Fig. 2: Computational molecular probabilistic map (MPM) workflow and identification of ground- truth in simulated datasets.

a MPM computational workflow. A corresponding complete spatial randomness (CSR) model is created for each metabolite-of-interest’s (MOI) spatial point pattern (SPP) with equal spatial point density. Kernel density is estimated for both, thus resulting in spatial density functions, \({\rho }_{{{{{{\rm{MOI}}}}}}}\left(x,y\right)\) and \({\rho }_{{{{{{\rm{CSR}}}}}}}\left(x,y\right)\). The intensity distribution function \({f}_{{{{{{\rm{CSR}}}}}}}\left(k\right)\), which converges to a normal distribution (Supplementary Fig. 12), then serves as the null distribution based on which null-hypothesis testing is carried out for each pixel intensity in \({\rho }_{{{{{{\rm{MOI}}}}}}}\left(x,y\right)\) with a significance level α of 0.05. MPM hotspots (red/white contours) and coldspots (blue/white contours) are accordingly defined as locations where the null hypothesis is rejected for the upper or lower-tail Benjamini–Hochberg corrected P-values (Supplementary Fig. 9), thus signifying areas of significant MOI relative spatial abundance and deficiency, respectively. b Simulated uniform Poisson SPP showing a ring-like area of high MOI abundance) with 30 and 20 length units for outer and inner radii, respectively (also see Supplementary Fig. 11d). Intensity values were sampled from above and below the upper quartile of the empirical intensities of a MALDI-FTICR-MSI measurement of a human glioblastoma tissue sample (Fig. 3a) at m/z 544.3009 (PE(20:1)[M+Na]⁺; FDR ≤ 0.2) for the simulated high-MOI and background areas, respectively (simulated high-MOI area: n = ~520 with a spatial point density of ~0.4 points per unit area; background n = ~1950 with a spatial point density of ~0.3 points per unit area; mean signal intensity of simulated high-MOI area/mean signal intensity background = ~2.3). First row: corresponding spatial density and 3D surface plots. MPM hotspot contours were able to localize the simulated high-MOI area (green contours in the SPP plot) and identify points exhibiting significant relative spatial abundance (green points on density and surface plots; bottom row). c Simulated SPP with a central circle of 20 length units radius and four adjacent smaller circles of 5 length units radius as simulated high-MOI areas (central circle area/peripheral circle area = 16; high-MOI area n = ~430; background n = ~1950; same spatial point density as in (b); mean signal intensity of simulated high-MOI area /mean signal intensity background = ~2.3).