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Sensitivity Analysis in Control versus Biology

Posted by alxholland on 30 Jun 2011 at 11:53 GMT

The complete analysis is available at:

Control in the realm of biology, and the more recent treatment of biological systems within the field of control theory, represent different approaches which should be clearly distinguished. Importantly, the mere presence of control mechanisms in biological systems does not ensure that the mathematical analysis borrows its fundamental principles from the control engineering field. The PLOS Biology article from Reeves and Fraser 2009 [1], as well as the PLOS article from Lander et al. [2] cited therein, both reinforce this amalgam, and the current failure of biologists to bridge the gap with engineers. These articles, however, may provide a long-awaited opportunity for clarifications.

The sensitivity analysis described by Reeves and Fraser [1] does not borrow its fundamentals from control theory. Sensitivity analysis in the context of control theory assumes the existence of a controller distinct from the controlled system ( [3] §3.4). [...]

In the absence of a controller, the system stability and dynamic characteristics can nonetheless be investigated using a control-theoretic analysis. In this direction, using the model presented in Reeves, we describe the process for the analysis of such a system. [...]

Interestingly, for this example, the Reeves and Fraser Sensitivity Coefficient SC is equivalent the normalized gain resulting from the control analysis. This reinforces the idea that the biology ‘Sensitivity Coefficient’ should be re-named as a ‘normalized gain’ to suit the engineering classifications. But, as a gain, this parameter should be evaluated using dynamic model analysis (control approach) and not linearization around the steady-state.

The two examples discussed above show the advantages of the control approach compared to the mathematical sensitivity analysis. The emergent efforts ( [8–10]) to bridge the gap between biology and engineering relies on:
• using the concepts of sensitivity and robustness solely in the control theoretic sense, which requires the clear definitions of control systems,
• using an input-output description of the biological system with clearly defined constraints,
• working with the concept of gain in lieu of the sensitivity coefficient,
• formulating the control stability and convergence conditions to gain insights on the system parameter values.

No competing interests declared.