Fig 1.
Overview of the serial-passaging experiments and example subpopulation dynamics in the SA1035-TNBC treatment arm.
(A) Sankey diagram showing data origin (cell line or PDX), replicate groups, and cisplatin treatment schedules. (B) Relative SP frequencies across origins and replicate groups, with colors indicating SP identities unique to each replicate group. (C) Schematic of serial-passaging in the TNBC-SA1035 PDX, illustrating tumor passaging under treatment and no treatment arms. Created in BioRender. Veith, T. (2026) https://BioRender.com/yq988eq. (D) Example SP dynamics from TNBC-SA1035 Replicate Group 2, highlighting SP frequency shifts over time. Shaded region indicates cisplatin administration.
Table 1.
Comparison of ECO-K vs FitClone performance across various TNBC lineages. The table summarizes the root mean squared error (RMSE), AICc, and BIC for both ECO-K and FitClone models. Each row represents an individual sample with column entries to denote replicate group (RG), the number of SPs in that replicate group, the number of non-zero interaction coefficients estimated by ECO-K, the number of those coefficients deemed significant during parametric bootstrapping, the mean absolute matrix entry value (payoff), the number of timepoints at which single-cell genomes were established, and at how many of those timepoints the sample had been exposed to cisplatin. Overall, ECO-K provided better fits (lower AICc and BIC) in two datasets, where FitClone was superior in two datasets. The remaining four datasets were unable to be analyzed by FitClone as it requires more than two SPs.
Fig 2.
Overview of the optimization routine used in our method.
The flowchart depicts the step-by-step process of optimizing the payoff matrix for SP interactions using ECO-K. The routine begins by initializing the interactions and setting up the optimization problem. An initial optimization was performed, and the BIC was calculated with all interactions. The method then evaluates the removal of matrix entries to determine if this improves the BIC score. All indices in the matrix were tested for removal, but only the one that gave the lowest BIC score was retained. This routine was designed to ensure the most parsimonious set of interactions was used to capture the subpopulation dynamics.
Fig 3.
Comparative analysis of framework performance on inferring payoff matrix rank and range.
(A) A density scatter plot correlation between true and inferred payoff matrix entry ranks for the 2-player, low-noise condition (,
). (B) Spearman correlations remain significant as noise and the number of SPs increase, though the effect size diminishes. (C) Scatter plot for the inference of payoff matrix range (max-min) for the same 2-player, low-noise condition (
,
). (D) Performance in range inference is shown across all conditions. Spearman rank correlation: o
*
, **
, ***
.
Fig 4.
Estimated frequency-dependent interaction coefficients between karyotype defined subpopulations in TNBC PDX mouse models.
(A) Observed (dashed lines) and replicator equation–predicted frequency dynamics (solid lines) for subpopulations (SPs) in TNBC-SA1035 Replicate Group 2. (B) Payoff matrix diagram illustrating interactions between SPs. Red bands represent a negative payoff matrix entry, green bands represent a positive entry. The width of the band represents the relative strength of the interaction, and the arrow gives the direction of the interaction (i.e., which SP receives the payoff). (C) Replicator phase diagram correlating to (B). (D) Ternary plots of replicator dynamics for selected SP combinations: A–F–H (left) and A–C–F (right). (E) Heatmap of copy number alterations (CNAs) across SPs, annotated by sampling timepoint and cluster. (F) Mean population fitness ( from Eq 3) trajectories under different SP compositions. Removing specific SPs alters overall fitness relative to the original composition (red).