Optimization of nonlinear dose- and concentration-response models utilizing evolutionary computation

Inclusion of Control Data in Fits to Concentration-Response Curves Improves Estimates of Half-Maximal Concentrations

Concentration-response curves, in which the effect of varying the concentration on the response of an assay is measured, are widely used to evaluate biological effects of chemical compounds. While National Center for Advancing Translational Sciences guidelines specify that readouts should be normalized by the controls, recommended statistical analyses do not explicitly fit to the control data. Here, we introduce a nonlinear regression procedure based on maximum likelihood estimation that determines parameters for the classical Hill equation by fitting the model to both the curve and the control data. Simulations show that the proposed procedure provides more precise parameters compared with previously prescribed practices. Analysis of enzymatic inhibition data from the COVID Moonshot demonstrates that the proposed procedure yields a lower asymptotic standard error for estimated parameters. Benefits are most evident in the analysis of the incomplete curves. We also find that Lenth's outlier detection method appears to determine parameters more precisely.

Evaluation of statistical approaches for association testing in noisy drug screening data

BACKGROUND

Identifying associations among biological variables is a major challenge in modern quantitative biological research, particularly given the systemic and statistical noise endemic to biological systems. Drug sensitivity data has proven to be a particularly challenging field for identifying associations to inform patient treatment.

RESULTS

To address this, we introduce two semi-parametric variations on the commonly used concordance index: the robust concordance index and the kernelized concordance index (rCI, kCI), which incorporate measurements about the noise distribution from the data. We demonstrate that common statistical tests applied to the concordance index and its variations fail to control for false positives, and introduce efficient implementations to compute p-values using adaptive permutation testing. We then evaluate the statistical power of these coefficients under simulation and compare with Pearson and Spearman correlation coefficients. Finally, we evaluate the various statistics in matching drugs across pharmacogenomic datasets.

CONCLUSIONS

We observe that the rCI and kCI are better powered than the concordance index in simulation and show some improvement on real data. Surprisingly, we observe that the Pearson correlation was the most robust to measurement noise among the different metrics.

A Universal Delayed Difference Model Fitting Dose-response Curves

PURPOSE

Dose-response curves, which fit a multitude of experimental data derived from toxicology, are widely used in physics, chemistry, biology, and other fields. Although there are many dose-response models for fitting dose-response curves, the application of these models is limited by many restrictions and lacks universality, so there is a need for a novel, universal dynamical model that can improve fits to various types of dose-response curves.

METHODS

We expand the hormetic Ricker model, taking the delay inherent in the dose-response into account, and develop a novel and dynamic delayed Ricker difference model (DRDM) to fit various types of dose-response curves. Furthermore, we compare the DRDM with other dose-response models to confirm that it can mimic different types of dose-response curves.

DATA ANALYSIS

By fitting various types of dose-response data sets derived from drug applications, disease treatment, pest control, and plant management, and comparing the imitative effect of the DRDM with other models, we find that the DRDM fits monotonic dose-response data well and, in most circumstances, the DRDM has a better imitative effect to non-monotonic dose-response data with hormesis than other models do.

RESULTS

The MSE of fits of the DRDM to S-shaped dose-response data (DS2-G) is not lower than those for four other models, but the MSE of fits to U-shaped (DS7) and inverted U-shaped dose-response data (DS10) were lower than for two other models. This means that the imitative effect of the DRDM is comparable to other models of monotonic dose-response data, but is a significant improvement compared to traditional models of non-monotonic dose-response data with hormesis.

CONCLUSION

We propose a novel dynamic model (DRDM) for fitting to various types of dose-response curves, which can reflect the dynamic trend of the population growth compared with traditional static dose-response models. By analyzing data, we have confirmed that the DRDM provides an ideal description of various dose-response observations and it can be used to fit a wide range of dose-response data sets, especially for hormetic data sets. Therefore, we conclude that the DRDM has a good universality for dose-response curve fitting.

Nonlinear Dose-Response Modeling of High-Throughput Screening Data Using an Evolutionary Algorithm

Nonlinear dose-response relationships exist extensively in the cellular, biochemical, and physiologic processes that are affected by varying levels of biological, chemical, or radiation stress. Modeling such responses is a crucial component of toxicity testing and chemical screening. Traditional model fitting methods such as nonlinear least squares (NLS) are very sensitive to initial parameter values and often had convergence failure. The use of evolutionary algorithms (EAs) has been proposed to address many of the limitations of traditional approaches, but previous methods have been limited in the types of models they can fit. Therefore, we propose the use of an EA for dose-response modeling for a range of potential response model functional forms. This new method can not only fit the most commonly used nonlinear dose-response models (eg, exponential models and 3-, 4-, and 5-parameter logistic models) but also select the best model if no model assumption is made, which is especially useful in the case of high-throughput curve fitting. Compared with NLS, the new method provides stable and robust solutions without sensitivity to initial values.

Current Methods for Quantifying Drug Synergism

The effectiveness of drug combinations for treatment of a variety of complex diseases is well established. "Drug cocktail" treatments are often prescribed to improve the overall efficacy, decrease toxicity, alter pharmacodynamics, etc in an overall treatment strategy. Specifically, if when combined, drugs interact in some way that causes the total effect to be greater than that predicted by their individual potencies, then drugs are considered synergistic. While there are established ways to quantify the impact of drug combinations clinically, it is an open challenge to quantitatively summarize a synergistic interaction. In this paper, we discuss an overview of the current statistical and mathematical methods for the study of drug combination effects, especially drug synergy quantification (where the interaction effect is not just detected, but quantified according to its magnitude). We first introduce two popular reference models for testing to null hypothesis of non-interaction for a combination, including the Bliss independence model and the Loewe additivity model. Then we discuss several methods for quantifying drug synergism. The advantages and disadvantages with these methods are also provided, and finally, we discuss important next directions in this area.

An Introduction to Terminology and Methodology of Chemical Synergy-Perspectives from Across Disciplines

The idea of synergistic interactions between drugs and chemicals has been an important issue in the biomedical world for over a century. As complex diseases, especially cancer, are being treated with various drug cocktails, understanding the interactions among these drugs is increasingly vital to ensuring successful treatment regimens. However, the idea of synergy is not limited to only the biomedical realm and these ideas have developed across many different disciplines, as well. In this review, we first discuss the various terminology surrounding the idea of synergy, providing a comprehensive list of terms defined across numerous disciplines. We then review the most common methodology for detection and quantification of synergy, including the two most prominent reference models for describing additive interactions: Loewe Additivity and Bliss Independence. We also discuss advantages and limitations to each method, with a focus on the Chou-Talalay Combination Index method. Finally, we describe how methods development and terminology have developed among disciplines outside of biomedicine and pharmacology, to synthesize the literature for readers.

Contextualizing Hepatocyte Functionality of Cryopreserved HepaRG Cell Cultures

Over the last decade HepaRG cells have emerged as a promising alternative to primary human hepatocytes (PHH) and have been featured in over 300 research publications. Most of these reports employed freshly differentiated HepaRG cells that require time-consuming culture (∼28 days) for full differentiation. Recently, a cryopreserved, predifferentiated format of HepaRG cells (termed here "cryo-HepaRG") has emerged as a new model that improves global availability and experimental flexibility; however, it is largely unknown whether HepaRG cells in this format fully retain their hepatic characteristics. Therefore, we systematically investigated the hepatocyte functionality of cryo-HepaRG cultures in context with the range of interindividual variation observed with PHH in both sandwich-culture and suspension formats. These evaluations uncovered a novel adaptation period for the cryo-HepaRG format and demonstrated the impact of extracellular matrix on cryo-HepaRG functionality. Pharmacologically important drug-metabolizing alleles were genotyped in HepaRG cells and poor metabolizer alleles for CYP2D6, CYP2C9, and CYP3A5 were identified and consistent with higher frequency alleles found in individuals of Caucasian decent. We observed liver enzyme inducibility with aryl hydrocarbon receptor, constitutive androstane receptor (CAR), and pregnane X receptor activators comparable to that of sandwich-cultured PHH. Finally, we show for the first time that cryo-HepaRG supports proper CAR cytosolic sequestration and translocation to hepatocyte nuclei in response to phenobarbital treatment. Taken together, these data reveal important considerations for the use of this cell model and demonstrate that cryo-HepaRG are suitable for metabolism and toxicology screening.

Beyond IC50s: Towards Robust Statistical Methods for in vitro Association Studies

Cell line cytotoxicity assays have become increasingly popular approaches for genetic and genomic studies of differential cytotoxic response. There are an increasing number of success stories, but relatively little evaluation of the statistical approaches used in such studies. In the vast majority of these studies, concentration response is summarized using curve-fitting approaches, and then summary measure(s) are used as the phenotype in subsequent genetic association studies. The curve is usually summarized by a single parameter such as the curve's inflection point (e.g. the EC/IC₅₀). Such modeling makes major assumptions and has statistical limitations that should be considered. In the current review, we discuss the limitations of the EC/IC₅₀ as a phenotype in association studies, and highlight some potential limitations with a simulation experiment. Finally, we discuss some alternative analysis approaches that have been shown to be more robust.

A comparison of association methods for cytotoxicity mapping in pharmacogenomics

Cytotoxicity assays of immortalized lymphoblastoid cell lines (LCLs) represent a promising new in vitro approach in pharmacogenomics research. However, previous studies employing LCLs in gene mapping have used simple association methods, which may not adequately capture the true differences in non-linear response profiles between genotypes. Two common approaches summarize each dose-response curve with either the IC50 or the slope parameter estimates from a hill slope fit and treat these estimates as the response in a linear model. The current study investigates these two methods, as well as four novel methods, and compares their power to detect differences between the response profiles of genotypes under a variety of different alternatives. The four novel methods include two methods that summarize each dose-response by its area under the curve, one method based off of an analysis of variance (ANOVA) design, and one method that compares hill slope fits for all individuals of each genotype. The power of each method was found to depend not only on the choice of alternative, but also on the choice for the set of dosages used in cytotoxicity measurements. The ANOVA-based method was found to be the most robust across alternatives and dosage sets for power in detecting differences between genotypes.

Zebrafish developmental screening of the ToxCast™ Phase I chemical library

Zebrafish (Danio rerio) is an emerging toxicity screening model for both human health and ecology. As part of the Computational Toxicology Research Program of the U.S. EPA, the toxicity of the 309 ToxCast™ Phase I chemicals was assessed using a zebrafish screen for developmental toxicity. All exposures were by immersion from 6-8 h post fertilization (hpf) to 5 days post fertilization (dpf); nominal concentration range of 1 nM-80 μM. On 6 dpf larvae were assessed for death and overt structural defects. Results revealed that the majority (62%) of chemicals were toxic to the developing zebrafish; both toxicity incidence and potency was correlated with chemical class and hydrophobicity (logP); and inter-and intra-plate replicates showed good agreement. The zebrafish embryo screen, by providing an integrated model of the developing vertebrate, compliments the ToxCast assay portfolio and has the potential to provide information relative to overt and organismal toxicity.

Ex-Vivo Modeling for Heritability Assessment and Genetic Mapping in Pharmacogenomics

The investigation of genetic factors that determine differential drug response is a key goal of pharmacogenomics (PGX), and relies on the often-untested assumption that differential response is heritable. While limitations in traditional study design often prohibit heritability (h²) estimates in PGX, new approaches may allow such estimates. We demonstrate an ex vivo model system to determine the h² of drug-induced cell killing and performed genome-wide analysis for gene mapping. The cytotoxic effect of 29 diverse chemotherapeutic agents on lymphoblastoid cell lines (LCLs) derived from family- and population-based cohorts was investigated. We used a high throughput format to determine cytotoxicity of the drugs on LCLs and developed a new evolutionary computation approach to fit response curves for each individual. Variance components analysis determined the h² for each drug response and a wide range of values was observed across drugs. Genome-wide analysis was performed using new analytical approaches. These results lay the groundwork for future studies to uncover genes influencing chemotherapeutic response and demonstrate a new computational framework for performing such analysis.