Inertial effect of cell state velocity on the quiescence-proliferation fate decision in breast cancer

Abstract

Energy landscapes can provide intuitive depictions of population heterogeneity and dynamics. However, it is unclear whether individual cell behavior, hypothesized to be determined by initial position and noise, is faithfully recapitulated. Using the p21-/Cdk2-dependent quiescence-proliferation decision in breast cancer dormancy as a testbed, we examined single-cell dynamics on the landscape when perturbed by hypoxia, a dormancy-inducing stress. Combining trajectory-based energy landscape generation with single-cell time-lapse microscopy, we found that initial position on a p21/Cdk2 landscape did not fully explain the observed cell-fate heterogeneity under hypoxia. Instead, cells with higher cell state velocities prior to hypoxia, influenced by epigenetic parameters, tended to remain proliferative under hypoxia. Thus, the fate decision on this landscape is significantly influenced by "inertia", a velocity-dependent ability to resist directional changes despite reshaping of the underlying landscape, superseding positional effects. Such inertial effects may markedly influence cell-fate trajectories in tumors and other dynamically changing microenvironments.

Figure 1:. Heterogeneity in quiescence-proliferation under hypoxia in MCF-7 cells is explained by a p21-Cdk2 toggle switch

(A) Schematic of the p21-Cdk2 dependence of the quiescence-proliferation decision (B) Quantification of western blots of p21 (left) and Cdk2 (right) expression under cobalt chloride treatment in MCF-7 cells at different times. Bar graphs and error bars represent the mean and s.d. of three independent experiments. p-values calculated by ANOVA followed by Dunn’s post-hoc test with multiple comparison corrections (* p < 0.05, ** p < 0.01, *** p < 0.001, **** p < 0.0001) (C) Immunostaining images of MCF-7 cells under hypoxia showing nuclei stained by DAPI (top left), Cdk2 (green, top right), p21 (red, bottom left), and merged (bottom right). Scale bar represents 200 μm. Image brightness and contrast adjusted for clarity. (D) Potential energy landscape of the p21-Cdk2 computational model as a function of total p21 and active Cdk2.

Figure 2:. Energy landscapes under normoxia and hypoxia and the role of position on the observed cell-fate divergence

(A) Computationally calculated energy landscapes under normoxia (E2f synthesis rate = 1.19 (i.e., 2^0.25) times the basal value) and hypoxia (E2f synthesis rate = 0.71 (i.e., 2^−0.5) times and p53 degradation rate = 10⁻² times the basal values). (B) Experimental energy landscapes (left) generated using single-cell tracking imaging data and the subpopulations of behavior (right) observed under normoxia followed by hypoxia: cells entering a quiescent state in normoxic conditions that remain quiescent under hypoxia (Cluster QQ), cells proliferative under normoxia but quiescent under hypoxia (Cluster PQ), and cells proliferative under normoxia that remain proliferative under hypoxia (Cluster PP). (C) Pictographic representation of the hypothesized dependence of cell fate on initial position. (D) Effect of initial p21 levels and Cdk2 activities on cell fate under hypoxia. Statistical comparison of mean ranks was carried out by Kruskal-Wallis test followed by Bonferroni correction for multiple comparisons. (E) Pictographic representation of the observed dependence of cell fate on initial position. (F) Effect of initial cell cycle position on cell fate. Distributions were compared using the Kolmogorov-Smirnov test for discrete distributions followed by Bonferroni correction for multiple comparisons. (** p < 0.01; *** p < 0.001; **** p < 0.0001).

Figure 3:. System parameters drive the inertial effect of velocity

(A) Ranking of system parameters based on S phase entry time sensitivity analysis in this work and local sensitivity analysis by Heldt et al. showing the commensurate effect of parameter variations on cell cycle velocity and cell behavior, respectively. (B) Distribution of cell cluster identity as a function of number of cell divisions prior to hypoxia. Division number distributions between different clusters were compared with a discrete version of the Kolmogorov-Smirnov test. (C) Probabilities of sister cells being in the same cluster or different clusters. Statistical significance is calculated by 10⁵ instances of probability calculation after randomization of cluster identities. (D) Schematic showing the effect of system bistability on cell fate. Cells in either extreme of the parameter space (i and iii) are likely to have the same fate, whereas cells either in the bistable region (ii) or at the cusp of bistability can exhibit divergent cell fates due to stochastic effects. (E) Phase space diagram showing the dependence of cell fate on the deviation of p53 degradation rate and E2f synthesis rate from basal values. Green and violet regions represent quiescence and proliferation, respectively. Yellow region represents a bistable region. The expected parameter ranges for each cluster are shown as hollow rectangles. Graph recolored and boundaries drawn post-analysis for clarity (F) Odds of the sister cell of a cell in clusters QQ, PQ, or PP being in the same cluster (for a given cell, probability of its sister cell belonging to the same cluster/probability of its sister cell belonging to a different cluster). Statistical significance was calculated by 10⁵ instances of probability calculation after randomization of cluster identities. (* p < 0.05; ** p < 0.01; *** p < 0.001; **** p < 0.0001).

Figure 4:. Cell decision-making on the p21-Cdk2 energy landscape under the classical position-only paradigm and the velocity-dependent paradigm.

Cells are typically proliferative under normal conditions. However, under stress, the landscape becomes biased towards quiescence. In the classical paradigm, we would expect all cells in the indicated position to enter quiescence. However, we observe that fates are velocity-dependent, with high-velocity cells having sufficient inertia to overcome the change in landscape conditions and continue being proliferative.