Frequency modulation of ERK activation dynamics rewires cell fate

Abstract Transient versus sustained ERK MAP kinase (MAPK) activation dynamics induce proliferation versus differentiation in response to epidermal (EGF) or nerve (NGF) growth factors in PC‐12 cells. Duration of ERK activation has therefore been proposed to specify cell fate decisions. Using a biosensor to measure ERK activation dynamics in single living cells reveals that sustained EGF/NGF application leads to a heterogeneous mix of transient and sustained ERK activation dynamics in distinct cells of the population, different than the population average. EGF biases toward transient, while NGF biases toward sustained ERK activation responses. In contrast, pulsed growth factor application can repeatedly and homogeneously trigger ERK activity transients across the cell population. These datasets enable mathematical modeling to reveal salient features inherent to the MAPK network. Ultimately, this predicts pulsed growth factor stimulation regimes that can bypass the typical feedback activation to rewire the system toward cell differentiation irrespective of growth factor identity.

A. Representative ERK activity trajectories identified using k-means clustering. Clusters were sorted according to the mean value of the response within the cluster at 62' after stimulation to differentiate between transient (clusters 1-4) and sustained responses (cluster 5), n = 112 measured cells.
B. Peak emission ratio intensity for each cluster shown in (B). Notched boxplots with median, interquartile (box) and 1.5 IQR (whiskers) range and raw datasets are shown. Waterfall plots of cell-averaged ERs are color coded (n= at least 30 cells for each experiment). GF pulse application is indicated by black bars. GF identity and concentration are also shown.    x x x x -1 An x-mark "x" indicates that this reaction is present in the model corresponding to this column, a dash "-" indicates that this reaction is absent. 1 -full model 2 -no receptor crosstalk to the feedback components 3 -no delay in the positive feedback and no receptor crosstalk 4 -without DUSP induction 5 -with receptor synthesis, internalisation and degradation 2 Setting kPFB to zero corresponds to removing the positive feedback loop; this is the case for EGF. 3 The values of k7 should be set such that a single 10 min pulse of NGF results in a heterogonous ERK response. To achieve that and compensate for the loss of the feed-forward crosstalk from the receptor in models 2 and 3, the value of k7 is reduced in these models. Because the positive feedback was so important for explaining our single cell pulsing data, we analyzed it more detail. The linear dependency of PFB on R* (Appendix Table I, equation 7a) is not critical, but was the simplest way of modeling this dependency. Albeit there are some minor quantitative differences when a Hill-shaped kinetic is used, model-simulated ERK* trajectories (Appendix Figure 2). Most importantly, the distribution of the time-course responses for the 3 and 10 min NGF pulses for low and high dosages are virtually identical to the main results where linear kinetics is used (compare Appendix Figure 7A and Fig 5E,F).
This also holds true for multipulse datasets (compare Appendix Figure 7B and Fig 6A).
To perform the above-mentioned analysis, we used the following equations.
Main results (linear dependency on receptor activation): In these equations for the positive feedback, the actual parameter values are more important than the form of the equation. The feedback has to be activated at low levels of receptor activity in order to explain our experimental data, which can be achieved by using a linear dependency, or a Hill-shaped dependency with relatively low values for the half-activation parameter K50 << 1 (here K50 = 0.25). For example, using a larger K50 of 0.5 in the above equation did not explain our experimental data because all simulated single cell responses were transient and there were no sustained responses for 10' NGF at high dosage. Moreover, these subtle parameter differences were not visible for sustained NGF stimulation, thus further highlighting the usefulness of our pulsing experiments. The dependency of the "fast" negative feedback on active receptor is implemented as Hill function with H=2 to facilitate a higher threshold (K3R = 0.85) for activation of the receptor cross-talk.