1521-0103/360/2/356–367$25.00 http://dx.doi.org/10.1124/jpet.116.236208THE JOURNAL OF PHARMACOLOGY AND EXPERIMENTAL THERAPEUTICS J Pharmacol Exp Ther 360:356–367, February 2017Copyright ª 2017 by The American Society for Pharmacology and Experimental Therapeutics

Characterization and Prediction of Cardiovascular Effects ofFingolimod and Siponimod Using a Systems PharmacologyModeling Approach s

Nelleke Snelder, Bart A. Ploeger, Olivier Luttringer, Dean F. Rigel, Randy L. Webb,David Feldman, Fumin Fu, Michael Beil, Liang Jin, Donald R. Stanski, and Meindert DanhofDivision of Pharmacology, Leiden Academic Centre for Drug Research, Leiden, The Netherlands (N.S., B.A.P., M.D.); LAP&PConsultants BV, Leiden, The Netherlands (N.S., M.D.); Modeling and Simulation Department, Novartis, Basel, Switzerland(O.L., D.R.S.); Cardiovascular and Metabolism Research, Novartis Institutes for BioMedical Research (D.F.R., D.F., F.F., M.B.,L.J.), and Cardiovascular Clinical Development (R.L.W.), Novartis Pharmaceuticals Corporation, East Hanover, New Jersey

Received September 23, 2016; accepted November 28, 2016

ABSTRACTSphingosine 1-phosphate (S1P) receptor agonists are associ-ated with cardiovascular effects in humans. This study aims todevelop a systems pharmacology model to identify the site ofaction (i.e., primary hemodynamic response variable) of S1Preceptor agonists, and to predict, in a quantitative manner, thecardiovascular effects of novel S1P receptor agonists in vivo.The cardiovascular effects of once-daily fingolimod (0, 0.1, 0.3,1, 3, and 10 mg/kg) and siponimod (3 and 15 mg/kg) werecontinuously recorded in spontaneously hypertensive ratsand Wistar-Kyoto rats. The results were analyzed using a re-cently developed systems cardiovascular pharmacology model,

i.e. the CVS model; total peripheral resistance and heart ratewere identified as the site of action for fingolimod. Next, theCVS model was interfaced with an S1P agonist pharmacokinetic-pharmacodynamic (PKPD) model. This combined model ade-quately predicted, in a quantitative manner, the cardiovasculareffects of siponimod using in vitro binding assays. In conclusion,the combined CVS and S1P agonist PKPD model adequatelydescribes the hemodynamic effects of S1P receptor agonists inrats and constitutes a basis for the prediction, in a strictlyquantitative manner, of the cardiovascular effects of novel S1Preceptor agonists.

IntroductionFingolimod and siponimod are effective in the treatment of

multiple sclerosis (Cohen et al., 2010; Gergely et al., 2012).Both drugs are sphingosine 1-phosphate (S1P) receptoragonists; fingolimod was approved by the Food and DrugAdministration in 2010, whereas siponimod is currently inclinical research (Selmaj et al., 2013; www.clinicaltrials.govNCT01665144). Next to their immunosuppressant effects,S1P receptor ligands have been associated with cardiovascu-lar effects in humans. In brief, following the administration offingolimod and siponimod, a dose-dependent decrease in heartrate was observed on the first day of treatment, with a gradualreturn to baseline with continued treatment (Kappos et al.,2006, 2010; Gergely et al., 2012; Selmaj et al., 2013). Inaddition, after administration of fingolimod, a small increaseof 1–2 mm Hg in mean arterial pressure (MAP) was observed

at a dose of 0.5 mg, and MAP was mildly increased by 4–6 mmHg after 2 months at doses of 1.25 and 5 mg (Kappos et al.,2006, 2010). No information has yet been published onpotential effects of siponimod on MAP.The immunosuppressant as well as the cardiovascular

effects of fingolimod and siponimod are mediated throughvarious S1P receptor subtypes (Subei and Cohen, 2015).Fingolimod, and more specifically its active metabolitefingolimod-phosphate (fingolimod-P), binds to four of the fivesubtypes of the S1P receptor (S1P1 and S1P3-5) with highaffinity (EC50 values of 0.3–3.1 nM) (Mandala et al., 2002;Brinkmann et al., 2004; Brinkmann, 2007). Siponimod ismoreselective, as it only binds to two of the five subtypes (S1P1 andS1P5) with high affinity, whereas its affinity for the S1P3

receptor is low (Gergely et al., 2012). In rodents, S1P1 andS1P3 receptor subtypes are involved in cardiovascular effectsof fingolimod-P and siponimod (Fryer et al., 2012). Thepurpose of our study was to 1) evaluate the site of action(i.e., primary hemodynamic response variable in terms ofheart rate, stroke volume, and peripheral resistance) offingolimod-P using a mechanistic and quantitative approach,

This investigation was financially supported by Novartis, Basel, Switzerland.dx.doi.org/10.1124/jpet.116.236208.s This article has supplemental material available at jpet.aspetjournals.org.

ABBREVIATIONS: BSL_CO, baseline value of cardiac output; BSL_HR, baseline value of heart rate; BSL_MAP, baseline value of mean arterialpressure; CO, cardiac output; CVS, cardiovascular system; fingolimod-P, fingolimod-phosphate; GTPgS, guanosine 59-3-O-(thio)triphosphate; HR,heart rate; MAP, mean arterial pressure; PK, pharmacokinetics; PKPD, pharmacokinetic-pharmacodynamic; PO, by mouth; SENS, first-order rate ofreceptor sensitization; SHR, spontaneously hypertensive rat; S1P, sphingosine 1-phosphate; SV, stroke volume; TPR, total peripheral resistance;WKY, Wistar-Kyoto rat.

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and 2) predict, in a quantitative manner, the cardiovasculareffects of novel S1P receptor agonists with different receptorselectivity profiles on the basis of information from in vitrobinding assays.To investigate the hemodynamic effects of S1P receptor

agonists, we elaborated on our previous work in which weinvestigated the cardiovascular effects of eight drugs withdifferent mechanisms of action (Snelder et al., 2013b, 2014a).To characterize drug effects on the inter-relationship betweenMAP, cardiac output (CO), heart rate (HR), stroke volume(SV), and total peripheral resistance (TPR) using hemody-namic data from rats, a systems cardiovascular pharmacologymodel, i.e. the CVS model was developed (Snelder et al.,2013b, 2014a). It was demonstrated that the CVS model issystem-specific by showing that successively removing datafrom one of the compounds that were used for model develop-ment does not affect the estimates of the system parameters.Furthermore, it was demonstrated that the site of action ofnew compounds (in terms of effects on HR, SV, and TPR,respectively) can be identified by amodel-based analysis of thetime course of the change in hemodynamic variables. To makethe CVS model suitable for providing a quantitative un-derstanding of the mechanisms underlying the cardiovasculareffects of S1P receptor agonists, combination with a receptorbinding and activation model is necessary.In this investigation, the recently proposed CVS model

was interfaced with an S1P agonist pharmacokinetic-pharmacodynamic (PKPD) model describing the targetbinding-activation and receptor downregulation and sensiti-zation of the S1P receptors. The combined model was used toidentify the site of action of fingolimod-P and to predictthe cardiovascular effects of novel S1P receptor agonists onthe basis of information from in vitro assays. Furthermore, themodel was externally validated using data from a separatestudy with fingolimod, the data from which were not used to

develop the model. Finally, for cross-validation, the combinedmodel was applied to predict the cardiovascular effects of adistinctly different S1P receptor agonist, siponimod. This showedthat themodel was able to adequately predict the cardiovasculareffects of siponimod after correction for the difference in S1Ppotency in a guanosine 59-3-O-(thio)triphosphate (GTPgS) bind-ing assay in vitro

Materials and MethodsAnimals

All studies involving animals are reported in accordance with theARRIVE (Animals in Research: Reporting In Vivo Experiments)guidelines for reporting experiments involving animals (Kilkennyet al., 2010; McGrath et al., 2010). The determination of the numberof animals per group was based on the complexity of the model and thetime and effort involved in the studies. Therefore, we included aminimal number of animals per experimental group that allowed usto adequately develop and evaluate the model. Experiments wereconducted on male, spontaneously hypertensive rats (SHRs) (TaconicFarms,Germantown,NY);Wistar-Kyoto (WKY) rats (TaconicFarms); andLewis rats in accordance with approved Novartis Animal Care and UseCommittee protocols (which have been accredited and conform to in-ternational animal welfare standards) and theGuide for theCare andUseof Laboratory Animals (National Research Council, 2011). At the timeof study, rats’ ages (body weights) were in the range of 24–50 weeks(331–504 g) and 24–36 weeks (477–781 g) for SHR and WKY rats,respectively. Rats were housed on a 12-hour light/dark cycle (light:0600–1800 hours), kept at room temperature (22°C), and were providednormal chow (Harlan Teklad 8604; Envigo, Indianapolis, IN) and waterad libitum.

Experimental Procedures

An overview of the experiments and the number of animals in eachgroup is presented in Table 1 and Supplemental Material 1. The effectof fingolimod-P on the CVS after repeated dosingwas evaluated in two

TABLE 1Study overview

Study Measures Study Designs Experiment Dose Rats

mg/kg1. CO multiple dosing

study to investigatethe cardiovasculareffects of fingolimod-P(PO once daily)

MAP, HR, andCO (TPR and SV)

Days 24–0: baseline 1 Vehicle SHR: n = 2Days 1–7: active treatment 0.1 SHR: n = 2Days 8–16: washout 0.3 SHR: n = 2

1 SHR: n = 33 SHR: n = 3

10 SHR: n = 3Days 26–0: baseline 2 Vehicle SHR: n = 1Days 1–14: active treatment WKY rat: n = 2Days 15–28: washout 10 SHR: n = 5

WKY rat: n = 5Days 25–0: baseline 3 Vehicle SHR: n = 2Days 1–28: active treatment WKY rat: n = 2Days 29–44: washouta 10 SHR: n = 3

WKY rat: n = 32. Telemetry multiple

dosing study to investigatethe effect of fingolimod-Pand siponimod on MAPand HR (PO once daily)

MAP and HR Days 26–0: baseline (SHR) 4 (externalmodelevaluation)

Vehicle SHR: n = 5Days 24–0: baseline (WKY rat) Fingolimod 0. 1, 0.3,

1, 3 and 10WKY rat: n = 5per treatment

groupDays 1–56: active treatment Siponimod 3 and 15Days 57–83: washoutDay 100: PK (only in SHR)

3. PK siponimod Bloodconcentrations

Single i.v. or PO siponimod dose;measurements at 0.25, 1, 2, 4,8, 24, and 48 h (i.v.) and 0, 0.5,1, 2, 4, 8, 24, 48, and 72 h (PO)

5 1 Lewis: n = 3per treatment

group

aThe duration of washout measurements varied per rat and was at least 16 days. In several rats, washout data were collected during a longer period, with a maximumduration of 53 days.

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studies. In addition, the effects of siponimod were studied in thesecond study (telemetry study). In both studies, rats were surgicallyinstrumented with an ascending aortic flow probe and/or a femoralarterial catheter/radiotransmitter to enable continuous recording ofCO and/or MAP and HR (Snelder et al., 2013b). After 5 weeks ofwashout in the second study (experiment 4), carotid arterial catheterswere implanted for conducting a single-dosing pharmacokinetics (PK)study after oral administration. Finally, the PK of siponimod afterintravenous and oral administration was investigated in Lewis rats,which were instrumented with a femoral venous and arterial cannula72 hours before for compound administration and for blood samplecollection, respectively.

Experimental Design

In study 1, baseline measurements were recorded 5–7 days prior toactive treatment with fingolimod, which was administered once dailyfor 1, 2, or 4 weeks at doses of 0, 0.1, 0.3, 1, 3, and 10 mg/kg by mouth(PO). Thereafter, washout data were collected during at least 9 days.In several rats, washout data were collected during a longer period(maximum of 53 days) to investigate if the hemodynamic variablesreturned to baseline. In total, 21 SHRs and 11WKY ratswere includedin this study. One SHR and two WKY rats died during the study. Allthree rats were in the fingolimod 10mg/kg treatment group. Causes ofdeath were variable, and there were no direct indications that theywere ascribable to systemic effects of the drug itself. Flow cables wereconnected to the flow probes by 7:00 a.m. and disconnected after5:00 p.m. Rats were dosed at 10:00 a.m., and collection of all datacontinued until 5:00 p.m. Thereafter, only MAP and HR data werecaptured until the flow probes were reconnected the next morning.Discrete hourly averages were calculated for each of the continuouslyrecorded CO, MAP, and HR measurements. To reduce run timesduring model development, only one out of four hourly averages wereincluded as observations in the data set; the time of that hourlyaverage was then also used.

In study 2, baseline measurements were recorded for 5 days.Thereafter, fingolimod (0, 0.1, 0.3, 1, 3, and 10mg/kg PO) or siponimod(3 and 10 mg/kg PO) was administered once daily for 8 weeks.Subsequently, washout data were collected during 3 weeks. Inaddition, after 6 weeks of washout from the repeated-dosing study,the PK of fingolimod and its active metabolite fingolimod-P wereinvestigated following a single oral administration of fingolimod (0.1,0.3, 1, 3, and 10 mg/kg) in SHRs. Blood samples were collected atpredosing and at 2, 4, 8, and 24 hours postdosing.

In study 3, siponimod blood concentrations were measuredfollowing i.v. and oral administration of 1 mg/kg siponimod, in maleLewis rats. Rats for the oral experiment were fasted approximately8 hours prior to and 2 hours post drug administration. For each route,three rats were used. After intravenous administration, blood samples

were taken at 0.25, 1, 2, 4, 8, 24, and 48 hours and after oraladministration at 0.5, 1, 2, 4, 8, 24, 48, and72hours post administration.

Compounds

In studies 1 and 2, fingolimod (PKF117-812-AA; synthesized atNovartis, Basel, Switzerland) and siponimod (NVP-BAF312-NX;synthesized at Novartis) were dissolved in water (study 1, experi-ments 1–3) or 1% carboxymethylcellulose (study 2, experiment 4) andformulated for administration at 5 ml/kg by oral gavage. The vehicle-treated animals received either water (study 1, experiments 1–3) or1% carboxymethylcellulose (study 2, experiment 4). In study 3,siponimod (NVP-BAF312-AA) was dissolved in polyethylene glycol200/glucose/water (pH-adjusted to 3–4) as previously described (Panet al., 2013) for administration at 1 ml/kg i.v. and 4 ml/kg PO.

Data Analysis

Pharmacokinetics of Fingolimod-P. Recently, a PK model wasdeveloped to characterize the PK of fingolimod and fingolimod-P inmale Lewis and Sprague Dawley rats in blood (Snelder et al., 2014b).This model was valid in the evaluated dose range of 0.1–3 mg/kg(Snelder et al., 2014b). As this excludes the 10-mg/kg dose, which wasadministered in the current studies, the predictive value of the modelto describe the PK data from the 10-mg/kg dose group in study 2 wasassessed. Details of this analysis can be found in SupplementalMaterial 2. Overall, the data from this dose group were adequatelydescribed, and the PK model could be used for PKPD model develop-ment. For this, the PK time course for doses between 0.1 and 3 mg/kgwas predicted with fixed PK parameters using the values from thepreviously developedPKmodel (Snelder et al., 2014b). For the 10-mg/kgdose, optimized parameters were used (Supplemental Material 2). Nointerindividual variability was estimated for the PK parameters. Anexample of a concentration-time profile after repeated oral dosing isshown in Fig. S2.2 in Supplemental Material 2.

Systems Pharmacology Model for the Inter-relationshipsbetween Hemodynamic Variables. The inter-relationships be-tween MAP, TPR, CO, HR, and SV are expressed by the equations1) MAP 5 CO*TPR and 2) CO 5 HR*SV (Levick, 2003). Recently, aCVS model was developed to describe drug effects on the inter-relationship between MAP, CO, HR, SV, and TPR (Snelder et al.,2013b, 2014a). This model consists of three differential equations (forHR, SV, and TPR, respectively) that are linked by negative feedbackthrough MAP (eq. 1; Fig. 1). In addition, a direct inverse relationshipbetween HR and SV was included in the model, representing therelationship between the cardiac interval and left ventricular fillingtime, i.e., when HR increases, the cardiac interval decreases, andtherefore, left ventricular filling time decreases and SV decreases. Thecircadian rhythm, which was observed in all five parameters ofthe CVS, is described by two cosine functions, one influencing the

Fig. 1. CVSmodel to characterize drug effects on the inter-relationship between MAP, CO, HR, SV, and TPR [copiedfrom Snelder et al. (2014a) with permission]. MAP equalsthe product of CO and TPR (MAP = CO*TPR), and COequals the product of HR and SV (CO = HR*SV). SV isinfluenced by indirect feedback (FB) through MAP (SV*)and by HR through a direct inverse log-linear relationship,where HR_SV represents the magnitude of this directeffect; LN is the natural logarithm and BSL_HR representsthe baseline for HR. Effect (EFF) on HR, SV, and TPR aredescribed by three linked turnover equations. In theseequations, kin_HR, kin_SV, and kin_TPR represent the zero-order production rate constants, and kout_HR, kout_SV, andkout_TPR represent the first-order dissipation rate constants.When MAP increases as a result of a stimulating effect onHR, SV, or TPR, the values of HR, SV, and TPR decrease asa result of the action of the different feedback mechanismsregulating the CVS. In this model, the magnitude offeedback on HR, SV, and TPR is represented by FB.

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production rate of HR (kin_HR) and one influencing the production rateof TPR (kin_TPR.):

MAP5CO ×TPR

CO5HR ×SV

SV5SVp × ð12HR SV ×LNðHR=BSL HRÞÞdHRdt

5kin HR × ð11CRHRÞ × ð12FB ×MAPÞ2 kout HR ×HR

dSVp

dt5kin SV × ð12FB ×MAPÞ2 kout SV ×SVp

dTRRdt

5 kin TPR × ð11CRTPRÞ  ×  ð12FB ×MAPÞ2kout TPR ×TPR

CRHR 5ampHR × cos�2p × ðt1horHRÞ

24

�

CRTPR 5ampTPR × cos�2p × ðt1horTPRÞ

24

�:

(1)

In these equations, SV* represents the SV influenced by thenegative feedback ofMAP; kin_SV represents the zero-order productionrate constant; and kout_HR, kout_SV, and kout_TPR represent the first-order dissipation rate constants of HR, SV, and TPR, respectively. Inaddition, amp represents the amplitude of the circadian rhythms, t isthe time, and hor is the horizontal displacement over time.

The CVS model was applied to characterize the time course of theeffect of fingolimod-P on the hemodynamic variables. All system-specific parameters were fixed to values reported by Snelder et al.(2014a), as the species used in the previous and current studies arethe same. However, the parameters of the circadian rhythm wereoptimized as the circadian rhythm varied between studies. Thehandling effect, i.e., the influence of a short manual restraint andoral dose administration, was excluded from the model, as only oneobservation every 4 hours was included in the data set for modeldevelopment, and the handling effect is only relevant on a muchshorter time scale. Previously, interindividual variability was iden-tified on the baseline values of MAP (BSL_MAP), CO (BSL_CO), andHR (BSL_HR). In contrast, in this analysis, the observed baselinevalues, calculated as the mean of all observations before activetreatment, were used to reduce runtimes. The residual errors ofMAP, CO, and HR were optimized using the available data. Inaddition, an exploratory graphical analysis revealed that, within thetime frame of these studies, HR decreases over time in both SHR andWKY vehicle-treated rats (approximately 0.3–0.4 beats/min/day),and that MAP decreases over time in WKY vehicle-treated rats only(approximately 0.1–0.2 mm Hg/day). The decrease in MAP over timeis related to a decrease in HR or TPR over time. Therefore,exponentially decreasing functions, linear, power, and Emax modelswere evaluated to describe the change over time of kin_HR and kin_TPR(eq. 2):

Exponential : kin 5kin 0 × expð2k × tÞLinear : kin 5kin 0 × ð12SL × tÞPower : kin 5kin 0 ×

�12SL × tPOW

�

Emax : kin 5kin 0 �12

Emax × tET50 1 t

�:

(2)

In these equations, k, SL, POW, Emax, and ET50 represent the first-order rate constants for decrease, slope of the linear relationship, thepower parameter in the power relationship, the maximum effect, andthe time at which half of the maximum effect is achieved in the Emax

relationship, respectively.S1P Agonist PKPDModel for Fingolimod-P. Data on the blood

concentrations of fingolimod-P and the changes in various hemody-namic variables were analyzed using the CVSmodel without changingthe system-specific parameters. In the first step, a model-basedhypothesis-testing procedure (Snelder et al., 2014a) was followed to

obtain insights into the site of action of fingolimod-P and thehemodynamics of its cardiovascular effects:

1) Different hypotheses on the site of action (i.e., HR, SV, andTPR) and direction of the effect (i.e., inhibiting or stimulat-ing) were formulated, resulting in six possible combinationsof effects.

2) For each hypothesis, the model was fitted to the MAP, CO,HR, SV, and TPR measurements.

3) Which hypothesis resulted in the best description of the datawas evaluated as judged by the agreement between theobserved and predicted direction and magnitude of effect andthe lowest minimum value of the objective function, asspecified in the Model Selection and Evaluation section.

The hypothesis that fingolimod-P has a stimulating effect on TPRresulted in the best description of the data. In brief, the effects onMAP, CO, TPR, and SV were adequately predicted, although themagnitude of the effect on SV was underpredicted (Table 2). Inaddition, although the nature of the HR response, i.e., an increaseor decrease in HR, was predicted adequately, the transient natureof this effect was not captured, indicating that fingolimod-P mighthave an additional effect on HR. Overall, it was found that theeffect of fingolimod-P on all variables of the CVS could be describedadequately while assuming multiple sites of action, i.e., TPR andHR (Snelder et al., 2013a). In total, three different effects werequantified: 1) a fast stimulating effect on TPR; 2) a slow sustainedstimulating effect on TPR which is only relevant in hypertensiverats following doses higher than 1 mg/kg; and 3) a transientinhibiting effect on HR, which could be described by a standardfeedback model (type I; Gabrielsson and Weiner, 2000). In this firststep, the changes in the hemodynamic variables were described byempirical models. This provided information on the most plausiblesite of action of fingolimod-P, but it also demonstrated that the CVSmodel can be applied to quantify the hemodynamics of the effect offingolimod-P on five different variables, i.e., MAP, CO, HR, SV, and

TABLE 2Investigation of the site of action of fingolimod-P

Site ofAction

Direction ofEffect Result

HR Stimulating Adequate prediction of the effect onMAP and SV; inadequate predictionof the direction of the effect on TPR,CO, and HR

HR Inhibiting Adequate prediction of the effect onTPR and CO; inadequate predictionof the direction of the effect on MAPand SV; transient nature of the effecton HR not captured

TPR Stimulating Adequate prediction of the effect onMAP, TPR, and CO; reasonableprediction of the effect on SV(magnitude of effect underestimated);transient nature of the effect onHR not captured

TPR Inhibiting Inadequate prediction of the directionof the effect on MAP, CO, HR, SV,and TPR

SV Stimulating Adequate prediction of the effect onMAP; inadequate prediction of thedirection of the effect on CO, TPR,and SV; transient nature of theeffect on HR not captured

SV Inhibiting Adequate prediction of the effect onSV and CO; reasonable predictionof the effect on TPR (magnitude ofeffect underestimated); inadequateprediction of the direction of theeffect on MAP and HR

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TPR, while assuming only two sites of action. The obtainedinformation on the site of action of fingolimod-P was in line withindependent information on the mechanism of action underlyingthe effect of fingolimod-P as discussed in detail in the Discussion.Therefore, receptor theory concepts for the characterization oftarget binding and target activation processes were incorporated inthe model (Fig. 2). The different components of the proposed S1Pagonist PKPD model are detailed here.

Effect of Fingolimod-P on Heart Rate

As fingolimod-P is an agonist for the S1P receptor, a competitiveinteraction between the endogenous agonist, S1P, and fingolimod-Pwas taken into account. This is especially important for the effect onHR since this effect is transient, which may be a result of internali-zation of the S1P receptor through binding of fingolimod-P (agonisticeffects), thereby reducing the boundS1P concentration, resulting in anopposite effect, i.e., an increase in HR.

It is assumed that the effect on HR is driven by the concentration ofreceptors activated by S1P or fingolimod-P (excluding the numberof internalized receptors). At baseline, the activated concentration ofreceptors (RAC_0) is given by eq. 3:

RAC 0 5FRAC 0 :RT 0

FRAC 0 5

�S1P

11S1P

�:

(3)

In these equations, RT_0 represents the apparent concentration ofreceptors at baseline, which was set to 1 to enable calculation of thefractional receptor occupancy. In addition, FRAC_0 represents thefraction of activated receptors at baseline.

In the presence of fingolimod-P, the activated receptor concen-tration is given by the equation for reversible competitive in-teraction between two agonists, which uses receptor dissociationconstants (Kd) (Ariëns and Simonis, 1964; Romero et al., 2012).Following the operational model of agonism (Black and Leff, 1983),the effect of the activated receptor concentration would be de-scribed by a transducer function. However, the available data didnot contain sufficient information to characterize all steps in thecascade from receptor binding to receptor activation and stimulusof the biologic system. Therefore, no transducer function wasapplied. Instead, a model based on the equation from Ariëns and

Simonis (1964) was applied in which the original model parameterKd (dissociation constant) was renamed to EC50 (potency) to reflectthat this parameter does not represent the “true” dissociationconstants (eq. 4):

FE 0 5

�S1P

11S1P

�

EHR 0 5FE 0 ×Emax 0

FE 5

S1P1CB

EC950

11S1P1CB

EC950

0BBB@

1CCCA

EHR 5FE ×Emax:

(4)

In these equations, FE_0 and FE represent the fractional effect, andEmax_0 and Emax reflect the maximum effect at baseline and duringtreatment with S1P agonists, respectively. EC509 represents theoperational EC50, which is composed of the receptor dissociationconstant and the midpoint location of the transducer for the effect offingolimod-P on HR. In addition, CB equals the fingolimod-P bloodconcentration as predicted by the PK model, and S1P represents theratio between the unknown S1P concentration and its EC509 forbinding to the S1P receptor. As the S1P concentration is unknown,this ratio is combined into one estimated parameter.

A turnover equation was used to describe the diminishment of themaximum effect caused by internalization of the S1P receptor(Romero et al., 2012) (eq. 5). Turnover models are also called indirectresponse models and can be used to describe hysteresis, i.e., the delaybetween a perturbation and a response (Dayneka et al., 1993):

dEmax

dt5kin E 2kout E ×Emax (5)

In this equation, kin_E represents the zero-order receptor synthesisrate constant, and kout_E represents the first-order degradation rateconstant. As mentioned previously, Emax_0 was assumed equal to 1;therefore, before pharmacological intervention, kin_R 5 kout_R.

During pharmacological intervention, the receptor is internal-ized and degraded, which may explain the observed tolerance inthe effect of fingolimod-P on HR (Mullershausen et al., 2009; Horgaet al., 2010) (eq. 6):

Fig. 2. S1P agonist PKPDmodel integrated with theCVS model to describe the cardiovascular effects offingolimod-P and siponimod. The effect of S1Pagonists on HR is thought to be mediated throughthe S1P1 receptor (S1P1R). Fingolimod-P and siponi-mod bind with high affinity to the S1P1R. Fingolimodand siponimod first act as full S1PR agonists, causinga decrease in HR, and thereafter function as S1PRantagonist, following the internalization and degra-dation of bound S1P1Rs. The effect of S1P agonists onTPR is thought to be mediated through the S1P3receptor (S1P3R). Fingolimod-P and siponimod bindwith high and low affinity to the S1P3R, respectively.The effect of siponimodwas considered negligible, andtherefore, was not included in this figure. The effectof fingolimod-P on TPR is a combination of a faststimulating effect and a slowly occurring stimulatingeffect (sensitization). The endogenous ligand (S1P)binds to both S1P1R and S1P3R as indicated by theplus (+). FB, feedback.

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dEmax

dt5kin E × ð12DEÞ2kout E ×Emax

DE 5FE 2FE 0

DF50 1FE 2FE 0

dkout E

dt5DEGR × ðFE 2FE 0Þ ×kout E:

(6)

In these equations, DE represents the proportion of the effect thathas been desensitized due to receptor internalization, which is drivenby the difference between FE and FE_0; DF50 represents the value ofthe difference between FE and FE_0 that elicits a half maximalreduction in kin_E; and DEGR represents the rate of receptordegradation. At baseline (FE 5 FE_0 and Emax 5 Emax_0 5 1), DE 50. An increase in FE caused by the binding of fingolimod-P to thereceptor is associated with an increase in DE and, consequently, with areduction in the synthesis of receptor and thus ETmax. In addition, anincrease in FE is associated with a sustained increase in kout_E,representing receptor degradation.

Effect of Fingolimod-P on TPR

The receptor activation underlying the effect of fingolimod-P onTPR was described using the same equations as were used for theeffect on HR (eq. 4), with one difference being that Emax was constant(fixed to 1) for the effect on TPR. In addition, an exploratory graphicalanalysis provided evidence of sensitization as reflected in an increasein the values of TPR andMAP. Here, a complex pattern was observed.Specifically, the values of both variables increased rapidly after thefirst administration of fingolimod in both SHRs and WKY rats.Subsequently, a more gradual increase over time in TPR and MAPwas observed during the whole active treatment period. This gradualincrease wasmore apparent in SHRs as compared withWKY rats. Forsome of the rats, the effect on TPR andMAP did not return to baselineafter the termination of treatment. Therefore, models including anirreversible receptor sensitization were evaluated for the effect offingolimod-P on TPR according to eq. 7:

dkout TPR

dt5 2SENS × ðFE - FE 0Þ ×kout TPR: (7)

In this equation, SENS represents the first-order rate of receptorsensitization. The change over time of kout_TPR is driven by thedifference between FE and FE_0. The baseline value of kout_TPR is fixedto the value from the CVS model. At baseline, FE equals FE_0, andtherefore, kout_TPR does not change over time. An increase in FE

caused by the binding of fingolimod-P to the receptor is associatedwith a decrease in kout_TPR and, consequently, with a sustainedincrease in TPR. As it was observed that the change over time wasdependent on the BSL_MAP, BSL_MAP was evaluated as a contin-uous covariate for SENS using linear, power, Emax, and sigmoid Emax

relationships (eq. 8). In the linear and power relationships, the effectof BSL_MAP on SENS was evaluated relative to the populationmedian of BSL_MAP:

Linear : SENS5TVSENS × ð11SENSSL × ðBSL MSP2 148:55ÞÞ

Power : SENS5TVSENS �

BSL MAP148:55

�SENSPOW

EMAX : SENS5SENSEMAX ×BSL MAP

SENSEC50 1BSL MAP

Sigmoid EMAX : SENS5SENSEMAX ×BSL MAPSENSNH

SENSSENSNHEC50 1BSL MAPSENSNH

:

(8)

In these equations, TVSENS represents the value of SENS fora typical subject; SENSSL, SENSpow, SENSEmax, SENSEC50, andSENSNH represent the slope of the linear relationship, the powercoefficient in the power relationship, the maximum effect, theBSL_MAP at which half of the maximum effect is achieved in the

Emax relationship and the Hill coefficient in the Sigmoid Emax

relationship, respectively.Overall, the effect of the activated concentration of TPR and HR

receptors (ETPR and EHR) was assumed to influence the productionrates of TPR and HR according to eq. 9 (Fig. 2):

dHRdt

5kin HR × ð11CRHRÞ × ð12FB ×MAPÞ × (1 -EHR)2 kout HR ×HR

dSVp

dt5kin SV × ð12FB ×MAPÞ2kout SV ×SVp

dTPRdt

5kin TPR × ð11CRTPRÞ × ð12FB×MAPÞ ×ETPR 2kout TPR ×TPR

dkout TPR

dt5 2SENS × (FE -FE 0) ×kout TPR:

(9)

In these equations, the differences comparedwith the CVSmodel asdescribed by Snelder et al. (2013b, 2014a) are highlighted in bold.

External Model Evaluation. The developed model was exter-nally evaluatedusing fingolimod-Pdata fromstudy 2. As the amplitude ofthe circadian rhythm and the change in kin_HR and kin_TPR over timemayvary between experiments due to different stress levels and differences inage and body weight, respectively, the parameters of the circadianrhythms and the change of kin_HR and kin_TPR over time were estimatedfirst based on the data from the vehicle groups. Subsequently, the effect offingolimod-P on MAP and HR was predicted using the developed model,and the predictions were compared with the actual data.

Prediction of the Effect of Siponimod: Cross-Validation ofthe Model. The CVS model, integrated with the developed S1Pagonist PKPD model, was used to predict the effect of siponimod onMAP and HR, on the basis of information from in vitro assays. First,the PK of siponimod was characterized using data from study 3, asdetailed in Supplemental Material 2. Subsequently, the developed PKmodel for siponimod and the CVSmodel combined with the developedS1P agonist PKPD model for fingolimod-P were used to predict theeffect of siponimod on MAP and HR. The operational EC50 values offingolimod-P for the effects on HR and TPR were adjusted forsiponimod by correcting them for the molecular weights (fingolimod-P: 387.46 g/mol; siponimod: 516.61 g/mol), the unbound fractions(fingolimod-P: 1–1.6%; siponimod: 0.03%) and the ratio of the poten-cies derived from in vitro binding assays. It was assumed thatfingolimod-P influences HR through binding to the S1P1 receptor(Koyrakh et al., 2005). The potencies of fingolimod-P and siponimodfor binding to the S1P1 receptor as derived from a GTPgS assay were2 and 0.2 nM, respectively (Lukas et al., 2014). The intrinsic activitywas the same for both compounds, i.e., 0.91–0.92 (Brinkmann et al.,2002; Gergely et al., 2012). Overall, the estimated EC509 for the effectof fingolimod-P onHR (total blood concentrations) wasmultipliedwith4.44 [(0.2*516.61/0.0003)/(2*387.46/0.01)] to obtain the EC509 forsiponimod (total blood concentrations).

Sykes et al. (2014) indicated that b-arrestin recruitment could playa role in the persistent internalization of the S1P1 receptor, whichmight explain the observed tolerance in the effect on HR. Since thepotencies derived from b-arrestin recruitment assays differ betweenfingolimod-P and siponimod, i.e., the EC50 values for b-arrestinrecruitment are 0.4 nM for fingolimod-P and 2.5 nM for siponimod(Sykes et al., 2014), it was investigated whether the estimated DF50

and/or kout_E should be corrected for this by multiplying the DF50 by6.25 (2.5/0.4) and/or the kout_E by 0.16 (0.4/2.5). Furthermore, it wasassumed that fingolimod-P influences TPR through binding to theS1P3 receptor (Coussin et al., 2002; Peters and Alewijnse, 2007;Fryer et al., 2012). The potencies of fingolimod-P and siponimod forbinding to the S1P3 receptor were 3.98 nM (Brinkmann et al., 2002)and .1000 nM (Gergely et al., 2012), respectively. Due to its marginalaffinity to the S1P3 receptor compared with fingolimod-P, it is unlikelythat siponimod changes TPR through S1P3 binding. Hence, the effect ofsiponimod on TPR was omitted from the model.

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Computation

The data from studies 1 and 2 were simultaneously analyzedusing the nonlinear mixed-effects modeling approach implementedin NONMEM (version 7.2.0; Icon Development Solutions, EllicottCity, MD). The models were compiled using Digital Fortran (version6.6C3; Compaq Computer Corporation, Houston, TX) and executed ona PC equipped with an AMD Athlon 64 processor 32001 (AdvancedMicro Devices, Inc.; Sunnyvale, California) under Windows XP(Microsoft, Redmond, WA). The results from the NONMEM analysiswere subsequently analyzed using the statistical software packageS-Plus for Windows (version 8.0 Professional; Insightful Corp.,Seattle, WA). Modeling techniques were detailed by Snelder et al.(2013b, 2014a). In addition, the NWPRI subroutine in NONMEMwasused to optimize the PK model for the 10-mg/kg dose. This allowed apenalty function based on a frequency prior to be specified, which wasadded to the 22log likelihood function (Gisleskog et al., 2002). Itcomputes a function based on a frequency prior that has amultivariatenormal form for THETA and an inverse Wishart form for OMEGA.

Model Selection and Evaluation

Models were developed and selected based on the ability to answerthe research question and predefined statistical criteria. For nestedmodels, a decrease of 10.8 points (corresponding to P , 0.001 in a x2

distribution) in the minimum value of the objective function, which isdefined as22 log likelihood, after adding an additional parameter wasconsidered statistically significant. In addition, standard errors of aparameter estimate should be less than 50%of the estimated parametervalue, and correlations between parameter estimates should lie be-tween 20.95 and 0.95. Overall, the simplest model that met theobjectives of this investigation and the predefined statistical criteriawas preferred in the process of model development. Model evaluationwas detailed by Snelder et al. (2013b).

ResultsSystems Pharmacology Model for the Inter-relationships

between Hemodynamic Variables. The CVS model asexpressed by eq. 1 and graphically represented in Fig. 1 wasapplied to characterize the hemodynamics of the effect offingolimod-P on the CVS. The amplitude [0.0726 (confidenceinterval: 0.0663–0.0789)] was significantly lower than theamplitude from the previous investigation [0.0918 (confidenceinterval: 0.825–1.01)] (Snelder et al., 2014a). The change inkin_HR and kin_TPR over time was best described by an Emax

model as expressed by eq. 2 with Emax fixed to 1. Since themaximum effect could not be estimated based on the availabledata, the developedmodel is only valid in the investigated timewindow of approximately 80 days. In SHRs, only kin_HR was

found to change over time, whereas in WKY rats, kin_HR andkin_TPR changed over time with the same ET50.S1P Agonist PKPDModel for Fingolimod-P. Themodel

as expressed by eqs. 1–9 was used to analyze the data fromstudy 1. The HR response was characterized by a rapiddecrease, which attenuated within 1–2 days. This transienteffect was described by a fast inhibiting effect on kin_HR

(receptor binding), which was followed by stimulation of HRdue to tolerance development (presumably receptor internali-zation and degradation). In addition, the change in TPR wasdescribed by a combination of a fast (receptor binding) and slowsustained (receptor sensitization) effect on TPR. The fast effectresulted in a rapid increase in TPR during active treatment.Due to the different feedback mechanisms between TPR, HR,and SV, the effect of fingolimod-P on TPR was expected totranslate into differential effects onMAP,CO,HR, andSV. Thiswas indeed observed in the data and adequately described bythe model (Fig. 3). The slow effect was best described bypermanent modulation of kout_TPR, resulting in a gradual in-crease in TPR during active treatment. As a result of themodulation of kout_TPR, TPR did not return to baseline aftertreatment was stopped. Because of the negative feedback, MAPwas increased and CO, HR, and SV were decreased aftertreatment was stopped. Consequently, the sustained increasein HR, which was mediated by the effect of fingolimod-P on HR,was partially reversed. Themodel parameter SENSwas found toincrease with BSL_MAP according to a sigmoid Emax relation-ship as expressedby eq. 8, andSENSwas126.3%higher inSHRs(typical BSL_MAP: 153.62 mmHg) as compared withWKY rats(typical BSL_MAP: 105.31mmHg).Within SHRs, SENS of a ratwith a BSL_MAP of 162.14 mm Hg (95th percentile of theBSL_MAP distribution) was 21.5% higher as compared witha rat with a BSL_MAP of 139.11 mm Hg (5th percentile ofthe BSL_MAP distribution). The baseline values, BSL_HR,BSL_MAP, and BSL_CO, were fixed to the individuallyobserved values.In general, the model adequately described the effect of

fingolimod-P on MAP, CO, HR, SV, and TPR in SHRs (Fig. 3;Supplemental Material 3). The effect of fingolimod-P on theMAP of one rat was overpredicted (Fig. 3A). The effect offingolimod-P on CO, HR, SV, and TPR in WKY rats was alsoadequately described (Fig. 3B). The effect onMAPwas slightlyunderpredicted in four out of seven WKY rats (Fig. 3B;Supplemental Material 3). All parameters could be estimatedwith good precision (Table 3). The residual error was bestdescribed by proportional residual error models. Addingparameters for additive residual errors to the model resulted

Fig. 3. Description of the effect of fingolimod-Pon MAP, CO, HR, SV, and TPR in SHRs (A) andWKY rats (B) after oral administration offingolimod at a dose of 10 mg/kg once daily at10:00 a.m. for 14 days using data from study 1,experiment 2. The dots represent the observa-tions (colored per rat), and the continuous linesrepresent the individual predictions. Start andstop of active treatment are indicated by thevertical gray lines. For clarity, only one observa-tion per day was plotted (hourly average of 16:00–17:00).

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in a significant drop in the minimum value of the objectivefunction. However, these parameters could not be estimatedwith good precision. Residual errors were small and compa-rable to the values from the previously developed CVS model(Snelder et al., 2014a). In addition, all correlations betweenstructural parameters were less than 0.95.External Model Evaluation for Fingolimod-P. An

external model evaluation using the data from study 2 dem-onstrated that the model adequately predicts the effect offingolimod-P on MAP and HR in SHRs and WKY rats (Fig. 4),as the median of the observations falls within the 90%confidence interval of the predictions. More precisely, the fasteffect on MAP was adequately predicted for all dose groups inSHRs and WKY rats. The slow sustained effect on MAP inSHRs was adequately predicted for all dose groups, except forthe 10-mg/kg group (Fig. 4A). In this group, the slow sustainedeffect was overpredicted. Furthermore, the magnitude of theinitial effect of fingolimod-P on HR was adequately predictedfor all dose groups in both SHRs and WKY rats, except for the10-mg/kg groups. In these groups, there seems to be a smalldifference in desensitization between SHRs and WKY rats,where the desensitization is stronger in WKY rats.Prediction of the Effect of Siponimod. The results of

the PK model development for siponimod can be found inSupplemental Material 2. In brief, the PK of siponimod in therats from study 3 was described adequately by a two-compartmental model with first-order elimination. The ab-sorption, whichwas characterized by two peaks, was describedby first-order absorption from two dose compartments. Theabsorption from the second dose compartment was delayedwith a lag time (Alag2).To predict the effect of siponimod on MAP and HR, we used

the developed PK model and the S1P agonist PKPD model andreplaced EC509_HR and kout_E (see Fig. 2 and section on Pre-diction of the Effect of Siponimod in theMaterials andMethods).More specifically, the EC509 for binding of fingolimod-P to the

S1P1 receptor was replaced with the EC509 for binding ofsiponimod to the S1P1 receptor. In addition, the kout_E forfingolimod-P–induced receptor internalization was replacedwith the kout_E for siponimod-induced receptor internalizationfrom in vitro assays.The effect of siponimod on MAP and HR in SHRs and WKY

rats was adequately predicted (Fig. 5), as the median of theobservations falls within the 90% confidence interval of thepredictions. In the 15-mg/kg group of WKY rats, the baselinewas underpredicted, but the magnitude of the effect wasreasonably well predicted. Overall, the effect of siponimod onHR was characterized by a small transient decrease in HRfollowed by a small increase in HR. The effect of siponimod onMAP was negligible.

DiscussionIn humans, S1P receptor agonists, which are effective in the

treatment of multiple sclerosis (Cohen et al., 2010; Gergelyet al., 2012), are associated with cardiovascular effects. Theimmunosuppressant effects, as well as the cardiovasculareffects, of these compounds are mediated through the S1Preceptor, which complicates the search for novel S1P receptoragonists that are devoid of cardiovascular effects. A quantita-tive understanding of the hemodynamics of these effects isimportant to select new compounds with an improved safetyprofile. Moreover, it may provide insights into how to phar-macologically prevent and reverse these effects for new S1Preceptor agonists (Kovarik et al., 2008) or design dose titrationschemes to attenuate these effects (Legangneux et al., 2013).Recently, a CVS model was developed to characterize

cardiovascular drug effects, which can be applied to predictthe cardiovascular effects of novel compounds (Snelder et al.,2013b, 2014a). In the current research, the CVS model wasinterfaced with an S1P agonist PKPD model to facilitate theprediction of cardiovascular effects in vivo using potency

TABLE 3Parameter values for the final S1P agonist PKPD model for the hemodynamic effect of fingolimod-PBlood-plasma ratio = 0.95, molecular weight = 387.46 g/mol, and unbound fraction = 1.3%.

Parameters Value RSE (%) LLCI ULCI

%EC9

50 HR (ng/ml)a 3740 24.4 1950 5530DF50_fr,, (ml/ng)b 1080 19.4 668 1490kout_E (1/h) 0.0720 14.7 0.0512 0.0928DEGR (1/h) 0.00286 28.0 0.00129 0.00443EC9

50 ΤPR (ng/ml)c 500 40.2 106 894SENSEMAX (1/h) 0.00267 44.2 0.000357 0.00498SENSEC50 (mm HG) 122 25.6 60.8 183SENSNH 4.87 44.8 0.597 9.14S1P 1.17 19.2 0.729 1.61horHR (h) 11.1 2.05 10.7 11.5ampHR 0.0726 4.52 0.0662 0.0790horTPR (h) 22.8 1.61 22.1 23.5ampTPR Fixed to ampHRET50_SHR 16,300 15 11,500 21,100ET50_WKY rats 7360 18.1 4750 9970Residual variability

Prop.Res.ErrorHR (CV%) 7.4 6.70 7.98Prop. Res.ErrorMAP (CV%) 5.7 4.88 6.41Prop. Res.ErrorCO (CV%) 8.2 6.60 9.55

CV, coefficient of variation; DEGR, rate of receptor degradation; LLCI, lower limit of 95% confidence interval; Prop.Res.Error, proportionalresidual error; RSE, relative standard error; ULCI, upper limit of 95% confidence interval.

aEC9502HR–based free plasma concentrations: 3740*0.013*1000/(387.46*0.95) = 132 nM.

bDF50 ¼ DF50 fr=EC950 HR: 1080/3740 5 0.29.

cEC9502TPR–based free plasma concentrations: 500*0.013*1000/(387.46*0.95) = 17.7 nM.

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estimates from in vitro experiments. By quantifying thecardiovascular effects of fingolimod-P, the S1P agonist–specificparameters were estimated. As a next step, the cardiovasculareffects of siponimod were predicted by correcting the value of

the operational EC509 of fingolimod-P on the basis of the potencyratio between fingolimod-P and siponimod in the GTPgSbinding assays. In this regard, it is important to realize thatthere is a difference between the absolute values of the in vitro

Fig. 4. Prediction of the effect of fingolimod-P on MAP and HR in SHRs (A and B) and WKY rats (C and D) after oral administration of fingolimod at adose of 0, 0.1, 0.3, 1, 3, or 10 mg/kg once daily for 8 weeks using data from study 2 (external model evaluation). The gray dots represent the observationsafter administration of fingolimod, and the continuous blue lines represent the observed median. The continuous black lines represent the predictedmedian, and the gray area represents the 90% prediction interval. The median of the observations falls within the 90% confidence interval of thepredicted median (not shown). The observations and predictions were corrected for the circadian rhythm and drug-independent change over time ascharacterized in the vehicle group. For clarity, only six (hourly average: one every 4 hours) and one (hourly average: 16:00–17:00) observations per daywere plotted for days 0–3 and 5–75, respectively. Start and stop of treatment are indicated by vertical gray dashed lines.

Fig. 5. Prediction of the effect of siponimod onMAP (A) andHR (B) in SHRs andWKY rats after oral administration of siponimod at a dose of 3 or 15mg/kgonce daily for 8 weeks using data from study 2. The gray dots represent the observations after administration of siponimod (3 or 15 mg PO), and thecontinuous blue lines represent the observed median. The continuous black lines represent the predicted median, and the gray area represents the 90%prediction interval. The median of the observations falls within the 90% confidence interval of the predicted median (not shown). The observations andpredictions were corrected for the circadian rhythm and drug-independent change over time as characterized in the vehicle group. For clarity, only six(hourly average: one every 4 hours) and one (hourly average: 16:00–17:00) observations per day were plotted for days 0–3 and 5–75, respectively. Startand stop of treatment are indicated by vertical gray dashed lines.

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potency in theGTPgS and the potencies undermore physiologicconditions in vivo. Since the experimental conditions of theGTPgS binding studies were the same for both compounds, andthe reported intrinsic activity is sufficient and comparable, theratio between the in vitro potency and the in vivo potency wasassumed to be constant.For fingolimod-P, the transient effect on HR was described

by a fast inhibiting effect depending on the degree of receptorbinding, which was followed by stimulation of HR due totolerance development presumably as a result of receptorinternalization and degradation. Furthermore, the effect offingolimod-P on TPR was adequately described by a combina-tion of a fast and a slow sustained effect. For siponimod, theeffect on MAP was negligible, and the effect on HR wascharacterized by a small transient decrease in HR followed bya small increase in HR. The simulated changes over time in allcomponents leading to the overall MAP, CO, HR, SV, and TPRresponses are illustrated in Fig. 6 following once dailyadministration of fingolimod or siponimod at doses of 10 and15 mg/kg, respectively. The identified effects of fingolimod-Pand siponimod are in line with the available information onthe mechanisms underlying the cardiovascular effects offingolimod-P and siponimod, which increases the confidencein the applied systems pharmacology modeling approach andthe predictive power of the model. In brief, the currentunderstanding of the mechanisms underlying the cardiovas-cular effects of fingolimod-P and siponimod are as follows.Fingolimod-P binds to four of the five subtypes of the S1P

receptor (S1P1 and S1P3-5) with high affinity (EC50 values of0.3–3.1 nM) (Mandala et al., 2002; Brinkmann et al., 2004;Brinkmann, 2007), whereas siponimod binds to only two of thefive subtypes (S1P1 and S1P5) with high affinity, and theaffinity for the S1P3 receptor is low (Gergely et al., 2012). S1P1

is thought to be the relevant receptor subtype involved in themodulation ofHR (Horga et al., 2010; Gergely et al., 2012). Theatrial muscarinic-gated potassium channel (IKACH) is acti-vated (Koyrakh et al., 2005), which results in a negativechronotropic effect. It is postulated that the transient natureof the effect on HR is most likely related to receptor in-ternalization and degradation (Mullershausen et al., 2009;Horga et al., 2010). The exactmechanismunderlying the effectof fingolimod-P on TPR, and thusMAP, is under debate. Threedifferent mechanisms have been proposed:

1. Fingolimod-P influences TPR through binding to theS1P3 receptor (Coussin et al., 2002; Peters and Alewijnse,2007).

2. Fingolimod-P influences TPR via a shift in thebalanced S1P-S1P1/S1P2/S1P3 signaling resulting fromfinglolimod-P–induced S1P1 receptor internalization(Bigaud et al., 2013).

3. Fingolimod (not fingolimod-P) induces TPR via in-hibition of sphingosine kinase (Spijkers et al., 2012).

In humans, the first hypothesis is thought to be unlikely, asthe blood concentrations of S1P as well as the affinities of S1Pfor the S1P3 receptor are considerably higher compared with

Fig. 6. Illustration of the change over time in the PK of fingolimod or siponimod, the effect resulting from receptor binding and activation, and theresponse in SHRs after administration of seven daily doses of fingolimod (10 mg/kg; black lines) or siponimod (15 mg/kg; gray lines) as predicted by theCVS model integrated with S1P agonist PKPD model using the parameters from Table 3. For fingolimod, the estimated EC509_TPR is in the same rangeas the total blood concentrations, whereas the EC509_HR is above the estimated total blood concentrations, resulting in a larger change in receptoroccupancy and a larger relative effect at the S1P3 receptor (S1P3R) than at the S1P1 receptor (S1P1R). For siponimod, the assumed EC509_HR is higherthan the EC509_HR for fingolimod, whereas the concentrations are in the same range. Therefore, the relative effect of siponimod onHR is smaller than theeffect of fingolimod. The plot of the change in Emax over time shows that approximately 20% of the receptor is internalized after treatment withfingolimod, whereas treatment with siponimod results in a lower degree of receptor internalization. The overall responses of MAP, HR, CO, SV, and TPRresult from the combined effects on HR and TPR. The predicted maximum decrease in HR is approximately 42 beats/min after administration offingolimod (10 mg/kg), of which ∼15 and 27 beats/min result from the effects on HR and TPR, respectively, and 10 beats/min after administration ofsiponimod (15 mg/kg). The nadir is reached at approximately 8 and 3 hours after the first dose for fingolimod and siponimod, respectively.

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fingolimod-P (Bigaud et al., 2013; Sykes et al., 2014). There-fore, due to the near-maximum receptor occupancy by S1P,fingolimod-P cannot influence TPR through the S1P3 receptor.However, for several reasons, it is possible that this hypothesisis valid in rats. For instance, the exact free S1P concentration indifferent tissues is unknown (Bigaud et al., 2013), a largeinterspecies difference may exist in S1P concentration (Grälerand Goetzl, 2004), and the receptor binding kinetics may varyconsiderably between rats and humans. The second hypothesis(fingolimod-P induced S1P1 receptor internalization) repre-sents the current understanding of the small, slow increase inMAP following a therapeutic dosing regimen in humans. Assiponimod also leads to internalization of the S1P1 receptors,this assumption implies that siponimodwould have an effect onMAP; however, such an effect has not been reported in humans.In our study, we have not observed this effect in rats, whichcould possibly be due to a limited experimental design, e.g., alow number of rats or too-low siponimod doses. Finally, thethird hypothesis seems implausible, as inhibiting S1P synthe-sis would influence the whole S1P biology. Overall, it seemsmost likely that the fast effect of fingolimod-P on TPR, whichwas observed in rats, is mediated through the S1P3 receptor.Furthermore, the slow effect on TPRmay be a result of receptorsensitization. More precisely, the major trigger for smoothmuscle cell contraction is a rise in intracellular calciumconcentration.Whereas the calcium-dependent phase of smoothmuscle cell contraction is rapid and relatively transient,calcium sensitization produced by agonist stimulation re-sults in a sustained contraction of vascular smooth musclecells (Watterson et al., 2005) and, thus, in a sustained increasein TPR. However, other mechanisms underlying the slow effecton TPR, including a shift in the balanced S1P-S1P1/S1P2/S1P3

signaling as proposed by Bigaud et al. (2013), may not beexcluded, as it is not possible to distinguish between differenthypotheses following a data-driven modeling approach whenthe expected effect is comparable.In general, the effect of fingolimod-P on MAP, CO, HR, SV,

and TPR in SHRs and WKY rats was adequately described bythe model (Fig. 3; Supplemental Material 3). However, theeffect on MAP was slightly underpredicted for four of sevenWKY rats. This could indicate that the feedback, which wasfixed to the value from the CVSmodel, was too strong forWKYrats. In the CVS model, the efficiency of the feedback wasfound to decrease with higher BSL_MAP values, indicating adecrease in the efficiency of blood pressure regulation inhypertensive subjects. Since the characterization of thefeedback relationship was based on data from a limitednumber of rats, i.e., 10 SHRs and 2WKY rats, the accuracy ofthe estimation of feedback might be low for WKY rats. Inaddition, it should be noted that, in study 1, the effect offingolimod-P on the CVS was investigated for only one doselevel (10 mg/kg). Since the external model evaluation dem-onstrated that the data from study 2 could be adequatelypredicted for all dose levels in both SHRs and WKY rats,except for the 10-mg/kg SHR group, the small underpredic-tion of the effect of fingolimod-P on MAP in WKY rats instudy 1 was accepted.The interindividual variability in the response was large

and originated mostly from variability in baselines andreceptor sensitization. Therefore, in the final model, thevariability in baselines was accounted for by using theobserved baseline values of MAP, CO, and HR (BSL_MAP,

BSL_CO, and BSL_HR) rather than the model predictions.Quantification of the covariate effect of BSL_MAP on SENSlargely explained the observed variability in sensitization.However, after accounting for these interindividual differ-ences, the effect of fingolimod-P on MAP in one SHR wasoverpredicted, indicating that not all variability between ratswas explained (Fig. 3A). This overpredictionwas also observedin the external model evaluation, i.e., the slow sustained effecton MAP in the 10-mg/kg SHR group was overpredicted (Fig.4A). As there were only four rats in this treatment group, andthe variability in the slow sustained effect is large, it could be achance finding that only one rat showed a large sustainedeffect in the study that was used for external model evalua-tion. Since, in general, the effect of fingolimod-P on MAP instudy 1 was adequately described by the model (Fig. 3;Supplemental Material 3), the random structure of the modelwas not further optimized.Finally, it should be noted that the identified parameters

from the S1P agonist PKPD model are estimated on the basisof hemodynamic data. Therefore, these estimates should onlybe interpreted in the context of this model. For the samereason, themodeling results do not provide definite conclusionson the plausibility of the different hypothesized mechanismsunderlying the effect of fingolimod-P on TPR and, thus, MAP.In summary, we applied a recently proposed CVS model to

study the cardiovascular effects of S1P receptor agonist inrats. For the prototype S1P receptor agonist fingolimod-P,total peripheral resistance and heart rate were identified asthe site of action. On the basis of this information, the CVSmodel was interfaced with an S1P agonist PKPD model toquantify the cardiovascular effects of fingolimod-P. Thecombined model adequately predicted, in a quantitativemanner, the cardiovascular effects of another S1P receptoragonist, siponimod. Therefore, it is anticipated that thedeveloped model can be applied to predict the effect of otherS1P receptor agonists on the cardiovascular system in rats.Thismay support an efficient design of rat experiments, whichis important because measuring CO has not been integratedinto daily practice due to difficulties associated with invasiveinstrumentation procedures (Doursout et al., 2001; Snelderet al., 2013b). Applications of the developed model, using theidentified set of system parameters, are currently limited toSHRs andWKY rats. However, since a systems pharmacologyapproach was applied, it is foreseen that accurate extrapola-tion between different rat strains and from one species toanother is possible. Ultimately, this quantitative pharmacol-ogy model may be used to predict the clinical response offingolimod-P and follow-up compounds in the cardiovascularsystem based on preclinical data. Before our model can beapplied for that purpose, the model should be scaled tohumans and validated for human MAP, CO, and HR measure-ments (Snelder et al., 2013b). In addition, interspecies differ-ences in plasma protein binding, blood-plasma distribution(Snelder et al., 2014b), and receptor binding, activation, signaltransduction, and expression should be taken into account.

Acknowledgments

The authors thank Corine Visser for editorial assistance.

Authorship Contributions

Participated in research design: Snelder, Ploeger, Luttringer,Rigel, Webb, Stanski, Danhof.

366 Snelder et al.

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Conducted experiments: Rigel, Webb, Feldman, Fu, Beil, Jin.Performed data analysis: Snelder, Ploeger, Luttringer, Rigel,

Stanski, Danhof.Wrote or contributed to the writing of the manuscript: Snelder,

Ploeger, Luttringer, Rigel, Webb, Feldman, Fu, Beil, Jin, Stanski,Danhof.

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Address correspondence to: Dr. Meindert Danhof, Division of Pharmacology,Leiden Academic Centre for Drug Research, Einsteinweg 55, P.O. Box 9502,2300 RA Leiden, The Netherlands. E-mail: m.danhof@lacdr.leidenuniv.nl

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