J Pharmacokinet Pharmacodyn (2014) 41:523–536 DOI 10.1007/s10928-014-9367-z


Review on modeling anti-antibody responses to monoclonal antibodies Jose´ David Go´mez-Mantilla • In˜aki F. Troco´niz Zinnia Parra-Guille´n • Marı´a J. Garrido

Received: 28 April 2014 / Accepted: 25 June 2014 / Published online: 16 July 2014  Springer Science+Business Media New York 2014

Abstract Monoclonal antibodies (mAbs) represent a therapeutic strategy that has been increasingly used in different diseases. mAbs are highly specific for their targets leading to induce specific effector functions. Despite their therapeutic benefits, the presence of immunogenic reactions is of growing concern. The immunogenicity identified as anti-drug antibodies (ADA) production due to the continuous administration of mAbs may affect the pharmacokinetics (PK) and/or the pharmacodynamics (PD) of mAbs administered to patients. Therefore, the immunogenicity and its clinical impact have been studied by several authors using PK modeling approaches. In this review, the authors try to present all those models under a unique theoretical mechanism-based framework incorporating the main considerations related to ADA formation, and how ADA may affect the efficacy or toxicity profile of some therapeutic biomolecules. Keywords Monoclonal antibodies (mAb)  Immunogenicity  Anti-drug antibodies (ADA)  Antiantibodies  PKPD modeling

Introduction Clinical use of monoclonal antibodies (mAbs) has increased dramatically through the last years. By May 2014 the Food and Drug Administration (FDA) has approved 45 mAbs, almost doubling the number of approved mAbs since 2009 [1]. mAbs are used to treat several diseases including autoimmune, cardiovascular, infectious diseases, cancer and inflammation [2]. However, the immunogenicity of a mAbs and its influence on the therapeutic response is of great concern for clinicians and pharmaceutical industries. The main objective of the current work is to review the efforts performed so far in modeling the impact of antiantibody or anti-drug antibody (ADA) presence on mAbs therapy. This review first provides a brief background on immunogenicity and its associated factors. Modeling examples in the literature will be discussed in detail recognizing the limitation of these models in that so far all published models have been established between ADAs and the pharmacokinetics (PK) of mAbs, and not between ADAs and pharmacodynamics (PD). Immunogenicity

J. D. Go´mez-Mantilla  I. F. Troco´niz (&)  M. J. Garrido Department of Pharmacy and Pharmaceutical Technology, School of Pharmacy, University of Navarra, Pamplona 31080, Spain e-mail: [email protected] Z. Parra-Guille´n Department of Clinical Pharmacy, School of Pharmacy, University of Berlin, Berlin, Germany

‘‘Biologics’’ are defined as agents produced by living organisms and cells (human and animal) using biotechnology-derived processes. Sethu et al. [3] have classified biologics into four groups based on their activity: Group I, biologics with enzymatic or regulatory activity; Groups II, biologics with special targeting activity, which include mAbs; Group III, vaccines and Group IV, diagnostic biologics. The specificity of mAbs for their targets confers effector functions such as receptor-ligand blockage and target cell cytotoxicity through specific cellular epitopes



[4]. However, mAb therapeutic efficacy and safety can be influenced by unwanted immunogenic responses following repeated administration as well as exaggerated pharmacology, and cytokine release. The immunotoxicity spectrum provides different manifestations like unwanted immunostimulations, ADA production and hypersensitivity reactions. When an immunogenic reaction mediated by ADAs takes place, the PK of the mAb may be altered, reducing its efficacy and in some instances, inducing allergic reactions thereby hampering its clinical application [5]. Types of ADAs There are two types of ADAs depending on the binding of the ADA to the epitope of the mAb: neutralizing Antibodies (NAb) are directed against the epitope responsible for the selectivity of the mAb, whereas binding Antibodies (BAb) bind to other non-selective epitopes of the mAb. The main difference lies in the mechanism. BAbs may increase either the clearance of the mAb–ADA complex or prolong the bioavailability of the biologic agent, while NAbs compromise therapeutic efficacy due to its neutralizing effect. Note that NAbs are a subset of BAbs, and when BAbs are detectable, NAbs may also be present [6]. An example of this phenomenon has been reported during interferon (IFN) Fig. 1 Schematic representation of the main immunogenic mechanism involved during mAbs (or other biologic agents) administration. A mAb is able to induce the activation of the T-cell dependent pathway involving the production of antibodies by B cells participation through the acquired immunity. These antibodies are known as ADA, which can be with neutralizing activity (NAb) blocking the specific epitope of mAbs decreasing their therapeutic effects and contributing to increase the mAb clearance by the complex formation; and with binding activity (BAb) to non-specific epitopes of mAbs enhancing the mAb clearance as in the case of NAb. Note that ADAs are represented with smaller size that mAb although both correspond to antibodies with similar size


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beta therapy. BAb titers were produced earlier, in greater amount and persistently longer than NAb titers which tended to disappear or reduce over time [3]. At the moment, the detection of both types of ADAs to mAbs and other protein biologics represent an analytical challenge [3, 7]. The immunogenic response to repeated administration of a mAb is characterized by the presence of immunoglobulins specific for the mAb with high and persistent titers of IgG, low and transient titers of IgM and in rare occasions IgE, which is responsible for anaphylaxis. IgG4 is the most common neutralizing antibody type and is considered a significant factor contributing to clinical treatment failure. Production of these ADAs is mainly mediated by the activation of T-cells and subsequent stimulation of B-cells leading to generation of plasma B cells (responsible for antibody production), some of which later become memory cells (Fig. 1). This process takes days/weeks after treatment exposure and represents an adaptive antibody response [4]. The presence and extent of immunogenicity after mAb administration is variable and depends on several factors, most of which are related to the patients themselves, the products, or treatment regimen. Table 1 shows the characteristics of the immunogenic response to some mAbs displaying the variability in immunogenicity and the difference between NAbs and BAbs.

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Table 1 Immune response to some fully human mAb (adapted from Harding et al. [4]) mAb



ADA (%)



Colorectal carcinoma

3–4 % 1–4.6 % BAb 1 % NAb 0%



Chronic lymphocytic leukemia



Rheumatoid arthritis

2–16 %

Ankylosing spondylitis

3–4 %







Rheumatoid arthritis

5–89 %

EGFR epidermal growth factor receptor, CAPS cryopyrin-associated periodic syndromes, BAb binding antibodies, NAb neutralizing antibodies

Factors associated with immunogenic reactions Product-mediated factors Include molecule design, manufacture procedure, type of formulation, presence of excipients, etc. For example, the presence of aggregates and adjuvantlike contaminants are known to influence the immunogenicity, some of which can be resolved during manufacturing and formulation processes. However, large heterogeneity of aggregates hinders the development of adequate quality control protocols [8]. On the other hand, mAbs are proteins with a large molecular weight which contain numerous disulphide bonds and post-translational modifications like glycosylation. Glycans can influence the physicochemical and biological properties of the proteins. The glycosylation profile is species-specific and depends on the cell-line and culture conditions during the production process. Changes associated with this structure impact the ADA formation. Cetuximab, a chimeric mAb targeting the EGF-receptor, was able to induce severe anaphylactic reactions due to the presence of a galactose-alpha-1,3-galactose sugar within a carboxylate structure on the Fab fragment of the mAb. Anaphylaxis could be reduced if cetuximab was manufactured using another cell line in which the sugar was not introduced [4]. In this respect, covalent conjugation of polyethylenglycol (PEG) to mAbs may decrease immunogenicity by shielding immunogenic epitopes and increasing the stability of the conformational structure. In order to avoid immunogenicity, therapeutic biotechnology-derived proteins must be as similar as possible in primary, secondary, and tertiary structures to its human homologue. The first therapeutic mAb, muromonab, produced with murine variable regions and human antibodies,

was able to induce more than 80 % of NAbs known as HAMA (human anti-mouse antibody) within 1 or 2 weeks of treatment. Despite efforts to engineer humanized and fully humanized antibodies, the abolishment of immune reactions has not been reached. For example, adalimumab, a fully humanized antibody, led to BAb production in 12 % of patients and production of low NAb titer in 5 % of patients after subcutaneous administration. Furthermore, in ADA-positive patients a dose-dependent loss of clinical response was observed [9]. Population and/or treatment regimen-mediated factors Include patient genetics, disease state and concomitant medications. It has been described that patients with weak immune systems or immunocompromised are less likely to develop ADAs than those with intact immune system. For instance, treatment with rituximab, a human mouse chimeric antibody against CD20 surface antigen, did not elicit ADAs in patients with B cell lymphocytic leukemia. In those patients, the observed B-depletion seems to be responsible for preventing the formation of ADAs [9]. Regarding factors associated with treatment, the route of drug administration plays a relevant role in ADA response, with subcutaneous injection being the most immunogenic route of administration followed by intramuscular, intranasal and intravenous, in that order. On the other hand, in a study carried out in monkeys treated with adalimumab factors like time exposure or dose were relevant in the ADAs formation. Low doses, short-term therapy and continuous therapy were all factors that led to a higher immunogenic response compared to high doses, long-term and intermittent administration [10]. In summary, the production of ADAs and their clinical implication are very complex and poorly understood processes, hampering its prediction. In order to evaluate the impact of immunogenicity on mAb PK and/or PD, several considerations need to be addressed to propose a theoretical mechanism-based framework able to explain and quantify the main concepts commented on here. Clinical impact of ADA The presence of ADA has been associated with lower mAb concentrations, loss of therapeutic effect, and increased risk of acute infusion reactions [11]. However for certain mAbs, these anti-antibodies do not seemed to impact the clinical response [12]. Contradictory findings regarding the relationship between ADA production and dose of mAbs are reported in the literature: from an inverse proportionality between ADA and mAb dose [10], to dose-dependent ADA



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Table 2 mAbs reported in the literature that are associated with ADA production Product




Immunogenicity %


Model Available



Murine IgG2a1






Murine IgG2a k



Graft Reject



Full Human IgG2






Chimeric Fab






Humanized IgG1



Graft Reject


Soluble Protein NA

Humanized IgG1 (modified)






Chimeric IgG1k






Humanized IgG4k






PEG-Humanized Fab’






Humanized IgG1 (modified)





Efalizumab Alemtuzumab

CD11a CD52

Humanized IgG1 k Humanized IgG1 k


6.3 2–8.3

Psoriasis CLL




Human IgG1 k







Chimeric IgG1 k



Colorectal CA





Human IgG k






Human IgG1 k







Human IgG1 k



Colorectal CA


The limit for immunogenicity was set up at 2 %. PK or PK/PD model availability is also specified. Data from packages inserts, www.fda.gov and [27–29] IV intravenous, SC subcutaneous, TNF tumor necrosis factor, NHL non-Hodgkin lymphoma, NA not available, RA rheumatoid arthritis, CD Chron´s disease, IBD inflammatory bowel disease, MS multiple sclerosis, CLL chronic lymphocytic leukemia, AS ankylosing spondylitis * Existence of published studies reporting modifications of mAb PK by ADA response. No effect of ADA on PD has been modelled so far

production [13, 14] to an interruption in ADA production at larger doses of the mAb leading to tolerance [15, 16]. As mentioned earlier, the measurement of ADA is an analytical challenge. One reason is that ADAs tend to be bound to the mAb. Only recently, effective methodologies to overcome this interference problem have been described [7, 17]. Therefore, the actual ADA concentration in previous works could have been higher than reported, raising the question about the true clinical impact reported for the ADA effect in those studies. In the same direction, it is difficult to asses whether changes in mAb PK are due to ADA–mAb interaction or to interference in the mAb analytics by the ADAs. A harmonization initiative has been published recently with the aim to develop ADA-tolerant PK methods and ADA-tolerant analytical methods as well [18]. Additionally, the biodistribution of mAbs is extensive, being detected and measured in several tissues and organs where their therapeutic action is exerted. Since the biodistribution of ADA and ADA–mAb complexes has not been studied, the behavior of ADA in different tissues and organs reached by the mAbs can only be speculated. As a result, and due to the complexity of the immunogenic response, the relationship between mAb PK and ADA production, and the impact on efficacy and safety is a topic that only few studies have addressed.


Table 2 lists the mAbs that have been associated with ADA production identifying for each mAb the target, type, route, clinical indications and reported percentage of immunogenicity. Note that murine and chimeric mAbs exhibit higher immunogenicity than humanized mAbs, as has been previously mentioned. Few pharmacokinetic studies of mAbs have incorporated the effect of ADA on mAb disposition. Examples include AMG-137, infliximab [19], golimumab [20] and ustekinumab [21]. In these models the influence of ADA has also been incorporated to investigate and quantify the impact of those antibodies in the ADME processes. On the other hand, few studies are available in the literature where a PK/PD modeling approach has been addressed to describe the mAb exposure–response relationship. As can be seen in tables 2 and 3, of those mAbs having an immunogenicity rate higher than 2 %, MTRX1011A [22], efalizumab [23, 24], AMG-317 [25] and adalimumab [16, 26] are the only mAbs with published PK/PD models. In the pharmacokinetic modeling of these mAbs, different assumptions have been used to describe the effect that ADAs may exert on mAbs. For example: (i) Modification of mAb clearance, (ii) alteration in tissue distribution of the ADA–mAb complex compared to the free mAb and (iii) neutralizing effect of the mAb active site. However, none of the proposed PK/PD models consider the

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Table 3 Description of the PK and PK/PD models reported in literature incorporating the ADA production mAb

Model description covariates

Impact of ADA (reference)


PK: two-compartment with linear CL [19, 30]

COVADA on CL [19]

Covariates incorporated: [16]: WG on V1, C-reactive protein basal concentration and inflammation on CL. [17]: WG and Gender on V1. [19]: Baseline DAS28 on CL. Golimumab

[30]: SAC on CL PK: one-compartment model with first-order absorption and elimination [20] Covariates incorporated:

COVADA on CL and V [20]

[20]: WG and sex, on CL Ustekinumab

COVADA on CL [21]

PK: one-compartment model with linear elimination Covariates incorporated: [21]: WG, sex, diabetes, albumin, creatinine clearance, alkaline phosphatase on CL WG, diabetes and race on V


PK: PBPK model (18 compartments) each tissue compartment, divided into vascular, endosomal, interstitial and cellular sub-compartments [26] PK/PD: DDAS28-[adalimumab] relationship [16]

Increase CL [10]

PK-ATA: two compartment model with linear and nonlinear (ADA associated) CL [10] AMG-317

PK/PD: Two compartment QSS target mediated. Linear and nonlinear CL [14, 25, 31] Covariates incorporated:

COVADA on CL and Rmax* [14, 31]

[25]: WG on CL and V1 Age on ka Cumulative AUC on IgE response Efalizumab

PK: mechanistic 2 compartment PK/PD model, linear and non-linear (target mediated) CL [23, 24]


PK/PD/efficacy: a receptor-mediated pharmacodynamics model with negative feedback. Rate of psoriasis skin production proportional to free surface CD11a [24] Covariates incorporated: MTRX1011A

[32]: WG on CL PK/PD: a receptor-mediated PK/PD model (2 compartments) [22]**


Cov covariates, WG body weight, Rmax non-linear clearance drug elimination rate, SAC serum albumin concentrations, DAS28 disease activity score, QSS quasy steady state * Effect of ADA on Rmax was significant on one study but not in another ** Model reported for TRX-1 precursor of MTRX1011A

effect that ADA may have directly on the PD of the mAb. This limitation would be explained by the restriction of ADA quantification in the different body compartments. Taking into account these issues, it is pertinent to review in depth the PK and PK/PD models reported for mAbs that cause immunogenic reactions (Table 3). In these models the influence that several covariates exert on the different PK or PD parameters has also been evaluated. A compartmental PK approach consisting of one or two compartments is the most common model applied for describing the mAb disposition. An exception is adalimumab which used a physiological PBPK consisting of 18 organ-blood compartments [26]. In all models, ADA was not treated as part of the structural model but rather

was incorporated as a covariate associated with parameters such as clearance or apparent volume of distribution thereby indirectly affecting the mAb PK (Fig. 2a). Nevertheless, since PD depends on the amount of mAb that reaches the target (antigens, surface molecules, cytokines, chemokines, …), the formation of ADA–mAb complexes before the targeting may influence the therapeutic response.

Approaches to model mAb PK, mAb PD and ADA response To date, modeling of ADA response is limited to PK analysis, and in some cases, defining specific PK



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each other on their complexity and underlying assumptions. Differences between all models are listed and commented in detail attempting to understand the advantages and limitations that each of them presents. Assumptions used in mAb and ADA modeling (1)

Production of ADA (1.1) Constant [10, 20, 21, 30] (1.2) mAb dose-dependent [13, 14, 33]


Onset of ADA production (2.1) Constant lag-time [10, 14] (2.2) A delay represented by transit compartments [13].


Fig. 2 Modeling effect of ADA on mAb PK/PD. a Binding of ADA to mAb can affect all the mAb PK parameters and modify the interaction of mAb with its target. b Schematic representation of a hypothetical PK/PD model, where all the main assumptions commented in Table 3 have been incorporated: 1—production of ADA. 2—Onset of ADA production. 3—Formation of ADA–mAb complex. 4—Biodistribution of mAb and ADA. 5—Elimination. 6—PK/PD Modeling

parameters for the ADA and the ADA–mAb complex. Few pharmacokinetic models for mAbs actually take into account ADAs, and none distinguish Nabs from Babs. There are only four available PK/PD models for mAbs that exhibit significant immunogenicity: MTRX1011A [22], efalizumab [23, 24], AMG-317 [25] and adalimumab [16, 26]. However these PK/PD models do not consider the effect of ADA response on mAb PK or PD. As the main interest in studying mAb immunogenicity is to evaluate its potential clinical impact, a PK/PD model which considers the ADA response would be valuable. In order to develop such a model, the features of the ADA PK models should be integrated with into the mAb PK/PD models. In this review, the different approaches to model mAb PK, mAb PD and ADA response are presented and discussed in order to establish a framework that can be used as a starting point in modeling the impact of ADA response in mAb PK/PD. Figure 2b illustrates the different approaches that have been used to describe ADA dynamics, its effects on the mAb PK and the potential effect that this dynamics could exert on PK/PD of mAbs. The different models differ from


Formation of ADA–mAb complex (3.1) Reversible binding [13, 14, 22] (3.2) Affinity maturation (polyclonal ADA) [13]


Biodistribution of mAb and ADA (4.1) Compartmental models [10, 13, 14, 19–22, 24, 25, 30–32] (4.2) Physiologically based PK (PBPK) models [26]


Elimination of mAb and ADA. (5.1) Linear process [13, 19–21, 30] (5.2) Target/ADA-mediated elimination [10, 14, 22, 24–26, 31, 32]


PK/PD modeling

Production of ADA Initial dynamics of antibody response to an antigen produce antibodies that gradually increase, plateau after several days post-exposition and then, gradually decline [34]. After further exposures to the antigen, the antibody response is normally more intense (higher antibody production), effective (higher antibody affinity) and efficient (faster). Surprisingly, however, sustained antigen exposure could lead to immunologic tolerance to the antigen.

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No antibodies are given as a single dose. mAb therapy requires repeated administration over an extended period of time which may enhance ADA production or induce tolerance. Both responses are possible and may have very different impact on clinical success. However, knowing a priori which mechanisms will be triggered in a specific subject is currently not possible. Additionally, not all patients treated with mAbs develop immunogenic reaction by producing ADAs, therefore the modeling assumptions applied in this points are: Constant ADA production This mechanism has been applied to explain the ADA production kinetics against adalimumab by Ng et al. [10]. The authors modelled the ADA appearance through a zero order synthesis rate (0.433 log titers/day in monkeys) though this does not describe completely the real physiological process. Further, inclusion of dose-dependent ADA synthesis did not produce a better model. As animal models are expected to present more immunogenicity against human mAbs like adalimumab, these approaches could be very valuable in understanding the dynamics of ADA production and mAb–ADA interaction. In the category of constant ADA production, we have also included models in which the ADA presence was incorporated as a covariate affecting the clearance of certain mAbs. Examples include infliximab [30], golimumab [20], and ustekinumab [21]. Covariate inclusion implies that ADA values remain constant through the experimental interval and that the effect of ADA is a constant for a given level of ADA. These models report an ADA level–mAb clearance (CLmAb) exponential relationship of the form: n Y ½ADA kicovi ð1Þ CLmAb ¼ hCL  kADA  i¼1 ½ADA

where hCL is the population mean clearance, kADA is a proportional constant raised to the power of ADA level [ADA] using the same calculation for all other covariates. This approach considerably reduces calculations and the number of parameters to be estimated, but not only lacks a mechanistic justification but also excludes from the analysis the impact of the ADA–mAb interaction on ADA levels. mAb dose-dependent ADA production Perez Ruixo and coworkers (2013) have proposed a model for panitumumab, including two phases to account for the production of ADA. The first phase is observed immediately after mAb exposure, when IgM is produced. This early ADA response dynamics is regulated by a saturable

mechanism described by Michaelis Menten equation, where the maximum immunogenic effect of the mAb (Emax), determines the magnitude of the immune response, while the drug concentration that provides 50 % of the maximum immune response (EC50) represents the sensitivity of a subject to develop an immune response. The second phase is characterized by IgG production that is mediated by activated T lymphocytes. This response is initiated several weeks after exposure and is described by a constant production rate mechanism. This model is the only one that includes the initial IgM response (phi pathway), followed by IgG response. However, the assumptions in these simulations of identical affinities of IgM and IgG and constant production of IgG are questionable as IgG antibodies are expected to exhibit a greater affinity [4, 34]. In an alternative approach, Chen et al. [13] modelled the ADA response against a mAb using a limited amount of ADA (Amax) that can be produced by dosing that mAb. In this mechanism, the Input dose of ADA (IdADA) depends on the Amax, the cumulative dose (CD) and the accumulated drug dose at which the ADA production reaches 50 % maximum (km). IdADA ¼

Amax xCD CD þ km


Considering that, even in the most anaphylactic reactions, there is a limited amount of antibodies that can be produced and that the antigen sensitivity depends on each mAb and subject, this approach seems plausible. Nevertheless, as most of the subjects do not develop ADA, the value of km for many subjects would tend towards infinity making very difficult the characterization of the population distribution of this parameter (biased to infinity). In that sense, Bonate et al. [33] have modelled the stochastic presence of immunogenicity by a zero-inflated poisson random effect model. It is the only approach that attempts to describe the lack of ADA production in most subjects exposed to mAb or therapeutic proteins. This model was employed to describe ADA response to a therapeutic recombinant human enzyme, Fabrazyme, used in the Fabry disease, but the modeling principles also apply to mAb immunogenicity. In this model, the probability of a subject developing a particular level of ADA follows a poisson distribution. Note that in this case, as the probability of ADA level being zero is expected to be much higher than in a normal poisson distribution, the probability is inflated (zero-inflated poisson model). Bonate and coworkers also attempted to model the problem of most patients not exhibiting ADA response by estimating the probability of immunogenicity using a set of predictor variables related to the patient status. The cumulative dose a patient received was identified as the only important predictor for the seroconversion.



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Thus, a 80 % chance for the seroconversion was estimated when the cumulative dose of Fabrazyme reached 209 mg under a constant dose every 2 weeks. No other investigations have succeeded in effectively predicting appearance of immunogenicity. Additionally, one of the main difficulties in modeling ADA response to mAb treatment is that antibodies are normally measured by titers, which are the maximum dilution in which an antibody is detected. Titers are useful to reflect simultaneously both concentration and affinity of the antibody but are not strictly a continuous variable, therefore, typical mathematical models to describe drug PK cannot be employed. Bonate model solves this issue by transforming titers to powers of a geometric series, and then analyzing the power term using the zero-inflated poisson model.

affinity response (see Sect. 1.2) which requires a transit time of 56 days. This constant value is defined as the amount of time required for the initial IgM response to disappear, and the specific immunogenic effects be driven by IgG. The authors used the term MTT as is normally used for mean transit time, but did not consider transit compartments.

A delay represented by transit compartments

This lag time (tlag) was included as a value estimated during the analysis of adalimumab [10] and panitumumab PKs [14]. In the first case (same model defined in Sect. 1.1 for adalimumab using data from monkeys), Ng et al. assumed fixed time threshold to describe the delay between the mAb administration and the onset of the ADA synthesis.

Transit compartments have been used in PK/PD modeling to describe a delay during the absorption process [35] and also, to describe the development of neutropenia [36, 37]. For ADA production Chen et al. [13] have proposed several transit compartments connected by a transfer rate constant (kTR) to describe the delay between mAb dosing and ADA appearance. This approach represents, in a more mechanistic way, the different physiological steps required for antibody production than the lag time. In this model the number of compartments (n) is flexible for a better resolution of the delay and the kTR is derived from tlag which represents the time needed for the entrance of ADA located in a depot to the central compartment: kTR = n/tlag. However, it is assumed that ADA response is initiated from the second dose. Therefore a new parameter tADA (time to start ADA production) is defined as tlag plus the dosing interval. In this case, the estimate of tADA is about 7-8 days regardless of the administered mAb, representing the immune stimulation in the same species. On the other hand, this model is not able to identify the nature of the different compartments assuming the same kTR. This evidently simplifies the calculations and reduces the number of parameters to be estimated as well as the biological representation of the process. A lag time seems to agree more with the time required for the appearance of ADA in vivo, but not with the dynamics of the process, which is better described by several delay compartments that are connected to the formation of the complexes ADA-drug.

dADA ¼ ksyn xTon  kdeg x ADA dt

Formation of ADA–mAb complex

Onset of ADA production Typically, high affinity IgG antibody production after exposure to antigen requires some weeks to be fully developed and several intermediate steps, including antigen presentation to T lymphocytes, clonal expansion of T lymphocytes, recruitment of several cell types, clonal expansion of B lymphocytes, antibody production and antibodies affinity maturation (Fig. 1). Although, most of the reviewed models do not consider an onset time for developing enough ADA levels to induce immunogenicity, some authors have applied the following assumptions: A constant lag time


where, ksyn represents the ADA synthesis zero rate constant in presence of mAb (see Sect. 1.1), kdeg the ADA degradation rate and Ton the constant time which determines the delay between mAb administration and the onset of the ADA synthesis. This parameter was estimated to 8.3 days and was associated with IIV (inter-individual variability) of 20 % approximately. In the second case, the authors proposed an immediate IgM with no lag time followed by a second IgG high


In general, low and transient levels of ADA expression rarely impact clinical response. In contrast, high titers with high affinity can alter the therapeutic activity by a neutralizing interaction with the specific epitope of mAb forming the ADA–mAb complex. The nature of this binding is not included by most models [10, 20, 21, 30], however some authors consider the ADA–mAb equilibrium using the following assumptions:

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A reversible ADA–mAb complex binding To address this point, Perez Ruixo et al. [14], Chen et al. [13] and Ng et al. [22] assume that the molecular interaction ADA–mAb is not covalent allowing a dissociable behavior (Elgert 2009). Thus, the kinetics of ADA–mAb complex formation is governed by the law of mass action in which, at equilibrium, the ratio between the concentration of the complex and the substrates (mAb and ADA) is constant [38], as is represented in equation 4: ½mAb  ADAcomplex ka ¼ ¼ keq ½mAbx½ADA kd


where ka, kd, and keq are the association, dissociation and equilibrium rate constants, respectively. The main advantage of this approach is that it captures the dynamical nature of the antibody–antigen equilibrium and allows a deeper study of the impact of ADA level variations on mAb PK by considering that the effect of ADA on mAb PK or PD depends not only on the concentration of both, but on all the factors that could affect this equilibrium. Furthermore this approach allows the inclusion in the model of antibodies of different affinities which occurs in vivo. Affinity maturation

Biodistribution Compartmental models

ADA response is polyclonal with different ADA isotypes and subtypes directed toward different epitopes of the mAbs [28]. These different ADAs with different affinities are present also at different concentrations. The incorporation of this immunogenic characteristic leads to a substantial increment on the complexity of the model and also the number of identifiable parameters. Considering that the entire variety of ADA on the immunogenic response to mAbs, its affinities and effects on the mAb-target are not well-known, it seems not possible to evaluate the impact of those effects assuming a representative keq for the polyclonal ADA response. Based on that fact, the model proposed by Chen et al. [13] is the only one which includes the affinity maturation process consisting of production of ADA with an increase in mAb affinity over time following successive drug administrations. Affinity maturation can represent a difference of 100 to 500 fold in the keq between early and matured antibodies produced due to somatically acquired point mutations in the B lymphocytes [39, 40]. This process was modeled by an exponential decrease of kd with time while keeping ka constant, and therefore increasing keq. axt kdt ¼ kd0:

where kdt is kd at time t and kd0 is the initial kd of early antibodies, and a is a maturation constant dependent on each mAb and patient. The initial kd is assumed constant among drugs. This approach seems to capture well the increase in affinity with time, however note that if a maturation time window is not defined, keq can increase asymptotically to infinity which is not expected or possible in vivo. Therefore it would be worth exploring whether there is a mAb-specific or patient related maximum keq. It must be considered that time to achieve equilibrium in the antibody-target reaction has been reported to be from 4 to 24 h [38, 41]. Although considerable, it does not seem to be of practical importance compared to the several weeks required for ADA appearance and normal therapeutic mAb dosing (separated by a minimum of two weeks). Hence, it seems acceptable to assume fast reaction equilibrium. However, antibody production after repetitive exposure to antigens in which memory B cells are involved can take only several hours, therefore time to reach equilibrium (4–24 h) may be of practical importance on the ADA–mAb interaction after repetitive doses.


Golimumab and ustekinumab were modelled using a monoexponential plasma profile estimating a volume of distribution of 22.6 and 15.7 L respectively. These values represent a volume higher than blood volume suggesting an extensive distribution for both mAbs [20, 21]. A bi-compartmental model was applied to describe the body disposition of infliximab [19, 30], AMG-317 [14, 25, 31], efalizumab [23, 24] and MTRX1011A [22]. Antibodies are immune substances expected to act against pathogenic agents that are not only located in blood. It is logical to assume a high level of mAb and ADA distributed into tissues. Thus, most of the models identify two main compartments associated with a total volume in the range of 5-9 liters [10, 13, 14, 19, 22, 24, 25, 30–32]. However, the ADA biodistribution or the effects of ADA on the drug distribution have not been identified. Physiological approach PBPK models represent a more realistic approach than empirical compartmental models. Nevertheless, the information required in these models is more complex because they attempt to describe the drug concentration in all the tissues reached by the drug and to depict the circulation of



plasma in all tissues, drug exchange between tissues, interactions, etc. In an attempt to create a platform to characterize the biodistribution of adalimumab, Shah and Betts in [26] used data from several publications to develop a structured PBPK model including 16 compartments plus tumor and lymph node compartments for mAb targeted to these tissues. In all tissues, except blood and lymph node, four subcompartments were also included: vascular, endosomal, interstitial and cellular. The complexity of the platform is expressed by its 820 equations to estimate four parameters. In this model, the immunogenic effect is not taken into account, although the most expected action would be present at the vascular space interacting with mAb to remove it from circulation and then decreasing its efficacy. However, the incorporation of all processes related to immune system activation and ADA production should be also incorporated to understand the main tissues where free ADA and ADA–mAb complex may be distributed. In order to be effective against all type of diseases, antibodies must have the capacity to distribute to all body organs. In distribution studies, mAb has been detected in different tissues and organs including lung, heart, kidney, muscle, skin, small and large intestine, spleen, liver, bone, bone marrow, stomach, lymph nodes, fat tissue, brain, pancreas, testes, thyroid and thymus [42, 43]. Consequently, more PBPK [26] models are expected to be developed in the PK/ PD modeling of mAb therapy and therefore of ADA–mAb interaction. However, deeper knowledge of mAb and ADA biodistribution will be required to that end. Interestingly, none of the models reviewed account for tissue distribution of the ADA or ADA–mAb complex. Considering that ADAs are themselves also antibodies, a similar ADA tissue distribution as the mAb biodistribution is expected. As the clearance of antibodies is presented mainly in tissues of high concentration of phagocytic cells [28], the biodistribution of ADA and ADA–mAb complexes may play an important role in the PK and PD of mAbs. Besides, factors like pH, ionic strength and enzyme presence affect the antigen–antibody equilibrium [38] emphasizing the expected effect of ADA and ADA–mAb complexes biodistribution on mAb PK/PD. Elimination The principal assumption regarding the influence that ADA exerts on mAb is in its clearance.Two main approaches have been followed: Linear process Some models describe mAb clearance as a linear process in which the clearance is not affected by time or mAb


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concentration. This is the case of models which use ADA titers as a covariate affecting mAb clearance [20, 21, 30]. However, as the ADA concentration changes over time and in response to accumulated doses of the mAb, assuming a mAb linear elimination process requires further justification. It is expected that the ADA–mAb complex exhibit a different clearance than the free mAb due to a more rapid removal from circulation by the action of macrophages. In principle, if ADA–mAb complex clearance is faster than mAb clearance, the mAb would exhibit a shorter half-life [15]. It has also been theorized that if the complex clearance is slower than mAb clearance, the mAb half-life can be longer since the complex would work as a mAb delayed release formulation [44, 45]. It should be noted though that decreased clearance due to ADA response has not been reported for the reviewed mAbs. Additionally, models that consider mAb linear elimination ignore the effect of the mAb-target equilibrium on the mAb PK. As the case for ADA, the mAb-target binding is expected to increase the mAb clearance in a non-linear way dependent on the concentration of both free mAb and target. Target/ADA-mediated elimination Alteration of mAb clearance because of the mAb-target interaction depends on concentrations of both mAb and target/ADA. As such, non-linear (receptor/target mediate) mAb elimination is probable and has been used to describe the PK of AMG-317 [14, 25, 31], MTRX1011A [22], efalizumab [24, 32] and adalimumab [10, 26]. Apart from normal mAb elimination mediated through the reticuloendothelial system [14, 28, 46], mAb elimination is affected by mAb-target or mAb–ADA binding. Once the mAb reaches its target, a different clearance for the mAb-target is expected, if the mAb target is a membrane receptor an internalization process may be also involved. The main possible alteration of ADA and mAb PK should be governed by the kinetics of the ADA–mAb complex elimination. Because ADA–mAb complex elimination has not been characterized experimentally for any mAb, assuming linear elimination of the ADA–mAbA complex in a model may be questionable. As mentioned before, the biodistribution of ADA and ADA–mAb complex is not completely understood. The presence of alternative pathways of ADA and ADA–mAb complex elimination in secondary compartments is unknown and assumed to be nonexistent in the reviewed mathematical models. It is accepted that antibody elimination occurs mainly in the endosomal space in the different tissues, specially liver and spleen [28], but this aspect is only included in PBPK models like those reported by Shah et al.

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[26] for adalimumab elimination. Similar models, however, have not been developed to describe mAb kinetics considering ADA response. The models from Perez Ruixo et al. and Ng et al. consider three simultaneous elimination pathways (linear dependent on mAb concentration, non-linear mediated by the target and non-linear mediated by ADA). Ng et al. [10] have described the elimination of adalimumab by firstly, a linear component dependent on mAb concentration via normal endosomal elimination, secondly, a non-linear elimination dependent on the mAb-target binding and lastly, Michaelis Menten elimination dynamics mediated by ADA. It must be considered that originally the Michaelis Menten expression is derived from the application of the law of mass action for enzyme reaction kinetics under some assumptions like concentration of enzyme (in this case the ADA) being much less than the substrate concentration (in this case the mAb). The main flaw of this approach is that these enzyme kinetics describe the increased elimination of mAb but assume that the concentration of the ADA (enzyme) is not affected by the production of the product (ADA/mAb complex) and depends only on the ADA synthesis and degradation rate, which does not agree with the antibody–antigen kinetics.

PK/PD modeling Although the mechanism of action of mAbs is known (they are specific molecules binding to specific targets), the regulation process to produce their effect is not fully


elucidated. It is evident that high specific binding of mAb to its target impacts the targets’ physiological function, but the whole PD of mAb effect still needs to be further investigated. Likewise, the physiological roles of many mAb targets are not totally understood. These facts partially explain why so far there are no PK/PD models that directly evaluate the impact of ADA on mAb PD. The therapeutic effect of mAbs have been linked to mAb concentration using mAb dose response relationships [16, 32] or by identification and modeling of biomarkers [24, 32]. These models were developed without considering the effect of ADA response, and therefore it is unknown wether the same model (same set of parameters and parameter values) would also apply to a subpopulation of patients with high ADA response. It is expected that alterations induced by ADA response in the PK of mAbs could also modify their response. However, the models reviewed have not included immunogenicity response, and so far, no model has described how intense should an ADA reaction be to significantly impact the mAb therapeutic action, or what factors control this relationship. Target mediated drug disposition models appear to be the basis to describe mAbs kinetics and to incorporate ADAs effects from a semi-mechanistic perspective [47, 48]. Recently Parra-Guille´n et al. [49], used a target mediated drug disposition model to describe the tolerance effects on the IL12 production mediated by the immune response via IFN gamma (Fig. 3). The complexity of the problem increases if it is considered that ADA response is polyclonal and could include not only different ADA with different affinities and gradual

Fig. 3 Schematic representation of a semimechanistic model for tolerance mediated by the IFN-IL12 positive and negative feedback. Antigenic stimulation (IL12 synthesis inductor); ksyn_IL12, ksyn_IFNc, ksyn_RIL12 and ksyn_RIFNc, zero order rate constants of IL12, IFNc, RIL12 and RIFNc synthesis respectively; kIL12, kIFNc, kdeg_RIL12 and kdeg_RIFNc, first order degradation rate constants of IL12, IFNc, RIL12 and RIFNc respectively; kint_RIL12, first order rate constant controlling the elimination and internalization of RILIL12 complex; KD_IL12 and KD_IFNc,dissociation equilibrium constants of IL12 and IFNc, respectively (adapted from [49])



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affinity maturation but also neutralizing and non-neutralizing ADA. It is not totally clear whether a mAb bound to a non-neutralizing ADA can still effectively bind to its target or if it would affect the mAb-target equilibrium constant affecting the mAb PD. Again, modeling such diverse responses represent a very challenging field that is only starting to be developed. Because of the higher immunogenicity of mAb from different species, animal models can be very valuable to study the ADA PK and its effect on mAb PK and PD.

Summary The use of mAbs as therapeutic agents is a fast growing field due to the possibility of targeting molecules with a high degree of specificity. However, some patients can develop immunogenicity against therapeutic mAbs compromising drug efficacy and patient safety. Immune response to mAbs is highly idiosyncratically and unpredictable, and factors controlling probability of ADA response have not been totally identified. Furthermore the clinical impact of ADA production in response to mAbs therapy also needs to be further investigated. Mathematical modeling of ADA response against mAbs and its impact on mAbs PD can help to improve the mAb posology and mAb selection by identifying drug-dependent and system-dependent factors controlling therapeutic failure and immunogenicity. It must be considered however, that the dynamics and controlling factors of ADA production are not totally understood and therefore, all the assumptions used in the modeling of ADA response are questionable and justified. Additionally the main difficulties in modeling ADA response are: •

• • •

• • •

Absolute levels of ADA and mAb are uncertain (titers are not continuous variables and depend on both concentration and affinity of the antibodies used in analytics). Most patients in mAb therapy do not develop immunogenicity. ADA response to mAbs is polyclonal, consisting of different types of antibodies with different affinities. Measuring ADA levels in serum in presence of mAbs and discriminating between neutralizing and non-neutralizing ADAs present major technical difficulties. PD of therapeutic mAbs are not completely understood. Extensive biodistribution of mAbs and uncharacterized distribution of its targets. Unknown biodistribution of ADAs and ADA–mAb complexes.

So far, modeling of ADA response has not addressed directly the impact of immunogenicity on mAb PD. Most


PK models quantify the effect of ADAs through a covariate effect of ADA levels on mAb clearance. However, by analyzing the different models that have been used to describe mAb PK/PD, a general theoretical mechanismbased framework that incorporates ADA formation, interaction, distribution and elimination has been identified and the advantages and drawbacks of the different assumptions that can be used at each point have been discussed. This proposed framework can be used as a starting point in modeling the impact of ADA response in mAb PK/PD. Pharmacometrics will definitely play a major role in this context by identifying different patient populations (responders vs non-responders in terms on ADAs production), screening covariates effects, and partly overcoming the limitation of quantitative analytical tools by including in PK/PD models negative/positive feedbacks resembling the ADAs time course [50].

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Review on modeling anti-antibody responses to monoclonal antibodies.

Monoclonal antibodies (mAbs) represent a therapeutic strategy that has been increasingly used in different diseases. mAbs are highly specific for thei...
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