Kocieniewski and Lipniacki (bioRxiv 2025; Scientific Reports 2026) built a rule-based model of the MAPK/ERK pathway covering RAF and MEK isoforms and RAF interactions with 14-3-3 proteins, and proposed that at low growth-factor concentration RAS is activated on only a fraction of the cell membrane, reconciling graded RAS/RAF responses with switch-like (ultrasensitive) ERK activation. The mechanism is implemented phenomenologically as a tuned membrane-activation fraction, and the model is deliberately not fitted to any cell line. The open problem is to make this account mechanistically explicit and quantitatively validated: replace the fractional-activation proxy with explicit spatial modeling of the membrane RAS module, parameterize the model for individual cell lines and compare its predictions quantitatively with experimental data, and test distinctive predictions such as weak ERK suppression upon BRAF knockout.

Background

The MAPK/ERK pathway is the canonical growth-factor signaling cascade in animal cells: upon epidermal growth factor (EGF) stimulation, the small membrane-anchored GTPase RAS switches to its active GTP-bound state and recruits the RAF kinases (of which mammals have three isoforms, ARAF, BRAF and CRAF); RAF phosphorylates MEK, MEK phosphorylates ERK, and active doubly phosphorylated ERK regulates hundreds of targets controlling proliferation, apoptosis and motility. The cascade is ultrasensitive: as shown theoretically and experimentally by Huang and Ferrell (1996), the requirement for double phosphorylation at the MEK and ERK tiers produces a switch-like, nearly all-or-none ERK response. Experiments in lymphoid cells by Das et al. (2009) showed that RAS activation itself is digital (all-or-none at the single-cell level) and hysteretic (dependent on the cell's prior stimulation history), driven by a positive feedback loop in which RAS-GTP recruits the SOS (Son of Sevenless) nucleotide-exchange factor that in turn generates more RAS-GTP. Theory by Das, Kardar and Chakraborty (2009) showed that this membrane feedback, under slow lateral diffusion, drives spatial clustering of active RAS and propagating activation waves on the membrane, and Markevich et al. (2006) showed that bistable kinase cascades can support long-range phosphoprotein waves. A long-standing puzzle is how graded (gradually increasing) activation at the upper RAS and RAF tiers coexists with switch-like ERK output. Kocieniewski and Lipniacki (2025 preprint; published 2026 in Scientific Reports) addressed this with a rule-based model, formulated in the BioNetGen language (BNGL), in which reactions are specified as patterns (rules) rather than enumerated species, allowing them to represent RAF isoform-specific interactions with 14-3-3 proteins — scaffold dimers that crosslink phosphorylated sites on RAF monomers, holding them in a closed inactive state, but which can also stabilize active RAF dimers containing BRAF — together with CRAF's non-kinase interactions with ROKα (a kinase promoting motility) and MST2/ASK1 (kinases in the pro-apoptotic Hippo pathway), and three negative feedbacks from ERK to SOS, RAF and MEK. The model reproduces relaxation oscillations (self-sustained ERK activity pulses driven by the ERK-to-SOS negative feedback frustrating the SOS-RAS positive feedback) and predicts, counterintuitively, only weak ERK suppression upon BRAF knockout. To reconcile graded RAS/RAF activation with ultrasensitive ERK activation, the authors assume that at low and intermediate EGF concentrations only a portion of the cell membrane carries activated receptors, so the bistable SOS-RAS switch activates RAS locally; this fraction is imposed as a phenomenological parameter rather than emerging from any spatial representation, and the model parameters are not fitted to any particular cell line (the authors explicitly state they explore parameter space instead of fitting cell-line responses, continuing the qualitative-modeling approach of their earlier MEK-isoform model, Kocieniewski and Lipniacki 2013). The published version adds the caveat, in light of cryo-electron-microscopy (cryo-EM, a technique that resolves protein-complex structures at near-atomic scale) structures of CRAF/MEK1/14-3-3 complexes by Jang et al. (2025), that the model's assumption about CRAF and ARAF 14-3-3 binding should be regarded as a model idealization. Systematic parameterization and uncertainty-quantification tooling for exactly this model class now exists (PyBioNetFit, demonstrated by Miller et al. 2026 on the authors' earlier MEK model), but has not been applied to this model or to any spatial extension of it.

Problem Statement

The overarching objective, posed by the limitations of the Kocieniewski-Lipniacki rule-based MAPK/ERK model, is to establish whether the localized-RAS-activation mechanism — together with 14-3-3-mediated, isoform-specific RAF regulation — is a mechanistically real and quantitatively valid account of cell-type-specific MAPK/ERK signaling. Concretely: (1) Spatial explicitness. Replace the phenomenological assumption that a tuned fraction of the cell membrane carries activated RAS with an explicit spatial model of the EGF-receptor/SOS/RAS membrane module coupled to the RAF-isoform/14-3-3 cascade, and determine whether the reconciliation between graded RAS and RAF activation and switch-like (ultrasensitive) ERK activation emerges from the SOS-RAS positive feedback with realistic lateral diffusion and clustering, rather than from the imposed fraction; characterize the resulting spatial phenomena (dynamics of RAS nanoclusters, i.e., small membrane-resident clusters of active RAS; and propagating activation waves). (2) Quantitative cell-line parameterization. Develop a systematic procedure to parameterize the model for individual cell types (given their protein expression levels) and test whether its predictions match experimental data quantitatively for each of the three observables — ERK oscillation periods, dose-response curves for EGF, and RAF dimer abundances; the parameterization is anchored to concrete cell types and to experimental datasets for each of these three observables. (3) Robustness of distinctive predictions. Determine whether the predicted weak ERK suppression upon BRAF knockout is robust across cell lines with different MEK and ERK expression levels (in the source, the weak suppression is attributed to the assumed high rates of MEK and ERK activation), and how sensitively the dynamics depend on the implementation of the ERK-to-RAF negative feedback, which the source models as ERK phosphorylation at the RAF dimerization interface (DIF) that both blocks dimer formation and disrupts existing dimers. The source additionally poses the refinement of representing ARAF and CRAF with distinct 14-3-3 binding kinetics and phosphatase sensitivities, and of adding CRAF's further non-kinase interactions (e.g., with Bcl-2 and DAPK1). No single one of (1)–(3) resolves the overarching objective on its own; the objective is resolved only by (1)–(3) jointly, and the source-posed refinements described in the preceding sentence lie outside its scope.

References

  1. Kocieniewski, P., Lipniacki, T. (2025). Regulation of the MAPK/ERK system: a computational rule-based model. bioRxiv 2025.07.16.665118. doi:10.1101/2025.07.16.665118. https://doi.org/10.1101/2025.07.16.665118
  2. Kocieniewski, P., Lipniacki, T. (2026). A computational rule-based model of MAPK/ERK system regulation. Scientific Reports 16, 14437. doi:10.1038/s41598-026-44353-3. https://doi.org/10.1038/s41598-026-44353-3
  3. Das, J., Kardar, M., Chakraborty, A. K. (2009). Positive feedback regulation results in spatial clustering and fast spreading of active signaling molecules on a cell membrane. The Journal of Chemical Physics 130, 245102. doi:10.1063/1.3149861. https://doi.org/10.1063/1.3149861
  4. Das, J., Ho, M., Zikherman, J., Govern, C., Yang, M., Weiss, A., Chakraborty, A. K., Roose, J. P. (2009). Digital Signaling and Hysteresis Characterize Ras Activation in Lymphoid Cells. Cell 136, 337-351. doi:10.1016/j.cell.2008.11.051. https://doi.org/10.1016/j.cell.2008.11.051
  5. Markevich, N. I., Tsyganov, M. A., Hoek, J. B., Kholodenko, B. N. (2006). Long-range signaling by phosphoprotein waves arising from bistability in protein kinase cascades. Molecular Systems Biology 2, 61. doi:10.1038/msb4100108. https://doi.org/10.1038/msb4100108
  6. Huang, C. Y., Ferrell, J. E. (1996). Ultrasensitivity in the mitogen-activated protein kinase cascade. Proceedings of the National Academy of Sciences 93, 10078-10083. doi:10.1073/pnas.93.19.10078. https://doi.org/10.1073/pnas.93.19.10078
  7. Kocieniewski, P., Lipniacki, T. (2013). MEK1 and MEK2 differentially control the duration and amplitude of the ERK cascade response. Physical Biology 10, 035006. doi:10.1088/1478-3975/10/3/035006. https://doi.org/10.1088/1478-3975/10/3/035006
  8. Miller, E. F., Mallela, A., Neumann, J., Lin, Y. T., Hlavacek, W. S., Posner, R. G. (2026). Using PyBioNetFit to leverage qualitative and quantitative data in biological model parameterization and uncertainty quantification. Frontiers in Immunology 17. doi:10.3389/fimmu.2026.1663008. https://doi.org/10.3389/fimmu.2026.1663008
  9. Jang, D. M., Boxer, K., Ha, B. H., Tkacik, E., Levitz, T., Rawson, S., Metivier, R. J., Schmoker, A., Jeon, H., Eck, M. J. (2025). Cryo-EM structures of CRAF/MEK1/14-3-3 complexes in autoinhibited and open-monomer states reveal features of RAF regulation. Nature Communications 16, 8150. doi:10.1038/s41467-025-63227-2. https://doi.org/10.1038/s41467-025-63227-2
  10. Hundsdorfer, L., Muenkel, M., Aparicio-Yuste, R., Sanchez-Rendon, J. C., Gomez-Benito, M. J., Balmes, A., Schäffer, T. E., Velic, A., Yeh, Y.-T., Constantinou, I., Wright, K., Özbaykal Güler, G., Brokatzky, D., Maček, B., Mostowy, S., Bastounis, E. E. (2025). ERK activation waves coordinate mechanical cell competition leading to collective elimination via extrusion of bacterially infected cells. Cell Reports 44, 115193. doi:10.1016/j.celrep.2024.115193. https://doi.org/10.1016/j.celrep.2024.115193
  11. Dayoub, A., Fokin, A. I., Leonov, S., Gautreau, A. M., Alexandrova, A. Y. (2026). Oncogenic PIK3CA enhances collective migration of mammary epithelial cells through ERK wave propagation. Journal of Cell Science 139. doi:10.1242/jcs.264916. https://doi.org/10.1242/jcs.264916