Influence of parameter perturbations on the reachability of therapeutic target in systems with switchings

Abstract

BackgroundExamination of physiological processes and the influences of the drugs on them can be efficiently supported by mathematical modeling. One of the biggest problems is related to the exact fitting of the parameters of a model. Conditions inside the organism change dynamically, so the rates of processes are very difficult to estimate. Perturbations in the model parameters influence the steady state so a desired therapeutic goal may not be reached. Here we investigate the effect of parameter deviation on the steady state in three simple models of the influence of a therapeutic drug on its target protein. Two types of changes in the model parameters are taken into account: small perturbations in the system parameter values, and changes in the switching time of a specific parameter. Additionally, we examine the systems response in case of a drug concentration decreasing with time.ResultsThe models which we analyze are simplified, because we want to avoid influences of complex dynamics on the results. A system with a negative feedback loop is the most robust and the most rapid, so it requires the largest drug dose but the effects are observed very quickly. On the other hand a system with positive feedback is very sensitive to changes, so small drug doses are sufficient to reach a therapeutic target. In systems without feedback or with positive feedback, perturbations in the model parameters have a bigger influence on the reachability of the therapeutic target than in systems with negative feedback. Drug degradation or inactivation in biological systems enforces multiple drug applications to maintain the level of a drug’s target under the desired threshold. The frequency of drug application should be fitted to the system dynamics, because the response velocity is tightly related to the therapeutic effectiveness and the time for achieving the goal.ConclusionsSystems with different types of regulation vary in their dynamics and characteristic features. Depending on the feedback loop, different types of therapy may be the most appropriate, and deviations in the model parameters have different influences on the reachability of the therapeutic target.

Application of Sensitivity Analysis to Discover Potential Molecular Drug Targets

“…The vector , which is a control vector in systems theory, represents external or internal excitation of the system. It is worth noting that the function does not have to be continuous and may contain stochastic switches representing random signaling events [ 6 ].…”

“…Computational models of dynamics of intracellular processes have been extensively used in recent years as a support tool in unveiling the structure of regulatory networks [ 1 , 2 ], crosstalk between signaling pathways [ 3 , 4 ], analysis of therapeutic drug effects [ 5 , 6 , 7 ] or in studies focused on general properties of such systems [ 8 , 9 , 10 ]. They facilitate preliminary testing of biological hypotheses and provide insights into systems that, for various reasons, cannot be explored experimentally.…”