{\rm{O}}}}\rangle ,\langle {u}_{{{\rm{G}}}}\rangle\)). Only the first and last critical lines are shown. The dashed black line corresponds to \(\left\langle {u}_{{{\rm{L}}}}\right\rangle =0\). (Note that the latter line does not appear in (f )). Inset: zoomed out view in the single-cell flux space \({{{\mathcal{F}}}}_{1}\) of Fig. 1b.
