Influence of parameter perturbations on the reachability of therapeutic target in systems with switchings
Abstract Background Examination 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 th...
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doaj-1ba269284eaf4c9bbc3871e0dc9471402020-11-25T00:26:08ZengBMCBioMedical Engineering OnLine1475-925X2017-08-0116S112410.1186/s12938-017-0360-9Influence of parameter perturbations on the reachability of therapeutic target in systems with switchingsMagdalena Ochab0Krzysztof Puszynski1Andrzej Swierniak2Silesian University of TechnologySilesian University of TechnologySilesian University of TechnologyAbstract Background Examination 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. Results The 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. Conclusions Systems 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.http://link.springer.com/article/10.1186/s12938-017-0360-9Biological modelSwitchesPiece-wise continuous nonlinear models |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Magdalena Ochab Krzysztof Puszynski Andrzej Swierniak |
spellingShingle |
Magdalena Ochab Krzysztof Puszynski Andrzej Swierniak Influence of parameter perturbations on the reachability of therapeutic target in systems with switchings BioMedical Engineering OnLine Biological model Switches Piece-wise continuous nonlinear models |
author_facet |
Magdalena Ochab Krzysztof Puszynski Andrzej Swierniak |
author_sort |
Magdalena Ochab |
title |
Influence of parameter perturbations on the reachability of therapeutic target in systems with switchings |
title_short |
Influence of parameter perturbations on the reachability of therapeutic target in systems with switchings |
title_full |
Influence of parameter perturbations on the reachability of therapeutic target in systems with switchings |
title_fullStr |
Influence of parameter perturbations on the reachability of therapeutic target in systems with switchings |
title_full_unstemmed |
Influence of parameter perturbations on the reachability of therapeutic target in systems with switchings |
title_sort |
influence of parameter perturbations on the reachability of therapeutic target in systems with switchings |
publisher |
BMC |
series |
BioMedical Engineering OnLine |
issn |
1475-925X |
publishDate |
2017-08-01 |
description |
Abstract Background Examination 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. Results The 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. Conclusions Systems 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. |
topic |
Biological model Switches Piece-wise continuous nonlinear models |
url |
http://link.springer.com/article/10.1186/s12938-017-0360-9 |
work_keys_str_mv |
AT magdalenaochab influenceofparameterperturbationsonthereachabilityoftherapeutictargetinsystemswithswitchings AT krzysztofpuszynski influenceofparameterperturbationsonthereachabilityoftherapeutictargetinsystemswithswitchings AT andrzejswierniak influenceofparameterperturbationsonthereachabilityoftherapeutictargetinsystemswithswitchings |
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