Understanding biomolecular systems is important both for the analysis of naturally occurring systemsas well as for the design of new ones. However, mathematical tools for analysis of such complex systems are generally lacking. Here, we present an application of the method of sinusoidal-input describing function for the analysis of such a system. Using this technique, we approximate the input-output response of a simple biomolecular signaling system both computationally and analytically. We systematically investigate the dependence of this approximation on system parameters. Finally, we estimate the error involved in this approximation. These results can help in establishing a framework for analysis of biomolecular systems through the use of simplified models .
Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of analytical and computational approaches, we adapt and develop the method of describing functions to represent the input-output responses of biomolecular signaling systems. We approximate representative systems exhibiting various saturating and hysteretic dynamics in a way that is better than the standard linearization. Further, we develop analytical upper bounds for the computational error estimates. Finally, we use these error estimates to augment the limit cycle analysis with a simple and quick way to bound the predicted oscillation amplitude. These results provide system approximations that can provide more insight into the local behaviour of these systems, compute responses to other periodic inputs, and to analyze limit cycles .
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Understanding biomolecular systems is important both
Mathematical methods provide useful framework
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of naturally occurring systemsas well as for the design of
and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop
R
However, mathematical tools for analysis of such complex systems are generally lacking. Here, we present an application of
Using a combination of analytical and computational approaches, we adapt and develop
R
sinusoidal-input describing function for the analysis of such a system. Using this technique, we approximate the
describing functions to represent the
R
response of a simple biomolecular signaling system both computationally and analytically. We systematically investigate the dependence of this approximation on system parameters. Finally, we estimate the error involved in this approximation. These results can help in establishing a framework for analysis of biomolecular systems through the use of simplified models
responses of biomolecular signaling systems. We approximate representative systems exhibiting various saturating and hysteretic dynamics in a way that is better than the standard linearization. Further, we develop analytical upper bounds for the computational error estimates. Finally, we use these error estimates to augment the limit cycle analysis with a simple and quick way to bound the predicted oscillation amplitude. These results provide system approximations that can provide more insight into the local behaviour of these systems, compute responses to other periodic inputs, and to analyze limit cycles