(cid:22)(cid:26)(cid:24)375
`J Pharmacokinet Phannacodyn (2014) 41:375-387
`DOI 10.1007/s]0928-014-9372-2
`J. Waack, RDR, CRR, CCR
`ORIGINAL PAPER
`
`EXHIBIT NO.
`
`Incorporating target-mediated drug disposition in a minimal
`physiologically-based pharmacokinetic model for monoclonal
`antibodies
`
`Yanguang Cao ° William J. Jusko
`
`“oo
`
`EXHIBIT NO.
`
`J. Waack, RDR, CRR, CCR
`
`Received: 21 March 2014/ Accepted: 15 July 2014/ Published online: 31 July 2014
`© Springer Science+Business Media New York 2014
`
`(TMDD)
`drug disposition
`Abstract Target-mediated
`usually accounts for nonlinear pharmacokinetics (PK) of
`drugs whose distribution and/or clearance are affected by
`their targets owing to high alfimily and limmied capacity.
`TMDD is frequently reported for monoclonal antibodies
`(mAb)
`for such reason. Minimal physiologically-based
`pharmacokinetic models (mPBPK), which accommodate
`the unique PK behaviors of mAb, provide a general
`approach for analyzing mAbs PK and predicting mAb
`interstitial concentrations in two groups of Ussues. This
`study assessed the feasibility of incorporating TMDDinto
`mPBPK models to consider target-binding in either plasma
`(cTMDD) orinterstitial fluid (SF) (pTMDD). The dose-
`related signature profiles of the pTMDD model reveal a
`parallel early decay phase,
`in contrast with the cTMDD
`model thal exhibits a faster initial decline for low doses.
`The parallel carly phase in the pTMDD model is associated
`with the slow perivascular extravasation of mAb, which
`restricts the initial decline regardless of interstitial target-
`mediated elimination. The cTMDD and pTMDD models
`both preserve the long terminal phase that
`is typically
`perceived in conventional
`two-compartment (2CM) and
`TMDD models. Having TMDD in /SF impacts the typical
`relationships between plasma concentrations and receptor
`occupancy, and between saturation of apparent nonlinear
`clearance
`and saturation of
`receptors. The vascular
`
`
`Electronic supplementary material The online version of this
`article (doi: 10.1007/s10928-014-9372-2) contains supplementary
`material, which is available to authonzed users.
`
`Y¥. Cao W. TJ. Jusko (24)
`Department of Pharmaccutical Sciences, School of Pharmacy
`ard Pharmaceutical Sciences, State University of New York at
`Buffalo, Buffalo, NY 14214, USA
`e-mau: wjjusko@ buffalo.edu
`
`(a,) was found to affect receptor
`reflection coefficient
`occupancy in JSF.
`In the cCTMDD model, saturation of
`nonlinear clearance is equivalent to saturation of receptors.
`However, in the pTMDDmodel, they are no longer equal
`and all parameters pertaining to receptors or receptor
`binding (Ryne. Kp, Kegs Kix) Shifts such relationships.
`Different TMDD models were utilized in analyzing PK for
`seven mAbsfromdigitized literature data. When the target
`is in plasma, the CTMDD model performed similarly to the
`2CM and TMDD models, but with one less
`system
`parameter. When the target exists in /SF,
`the pTMDD
`functioned well
`in analyzing only plasma data to reflect
`interstitial
`target binding properties. Assigning TMDD
`consistent with target-expressing tissues is important
`to
`obtain reliable characterizations of receptors and receptor
`binding. The mPBPK model exhibits excellent feasibility
`in integrating TMDDnot only in plasma but also in /SF.
`
`Keywords Minimal PBPK Monoclonal antibody -
`Target-mediated drug disposition - PBPK
`
`Introduction
`
`Monoclonal antibodies (mAb) have emerged as effective
`therapeutic agents for a variety of diseases and the mAb
`market is expected to continue witnessing rapid growth over
`the next decade [1]. More than 30 antibodies have been
`approved by the U.S. Food and Drug Administration, and
`hundreds of candidates are under clinical investigation [2].
`The pharmacokinetic (PK) behaviors of mAb are different
`from small molecules in aspects such as limited vascular
`permeability, neonatal Fe receptor recycling, and more
`frequent receptor-mediated nonlinearity [3]. Accommoda-
`tion of their unique PK properties can assist
`in better
`
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`

`376
`
`J Pharmacokinet Pharmacodyn (2014) 41:375-387
`
`perivascular extravasationrestricts interstitial target-medi-
`ated elimination.
`
`Theoretical
`
`Model structure and simulation
`
`structures with TMDD in either
`The proposed model
`plasma (Model A, cTMDD) or /SF (Model B, pTMDD)
`compartments in the mPBPK model are shown in Fig. 1.
`The mPBPK model] has the same structure and symbol
`designations as our previous one [5]. Plasma clearance
`(CL,)
`is
`the only nonspecific clearance in this model
`because CL, appears to reflect the most common nonspe-
`cific clearance mechanism as found in our recent assess-
`
`the location of TMDD should be
`[6]. In principle,
`ment
`chosen consistent with target-expressing Ussues. Here, for
`the case studies, we considered TMDD in both V,,,,,, and
`Vieakys tWO groups Of lumpedtissues defined according their
`endotheliumstructure [5], as most ofthe interstitial targets
`assessed in this study are ubiquitously expressed in various
`ussues. The same target dynamics and antibody-target
`binding properties are assumed in two groups of tissues.
`The target-binding process is approximated by a quasi-
`steady-state model, where the binding rate is balanced by
`the sum of the dissociation and internalization rates [13].
`The differential equations for Model B are:
`
`dC,
`Input
`f= i
`+ [Crymph i= eo Ly a _ a1) _ Cp
`‘dt
`Y,
`Lo ( — 42) — CL, Col/Vp
`IC = 0
`
`@)
`
`Chet_jiee| Kian©Vent~ ARviens (2)
`
`ARyet _toial
`dt
`
`— Keown
`Kint
`IC = Kosi [Race
`
`- (Riight_totat ~ ARaghi) Keer - ARjight
`
`(3)
`
`4
`
`(
`
`)
`
`understanding and assessing factors that determine mAb PK
`and pharmacodynamics (PD). Minimal physiologically-
`based pharmacokinetic models (mPBPK) offer a simple
`modeling approach that incorporates physiological elements
`into PK analysis when only plasma data are available [4].
`Our second-generation mPBPK model was developed for
`mAbs with this modeling concept [5]. We applied this model
`to extensively survey mAb PK for humans inthe literature
`and demonstrated the feasibility of this model as a general
`approach in analysis of mAbs with linear PK [6].
`The term “target-mediated drug disposition” (TMDD)
`was introduced by Levy [7] and the modeling framework
`was established by Mager and Jusko [8]. Drugs exhibiting
`TMDD often bind with high affinity and to a significant
`extent (relative to dose) to their target. Such drug-target
`interaction can be reflected in their PK profiles. TMDDis
`frequently reported for mAbs with strong target binding
`affinity and high target abundance [9]. Applying TMDD
`models in mAb PKanalysis can reveal more insights about
`their targets and target binding dynamics. Although the
`reductionist feature of mPBPK was emphasizedpreviously
`[4, 5],
`the model has flexibility for integrating TMDD
`mechanisms. The present study demonstrates this feasibility.
`Most of the previous TMDD models utilized compart-
`mental models [8-12], and considered target binding in the
`central compartment (2CM + TMDD) under an assump-
`tion that the target is in either blood or Ussues that are at
`rapid equilibrium with blood. For PK analysis of mAbs,
`this assumption usually yields better parameter identifi-
`ability but sometimes gives inconsistent parameter esti-
`mates, particularly relating to receptor binding and
`dynamics [12]. One possible reason is that many mAbs
`have targets in extravascular space where rapid distribu-
`(1 - a2)
`- a1) -C, - Ly=
`«(1
`shes = [Li
`tional equilibrium does not occur due to their
`limited
`vascular permeability. The “rapid equilibrium” assumption
`
`
`
`that is commonly applied for small molecules in TMDD
`IC =0
`models likely causes model misspecifications and yields
`biased parameters for mAbs when their targets are in
`extravascular space. Therefore, for these mAbs, building
`TMDD in the interstitial
`fluid USF) may appropriately
`reflect and characterize target binding properties. The
`second-generaion mPBPK model provides
`a
`simple
`approach to predict interstitial concentrations of mAbs in
`two groups of lumped tissues. Thereby, mPBPK models
`can implement peripheral (interstitial) TMDDfeatures. The
`present study evaluates this feasibility and further com-
`pares model properties where TMDDis present in plasma
`or JSF. Related issues to be addressed are the influences of
`
`TA peaky
`f
`
`oteett = Thy (I ~ 92) Cy—Ly
`(1-41)
`Crenigesfree! — ARieak Kin Vieaky
`
`iC=0
`
`reflection coeffi-
`perivascular extravasation or vascular
`cients on the interstitial target dynamics and target occu-
`pancy, how the interstitial
`target-mediated elimination
`affects the apparent nonlinear clearance, and how the
`
`Q Springer
`
`ARpeaks _total
`dt
`
`— kein ~~
`. Aan
`IC — Keon | Kaew
`
`(Rieaks _fotal AReaky) . Kaex _ ARwaky
`
`)
`
`

`

`377
`
` Model A- cTMDD
`
`Keynl K,,
`
`(er) Le laptR] ofan] (1-62) La
`
`Greenest
`
`J Pharmacokinet Pharmacodyn (2014) 41:375-387
`
`dc. yphenPh a [Ly - (1 — a2) * Criet_jiee + La
`Ceaky_five ~ Champh L]{Vinmpn
`
`C= 0
`
`(1 — 67)
`
`6
`
`(
`
`)
`
`total mass of
`where Aziehs rat ANG Ajeaky sort Yepresent
`MAD, Cremfree ANd Cieakysree Indicate free concentrations
`Of MAB, Ryjensora! ANG Rreaky_sorai Tefer to total concentra-
`tions of target, and AR,ej, and ARyeaxy are Concentrations of
`drug-target complex in the two groups of Jumped tissues
`Vien AND Vieaky- The IC is the Initial Condition. The V,, is
`plasma volume, Cy, 18 mAb concentrations in lymph,
`and L, and L, are lymphflows in two lumpedtissues. The
`a, and o> are vascular reflection coefficients for Vjie,, and
`Vieakys and Gy,is lymphatic reflection coefficient, predefined
`as 0.2 in this model, as in several previous PBPK models
`[14]. Rate constantsare k,,,, for target biosynthesis, Kye, for
`target degradation, and &;,, for antibody-target complex
`internalization. Considering that TMDD is mostly associ-
`ated with antibodies that bind with cell membrane recep-
`tors, only free mAb is assumed to be collected in lymph
`and further recycled back to plasma, and the drug-receptor
`complex is immobile in JSF. The free antibody concen-
`trations are:
`
`Ciieht_free =0.5- ((Crighttotal P Kys ~ Riight_totat}
`,
`2
`as VvCright_sonal ~~ Ks ~~ Riient_sotal) + 4. Cright_sotal Ky)
`(7)
`
`Cleaky_free =05- ((Cheaky_sotat ~ Ky, _ Rreaky_torat)
`2
`Ti VvCheaky_total _— K., _ Ricaky_toiat) + 4. Cleaky_total Ks)
`(8)
`
`is a steady-state constant defined by Gibiansky
`The K,,
`et al. [13] as:
`
`kon
`
`Kin
`
`kyLt Kost
`
`Kss —_
`
`(9)
`
`The &,,, and &,, are antibody-receptor association and
`antibody-receptor dissociation rate constants. The anti-
`body-target complex concentrations are:
`
`Riight_ioial Cright_free
`ARiight = SO
`Ks + Cight_free
`
`(10)
`
`CLp
`
`Fig. 1 Model structures of second-generation minimal PBPK models
`with target-mediated drug disposition in either plasma (eTMDD,
`Model A) or
`interstitial uid (pTMDD, Model B). Symbols and
`physiological restrictions are defined in Eqs. (1)-(12). The plasma
`compartment in the /eft box represents the venous plasma as in full
`PBPK models but is not applied in this model
`
`Table 1 Parameter values employed for model simulations
`Parameter Definition
`Value Unit
`
`CG)
`
`ay
`
`0.945
`
`0.687
`
`—
`
`—-
`
`Vascular reflection coefficient for
`Viight
`Vascular reflection coefficient for
`Vieaky
`Lih/kg
`0.00!
`Systemic clearance
`GI
`i/(nM h)
`0.100
`Drug receptor association rate
`Kon
`I/h
`0.001
`Complex dissociation rate
`kag
`nM/h
`0.100
`Target biosynthesis rate
`Kvn
`I/h
`0.010
`Free target degradation rate
`Kaew
`
`
`
`Complex internalization rate 0.030Ray I/h
`
`where /SF is total volumeofsystem interstitial fluid, and K,,
`is available fraction of /SF for antibody distribution. The
`relative fractions of Viien, (0.65) and Vieaxy (0.35) to total
`free
`Cheaky
`Rreaky otal
`ARteaky — eeeeee(11)
`JSF were calculated based upon the values used in full-
`Ky5 + Cleaky_free
`PBPK models, as were the fractions of L,
`(0.33) and L»
`(0.67) to L[14, 15]. The physiologic parameters [14, 15] for
`a70 kg body weight person are: L = 2.9 Liday, ISF = 15.6
`Ly Viynpn = 5.2 L, and V, = 2.6 L. The physiologic
`parameters
`for
`a 2.6kg body weight monkey are:
`L= 0.275 Liday, ISF = 0.579 L, Vip, = 0.193 L, and
`V, = 0.0966 L. The physiologic parameters for a 20 g body
`
`is actual plasma
`restrictions are: V,
`The physiological
`volume and Vin), is total lymph volume, and:
`
`a,<1 and
`
`o2<1
`
`Vig = 0.65-ISF Ky
`
`and
`
`(12)
`
`Viegky = 0.35 « ISF : Ky,
`(13)
`
`Q) Springer
`
`

`

`378
`
`JSF = 4.35 mL,
`are: L=0.12 mL/h,
`weight mouse
`Vismph = 1.7 mL, and V, = 0.85 mL. Also, K, = 0.8 for
`native IgG, and 0.4 for native IgGy. Given the similar iso-
`electric point (p/) values (in the range of 8-9) of the cur-
`rently assessed antibodies with native IgG, (8.6 for human
`IgG) [16], K, was set to 0.8 for the following analysis.
`Typical plasma concentration versus time profiles were
`simulated for
`three conditions when target-binding is
`assumed present in either plasma or Vieugy OF Viiein A full
`TMDD modet (with &,,, and &,,,) was applied in the sim-
`ulations and the differential equations are provided in the
`Supplementary materials. The parameters used for
`this
`simulation are listed in Table |
`
`J Pharmacokinet Pharmacodyn (2014) 41:375-387
`
`L
`(1 —a,).
`where » = Rio) Kim 184 and w = Ky,
`The relauonship between RO and aywasthen simulated
`according to Eq. (16) with a changing value ofC,, from 500
`to 4,000 nM. The other parameters used in this simulation
`and for
`the following analysis of human PK data are:
`L=2.9 Liday and Vip = 15.6 L for
`a 70 kg person,
`6, = 0.2. Rio: = 100M, K,, = 20 nM, and &;,, = 2 ho.
`
`Saturation of nonlinear clearance versus saturation
`
`of receptor
`
`Receptor occupancy (RO) as a function of o,,
`
`In Model B, the apparent target-mediated nonlinear clear-
`ance (CLy,,) can be derived in a similar manner as the well-
`surred hepatic clearance model where plasma apparent
`clearance is a function of blood flow and hepatic intrinsic
`the relationship
`space,
`When targets are in interstitial
`clearance [17]. The well-stirred distribution of antibodyin
`between plasma concentrations and ROis expected todiffer
`interstiual space was based on the fact that antibody has
`from that when targets in blood. Their relationship would be
`much higher diffusivity in /SF than for perivascular
`affected by distribution rate and extent. A simulation was
`extravasation [18, 19]. The apparent CLyy 1s,
`performedto evaluate how interstitial distribution alters the
`L (1 —o r}RrrakimVise
`Yi
`Ky +Cny
`5
`relationship between plasma concentrations and RO. Com-
`CLyry =
`a
`(17)
`L- (1 —a))+ Rinai Kin Vise
`bining Eqs. (10) and (2) produces:
`Ky +Cisr
`Li
`
`dApsFsora _
`dt
`
`L-(1 — oy) Cy,-L-(1 — 61) > Cise
`Riotal Aim Cise Vise
`Kus
`1 Cisr
`
`14
`4)
`
`In Eq. (14), a1, £3, and Viign, were replaced with o,. L.
`and Vis to represent a general situation. The Ajgpejyraz 18
`total amount of antibody in /SF that could be either Apusy-
`torat OF Anetrrorat OF antibody mass in any other tissue JSF.
`An equilibrium state is obtained when dAjyrpyj_/dt = 0.
`This could approximate the situation where antibody con-
`centrations reach steady-state in both plasma and /SF after
`infusion or multiple-dosing. This approximation factors out
`“rf (time) to produce an explicit equation evaluating the
`relationships of other factors. Then,
`
`L-(l-oy)-C,-L (l= o,) + Cisr
`| Rot Kim Cisse Vise 0
`Ky + Cisr
`
`chet!
`,
`ROK.
`ee
`Gi
`From RO =< arr yields Cyyp = 75. and substitut-
`ing Cysr in Eq. (15), after rearrangement, generates:
`
`(15)
`
`This derivation was made assuming a constant Rjoig;, Which
`entails an assumption of ky = kj, This assumption
`allows a simple derivation of CLrjyy, which otherwise may
`not be easily solved explicitly. The CLyy will reach its
`maximum value (CLyyqjax) When Cysp > 0, then,
`
`Ly m=
`C TM_max
`
`K,
`L: (1 = oy) - SwathoVise
`=
`L a
`C1) Boeter
`n
`
`(18)
`
`For a mAb with nonlinear clearance, the clearance usually
`increases with a decrease of plasma concentration and a
`maximum clearance
`is
`expected when concentration
`approaches to zero. The clearance saturation (1 — CLya;/
`CLrypax) 18 defined to reflect the remaining fraction of
`nonlinear clearance at a given concentration. When the
`target is present in plasma, clearance saturation is equiva-
`lent to target saturation (RO) given that antibody concen-
`trations are usually much higher than target concentrations.
`If the target exists in JSF,
`the two are no longer equal.
`Combining Eqs. (17) and (18), their relationship is:
`
`
`
` a w
`
`40-(1—oy)-C,
`+ o|
`
`(16)
`
`
`
`g) Springer
`
`

`

`
`
`0
`
`14
`
`oN
`
`=u
`
`ec
`9°
`
`SE
`
`
`
`V, = (intercept + slope-Y(t;)) (20)
`
`1000 5
`
`Vtight
`
`44
`
`ee
`
`
`
`is the variance of the response at the ith time
`where V;
`point, f; is the actual time at the ith time point, and Y(t;) is
`the predicted response at time ¢; from the model. Variance
`parameters intercept and slope were estimated together
`with system parameters.
`_ NN —eh
`Model performance was evaluated by goodness-of-fits,
`visual
`inspection, sum of square residuals, Akaike Infor-
`mation Criterion (A/C), Schwarz Criterion (SC),
`and
`Seo
`wo
`Coefficient of Variation (CV) of the estimated parameters.
`Dig ne
`Oi 5 a=eee——n
`Joint fittings were performed for all dose levels of each
`mAb.
`
`0.01
`
`0
`
`T
`200
`
`T
`600
`400
`Time (hr)
`
`800
`
`1000
`
`Fig. 2 Plasma concentration versus time profiles for increasing doses
`from 2.6 to 1,300 nmol based on target-mediated drug disposition in
`either plasma (top), Vieasy (middle), OY Vien, (bottom) in the mPBPK
`modeling framework. Differential equations for the simulations are
`shownin Supplementary Materials and parametervalues are listed in
`Table |
`
`«RO
`Clr
`]Se
`CLry_max +0. (1 — RO)
`
`(19)
`
`wherethe parameters relating to » and ware the same as in
`Eq. (16). The association between clearance saturation and
`target saturation was simulated and the factors that influ-
`ence their relationship were also assessed. The parameters
`used in this simulation are the same as used for Eq. (16):
`L=2.9 Liday and Vise = 15.6 L for
`a 70 kg person,
`o, = 0.2, Riva) = 10 nM, K,, = 20 nM, and k;,, = 2 h7!.
`
`Results
`
`General simulations and evaluations
`
`The simulated plasma concentration versus time profiles
`with target-binding in either plasma (CTMDD), or Vjeaky
`(PTMDD-Vieaky), OF Viren, (PTMDD-Viignt) are shown in
`Fig. 2. The first two cases exhibit typical nonlinearprofiles
`(concentration-dependent decline slopes) while the last one
`does not. The PK profiles of the cTMDD model reveal a
`rapid initial decline phase for low doses, which is similar to
`the 2CM + TMDD mode]
`[8].
`In contrast,
`the plasma
`concentrations in the pr(MDD-Vj..,, model decline in
`parallel for all doses in the early phase. The cTMDD and
`pTMDD-V).;, models both exhibit a prolonged terminal
`phase.
`Additional simulations, assuming extremely high target
`densities and fast complex internalization rates,
`indicate
`
`Q Springer
`
`379
`J Pharmacokinet Pharmacodyn (2014) 41:375-387
`
`1000 =
`
`Plasma
`
`Data analysis
`
`
`
`e
`
`‘
`
`0.01
`1000 5
`
`_—
`
`NN
`
`wy
`
`Dose, nmol
`—a— 4300
`—m 650
`Pa
`en
`—4— 260
`100 aeae—r 76
`The proposed models were applied to nonlinear PK data for
`“ eg An
`seven mAbs that were foundin the literature: zalutumumab
`ee ee =
`404 i ——.
`[20]. transzusumab [21], onartuzumab [22], MEDH7945A
`i
`\
`7.
`a
`'e
`N
`[23],
`romosozumab [24], mavrilimumab [25], and ef-
`alizumab [26]. Plasma concentrations versus time data for
`144°:
`a
`J
`these antibodies were extracted using Digitizer software
`i
`[27]. Where possible, a wide range of doses were utilized
`o14 4
`.
`‘e
`with all data for each mAb fitted jointly. Different models
`
`i
`\
`T
`T
`T
`T
`T
`1
`(2CM + TMDD, pTMDD, cTMDD) were compared in
`analyzing these data. The model structure of 2CM +
`TMDD is identical as previously proposed [8]. The dif-
`ferential equations for the 2CM + TMDD and cTMDD
`and all model codes are provided in the Supplementary
`Materials.
`
`a
`
`ae
`
`oN
`
`Computer simulations were performed using ADAPT 5
`and fittings utilized the maximum likelihood method in
`ADAPT 5 with naive pooling data modeling [28]. The
`variance model was:
`
`woe
`°
`oO
`Ea
`0.4
`2
`ae
`S
`
`a
`i.
`0.04
`
`

`

`1.0
`
`J Pharmacokinet Pharmacodyn (2014) 41:375-387
`
`
`TMDD in blood1
`———— if
`8.4 Fe
`
` T
`
`0.4
`
`0.6
`
`
`
`1-Cliy!Clinmax
`
`—* C= 4000 nM
`°
`ELSSPOSCCCCCOSC
`—7— €,
`i
`*e
`3 YETI
`= 2000 nM
`a uty —*~ ¢,= 1000 nM
`iy
`So ©, = 500 nM
`*s
`.)
`»
`
`COC e,
`
`a
`
`A
`
`x
`
`os
`
`/
`
`2a
`
`.
`
`‘x
`
`.
`
`»
`
`380
`
`1.0
`
`S
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`Vascular Reflection Coefficient (c,)
`
`Receptor Occupancy (RO)
`
`receptor occu-
`Fig. 3 Simulated relationships between interstitial
`pancy (RQ) and vascular reflection coefficient (a,) at given plasma
`antibody concentrations. The simulation is based on Eq. (16) and
`parameters listed in Table | Zone |
`indicates the range of o,. for
`Ussues with fenestrated or discontinuous vascular endothelium
`Veaky) and Zone I reflects the range for tissues with continuous
`vascular endothelium (Vj,.i)
`
`Fig. 4 Simulated relationships between saturation of plasma nontin-
`ear clearance (1 — Chyad/Clery.) and saturation of targets (RO).
`Whenthe target is in /SF, any parameters that are related to target and
`target binding contribute to the deviation of their relationship from
`that with target in blood. The simulation 1s based on Eq, (19) and
`parameters fisted in Table |
`
`that no matter howhigh the target-mediated clearance, the
`PK profiles of the pTMDD-Vj.,,, model never declined at
`a slope greater than that
`in the early phase (a-phase) of
`relatively high doses. This is in contrast with the cTMDD
`and TMDD + 2CM models where an extremely high
`decline slope is usually seen for low doses [8]. The early
`parallel decay phase, as seen in the signature profiles of the
`pIMDD model,
`is associated with the slow perivascular
`extravasation of mAb, which restricts the initial decline
`
`regardless of interstitial target-mediated elimination. This
`is the reason why there was no noticeable nonlinearity
`whentarget-binding is in Vier; as the limited extravasation
`rate to Ving, (Ly x (1 — @,)) cannot support a significant
`CLyy. Based on estimations of average ¢, and gvalues for
`Viren AND Vyeagy [6]. the Chay pay are expected to be around
`3.4 mL/kg for V,;.,, and 54 mL/kg for Vag. in a 70 kg
`person. The CL747 jnay 18 expected to be even smaller if
`targets are exclusively expressed within a limited intersti-
`tial space (such as a small solid tumor).
`In themPBPK model, vascular reflection (¢,.) 1s the major
`factor governing the extravasation process. A higher value of
`cg, generally produces lesser interstitial distribution. As
`shown by the simulatedrelationship between ROand a, at an
`equilibrium state (dAjyp jojqi/dt = 0) in Fig. 3, the o,. nega-
`tively influences RO at a given plasma concentration. Zone |
`indicates the range of ¢,. for tissues with fenestrated or dis-
`continuous vascular endothelium (Vj...) and Zone I rep-
`resents o,
`range for
`tissues with continuous vascular
`endothelium (V,ie;,). Interestingly,
`there appears to be a
`stronger plasma concentration-(or dose-) dependency for
`lower o,. values (Zone I) than for the relatively high o,, values
`
`® Springer
`
`(Zone []) in increasing RO (efficacy). In other words, an
`improvement of RO (efficacy) may be easier achieved by
`increasing administered mAb doses for tissues with low a,
`than those with relatively high a,. In contrast, ussues with
`high o, exhibit a greater o-dependency and enhancing
`extravasation (or reducing o,), such as modulating epithelial
`junctions {29, 30]. seems to be a moreefficient strategy than
`increasing doses to make an improvement of RO.
`With an assumption ofconstant R,,,,./. Fig. 4 displays the
`relationship between saturation of nonlinear clearance (1 —
`CLyra//CLmay) and saturation of receptors (RO) with dif-
`ferent values of parameters pertaining to receptors and
`receptor binding properties. When TMDDexists in blood
`(sohd line, Fig. 4), the saturation of nonlinear clearance is
`equivalent to saturation of targets if one considers that mAb
`concentrations are normally much higherthan their targets.
`However, as shown in Fig. 4, their relationship is signifi-
`cantly shifted when the target is present in extravascular
`space and missing the target
`location in plasma for the
`TMDD model would lead to a biased inference of RO. Sat-
`
`uration of the apparent nonlinearclearance does notdirectly
`imply RO in the p(MDD model. Any parameter pertaining
`to v and w (Eq. (19)) is expected to contribute to the degree of
`shift. The higher values of R,,,.; and k,,,, and higher binding
`affinity (K,,, Kp) would predict a larger shift. Although a,
`considerably affects interstitial receptor saturation (Fig. 3),
`it does not seem to contribute to this relationship shift.
`In general,
`the higher clearance saturation (1 — CLyy/
`CLryy_max) Tequires higher plasma drug concentrations. The
`steep rise (on the right of Fig. 4) indicates that a further
`improvement of RO needs a large escalation of plasma
`concentrations (or doses). In other words, when the targetis
`
`

`

`
`
`J Pharmacokinet Pharmacodyn (2014) 41:375-387 38]
`
`Traszusumab
`
`[21] evaluated the PK of traszusumab,
`Tukoda et al.
`another humanized IgG,
`targeting HER2 after ascending
`doses were given to patients with metastatic breast cancer.
`The plasma PK profiles showed nonlinear behavior with
`dose-dependent terminal half-lives. The mean plasmadata
`were analyzed with the pTMDD model. The value of Kueg
`was assumed equal
`to k;,,. The model captured the PK
`profile well (Fig. 6) with reasonable parameter estimates
`(Table 2).
`
`On artuzumab
`
`(one-armed) humanized
`a monovalent
`Onartuzumab is
`IgG, directed against the hepatocyte growth factor receptor
`(c-Met) with potential antineoplastic activity. Xiang et al.
`[22] found nonlinear PK of onartuzumabovera dose range
`of 0.5-30 mg/kg in monkeys. Onartuzumab exhibited a
`parallel early decline phase for all doses followed by
`concentration-dependent elimination. The data were fitted
`with the pTMDD model. The model nicely captured the PK
`profiles (Fig. 7) and resulted in parameters with reasonable
`precision (Table 2).
`
`MEHD7945A
`
`MEHD7945A is a human IgG, with dual binding speci-
`ficity that
`is designed to target both HER3 and EGER.
`Kamath et al. [23] assessed its PK in SCID beige mice and
`monkeys and described the PK using a two-compartment
`model with linear and nonlinear plasma clearances.
`In
`principle, a two-target-mediated drug disposition model is
`mechanistically preferred for MEHD7945A PK analysis.
`However,
`the separate contribution of each target to the
`nonlinear plasma profile could not be successfully identi-
`fied in our initial analysis, particularly when only based on
`the mean plasma data. The pTMDD model with one target
`was then applied and the model captured the PK profiles
`well in both species (Fig. 8). The parameter estimates are
`listed in Table 2. According to our analysis, monkeys seem
`to have higher binding affinity than mice, suggested by a
`much lower K,, value (0.094 vs 206 nM).
`
`Romosozumab
`
`Romosozumab 1s a humanized IgG. that binds to sclero-
`stin, a protein secreted by bone cells, which inhibits bone
`formation. A first-in-human study by Padhi et al.
`[24]
`investigated the PK of romosozumabin healthy men and
`postmenopausal women. Nonlinear PK was observed,
`which is likely due to sclerostin-mediated disposition and
`elimination. The cTMDD model wastested first. Even
`
`¥ Springer
`
` O
`
`40 mg/kg
`20 mg/kg
`vy
`2mg/kg
`G
`pTMDD
`-~-- cTMDD
`
`aS
`
`le
`Deas a Tae .
`“Pa 5
`9
`
`1000
`
`100
`
`: i
`
`
`
`
`
`PlasmaZalutumumab(mg/L)
`
`2 T
`
`400
`
`600
`
`T
`800
`
`Time(hr)
`
`Fig. 5 Pharmacokinetic profiles of zalutumumab in monkeys. Swn-
`bols are observations for the indicated doses and curves are model
`fittings based on the pTMDD model (solid line) or the cCTMDD model
`(dashed line). Fitted parameters are listed in Table 2
`
`in /SF, further improvement of RO by increasing doses
`appears to be more challenging for high RO, even though itis
`important for effective therapeutics. In any case, because of
`the lower concentrations of mAb in /SF than in plasma, a
`higher concentration (or dose) of mAb is warranted to
`achieve the same level of RO as that in plasma.
`
`Case studies
`
`Zalutumumab
`
`that targets the epidermal
`Zalutumumab is a human IgG,
`growth factor receptor (EGFR). Lammerts van Bueren
`et al.
`[20] conducted a PK study of zalutumumab in
`monkeys. Their analysis revealed nonlinear PK that was
`attributed to extensive interstitial] EGFR binding. The
`authors successfully applied a two-compartment model
`with a linear plasma clearance and an EGFR-mediated
`nonlinear clearance in JSF to simulate the plasma PK
`profiles. The model simulations showed good agreement
`with measurements. We extracted the data and applied
`two models to re-analyze the data: cCTMDD and pTMDD
`(Fig. 1). In both models, kj. was assumed equal
`to Kin,
`due to a close estimate of the two parameters in inital
`fittings. Both models well-captured the PK profiles
`(Fig. 5)
`and the
`estimated parameters
`are
`listed in
`Table 2. However, as discussed in the original paper,
`EGFRare prevalent
`in the /SF and the pT[MDD model
`should represent the system more mechanistically. This is
`reflected by more
`robust parameter estimates
`(lower
`CV%) and slight
`improvement offittings (smaller Obj,
`233 vs 236) for the pTMDD than for the cCTMDD model.
`
`

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`J Pharmacokinet Pharmacodyn (2014) 41:375-387
`
`it predicted a
`though this model captured the profile well,
`:
`:
`(Kyalkieg =
`plasma
`basal
`sclerostin§
`concentration
`-
`‘
`:
`:
`19.4 nM) much higher than experimental measurements
`.
`(~0.05 nM) [31]. Such low plasma sclerostin concentra-
`tions cannot adequately support a large nonlinear clearance
`if sclerostin-mediated elimination is the reason for non-
`.
`.
`.
`.
`.
`:
`.
`linear PK, suggesting that sclerostin-mediated elimination
`p
`,
`,
`:
`.
`.
`.
`.
`may primarily occur in extravascular space, a relatively
`large pool and/or a pool with high sclerostin expression.
`The pTMDD model seems to be a reasonable option. The
`pIMDD model captured the profile well
`(Fig. 9) and
`yielded reasonable parameter estimates (Table 2). The
`.
`. - wo
`.
`estimated basal sclerostin concentration in interstiual fluid
`Le
`was about 14.2 nM. which is lower than the plasma pre-
`dicted value, but still much higher than plasma measure-
`ment values. Given that sclerostin is primarily produced
`oo.
`ee
`:
`:
`and secreted in ussues, it is likely that tissue concentrations
`;
`_
`are higher than in plasma. With more data,
`it might be
`Sod
`tne
`Td
`ema ¢
`SE
`possible to include joint plasma and /S*F TMDD models.
`
`Mavrilinuwmab
`aa
`a
`-
`Mavrilimumabis full human IgG, targeting granulocyte—
`macrophage colony-stimulating factor receptor. A first-in-
`human study by Bemester et al. [25] assessed the PK of
`mavrilimumab in subjects with rheumatoid arthritis. Pro-
`found nonlinearity was observed over a wide dose range of
`y
`g
`.
`0.01-10 mg/kg. Wanget al. further analyzed the data with
`a model consisting of a 2CM model with both linear and
`nonlinear clearance (larget-mediated) in the central com-
`partment (2CM + TMDD). The mean PK data were dig-
`.
`.
`.
`itized and reanalyzed in our study with the cCTMDDaswell
`as 2CM models. Both models captured the profiles well
`and produced comparable parameter values (Table 2). The
`cTMDD model adequately describes the plasma data
`(Fig. 10) with one Jess
`systemic parameter
`than the
`:
`2CM + TMDD model (AObj < 0.1).
`Efalizumab
`
`
`
`
`
`Efalizumab is a humanized IgG, that binds to the x-subunit
`of LFA-1 (lymphocyte function-associated antigen-1). Ef-
`.
`:
`a
`.
`alizumab was approved for use in psoriasis but was later
`.
`withdrawn from the market due to fatal brain infections.
`Seaaqataa
`a
`-
`-
`oo
`7 >
`tT OAD
`=
`The PK data of efalizumab from a number of clinical
`a eo Ce Som ome)
`g
`z
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`a + & < = = =
`studies was re