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12 • Recent Advances in PK/PD 321
mRNA therapeutics involve the delivery of synthetic mRNA molecules to cells, with the goal of inducing the production of a specic protein. siRNA therapeutics involve the delivery of small interfering RNAs (siRNAs) to cells, with the goal of inhibiting the expression of specic genes [63]. Oligonucleotide therapeutics involve the delivery of short, synthetic nucleic acid molecules to cells, with the goal of mod‑ ulating gene expression. The mRNA/siRNA/oligonucleotide molecules are typically delivered to cells via a lipid nanoparticle (LNP) delivery system, which allows for the efcient and targeted delivery of the mRNA to cells. PK considerations for these therapeutics include the efciency of the LNP delivery system, the stability of the mRNA/siRNA/oligonucleotide within the target cells, and the pharmacokinetics of the LNP delivery system. The LNP delivery system should be able to effectively target the cells where these therapeutics will be needed and should be stable enough to allow for efcient translation into the desired protein/inhibition of gene expres‑ sion [61,63].
The level of gene expression will depend on a number of factors, including the efciency of the LNP delivery system, the stability of the nucleic acid within the tar‑ get cells, and the activity of the nucleic acid. Factors that can affect the stability of the nucleic acid include the presence of epigenetic modications, such as methyla‑ tion or histone modication, and the activity of the cell’s DNA repair machinery [62]. Moreover, the nucleic acid may be subject to degradation by cellular enzymes, such as nucleases.
There is a potential for off‑target effects, the risk of mutagenesis, and immune response to the LNP delivery system or nucleic acid. Additionally, the specic disease being targeted will also play a role in the design and development of the therapy. For example, a therapy for a chronic disease like cancer will have different PK/PD consid‑ erations than a therapy for a genetic disorder like cystic brosis [62,63].
12.3 USE OF M&S APPROACHES
IN THE DISCOVERY AND DEVELOPMENT
OF BIOTHERAPEUTICS AND
NOVEL MODALITIES
Computational and mathematical modeling approaches can aid in a better understand‑ ing of the complexities associated with biotherapeutics and novel modalities. To that end, quantitative decision‑making to guide the design of the molecule, nal lead selec‑ tion, preclinical to clinical translation, and designing clinical studies can substantially boost the overall R&D efciency and productivity of biotherapeutic drugs.
Various model‑based approaches (top‑down and/or bottom‑up) can be lever‑ aged at various stages of the discovery and development of biotherapeutics and novel modalities. At early stages in discovery, it can be used in early target feasibility
322 Biopharmaceutical Informatics
assessments to identify a promising and viable target for a particular disease or indi‑ cation. Known biology of the target (e.g., whether it is a driver of the disease or upstream/downstream of specic signaling pathways, endogenous ligands, etc.) and learnings from competitive space (e.g., successes and failures) or clinical precedence with the target can be leveraged to inform the models and for GO/NO‑GO decisions. A quantitative framework can also guide target molecule prole (e.g., ideal binding afnity range, desired mechanism of action, and molecular format) and modality selection for a particular target with a higher probability of clinical success during early stages of discovery. In addition, they can help with the designing of in vitro and in vivo (PK/PD, safety, and efcacy) studies (e.g., selection of doses and dosing regimen), as well as leveraging the preclinical data for triaging lead molecules and selecting the nal lead candidate. Interspecies scaling and translation to humans for PK, safety, and efcacy can also be accomplished with allometric scaling and translational quantitative PK/PD approaches. Such approaches eventually support the design of clinical studies, including starting dose selection for the rst‑in‑human (FIH) study, dose‑escalation strategy based on efcacious dose and therapeutic win‑ dow predictions, and RP2D selection. Finally, reverse translation learnings from suc‑ cessful and failed clinical programs to guide the development of next‑generation molecules can also be accomplished.
Depending on the stage of the program and the availability of data, various mod‑ eling‑based analyses can be carried out for biotherapeutics. A quantitative framework should typically integrate various types of data (in vitro, in vivo, and clinical) and data from various sources (literature and/or molecule‑specic) based on the model structure and objective of the modeling work. On the one hand, classic, empirical, and compart‑ mental PK or PK/PD models can be used to answer simple questions such as dose‑ exposure‑response analysis, human dose and TI predictions, or designing of preclinical or clinical studies. On the other hand, semi‑mechanistic or mechanistic models such as TMDD‑, PBPK‑, and QSP‑based approaches can be leveraged to better understand the mechanism of action in a quantitative fashion where information on the molecule prop‑ erties and target pharmacology is also included.
Over the past decade or two, the use of M&S approaches has exponentially grown for various purposes in the discovery and development of drugs. For instance, popu‑ lation PK/PD models for dose selection or PBPK models to characterize drug‑drug interactions (especially for small molecules) are routinely used [64]. Moreover, regu‑ latory agencies are now more open towards the use of model‑informed drug develop‑ ment (MIDD) to support product development and regulatory lings than ever before. In addition, recent advances in analytical technologies have enabled the capturing of newer, diverse, and more comprehensive datasets, during the preclinical and clinical developmental stages, which were perhaps not available earlier. Similarly, of late, there has been a huge investment in advancing computational approaches, including the use of real‑world data, big data, AI, and ML in the drug development industry [65]. Overall, there are increasing trends in developing and using mathematical mod‑ eling approaches for biotherapeutics. Fit‑for‑purpose mindset depending on factors such as scientic question, data availability, stage of the program, model assumptions, gaps/limitations, and relevance is crucial for the effective and impactful utilization of MIDD in biotherapeutics.
12 • Recent Advances in PK/PD 323
In the next section, we highlight case studies from literature where various M&S approaches (population PK, PK/PD, TMDD, PBPK/PD, and/or QSP) were leveraged for various applications at different stages of drug development across different modalities and therapeutic indications.

12.4 CASE STUDIES

12.4.1 Application of Mechanistic PK/PD
Models to Inform Early Drug Discovery Decisions for Biotherapeutics
Key decisions at the early stages of biotherapeutic drug discovery include determining the feasibility of drugging a target, prioritizing between targets, and dening optimal drug design properties. To avoid the synthesis and screening of large numbers of tool molecules, these decisions can be informed initially using model‑based approaches and data from the public domain. A model framework describing the intended pharmacol‑ ogy of the biotherapeutic can be constructed and parameterized with physiological or system properties available from the literature, including compartment volumes, cell numbers, receptor expression levels, soluble protein concentrations, and internalization rates. Drug properties, such as afnity of the individual binding arms and PK half‑life, can be set to nominal values and tested for sensitivity. These models can be used to pre‑ dict PK (including non‑linearities due to TMDD), target engagement, and effective dose.
Marcantonio et al. [66] presented a workow for the application of mechanistic PK/PD models, for early feasibility analysis (EFA) of biotherapeutics in early drug dis‑ covery stages. The approach was validated by the prediction of clinically efcacious dose, without tting to PK or PD data, for nine approved biotherapeutics across a range of targets and indications. Separate mechanistic PK/PD models were developed for each target class analyzed, including soluble targets, membrane receptors, and bispecic tar‑ gets. All were human models describing drug administration, PK, target binding, and target dynamics in one or more compartments. For each drug, a criterion for defining effective dose (e.g., 90% sustained target inhibition) was chosen. Models were then simulated to predict PK, target engagement, and target inhibition at different doses, to determine the dose required to achieve the criterion. This model‑predicted effective dose was compared to clinically approved doses for each drug. For the nine biothera‑ peutics tested, the predicted efcacious dose from the modeling analyses was generally within ~ threefold of the clinically approved doses.
The PK/PD model‑based approach was able to successfully predict the effective doses of two anti‑TNF‑α drugs: adalimumab and iniximab, for the treatment of rheu‑ matoid arthritis (RA). Despite binding to the same target, these drugs have very differ‑ ent PK and binding properties, leading to different approved doses and regimens. The modeling analysis was able to provide mechanistic insight as to why the effective doses
324 Biopharmaceutical Informatics
are signicantly higher than the dose predicted from a more straightforward exposure versus potency comparison. The efcacious concentrations are much higher than the Kd (~ 1,000‑fold), which is due to an increase of total TNF‑α above baseline on drug bind‑ ing to this soluble target. This has been shown to occur due to HLE effects where the short‑lived soluble targets form long‑lived complexes with the administered antibodies. These analyses demonstrate the advantage of applying a mechanistic PK/PD model for dose predictions. In addition, a sensitivity analysis showed that TNF‑α half‑life was a sensitive target parameter impacting predicted clinical dose, enabling prioritization of experiments during drug development.
The EFA approach was also able to accurately predict the effective dose for ami‑ vantamab, an anti‑EGFR, anti‑c‑met bispecic antibody, approved for the treatment of patients with non‑small cell lung cancer. Interestingly, PK data from a monospecic EGFR mAb (panitumumab) and an anti‑c‑met antibody (emibetuzumab) were used to benchmark target expression levels, as they both exhibit non‑linear PK due to TMDD. These target expression levels were then applied to predict PK and the effective dose of amivantamab, showing the exibility of this model‑based approach to make use of data already available from the literature. These analyses show how model‑based approaches can be used to inform key decisions for biotherapeutics early in drug discovery, before the collection of PK/PD data.
12.4.2 QSP Modeling of ADCs for Preclinical to
Clinical Translation and Optimization of Doses for Different Oncology Indications
A QSP model was developed for inotuzumab ozogamicin, a CD22‑targeting ADC for B‑cell malignancies [44]. The model was used for preclinical to clinical translation and to optimize doses and regimens for a new indication being explored (acute lymphocytic leukemia [ALL]) versus the original indication (non‑Hodgkin’s lymphoma [NHL]), which had been terminated due to lack of superiority versus standard of care.
The model included a plasma PK model characterizing the disposition and clear‑ ance of inotuzumab ozogamicin and its released payload N‑Ac‑γ‑calicheamicin DMH, a tumor disposition model describing ADC diffusion into the tumor extracellular envi‑ ronment, and a cellular model describing inotuzumab ozogamicin binding to CD22 on tumor cells, internalization, intracellular N‑Ac‑γ‑calicheamicin DMH release, binding to DNA, or efflux from the tumor cell (Figure12.2). Key preclinical data used to param‑ eterize the model included receptor expression on cancer cell lines, binding afnities, internalization rates, and PK data. The model was used to predict intracellular payload concentrations, which were linked to a tumor growth inhibition (TGI) model and cali‑ brated to TGI data from mouse xenograft studies. The preclinical model was translated to the clinic by incorporating human PK for inotuzumab ozogamicin and clinically relevant tumor volumes, tumor growth rates, and values for CD22 expression in the relevant patient populations. The resulting stochastic models predicted progression‑free survival (PFS) rates for inotuzumab ozogamicin in patients comparable to the observed clinical results. The model suggested that a fractionated dosing regimen was superior to a conventional dosing regimen for ALL but not for NHL.
12 • Recent Advances in PK/PD 325
FIGURE 12.2 (a) A schematic representation of a QSP model with relevant param­eters describing the PK, penetration into solid tumors (dotted box), and PD. Parameters related to the drug penetration into the solid tumors were excluded for liquid tumor indications. (b) Representative model-based PFS rate predictions in NHL patients (with
2
different growth rates) for nimotuzumab ozogamicin at 1.8 mg/m
every 4 weeks. Figure
adapted from [44].
326 Biopharmaceutical Informatics
A sensitivity analysis was performed to give insight into the parameters dening, or even limiting, efcacy of inotuzumab versus NHL. Tumor growth rate was found to be the most sensitive parameter and suggested that for the more aggressive NHL subtypes like diffuse large B‑cell lymphoma (DLBCL) patients would require signi‑ cantly higher doses for efcacy, compared with slower‑growing NHL subtypes such as follicular lymphoma. Calicheamicin efux from the tumor cell was a sensitive param‑ eter, which is important as N‑Ac‑γ‑calicheamicin DMH is known to be a substrate for MDR1, an efux transporter that is upregulated on many tumor cell types. The least sensitive parameter was CD22 receptor expression, which indicated the suitability of this receptor as an ADC target due to its high expression across B cells and rapid internalization rate. These ndings suggest that MDR1 status in patients would be a more useful diagnostic of efcacy than CD22 receptor expression. In summary, the QSP model developed for inotuzumab ozogamicin was able to give useful mechanistic insight into optimal dosing regimens and sensitive parameters impacting outcomes. This knowledge could be applied to optimize the design of ADCs in the discovery phase of research and/or for the selection of predictive diagnostics in the clinic.
12.4.3 A Translational Platform PBPK Model
for Antibody Disposition in the Brain
For many monoclonal antibodies (mAbs) and other targeted drug modalities, the molecular target may be located within the tissues. As a result, their pharmacodynamic (PD) and exaggerated PD/toxic effects are a function of tissue concentrations. Unlike small mole‑ cules, the tissue pharmacokinetics (PK) of mAbs cannot be assumed to be in rapid equilib‑ rium with plasma concentrations. One particularly challenging case is the delivery of mAbs to specic sites of action in the brain. Methodologies available to measure brain exposure of antibodies in the clinic are usually limited to cerebrospinal uid (CSF) concentrations, which do not represent delivery of mAbs across the blood‑brain barrier (BBB) endothelial cells. Preclinically, mAb concentrations in brain homogenate are routinely used to deter‑ mine mAb exposure, which may not accurately represent concentration at the site of action.
An alternative option is to use a model‑based approach such as PBPK modeling to predict the concentration of mAbs in different regions of the brain. These models are particularly attractive, as they incorporate anatomical and physiological factors which are very amenable to translation across species. PBPK models account for mechanism specics such as FcRn or target binding and are exible enough to adapt to changes in pathological conditions.
A platform PBPK model for the disposition of mAbs in the brains of mouse, rat, mon‑ key, and human was developed by [67] Chang etal. The model accounts for known anat‑ omy and physiology of the brain, including the presence of distinct BBB and blood‑CSF barrier (BCSFB). Physiological processes responsible for the disposition of non‑targeting mAbs in the brain, including CSF circulation, movement of macromolecules within the brain, and FcRn‑mediated mAb disposition, are described in the model. The model builds upon a platform model previously developed to characterize the plasma and tissue disposi‑ tion of mAbs in preclinical species and human [10]. The complete PBPK model includes 16 tissue compartments (blood, lung, heart, kidney, muscle, skin, liver, adipose, thymus, bone, small intestine, large intestine, spleen, pancreas, other/carcass, and brain) and a
12 • Recent Advances in PK/PD 327
lymph node compartment, connected to each other in an anatomical manner using blood and lymph flow. Each tissue compartment, except the brain, is composed of vascular, endo‑ somal, interstitial, and cellular sub‑compartments (Figure12.3). The brain compartment is divided into CSF circulation system and brain parenchyma and describes the limited
FIGURE12.3 Representative scheme of the whole-body and brain-specic PBPK model for mAb disposition across species. (A) Whole-body PBPK model represented at the anatomical level, (B) Standard tissue compartment within the PBPK framework, and (C) Brain compart­ment divided into brain parenchyma and CSF sections (Figure adapted from [67]).
328 Biopharmaceutical Informatics
mAb entry into the brain via bulk ow through the BBB or BCSFB or via non‑specic pinocytosis/transcytosis. FcRn‑mediated efflux, recycling, and transcytosis of mAb across BBB and BCSFB were also incorporated into the brain capillary endosomal spaces.
First, the model was used to characterize PK data (from disparate sources) describing the disposition of mAbs in the rat brain, including data determined using microdialysis to quantify PK in different brain regions. Most of the model parameters were fixed based on literature‑reported values, and only three parameters were estimated using rat data. The rat PBPK model was then translated to mouse, monkey, and human, simply by changing the values of physiological parameters corresponding to each species. The translated PBPK models were validated by a priori prediction of brain PK of mAbs in all three species, comparing predicted exposures with observed data. The platform PBPK model was able to predict all the validation PK profiles reasonably well (within threefold), without estimating any parameters.
The platform PBPK model described provides an unprecedented quantitative tool for the prediction of mAb PK at the site of action in the brain, and preclinical to clinical translation of mAbs is developed against central nervous system (CNS) disorders. The proposed model could be further expanded to account for target engagement, disease pathophysiology, and novel mechanisms, to support the discovery and development of novel CNS targeting mAbs.
12.4.4 Empirical Model‑based Cellular Kinetic
Analysis of CAR‑Ts in Clinical Studies, Investigation of Dose‑exposure‑response Relationship, and Covariate Modeling
The rst empirical, NLME population model for CAR‑T therapy was developed by Stein et al. [68] to characterize the clinical CK of an anti‑CD19 CAR‑T therapy (tisa‑cel) and to investigate the impact of various covariates on the CAR‑T peak and expansion. Specically, the study also focused on assessing the impact of CRS‑treating therapies (tocilizumab and corticosteroids) on the kinetics of in vivo tisa‑cel expansion, comparing the peak levels and the expansion rates in patients treated with tocilizumab or corticosteroid therapy against those who did not receive such therapies. Data from relapsed/refractory B‑cell ALL patients on tisa‑cel in two phase II studies were used for this modeling exercise. As shown in Figure12.4, the model assumes two types of cell population (short‑lived effector and long‑lived memory phenotype) and uses piecewise function to capture three distinct phases of CAR‑T CK prole–expansion, contraction, and persistence–each with distinct rate constants. Based on the modeling‑based analysis, the doubling time for the expan‑ sion phase, the half‑life for the initial decline/contraction phase, and the half‑life for the terminal persistence phase were estimated. Besides, both NCA‑based and model‑based estimates for Cmax and AUC at day 28 were determined to have a good correlation. The model predicted that there was no effect of CRS‑treating therapies
12 • Recent Advances in PK/PD 329
FIGURE12.4 A compartmental model to characterize T-cell kinetics. Key denitions, initial conditions, and equations for the model are shown in the gure. The model includes effector cells (E) with an exponential growth rate ρ up to the time to maximal expansion (T cells at the rate k. The memory cells then undergo decline at a rate β. Additional details on the model can be found at [68]. Cmax, maximal concentration; foldx, fold expansion; Fster, effect of steroids; Ftoci, effect of tocilizumab; Tster, time to maximal expansion with steroid therapy; Ttoci, time to maximal expansion with tocilizumab therapy; FB, fraction of transgene copies present during the decline at the gradual rate β, starting from Tmax. Reproduced from [68].
) and then they decline at the rate (α‐k) or get converted to the memory
max
(tocilizumab and corticosteroids) on the CAR‑T expansion rate. The model estimated that the Cmax was twofold higher in patients who required tocilizumab, which is consistent with other reported ndings that show higher exposure (Cmax) leads to higher CRS and therefore the need for medication. Finally, none of the evaluated covariates were determined to signicantly correlate with the peak CAR‑T levels. It should be noted that the pre‑infusion tumor burden after lymphodepletion, which has previously been shown to affect CAR‑T kinetics in several studies, was not measured and hence not included as a covariate in the analysis. In addition, some patients may have received multiple doses of CRS‑treating medications, but the model evaluated the impact of only the rst dose. In addition, no interaction term was included due to the sequential administration of corticosteroids after tocilizumab in most cases. Other co‑medications (e.g., IL‑6 and TNF‑α antagonist) were utilized only in a few
330 Biopharmaceutical Informatics
patients, hence not considered in the analysis. Overall, such a modeling framework provides a methodology to characterize clinical CK proles of CAR‑T therapy and to examine the impact of prophylactic CRS‑treating medications on CK and efcacy for future clinical studies. The Stein model was recently adopted by Ogasawara etal. [69] and Wu etal. [70] to carry out a similar analysis for liso‑cel (another anti‑CD19 CAR‑T therapy) in LBCL patients and cilta‑cel (anti‑BCMA CAR‑T therapy) in MMpatients.
Liu etal. [71] further developed a modied cellular kinetic model. In contrast to the Stein model, the piecewise model here was used to capture four (instead of three) distinct phases–rapid distribution, expansion, contraction, and persistence, of the multiphasic CAR‑T CK prole. For this analysis, the authors utilized published, indi‑ vidual cellular kinetic data from different CAR‑T therapies (anti‑CD19, anti‑BCMA, and anti‑EGFR) across seven different clinical trials, including diverse patient popu‑ lations, such as B cell Acute Lymphocytic Leukemia (ALL), Chronic Lymphocytic Leukemia (CLL), Diffuse Large‑B Cell Lymphoma (DLBCL), Glioblastoma (GBM), Non‑Small Cell Lung Cancer (NSCLC), and Multiple Myeloma (MM). The main goal of the meta‑analysis was to characterize, compare, and contrast CK proles across multiple tumor types, identify differences between responders and non‑responders or hematological malignancies and solid tumors, and investigate the impact of different covariates on clinical outcomes. The model predicted similar multiphasic CK proles for different CAR‑T therapies across various tumor types. Across most trials, the model‑based analysis determined a signicantly higher prolif‑ eration rate constant and thereby higher proliferative capacity (Cmax) in responders against non‑responders. In addition, longer duration of contraction and differentia‑ tion attributing to a more durable persistence phase was consistent in responders. The model also determined higher proliferative capacity (Cmax) and longer duration of proliferation in hematological malignancies, including ALL, CLL, and MM, as compared to lymphomas and solid tumors, which can be attributed to the limited antigen accessibility and distribution requirement of the CAR‑Ts to the solid tumors. In contrast, analysis revealed higher contraction and memory differentiation rates in solid tumors. In addition, the doses (available for CLL, MM, GBM, and NSCLC) showed a weak correlation with responses and no correlation with any model‑ estimated parameters, thereby suggesting a steep dose‑response curve consistent with previous reports. In contrast to previously published reports, baseline tumor burden of MM and CLL showed no correlation with CAR‑T proliferation or expan‑ sion and responses. The authors indicated the use of circulating biomarkers to assess tumor burden as one of the factors contributing to the inconsistency. Finally, analysis determined the CD4:CD8 ratio of the CAR‑T product to be close to one in responders while higher or diverse ratios in non‑responders for MM and NSCLC trials. Overall, such a model‑based meta‑analysis approach can be used to systematically compare cellular kinetic proles, determine critical drivers of clinical outcomes across differ‑ ent CAR‑T products, clinical trials, and indications, and guide the future discovery and development of next‑generation cell therapies.