Applying quantitative and systems pharmacology to drug development and beyond: An introduction to clinical pharmacologists

Abstract

Quantitative and systems pharmacology (QSP) is an innovative and integrative approach combining physiology and pharmacology to accelerate medical research. This review focuses on QSP’s pivotal role in drug development and its broader applications, introducing clinical pharmacologists/researchers to QSP’s quantitative approach and the potential to enhance their practice and decision-making. The history of QSP adoption reveals its impact in diverse areas, including glucose regulation, oncology, autoimmune disease, and HIV treatment. By considering receptor–ligand interactions of various cell types, metabolic pathways, signaling networks, and disease biomarkers simultaneously, QSP provides a holistic understanding of interactions between the human body, diseases, and drugs. Integrating knowledge across multiple time and space scales enhances versatility, enabling insights into personalized responses and general trends. QSP consolidates vast data into robust mathematical models, predicting clinical trial outcomes and optimizing dosing based on preclinical data. QSP operates under a “learn and confirm paradigm,” integrating experimental findings to generate testable hypotheses and refine them through precise experimental designs. An interdisciplinary collaboration involving expertise in pharmacology, biochemistry, genetics, mathematics, and medicine is vital. QSP’s utility in drug development is demonstrated through integration in various stages, predicting drug responses, optimizing dosing, and evaluating combination therapies. Challenges exist in model complexity, communication, and peer review. Standardized workflows and evaluation methods ensure reliability and transparency.

Introduction

Quantitative and systems pharmacology (QSP) represents an innovative and quantitative approach that integrates the disciplines of physiology and pharmacology. This review introduces QSP for clinical pharmacologists actively engaged in drug development, dosing decisions, and personalized medicine. The primary focus of this review centers on the role of QSP in drug development, although it is important to acknowledge the potential broader applications of this approach. By utilizing QSP, researchers and practitioners can attain a more profound comprehension of the intricate interactions between the human body, diseases, and drugs, thereby facilitating the development of more effective treatments and ultimately yielding improved patient outcomes.

Enhancing Drug Development through Quantitative and Systems Pharmacology: Addressing Inefficiencies and Improving Integration

The majority of drugs fail in the clinical trial development process.[1] Various strategies have been proposed to enhance the productivity of research and development. One potential approach is to improve our understanding of individual drugs and the overall pipeline of a company by integrating mechanistic and clinical data using QSP models.[2] QSP has been defined as the quantitative analysis of the dynamic interactions between drugs and a biological system that aims to understand the behavior of the system as a whole, as opposed to the behavior of its individual constituents.[3] The major advantage of the QSP approach is the ability to integrate data and knowledge, and this is often thought of as “horizontal” and “vertical” integration.[4] Horizontal integration entails going beyond a narrow focus on specific pathways or targets and understanding them within a broader context by simultaneously considering multiple receptors, cell types, metabolic pathways, or signaling networks. Such comprehensive integration is crucial because target manipulation does not occur in isolation in drug development. Instead, it occurs within intricate multicomponent networks governed by strong homeostatic mechanisms. Vertical integration involves integrating knowledge by spanning multiple time and space scales. For example, a QSP model may capture hourly variations in plasma glucose in response to intravenous glucose challenge and slower variations (months to years) in glucose regulation as represented by HbA1c levels. Furthermore, QSP models are versatile, and they are developed to encompass both the individual and population scales. In other words, these models have the capability to depict the physiological dynamics unique to an individual patient while also taking into account variability across a population by adjusting physiological parameters accordingly. This approach allows researchers to gain insights into personalized responses and general trends, making QSP an invaluable tool in understanding and predicting drug actions at different levels of granularity.

Pharmacokinetics (PK) and pharmacodynamics (PD) form the foundational pillars of drug development, encompassing the intricate processes of drug absorption, distribution, metabolism, and elimination and their interactions with specific drug targets to produce desired therapeutic effects. In recent times, the integration of computational modeling, notably the innovative QSP approach, has witnessed a surge in its application for predicting PK and PD properties during the drug development process. Unlike traditional statistical or empirical modeling, QSP stands out by consolidating a vast array of data and knowledge from diverse sources into meticulous and robust mathematical models.

A well-designed QSP model possesses the capacity to predict potential clinical trial outcomes (such as determining the optimal minimum effective dosage based on preclinical data) and enables the execution of “what-if” experiments (for example, predicting the effects of combining drugs with different mechanisms of action). QSP models enable the scientific teams to quantitatively evaluate their assumptions and to identify any inconsistencies found within the data. This is achievable due to the mathematical nature of the models rather than being reliant on verbal descriptions. Moreover, QSP models are mechanistic rather than empirical. To illustrate, let’s consider the results from an intraVenous Glucose Tolerance Test (IVGTT). We could create an empirical model that simply depicts plasma glucose over time [Figure 1]. However, we have the option to use well-established physiological principles to develop a theory of glucose disposition. This approach allows us to make predictions for future challenge experiments, conduct “what-if” experiments, and even incorporate additional physiological aspects into the model.

Figure 1.

Experimental data can be described in various ways. Here, we show (the mockup) an experiment where glucose is infused in the plasma of subjects, and its clearance dynamics are measured

In the realm of drug development, physiological modeling operates under a paradigm of “learn and confirm,” where experimental findings are systematically integrated into the model to generate testable hypotheses, which can be further refined through precise experimental designs. QSP represents a holistic system-level approach that transcends the narrow focus on individual genes, molecules, or pathways, mandating interdisciplinary collaboration among experts spanning diverse domains, including pharmacology, biochemistry, genetics, mathematics, and medicine.

Past, Present, and Future Outlook of Quantitative and Systems Pharmacology

Over the years, several publications in the scientific literature have shown mathematical models that combine physiology and pharmacology, addressing various areas of basic science, health care, and drug discovery. These models have been published under different topics such as “mathematical biology,” “in silico modeling,” or “systems biology.” They have significantly contributed to enhancing our knowledge of diverse physiological processes, including glucose regulation,[5] neuronal signaling,[6] electrolyte balance,[7] and HIV treatment.[8]

Mathematical modeling has been a valuable tool in drug development, even though it has not always been formally integrated within pharmaceutical companies. Instead, it has been employed based on specific needs and the availability of internal or external modeling groups to support decision-making processes. The challenges of expanding the adoption and scale of mathematical modeling in drug development were highlighted in a 2004 publication,[9] which emphasized the field’s status and potential hurdles.

In 2011, a significant milestone was reached with the NIH white paper[3] by the QSP workshop group, which brought together various research activities in drug development under the term “QSP.” This initiative aimed to revitalize traditional pharmacology by delving into the mechanisms of drug action, ultimately paving the way for improved decisions in drug development. A vision for the future of QSP was further outlined during a symposium of QSP scientists and leaders in 2016, focusing on building a community comprising pharmacologists and other scientists working collaboratively to propel the field forward.[10]

Drug development benefits from mechanistic and statistical approaches to understand drug PK and PD along the pipeline.[11,12] Physiology-based PK models are particularly helpful in providing mechanistic insights into complex and novel modalities, estimating drug distribution in remote compartments (e.g., the lung), and accommodating different populations (such as pediatrics, elderly, and those with impaired renal function).[13,14,15,16,17] These models describe PK in a mechanistic way in order to support key decision-making but do not incorporate the physiology of the concerned disease or PD of concerned drugs unless necessary. These models also use similar processes and are considered to be QSPs by most groups.[18]

Mechanistic QSP approaches have seen a remarkable surge in adoption within drug development and academic research. QSP is now extensively utilized in diverse drug development projects, with several literature[19,20,21,22,23,24] highlighting its substantial impact. Particularly, in the realm of emerging modalities such as antibody drug conjugates, T-cell dependent bispecifics, and cell and Gene THERAPIES, QSP can play a pivotal role. The complex interactions between these interventions and physiology demand a thorough understanding, making QSP an invaluable tool in advancing these drug development programs.

In addition to its prominent role in drug development, QSP extends its applications to inform health care and life sciences. It can align with increasingly significant technologies such as physiological monitors, wearable devices, personalized medicine, and artificial intelligence-informed health care. By leveraging QSP, health-care professionals and researchers can gain valuable insights into the intricate relationships between interventions and patient physiology, ultimately contributing to more effective and personalized health-care strategies. This broader utility of QSP showcases its potential to revolutionize various aspects of health care and life sciences beyond traditional drug development.

Quantitative and Systems Pharmacology Approach and Model Structure – Diabetes as an Exemplar

In QSP, sophisticated mathematical models, frequently represented as Ordinary Differential Equations (ODEs), are formulated to capture the intricate mechanistic details of pathophysiology. These models encompass data from various scales, encompassing both a “top-down” clinical perspective (e.g., plasma HbA1c and glucose and in a model of diabetes) and a “bottom-up” approach (e.g., rates of insulin secretion by the pancreas and glucose uptake in muscles). The level of granularity within these models, including the explicit incorporation of intracellular signaling pathways, is contingent on the specific objectives of the model. Previous perspectives have addressed design considerations and the evolutionary progress of a widely utilized mathematical model for glucose regulation founded on fundamental physiological principles.[5,25,26]

Establishing Project Objectives and Scope

In a study by Bergman,[5] the authors build a mathematical model that is able to describe the return to baseline plasma glucose levels after glucose injection. Drawing upon a fundamental comprehension of physiology, their “mental model” of plasma glucose regulation encompassed the inflow (input) and outflow (clearance) of glucose from the plasma into distinct physiological compartments, such as the muscles, liver, and brain. Further, multiple hormones, including insulin and glucagon, regulate the glucose flux across these compartments. Considering various complexities, the modelers proposed the minimal physiological aspects necessary to achieve their specific goal, which included monitoring the plasma glucose time dynamics postinjection. Within this model, they identified crucial “states,” namely plasma insulin, plasma glucose, and interstitial (remote) insulin, as essential components.

Describing Biological Mechanisms

The model’s relationships between different states are often visually represented using diagrams that provide a clear depiction of the tracked states and the flow of inputs into and outputs out of them. For example, the model monitors plasma glucose (measured in mg/dL) and takes into account various sources of input, such as oral ingestion or glucose injection (measured in mg/dL/min) and endogenous glucose production from the liver (measured in mg/dL/min). Plasma glucose can be cleared through mechanisms that are either insulin-dependent or insulin-independent, both measured in mg/dL/min. These relationships are translated into mathematical equations that incorporate parameters known as rate constants, which serve to connect the different states within the model [Figure 2].

Figure 2.

Approach to developing a mechanistic model. Understanding the physiology by laying out the compartments and fluxes of interest[5] under creative commons attribution license). This is then converted to a “model diagram” with a clear demarcation of compartments and marking glucose fluxes across compartments. The last panel shows the conversion of this understanding into mathematical equations which can be quantified

Capturing the Model Behaviors and Building Confidence

In the original publication authored by Bergman and Cobelli in 1979, experiments were conducted on healthy dogs.[25] They received various glucose infusions (ranging from 100 to 300 mg/kg over 1 min), and their plasma glucose and plasma insulin levels were regularly measured for the subsequent 120 min. This experimental data played a crucial role in validating the mechanistic model. The model parameters associated with transfer rates, clearance rates, and insulin sensitivity were determined based on physiological knowledge and the collected experimental data (commonly known as “model calibration”). The success of this model in accurately representing the glucose infusion data, particularly by explicitly incorporating the subjects’ insulin sensitivity, has rendered it an invaluable tool for interpreting clinical glucose infusion experiments. To enhance the model’s accuracy, additional refinements were introduced by this and other research groups. These refinements involved integrating important aspects of glucose regulation, such as biphasic insulin secretion by the pancreas, the influence of glucagon, and the impact of exercise. These improvements have further solidified the model’s ability to capture behaviors related to glucose regulation and have increased researchers’ confidence in its utility for studying and interpreting clinical glucose infusion studies.

Challenges in Model Complexity

As outlined in the aforementioned study,[5] modeling teams typically start with a simple physiological model to address the specific research question and gradually introduce complexity as needed. Nevertheless, numerous models have been created to address even more intricate inquiries in diabetes research, encompassing additional mediators such as glucagon and GLP-1, incorporating extra compartments (e.g., kidney) to account for urinary glucose excretion, introducing further behaviors such as long-term disease progression, response to exogenous insulin, and response to weight loss, and considering additional disease conditions, such as both type 1 and type 2 diabetes.[27,28,29] These expanded models aim to provide a more comprehensive and detailed understanding of the complex dynamics involved in diabetes, offering valuable insights into various aspects of the disease and its management. As scope and complexity of physiological behavior to be reproduced in a model increase, so does the model’s overall complexity.

For instance, a comprehensive model designed to understand the progression of type 1 diabetes involves simulating the evolution of the disease in a “nonobese diabetic” mouse model. This model, published by Shoda et al. in 2010, incorporates the immunological factors contributing to type 1 diabetes, including diverse cytokines, immune cells, and a detailed representation of islets of the pancreas. Its development aimed to facilitate the testing of hypotheses for novel drug development in type 1 diabetes.[30,31]

With the emergence of models exhibiting varying levels of complexity and physiological representations, the field has made efforts to propose standardized workflows and evaluation methods. These endeavors are undertaken to ensure that these models have a significant impact on decision-making processes related to diabetes research and health-care management. Standardized approaches enable better comparison and validation of models, ultimately enhancing their credibility and utility in advancing our understanding of diabetes and its treatment.[32,33,34]

Quantitative and Systems Pharmacology Case Studies in Drug Development

Utility of quantitative and systems pharmacology in developing multiple sodium-glucose cotransporter 2 inhibitors

The application of QSP approaches in drug development has yielded significant benefits across various therapeutic areas. Specifically, mechanistic models, such as the one published by Bergman et al.,[5] have played a crucial role in the development of sodium-glucose cotransporter 2 (SGLT2) inhibitors for diabetes. These inhibitors, utilized in the treatment of type 2 diabetes, function by blocking the action of SGLT2, which is responsible for glucose reabsorption in the kidneys. To exemplify the impact of mechanistic modeling in the development of SGLT2 inhibitors, we review published studies that demonstrate how this QSP approach contributed to decision-making and increased understanding across different companies and specific research questions.

One notable study by Fediuk et al. in 2021[35] provides a comprehensive outline of modeling techniques that significantly improved the efficiency and expediency of decision-making during the development of ertugliflozin, an SGLT2 inhibitor. The study highlighted the implementation of a meticulous QSP model that seamlessly integrated known physiology, published competitor data, and clinical development decision-making. This model simulated the complex interplay between increased urinary glucose excretion, glycemia reduction, and the impact on weight loss. As additional data became available during drug development, the model was continuously improved, following a “learn and confirm” paradigm. The mechanistic considerations within the model guided dose selection trial designs and facilitated less risky decision-making.

Another study by Polidori et al. in 2014[36] employed a mathematical model akin to the minimal model of glucose regulation to demonstrate an extended administration of canagliflozin-enhanced pancreatic islet function, as evidenced by improvements observed in a glucose challenge test. By analyzing plasma glucose and C-peptide levels and calculating model-based beta cell function parameters, they observed significant improvements in these indices with canagliflozin treatment over a period of 6–12 months.

Furthermore, several research groups[37,38,39] have utilized mechanistic modeling to investigate the impact of SGLT2 inhibitors on SGLT1 receptors, which play a crucial role in glucose absorption in the gut. Modeling studies using labeled glucose data from healthy individuals and patients with type 2 diabetes, with and without treatment, revealed that higher doses of canagliflozin also inhibit the gut SGLT1 receptor. This inhibition leads to reduced postprandial glucose excursions.

Yakovleva et al.[40] utilized the QSP approach to investigate the reason behind SGLT2 inhibitors’ ability to inhibit only 30%–50% of glucose reabsorption in type 2 diabetes mellitus (DM) patients, despite SGLT2 channels being responsible for over 80% of glucose reabsorption in the proximal tubule. They constructed a structural QSP model using ODEs to represent renal functions, glucose filtration, reabsorption, and drug filtration. The model was calibrated and validated using literature data and outcomes from studies exploring renal glucose excretion. The study successfully made accurate predictions of cumulative urinary glucose excretion rates and total glucose reabsorption both with and without therapy, providing insights into the transition from SGLT2 to SGLT1 in glucose reabsorption among patients with type 2 DM.

Shah et al.[41] developed a predictive model aimed at forecasting the long-term reduction in HbA1c levels following dapagliflozin administration. The model was constructed using various factors, including PK variables, plasma insulin levels, plasma glucose levels, and data on urinary glucose excretion. These data were gathered during a Phase IIa clinical trial involving patients with type 2 DM who were treated with dapagliflozin. The model’s success was evident in accurately projecting the HbA1c reduction achieved with dapagliflozin treatment. Furthermore, the model’s noteworthy finding was that patients with poor glycemic control and those already on insulin therapy would experience substantial long-term benefits from dapagliflozin interventions. This valuable information has significant implications for optimizing the use of dapagliflozin as a therapeutic option in patients with Type 2 DM and could potentially lead to improved management of their condition. Table 1 summaries other few selected examples from recently published QSP models in different Stages of Drug Development.

Table 1.

A few selected examples from recently published quantitative and systems pharmacology models in different stages of drug development

Stage of drug development	Aim of the model	Model description
Preclinical	To predict the in vivo antitumor efficacy from in vitro data	Bouhaddou et al.[42] developed a semi-mechanistic PK/PD mathematical model for an anticancer drug ORY-1001 (epigenetic inhibitor) using the in vitro cell culture data sets. They predicted the in vivo tumor growth dynamics
	To predict the effects of an individual’s sex and individual pathophysiology on treatment response for different classes of antihypertensive drugs in rat models	Ahmed et al.[43] developed the first sex-specific QSP model of primary hypertension in rats based on previously published models of blood pressure regulation. They integrated it with a machine learning model and predicted that women respond better than men to ACEi, ARB/TZD dual therapy, and CCB
Translational (preclinical to clinical)	To predict its toxicity and clinical response from preclinical data and to aid in FIH dose selection	Mosunetuzumab is a T cell-dependent bispecific antibody approved by the FDA for treating relapsed or refractory follicular lymphoma. However, it carries the risk of causing a cytokine storm due to its ability to release IL-6. To aid in its clinical development, Hosseini et al.[44] developed a QSP model, by using preclinical animal data to predict its toxicity (IL-6 release) and clinical response. The model predicted that a single-step fraction dosing of mosunetuzumab would reduce peak IL-6 release while effectively killing tumor cells. These predictions were consistent with the Phase 1 trial data
Clinical pharmacology	To predict the efficacy of drug combination therapy	Coletti et al.[45] developed a QSP model for prostate cancer using ODEs describing tumor and immune system components along with seven different therapies. They simulated the different combinational therapies and predicted that a cancer vaccine combined with immune checkpoint blockade was the most effective in subjects with resistance to androgen deprivation therapy
	To support regulatory decision-making in assessing the adequacy of the proposed dosing regimen	In 2015, Natpara was approved by the FDA to treat hypocalcemia in hypoparathyroidism patients. Doses tested in clinical trials resulted in normal calcemic but could not hypercalciuria. By using the QSP model, Khurana et al.[46] suggested a more frequent dosing regimen of Natpara to better control hypercalciuria while maintaining normocalcemia and provided information to support the postmarketing trial
	To predict INR and aPTT measurements of patients receiving steady-state anticoagulation therapy	Hartmann et al.[47] modified a previously developed QSP model by considering the effects of genetic polymorphisms (CYP2C9, VKORC1) that influence warfarin’s dose-response and described the INR measurements of patients receiving long-term warfarin therapy and predict aPTT measurements for patients receiving long-term rivaroxaban therapy. The researchers used virtual patient populations to assess the model’s ability to predict routine measurements. Various literature[48,49,50,51] also describe the similar virtual population utilization

QSP: Quantitative and systems pharmacology, PK: Pharmacokinetic, PD: Pharmacodynamic, FIH: First in human, IL-6: Interleukin-6, ODEs: Ordinary differential equations, INR: International normalized ratio, aPTT: Activated partial thromboplastin time

Regulators’ Perspective

Over the years, there has been growing awareness of QSP approaches within regulatory authorities as modeling techniques become more prevalent in drug development. Regulatory agencies, including the FDA, have issued recommendations that should be applied to all QSP modeling practices.[52] These recommendations are designed to ensure the reliability and transparency of QSP models and include the following key points:

1. Achieving the appropriate qualification and validation of a QSP model relies on finding a suitable balance between the available data for model calibration/validation and ensuring alignment with the underlying physiological mechanisms involved

2. Model reproducibility and transparency are crucial aspects that allow reviewers to access all parameters and equations utilized in the model, facilitating the replication and interpretation of simulation outcomes

3. The QSP model should incorporate relevant PD indicators and clinical endpoints of the drug candidate, with the level of molecular granularity in detail based on the intended use (whether it’s for preclinical or clinical stages). Utilizing a preclinical model for late-stage clinical development can lead to identifiability and uncertainty issues, so appropriate modifications or the development of a new clinical-oriented model may be necessary

4. Similar to clinical trials, predetermined quantitative and statistical criteria should be established to guide the decision-making process when accepting QSP model extrapolation. These criteria should be dependent on the specific decision risk being made.

Over the past few years, there has been a significant rise in the number of regulatory submissions documenting the utilization of QSP modeling. Bai et al.[53] summarized FDA submissions involving QSP models to gain insights into the specifics of the models used and their intended applications.

1. Landscape analysis revealed a consistent and substantial increase in QSP submissions from 2013 to 2020, with a total of 157 identified submissions, of which 57 were recorded in 2020 alone

2. QSP submissions were observed across all stages of drug development, with the majority being in the investigational new drug stage, indicating widespread utilization of QSP in early drug development

3. QSP models found application in various therapeutic areas, including oncology, infectious diseases, neurology, nephrology, and cardiology, with oncology being the most prominent area of interest among the submissions

4. The versatility of QSP applications was evident in the submissions, as they addressed a wide range of efficacy and safety-related questions. Efficacy-focused inquiries primarily centered around dosing strategies, encompassing Phase I dose-finding and escalation, Phase II dose-range studies, and Phase III dose selection. Safety applications covered liver toxicity, plasma ion concentration, cardiotoxicity, and bone mineral density.

Conclusion

Integrating QSP approaches in drug development has shown promising results in various aspects of the field. By mechanistically modeling drug PK and PD alongside disease pathophysiology, QSP provides valuable insights and has the potential to address key challenges in the drug development process. QSP has demonstrated its ability to identify optimal targets and biomarkers for specific diseases, improve therapeutic effectiveness through drug combination strategies, predict human response doses based on preclinical data, and repurpose existing drugs for new indications. In addition, QSP can facilitate individualized dosing regimens based on patient characteristics, leading to the adoption of personalized medicine and potentially enhancing treatment outcomes.

Despite the advancements in QSP and its potential for drug development, challenges persist. Among these challenges, the peer review and interpretation of results from complex models with multiple assumptions remain significant barriers to the widespread impact of QSP. Communicating model results, limitations, and assumptions to diverse audiences in the drug development field require explicit attention to improve impact. Efforts to establish standardized model evaluation and enhance transparency, such as open-sourced publications and clear evaluation standards, have been suggested to address these challenges. Developing talent in the QSP field is crucial for its adoption and success. Training and fostering multidisciplinary expertise at scale are essential to proposing, developing, and effectively communicating QSP modeling analyses. Pharmacologists, with their clinical research training and understanding of pathology and pharmacotherapy, can play a vital role in bridging the gap between physiologists and modeling engineers. They can act as interpreters, utilizing the expertise of QSP teams to support decision-making in the clinical trial process and the development of novel molecules.

Financial support and sponsorship

Nil.

Conflicts of interest

There are no conflicts of interest.