A nested bistable module within a negative feedback loop ensures different types of oscillations in signaling systems

Marrone, Juan Ignacio; Sepulchre, Jacques-Alexandre; Ventura, Alejandra C.

doi:10.1038/s41598-022-27047-4

Cited by 4 publications

(2 citation statements)

References 57 publications

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“…The parameter set we chose comes from our previous work ( Marrone et al, 2023 ), where the DP cycle displayed bistability when scanning the input kinase. This was a necessary condition to obtain oscillations in the motifs studied and valuable for this work since the presence of oscillations in the model and bistability in each of the two modules (emergent through SN or fold bifurcations) will test the pseudo-nullclines method.…”

Section: Resultsmentioning

confidence: 99%

Pseudo-nullclines enable the analysis and prediction of signaling model dynamics

Marrone,

Sepulchre,

Ventura

2023

Front. Cell Dev. Biol.

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A powerful method to qualitatively analyze a 2D system is the use of nullclines, curves which separate regions of the plane where the sign of the time derivatives is constant, with their intersections corresponding to steady states. As a quick way to sketch the phase portrait of the system, they can be sufficient to understand the qualitative dynamics at play without integrating the differential equations. While it cannot be extended straightforwardly for dimensions higher than 2, sometimes the phase portrait can still be projected onto a 2-dimensional subspace, with some curves becoming pseudo-nullclines. In this work, we study cell signaling models of dimension higher than 2 with behaviors such as oscillations and bistability. Pseudo-nullclines are defined and used to qualitatively analyze the dynamics involved. Our method applies when a system can be decomposed into 2 modules, mutually coupled through 2 scalar variables. At the same time, it helps track bifurcations in a quick and efficient manner, key for understanding the different behaviors. Our results are both consistent with the expected dynamics, and also lead to new responses like excitability. Further work could test the method for other regions of parameter space and determine how to extend it to three-module systems.

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Section: Resultsmentioning

confidence: 99%

Pseudo-nullclines enable the analysis and prediction of signaling model dynamics

Marrone,

Sepulchre,

Ventura

2023

Front. Cell Dev. Biol.

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“…In [55], the stable limit cycle has been observed in autocatalytic systems through the characteristics of the Hopf bifurcation. In, [56], the exhibition of limit cycling oscillations has been observed in Biological Oscillators having both positive and negative feedbacks. The authors, [57], have observed in natural systems a closed loop as in a stable limit cycle through reviewing empirical dynamic modelling.…”

Section: Introductionmentioning

confidence: 99%

Investigation of the Existence of Limit Cycles in Multi Variable Nonlinear Systems with Special Attention to 3X3 Systems

Patra

Patnaik

2023

International Journal of Applied Mathematics, Computational Science and Systems Engineering

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The proposed work addresses the dynamics of a general system and explores the existence of limit cycles (LC) in multi-variable Non-linear systems with special attention to 3x3 nonlinear systems. It presents a simple, systematic analytical procedure as well as a graphical technique that uses geometric tools and computer graphics for the prediction of limit cycling oscillations in three-dimensional systems having both explicit and implicit nonlinear functions. The developed graphical method uses the harmonic balance/harmonic linearization for simplicity of discussion which provides a clear and lucid understanding of the problem and considers all constraints, especially the simultaneous intersection of two straight lines & one circle for determination of limit cycling conditions. The method of analysis is made simpler by assuming the whole system exhibits the limit cycling oscillations predominantly at a single frequency. The discussions made either analytically/graphically are substantiated by digital simulation by a developed program as well as by the use of the SIMULINK Toolbox of MATLAB Software.

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Suppression Limit Cycles in 2x2 Nonlinear Systems with Memory Type Nonlinearities

Patra,

Kar,

Patnaik

2024

Design, Construction, Maintenance

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For several decades, the importance and weight-age of prediction of nonlinear self-sustained oscillations or Limit Cycles (LC) and their quenching by signal stabilization have been discussed, which is confined to Single Input and Single Output (SISO) systems. However, for the last five to six decades, the analysis of 2x2 Multi Input and Multi Output (MIMO) Nonlinear Systems gained importance in which a lot of literature available. In recent days’ people have started discussing suppression of LC which limits the performance of most of the physical systems in the world. It is a formidable task to suppress the limit cycles for 2x2 systems with memory type nonlinearity in particular. Backlash is one of the nonlinearities commonly occurring in physical systems that limit the performance of speed and position control in robotics, automation industry and other occasions like Load Frequency Control (LFC) in multi area power systems. The feasibility of suppression of such nonlinear self-oscillations has been explored in case of the memory type nonlinearities. Backlash is a common memory type nonlinearity which is an inherent Characteristic of a Governor, used for usual load frequency control of an inter-connected power system and elsewhere. Suppression LC using pole placement technique through arbitrary selection and optimal selection of feedback Gain Matrix K with complete state controllability condition and Riccati Equation respectively and is done through state feedback. The Governing equation is d/dt [X(t)] =(A-BK) X: which facilitates the determination of feedback gain matrix K for close loop Poles / Eigen values placement where the limit cycles are suppressed/eliminated in the general multi variable systems. The complexity involved in implicit non-memory type or memory type nonlinearities, it is extremely difficult to formulate the problem for 2x2 systems. Under this circumstance, the harmonic linearization/harmonic balance reduces the complexity considerably. Still the analytical expressions are so complex which loses the insight into the problem particularly for memory type nonlinearity in 2x2 system and the method is made further simpler assuming a 2x2 system exhibits the LC predominately at a single frequency. Hence in the proposed work an alternative attempt has been made to develop a graphical method for the prediction of Limit Cycling Oscillations in 2x2 memory type Nonlinear systems which not only reduces the complexity of formulations but also facilitates clear insight into the problem and its solution. The present techniques are well illustrated with an example and validated / substantiated by digital simulation (developed program using MATLAB codes) and use of SIMULINK Tool Box of MATLAB software. The present work has the brighter future scope of: Adapting the Techniques like Signal Stabilization and Suppression LC for 3x3 or higher dimensional nonlinear systems through an exhaustive analysis. Analytical/Mathematical methods may also be developed for signal stabilization using both deterministic and random signals based on Dual Input Describing function (DIDF) and Random Input Describing Function (RIDF) respectively. The phenomena of Synchronization and De-synchronization can be observed/identified analytically using Incremental Input Describing Function (IDF), which can also be validated by digital simulations.

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A nested bistable module within a negative feedback loop ensures different types of oscillations in signaling systems

Cited by 4 publications

References 57 publications

Pseudo-nullclines enable the analysis and prediction of signaling model dynamics

Pseudo-nullclines enable the analysis and prediction of signaling model dynamics

Investigation of the Existence of Limit Cycles in Multi Variable Nonlinear Systems with Special Attention to 3X3 Systems

Suppression Limit Cycles in 2x2 Nonlinear Systems with Memory Type Nonlinearities

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