British Journal of Clinical
`Pharmacology
`
`Mechanism-based
`population modelling of the
`effects of vildagliptin on
`GLP-1, glucose and insulin in
`patients with type 2 diabetes
`
`Cornelia B. Landersdorfer,1,2 Yan-Ling He3 & William J. Jusko1
`
`1Department of Pharmaceutical Sciences, State University of New York at Buffalo, Buffalo, NY, USA,
`2Centre for Medicine Use and Safety, Faculty of Pharmacy and Pharmaceutical Sciences, Monash
`University, Melbourne, VIC, Australia and 3Translational Science-Translational Medicine, Novartis
`Institutes for BioMedical Research, Cambridge, MA, USA
`
`DOI:10.1111/j.1365-2125.2011.04109.x
`
`Correspondence
`William J. Jusko PhD, Department of
`Pharmaceutical Sciences, State University
`of New York at Buffalo, Buffalo, NY 14260,
`USA.
`Tel.: +716 645 2855
`Fax: +716 645 3693
`E-mail: wjjusko@buffalo.edu
`----------------------------------------------------------------------
`Part of this work has been presented as
`posters at the NIH Workshop on
`Quantitative and Systems Pharmacology,
`Bethesda, MD; September 25–26, 2008
`and the American Conference of
`Pharmacometrics (ACoP), Mashantucket,
`CT; October 4–7, 2009. The data without
`modelling analysis have been published
`in: He Y-L et al. Clin Pharmacokinet 2007;
`46: 577–588.
`----------------------------------------------------------------------
`Keywords
`GLP-1, glucose, insulin, mechanism-based
`population modelling, type 2 diabetes
`mellitus, vildagliptin
`----------------------------------------------------------------------
`Received
`1 December 2010
`Accepted
`14 September 2011
`Accepted Article
`Published Online
`10 October 2011
`
`WHAT IS ALREADY KNOWN ABOUT
`THIS SUBJECT
`(cid:129) Vildagliptin is a potent and selective
`inhibitor of dipeptidylpeptidase-IV (DPP-4).
`(cid:129) DPP-4 inhibition leads to increased active
`glucagon-like peptide 1 (GLP-1)
`concentrations and decreased plasma
`glucose in patients with type 2 diabetes.
`
`WHAT THIS STUDY ADDS
`(cid:129) No mechanism-based population PD
`modelling has been conducted to
`understand the effects of vildagliptin on
`active GLP-1, glucose and insulin.
`(cid:129) Active GLP-1 concentrations could be
`described by secretion of active GLP-1 from
`the gut in response to a meal and
`elimination by DPP-4 and an additional
`non-saturable elimination pathway.
`(cid:129) The effects of vildagliptin on glucose and
`insulin are primarily via enhanced GLP-1
`concentrations which could be modelled by
`its effects on insulin secretion and
`peripheral insulin sensitivity.
`(cid:129) Parallelized S-ADAPT but not NONMEM VI
`proved to be an excellent choice for
`estimating a complex population model
`such as the current PK/PD model.
`
`AIM
`To build a mechanism-based population pharmacodynamic model to describe
`and predict the time course of active GLP-1, glucose and insulin in type 2
`diabetic patients after treatment with various doses of vildagliptin.
`METHODS
`Vildagliptin concentrations, DPP-4 activity, active GLP-1, glucose and insulin
`concentrations from 13 type 2 diabetic patients after oral vildagliptin doses of
`10, 25 or 100 mg and placebo twice daily for 28 days were co-modelled. The
`population PK/PD model was developed utilizing the MC-PEM algorithm in
`parallelized S-ADAPT version 1.56.
`RESULTS
`In the PD model, active GLP-1 production was stimulated by gastrointestinal
`intake of nutrients. Active GLP-1 was primarily metabolized by DPP-4 and an
`additional non-saturable pathway. Increased plasma glucose stimulated
`secretion of insulin which stimulated utilization of glucose. Active GLP-1
`stimulated both glucose-dependent insulin secretion and insulin-dependent
`glucose utilization. Complete inhibition of DPP-4 resulted in an approximately
`2.5-fold increase of active GLP-1 half-life.
`CONCLUSIONS
`The effects of vildagliptin in patients with type 2 diabetes on several PD
`endpoints were successfully described by the proposed model. The mechanisms
`of vildagliptin on glycaemic control could be evaluated from a variety of aspects
`such as effects of DPP-4 on GLP-1, effects of GLP-1 on insulin secretion and
`effects on hepatic and peripheral insulin sensitivity. The present model can be
`used to predict the effects of other dosage regimens of vildagliptin on DPP-4
`inhibition, active GLP-1, glucose and insulin concentrations, or can be modified
`and applied to other incretin-related anti-diabetes therapies.
`
`© 2011 The Authors
`British Journal of Clinical Pharmacology © 2011 The British Pharmacological Society
`
`Br J Clin Pharmacol
`
`/ 73:3 / 373–390 / 373
`
`MPI EXHIBIT 1055 PAGE 1
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`DR. REDDY’S LABORATORIES, INC.
`IPR2024-00009
`Ex. 1055, p. 1 of 18
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`

`

`C. B. Landersdorfer et al.
`
`Introduction
`
`Vildagliptin is a potent and selective inhibitor of dipeptidyl
`peptidase IV (DPP-4), leading to increased concentrations
`of active glucagon-like peptide 1 (GLP-1) and thereby
`decreased plasma glucose concentrations. Vildagliptin is
`approved for treatment of type 2 diabetes mellitus in more
`than 76 countries including the European Union and Japan
`where 85 to 95% of all diabetes cases are type 2 [1].
`Such patients exhibit insufficient insulin activity due
`to decreased insulin action in glucose-utilizing tissues
`(peripheral insulin resistance) and impaired insulin secre-
`tion from the b-cells in the pancreas (b-cell failure).
`After ingestion of a meal, GLP-1, an incretin hormone,
`is released from the L-cells in the gut wall. Its secretion
`is stimulated both by endocrine and neural signals and
`by direct stimulation of the intestinal cells by digested
`nutrients in the gut. Active GLP-1 stimulates glucose-
`dependent insulin secretion from b-cells, enhances b-cell
`proliferation and increases b-cell resistance to apoptosis
`[2]. GLP-1 has also been demonstrated to suppress hepatic
`glucose production and delay gastric emptying [3],
`thereby decreasing high blood glucose concentrations
`after food intake. GLP-1 is rapidly inactivated by the ubiq-
`uitous enzyme DPP-4 with a half-life of approximately
`2 min in humans. Reduced secretion of GLP-1 in type 2
`diabetic patients compared with healthy subjects has
`been reported [4, 5]. Vildagliptin, a DPP-4 inhibitor, pro-
`longs the action of active GLP-1 by inhibiting its inactiva-
`tion by the DPP-4 enzyme.
`While the effects of vildagliptin from this study in type
`2 diabetic patients were previously described by non-
`compartmental analysis (NCA) [6], a mechanism-based
`compartmental modelling approach has not been applied.
`Simultaneous modelling of PD endpoints such as DPP-4,
`GLP-1, insulin and glucose by taking the pathophysiology
`into account allows the exploration of the dynamic aspects
`of mechanisms of action and the interactions between
`these PD endpoints when vildagliptin intervenes. In addi-
`tion the population approach takes into account the
`variability between patients and adequately considers
`measurements below the quantification limit. Utilizing
`parallelized S-ADAPT with the Monte Carlo parametric
`expectation maximization (MC-PEM) algorithm, a state-of-
`the-art algorithm which calculates the exact log likelihood,
`allows the estimation of the whole system by a full popu-
`lation approach which was not possible in NONMEM.
`Our companion article describes a mechanism-based
`population model that simultaneously captures the PK of
`vildagliptin and its effects on DPP-4 activity in type 2 dia-
`betic patients at different dose levels [7]. In the present
`report, we further developed a mechanism-based PK/PD
`model
`including downstream PD endpoints of GLP-1,
`insulin and glucose based on our PK/DPP-4 model to
`understand further the dynamics of the mechanism of
`action of vildagliptin.
`
`374 / 73:3 / Br J Clin Pharmacol
`
`The overall aim of our study was to develop a
`mechanism-based population PK/PD model that simulta-
`neously describes vildagliptin PK, inhibition of DPP-4 activ-
`ity and changes in active GLP-1, glucose and insulin at
`different dose levels based on the mechanism of action of
`vildagliptin.
`
`Methods
`
`A detailed report on the clinical and bioanalytical proce-
`dures that are not described here was published [6]. A
`brief description is provided in the companion article [7].
`
`Study participants
`Thirteen adult patients who had been diagnosed with type
`2 diabetes for at least 3 months prior to screening were
`included in the study. A washout period from hypoglycae-
`mic drugs of up to 4 weeks was required. The study was
`approved by the local ethics committee and conducted
`in full compliance with the Declaration of Helsinki. All
`patients signed written informed consent.
`
`Study design and drug administration
`The study was a randomized, placebo-controlled, double-
`blind, four-way crossover trial. The subjects received twice
`daily oral doses of 10, 25 or 100 mg vildagliptin (GalvusTM)
`and placebo as tablets for 28 days. Patients were at the
`study site on day 1 and from the evening of day 26 to the
`morning of day 29 in each study period. During the con-
`finement periods the patients received a standard diet
`with identical meals for all four treatments. Breakfast and
`dinner were consumed at approximately 30 min after the
`doses. The duration of food intake was reported for each
`individual patient and meal.
`
`Sampling schedule and bioanalysis
`Blood samples for measurement of active GLP-1, glucose
`and insulin concentrations were obtained on day 28 of
`each treatment period. Samples for GLP-1 were taken pre-
`dose and at 0.5, 0.58, 0.67, 0.75, 1, 1.5, 2, 3, 5, 8, 10.5, 10.58,
`10.67 10.75, 11, 11.5, 12, 14 and 16 h after the morning
`dose. Blood samples for determination of glucose and
`insulin were collected prior to dosing and at 0.75, 1, 1.25,
`1.5, 2, 2.5, 3, 4, 5, 5.5, 5.75, 6, 6.5, 7, 8, 9.75, 10.25, 10.75, 11,
`11.25, 11.5, 12, 12.5, 13 and 14 h after the morning dose. All
`samples were centrifuged and plasma was frozen at -70°C
`or lower until analysis.
`Active GLP-1 in plasma was determined utilizing the
`GLP-1 (active) ELISA kit (Linco Research, Inc., St. Charles,
`MO, USA). The lower limit of quantification (LLQ) was
`2 pmol l-1. The glucose assay was performed on a Hitachi
`747–200 Autoanalyzer (Roche Diagnostics, Indianapolis, IN,
`USA) and had a linear range up to 750 mg dl-1. Insulin was
`
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`measured by electrochemiluminescence on a 2010 Elecsys
`System (Roche Diagnostics) with an LLQ of 0.2 mIU ml-1.
`
`Non-compartmental analysis
`The individual areas under the curve (AUC) for vildagliptin,
`active GLP-1, glucose and insulin were calculated using the
`linear up/log down (linear interpolation when concentra-
`tions are increasing, logarithmic interpolation for decreas-
`ing concentrations) as implemented in WinNonlin Pro
`version 5.0.1 (Pharsight Corporation, Mountain View, CA,
`USA).
`
`Compartmental modelling
`All GLP-1, glucose, and insulin profiles from the three differ-
`ent treatments and placebo were modelled simultaneously
`utilizing the MC-PEM algorithm in S-ADAPT version 1.56 [8]
`with the Beal M3 method for handling data below the limit
`of quantification [9].Model discrimination was based on the
`following four criteria: 1) visual inspection of the observed
`and predicted profiles, 2) visual comparison of the patterns
`of systematic and random residuals, 3) the objective func-
`tion and 4) visual predictive checks.
`For the visual predictive checks, GLP-1, glucose and
`insulin concentration-time profiles were simulated for
`5000 subjects for each competing model
`in S-ADAPT
`version 1.56. The median and non-parametric prediction
`intervals were calculated and compared with the observed
`data as described in the companion report. Ideally, the
`median should mirror the central tendency of the data and
`20% of the observed data points should fall outside the
`80% prediction interval over all time points.
`Standard errors were obtained from the full PK/PD
`model by utilizing the type 1 bootstrap method (see
`S-ADAPT manual under heading poperr_type) as imple-
`mented in S-ADAPT [8] in order to obtain a measure for
`precision of parameter estimates. This method randomly
`selects sets of patients from the dataset. A number of 200
`bootstrap runs was performed to obtain standard errors.
`
`Population PK model
`Details on the PK model are provided in the companion
`article [7]. Briefly, the vildagliptin PK and DPP-4 activity
`were described simultaneously by a model for target-
`mediated drug disposition (TMDD), which accounts for the
`high affinity capacity-limited binding of vildagliptin to
`DPP-4 in both plasma and tissues.The model assumes that
`after the drug-enzyme complex has been formed, a frac-
`tion of the vildagliptin molecules is hydrolyzed by DPP-4.
`
`Structural PD model
`The diagram of the full structural PD model is illustrated in
`Figure 1. First
`the active GLP-1 concentrations were
`included in the previously developed model for vildaglip-
`tin PK and DPP-4 activity. Active GLP-1 secretion is stimu-
`lated by the presence of glucose in the gut.The amounts of
`glucose in the gut after breakfast, lunch, dinner and snack
`
`Modelling of vildagliptin PD
`
`kin_glc
`
`Plasma
`glucose
`
`S2
`
`S3
`
`kin_ins
`
`kout_ins
`
`Insulin
`
`S5
`
`ka glc
`
`kout_glc
`
`S4
`
`(RmaxC - DRC) x cf2
`
`GLP-1
`
`S1
`
`Glucose in
`the gut
`
`DPP-4 inhibition
`by vildagliptin
`(TMDD model)
`
`kin_glp
`
`kout_glp_lin
`
`Meals
`tk0, F
`
`Figure 1
`Model diagram. Symbols are defined in the text and in Table 1
`
`were modelled by assuming an arbitrary value of
`75000 mg glucose for each meal and then estimating
`glucose bioavailability from the meal by which the input
`was multiplied. Different glucose bioavailabilities, and
`therefore different amounts of glucose absorbed, were
`estimated for each type of meal to account for the different
`amounts of glucose absorbed after breakfast (75 g ¥ FB),
`lunch (75 g ¥ FL), dinner (75 g ¥ FD) and snack (75 g ¥ FS), as
`described below. As the meals were standardized through-
`out all study periods and no between treatment period
`variability was applied, the four different bioavailabilities
`could be estimated. The input of glucose (as food) into the
`gut compartment was modelled as a zero-order process
`with the duration (tk0) being the actual recorded duration
`of food intake for each individual patient and each meal.
`The amounts of glucose in the gut (mg) after breakfast
`(AGB), lunch (AGL), dinner (AGD) and snack (AGS) were
`
`dA
`GB
`dt
`
`dA
`GL
`dt
`
`dA
`GD
`dt
`
`=
`
`Input
`
`× −
`F
`B
`
`k
`
`aB
`
`×
`
`A
`GB
`
`=
`
`Input
`
`× −
`F
`L
`
`k
`
`aL
`
`×
`
`A
`GL
`
`=
`
`Input
`
`×
`
`F
`D
`
`−
`
`k
`
`aD
`
`×
`
`A
`GD
`
`× −
`F
`S
`
`k
`
`aS
`
`×
`
`A
`GS
`
`=
`
`Input
`
`dA
`GS
`dt
`where kaB, kaL, kaD and kaS (h-1) are the first order absorption
`rate constants after breakfast, lunch, dinner and snack. The
`FB, FL, FD and FS are factors for the estimation of the total
`
`Br J Clin Pharmacol
`
`/ 73:3 / 375
`
`MPI EXHIBIT 1055 PAGE 3
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`DR. REDDY’S LABORATORIES, INC.
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`

`

`C. B. Landersdorfer et al.
`
`amounts of glucose absorbed after ingestion of the corre-
`sponding meals. All
`initial conditions were zero. Input
`(mg h-1) is the rate of glucose input into the gut compart-
`ment calculated as
`
`)
`(
`75000 mg glucose
`( )
`Individual duration of food intake h
`
`The total amount of glucose in the gut compartment
`(Glcgut, mg) was
`
`GlcGut
`
`=
`
`A
`GB
`
`+
`
`A
`GL
`
`+
`
`A
`GD
`
`+
`
`A
`GS
`
`The concentration of active GLP-1 in plasma (Cglp, pM)
`was
`
`dC
`glp
`dt
`
`=
`
`in_glp
`
`k
`[[
`
`k
`
`out_glp_lin
`
`× + ×
`(
`1
`S
`1
`+
`(
`
`R
`max
`
`Glc
`−
`
`) −
`
`Gut
`
`DR
`C
`
`)×
`
`]×Cglp
`
`cf
`2
`
`C
`
`=
`
`k
`
`in_glc
`
`+
`
`Glc
`
`GutAb
`
`−
`
`k
`
`× +
`[
`1
`
`ST
`ins
`
`×
`
`(
`
`C
`
`ins
`
`−
`
`B
`ins
`
`)
`
`]×
`
`C
`
`g
`
`llc
`
`out_glc
`
`dC
`glc
`dt
`where kin_glc (mg dl-1 h-1) is the endogenous production
`rate of glucose, kout_glc (h-1) is the first-order rate constant of
`glucose elimination, Cins (mIU l-1) is insulin concentration,
`and Bins is insulin concentration at baseline. The initial con-
`dition is the glucose concentration at baseline (Bglc). The
`steady-state condition was
`=
`
`k
`
`in_glc
`
`×
`
`k
`
`B
`glc
`
`out_glc
`
`The STins (l mIU-1) describes the extent of stimulation of
`glucose utilization by insulin concentrations above base-
`line (Cins - Bins) and therefore is a measure of peripheral
`insulin sensitivity based on the model described here. The
`STins value depends on the GLP-1 concentration (Cglp):
`=
`× +
`×
`−
`[
`]
`(
`)
`1
`
`S
`
`4
`
`C
`
`glp
`
`B
`glp
`
`ST
`ins
`
`S
`5
`
`where S5 (l mIU-1) is the stimulation factor for glucose uti-
`lization by insulin when GLP-1 concentrations are at base-
`line (Cglp = Bglp). The proportionality factor S4 (l pmol-1)
`describes the increase of peripheral insulin sensitivity by
`active GLP-1 concentrations above baseline (Cglp > Bglp),
`i.e. the same concentration of insulin has a larger effect
`on glucose utilization when GLP-1 concentrations are
`increased compared with when GLP-1 concentrations are
`low.
`The concentration of insulin in plasma (mIU l-1) was
`
`(
`
`)
`
`×
`
`where kin_glp (pM h-1) was the rate of active GLP-1 secretion
`at baseline, i.e. in the fasting state, and kout_glp_lin (h-1) was
`the first-order elimination rate constant for active GLP-1
`eliminated by a non-saturable pathway. The elimination of
`GLP-1 by DPP-4 was saturable and described by (RmaxC -
`DRC ¥ cf2, as explained below. The initial condition was the
`active GLP-1 concentration at baseline (Bglp).
`The extent of stimulation of active GLP-1 secretion was
`assumed to be proportional to the total amount of glucose
`in the gut (Glcgut, mg) which was changing over time and S1
`(mg-1) was the proportionality factor. The (RmaxC - DRC)
`described the amount of free DPP-4 enzyme in plasma
`changing over time, calculated as the difference between
`the amount of total DPP-4 (DPP-4 available for binding of
`vildagliptin at zero concentration of vildagliptin) and the
`amount of the DPP-4-vildagliptin complex. The (RmaxC -
`DRC) denotes the free DPP-4 enzyme and comes from the
`PK model for vildagliptin and DPP-4 described in the com-
`panion article [7].The rate of elimination of active GLP-1 by
`DPP-4 changed over time and was proportional to the
`amount of free DPP-4 in plasma (nmol) with cf2 (h-1 nmol-1)
`as the proportionality factor. The steady-state condition
`was
`
`k
`
`in_glp
`
`=
`
`B
`glp
`
`×
`
`(
`
`k
`
`out_glp_lin
`
`+
`
`R
`max
`
`×
`C cf2
`
`
`
`)
`
`The GLP-1 model parameters were estimated simulta-
`neously with the equations for vildagliptin PK and DPP-4
`activity described in the companion article [7]. Then the
`equations for glucose and insulin were added.
`The glucose absorption rate from the gut compart-
`ment was
`
`GlcGutAb
`
`=
`
`k
`
`aB
`
`×
`
`A
`GB
`
`+
`
`k
`
`aL
`
`×
`
`k
`
`+
`A
`GL
`V
`glc
`
`×
`
`A
`GD
`
`+
`
`k
`
`aS
`
`×
`
`A
`GS
`
`aD
`
`where Vglc (dl) is the volume of distribution of glucose.
`The glucose concentration in plasma (Cglc) was
`
`376 / 73:3 / Br J Clin Pharmacol
`
`=
`
`k
`
`in_ins
`
`× +
`[
`1
`
`ST
`glc
`
`×
`
`C
`
`glc
`
`−
`
`B
`glc
`
`]−
`
`k
`
`out_ins
`
`C
`
`ins
`
`dC
`ins
`dt
`where kin_ins (mIU l-1 h-1) is the endogenous production rate
`of insulin and kout_ins (h-1) is the first order rate constant for
`insulin elimination. The initial condition is the insulin con-
`centration at baseline (Bins).The steady-state condition was
`=
`×
`
`k
`
`in_ins
`
`B
`ins
`
`k
`
`out_ins
`
`The STglc (dl mg-1) describes the extent of stimulation of
`insulin secretion by glucose concentrations above baseline
`which is enhanced by active GLP-1
`=
`× +
`×
`[
`(
`1
`
`S
`2
`
`C
`
`glp
`
`−
`
`B
`glp
`
`)
`
`]
`
`ST
`glc
`
`S
`3
`
`where S3 (dl mg-1) is the stimulation factor for insulin secre-
`tion by glucose when GLP-1 concentrations are at baseline.
`(l pmol-1) describes the
`The proportionality factor S2
`increase of pancreatic glucose sensitivity by active GLP-1
`concentrations above baseline.
`In the full PK/PD model all PK (shown in the companion
`report [7]) and PD parameters were estimated at the same
`time.
`
`Individual PD model
`Between subject variability (BSV) was included for all esti-
`mated PD parameters. A log-normal distribution was
`assumed and a full variance-covariance matrix for the PD
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`MPI EXHIBIT 1055 PAGE 4
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`

`parameters was included. A full variance-covariance matrix
`was also implemented for the PK parameters. No covari-
`ance was included between PK and PD parameters.
`S-ADAPT estimates the BSV as variance. The square root of
`the variance is reported for BSV, as this is an approximation
`to the apparent coefficient of variation of a normal distri-
`bution on log-scale. Between occasion variability was not
`included.
`
`Observation model
`The residual unidentified variability was described by a
`combined additive and proportional error model for active
`GLP-1, glucose and insulin concentrations.
`
`Results
`
`All four periods of the study were completed by 12 sub-
`jects and one patient completed only the treatments with
`10 and 25 mg vildagliptin. The average (range) weight of
`the subjects was 91 (65–116) kg, height 166 (148–183) cm
`and age 53.5 (37–64) years. Seven patients were female
`and six were male.
`The observed concentrations of active GLP-1, glucose
`and insulin from all individual subjects and for all study
`periods are shown in Figures 2 to 4. Plots of the individual
`profiles of active GLP-1, glucose and insulin (not shown
`here) revealed a relatively high variability between the
`patients with various degrees of type 2 diabetes. Post hoc
`fits for one subject and two different doses of vildagliptin
`are shown in Figure 5.
`The individual ratios of AUCtreated : AUCplacebo for GLP-1,
`glucose and insulin vs. the AUC of vildagliptin are pre-
`sented in Figure 6. The AUC of active GLP-1 was higher
`during vildagliptin treatment than during placebo treat-
`ment and the AUCtreated : AUCplacebo increased with increas-
`ing AUCvildagliptin
`for all subjects except one. At an
`AUCvildagliptin of 500 ng ml-1 h or
`larger, the individual
`AUCglucose values were lower than with placebo treatment
`for almost all subjects. Overall the AUCtreated : AUCplacebo for
`glucose decreased with increasing AUCvildagliptin. The
`AUCtreated : AUCplacebo for insulin did not show a clear trend
`with increasing AUCvildagliptin as insulin concentrations and
`insulin AUC were similar among all treatments.
`
`Mechanism-based compartmental modelling
`The parameter estimates and their BSV are reported in
`Table 1. The inclusion of each of the main model features
`based on objective function differences and mechanistic
`reasons is substantiated in Table 2. The profiles of active
`GLP-1, glucose and insulin were described by one set of
`parameter estimates for all three doses of vildagliptin and
`placebo treatment. The parameters S1 to S5 are stimulation
`factors which are multiplied by the changing GLP-1,
`glucose or insulin concentrations and thereby describe
`their effects. The newly developed model
`includes the
`
`Modelling of vildagliptin PD
`
`secretion of active GLP-1 which is stimulated by food
`intake and the elimination of active GLP-1 by saturable
`metabolism due to DPP-4 and an additional linear elimina-
`tion pathway.
`Inclusion of the additional elimination
`pathway which is not saturable at the achieved GLP-1 con-
`centrations was necessary to describe the profiles. The
`model suggests that, at complete inhibition of DPP-4 in
`plasma, the half-life of active GLP-1 in plasma was
`increased by approximately 2.5-fold compared with no
`inhibition of DPP-4. The half-life of active GLP-1 at com-
`plete DPP-4 inhibition was calculated from the estimate of
`kout_glp_lin and the half-life at 0% (absence) of DPP-4 inhibi-
`tion was calculated from (kout_glp_lin + RmaxC ¥ cf2).The profiles
`of active GLP-1 elimination by DPP-4 ((RmaxC - DRC) ¥ cf2),
`expressed as a ‘rate constant’ which changes over time, are
`shown in Figure 7A. The GLP-1 elimination due to DPP-4
`depends on the available free DPP-4 and therefore
`decreases with decreasing DPP-4 activity (see companion
`article [7], vildagliptin is both an inhibitor and substrate of
`DPP-4) after a vildagliptin dose and is constant for placebo
`treatment.
`The model includes the reciprocal feedback between
`glucose and insulin with stimulation of insulin secretion
`by glucose (STglc) and stimulation of glucose utilization by
`insulin (STins). These effects occur at baseline GLP-1 con-
`centrations (where STglc = S3 and STins = S5) and are
`increased at higher concentrations of GLP-1. The changes
`in STglc and STins over time are depicted in Figure 7B, C.
`Both the stimulation of insulin secretion per concentra-
`l mg-1) and stimulation of
`tion unit of glucose (STglc,
`glucose utilization per concentration unit of insulin (STins,
`l mIU-1) depend on active GLP-1 concentration. Therefore
`STglc (Figure 7C) and STins (Figure 7B) are increased when
`vildagliptin is given compared with placebo. The GLP-1
`effect of increasing the stimulation of insulin secretion (S2
`¥ (Cglp - Bglp)) by glucose reflects an increase in pancreatic
`glucose sensitivity. The effect of GLP-1 on increasing the
`insulin-dependent glucose utilization (S4 ¥ (Cglp – Bglp))
`describes enhanced peripheral insulin sensitivity due to
`GLP-1. Thereby the decrease in glucose concentrations
`with the higher vildagliptin doses despite similar insulin
`concentrations among treatments could be successfully
`described. Inclusion of both GLP-1 effects (S2 and S4) was
`necessary in order to describe adequately the data. Com-
`parison of simulated glucose profiles when one of the two
`effects was set to zero suggests that the effect on periph-
`eral insulin sensitivity (described by S4) was slightly larger
`than the effect on pancreatic glucose sensitivity
`(described by S2).
`Insulin secretion (mIU l-1 h-1) as predicted by the model
`from (kin_ins ¥ (1 + STglc ¥ (Cglc – Bglc)) is shown in Figure 7D.
`Based on comparison of the profiles between placebo and
`the three different doses of vildagliptin the model sug-
`gests that insulin secretion was similar for all four treat-
`ments. The profiles for STglc, STins and insulin secretion in
`Figure 7B, C, and D suggest that the effect of vildagliptin
`
`Br J Clin Pharmacol
`
`/ 73:3 / 377
`
`MPI EXHIBIT 1055 PAGE 5
`
`DR. REDDY’S LABORATORIES, INC.
`IPR2024-00009
`Ex. 1055, p. 5 of 18
`
`

`

`C. B. Landersdorfer et al.
`
`10 mg
`
`25 mg
`
`50
`
`40
`
`30
`
`20
`
`10
`
`50
`
`40
`
`30
`
`20
`
`10
`
`1322
`
`1326
`
`1330
`
`1334
`
`1338
`
`01
`
`318
`
`650
`
`654
`
`658
`
`662
`
`666
`
`0
`646
`
`100 mg
`
`Placebo
`
`50
`
`40
`
`30
`
`20
`
`10
`
`50
`
`40
`
`30
`
`20
`
`10
`
`GLP-1 concentration (pmol l-1)
`
`2666
`
`2670
`
`2674
`
`2678
`
`2682
`
`02
`
`662
`
`0
`1990
`
`1994
`
`1998
`
`2002
`
`2006
`
`2010
`
`Time (h)
`
`Figure 2
`Visual predictive checks for plasma concentrations of active GLP-1.The plots show the observed data (filled diamonds),the median predicted concentrations
`(solid line) and the 80% prediction interval (10–90% percentile, broken lines). In order to show all data from each dose level in the same plot it was assumed
`in the graphs that everyone received the doses in the same sequence. The actual sequence of dosing was observed for every subject for all modelling and
`simulations
`
`was not mainly due to an increase in insulin secretion but
`due to increased insulin sensitivity.
`The model estimates for FB, FL, FD and FS, suggested that
`the amount of glucose absorbed was highest after lunch
`
`and lowest after a snack. The rate of glucose absorption
`appeared to be most rapid after breakfast (kaB).
`The estimates for BSV and residual variability in
`Table 1 suggest that the majority of the variability appar-
`
`378 / 73:3 / Br J Clin Pharmacol
`
`MPI EXHIBIT 1055 PAGE 6
`
`DR. REDDY’S LABORATORIES, INC.
`IPR2024-00009
`Ex. 1055, p. 6 of 18
`
`

`

`Modelling of vildagliptin PD
`
`10 mg
`
`25 mg
`
`500
`
`400
`
`300
`
`200
`
`100
`
`500
`
`400
`
`300
`
`200
`
`100
`
`1322
`
`1326
`
`1330
`
`1334
`
`1338
`
`01
`
`318
`
`0
`645
`
`650
`
`655
`
`660
`
`665
`
`100 mg
`
`500
`
`400
`
`300
`
`200
`
`100
`
`Placebo
`
`500
`
`400
`
`300
`
`200
`
`100
`
`Glucose concentration (mg dl-1)
`
`2665
`
`2670
`
`2675
`
`2680
`
`02
`
`660
`
`0
`1990
`
`1994
`
`1998
`
`2002
`
`2006
`
`2010
`
`Figure 3
`Visual predictive checks for plasma concentrations of glucose vs. time. Symbols are defined in Figure 2
`
`Time (h)
`
`ent in the observed data was due to variability between
`the individual patients as compared with assay variability
`and other unexplained residual variability. Standard
`errors reported in Table 1 were obtained by bootstrap
`method 1 as implemented in S-ADAPT [8]. For several
`
`parameters standard errors were smaller than expected
`and should be interpreted conservatively. Several other
`methods for obtaining standard errors available in
`S-ADAPT were tested and provided overall comparable
`results.
`
`Br J Clin Pharmacol
`
`/ 73:3 / 379
`
`MPI EXHIBIT 1055 PAGE 7
`
`DR. REDDY’S LABORATORIES, INC.
`IPR2024-00009
`Ex. 1055, p. 7 of 18
`
`

`

`C. B. Landersdorfer et al.
`
`10 mg
`
`25 mg
`
`120
`
`100
`
`80
`
`60
`
`40
`
`20
`
`150
`
`120
`
`90
`
`60
`
`30
`
`1322
`
`1326
`
`1330
`
`1334
`
`1338
`
`01
`
`318
`
`0
`645
`
`649
`
`653
`
`657
`
`661
`
`665
`
`Placebo
`
`100 mg
`
`120
`
`100
`
`80
`
`60
`
`40
`
`20
`
`120
`
`100
`
`80
`
`60
`
`40
`
`20
`
`Insulin concentration (mIU l-1)
`
`0
`1990
`
`1994
`
`1998
`
`2002
`
`2006
`
`2010
`
`0
`2660
`
`2664
`
`2668
`
`2672
`
`2676
`
`2680
`
`Time (h)
`
`Figure 4
`Visual predictive checks for plasma concentrations of insulin vs. time. Symbols are defined in Figure 2
`
`The visual predictive checks are presented in Figures 2
`to 4 and show highly sufficient predictive performance for
`active GLP-1, glucose and insulin at the three different
`dose levels and placebo, also considering that no between
`occasion variability was included due to model complexity
`and in order to avoid potentially masking any systematic
`
`differences. Also due to lack of between occasion variabil-
`ity in the model, misfits of the observed glucose baseline
`which had high variability occurred in some patients and
`periods. However overall the fittings and predictions were
`acceptable considering the model complexity and the
`variability in the observed data.
`
`380 / 73:3 / Br J Clin Pharmacol
`
`MPI EXHIBIT 1055 PAGE 8
`
`DR. REDDY’S LABORATORIES, INC.
`IPR2024-00009
`Ex. 1055, p. 8 of 18
`
`

`

`Modelling of vildagliptin PD
`
`Active GLP-1
`
`Glucose
`
`Insulin
`
`25 mg vildagliptin dose
`
`210
`200
`190
`180
`170
`160
`150
`140
`130
`1318 1322 1326 1330 1334 1338
`
`60
`55
`50
`45
`40
`35
`30
`25
`20
`15
`10
`1318 1322 1326 1330 1334 1338
`
`100 mg vildagliptin dose
`
`240
`
`220
`
`200
`
`180
`
`160
`
`140
`
`60
`
`50
`
`40
`
`30
`
`20
`
`120
`1990 1994 1998 2002 2006 2010
`
`10
`1990 1994 1998 2002 2006 2010
`
`Time (h)
`
`22
`
`20
`
`18
`
`16
`
`14
`
`12
`
`10
`
`81
`
`318 1322 1326 1330 1334 1338
`
`18
`16
`14
`12
`10
`
`8 6 4 1
`
`2
`990 1994 1998 2002 2006 2010
`
`Concentration (pM, mg dl-1 or mIU l-1)
`
`Figure 5
`Post hoc fits for active GLP-1, glucose and insulin from one subject
`
`further evaluation of model performance,
`For
`observed vs. individual fitted and observed vs. population
`fitted GLP-1, glucose and insulin concentrations are
`shown in Figures 8 and 9, both on linear and on logarith-
`mic scales. The plots show adequate fits for all three PD
`outcomes, as a similar number of points is distributed on
`each side of the line of identity. The plots for GLP-1 might
`appear to show a bias but this is due to the fact that for
`GLP-1 a considerable fraction of the observations (14% in
`total, 28% for the placebo treatment) was below the LLQ
`of 2 pmol l-1. Those observations were taken into account
`by the Beal M3 method in the model, however they
`cannot be shown in the goodness of fit plots. The LLQ is
`shown in Figures 8 and 9 by the horizontal
`line at an
`observed concentration of 2 pmol l-1 and the part of the
`graph below that line is necessarily blank. Some patients
`had a few very high concentrations for GLP-1 and insulin
`which were not captured by the population fits as they
`were only observed in some patients. The normalized pre-
`diction distribution errors for each dose and PD outcome
`are shown in Figure 10.
`
`Discussion
`
`Most of the published models describing drug effects of
`anti-diabetic agents focus on glucose or insulin [10]. In
`most models which include both, glucose and insulin are
`not modelled simultaneously but one is fixed while the
`other is modelled and vice versa [11]. The reciprocal
`glucose insulin feedback was previously modelled utilizing
`indirect response models which describe the production
`and loss of glucose and insulin, the effect of glucose on
`insulin secretion and the effect of insulin on glucose utili-
`zation [12]. The effect of the incretin analogue, exenatide,
`on insulin secretion during a hyperglycaemic clamp study
`was explored by Mager et al. [13] through an adapted
`minimal model [14]. Silber et al. and Jauslin et al. [15, 16]
`developed a model which simultaneously described
`glucose and insulin profiles after various diagnostic tests,
`such as i.v. and oral glucose tolerance tests and clamp
`studies. As data from both i.v. and oral glucose doses were
`available, an incretin effect could be included despite the
`GLP-1 concentrations not being measured. Recently, Chan
`
`Br J Clin Pharmacol
`
`/ 73:3 / 381
`
`MPI EXHIBIT 1055 PAGE 9
`
`DR. REDDY’S LABORATORIES, INC.
`IPR2024-00009
`Ex. 1055, p. 9 of 18
`
`

`

`C. B. Landersdorfer et al.
`
`GLP-1
`
`Glucose
`
`500
`1000
`1500
`AUCvildagliptin (ng ml-1 h)
`
`2000
`
`2500
`
`1.3
`
`1.2
`
`1.1
`
`1.0
`
`0.9
`
`0.8
`
`0.7
`
`0.6
`
`0.5
`
`0
`
`6
`
`5
`
`4
`
`3
`
`2
`
`1
`
`0
`
`0
`
`500
`
`1000
`
`1500
`
`2000
`
`2500
`
`2.2
`
`2.0
`
`1.8
`
`1.6
`
`1.4
`
`1.2
`
`1.0
`
`0.8
`
`0.6
`
`Insulin
`
`0
`
`500
`1000
`