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Updated: Apr 18, 2026

Spatiotemporal Control of Protein Activity through Optogenetic Allosteric Regulation
Published on: October 4, 2024
MAPK's networks and their capacity for multistationarity due to toric steady states
Mercedes Pérez Millán1, Adrián G Turjanski2
1Dto. de Matemática, FCEN, Universidad de Buenos Aires, Ciudad Universitaria, Pab. I, C1428EGA Buenos Aires, Argentina; Dto. de Ciencias Exactas, CBC, Universidad de Buenos Aires, Ramos Mejía 841, C1405CAE Buenos Aires, Argentina.
Abstract:
Mitogen-activated protein kinase (MAPK) signaling pathways play an essential role in the transduction of environmental stimuli to the nucleus, thereby regulating a variety of cellular processes, including cell proliferation, differentiation and programmed cell death. The components of the MAPK extracellular activated protein kinase (ERK) cascade represent attractive targets for cancer therapy as their aberrant activation is a frequent event among highly prevalent human cancers. MAPK networks are a model for computational simulation, mostly using ordinary and partial differential equations. Key results showed that these networks can have switch-like behavior, bistability and oscillations. In this work, we consider three representative ERK networks, one with a negative feedback loop, which present a binomial steady state ideal under mass-action kinetics. We therefore apply the theoretical result present in to find a set of rate constants that allow two significantly different stable steady states in the same stoichiometric compatibility class for each network. Our approach makes it possible to study certain aspects of the system, such as multistationarity, without relying on simulation, since we do not assume a priori any constant but the topology of the network. As the performed analysis is general it could be applied to many other important biochemical networks.
Insights
This study identifies rate constants for Mitogen-activated protein kinase (MAPK) networks, enabling two stable states for cancer therapy targets. The findings allow for studying multistationarity without complex simulations.
Area of Science:
- Biochemistry
- Systems Biology
- Computational Biology
Background:
- Mitogen-activated protein kinase (MAPK) pathways regulate crucial cellular processes like proliferation and cell death.
- Aberrant activation of the extracellular signal-regulated kinase (ERK) cascade is common in many human cancers, making it a therapeutic target.
- MAPK networks are often modeled using differential equations, revealing behaviors like bistability and oscillations.
Purpose of the Study:
- To determine rate constants for specific ERK networks that exhibit multistationarity.
- To apply theoretical results to identify conditions for two distinct stable steady states in biochemical networks.
- To enable the study of multistationarity without relying on computational simulations.
Main Methods:
- Analysis of three representative ERK networks, including one with negative feedback.
- Application of theoretical results for mass-action kinetics to find rate constants.
- Focus on network topology rather than specific constant values to ensure generality.
Main Results:
- Identified sets of rate constants for three ERK networks that support two significantly different stable steady states.
- Demonstrated that multistationarity can be achieved within the same stoichiometric compatibility class.
- Validated the theoretical approach for predicting network behavior.
Conclusions:
- The developed approach allows for the study of multistationarity in biochemical networks, such as ERK pathways, without direct simulation.
- This method provides a general framework applicable to various biological networks with potential implications for cancer therapy.
- Understanding bistability in MAPK signaling could lead to novel therapeutic strategies targeting cancer.
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