Frequency-Domain Response Analysis for Quantitative Systems Pharmacology Models

COMPUTING THE FREQUENCY RESPONSE OF BIOCHEMICAL NETWORKS: A PYTHON MODULE

In this paper, a set of Python methods is described that can be used to compute the frequency response of an arbitrary biochemical network given any input and output. Models can be provided in standard SBML or Antimony format. The code takes into account any conserved moieties so that this software can be used to also study signaling networks where moiety cycles are common. A utility method is also provided to make it easy to plot standard Bode plots from the generated results. The code also takes into account the possibility that the phase shift could exceed 180 degrees which can result in ugly discontinues in the Bode plot. In the paper, some of the theory behind the method is provided as well as some commentary on the code and several illustrative examples to show the code in operation. Illustrative examples include linear reaction chains of varying lengths and the effect of negative feedback on the frequency response.

Software License

MIT Open Source.

Availability

The code is available from https://github.com/sys-bio/frequencyResponse.

Optimization of Cancer Treatment in the Frequency Domain

Thorough exploration of alternative dosing frequencies is often not performed in conventional pharmacometrics approaches. Quantitative systems pharmacology (QSP) can provide novel insights into optimal dosing regimen and drug behaviors which could add a new dimension to the design of novel treatments. However, methods for such an approach are currently lacking. Recently, we illustrated the utility of frequency-domain response analysis (FdRA), an analytical method used in control engineering, using several generic pharmacokinetic-pharmacodynamic case studies. While FdRA is not applicable to models harboring ever increasing variables such as those describing tumor growth, studying such models in the frequency domain provides valuable insight into optimal dosing frequencies. Through the analysis of three distinct tumor growth models (cell cycle-specific, metronomic, and acquired resistance), we demonstrate the application of a simulation-based analysis in the frequency domain to optimize cancer treatments. We study the response of tumor growth to dosing frequencies while simultaneously examining treatment safety, and found for all three models that above a certain dosing frequency, tumor size is insensitive to an increase in dosing frequency, e.g., for the cell cycle-specific model, one dose per 3 days, and an hourly dose yield the same reduction of tumor size to 3% of the initial size after 1 year of treatment. Additionally, we explore the effect of drug elimination rate changes on the tumor growth response. In summary, we show that the frequency-domain view of three models of tumor growth dynamics can help in optimizing drug dosing regimen to improve treatment success.

In vitro and in silico analysis of the effects of D2 receptor antagonist target binding kinetics on the cellular response to fluctuating dopamine concentrations

Background and Purpose

Target binding kinetics influence the time course of the drug effect (pharmacodynamics) both (i) directly, by affecting the time course of target occupancy, driven by the pharmacokinetics of the drug, competition with endogenous ligands and target turnover, and (ii) indirectly, by affecting signal transduction and homeostatic feedback. For dopamine D₂ receptor antagonists, it has been hypothesized that fast receptor binding kinetics cause fewer side effects, because part of the dynamics of the dopaminergic system is preserved by displacement of these antagonists.

Experimental Approach

Target binding kinetics of D₂ receptor antagonists and signal transduction after dopamine and D₂ receptor antagonist exposure were measured in vitro. These data were integrated by mechanistic modelling, taking into account competitive binding of endogenous dopamine and the antagonist, the turnover of the second messenger cAMP and negative feedback by PDE turnover.

Key Results

The proposed signal transduction model successfully described the cellular cAMP response for 17 D₂ receptor antagonists with widely different binding kinetics. Simulation of the response to fluctuating dopamine concentrations revealed that a significant effect of the target binding kinetics on the dynamics of the signalling only occurs at endogenous dopamine concentration fluctuations with frequencies below 1 min⁻¹.

Conclusions and Implications

Signal transduction and feedback are important determinants of the time course of drug effects. The effect of the D₂ receptor antagonist dissociation rate constant (k_off) is limited to the maximal rate of fluctuations in dopamine signalling as determined by the dopamine k_off and the cAMP turnover.

Outside-In Systems Pharmacology Combines Innovative Computational Methods With High-Throughput Whole Vertebrate Studies

To advance the systems approach in pharmacology, experimental models and computational methods need to be integrated from early drug discovery onward. Here, we propose outside‐in model development, a model identification technique to understand and predict the dynamics of a system without requiring prior biological and/or pharmacological knowledge. The advanced data required could be obtained by whole vertebrate, high‐throughput, low‐resource dose‐exposure‐effect experimentation with the zebrafish larva. Combinations of these innovative techniques could improve early drug discovery.