Modeling and Simulation of Anti-Sclerostin Therapy for the Treatment of Osteoporosis

MODELING AND SIMULATION OF ANTI-SCLEROSTIN THERAPY FOR THE TREATMENT OF OSTEOPOROSIS

TANG CHENG CAI (B.Sc. (Hons), NUS)

A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF PHARMACY NATIONAL UNIVERSITY OF SINGAPORE

2016

DECLARATION

I hereby declare that the thesis is my original work and it has been written by me in its entirety. I have duly acknowledged all the sources of information that have been used in the thesis

This thesis has also not been submitted for any degree in any university previously.

Tang Cheng Cai May 2016

Acknowledgement

Part of the project includes the pharmacokinetic and pharmacodynamics (PK- PD) modeling of the investigational drug, blosozumab, an anti-sclerostin antibody for the treatment of osteoporosis that was done in my capacity as an employee of Eli Lilly and Company (Eli Lilly). Eli Lilly is the copyright owner of the data, figures and tables included in sections 3 and 4 of this thesis and permission was sought and obtained to use and reproduce the data, figures and tables here. Results of the PK-PD models were previously presented at the 6th Annual Meeting of the American Conference of Pharmacometrics 2015 (ACoP6, Crystal City, VA).

I would like to thank the blosozumab and functional teams within Eli Lilly, special thanks to Dr. Thomas Raub, Dr. Bruce Mitlak and Gregory Cox, J.D, for their support, time and effort to review and comment on this thesis.

I would like to thank my company supervisor for this project Dr. Hu Leijun within Eli Lilly for the useful discussion on the blosozumab clinical data. He supported, mentored and advised me on the project as well as gave me career guidance outside of his working hours.

I would also like to express appreciation for my NUS supervisors Prof. Paul Ho Chi Lui and Dr. Yau Wai Ping for the numerous useful discussion and insights throughout this period of project work

I would like to thank my company supervisor Dr. Tham Lai San within Eli Lilly for supporting and administering the PhD program with EDB to make this project possible as well as giving me one-to-one mentoring on career planning and progression.

Lastly, I would like express my love and appreciations to my wife, Pei Wen, for her understanding and tremendous support during this period of time. She worked tirelessly to care for the household, our two young, energetic and lovely children Benjamin and Grace; and allowed time for me to meet the demands of this project.

Publications and Posters Related to the Project

Poster Presentations:

Tang CC, Benson C, McColm J, Sipos A, Mitlak B, Hu L. Population pharmacokinetics and pharmacodynamics of Blosozumab. 6th Annual Meeting of American Conference on Pharmacometrics; 2015 Oct 4-7. Crystal City, VA

Publications:

McColm J, Hu L, Womack T, Tang CC, Chiang AY. Single- and multiple- dose randomized studies of blosozumab, a monoclonal antibody against sclerostin, in healthy postmenopausal women. J bone Miner Res. 2014;29(4):935-943.

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Table of Content

Sections Page Acknowledgement ...... II Publications and Posters Related to the Project ...... III Table of Content ...... IV Summary ...... VII List of Tables ...... IX List of Figures ...... XI List of Abbreviations ...... XV 1. Introduction ...... 1 1.1. Bone Morphology and Functions ...... 1 1.2. Bone Cells ...... 2 1.3. Osteoporosis ...... 5 1.4. Targeting the Wnt Pathway ...... 9 1.5. Development of Anti-Sclerostin Therapy for Osteoporosis Treatment ...... 11 1.6. Development of Blosozumab ...... 13 2. Objectives ...... 16 3. Population PK-PD Models of Blosozumab Materials and Methods ...... 19 3.1. Blosozumab Clinical Studies Background ...... 19 3.1.1. Sample Collections ...... 23 3.1.2. PK-PD Dataset Preparation ...... 25 3.2. Population Pharmacokinetic/Pharmacodynamics Modeling Strategy ...... 27 3.2.1. General PK/PD Model Development Approach ...... 27 3.2.2. Model Evaluation ...... 30 3.2.3. Pharmacokinetic Model ...... 32 3.2.4. Pharmacodynamics Model ...... 34 4. Population PK-PD Models of Blosozumab Results ...... 38 4.1. PK Data Disposition ...... 38 4.2. Final PK Model ...... 40 4.3. PK Model Covariate Analysis ...... 47 4.3.1. Effect of Body Weight on Blosozumab Clearance ...... 47 4.3.2. Effect of Body Weight on Blosozumab Volumes of Distribution .. 48 4.4.3. Effect of Anti-Drug Antibody (ADA) on Blosozumab ...... 48 4.4. BMD Data Disposition ...... 48 4.5. Final BMD Model ...... 51

4.6. BMD Model Covariate Analysis...... 58 5. System Pharmacology Model of Anti-Sclerostin Treatment Materials and Methods ...... 60 5.1. Bone Remodeling Model Background ...... 60 5.2. Dataset and Model Description ...... 64 5.2.1. Mathematical Description of Target-Mediated Drug Disposition Kinetics ...... 66 5.2.2. Mathematical Description of the Bone Remodeling Model...... 72 5.2.3. Mathematical Description of the Bone Mineral Density Model ..... 79 6. System Pharmacology Model of Anti-Sclerostin Treatment Results...... 81 6.1. Anti-Sclerostin mAb Target-Mediated Drug Disposition ...... 81 6.1.1. Blosozumab TMDD model ...... 81 6.1.1. Romosozumab TMDD model ...... 82 6.2. Bone Biomarker Turnover Model ...... 85 6.3. Bone Mineral Density Model ...... 91 6.4. Model Qualification ...... 93 6.4.1. Romosozumab TMDD Model ...... 93 6.4.2. Bone biomarker and BMD prediction ...... 95 6.4.3. Defining the Boundary of Model Simulation...... 98 7. Simulation Experiments and Applications of the Models ...... 101 7.1. Population PK-PD Model Simulations ...... 101 7.1.1. Effect of Dosing Interval on Drug Exposure and BMD Responses ...... 102 7.1.2. Effect of Body Weight on Drug Exposure and BMD Responses . 107 7.2. Extended Bone Remodeling Model Simulations ...... 110 7.2.1. Effect of Dosing Interval on Drug Exposure and BMD Responses ...... 111 7.2.2. Duration of Precursor Osteoblast Suppression and Replenishment ...... 115 7.2.3. Long-Term Anti-Sclerostin Treatment ...... 116 7.2.4. Dose-Response Curve of BMD improvement ...... 119 7.3. Comparison of Population PK-PD and Bone Remodeling Model ...... 124 7.3.1. Discussions, Strengths and Limitations of Population PK-PD Model ...... 130 7.3.2. Discussions, Strengths and Limitations of the Extended Bone Remodeling Model ...... 131 8. Summary and Conclusion ...... 140

9. References ...... 145 10. Appendix ...... 155 10.1. Equations for the Extended Bone Remodeling model ...... 156 10.2. Derivation of the Quasi-Equilibrium Target-Mediated Drug Disposition for Anti-Sclerostin Therapy and Unbound Sclerostin ...... 159 10.3. Derivation of RANK-RANK-OPG regulation (흅푳) in Bone Remodeling Model as Described by Lemaire et al, 2004...... 162 10.4. Berkeley Madonna Code for the Extended Bone Remodeling Model. . 165

Summary Osteoporosis is a degenerative bone disease characterized by low bone mineral density (BMD) and increased risk of fracture associated with higher morbidity and mortality. Current treatments for osteoporosis included antiresorptives that reduce bone turnover and halt the bone loss and anabolics that enhance bone turnover and encourage new bone formation. The majority of osteoporosis therapies are antiresorptives and there is only one type of anabolic therapy based on parathyroid hormone (PTH) analogue. Current available treatments have their limitations and there is a medical need for new anabolic bone treatment.

Anti-sclerostin therapy is currently being developed as a bone anabolic treatment for degenerative bone diseases. Sclerostin is a protein produced by osteocytes which inhibits bone formation. Monoclonal antibodies (mAbs) that target and disrupt the sclerostin actions demonstrated increase in bone formation and BMD in preclinical experiments and clinical trials. The increased anabolic bone activities were not associated with elevated bone resorption, unlike PTH based therapy. This novel therapeutic mechanism is a promising new treatment option for osteoporosis.

In the first part of this report, we built a population pharmacokinetic- pharmacodynamics (PK-PD) model investigating the exposure and efficacy of blosozumab. Blosozumab is a humanized mAb against sclerostin tested clinically for the treatment of osteoporosis by Eli Lilly and Company. The population PK of blosozumab was characterized by a two-compartment model with first-order absorption and both linear and saturable clearance (CL). Body weight was found to influence volume of distribution and saturable CL. The population PK-PD model was an indirect response model linked to a

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hypothetical target engagement module which drives up production rate of

BMD.

In the second part of this report, we assembled publicly available information of anti-sclerostin clinical trials and built an integrated systems biology bone remodeling model with the actions of sclerostin on osteoblast and osteoclast regulations. A target-mediated drug disposition model was first developed based on the reported PK and total sclerostin level to quantify the level of target engagement and predict the unbound sclerostin profiles. The regulatory actions of sclerostin on osteoblast and osteoclast were added to a bone remodeling model as described by Lemaire et al., 2004. Sclerostin regulate bone formation by enhancing apoptosis and repressing the maturation of active osteoblasts as well as activate osteoclast maturation. The osteoblast and osteoclast were then linked to the BMD formation and destruction rates to describe the lumbar spine and total hip BMD response.

Both models were compared and used to predict and optimize dose regimens for future clinical trials. The systems biology model was used to predict clinical efficacies of a wide range of dose regimens and generate hypothesis of sclerostin regulation of bone formation. The population PK-PD model was used to quantify variability, identify potential covariates, refine the dose regimens and assess impact of patient factors on drug exposure and clinical efficacies.

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List of Tables

Tables Page

Table 1 Clinically Relevant Patient Factors Assessed in the Population PK Model ...... 34 Table 2 Clinically Relevant Patient Factors Assessed in the Population BMD Models ...... 37 Table 3 Demographic and baseline characteristics of subjects included in the population pharmacokinetics model ...... 39 Table 4 Pharmacokinetic and Covariate Parameters in Final Population Model...... 44 Table 5 Demographic and baseline characteristics of subjects included in the population BMD model ...... 50 Table 6 Pharmacodynamic Parameters in Final Population BMD Model ...... 53 Table 7 Pharmacokinetic/pharmacodynamics parameters for blosozumab and romosozumab sclerostin target-mediated disposition model...... 83 Table 8 Parameter Estimates for the Bone Remodeling Model ...... 88 Table 9 Parameter Estimates for sclerostin effect on P1NP and CTX profiles using the bone remodeling model ...... 88 Table 10 Parameter Estimates of the Lumbar Spine and Total Hip BMD Model...... 91 Table 11 Comparison of observed and model predicted romosozumab exposure ...... 94 Table 12 Comparison of simulated average steady state blosozumab exposure following subcutaneous administration of various dose and dosing interval of blosozumab for 1 year ...... 106 Table 13 Summary of population PK-PD model predicted median BMD change from baseline following 1 year of blosozumab treatment administered subcutaneously ...... 106 Table 14 Comparison of simulated steady state blosuzumab exposure stratified by body weight following 1 year treatment of blosozumab administered subcutaneously...... 108

Table 15 Summary of bone remodeling model predicted mean BMD change from baseline following 1 year of blosozumab treatment administered subcutaneously ...... 113 Table 16 Initial Conditions for Differential Equations A1 to A7...... 158

List of Figures

Figures Page

Figure 1 Schematic representation of the study design of four blosozumab studies ...... 22 Figure 2 General process for pharmacokinetic and pharmacodynamic model development...... 31 Figure 3 Schematic representation of the population pharmacokinetic model for blosozumab...... 33 Figure 4 Schematic representation of the population target-engagement and bone mineral density model for blosozumab...... 36 Figure 5 Goodness-of-fit diagnostic plots of blosozumab final pharmacokinetic model ...... 45 Figure 6 Visual predictive check for the final pharmacokinetics model ...... 46 Figure 7 Goodness-of-fit diagnostic plots of blosozumab final pharmacodynamics model. First and Second Row: Lumbar Spine BMD. Third and Fourth Row: Total Hip BMD...... 55 Figure 8 Visual predictive check for the final Lumbar Spine BMD model. (A) Absolute value. (B) Percent change from baseline...... 56 Figure 9 Visual predictive check for the final Total Hip BMD model. (A) Absolute value. (B) Percent change from baseline...... 57 Figure 10 The distribution of lumbar spine and total hip BMD percent change from baseline at 1-year observed in Study 4 (Obs) or predicted with the Population BMD models (Base: final base model; Final: final model with covariates)...... 59 Figure 11 Schematic representation of the blosozumab target-mediated drug disposition model...... 67 Figure 12 Schematic representation of the bone remodeling model with extension of sclerostin mechanism on bone interaction...... 78 Figure 13 Schematic representation of the bone mineral density model for blosozumab ...... 80 Figure 14 Goodness of fit of (A) sclerostin concentration time profile and model predictions following blosozumab treatment and (B) romosozumab

concentration time profile and model predictions following single dose romosozumab treatment...... 84 Figure 15 Predicted percentage change from baseline of (A) total sclerostin and (B) unbound sclerostin concentration-time profile after singles and multiple doses of blosozumab treatment in phase 1 and 2 clinical trials...... 86 Figure 16 Predicted percentage change from baseline of (A) total sclerostin and (B) unbound concentration-time profiles after single and multiple doses of romosozumab treatment in phase 1 and 2 clinical trials...... 87 Figure 17 Goodness-of-fit of percent change from baseline of observed (A) P1NP and (B) CTX concentration-time profiles and model predictions after single and multiple doses of blosozumab treatment in phase 1 and 2 clinical trials...... 90 Figure 18 Goodness-of-fit of (A) lumbar spine and (B) total hip BMD overlay with observed data following single and multiple doses of blosozumab in phase 1 and 2 clinical trials...... 92 Figure 19 Prediction of (A) P1NP and (B) CTX concentration time profile against observed data after single and multiple doses of romosozumab treatment in phase 1 and 2 clinical trials...... 96 Figure 20 Prediction of (A) lumbar spine and (B) total hip BMD overlay with observed percent change from baseline (± 95% CI) following single and multiple doses of romosozumab in phase 1 and 2 clinical trials...... 97 Figure 21 Estimated BMD differences compared to reference population in Van Buchem disease and sclerosteosis and model prediction of maximum BMD response in complete sclerostin inhibition...... 100 Figure 22 Simulated median (90% PI) (A) blosozumab serum concentration at steady state and (B) lumbar spine and (C) total hip BMD response as percent change from baseline (%CFB) following various regimens of 1-year subcutaneous blosozumab treatment and 1-year follow-up ...... 105 Figure 23 Simulated median (90% PI) (A) blosozumab serum concentration at steady state and (B) lumbar spine and (C) total hip BMD response as

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percent change from baseline (%CFB) following various regimens of 1-year treatment of blosozumab administered subcutaneously and 1- year follow-up stratified by body weight ...... 109 Figure 24 Prediction of (A) blosozumab concentration and (B) unbound sclerostin (C) P1NP, (D) CTX, (E) lumbar spine BMD and (F) total hip BMD following various dose regimens of blosozumab administered subcutaneously ...... 114 Figure 25 Prediction of (A) P1NP and (B) ROB following various dose regimens blosozumab treatment administered subcutaneously for 36 months ...... 116 Figure 26 Prediction of (A) Lumbar Spine BMD and (B)Total Hip BMD following various dose regimens of blosozumab treatment administered subcutaneously for 30 years followed by 20 years observation ...... 119 Figure 27 Temporal responses of (A) lumbar spine and (B) total hip BMD following various dose regimens of blosozumab treatment administered subcutaneously for 10 years ...... 122 Figure 28 Dose-Response relationship of (A) lumbar spine and (B) total hip BMD at 1 year following various dose regimens of blosozumab treatment administered subcutaneously. Left Panel: normal x-axis. Right Panel: logarithmic x-axis...... 123 Figure 29 Predicted blosozumab serum concentration using (A) population PK model and (B) TMDD model at various blosozumab regimens administered subcutaneously for 1 year ...... 126 Figure 30 Predicted lumbar spine BMD percent change from baseline using (A) population PK-PD model and (B) extended bone remodeling model at various blosozumab regimens administered subcutaneously for 1 year ...... 128 Figure 31 Predicted total hip BMD percent change from baseline using (A) population PK-PD model and (B) extended bone remodeling model at various blosozumab regimens administered subcutaneously for 1 year ...... 129 Figure 32 Predicted (A) sclerostin concentration, (B) 흅푺푹, (C) 흅푺푩, (D) 흅푺푳, (E) 흅푺푶, and (F) sclerostin, (G) P1NP, (H) CTX, (I) lumbar spine and (J) total hip BMD percent change from baseline

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following Q1W blosozumab regimens of various doses administered subcutaneously for one year followed by one year observation ...... 134 Figure 33 Comparison of (A) bone modeling and (B) bone remodeling...... 138

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List of Abbreviations

AOB active osteoblast AOC active osteoclast APC adenomatous polyposis coli AUC area under the concentration-time curve BQL below the lower limit of the quantitation BMD bone mineral density BMI body mass index BMU basic multicellular unit BSAP bone-specific alkaline phosphatase C50 Michaelis-Menten constant CI confidence interval CL clearance CLSAT saturable clearance Cmax maximum concentration CTX serum type 1 C-terminal procollagen DKK-1 Dickkopf-1 Dlx5 distal-less homeobox 5 Dsh Disheveled DXA dual energy x-ray absorptiometry EBE empirical Bayes estimate ELISA enzyme-linked immunosorbent assay F absolute bioavailability Fzd Frizzled FDA Food and Drug Administration FGF23 fibroblast growth factor 23 GSK-3β glycogen synthase kinase 3 beta HSC hematopoietic stem cell IgG4 immunoglobulin G4 IV / i.v. intravenous Ka first-order absorption rate Lrp5/6 low-density lipoprotein receptor-related proteins 5 or 6 LOCF last-observation-carried-forward mAb monoclonal antibody M-CSF macrophage colony-stimulating factor MSC mesenchymal stem cell Msx2 Msh homeobox 2 NAA10 N-α-acetyltransferase 10 OFV objective function value OPG osteoprotegerin P1NP procollagen type I N-terminal propeptide PD pharmacodynamics PI prediction interval PK pharmacokinetics

PMP postmenopausal PTH parathyroid hormone Q intercompartmental clearance Q2W every 2 weeks Q4W every 4 weeks QM / Q1M every 1 month Q3M every 3 months Q6M every 6 months Q12M every 12 months Q18M every 18 months RANK receptor activator of nuclear factor κB RANKL RANK ligand ROB responding osteoblast Runx2 Runt-related transcription factor 2 SC / s.c. subcutaneous SD standard deviation SE standard error %SEE standard error of estimate TGF-β transforming growth factor beta tmax time to maximum concentration t1/2 half-life V2 central volume of distribution V3 peripheral volume of distribution VPC visual predictive check Vss/F apparent volume of distribution at steady state WHO World Health Organization

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1. Introduction

1.1. Bone Morphology and Functions The human bone is a dynamic system that performs several important roles to ensure the proper operations of the human body. It performs structural, mechanical and metabolic tasks. The human bones make up the skeletal framework that gives structural support to the body and protect the internal organs from external forces. To perform these mechanical tasks, a strong and lightweight structural framework is essential. The bone is a living tissue that continuously undergoes dynamic remodeling process to repair the micro- fractures sustained from the daily mechanical stresses1. It was discovered that mechanical loading stimulates the bone formation activities, whereas lack of physical exercise causes bone loss. Bone strength and bone strain play a balancing act to govern the bone resorption and formation rate in a process known as mechanostat2. Bone strength is dependent on bone mass and the architectural construction. Although the effect of three-dimensional bone construction on bone strength is unclear, increasing bone mass will improve bone strength. Bone strain, on the other hand, measures the elastic deformation of the bone due to mechanical loading. There is a natural feedback between these two factors; where high bone mass discourages active bone formation whereas bone strain is necessary to maintain the bone integrity3. Additionally, the bone is also a metabolically active site where hematopoiesis primarily takes place and where mineral store and serum mineral content balance is actively maintained2,4.

Although the human bone can come in different shapes and sizes, the general gross anatomy is similar and is composed of multiple layers.

Periosteum is a membranous layer that encases the outer surface of the bone.

Beneath the periosteum is a dense cortical bone layer surrounding an inner, more matrix-like, porous trabecular bone. The endosteum separates the cortical bone and the trabecular bone. The cortical bone consists of multiple concentric structures called an osteon. The osteons are made up of bone cells enveloping a central canal called the Haversian canal. Neighboring osteons are connected by Volkmann's canals at right angles, allowing direct communications between the bone cells across the structure. Osteons are metabolically active site where bone resorption and bone formation take place.

Beneath the cortical layer is the trabecular layer that is made up of crisscrossing trabeculae forming a mesh-like structure with open spaces in- between. Within these irregular open spaces are bone marrow and hematopoietic stem cells. These stem cells will later develop into platelets, red blood cells and white blood cells. The bone is a metabolically active tissue and contains several different cell types that are involved in the maintenance, break down, construction and mineralization of bone tissue. The unique trabecular structure, with its honeycomb-like configuration, contributes to the bone’s light-weight but yet strong structure so as to support the bone’s mechanical functions.

1.2. Bone Cells The main cell types that are found in the bones are: osteoblasts, osteoclasts, and osteocytes. The cells are bathed in an extracellular matrix that consists of both organic and inorganic components. The organic portion is composed mainly of collagen that is a structural protein that gives the matrix its gelatinous consistency and contributes to the bone’s tensile strength. The

inorganic portion is composed primarily of hydroxyapatite, which is the salt of calcium and phosphate, and contributes to the bone’s compressional strength.

Other minerals such as magnesium, sodium, potassium and carbonate are also often found in trace quantities in the bone matrix. Osteoblasts are responsible for building new bones while osteoclasts break down bone. Osteocytes have the function of regulating the balance of bone resorption and formation.

Osteoblasts are single nuclei cells that are involved in the synthesis of new bone materials. Osteoblasts originate from the multipotent mesenchymal stem cells (MSCs), under the influence of transcription factors such as Runx2

(Runt-related transcription factor 2), Dlx5 (distal-less homeobox 5) and Msx2

(Msh homeobox 2)5. These local factors induce the MSCs to commit and develop into preosteoblasts. The differentiation of preosteoblast into osteoblast takes several different stages, identified by different cell surface chemical markers, with Wnt signaling playing critical role to push the cells through these different developmental phases. Besides Wnt signal, other factors, such as estrogens, glucocorticoid, vitamin D, parathyroid hormone (PTH) and transforming growth factor beta (TGF-β), also play important function in the osteoblastic maturation. PTH is thought to induce osteoblast maturation by engaging the PTH receptors that are found on the preosteoblast surface6–9. In the process of bone formation, osteoblasts function as a group with neighboring cells. The consortium of osteoblast secretes specific protein which forms an unmineralized matrix layer, called an osteoid, on existing bone surfaces. The osteoid are then mineralized by incorporating extracellular calcium and phosphate aided by PTH and vitamin D signaling action on the osteoblasts10.

Osteoclasts, on the other hand, are large multinucleated cell that are involved in the resorption of bone tissue. Osteoclasts originate from hematopoietic stem cells (HSCs). Under the M-CSF (Macrophage colony- stimulating factor) influence, HSCs differentiate into preosteoclasts that circulate in the blood stream. The preosteoclasts are recruited to bone resorption sites where they will fuse to form mature osteoclasts under M-CSF and RANKL (receptor activator of nuclear factor κB ligand) signaling. The mature osteoclast adheres to the bone surface to be resorbed and secretes a myriad of factors that lower the pH of the contact surface, demineralize the bone and aid in the removal of the organic structure. The calcium will then be released into the surrounding matrix and recycled back into the circulation.

Osteocytes are the most abundant cells in the mature bone. During bone formation, some of the osteoblasts become encased in the mineralized bone and these cells subsequently become osteocytes. Osteocytes have long processes that stretch out from the cell body and these processes links one osteocyte to another osteocyte in an elaborate network, much like the neuronal network. Each osteocyte occupies a lacuna that is bathed in extracellular fluid.

Through various mechanosensory mechanisms, osteocytes detect stresses or fracture in the bone tissue and send out signals to initiate bone remodeling.

Surprisingly, the osteocytes also secrete fibroblast growth factor 23 (FGF23) for renal control of serum phosphate levels11,12, suggesting that bone plays a role in the renal mineral homeostasis.

Bone remodeling is a process by which bone tissue is broken down coupled by subsequent new bone replacement. Bone remodeling requires the tight regulation of osteoclastic and osteoblastic actions. Osteoclast formation

requires the presence of RANKL and M-CSF. These membrane-bound proteins are produced by neighbouring stromal cells and osteoblasts, and require the osteoclast precursors to have direct contact with these nearby cells to initiate the maturation cascade of osteoclast development. It was recognized that the RANK-RANKL-OPG pathways is an important regulatory mechanism that controls the osteoclastic action. The preosteoclasts express membrane- bound receptor activator of nuclear factor κB (RANK)13, while the preosteoblasts express RANKL on the cell surface. RANKL binds to RANK on the preosteoclast, triggering the maturation into active osteoclast and activating the resorption process4,6,13–15. Osteoclastic activation, however, can be negatively countered by osteoprotegerin (OPG). OPG is a soluble receptor secreted by osteoblasts and binds to the RANKL thereby competitively antagonizing the RANK-RANKL binding, leading to less osteoclast activation. This mechanism of osteoblast and osteoclast control is basis for the anti-OPG antibody therapy as an anti-resorptive treatment for osteoporosis. In contrast, bone modeling decouples the bone resorption and formation, where these two processes do not have to occur on the same bone surfaces16. Bone modeling is an important activity during the growth period where bones acquire mass and shape their morphology. This process of bone modeling occurs throughout the human lifetime and is needed to adapt the bone to changing mechanical loading.

1.3. Osteoporosis Osteoporosis is the thinning of bone tissue and loss of bone density over time, which results in the increased risk of fracture17. According to the

World Health Organization (WHO) classification, osteoporosis is defined as a

patient who has a bone mineral density (BMD) at the hip or spine that is 2.5 standard deviations or more below that of normal healthy controls18. It is estimated that 200 million people worldwide have osteoporosis19. While osteoporosis is often described as a “silent disease” because there are often no symptoms or cause slight pain in the bone and muscle in more severe cases; it can potentially cause debilitating complications and has high burden of disease20. The most severe consequence of osteoporosis is fracture.

Worldwide, there may be as many as 9 million osteoporotic fractures, of which 1.6 million are in the hip21. These fractures place a huge economic burden on the society20. It is estimated that more than 2 million osteoporotic fractures occur in the United States (US) each year, at a cost of more than $17 billion22. At the individual level, fractures occur commonly at the spine, hip, arms and the humerus and these causes immense pain, disability and death.

Fracture at the hip often requires extended hospital care and more severe fractures often limit a person’s mobility and require assistance in daily activities. Although osteoporotic fractures do not directly cause death, high morbidity often follows fracture incidences23.

Osteoporosis can be prevented and treated. Even after the development of a fracture, the risk of subsequent fractures can be reduced with therapy.

Osteoporosis occurs in both women and men, but is most common in women after menopause, when decreases in estrogen levels lead to an imbalance between dynamic mechanisms regulating bone resorption (osteoclast cells) and bone formation (osteoblast cells)24. Current available treatments of osteoporosis can be broadly classified into two groups: anti-resorptive agents and anabolic agents. Additionally, osteoporotic patients can benefit from

agents that seek to improve the calcium balance. For early osteoporotic patients, restoring calcium homeostasis and bone metabolism can be a treatment option. There are many different therapies available to achieve this purpose and they include calcium and vitamin D supplements, calcitonin- salmon and strontium.

There are many different anti-resorptive agents in the market and they work by preventing the breakdown of bone through various mechanisms.

Examples of anti-resorptive agents include selective estrogen receptor modulators (SERMs, e.g., raloxifene), bisphosphonates (e.g., alendronate) and, denosumab, which is a fully humanized antibody neutralizing RANKL25.

These different drug classes target the different pathways of osteoclast activation and reduce the resorption of the bone. SERMs regulate the estrogen levels and decrease the pro-inflammatory factors that enhance osteoclast activity26. Bisphosphonates has been in clinical use for the treatment of calcium-related bone disease for the past 40 years27,28. They have inhibitory properties on the osteoclast survival and activity29. There are many different bisphosphonates available for the treatment or prevention of osteoporosis.

Most of the modern bisphosphates are nitrogenous bisphosphonates. The nitrogenous bisphosphonates work by interfering with the melavonate pathway for cholesterol production and disrupting the proper formation of protein post- translational modification. This leads to disruption in small GTPases production and eventually affecting the resorptive activities of osteoclasts.

Some examples of nitrogenous bisphosphonates include alendronate, ibandronate, and zoledronate. The different bisphosphonates differ in potency, dosage form and dosing frequency. Because of its bone specificity, positive

effect on BMD and fracture rate reduction, bisphosphonate is being used clinically for the treatment for osteoporosis and many other bone-related diseases30. Denosumab is a fully humanized antibody neutralizing RANKL approved by the FDA in 2010. Denosumab works by sequestering RANKL and removes the activating signal for maturation of pre-osteoclasts and thereby reduce the resorption of the bone. Denosumab provides another antiresorptive treatment option to patients who cannot tolerate bisphosphonates31.

The options for anabolic drug treatment, on the other hand, are limited.

The only options available currently are parathyroid hormone (PTH) 1-34

(teriparatide, Forteo®) and PTH 1-84 (Preotact®). Teriparatide, at a subcutaneous (SC) dose of 20 μg daily, is available in the US and Europe for the treatment of osteoporosis in both men and women at high risk for osteoporotic fracture, while PTH 1-84 is currently approved only in Europe.

PTH is secreted by the parathyroid glands to increase the concentration of calcium in the blood by releasing the calcium store in the bone, thereby playing an important role in calcium homeostasis. PTH stimulates the bone resorption process and increases calcium release from the bone. In fact, if PTH is given continuously, bone resorption is increased leading to bone loss and weaker bone. Interestingly, PTH when given intermittently has the opposite effect of stimulating bone growth. This can be understood as the coupling of bone resorption and formation in bone remodeling. Osteoblasts are stimulated by the resorption signals and the intermittent PTH exposure generates more osteoblastic than osteoclastic response, resulting in more bone formation activities. Both teriparatide and PTH 1-84 are administered daily via SC injection. In a toxicology study done in rats, high dosage and prolonged use of

teriparatide was associated with tumor growth in the bones32. However, FDA considers the risk of osteosarcoma in humans is remote and “extremely rare” and no osteosarcoma was reported in the large registration trial involving approximately 2800 patients32–34. PTH therapy is therefore limited to 2 years.

As peptide products, both teriparatide and PTH 1-84 require daily dosing by

SC injection. There exists a need for an agent with enhanced bone building efficacy, no restriction on duration of treatment, and less frequent dosing relative to PTH.

1.4. Targeting the Wnt Pathway Wnt signaling pathway is gaining recognition for its role in both bone modeling and bone remodeling processes4,16,35. Wnt signaling activation initiates both bone remodeling and bone modeling which increase bone formation in excess of bone resorption resulting in increased bone mass16.

Also, the loss-of-function of downstream Wnt signal molecules causes weak bone diseases, suggesting that Wnt has an important role in stimulating bone formation. Wnts are cysteine-rich, secreted glycoproteins that bind to the cell surface receptor Frizzled (Fzd) and co-receptor low-density lipoprotein receptor-related proteins 5 or 6 (Lrp5/6). The binding of Wnt ligand to the receptor and co-receptors can stimulate a variety of downstream signals and the major one being the β-catenin pathway. In the canonical β-catenin pathway, binding of the Wnt ligand to the Frizzled receptor activates it and initiates the recruitment and activation of a cytoplasmic phosphoprotein

Disheveled (Dsh). Dsh then inhibits the cytoplasmic complex, composed of glycogen synthase kinase 3 beta (Gsk-3β), Axin, and adenomatous polyposis coli (APC) which binds to β-catenin, and prevents the degradation of β-

catenin. This raises the β-catenin levels in the cytoplasm and facilitates its translocation into the cell nucleus and where it functions as transcription factor to increase the gene expression of principal bone formation proteins.

Hoeppner, Secreto, & Westendorf (2009)36 reviewed a list of molecules involved in the Wnt signaling pathway and how altering these individual components impact the bone phenotype. These are potential drug targets for the treatment of osteoporosis and they can generally be classified into two classes: intracellular and extracellular.

Within the cell, Gsk-3β is a critical molecule that phosphorylates the β- catenin and targets it for degradation when Wnt signal is absent. Therefore, a treatment strategy for increasing the bone formation is to inhibit Gsk-3β. And indeed several specific Gsk-3β inhibitors or general inhibitors (e.g., lithium metal ions) were demonstrated to increase BMD37–39. One possible difficulty with such a treatment is that Gsk-3β is a kinase that is involved in many other signaling pathways and implicated in many other diseases such as diabetes and

Alzheimer's disease40,41. Targeting this protein for the treatment of bone disease might have adverse effects on other physiological functions.

Outside the cells, sclerostin and Dickkopf-1 (DKK-1) are natural inhibitors of Wnt signaling. Sclerostin is a protein produced by the osteocytes42 and chondrocytes43 that negatively regulates the bone formation process. Sclerostin binds to LRP5/6 receptors, blocking Wnt from binding to its receptors and thereby inhibiting the Wnt signaling pathway44. Loss-of- function of the SOST gene that encodes for sclerostin leads to painful bone overgrowth diseases such as sclerosteosis and van Buchem disease42.

Additionally, intermittent PTH, a proven bone formation treatment, is

associated with sclerostin inhibition45,46. Sclerostin, therefore, makes a good drug target for the treatment of osteoporosis due to its specificity to the bone and cartilage cells. The association between low level of sclerostin and high bone mass phenotype, such as van Buchem disease and sclerosteosis, further strengthens the hypothesis47,48.

The use of anti-sclerostin antibody in animals demonstrates the viability of this agent as a bone formation therapy. Sclerostin inhibition reversed bone loss in estrogen-deficient rats and rats with chronic inflammation as well as increased the bone mass and bone strength for normal rats and enhanced fracture healing49–53. Similarly, sclerostin inhibition in cynomolgus monkeys increased bone formation and improved bone mass and strength54. Human trials of anti-sclerostin antibody also demonstrated that the treatment increased bone formation markers and improved the BMD55–60.

1.5. Development of Anti-Sclerostin Therapy for Osteoporosis Treatment BPS804 is an anti-sclerostin antibody being developed by Novartis.

Four completed clinical trials were posted in the ClinicalTrials.gov website.

These included clinical pharmacology trials to characterize pharmacokinetics

(PK) and pharmacodynamics (PD) of BPS804 in brittle bone disease61, in metabolic bone diseases62, and in patients with renal function deficiencies63.

BPS804 was also investigated for safety and efficacy in PMP women with low

BMD following multiple dosing in a randomized, investigator and subject blind, placebo-controlled phase 2 trial64. No results were posted so far.

Romosozumab (also known as AMG785) is an anti-sclerostin antibody being co-developed by Amgen and UCB for osteoporosis in PMP women.

Phase 3 trials are currently on-going65–68 and completed phase 2 trials include trials investigating multiple dose range69, effects on fracture healing69,70 and efficacy, safety and tolerability in PMP women. Completed phase 1 trials include single and multiple dose escalation studies71,72, effects on Japanese subjects73, renal deficiency74, previous bisphosphonate exposure75 and bone quality76.

In the phase 1 single dose and multiple dose studies, PK analysis shows that romosozumab demonstrated nonlinear kinetics that is typical of monoclonal antibodies (mAbs)77. The half-life of romosozumab was estimated to be about one week and serum exposure increased more than dose proportional55,56. Following romosozumab administration, there were dose- dependent increases in bone formation markers. In the phase 1 multiple dose study, the bone formation markers procollagen type I N-terminal propeptide

(P1NP), bone-specific alkaline phosphatase (BSAP) and osteocalcin peaked at

148%, 67% and 90% from baseline respectively after 3mg/kg SC once every four weeks (Q4W). Lumbar spine and total hip BMD increased 7% and 4% from baseline at 18 weeks following three doses of 3mg/kg Q4W SC56.

The phase 2 romosozumab trial investigated SC romosozumab administered monthly (QM) and quarterly (Q3M). The dosing arms included

70mg QM, 140mg QM, 210mg QM, 140mg Q3M and 210mg Q3M administered for 2 year followed by one year of denosumab or placebo58,60.

Following a two-year treatment of 210mg QM romosozumab regimen, lumbar spine BMD increase 11.3% and 15.7% from baseline at 12 and 24 months respectively58; and subsequently the subjects were randomized to either 60mg denosumab once half-yearly (Q6M) or placebo for one year, with

denomsumab treatment maintaining and increasing the lumbar spine BMD to

19.1% at 36 months, while placebo treatment resulted in lumbar spine BMD returning towards baseline level at 4.6% at 36 months60.

1.6. Development of Blosozumab Blosozumab is a humanized immunoglobulin G4 (IgG4) anti-sclerostin mAb, for the treatment of osteoporosis in PMP women. There were six clinical studies (5 phase 1 studies and one phase 2 study) conducted to date57,78–82.

Two phase 1, single dose and multiple ascending dose clinical studies was reported and demonstrated the safety, tolerability and characterize the PK and PD properties of blosozumab57. Single and multiple doses of intravenous

(IV) and SC blosozumab were given to PMP women for up to single 750mg

IV and 750mg Q2W for 8 weeks. The top dose regimen for SC administration was 270mg Q2W for 8 weeks. Bone formation biomarkers showed an increase in P1NP, BSAP and osteoclacin following five SC doses of 270mg Q2W were

212%, 107% and 94% respectively. The lumbar spine BMD increased 5.61% at 3 months after 270mg Q2W treatment for 8 weeks57. Following a one-year administration of SC 270mg Q2W blosozumab, lumbar spine BMD increased

18% from pre-treatment level and bone formation biomarkers also showed positive increase59. The increase in bone mass resulting from anti-sclerostin therapy is larger than PTH treatment83.

Despite the deep knowledge in bone biology, osteoporosis etiology and mechanism of drug action, to aid in target selection; the development of new drug product for osteoporosis remains an expensive and time-consuming endeavor. It was estimated that to successfully bring a drug into market, it costs between US$500 million to US$2 billion depending on the disease, type

of drugs and development strategy84; with the clinical phase of drug development process being the most costly and laborious. To gain approval from the regulatory agencies for a new osteoporosis therapy, demonstration of the potential drug’s ability to reduce fracture rates is required. This proves to be a major hurdle where large studies are required to demonstrate statistically significant reduction in fracture incidences. Early proof-of-concept trials use

BMD as a surrogate to predict bone strength and fracture risk reduction.

Granted that BMD is a good indicator for bone strength and fracture risk85, the observation period requires three months to one year for meaningful bone accruement. Besides, BMD is not the only factor that determines the bone strength, bone turnover markers are also useful indicators that can potentially inform efficacy of new drug products in improving bone strength85.

Additionally, adequate dosing regimen is crucial to improve efficacy and reduce adverse effects. Many drugs failed clinical development because of inefficacious dose or due to adverse effects occurrence.

With so many variables playing a part in the drug development of new osteoporotic treatments, a systematic approach to integrate all useful information using mathematical and computational power is becoming more critical. Model-based drug development can play a part to aid the drug development process by integrating the myriad of information through mathematical formulation, then using the model to test hypothesis, such as different dose regimens, in virtual patient populations. This increases the scientific awareness of the disease and drug characteristics as well as reduces the patient burden in clinical trials by selecting the optimal sample size and dose regimen. Increasingly, regulators are accepting modeling and simulation

in supporting drug development86. More recently, regulators are accepting drug product labels to be based on model-based scientific reasoning instead of solely insisting on clinical investigation to support each claim87–89.

2. Objectives In this project, we aimed to demonstrate the utility of model and simulation in supporting the drug development of anti-sclerostin therapy for the treatment of osteoporosis. We constructed PK-PD models to describe the drug exposure-response relationship using the nonlinear mixed effects approach. We also developed a systems pharmacology model that describes the underlying biology of sclerostin regulation on bone cell homeostasis. The models were then used to predict the optimal dose regimens for the anti- sclerostin mAb for the treatment of osteoporosis.

This project is organized into three parts. The first part described the population PK-PD modeling and simulation approach for analyzing the clinical data collected from the blosozumab trials and discussed the methodology for analyzing a patient level meta-analysis dataset comprised of three phase 1 and one phase 2 blosozumab clinical trials (Sections 3 and 4).

The second part described the systems modeling approach to integrate current knowledge of the bone biology with the sclerostin’s mechanism of regulating bone remodeling (Sections 5 and 6). In the third part, we then compared the population PK-PD model and the systems biology model and discuss the appropriateness for using either model for predicting efficacy responses for different dose regimens of anti-sclerostin therapy. Simulation experiments were also performed using both population PK-PD and the systems biology model to investigate the how dose, dosing frequencies and covariate effects impacted drug exposures and clinical efficacy responses (Section 7).

In the first part, we aimed to build a population PK-PD model to characterize exposure-response relationship between serum blosozumab

concentration and lumbar spine and hip BMD and their disease progression.

The model will help identify important patient factors (covariates) that have impact on the absorption, disposition and elimination of blosozumab as well as efficacy responses and BMD deterioration in PMP women. The population modeling approach allows information from different clinical trials to be assimilated and variability to be quantified. The PK-PD model incorporated the understanding of the mechanism of action of the drug and its impact on the outcome response into a mathematical framework that allowed us to perform simulations for investigating efficacious and safe dose regimens, within drug exposures tested in clinical trials, for subsequent studies.

In the second part, a systems biology modeling and simulation approach was utilized to model the interactions involved in osteoblast and osteoclast homeostasis. We started with a published bone remodeling model that had been widely used to model different osteoporosis therapies and incorporated current knowledge of the impact of sclerostin on the bone remodeling process6,90. The bone remodeling model described the interaction between osteoblast and osteoclast through the RANK-RANKL-OPG axis and

TGF-β feedback. The sclerostin effect on osteoblast and osteoclast regulation was proposed and added to the bone remodeling model. A BMD model then linked the bone homeostasis model to the phase 2 primary clinical endpoint.

The extended model was able to characterize the bone formation and resorption markers and linked the osteoblast and osteoclast actions to changes in BMD, allowing for simulation experiments to investigate the optimal dosing regimen beyond the dose regimens tested in the clinical trials.

Lastly, we compared the performance of the population PK-PD model and the systems biology model and discuss the strengths and limitations and how the models should be used to answer the question we have on hand.

3. Population PK-PD Models of Blosozumab Materials and Methods

3.1. Blosozumab Clinical Studies Background Blosozumab is a humanized IgG4 mAb targeted against sclerostin, which is a naturally occurring protein produced by osteocytes and is a negative regulator of bone formation. Blocking the action of sclerostin leads to promotion of bone formation that is not associated with increased resorption.

Three phase 1 and one phase 2 clinical studies have been completed and are included in this meta-analysis to characterize the PK profile and explore exposure-PD response relationship.

Figure 1 shows the schematic representation of the study design for the four blosozumab clinical studies. Study 1 was a first-in-human, single dose- escalation Phase 1 study to assess blosozumab. Rich PK profile, PD response, and immunogenicity (development of anti-drug antibody) following single IV and SC doses of blosozumab were collected. The study was a randomized, parallel-design, investigator and subject blind, placebo-controlled, single-dose, dose-escalation study in PMP women, exploring the doses 7.5, 25, 75, 225, and 750mg as IV infusion and 150 mg administered by SC injection. Study 1 included an open-label phase where subjects who have previously been exposed to bisphosphonates were randomized to receive either 225 mg IV or

750 mg IV of blosozumab. Following study drug administration, all subjects were followed for 12 weeks for safety, PK, and PD assessments.

Study 2 was a Phase 1 study to investigate the safety and tolerability as well as to evaluate the PK profile and bone biomarker responses following single IV and SC doses of blosozumab in Japanese subjects. Study 2 was a placebo-controlled, investigator and subject blind, randomized, single-dose

study in Japanese men and Japanese PMP women, exploring the doses 75, 750 and 1100 mg administered as IV infusion and 150 mg as SC injection. Dense

PK and PD samples were collected to characterize the PK and biomarker responses in Japanese subjects.

Study 3 was a multiple ascending dose Phase 1 study to evaluate blosozumab in healthy PMP women. Study 3 was a multicenter, randomized, investigator and subject blind, placebo-controlled, parallel-design study, investigating the doses 180 mg SC Q4W, 270 mg SC Q4W, 270 mg SC Q2W,

540 mg IV Q4W, and 750 mg IV Q2W. Blosozumab or placebo was dosed every other week for all dosing arms, with the final dose administered at Week

8. Subjects were followed up for an additional 12 weeks after the final dose of study drug. Trough PK samples during intermediate doses, and dense PK samples after the last dose, were collected to characterize blosozumab PK at steady state. Biomarkers samples were also collected to investigate the mechanism of action of anti-sclerostin treatment on bone formation and resorption.

Study 4 was a one-year phase 2 study with an additional one-year follow-up in PMP women with low BMD, defined as a T-score between -3.5 and -2.0, inclusive. Study 4 was a phase 2, randomized, parallel design, investigator and subject blind, placebo-controlled study, investigating the doses 180 mg every Q4W, 180 mg Q2W, 270 mg Q2W, 270 mg Q12W (once every 12 weeks) administered by SC injections. All patients also received a 4- to 8-weeks run-in period of treatment with calcium (1000 mg/kg/day) and

Vitamin D (1000 IU/day). Sparse PK sampling strategy was utilized due to the outpatient nature of the study design.

Of note, there was a change in the manufacturing process during the clinical development and two blosozumab formulations were used in the clinical investigations; studies 1 and 2 used formulation 1 while studies 3 and

4 used formulation 2.

Study 1 Study 2 Study 3

7.5mg IV 7.5mg IV 180mg Q4W SC 25mg IV 750mg IV 270mg Q4W SC 75mg IV 150mg SC 270mg Q2W SC 150mg SC 1100mg IV 540mg Q4W IV 225mg IV 750mg Q2W IV 225mg IV (BP) Placebo Q2W IV 750mg IV Placebo Q2W SC

Phase 1 Trials 1 Phase 750mg IV (BP)

0 2 4 6 8 10 12 0 2 4 6 8 10 12 -4 0 2 4 6 8 10 12 14 16 weeks weeks weeks Q4W

Q2W Study 4

180mg SC Q4W 180mg SC Q2W 270mg SC Q2W 270mg SC Q12W

Phase 2 Trial 2 Phase Placebo

-4 0 24 52 64 104 weeks

Abbreviations: BP=prior bisphosphonate exposure; IV=intravenous infusion; Q2W= once every 2 weeks; Q4W= once every 4 weeks; Q12W= once every 12 weeks; SC=subcutaneous.

= 7-day safety evaluation after first dose in each cohort = remaining subjects in each cohort receives blosozumab or placebo, one subject per day = 15-day evaluation of all safety data including 6th subject in each cohort before dose escalation = observation period = screening period = treatment period = blosozumab dose = placebo dose

Figure 1 Schematic representation of the study design of four blosozumab studies

3.1.1. Sample Collections Studies 1 to 3 collected rich PK samples that covered the absorption, distribution and elimination phases of blosozumab concentration-time profile and allowed for good characterization of the PK properties. Study 4 collected sparse PK samples that were mainly trough pre-dose samples. The samples were analyzed for blosozumab using a validated enzyme-linked immunosorbent assay (ELISA) method. The lower limit of quantification was

200 ng/mL, and the upper limit of quantification was 12,800 ng/mL. Samples above the limit of quantification were diluted and reanalyzed to yield results within the calibrated range. The inter-assay accuracy (% relative error) during validation ranged from 0.266% to 13.7%. The inter-assay precision (% relative standard deviation) during validation ranged from 1.02% to 8.10%. Blosozumab was stable for up to 603 days when stored at approximately -70 °C. The samples were analyzed at ICON

Development Solutions, LLC located in Whitesboro, New York, USA.

BMDs at various skeletal sites were collected, including the lumbar spine and the hip, and assessed by dual energy x-ray absorptiometry (DXA) using either Hologic or Lunar equipment in study 4. Initial densitometry results were interpreted at the individual study centers so that study investigators can exclude patients who obviously fail to meet the BMD entry criterion. The baseline and all subsequent bone density scans were submitted directly to the central quality assurance center. Systematic differences in BMD obtained with the Hologic and Lunar equipment were reconciled by employing a cross-calibration adjustment method developed and routinely used by the central quality assurance center.

For the purpose of PK-PD modeling, the Lunar BMD readings were standardized to Hologic equivalent. The formula for recalculating the Lunar

BMD readings into Hologic equivalent readings are shown in (E.1 and E.2)

퐿푢푛푎푟 푆푝푖푛푒 퐵푀퐷 퐻표푙표푔푖푐 푆푝푖푛푒 퐵푀퐷 푒푞푢푖푣푎푙푒푛푡 = 1.1295 E.1 퐿푢푛푎푟 푇표푡푎푙 퐻푖푝 퐵푀퐷 − 0.038 E.2 퐻표푙표푔푖푐 푇표푡푎푙 퐻푖푝 퐵푀퐷 푒푞푢푖푣푎푙푒푛푡 = 1.030

3.1.2. PK-PD Dataset Preparation Blosozumab serum concentrations were combined with dosing information, covariate data (for example, gender, body weight, habits, clinical lab data) using S-Plus (version 8.2, TIBCO Software Inc., Somerville,

Massachusetts, USA) to produce the NONMEM meta-analysis dataset for population PK/PD analysis.

3.1.2.1. Independent variable Missing patient characteristic data were imputed based on the following criteria. When all independent variable values for a patient are missing, then the median value of patient population was used as an imputed value. When some independent variables for a patient are missing, data were imputed, within a patient, using the last observation carried forward (LOCF) method and missing baseline values of independent variables were imputed backward.

3.1.2.2. PK data The final PK analysis dataset pooled together three phase 1 studies and one phase 2 study. Extreme data points in the dataset were evaluated using an outlier range test to determine if they should be included in the analysis. The range test was performed by computing the arithmetic mean and standard deviation of the log-transformed values of all blosozumab concentrations, except for the most extreme value, and stratified by dose and elapsed time. If the most extreme value was outside the range of three standard deviations below and above the arithmetic mean of the log-transformed values, then the extreme data point was deemed an outlier and excluded from the analysis.

Suspected outlying data were examined one at a time. Other suspicious outlying data points were inspected individually and reasons for exclusion in

the analysis were documented. After excluding outlying records and samples that were below quantitation limits (BQL), the final PK analysis dataset contained 1744 observations from 225 subjects who received blosozumab treatment. Of which 450 observation from 48 subjects were from study 1, 187 observations from 18 subjects were from study 2, 543 observations from 44 subjects were from study 3 and 564 observations from 116 subjects were from study 4.

3.1.2.3. BMD data The BMD data for the analyses were from Study 4 only. Compared with Phase 1 studies, the design of the Phase 2 study better represents a Phase

3 study in terms of longer treatment duration, more comparable subjects, and more extended BMD measurements. Specifically, the BMD measures in all

Phase 1 studies were conducted up to 3 months following the first blosozumab dose. This led to high variability due to relatively small magnitude of changes and was not ideal to provide inferences on the trajectory of the BMD responses following chronic repeated treatment. Immunogenicity that occurred in one subject in phase 2 impacted blosozumab exposure and BMD responses and this subject was excluded from the analysis. In summary, the

BMD analysis dataset consisted of 997 lumbar spine and 854 total hip BMD observations from 152 subjects who received placebo or blosozumab treatment in study 4.

3.2. Population Pharmacokinetic/Pharmacodynamics Modeling Strategy

3.2.1. General PK/PD Model Development Approach A population analysis approach was used to characterize the time course of blosozumab serum concentrations following administration of blosozumab as well as the BMD profiles following placebo and blosozumab treatments. Nonlinear mixed-effect population analysis was conducted with

NONMEM (Version VII, ICON Development Solutions, Ellicott City,

Maryland, USA) with or without Perl-Speaks NONMEM (PsN, version 3.6.2) as an interface to run NONMEM. R (version 3.1.0) and Xpose 4 or S-Plus

(version 8.2, TIBCO Software Inc., Somerville, Massachusetts, USA) were used for diagnostic plots.

The general process for the model development was as follows and an overview is depicted in Figure 2. A base structural model was first identified to describe the kinetics profile of blosozumab and BMD. The PK and PD kinetic models were coded in differential equations and ADVAN6 TRANS1 subroutine together with the First-Order Conditional Estimation with

Interaction (FOCE-I) method was utilized to fit the model to the observed data.

Models for inter-individual variability were examined on parameter estimates as shown in (E.3) whereby P represents individual empirical Bayes estimate (EBE), θμ represents the mean parameter value, and η is a random variable with a mean of 0 and variance of ω2.

휂 2 푃 = 휃휇 ∙ 푒 , where 휂 ~푁(0, 휔 ) E.3

Combined proportional and additional residual error model was selected which best described the difference between model-predictions and the observed concentration (E.4)

2 푌푖푗 = 퐼푃푅퐸퐷 ∙ (1 + 휀1) + 휀2 , where 휀 ~푁(0, 휎 ) E.4 th th where Yij is the j observation in the i subject, IPRED is the model predicted blosozumab concentration in that individual, residual random error (ε) is a random variable normally distributed with a mean of zero and variance σ2, and the estimated σ2 accounts for variability in the bioanalytical assay, and errors associated with dose administration and sample collection, as well as errors with data transcription of dosing and sample collection time. .

The base model was examined for the precision of the parameter estimates using standard error estimates as well as 95% confidence interval obtained using log-likelihood profiling.

Once an appropriate base model had been identified, the potential covariates were investigated for their effects on the individual parameters estimates. Potential covariates were evaluated based on the improvement of model fit using the log-likelihood test as well as on the magnitude of reduction in the inter-individual variability on the parameter estimates tested. The relationship between each factor and a PK parameter was assessed using a variety of linear and nonlinear models for continuous covariates (E.5 to E.7) and categorical covariates (E.8).

푃 = 휃휇 + 휃푐표푣 ∙ (퐶푂푉 − 푚푒푑푖푎푛) E.5

휃푐표푣∙(퐶푂푉−푚푒푑푖푎푛) 푃 = 휃휇 ∙ 푒 E.6 퐶푂푉 휃푐표푣 푃 = 휃 ∙ ( ) E.7 휇 푚푒푑푖푎푛

푃 = 휃휇 ∙ (1 + 퐼푁퐷 ∙ 휃푐표푣) E.8

where P is the individual’s estimate of the parameter, θµ represents the typical population value of the parameter, θcov represents the effect of the covariate,

COV is the value of the covariate, MED median represents the median value of all values for the covariate, and IND is a dichotomous indicator variable with values of 1 or 0 that represents presence or absence of the covariate effect..

Covariates were introduced into the model using a stepwise forward addition and backward elimination method91. If the addition of the covariate to the model improved the model fit with at least 6.635 points reduction (χ2 distribution, 1 degree of freedom, p <0.01) in the objective function value

(OFV) and a reduction in the inter-individual variability, the covariate will be retained and added to the full model. Highly correlated or physiologically- related factors (such as weight and body mass index [BMI]) will be evaluated individually in the base model, and the most relevant covariate retained. For example, if both body weight and BMI resulted in similar improvement in model fit (similar reduction in objective function value and interindividual variability), body weight will be retained in the final model as it is a more useful patient factor that is routinely taken clinically.

Once the full model had been established, the significance of the potential covariates was evaluated using a backward selection (model reduction) technique. Beginning with the full model, each covariate was individually removed and its effect on the OFV evaluated. The least significant covariate not resulting in an increase 10.828 points (χ2

distribution, 1 degree of freedom, p <0.001) was dropped. The reduced model was successively refitted by applying the same reduction technique and criterion until all remaining covariates were deemed statistically significant.

3.2.2. Model Evaluation

3.2.2.1. Goodness-of-fit and Residuals Diagnostic Plots Model predictions and observations were plotted to visually examine the fit. Residuals errors were plotted against the model predictions and visually inspected for trends of deviations.

3.2.2.2. Visual Predictive Check Visual predictive check (VPC) was performed on the model to ensure that the model maintained fidelity with the data used to develop it. The simulation dataset was based on replicating the patients in the final dataset

1000 times and comparing simulated data against observed PK data, taking into account variability in all parameters, as given by the inter-individual variability and residual error terms. The distributions of simulated concentrations, conditional on the posterior distribution of model parameters, were compared to the actual concentration distributions as stratified by dose to ensure concordance.

3.2.2.3. Bootstrap Analysis 1000 bootstrap analyses sampling the analysis dataset with replacement, and stratified by study to maintain the proportion of dense and sparse PK observations (for PK model), were performed to check the model stability and robustness.

Develop Base Model

Evaluate parameter estimate precision, eg. %SEE and sensitivity analysis

Included Forward into model covariate selection

Yes

• Evaluate parameter estimate precision • Log-likelihood ratio test objective function values decrease > 6.635 (χ2, 1.d.f. p=0.01) • decrease in inter-individual variability

Full Model

Backward Remove covariate from model elimination

Yes

• Log-likelihood ratio test objective function values increase < 10.828 (χ2, 1.d.f. p=0.001)

Final Model

Abbreviation: d.f.=degree of freedom; %SEE = standard error of estimate.

Figure 2 General process for pharmacokinetic and pharmacodynamic model development.

3.2.3. Pharmacokinetic Model

3.2.3.1. Base Model Development A two-compartment open model, where blosozumab was assumed to

be eliminated from the central compartment, was identified as optimal to

describe the PK profile. A schematic representation of this model is shown in

Figure 3. The differential equations describing the mass balance of the drug

following IV infusion or SC injection are as (E.9 to E.11). PK parameters

estimated were clearance (CL), saturable-clearance (CLSAT), Michaelis-

Menten constant (C50), central volume (V), peripheral volume (V2),

distribution clearance (Q), SC route specific parameters (i.e., first-order

absorption rate constant from a depot [Ka] and absolute bioavailability [F]).

All parameters were estimated by fitting the IV and SC data simultaneously.

Residual error terms (proportional and additive errors) were estimated for each

study.

푑(퐴1) 퐷표푠푒 = −푘푎 ∙ 퐴1 + 푠.푐. E.9 푑푡 퐹

푑(퐴2) 푘 = 푘푎 ∙ 퐴1 + 퐷표푠푒 + 푘 ∙ 퐴3 − (푘 + 푚푎푥 + 푘) ∙ 퐴2 E.10 푖.푣. 32 23 퐶표푛푐 푑푡 1 + 퐶50 푑(퐴3) = 푘 ∙ 퐴2 − 푘 ∙ 퐴3 푑푡 23 32 E.11

퐶퐿푆퐴푇 where 푘 = represents the limit of the nonlinear elimination rate, 푚푎푥 푉

푄 푘 = represents the rate of transfer of blosozumab from the central to 32 푉

푄 peripheral compartment, 푘 = represents the rate of transfer of 23 푉2

퐶퐿 blosozumab from the central to peripheral compartment, 푘 = represents the 푉

rate blosozumab elimination from the central compartment. A1, A2 and A3

represent the amount of free drug in the depot, central and peripheral compartments respectively.

SC IV depot Dose Dose F Ka

Peripheral Q Central Volume Volume V2 V CLSAT CL

Abbreviation: CL = systemic clearance of drug; CL = apparent systemic clearance of drug; CLSAT = saturable systemic clearance; F=absolute bioavailability; IV= intravenous infusion; Ka = absorption rate constant; Q = distribution clearance; SC=subcutaneous.

Figure 3 Schematic representation of the population pharmacokinetic model for blosozumab.

3.2.3.2. Covariate Model Development Patient factors examined as potential covariates in the PK analysis are presented in Table 1. Patient factors were screened graphically for possible correlation with NONMEM-derived Bayesian estimates of individual PK parameters. Factors showing visible trend for correlation with a PK parameter or anticipated to be physiologically related to a PK parameter were further assessed to confirm any covariate effect on population PK parameters.

Table 1 Clinically Relevant Patient Factors Assessed in the Population PK Model

Potential covariate Type of Variable Parameters Tested Age Continuous Ka, CL, CLSAT, V, V2 Body size (body weight, body mass index) Continuous Ka, CL, CLSAT, V, V2 Baseline sclerostin level Continuous Ka, CL, CLSAT, V, V2 Ethnic origin Categorical CL, CLSAT, V, V2 Anti-blosozumab antibodies (neutralizing assay)a Categorical CL, CLSAT Anti-blosozumab antibodies (screening assay) Categorical/ CL, CLSAT continuous a The immunogenicity data included in this covariate analysis were restricted to those from study 4 because immunogenicity in Phase 1 studies were evaluated by a screening assay only, and most immunogenicity positive samples were detected when blosozumab concentrations were below the detection limit of the PK assay.

3.2.4. Pharmacodynamics Model

3.2.4.1. Base Model Development A schematic representation of the structure model is depicted in Figure

4. The target-engagement of blosozumab and sclerostin was modeled with two differentiation equations representing the kinetics of free target and drug- target complex (E.12 and E.13). Both the free target and the drug-target complex are theoretical quantities and represent the fraction of target in free or drug-bound forms, and are comparable to those in a receptor occupancy model, i.e., the sum of their quantity is always 1. Before dose administration, the values in free target and blosozumab-target complex compartments are 1 and 0, respectively, indicating the target is 100% in the free form and 0% bound to the drug. After a certain blosozumab dose, if the complete target engagement is achieved, the values in the free target compartment and blosozumab-target complex become 0 and 1, respectively.

푑(퐴4) = −푘 ∙ 퐶표푛푐 ∙ 퐴4 + 푘 ∙ 퐴5 E.12 푑푡 표푛 표푓푓

푑(퐴5) = 푘 ∙ 퐶표푛푐 ∙ 퐴4 − 푘 ∙ 퐴5 E.13 푑푡 표푛 표푓푓

푘표푓푓 where 퐾퐷 = represents the binding constant between blosozumab and its 푘표푛 target, 푘표푓푓 represents dissociation rate constant and 푘표푛 represents binding rate constant. A4 and A5 represent the amount of free unbound target and drug-target complex respectively.

The change in the BMDs, both lumbar spine and total hip, were modeled using an indirect response model to reflect delay in the effect and drug administration. The blosozumab-target complex was the driving force to increase the rate of BMD formation. Observation of the placebo cohort showed slight BMD deterioration during the 1-year treatment and 1-year observation periods. A zero-order linear disease progression rate was included to represent the decline in BMD during this period.

푑(퐴6) = 푘푖푛 ∙ (1 + 퐸푚푎푥 ∙ 퐴5) + 푘표푢푡 ∙ 퐴6 푑푡 퐿푆퐵푀퐷 퐿푆퐵푀퐷 퐿푆퐵푀퐷 E.14 − 푘푑푖푠퐿푆퐵푀퐷

푑(퐴7) = 푘푖푛 ∙ (1 + 퐸푚푎푥 ∙ 퐴5) + 푘표푢푡 ∙ 퐴7 푑푡 푇퐻퐵푀퐷 푇퐻퐵푀퐷 푇퐻퐵푀퐷 E.15 − 푘푑푖푠푇퐻퐵푀퐷

where 푘푖푛 = 푘표푢푡 ∙ 퐵퐿 represents the zero-order rate of BMD formation,

푘표푢푡 represents the first-order rate of BMD degradation, 퐵퐿 represents the baseline BMD prior to the start of drug administration, 푘표푢푡 represents the first-order rate of BMD destruction, 퐸푚푎푥 represents maximal the drug effect on the rate of BMD formation, and 푘푑푖푠 represents the rate of disease

progression; 퐿푆퐵푀퐷 refers to lumbar spine BMD and 푇퐻퐵푀퐷 refers to total hip BMD. A6 and A7 represent the lumbar spine and total hip BMD respectively

PK Model Target Engagement SC IV depot Dose Dose Ka

kon Q Central Free Drug- Peripheral Volume + Target Target Volume V koff Complex V2 CLSAT CL

BMD Model

kinLSBMD LS koutLSBMD KinTHBMD TH koutTHBMD BMD BMD kdisLSBMD kdisTHBMD

= distribution clearance; SC=subcutaneous; kon=binding constant; koff=dissociation constant; kinLSBMD=rate of lumbar spine BMD formation; kinTHBMD=rate of total hip BMD formation; koutLSBMD=rate of lumbar spine BMD destruction; koutTHBMD=rate of total hip BMD destruction; kdisLSBMD=rate of lumbar spine BMD disease progression; kdisTHBMD=rate of total hip BMD disease progression.

Figure 4 Schematic representation of the population target- engagement and bone mineral density model for blosozumab

3.2.4.2. Covariate Model Development Patient factors examined as potential covariates in the PD analysis are presented in Table 2. Patient factors were screened graphically for possible correlation with NONMEM-derived Bayesian estimates of individual PK parameters. Factors showing visible trend for correlation with a PD parameter or anticipated to be physiologically related to a PD parameter were further assessed to confirm and covariate effect on population PD parameters

Table 2 Clinically Relevant Patient Factors Assessed in the Population BMD Models

Potential covariate Type of Variable Parameters Tested Age Continuous BL, kin, KD, EMAX kdis Body size (body weight, body mass index) Continuous BL, kin, KD, EMAX kdis Baseline sclerostin level Continuous BL, kin, KD, EMAX kdis Baseline P1NP level Continuous BL, kin, KD, EMAX kdis Baseline BSAP level Continuous BL, kin, KD, EMAX kdis Baseline Osteocalcin level Continuous BL, kin, KD, EMAX kdis Baseline CTX level Continuous BL, kin, KD, EMAX kdis Ethnic origin Categorical BL, kin, KD, EMAX kdis Anti-blosozumab antibodies (neutralizing assay) Categorical BL, kin, KD, EMAX kdis Anti-blosozumab antibodies (screening assay) Categorical/ BL, kin, KD, EMAX kdis continuous Abbreviation: BSAP=serum bone-specific alkaline phosphatase; CTX=serum collagen type 1 cross-linked C-telopeptide; P1NP=serum type-1 procollagen N- terminal; BL=baseline BMD; kin=rate of BMD formation; KD=dissociation constant; EMAX= maximum response; kdis=rate of BMD disease progression.

4. Population PK-PD Models of Blosozumab Results

4.1. PK Data Disposition There were a wide range of samples that covered the absorption, distribution and elimination phases of the blosozumab PK profile. The dose ranges that were tested were wide and ranged from single dose 7.5mg IV to

750mg Q2W IV. The wide range of doses tested allowed for better characterization of the PK and PD profiles. In particular, the IV regimens allowed for estimation of the bioavailability of blosozumab and revealed the non-linear kinetics of the drug. Table 3 summarized the baseline demographics and the biomarker characteristics of the patients included in the meta-analysis.

Table 3 Demographic and baseline characteristics of subjects included in the population pharmacokinetics model

Study 1 2 3 4 All N 48 18 44 115 225 Continuous Covariates (Mean (SD)) Age (years) 57.9 50.9 58.4 65.4 61.3 (5.69) (11.8) (7.55) (8.16) (9.14) BMI (kg/m2) 25.6 22.7 25.6 23.8 24.4 (3.07) (3.18) (3.2) (4.01) (3.73) Weight (kg) 67.5 58.4 66.6 58.5 62 (9.37) (10) (10.5) (11.7) (11.7) BSAP (µg/L) 12.7 13.3 13 35.7 24.6 (4.26) (2.7) (4.57) (14.2) (15.5) CTX (ng/mL) 0.578 0.617 0.527 0.38 0.469 (0.307)a (0.207) (0.189) (0.227) (0.255)b Osteocalcin (ng/mL) 20.3 22.7 23.3 25.7 23.8 (10) (6.9) (6.5) (10.3) (9.55) P1NP (µg/L) 47.6 54.5 54.7 60.2 56 (25.4) (19.3) (21.6) (23) (23.4) Sclerostin (nM) 0.36 0.0131 0.245 0.123 0.191 (0.396)a (0.0111)c (0.124)d (0.0704) (0.224) Categorical Covariates (N) Race African American 2 - - - 2 Western Asian - - 8 - 8 Caucasian 45 - 36 65 146 Japanese - 18 - 50 68 Native American 1 - - - 1 Abbreviation: N=number of subjects; BMI=body mass index; BSAP=serum bone-specific alkaline phosphatase; CTX=serum type 1 C-terminal procollagen; P1NP=serum type-1 procollagen N-terminal. a N=47 b N=224 c N=13 d N=43

4.2. Final PK Model The final PK model was a two-compartment model with first-order SC absorption. Blosozumab was assumed to be eliminated from the central compartment. The elimination of blosozumab is modeled using a parallel linear and non-linear clearance. This non-linear portion was modeled mathematically using the classical Michaelis-Menten equation (E.16).

퐶퐿푚푎푥 퐶퐿푛표푛푙푖푛푒푎푟 = 퐶표푛푐 1+ E.16 퐶50

where CLnonlinear represents the capacity limited clearance, CLmax the upper limit of the elimination process, C50 the affinity constant and Conc the drug concentration.

The total clearance of the drug is thus a combination of the non-specific linear component and a capacity-limited, target-mediated non-linear component

(E.17).

퐶퐿푡표푡푎푙 = 퐶퐿푙푖푛푒푎푟 + 퐶퐿푛표푛푙푖푛푒푎푟 E.17

The non-linearity is most obvious in the higher doses of the IV administration arms, where the concentration time profile informed the elimination process of the drug following IV infusion. Compared to the SC administration, competing absorption and elimination processes were confounded and the observed concentration-time profiles appeared to decline in a monophasic fashion. Generally, drugs can be removed from the body through renal excretion and destruction by metabolism. Blosozumab is an IgG antibody that has a large molecular size of approximately 150kDa. Therefore, it is expected that very little intact blosozumab molecule can pass through the

renal filtration and be excreted in urine. In addition, there are neonatal Fc receptor (FcRn) expressed in the human renal glomerular epithelial cells that could potentially bind and reabsorb filtered IgG92. Instead, elimination of antibodies is normally via catabolism. Typical IgG molecules have a serum half-life of about 23 days and elimination is subjected to influence by concentration93. Besides the non-specific protein catabolism, blosozumab concentration can also be affected by binding to its target, where the process is often limited by the availability of the target, and contributes to the non-linear kinetics.

After an IV dose, blosozumab concentration followed a bi-exponential decline from the Cmax, which was achieved at the end of the infusion. In the

SC cohort, due to the slow drug absorption, the median tmax was approximately

3 to 6 days postdose. The PK of blosozumab demonstrated clear nonlinearity, evident by the changing slope of the terminal phase over time (Figure 6). This nonlinear PK appeared to be drug concentration-dependent, where at higher dose levels, there was decreased clearance and increased terminal t1/2.

The model adequately described blosozumab disposition characteristics. Generally, precision around PK parameter estimates was good as evident by low %SEEs (standard error of estimate) not exceeding 30% and tight 95% CIs (confidence interval). The PK parameter estimates from the final model, inclusive of covariate effect, are summarized in Table 4. Figure 5 illustrates a good fit between the population and individual predictions against the observations; also residuals against model predictions did not show any obvious deviations. There are two samples with individual weighted residual

(iWRES) more than 10 (Figure 5, lower left corner). Visual inspection of these

two records did not show any anomalies and conditional weighted residuals profiles did not show any obvious trends of model misspecification (Figure 5, lower right corner).

A visual predictive check (VPC) comparing observed serum blosozumab concentrations versus time profiles against the posthoc model- predicted profiles showed that the model adequately described the data across all dose levels (Figure 6). The median, 5th, and 95th percentile of the model predictions were in close agreement with the observations, suggesting that the structural model and the variability estimates were appropriate. The majority of observed blosozumab concentrations were within the 90% prediction intervals from the population PK model.

Two SC formulations were used in the clinical trials to date. There appears to be slight differences in the bioavailabilities of these two formulations. The absolute bioavailability for SC formulations was estimated to be approximately 54% (formulation 1, dosing solution concentration ~ 30 mg/mL, used in Studies 1 and 2) and 69% (formulation 2, dosing solution concentration ~ 60 mg/mL, used in Studies 3 and 4), respectively. The bioavailability of blosozumab is consistent with typical antibodies where most have reported bioavailabilities of between 50 and 100%93. The factors that affects the amount of drug absorbed varied, affected by the amount of presystemic degradation, molecular size and the limit of injection volume that is allowed due to associated pain. Formulation 2 allows for the more molecules to be packed into a smaller injection volume and demonstrated better bioavailability and possibly better pain tolerability since the injection volume is reduced.

The t1/2 was calculated using the empirical Bayes estimates from the population PK model using the kinetics micro-constants in the equation below.

ln (2) 푡 = E.18 1/2 훽 where, 1 훽 = ∙ (푘 + 푘 + 푘 − √(푘 + 푘 + 푘)2 − 4 ∙ 푘 ∙ 푘 2 23 23 23 23 32

Since blosozumab follows concentration-dependent PK, the terminal half-life

(t1/2) varies with drug concentration, which was expected to be between approximately 3 days (when C50 >> Conc and hence 퐶퐿푡표푡푎푙 ≈ 퐶퐿푙푖푛푒푎푟 +

퐶퐿푛표푛푙푖푛푒푎푟) and 14 days (when C50 << Conc and hence 퐶퐿푡표푡푎푙 ≈ 퐶퐿푙푖푛푒푎푟).

Table 4 Pharmacokinetic and Covariate Parameters in Final Population Model

Inter-subject Population Estimate Bootstrap Analysisf Variability Mean (%SEE; and 95% Parameter Description (%SEE; and 95% CI) (%SEE)a CI) Absorption rate constant (Ka, 1/h) 0.00697 40.10% 0.00698 Parameter for (4.33%; 0.00641, 0.00768) (16.8%) (0.0438%, 0.00643, 0.00763) Constant clearance (CL, mL/h) 8.82 32.90% 8.88 (5.24%; 8.09, 9.77) (22.8%) (0.0596%, 7.95, 10.1)

Saturable clearance (CLSAT, mL/h) 122 26.00% 127 (11.0%; 102, 150) (15.7%) (0.124%, 102, 166)

Inter-compartmental clearance (Q, mL/h) 16.8 - 16.8 (5.20%; 15.5, 18.4) (0.0537%, 15.1, 18.7)

Michaelis Menten constant (C50, nM) 12.8 - 12.5 (15.5%; 9.76, 16.6) (0.166%, 8.39, 16.7) Central volume (V, mL) 2520 13.40% 2520 (1.73%; 2430, 2610) (24.9%) (0.0176%, 2430, 2600)

Peripheral volume (V2, mL) 1440 19.60% 1440 (3.84%; 1330, 1540) (40.3%) (0.0404%, 1330, 1560)

Absolute bioavailability (%)

F for formulation 1 54 - 53.9 (6.17%; 47.7, 61.5) (0.0636%, 47.1, 60.5)

F for formulation 2 69.1 - 69.2 (3.30%; 65.8, 73.9) (0.0348%, 64.5, 74.0)

Covariate - BW on CLSAT b 0.0157 - 0.0156 (13.7%; 0.0113, 0.0201) (0.139%, 0.0115, 0.0200)

Covariate - BW on V and V2 c 0.0108 - 0.0108 (10.9%; 0.00843, 0.0132) (0.112%, 0.00853, 0.0132) Residual Error (Proportional, %)d | (Additive, nM)e Study 1 8.43% (9.59%) | 2.39 (40.4%) Study 2 23.4% (11.2%) | 2.40 (74.9%) Study 3 6.18% (19.4%) | 2.40 (38.8%) Study 4 11.8% (25.1%) | 6.83 (42.0%) Abbreviations: %SEE = relative standard error of estimation; “-” = fixed to zero; BW= body weight; C50 = Michaelis-Menten constant; CI = confidence interval; CL = systemic clearance of drug; CL/F = apparent systemic clearance of drug; CLSAT = saturable systemic clearance; Ka = absorption rate constant; Q = distribution clearance. a Reported as %CV, calculated by equation: 100 ∙ √푒푂푀퐸퐺퐴(푁) − 1, where OMEGA(N) is the NONMEM output for the between-subject variability of the Nth parameter. b CLSAT = 122 * [1+0.0157*(BW-61.5)], where median BW=61.5kg. c Vi = typical value Vi* [1+0.0108*(BW-61.5)], where median BW=61.5kg. where Vi is V or V2 d Reported as %CV, calculated by equation: 100 ∙ √푆퐼퐺푀퐴(푁), where SIGMA(N) is the NONMEM output for the proportional residual error for the Nth study. e Reported as nM, calculated by equation: √푆퐼퐺푀퐴(푁), where SIGMA(N) is the NONMEM output for the additive residual error for the Nth study. f 1000 bootstrap analyses sampling original data with replacement

Abbreviations: iWRES = individual weighted residual.

Figure 5 Goodness-of-fit diagnostic plots of blosozumab final pharmacokinetic model

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Figure 6 Visual predictive check for the final pharmacokinetics model

4.3. PK Model Covariate Analysis In summary, only body weight was found to be an important patient factor that impact the distribution and elimination of blosozumab. Of note, since body surface area (BSA) and body weight are both size descriptors so they are confounding factors. The change in OFV and reduction in inter- individual variability for BSA as a covariate on clearance were consistently lower than those models where body weight was applied on clearance.

Therefore, only body weight was retained as a significant covariate on the clearance and volumes of distribution of blosozumab.

In addition, since blosozumab is a large molecule, its elimination is anticipated to be via normal protein catalysis and is not expected to be dependent on renal function for excretion. Therefore, the CL of blosozumab is unlikely to be closely associated with the renal function of the patient and thus renal function was not tested as a covariate.

Prior bisphosphonate exposure (BP) did not appear to have an effect on the PK of blosozumab. It was observed that the PK profiles overlapped between naïve and BP subjects given the same doses.

Anti-drug antibodies were analyzed by a validated screening assay and positive samples were then titrated to report a titer value.

4.3.1. Effect of Body Weight on Blosozumab Clearance A statistically significant association was found between body weight and blosozumab CLSAT. Mean population blosozumab CLSAT was estimated to be 122 ml/L for a 61.5kg PMP woman. Every one-kilogram increase in body weight increased the CLSAT by 1.57%. The estimated interindividual variability for CLSAT was 26.0%. Objective function

decreased by 44.4 points (1 degree of freedom, p<.001), accompanied by a 5% reduction in interindividual variability, down from 31%.

4.3.2. Effect of Body Weight on Blosozumab Volumes of Distribution A statistically significant association was found between body weight and blosozumab V and V2. Mean population blosozumab V and V2 were estimated to be 2520 ml and 1440 ml for a 61.5kg PMP woman respectively.

Every one-kilogram increase in body weight increased the volume of distributions (V and V2) by 1.08%. The estimated interindividual variability for V and V2 were 13.4% and 19.4%, respectively.

4.4.3. Effect of Anti-Drug Antibody (ADA) on Blosozumab Only 11% of all samples collected for immunogenicity analysis were tested positive for the presence of anti-drug antibody. Only one subject (study

4, 180mg Q2W SC) had obvious anti-drug antibody effect on the blosozumab exposure and this subject was excluded from the analysis. This subject had reduced blosozumab exposure, low BMD, and had a positive ADA screening titer at baseline (1:10). Review of this patient suggested no adverse systemic effects in this patient. Screening ADA status (yes/no) [categorical] and the titer [continuous] were investigated as time-varying covariates to explore if they had any effect on the PK parameters. Adding ADA as covariate to CL and CLSAT reduced the objective function values (about 17 points) but not the inter-individual variability on the PK parameters. There was no strong evidence to suggest that ADA had any significant effect on the PK of blosozumab.

4.4. BMD Data Disposition The final dataset for PD analyses contained a total of 1851 BMD samples from 152 patients who received blosozumab or placebo treatment in

study 4. Table 5 summarized the demographics and baseline characteristics of the patients included for in the BMD analysis. Blosozumab was administered for one year and the subjects were observed for an additional one-year post treatment termination. The second year follow-up observation period allowed for the estimation of rate of return to baseline. There were approximately 20% of the data between 15 and 24 months of the study period and this provided sufficient information for good data fitting. Blosozumab treatment for 12 months resulted in significant increases in lumbar spine and total hip BMD.

During the follow-up phase (12-24 months), lumbar spine BMD percent change from baseline decreased for all blosozumab treatment groups. The percent change from baseline BMD at 24 months was significantly different from baseline and placebo for the blosozumab treatments, suggesting that although the treatment effect peaked at the end of the 12-months treatment, the bone formation effect persisted for more than one year as the BMD returned towards baseline. In addition, there were small declines from baseline in both the lumbar spine and total hip BMD in the placebo cohort at the end of 24 months, suggesting a worsening of the osteoporosis disease state during the two-year period.

Table 5 Demographic and baseline characteristics of subjects included in the population BMD model

Study 4

N 152 Continuous Covariates (Mean (SD)) Age (years) 65.3 (8.32) BMI (kg/m2) 23.9 (4.32)

Weight (kg) 58.5 (12.3) BSAP (μg/L) 35.5 (13.6) CTX (ng/mL) 0.391 (0.225) Osteocalcin (ng/mL) 26.4 (9.92) P1NP (μg/L) 61.5 (23.6) Sclerostin (nM) 0.135 (0.116) Lumbar Spine BMD (g/cm2) 0.743 (0.056) Total Hip BMD (g/cm2) 0.747 (0.121) Categorical Covariates (N) Race African American 1 Caucasian 87 Japanese 64 Abbreviation: N=number of subjects; IV=intravenous infusion; SC=subcutaneous injection; BMI=body mass index; BSAP=serum bone-specific alkaline phosphatase; CTX=serum collagen type 1 cross-linked C-telopeptide; P1NP=serum type-1 procollagen N- terminal.

4.5. Final BMD Model The structural PD base model is an indirect-response pharmacological model that describes the exposure-response relationships of blosozumab concentration, exerting a stimulatory effect on the formation of BMD (Figure

4). A linear slope was estimated to describe the deterioration of BMD over time. Japanese patients were found to have lower baseline BMD values than non-Japanese patients in both lumbar spine and total hip BMD. This difference in the BMD levels between Japanese and non-Japanese subject is therefore included into the base model. A pseudo target-engagement describing free target and blosozumab-target complex was used to link the PK and PD models. Of note, the 2 compartments representing free target and blosozumab- target complex are both with theoretical quantities, inform the percentage of target in free or drug-bound forms, and are comparable to those in a receptor occupancy model, i.e., the sum of their quantity is always 1.

Table 6 summarizes the parameter estimates from the population PD model. The mean baseline lumbar spine BMD were 0.711 g/cm2 and 0.767 g/cm2 for Japanese and non-Japanese subjects respectively; while the mean total hip BMD were 0.653 g/cm2 and 0.805 g/cm2 for Japanese and non-

Japanese subjects respectively. The inter-individual variability for lumbar spine and total hip baseline BMD were 6.53% and 12.8%. The total hip BMD measurements were more variable though the variability was small in general.

The difference in the BMD between Japanese and non-Japanese subjects could be due to the body mass differences in the two groups. Japanese subjects on the average weights about 15.2 kg lesser than the non-Japanese subjects and

there is a strong positive association with between higher body mass and

BMD94.

Bone turnover was assumed to remain at a steady state with turnover rate that is controlled by the zero-order rate of bone formation, 푘푖푛, and the first-order rate of bone destruction, 푘표푢푡. The 푘푖푛 values estimated for lumbar spine BMD and total hip BMD were 0.340 and 0.0156 g/cm2/week, respectively, suggesting that the bone turnover is approximately two-fold higher in lumbar spine that in total hip. This faster bone turnover rate dictates that under the same regimen, the drug effect in lumbar spine is achieved faster than in total hip and for the same reason, with the discontinuation of the treatment, the BMD loss in lumbar spine is faster than in total hip.

The rate of disease progressions estimated for lumbar spine and total hip BMD were 0.0121 g/cm2/year and 0.00780 g/cm2/year, respectively, suggesting that bone loss is faster in lumbar spine compared with total hip.

The estimated disease progression was limited by the two-year placebo data that were collected in blosozumab clinical study 4 and a parsimonious linear rate of decline. Nonetheless, the rates of disease progression added to the model improved the overall model fit and provides an assessment of the rate of decline of BMD over time.

Correlation was identified between baseline lumbar spine BMD and baseline total hip BMD in both Japanese and non-Japanese subjects.

Similarly, correlation between the maximum BMD responses in lumbar spine and total hip was found.

Table 6 Pharmacodynamic Parameters in Final Population BMD Model

Inter-subject Population Estimate Bootstrap Analysisc Parameter Description Variability (%SEE; and 95% CI) (%SEE)a Mean (%SEE; and 95% CI) BMD baseline (g/cm2)

Lumbar spine (Japanese) 0.711 6.53% 0.710 (0.864%; 0.699, 0.723) (13.8%) (0.00897%; 0.699, 0.724)

Lumbar spine (non-Japanese) 0.767 6.53% 0.767 (0.932%; 0.756, 0.778) (13.8%) (0.00650%; 0.757, 0.776)

Total hip (Japanese) 0.653 12.80% 0.652 (1.61%; 0. 633, 0.674) (14.4%) (0.0180%; 0. 627, 0.675)

Total hip (non-Japanese) 0.805 12.80% 0.804 (1.70%; 0.783, 0.826) (14.4%) (0.0119%; 0.784, 0.822)

Correlation coefficient between 0.435

lumbar spine and total hip baseline values (25.8%)

Emax of BMD increase (%)

Lumbar spine 20.5 24.80% 21.5 (7.02%; 17.9, 24.0) (32.1%) (0.147%; 17.7, 31.5) Total hip 9.27 48.70% 10.1 (15.1%; 6.96, 13.2) (39.9%) (0.249%; 7.02, 17.3)

Correlation coefficient between - 0.879 - lumbar spine and total hip Emax (33.7%)

BMD Production rate (Kin, g/cm2/week)

Lumbar spine 0.034 20.9% (74.8%) 0.0333 (12.1%; 0.0270, 0.0427) (0.173%; 0.0189, 0.0437)

Total hip 0.0156 45.3% (55.6%) 0.0154 (15.2%, 0.0110, 0.0207) (0.226%, 0.00784, 0.0220)

Disease progression (BMD loss, g/cm2/year)

Lumbar spine -0.0121 161% -0.0129 (38.2%; -0.0241, -0.00576 ) (52.0%) (0.483%; -0.00727, -0.0257)

Total hip -0.00780 115% -0.00801 (27.6%; -0.0130, -0.00344) (59.5%) (0.324%; -0.00285, -0.0134)

Dissociation rate constant (Koff, 10-3/hr) 0.458 76.90% 0.556 (21.5%; 0.325, 0.711) (48.8%) (0.614%; 0.305, 1.56) Dissociation coefficient (K , nM) 21.4 22.6 D (22.9%; 13.2, 31.9) (0.278%; 12.8, 35.5)

Residual Error (Proportional, %)b Lumbar spine 2.05 (3.54%) Total hip 1.39 (4.35%) Abbreviations: %SEE = relative standard error of estimation; “-” = fixed to zero; BMD= bone mineral density. a Reported as %CV, calculated by equation: 100 ∙ √푒푂푀퐸퐺퐴(푁) − 1, where OMEGA(N) is the NONMEM output for the between-subject variability of the Nth parameter. b Reported as %CV, calculated by equation: 100 ∙ √푆퐼퐺푀퐴(푁), where SIGMA(N) is the NONMEM output for the proportional residual error. c 1000 bootstrap analyses sampling original data with replacement.

Figure 7 illustrates the goodness-of-fit between the model the observed lumbar spine and total hip BMD and the model predictions. There was good agreement between the population and individual model predictions and the observed data. Inspection of the residual errors also showed no obvious irregular trends. In general, the model can describe the data adequately. The precision of the parameter estimates was good as demonstrated by the low standard error of estimates (%SEE) (Table 6).

To evaluate the performance of the final base population exposure-

BMD model, VPC was conducted by simulating 1000 replicates of the trials.

Figure 8 and Figure 9 overlay the observed and model-predicted percent change of BMD from baseline (population median and 90% prediction intervals) for lumbar spine and total hip at each dose level in Study 4, respectively. This VPC illustrates that the distribution of simulated BMD responses from the population BMD model is in agreement with observed distributions of BMD gain from Study 4.

Abbreviations: IWRES = individual weighted residual. Figure 7 Goodness-of-fit diagnostic plots of blosozumab final pharmacodynamics model. First and Second Row: Lumbar Spine BMD. Third and Fourth Row: Total Hip BMD.

Note: Open blue circles represent the observed BMD measurements. Solid and dashed red lines represent median and 5th and 95th percentiles of the observed BMD measurements. The red and blue shaded areas represent the 95% confidence interval of 50th, 5th and 95th percentiles of the observed BMD measurements. Figure 8 Visual predictive check for the final Lumbar Spine BMD model. (A) Absolute value. (B) Percent change from baseline.

Note: Open blue circles represent the observed BMD measurements. Solid and dashed red lines represent median and 5th and 95th percentiles of the observed BMD measurements. The red and blue shaded areas represent the 95% confidence interval of 50th, 5th and 95th percentiles of the observed BMD measurements. Figure 9 Visual predictive check for the final Total Hip BMD model. (A) Absolute value. (B) Percent change from baseline.

4.6. BMD Model Covariate Analysis For hypothesis generation purposes, a limited covariate search was conducted to identify potential factors that may influence BMD responses.

The potential covariates evaluated include body weight, age, ethnicity, baseline BMD, baseline sclerostin level, and baseline values of major bone biochemical markers (P1NP, CTX, osteocalcin, and BSAP). The impact of immunogenicity in the format of neutralizing antibody on bone formation activity was also evaluated.

Body weight and baseline P1NP were identified to impact certain model parameters. However, it was determined that these factors were not considered to be clinically meaningful. Figure 10 shows the final base model and the final BMD model are equally good in predicting distributions of patient BMD responses in lumbar spine and total hip at week 52. Additionally,

P1NP levels on the rate of BMD formation were limited to the overall turnover of the bone. This has limited effect on the overall formation of the

BMD since both the rate of formation and destructions were elevated over the time course of observations. The drug and placebo effects (Emax, KD and disease progression parameter) were not meaningfully altered with different levels of baseline P1NP level. Adding body weight as a covariate to the baseline total hip BMD had little impact on reducing the inter-individual variability and will have little drug development usefulness since baseline

BMD are controlled within the study inclusion/exclusion criteria. In summary, the final model that best describes the BMD observations did not include the effect of body weight on total hip BMD baseline and P1NP baseline level on the rate of BMD formation.

Note: thick solid lines in the middle represent the median; box represents the inter-quantile range (IQR). black solid circles represent the data outside the 1.5x IQR.

Figure 10 The distribution of lumbar spine and total hip BMD percent change from baseline at 1-year observed in Study 4 (Obs) or predicted with the Population BMD models (Base: final base model; Final: final model with covariates).

5. System Pharmacology Model of Anti-Sclerostin Treatment Materials and Methods The purpose of the second part of the report was to integrate the sclerostin regulation mechanism on bone activities with a physiological-based bone remodeling mathematical model that accounts for the tight coupling of osteoblast and osteoclast actions6. The kinetic profiles of the total and unbound sclerostin after anti-sclerostin therapy were characterized using target-mediated drug disposition (TMDD) model, based on the range of blosozumab and romosozumab doses available from published reports. The drug action of anti-sclerostin was then incorporated in the bone remodeling model through the unbound sclerostin control of osteoblasts and osteoclasts.

The model was calibrated with blosozumab and validated with romosozumab using data on bone biomarkers temporal responses extracted from published clinical trials. The model was then further extended by integrating the BMD time course model through linking the osteoblast actions and bone formation rate. Similarly, the model parameters were calibrated and validated using the

BMD observations from the blosozumab and romosozumab clinical trials, respectively.

5.1. Bone Remodeling Model Background The bone remodeling model by Lemaire et al. forms the base structural model that describes the interactions between cellular bone interaction and how the cells change in response to perturbation6,95–100. The original model was developed to describe osteoblasts and osteoclasts regulation and interaction in bone remodeling process. The model was used to investigate different bone diseases and their possible therapeutic interventions by altering model components and extrapolating the results with osteoblast and osteoclast

changes. The model was successful in replicating the osteoblast and osteoclast responses (increased or decreased) in certain bone diseases, as caused by loss of estrogen in menopause and degradation by glucocorticoid for example, and made plausible predictions of the efficacies of potential anti-resorptive and anabolic bone therapies. The original Lemaire model was since adapted to describe different bone deficiencies with extension to quantify biomarkers, bone mineral density or bone volume changes in theoretical scenarios or calibrated with different osteoporosis treatments90,96–99,101–103. Of particular note, the University at Buffalo group adapted the original model, but used most parameter estimates as reported in original Lemaire paper, to describe the bone resorption marker responses after denosumab treatments97,98. More recently, the Metrum research group reported a systems pharmacology model102 and included sclerostin pathway in bone remodeling90, based on the original Lemaire model, but reparameterized extensively with additional components that included hypotheses of PTH intracellular signaling104 and calcium homeostasis105.

In this project, we aim to extend the original model with the sclerostin regulation but keep only the most important components of bone remodeling, similar to the approach used by the University at Buffalo. This approach affords us the flexibility and options to then combine reported models, which are based on the original Lemaire model, into a single unified model that will allow predictions of treatment efficacies in combination therapies for bone diseases.

Important aspects of the model pertinent to the analysis of the sclerostin mechanism of action are described below and the full set of equations describing the extended bone remodeling model is in Appendix A.

The cellular model composes of 3 distinct cellular groups namely the responding osteoblasts (ROBs), active osteoblasts (AOBs) and the active osteoclasts (AOCs). The model represents four major differentiation stages of the bone cells with two representing the cells of bone-forming osteoblastic lineage and two representing the cells of bone-resorbing osteoclastic lineage.

The osteoblastic lineage cells are represented by two states (ROBs and

AOBs) which were modeled as two differential equations (Section 5, E.25 and

E.26). ROBs represent a diverse group of precursor cells that have the potential to develop into AOBs and carry out bone formation. The ROBs were assumed not to have direct involvement in bone formation but rather act as a precursor pool of cells that is subject to regulation and thus controls the input rate of AOBs. Physiologically, the ROBs represent the uncommitted progenitor cells of osteoblastic lineage that include myocytes, adipocytes and mesenchymal progenitors. TGF-β signals for the aggregation of the ROBs to the site of bone remodeling but prevents further maturation of the ROBs into

AOBs. When the TGF-β signal diminishes as resorption activities decrease, inhibitory signals are removed allowing ROBs to proceed to differentiate into

AOBs. The AOBs then carry out the bone forming responsibilities and after which the cells then differentiate into lining cells and osteocytes, or are destroyed via apoptosis. The osteoclastic lineage cells are similarly divided into two states, namely, the precursors and active osteoclasts (AOCs). The source of osteoclast precursors was assumed to be unlimited and only the

AOC was modeled as a differential equation (Section 5, E.27). The precursor osteoclasts under the influence of RANK-RANKL binding will differentiate into AOCs that carry out bone resorption. The AOCs break down bone matrix and release the TGF-β stored within the bone matrix. The AOCs then, under

TGF-β feedback, are destroyed via apoptosis.

The bone remodeling process is thus a tightly coupled process where osteoclastic and osteoblastic processes follow strict temporal regulation.

Homeostasis is achieved via the RANK-RANKL-OPG axis and the TGF-β signaling. The AOBs express cell surface RANKL that binds to RANK on precursor osteoclasts and converts them into AOCs. On the other hand, the osteoclasts when breaking down the bone, release the TGF-β stored within bone matrix. The TGF-β was assumed to increase the recruitment of ROBs to the site of the bone remodeling but then block the ROBs from further differentiation into AOBs. The different TGF-β effect contributes to the temporal regulation whereby bone formation only begins after bone formation completes.

Additionally, PTH is added as affecting the RANKL and OPG production through binding with PTH receptors on the ROBs and AOBs. PTH enhances RANKL but reduces OPG production. This effectively enhances the

AOC level and leads to increased bone resorption. The current understanding of the PTH’s mechanism of action of bone formation and resorption is not entirely clear and this segment of the bone homeostasis model will need to be updated when more information becomes available.

This project extended the base model as described above by incorporating the PK of anti-sclerostin mAb drug treatment with its binding to sclerostin, and regulatory actions of sclerostin on osteoclasts and osteoblasts.

5.2. Dataset and Model Description The data for building sclerostin regulation of bone remodeling was extracted from publicly available information in clinical reports of blosozumab and romosozumab. PK information for blosozumab were available in a poster presentation at 6th Annual Meeting of American

Conference of Pharmacometrics 2015 (ACoP6)106 and details of the model development and results were in population PK-PD analysis section of this report (Sections 3 and 4). However, mean PK profiles were not available publicly. PK information for romosozumab were reported in two journal articles55,56. The concentration-time profiles of romosozumab after single ascending doses of romosozumab were digitized to characterize the PK parameters. The non-compartmental PK parameters of romosozumab after multiple doses of romosozumab were used as comparison to assess the validity of the PK parameters.

Total sclerostin levels following single and multiple doses of blosozumab administration in phase 1 and phase 2 clinical trials were reported57,107 and the data were digitized and used to develop the kinetics model of sclerostin levels. Sclerostin levels after romosozumab treatment were not available.

Bone turnover markers of bone formation, specifically serum P1NP, and bone resorption, specifically serum CTX, were reported in two phase 1 and one phase 2 blosozumab trials as well as two phase 1 and one phase 2

romosozumab trials57,59. The bone turnover markers were used to inform the anti-sclerostin treatment effect of the bone remodeling model. Graphical data were extracted using PlotDigitizer (version 2.6.3).

The target-mediated drug disposition as well as the bone remodeling model with the sclerostin effect extension was estimated using Berkeley

Madonna (version 8.0.1, University of California at Berkeley), utilizing simplex search algorithm based on least square minimization method implemented within the software. The Runge-Kutta integration algorithm

(RK4) was used to solve the ordinary differential equations. The Berkeley

Madonna code for the extended bone remodeling model is in Appendix D.

Graphical results were plotted using either S-PLUS (version 8.2, TIBCO

Software Inc., Palo Alto, CA) or R (version 3.2.2).

5.2.1. Mathematical Description of Target-Mediated Drug Disposition Kinetics A semi-mechanistic model was proposed to describe the kinetics of sclerostin levels following blosozumab treatment. The basic model structure describing the kinetics of blosozumab and sclerostin is illustrated in Figure 11.

Blosozumab given subcutaneously into the interstitial layer will move into the vasculature through fluid convection exerted by the higher fluid pressure caused by the high concentration of drug at the site of drug administration. In the vasculature, blosozumab largely circulates in the serum because of its large molecular size. However, a small amount of the drug can distribute into the peripheral tissue through gaps and channels within the endothelial or be taken up through non-specific endocytosis. We assumed that limited blosozumab are distributed in the bone compartment and modeled the distribution of blosozumab as one general peripheral tissue compartment. The blosozumab concentration follows a two-compartment model as described in Section 3.2 on the population PK model (Figure 3), where blosozumab follows first-order absorption after SC injection. Blosozumab distributes between serum and tissue compartments. The elimination of blosozumab follows that of the typical protein antibody which was modeled as two clearance pathways - one linear clearance and one saturable non-linear clearance. The saturable clearance is due to the binding of blosozumab to its target where the level of the target molecule can be limited. In this case, blosozumab binds to the serum sclerostin where the blosozumab-sclerostin complex is then internalized via pinocytosis to be eliminated from the body system.

Abbreviation: As.c = amount of drug in subcutaneous injection depot

compartment; A = amount of drug in central compartment; At = amount of

drug in peripheral compartment; C = serum drug concentration; Ct = tissue

drug concentration; Scl = serum unbound sclerostin concentration; Cplx = serum drug-sclerostin complex concentration; k = rate of drug elimination;

ksyn = rate of sclerostin production;kdeg= rate of sclerostin elimination; kint=

rate of drug-sclerostin complex internalization; Doses.c = subcutaneous drug administration; Int(t) = intravenous drug administration; V=central volume of distribution; V2=peripheral volume of distribution.

Figure 11 Schematic representation of the blosozumab target- mediated drug disposition model.

Sclerostin is a soluble protein produced only by the osteocytes within the bone matrix42. The local level of sclerostin therefore determines the level of inhibition of bone formation. There is a strong correlation between serum sclerostin level and bone sclerostin level suggesting that the sclerostin molecule distributes between the serum and the bone matrix108,109.

Furthermore, the bone is a densely vascularized structure with leaky sinusoidal capillaries that allows exchange of materials between the vasculature and the bone tissue110. When compared with normal control subjects, patients with sclerosteosis has undetectable levels of serum sclerostin, while patients with heterozygous deleterious sclerostin mutation has only half the normal level of serum sclerostin level111. This shows that the serum sclerostin level is a suitable surrogate (for bone sclerostin level) for predicting sclerosteosis disease severity with respect to sclerostin inhibition on bone growth. For model parsimony, only the serum sclerostin level is modeled and described by a turnover model with a zero order production rate and first order distribution rate. The level of serum sclerostin was then linked to bone remodeling model assuming that the serum sclerostin level is proportional to the bone sclerostin level.

Blosozumab was assumed to only bind sclerostin in the vasculature and was thus limited by the serum sclerostin that is available for binding to the drug. Binding of blosozumab to sclerostin forms the drug-target complex that will then be eliminated. Removal of unbound serum sclerostin increases the fluid pressure which draws more unbound sclerostin from the bone into the serum. Hence, a decrease in the serum unbound sclerostin was assumed to cause a proportional decrease in the sclerostin in the bone matrix.

A quasi-equilibrium target-mediated drug disposition model was used to describe the kinetics of the drug and sclerostin. It was assumed that the binding of drug to sclerostin occurred at a much faster rate (milliseconds) than the kinetics of the drug and target distribution and elimination (hours); therefore the binding and unbinding appears to be at a quasi-steady state for our modeling and simulation purposes. The binding and unbinding rate constants (푘표푛 and 푘표푓푓) were thus be collapsed into the dissociation constant

(퐾퐷).

simplified to

where 퐶 represents serum blosozumab concentration; 푆푐푙 represents serum unbound sclerostin concentration; and 퐶푝푙푥 represents serum drug-sclerostin complex concentration.

Equations E.19 to E.23 show the full set of equations that described the quasi-equilibrium TMDD model and the derivation of the equations are detailed in Appendix B.

푑(퐴푠.푐.) E.19 = −푘푎 ∙ 퐴 + 퐷표푠푒 푑푡 푠.푐. 푠.푐. 푑(퐶푡표푡푎푙) 퐴푠.푐. 퐴푡 푆푐푙푡표푡푎푙 ∙ 퐶 E.20 = 퐼푛(푡) + 푘푎 ∙ − (푘 + 푘23) ∙ 퐶 + 푘32 ∙ − 푘푖푛푡 ∙ ( ) 푑푡 푉 푉 퐾퐷 + 퐶 푑(퐴푡) E.21 = 푘 ∙ 퐶 ∙ 푉 − 푘 ∙ 퐴 푑푡 23 32 푡

푑(푆푐푙푡표푡푎푙) 푆푐푙푡표푡푎푙 ∙ 퐶 E.22 = 푘푠푦푛 − 푘푑푒푔 ∙ 푆푐푙푡표푡푎푙 − (푘푖푛푡 − 푘푑푒푔) ∙ ( ) 푑푡 퐾퐷 + 퐶 where, (퐶 − 푆푐푙 − 퐾 ) + √(퐶 − 푆푐푙 − 퐾 )2 + 4 × 퐾 ∙ 퐶 E.23 퐶 = 푡표푡푎푙 푡표푡푎푙 퐷 푡표푡푎푙 푡표푡푎푙 퐷 퐷 푡표푡푎푙 2 푘푠푦푛 = 푘푑푒푔 ∙ 푆푐푙0 E.24

where 퐴푠.푐. represents the amount of blosozumab in the depot compartment; 퐴 represents the amount of serum blosozumab; 퐴푡 represents the amount of blosozumab in the peripheral compartment; 푆푐푙 represents the serum free unbound serum sclerostin concentration; 퐶푝푙푥 represents the serum drug- target complex; 푘표푛 represents the binding constant and 푘표푓푓 the unbinding coefficient of drug and target; 푘푠푦푛 and 푘푑푒푔 represent the synthesis and degradation of sclerostin, respectively, and 푘푖푛푡 represents the elimination of the drug-target complex; 퐷표푠푒푠.푐. represents the subcutaneous administration of 퐹 blosozumab and F represents the absolute bioavailability; 퐼푛(푡) represents input rate of intravenous administration of blosozumab; and 푆푐푙0 represents baseline unbound sclerostin concentration.

The TMDD model was fitted to publicly available sclerostin data from blosozumab trials57,136. The parameters related to the PK portion of the model were fixed to the population estimates reported in Table 4106. The TMDD model fitted with blosozumab was then used to inform the sclerostin kinetics in romosozumab.

The concentration-time profiles of romosozumab after single dose SC and IV administration was reported previously55. The data were extracted and used to estimate the PK parameters related to romosozumab using the same

PK model developed for blosozumab (Figure 3). The doses reported in literature were in mg/kg, but the average weights of the subjects were not available. For modeling purposes, it was assumed that the average weight of the subjects in each treatment arm was 70kg112. The single-dose romosozumab trial enrolled both healthy men and PMP women. PMP women generally

weigh less (average 60kg, Table 3) than men, but 70kg is a reasonable assumption for the dose cohort and was consistent with the doses of 70mg

QM, 140mg QM/Q3M and 210mg QM/Q3M tested in the phase 2 romosozumab trial.

Sclerostin kinetics was then linked to the bone remodeling model through the sclerostin effects on osteoblast and osteoclast actions.

5.2.2. Mathematical Description of the Bone Remodeling Model Figure 12 illustrates the schematic representation of the bone remodeling model with sclerostin regulation extension added. The equations governing bone cell interaction with sclerostin regulation added are as follow6:

푑(푅푂퐵) 퐷퐵 E.25 = 퐷푅 ∙ 휋퐶 − 휋푆푅 ∙ ∙ 푅푂퐵 푑푡 휋퐶 푑(퐴푂퐵) 퐷퐵 E.26 = 휋푆푅 ∙ ∙ 푅푂퐵 − 푘퐵 ∙ 휋푆퐵 ∙ 퐴푂퐵 푑푡 휋퐶 푑(퐴푂퐶) E.27 = 퐷퐶 ∙ 휋 − 퐷퐴 ∙ 휋 ∙ 퐴푂퐶 푑푡 퐿 퐶

where 푅푂퐵 is the responding osteoblasts; 퐴푂퐵 is the active osteoblasts; 퐴푂퐶 is the active osteoclasts; 퐷푅 is the differentiation rate of osteoblast progenitors; 퐷퐵 is the maturation rate of responding osteoblasts; 푘퐵 is the rate of elimination of active osteoclasts; 퐷퐶 is the maturation of the osteoclast precursors; and 퐷퐴 is the rate of osteoclast apoptosis. The parameters that regulates the interactions of osteoblast and osteoclasts, as defined by Lemaire

6 and colleagues (휋퐶, 휋퐿, and 휋푃) as well as the proposed sclerostin regulation of the bone remodeling process (휋푆푅, 휋푆퐵, 휋푆퐿, and 휋푆푂) are further described below (Sections 5.2.2.1 to 5.2.2.7).

5.2.2.1. TGF-β regulation

휋퐶 is the TGF-β feedback upon receptor binding. It was assumed that the TGF-β kinetics proceeds at a much faster rate than the cellular changes.

The TGF-β levels, on the time-scale of cellular changes, are therefore at steady state and are proportional to the number of osteoclasts. TGF-β was thus not modeled as a separate compartment. Instead, 휋퐶 is a function of the change in the level of osteoclast from baseline (E.28).

퐴푂퐶 + 푓0 ∙ 퐶푠 E.28 휋퐶 = 퐴푂퐶 + 퐶푠 where 퐶푠 is the value of AOC to get half differentiation flux; 푓0 is a fixed proportion as defined in Lemaire et al., 20046.

The release of TGF-β from the bone matrix as osteoclasts break down the bone inhibits further resorption action from the AOCs. This self-regulation is mathematically instituted by increasing the osteoclast elimination 퐷퐴 ×

휋퐶 × 퐴푂퐶. TGF-β was assumed to have distinct effects on ROBs and AOBs.

The preosteoblastic cells are recruited and then flow into the ROB compartment by 퐷푅 × 휋퐶. TGF-β, on the other hand, prevents the maturation of the preosteoblasts into AOB until the bone resorption process completes.

Thus there is an inverse relationship between osteoblast maturation and TGF-

퐷퐵 β given by × 푅푂퐵. 휋퐶

5.2.2.2. RANK-RANKL-OPG regulation

πL is the RANKL regulation of the osteoclast maturation. RANKL is a cell surface molecule on osteoblasts. The number of RANKL is, therefore, limited by the cell membrane carrying capacity and the upper limit of RANKL production is set at KPL=3 x 106 per cell. The RANKL competes with OPG for binding with RANK. The binding (k3) and unbinding (k4) of RANKL and

RANK to form RANKL-RANK complex, and the binding (k1) and unbinding

(k2) of OPG and RANK to form OPG-RANK complex were assumed to occur at a much faster rate as compared with cellular changes, and that the species

(RANKL, OPG, RANK) are at a quasi-steady state. The RANK receptor occupancy at quasi-steady state is as (E.29) and the derivation of the equation as per Lemaire et al.6 is detailed in Appendix C.

푘 퐾푃퐿 ∙ 휋 ∙ 퐴푂퐵 E.29 휋 = 3 × 푃 퐿 푘 푘 푘4 (1 + 1 ∙ 푂푃퐺 + 3 ∙ 푅퐴푁퐾) 푘2 푘4

5.2.2.3. PTH regulation

휋푃 is the PTH regulation of RANKL and OPG production. PTH increases the RANKL and decreases OPG production. This results in an overall increase in osteoclast activation and bone resorption level. The model is thus not able to describe the intermittent PTH treatment that will increase bone formation113,114. This limitation will need to be further evaluated. But for our purpose it is not anticipated to affect sclerostin mechanism of action because sclerostin was assumed to act directly on the cells and not through

PTH. The same parameterization and parameter values, per the original bone

6 remodeling model , for 휋푃 was used and the PTH level was kept constant.

푃푇퐻 휋푃 = where, 푃푇퐻 = 3.6nM and 푃푆 = 150nM 푃푇퐻 + 푃푆 = 0.0234 E.30

5.2.2.4. Sclerostin Regulation Sclerostin is mainly secreted by the osteocytes embedded in the bone matrix as a potent bone formation inhibitor111. The temporal changes in sclerostin will subsequently affect the downstream Wnt pathway regulations and have differential effects on osteoblasts and osteoclasts. Although osteocytes are the main contributor to the circulating sclerostin levels, temporal changes in the osteocyte numbers were not considered in the model.

Osteocytes are the most common bone cells and make up more than 95% of all bone cells23,115. The average life span of the osteocytes goes beyond 20 years116,117. Therefore, the number of osteocytes can be assumed to remain relatively constant during the period of clinical experiments and thus

osteocytes are not modeled as a compartment. The temporal changes in the sclerostin levels were assumed to be independent of osteocytes in the current model and is produced with a zero-order rate and eliminated with a first-order rate (Figure 11). The modeling of the kinetics of sclerostin is described in section 6.

The effect of sclerostin was added at four intersections: namely, on the maturation of ROBs into AOBs, on the apoptosis of AOBs, on the RANKL levels and, on the OPG levels. Activating and repressing actions of sclerostin were introduced to the model using Hill functions E.31 and E.32 respectively.

훽 ∙ 푆푐푙 E.31 휋 = 1 + 푎푐푡푖푣푎푡표푟 (푆푐푙 + 훿) 훽 E.32 휋 = 푟푒푝푟푒푠푠표푟 푆푐푙 (1 + ) 훿 where 휋푎푐푡푖푣푎푡표푟 represents the stimulatory effect of sclerostin; 휋푟푒푝푟푒푠푠표푟 represents the inhibitory effect of sclerostin; 훽 represents the maximum response and 훿 represents the sclerostin level needed to attain half maximum response; 푆푐푙 represents the concentration of the unbound sclerostin in serum.

5.2.2.5. Sclerostin regulation on ROB maturation

휋푆푅 is the sclerostin regulation of ROB maturation. Sclerostin is a repressor for AOB maturation118–120. When anti-sclerostin therapy is given, this inhibition is relieved and more ROBs differentiates into AOBs. This corresponds to increasing the removal of the precursor ROBs as the active osteoblast numbers builds up. An inhibitory relation (E.32) between sclerostin effect was added to the flux of ROBs maturating into AOBs given by 휋푆푅 ×

퐷퐵 ∙ 푅푂퐵. Adding this signal rapidly increases the number of AOBs but 휋퐶∙

depletes the ROB pool. This causes a reduction in AOB numbers in later time points as the depleted ROB needs time to replenish. This is consistent with the observed bone formation marker turnover following repeated doses of anti- sclerostin treatments. There was attenuation in the maximum response in

BSAP, P1NP and osteocalcin following repeated dosing, where the bone formation marker response started to decline despite being in the treatment period56–59.

5.2.2.6. Sclerostin regulation on AOB apoptosis

휋푆퐵 is the sclerostin regulation of the AOB apoptosis. In vitro experiments demonstrated that sclerostin accelerated the apoptosis of osteoblasts120. Sclerostin was shown to disrupt the various growth factors that are essential to the survival of osteoblasts and hasten the apoptosis. An activating hill function, 휋푆퐵 (E.31), was added to the 푘퐵 term to increase the removal of AOB when sclerostin levels increase, given by 휋푆퐵 × 푘퐵 ∙ 퐴푂퐵.

5.2.2.7. Sclerostin regulation on AOC The effect of sclerostin on osteoclasts is more complex and not entirely clear. In mice experiments, an increase in sclerostin levels led to an increase in

RANKL production, which was then followed by an increase in osteoclastic bone resorption121,122. Conversely, when anti-sclerostin treatment was given, it reduced sclerostin levels, and the Wnt signaling pathway became uninhibited and downstream signaling enhanced. RANKL production was reduced and bone resorption was inhibited. 휋푆퐿 , an activating Hill function, is the sclerostin regulation of RANKL level. Additionally, OPG production was lowered in β-catenin knock-out mice46, suggesting that up-regulating Wnt-

signaling would instead increase OPG expression. 휋푆푂 , a repressor Hill function, is the sclerostin regulation of the OPG level.

5.2.2.8. Biomarker Responses P1NP and CTX are the bone turnover biomarkers that closely relate to the activity of the osteoblast bone formation and osteoclast resorption activity respectively123. The percentage change from baseline of P1NP and CTX were assumed to vary proportionally with the normalized cell numbers. The percent change from baseline (%CFB) in AOB and AOC were equated to the percent change from baseline (%CFB) in P1NP and CTX, respectively (E.33 and

E.34).

퐴푂퐵 E.33 푃1푁푃 %퐶퐹퐵 = 100 ∙ ( − 1) 퐴푂퐵푏 퐴푂퐶 E.34 퐶푇푋 %퐶퐹퐵 = 100 ∙ ( − 1) 퐴푂퐶푏

where AOB represents active osteoblast; AOBb represents pretreatment active osteoblast baseline; AOC represents active osteoclast; and AOCb represents pretreatment active osteoclast baseline.

All other parameters were fixed as previously reported6. The parameters related to sclerostin’s control of the bone cell interaction were estimated using the P1NP and CTX profiles reported in blosozumab clinical

57,59 reports . 푅푂퐵푠푠 , 퐴푂퐵푠푠 and 퐴푂퐶푠푠 are the pretreatment baseline, steady state, ROB, AOB and AOC numbers. The values are fixed to the steady-state

-4 values. The 퐴푂퐶푠푠 was fixed to the 9.127 x 10 pM while 퐴푂퐵푠푠, 푅푂퐵푠푠 and

DC were solved at the initial conditions to maintain steady-state (E.35 to

E.37).

퐷푅 ∙ 휋푐,푠푠 E.35 퐴푂퐵푠푠 = 푘퐵 ∙ 휋푆퐵,푠푠 2 퐷푅 ∙ 휋푐,푠푠 E.36 푅푂퐵푠푠 = 퐷퐵 ∙ 휋푆푅,푠푠

퐷퐴 ∙ 휋푐,푠푠 E.37 퐷퐶 = ∙ 퐴푂퐶푠푠 휋퐿,푠푠 ∙ 휋푆퐶,푠푠

Scl

AOB RANKL DC PTH RANK

DB OPG AOC

ROB DA P1NP CTX DR

rate related repressor activator

constants to function function

Abbreviation: AOB=active osteoblast; AOC=active osteoclast; CTX= serum type I C-terminal procollagen; DA=rate of osteoclast apoptosis caused by TGF-β; DB=rate of responding osteoblast differentiation; DC=rate of osteoclast precursor differentiation; DR=rate of osteoblast progenitor differentiation; kb=rate of elimination of active osteoblast; OPG=osteoprotegerin; P1NP=procollagen type I N-terminal propeptide; PTH=parathyroid hormone; RANK=Receptor activator of nuclear factor κ-B; RANKL=RANKL ligand; ROB=responding osteoblast, Scl=sclerostin.

Figure 12 Schematic representation of the bone remodeling model with extension of sclerostin mechanism on bone interaction.

5.2.3. Mathematical Description of the Bone Mineral Density Model The primary end-point for phase 2 clinical trials in the treatment of osteoporosis is increase in BMD. BMD is currently used as diagnostic marker for determining osteoporosis and is highly predictive of fracture risk124. Two bone sites of interest in particular, lumbar spine and total hip, are indicative of the respective risk in spinal and hip fracture which are of clinical importance.

An indirect response model forms the structural base for the BMD model in the bone homeostasis model. Instead of using the pseudo-drug- target complex as a driving force to increase the bone formation rate, as in the population PK-PD model; AOB was used to affect the bone formation and AOC was used to affect the bone destruction. A power model that scales the steepness of the response was used to link the cellular component of the bone homeostasis model to the BMD models90,103. Lumbar spine and total hip BMD were modeled separately and parameters were estimated using the clinical observations from phase 2 blosozumab trial59.

The AOB was used to drive the increase in the BMD production rate. However, the osteoblast signal increases rapidly and then attenuates during the treatment period. This suggests that there is a delay between the increase in bone formation marker and the building of BMD. This is expected as the BMD accretion required that the osteoblasts produce and secrete the unmineralized bone matrix and then calcify it subsequently to form the mineralized bone matrix, which take a considerable amount of time. The average duration of a basic multicellular unit (BMU), which consists of a cutting cone of osteoclasts removing bone materials at the front

followed by osteoblasts filling the gaps with new bone materials trailing at the back, is between two to eight months, suggesting that bone formation takes roughly the same amount of time to be completed125,126. To account for the delay between the osteoblast formation and the BMD increase, an effect compartment was added to model this delay between osteoblast response and BMD increase (E.38).

AOB Effect

AOC

BMD

Abbreviation: AOB = active osteoblasts; AOC = active osteoclasts;

BMD = bone mineral density; kinBMD=rate of BMD formation; koutBMD=rate of BMD destruction

Figure 13 Schematic representation of the bone mineral density model for blosozumab

푑(퐸푓푓푒푐푡) E.38 = 푘 ∙ (퐴푂퐵 − 퐸푓푓푒푐푡) 푑푡 푒0

푑(퐵푀퐷) 퐸푓푓푒푐푡 훾푘푖푛 퐴푂퐶 훾푘표푢푡 E.39 = 푘푖푛퐵푀퐷 ∙ ( ) − 푘표푢푡퐵푀퐷 ∙ ( ) ∙ 퐵푀퐷 푑푡 퐴푂퐵푏 퐴푂퐶푏 where 퐸푓푓푒푐푡 represents transit component that delays the effect of osteoblasts on BMD formation rate constant, 푘푖푛퐵푀퐷 represents the rate of

BMD production, 푘표푢푡퐵푀퐷 represents the rate of BMD resorption, 퐴푂퐵푏 represents the pretreatment baseline value of AOB, 퐴푂퐶푏 represents the pretreatment baseline value of AOC, 훾푘푖푛 represents the coefficient that regulates effect of AOB and 훾푘표푢푡 represents the coefficient that regulates effect of AOC on BMD resorption.

6. System Pharmacology Model of Anti-Sclerostin Treatment Results

6.1. Anti-Sclerostin mAb Target-Mediated Drug Disposition

6.1.1. Blosozumab TMDD model Only mean sclerostin profiles after single and multiple doses of SC and

IV blosozumab57,136 and population PK model parameter estimates106 were available in the literature. Due to the lack of meaningful blosozumab PK profiles, simultaneous estimation of all the TMDD model parameters was not possible. Instead, the PK-related parameters ( 푉 , 푉2 , 퐶퐿 , 푄 , 푘푎 ,

퐹 [Biovailability]) were fixed to the values reported106; and only sclerostin- related parameters (푘푑푒푔 [degradation rate of sclerostin], 푘푖푛푡 [rate of drug- target complex internalization], 퐾퐷 [binding constant], and baseline sclerostin

[푆푐푙0]) were estimated (Table 7). Estimated 푘푑푒푔 , 푘푖푛푡, 퐾퐷, and 푆푐푙0 were

1.53 h-1, 0.0272h-1, 0.362 pmol/ml and 0.259 pmol/ml, respectively. Serum sclerostin levels increased following blosozumab administration57,136, which confirms target engagement of blosozumab, based on the assumption that binding of sclerostin by the antibody reduces the sclerostin clearance and thereby increases total sclerostin levels in the blood stream. The increase in total sclerostin levels was dose-dependent with higher blosozumab doses resulting in a larger increase in the sclerostin levels and the increase was generally maintained during the treatment phase. After blosozumab was discontinued, sclerostin levels rapidly fell then maintained around pretreatment baseline through the rest of the observation period. It was reported that the individual baseline sclerostin values were variable. The

750mg IV Q2W blosozumab regimen had a higher mean baseline compared with other dose arms but showed a lower change from baseline values

compared to the 540mg IV Q4W blosozumab regimen. This affected the change from baseline sclerostin levels not following the dose levels and dose intervals rank order57. Including this 750mg IV Q2W dose arm in the TMDD model resulted in resulted in a worse fit of the model. Therefore, the 750mg

IV Q2W dose arm from the model was excluded from the model fit because the baseline sclerostin level was more than ten-folds higher than the other dose arms and that the dose-response changes were not consistent with the other dose arms. Excluding this 750mg IV Q2W dosing arm resulted in a better fit in all other doses arms and the total sclerostin profile demonstrated a dose- dependent relationship. Figure 14 illustrates the model prediction adequately described the observed sclerostin profiles.

6.1.1. Romosozumab TMDD model Only mean romosozumab serum concentration profiles after single doses of SC and IV romosozumab55 and no sclerostin information was available in the literature. The mean PK profile demonstrated similar nonlinear clearance mechanism as blosozumab with distinct slopes in the terminal phase that varied with the drug concentration suggesting saturable kinetics.

Furthermore, both blosozumab and romosozumab are IgG antibodies and therefore it was reasonable to assume that both molecules have similar model structure and PK characteristics. We elected to fix the sclerostin-related kinetics (푘푑푒푔and 푆푐푙0) to the parameter estimates obtained from blosozumab because of the lack of sclerostin information from romosozumab trials. This approach assumed that since the target and receptors are shared parameters that differ not by the drug therapies but by patient population; and both drugs are both indicated osteoporosis for the same patient population. Binding

properties and drug distribution kinetics, however, varies with different drugs and 푉, 푉2, 퐶퐿, 푄, 푘푎, 퐹, 푘푖푛푡 and 퐾퐷 , were estimated using phase 1 single dose romosozumab PK profiles55.

Estimated bioavailability of the romosozumab after SC injection was about 70.7%. The central and peripheral volumes of distribution of romosozumab were estimated to be 2770 mL and 2870 mL, respectively, and the linear clearance and rate of absorption were 7.76 ml/h and 0.0129 h-1, respectively, and the estimated binding coefficient (퐾퐷) for romosozumab was

0.216 pmol/ml (Table 7).

Table 7 Pharmacokinetic/pharmacodynamics parameters for blosozumab and romosozumab sclerostin target-mediated disposition model.

Estimate Parameter Blosozumab Romosozumab Volume of central compartment , 푉 (mL) 2520a 2770d Volume of peripheral compartment , 푉2 (mL) 1440a 2870d Linear clearance, 퐶퐿 (mL/h) 8.82a 7.76d Inter-compartmental clearance, 푄 (mL/h) 16.8a 33.1d Rate of absorption, 푘푎 (1/h) 0.00697a 0.0129d Bioavailability, 퐹 Formulation 1 (fraction) 0.540a 0.707d Formulation 2 (fraction) 0.691a

b d Dissociation constant, 퐾퐷 (pmol/ml) 0.362 0.216 b d Rate of drug-sclerostin elimination, 푘푖푛푡 (1/h) 0.0272 0.0155 b,c Rate of sclerostin degradation, 푘푑푒푔 (1/h) 1.53 Baseline sclerostin, 푆푐푙0 (pmol/ml) 0.259b,c a Fixed to values in Table 4 b Estimated with the phase 1 and 2 sclerostin profiles from blosozumab studies57,136. c Assumed to be independent of drug and fixed for blosozumab and romosozumab. d Estimated with the phase 1 single dose romosozumab PK profile55.

Abbreviation: Q2W=once every 2 weeks, Q4W=once every 4 weeks; P1=phase 1 trial; P2=phase 2 trial. i.v.=intravenous infusion; s.c.=subcutaneous injection. Note: 750mg i.v. Q2W was not included in the target-mediated drug disposition model. See discussion in section 6.1.1.

Figure 14 Goodness of fit of (A) sclerostin concentration time profile and model predictions following blosozumab treatment and (B) romosozumab concentration time profile and model predictions following single dose romosozumab treatment.

6.2. Bone Biomarker Turnover Model With the knowledge of the kinetics profile of total and unbound sclerostin, we integrated the mechanism of sclerostin regulation, using the unbound sclerostin level as a driving force, into the bone remodeling model.

Recently, the Metrum research group published a model with sclerostin regulation added to a multi-scale bone systems model90. Our attempt to add sclerostin effect on bone homeostasis was similar but was based on the minimal model6 instead of the expanded multi-scale model102. The minimal model retained only the most important characteristics of bone cells interaction and minimized the number of number of parameters that need to be estimated.

Table 8 summarizes the parameter estimates associated with the bone remodeling model. Most of the parameters were from the original model6. The rate of osteoclast apoptosis (퐷퐴) was estimated by fitting the P1NP and CTX biomarkers as described in Section 5.2.2.8. The development of the biomarker responses were much slower compared with the profiles in the original model and the rate of elimination of AOBs (푘푏), differentiation rate of ROBs (퐷푅), and maturation of ROBs (푑퐵) were decreased by one order of magnitude from the original parameter estimates, to reflect the slower rate of cellular turnover.

Table 9 summarized the parameter estimates of the sclerostin regulation of bone remodeling fitted with phase 1 and phase 2 blosozumab data. Figure 15 and Figure 16 show predicted total and unbound sclerostin levels following blosozumab and romosozumab treatments. The unbound sclerostin was used as the input signal for the regulating the bone remodeling model as per described in Section 5.

Abbreviation: Q2W=once every 2 weeks, Q4W=once every 4 weeks; P1=phase 1 trial; P2=phase 2 trial. i.v.=intravenous infusion; s.c.=subcutaneous injection.

Figure 15 Predicted percentage change from baseline of (A) total sclerostin and (B) unbound sclerostin concentration-time profile after singles and multiple doses of blosozumab treatment in phase 1 and 2 clinical trials.

Abbreviation: Q2W=once every 2 weeks, Q4W=once every 4 weeks; QM=once every month; Q3M=once every 4 months. i.v.=intravenous infusion; s.c.=subcutaneous injection; P1=phase 1 trial; P2=phase 2 trial.

Figure 16 Predicted percentage change from baseline of (A) total sclerostin and (B) unbound concentration-time profiles after single and multiple doses of romosozumab treatment in phase 1 and 2 clinical trials.

Table 8 Parameter Estimates for the Bone Remodeling Model

Parameter Description Estimate a -4 퐴푂퐶푠푠 osteoclast numbers at steady state 9.13 x 10 pM 퐶푠 value of C to get half differentiation flux 0.005 pM 퐷퐴 rate of osteoclast apoptosis caused by TGF-β 0.0533 1/h b -4 b 푑퐵 differentiation of responding osteoblast 2.92 x 10 1/h 퐷푅 differentiation rate of osteoblast progenitors 2.92 x 10-6 pM/h b 푓0 fixed proportion 0.05 (unitless) 푅퐴푁퐾 fixed concentration of RANK 10 pM -4 푘1 rate of OPG-RANKL binding 4.17 x 10 1/pM/h 푘2 rate of OPG-RANKL unbinding 0.417 1/h -5 푘3 rate of RANK-RANKL binding 2.42 x 10 1/pM/h -4 푘4 rate of RANK-RANKL unbinding 7.08 x 10 1/h -4 푘5 rate of PTH binding with its receptor 8.33 x 10 1/pM/h 푘6 rate of PTH unbinding 0.125 1/h 푘퐵 rate of elimination of active osteoblast 7.88 x 10-4 1/h b maximum number of RANKL attached on 3.00 x 106

퐾푃퐿 each cell surface pmol/pmol cell 푘푂 rate of elimination of OPG 0.0146 1/h 8.33 x 103 minimal rate of production of OPG per cell 퐾푃푂 pmol/h/pmol cell 푘푝 rate of elimination of PTH 3.58 1/h 푃푇퐻0 PTH concentration at steady state 50.4 pM/h Abbreviation: AOC=active osteoclast; TGF-β=transforming growth factor; OPG=osteoprotegerin; PTH=parathyroid hormone; RANK=Receptor activator of nuclear factor κ-B; RANKL=RANKL ligand. a Fixed to estimates reported in Lemaire et al., 2004.6 b Estimated / calibrated with the blosozumab biomarkers observations

Table 9 Parameter Estimates for sclerostin effect on P1NP and CTX profiles using the bone remodeling model

Parameter Description Estimate Maximum inhibition of sclerostin on osteoblast 10.9

훽푂푅 maturation (unitless) Concentration of sclerostin that cause half maximal 0.198 nM 훿푂푅 inhibition of osteoblast maturation Maximum stimulation of sclerostin on osteoblast 5.13

훽푂퐵 apoptosis (unitless) Concentration of sclerostin that cause half maximal 0.0153 nM 훿푂퐵 stimulation of osteoblast apoptosis 1.77 Maximum stimulation of sclerostin on RANKL 훽푅퐴푁퐾퐿 (unitless) Concentration of sclerostin that cause half maximal 0.0691 nM 훿푅퐴푁퐾퐿 stimulation on RANKL 1.80 Maximum stimulation of sclerostin on OPG 훽푂푃퐺 (unitless) Concentration of sclerostin that cause half maximal 0.0179 nM 훿푂푃퐺 inhibition of OPG

Figure 17 shows the goodness-of-fit between the observed P1NP and

CTX in the phase 1 and phase 2 blosozumab studies used to calibrate the model parameters. The model was able to describe the general trend of the bone formation and bone resorption. There was a rapid increase in the P1NP level following anti-sclerostin treatment. After repeated dosing, the maximum response began to decline despite serum sclerostin remaining neutralized and suppressed at a steady level (Figure 15). The model can reasonably describe this development of tolerance in the bone formation marker response. The

CTX response was more varied. After anti-sclerostin treatment, there was an initial decline in the total CTX level, followed by a return to baseline and rebound beyond baseline during repeated dosing. There was a sharp rebound of the CTX levels beyond baseline after the treatments were discontinued.

Although the model fit was not perfect, the model was able to describe the trend of the CTX levels to a reasonable extend whereby the initial CTX drop and the subsequent rebound toward baseline levels and beyond were consistent with the observations. Large variability associated with the CTX response were well documented127. Intrinsic biological variations play a part in CTX measurements variations. For example, daily and seasonal circadian cycle, effects of food intake as well as age and physical activities level can all affect.

These factors affect bone resorption levels and CTX measurements can vary in the range of ± 30%127. Therefore, the goal of the model fit of CTX is not for the model to pass through all the observation points, which is not possible due to the inherent large biological variability in the CTX measurement, but rather to have the model describe the general trend of the CTX kinetics. The model performed satisfactorily in this regard.

Abbreviation: Q2W=once every 2 weeks, Q4W=once every 4 weeks; i.v.=intravenous infusion; s.c.=subcutaneous injection; P1=phase 1 trial; P2=phase 2 trial; CI=confidence interval.

Figure 17 Goodness-of-fit of percent change from baseline of observed (A) P1NP and (B) CTX concentration-time profiles and model predictions after single and multiple doses of blosozumab treatment in phase 1 and 2 clinical trials.

6.3. Bone Mineral Density Model Table 10 summarizes the parameter estimates obtained from the BMD model fitted with the lumbar spine and total hip BMD responses from blosozumab trial59. Figure 18 illustrates the goodness-of-fit of the BMD model overlaying the model predictions with the observed BMD that was used to estimate the model parameters. Generally, the goodness-of-fit of the model demonstrated that the model could adequately describe the observed data.

Table 10 Parameter Estimates of the Lumbar Spine and Total Hip BMD Model

Parameter Description Estimate Lumbar spine

푘푖푛퐿푆퐵푀퐷 Rate of lumbar spine BMD production 0.0769 1/week -5 푘푒0 퐿푆퐵푀퐷 Rate of flow effect compartment transduction 7.19 x 10 1/h Exponent scaling active osteoblast activity to 훾 0.496 (unitless) 푘푖푛,퐿푆퐵푀퐷 BMD production Exponent scaling active osteoclast activity to 훾 0.191 (unitless) 푘표푢푡,퐿푆퐵푀퐷 BMD destruction Total Hip

푘푖푛퐻퐼푃퐵푀퐷 Rate of Total Hip BMD production 0.0714 1/week -5 푘푒0퐻퐼푃퐵푀퐷 Rate of flow effect compartment transduction 2.83 x 10 1/h Exponent scaling active osteoblast activity to 0.451 (unitless) 훾푘푖푛퐻퐼푃퐵푀퐷 BMD production Exponent scaling active osteoclast activity to 0.0267 (unitless) 훾푘표푢푡퐻퐼푃퐵푀퐷 BMD destruction

Abbreviation: Q2W=once every 2 weeks, Q4W=once every 4 weeks; CI=confidence interval.

Figure 18 Goodness-of-fit of (A) lumbar spine and (B) total hip BMD overlay with observed data following single and multiple doses of blosozumab in phase 1 and 2 clinical trials.

6.4. Model Qualification

6.4.1. Romosozumab TMDD Model For model validation, the romosozumab PK model was used to predict the exposures after multiple doses of romosozumab and compare with the reported values of drug exposure as reported in multiples dose romosozumab study (Table 11)56. 1000 Monte-Carlo simulations per dosing arm were simulated with 15% (coefficient of variation, CV%) inter-individual variability added to the PK parameters. The non-compartmental analysis parameters were computed and summarized from the simulations and reported in Table 11. The model was able to predict the drug exposure within the reported confidence limits56. The TMDD model for romosozumab was adequate and can predict the PK profiles reasonably well, despite only limited

PK data from the single-dose romosozumab study were available55.

Table 11 Comparison of observed and model predicted romosozumab exposure

Mean ± SD Observed a Predicted b 1mg/kg 2mg/kg 2mg/kg 3mg/kg 1mg/kg 2mg/kg 2mg/kg 3mg/kg Q2W Q4W Q2W Q4W Q2W Q4W Q2W Q4W Parameter (n=5) (n=6) (n=5-6) (n=5) At first dose c tmax (day) 3 (2-5) 3 (3-5) 4.5 (3-7) 3 (3-5) 4 (2-6) 4 (2-6) 4 (2-6) 4 (2-6)

Cmax (μg/mL) 6.80 ± 1.86 15.7 ± 4.6 14.8 ± 6.0 24.5 ± 6.8 5.32 ± 1.19 12.1 ± 2.38 12.1 ± 2.39 19.1 ± 3.48 d AUCτ (μg*day/mL) 65.5 ± 15.6 202 ± 48 152 ± 63 340 ± 73 50.8 ± 12.4 170 ± 43.4 126 ± 25.3 298 ± 65.7 At last dose c tmax (day) 3 (0-5) 3 (1-4) 3.5 (3-5) 5 (2-7) 3 (2-4) 4 (2-6) 4 (2-4) 4 (2-6)

Cmax (μg/mL) 14.2 ± 4.3 16.7 ± 3.3 27.8 ± 8.4 29.5 ± 8.7 9.30 ± 2.83 14.0 ± 3.25 26.0 ± 6.2 23.7 ± 5.26 d AUCτ (μg*day/mL) 141 ± 41 231 ± 58 321 ± 97 462 ± 97 97.9 ± 35.7 207 ± 68.0 301 ± 80.6 393 ± 118

t1/2 (day) 7.02 ± 3.52 6.51± 1.37 9.32 ± 1.88 6.84 ± 1.79 5.50 ± 1.85 4.97 ± 1.23 8.72 ± 3.73 5.28 ± 1.84 AUC ratio, last/first 2.15 ± 0.45 1.17 ± 0.26 2.35 ± 0.90 1.35 ± 0.19 1.88 ± 0.33 1.2 ± 0.11 2.37 ± 0.35 1.3 ± 0.14 Abbreviation: AUC=area under the concentration-time curve; AUCτ=AUC during one dosing interval; Cmax=maximum observed concentration; tmax=time of Cmax; t1/2=terminal half-life; Q2W=once every 2 weeks, Q4W = once every 4 weeks; SD= standard deviation a Padhi et al., 201356 b 1000 Monte-Carlo simulations. c Median (minimum – maximum) d AUCτ range was 0-14 days for Q2W dose cohort and 0-28 days for Q4W dose cohort

6.4.2. Bone biomarker and BMD prediction For model qualification, the model was used to predict the P1NP and

CTX responses following romosozumab administration (Figure 19). The simulated P1NP profiles were consistent with the observed data from the phase 1 and phase 2 romosozumab trials. In particular, the model was able to predict the P1NP response in the longer frequency regimens (Q3M), despite the Q3M regimen was not in the blosozumab model calibration dataset. The model could reliably predict the magnitude of the P1NP increase initially and the decline in the response during treatment subsequently. The model was also able to predict the drop in the P1NP level below the pretreatment baseline level early in the treatment period. The mean model predictions were within the standard error or the 95% confidence interval of the observed data. The

CTX response following romosozumab treatment, however, was less well predicted (Figure 19). In the phase 1 single-dose romosozumab CTX response, the model predicted sharp rebound after the initial decrease in the CTX levels.

The treatment regimens in multiple-dose romosozumab trials employed longer interval dosing frequency (Q4W, QM and Q3M) and the model predicted large fluctuations in the CTX levels occurring in the intervals between dosing events. Nonetheless, the model predictions passed through most of the observation data points and could account for the initial CTX level decrease following anti-sclerostin therapy. Figure 20 shows the model prediction of the lumbar spine and total hip BMD predictions against the observations following romosozumab treatments. The model predictions of BMD changes were consistent with the observations.

Abbreviation: Q2W=once every 2 weeks, Q4W=once every 4 weeks; i.v.=intravenous infusion; s.c.=subcutaneous injection; QM=once every month; Q3M=once every 3 months; CI=confidence interval; SE=standard error.

Figure 19 Prediction of (A) P1NP and (B) CTX concentration time profile against observed data after single and multiple doses of romosozumab treatment in phase 1 and 2 clinical trials.

Abbreviation: Q2W=once every 2 weeks, Q4W=once every 4 weeks; i.v.=intravenous infusion; s.c.=subcutaneous injection; QM=once every month; Q3M=once every 3 months; CI=confidence interval.

Figure 20 Prediction of (A) lumbar spine and (B) total hip BMD overlay with observed percent change from baseline (± 95% CI) following single and multiple doses of romosozumab in phase 1 and 2 clinical trials.

6.4.3. Defining the Boundary of Model Simulation We simulated the scenario when sclerostin was fully inhibited and predicted what the maximum increase in lumbar spine BMD will be. This defines the upper limit of lumbar spine BMD increase and physiologically this corresponds to sclerosteosis or van Buchem disease.

Sclerosteosis and van Buchem disease are two diseases that cause high bone mass in sufferers. The diseases are very rare and are limited mainly to a small European population in South Africa and Netherlands111,128. There are less than 30 literature reported cases of van Buchem disease129 and about 60 reported cases of sclerosteosis130. Sclerosteosis and van Buchem disease are both autosomal recessive disorders that display impressive increases in

BMD131. Sclerosteosis patients are characterized by facial bone deformation, tall stature and syndactyly (fused fingers). Van Buchem disease, on the other hand, is a more benign condition whereby the patients display less prominent bone enlargement symptoms. Both sclerosteosis and van Buchem disease are caused by a defective SOST gene that produces non-function sclerostin132.

Mutation in a regulatory region downstream of the SOST gene was found in all van Buchem disease patients, suggesting that the condition can be caused by a loss-of-function gene or an impairment of the gene expression regulation. Low levels of sclerostin can be measured in van Buchem disease patients whereas no detectable level of sclerostin is found in sclerosteosis patients111,128, linking the level of serum sclerostin to the disease severity.

The lumbar spine BMD response was simulated by setting sclerostin production (푘푠푦푛) parameter to zero to replicate when sclerostin is completely eliminated. The model-predicted BMD response was then compared with the

estimated BMD (based on reported z-scores) of van Buchem disease and sclerosteosis patients compared with the reference population. BMD is higher in both van Buchem disease and sclerosteosis patients compared with the reference population128,131,133. The BMD in van Buchem disease and sclerosteosis patients were more than 50%-150% compared with healthy age- matched subjects (Figure 21). There was a wide range of BMD measurements reflecting the wide extent of disease severity as well as a large age interval in the data from a limited patient population of these rare diseases. Our model predicted that the lumbar spine BMD response in complete sclerostin shutdown after anti-sclerostin therapy was 142% of the pre-treatment baseline

(Figure 21). Our model suitably predicted BMD responses in the small patient population with sclerostin deficiency and reasonably defined a maximum

BMD response within a realistic range.

Note: BMDs were estimated from the z-scores extracted from the references. The reference population for the van Buchem disease patients and carriers were Caucasian males stratified by age; and the reference population for the sclerosteosis patients and carriers were Caucasian stratified by gender and age from the NHANES III database. Abbreviations: NHANES=National Health and Nutrition Examination Survey a NHANES III database134 b Gardner et al., 2005133 c Lierop et al., 2013128

Figure 21 Estimated BMD differences compared to reference population in Van Buchem disease and sclerosteosis and model prediction of maximum BMD response in complete sclerostin inhibition.

7. Simulation Experiments and Applications of the Models The final models from the population PK-PD analysis and the extended bone remodeling systems pharmacology analysis were used to carry out simulation experiments to translate the model parameters and mathematical equations into useful visualizations and meaningful metrics that can be better interpreted and applied to improve trial design and dosing strategies for anti- sclerostin therapies. Note that all the simulations experiments were performed using the subcutaneous administration of blosozumab as this is the intended route for the anti-sclerostin antibody therapies. The population PK-PD model was used to perform Monte Carlo simulations, by incorporating the inter- individual and residual variability, to assess the impact of dosing interval and body weight within the clinically relevant dose ranges and reasonable clinical observation periods (Section 7.1). Correspondingly, the extended bone remodeling bone was used to performed summary level simulations (i.e., no variability on the parameter estimates) to evaluate the effects of longer durations, wider dose ranges and dose intervals on the drug exposures, biomarker and BMD responses (Section 7.2). The differences, advantages and limitations of the population PK-PD model and the extended bone remodeling model were then compared and recommendations for how to use the different models to answer different questions were discussed in Section 7.3.

7.1. Population PK-PD Model Simulations The population PK-PD model was used to refine and investigate the impact of the body weight on the drug exposure and BMD efficacy of different clinically meaningful dose regimens predicted by the extended bone remodeling model (Section 7.2). 200 trials each with 200 non-Japanese virtual

subjects with body weights of 30, 50, 70, 90 and 110kg (total 1000 subjects per trial) were simulated to predict the blosozumab exposure and BMD responses following 1 year of 135mg Q1W , 270mg Q2W, 540mg Q1M,

1620mg Q3M, 3240mg Q6M, 540mg Q3M and 540mg Q6M blosozumab administered subcutaneously.

7.1.1. Effect of Dosing Interval on Drug Exposure and BMD Responses Figure 22 (A) illustrates the predicted median and 90% prediction interval of blosozumab steady state PK profiles of the different dose regimens.

Based on the theoretical dissociation coefficient (KD, 21.4 nM [Table 6]), the estimated drug concentrations that would achieve 50%, 80% and 90% target engagement were 21.4 nM, 85.6 nM and 192 nM, respectively. The trial simulations showed that 135mg Q1W, 270mg Q2W and 540mg Q1M regimens were able to attain above 50% target engagement at steady-state exposures. Additionally, 135mg Q1W and 270mg Q2W regimens could consistently attain above 80% target engagement even at the lower end of the prediction interval. On the other hand, the regimens with longer treatment dosing intervals (1620mg Q3M, 3240mg Q6M, 540mg Q3M and 540mg

Q6M) had periods where the exposure fell below 50% target engagement.

There is also greater difference between the maximum and minimum concentrations. The average concentrations at steady state (Cav,ss) were also most similar between the 135mg Q1W, 270mg Q2W and 540mg Q1M regimens and they have the most stable concentration profiles (i.e., lower peak-to-through concentration ratio) (Table 12 and Figure 22).

Figure 22 (B) and (C) show the predicted lumbar spine and total hip

BMD response following various dosing regimen. Q1W, Q2W and Q1M

regimens were the most similar and gave similar BMD responses. The predicted lumbar spine BMD increase at one year for 135mg Q1W, 270mg

Q2W and 540mg Q1M were 17.2% (95% CI: 15.0, 20.3), 17.3% (95% CI:

15.2, 20.5) and 17.2% (95% CI: 15.2, 20.0), respectively; and the predicted total hip BMD increase at one year for 135mg Q1W, 270mg Q2W and 540mg

Q1M were 5.65% (95% CI: 4.34, 7.22), 5.72% (95% CI: 4.44, 7.26), 5.67%

(95% CI: 4.48, 7.15), respectively (Table 13). These regimens are considered similar, in terms of efficacy, and can be considered for further investigations.

Two regimens with longer dosing interval 540mg Q3M and 540mg

Q6M were also simulated. The predicted lumbar spine BMD increase at one year for 540mg Q3M and 540mg Q6M were 10.4% (95% CI: 8.03, 12.4) and

5.27% (95% CI: 3.31, 6.95); and the predicted total hip BMD increase at one year for were 3.27% (95% CI: 2.22, 4.37), 1.54% (95% CI: 0.77, 2.32) respectively (Table 13). The longer dosing interval regimens were predicted to have a lower BMD response, suggesting that more frequent dosing is required to maintain efficacy despite tolerance development in the bone formation marker response.

The simulation predicted that the 135mg Q1W regimen would produce the most consistent drug exposure and provide the best target neutralization profile throughout the treatment duration. The 540mg Q1M regimen, however, can also be considered based on the similar efficacy response with the 135mg

Q1W and 270mg Q2W regimens. Weekly or monthly dosing frequency could potentially be a more attractive dose regimen to implement, compared to once every 2 weeks, as it may be easier for patients to remember. A monthly dose regimen can further ease the inconvenience and discomfort as the number of

subcutaneous injections patients will have to administer is reduced; potentially improve compliance and adverse events profiles associated with subcutaneous injections.

Abbreviation: Q1W= once every week; Q2W= once every two weeks; Q1M= once every month; Q3M= once every two months; Q6M= once every six months; TE=target engagement.

With the final population PK model, simulations with 1-year treatment of blosozumab administered subcutaneously were conducted in 1000 virtual patients to achieve steady state. The medians and 90% prediction intervals were presented. Horizontal lines were blosozumab concentrations associated with 50%, 80%, or 90% target

engagement (based on the dissociation coefficient (KD= 21.4nM).

Figure 22 Simulated median (90% PI) (A) blosozumab serum concentration at steady state and (B) lumbar spine and (C) total hip BMD response as percent change from baseline (%CFB) following various regimens of 1-year subcutaneous blosozumab treatment and 1-year follow-up

Table 12 Comparison of simulated average steady state blosozumab exposure following subcutaneous administration of various dose and dosing interval of blosozumab for 1 year

Median (90% Prediction Interval)

AUCτ,ss Cav,ss Regimen (pmol·hr/mL) (nM) 135mg Q1W 42000 (17800,80300) 250 (106,478) 270mg Q2W 83200 (34500,164000) 248 (103,489) 540mg Q1M 158000 (76100,313000) 217 (104,430) 540mg Q3M 130000 (68500,255000) 59.7 (31.4,117) 540mg Q6M 133000 (68500,257000) 30.5 (15.7,58.9)

Abbreviation: AUC=area under the concentration time curve; AUC(0-168)=AUC from zero

to 168 hours; AUCτ,ss=AUC during one dosing interval at steady state; Cav,,ss=average concentration at steady state; Q1W= once every week; Q2W= once every two weeks; Q1M= once every month; Q3M= once every two months; Q6M= once every six months.

Table 13 Summary of population PK-PD model predicted median BMD change from baseline following 1 year of blosozumab treatment administered subcutaneously

Median (90% Prediction Interval) a Lumbar Spine Total Hip Regimen Year 1 Year 2 Year 1 Year 2 17.2 4.32 5.65 2.51 135mg Q1W (15.0, 20.3) (3.35, 5.68) (4.34, 7.22) (1.84, 3.52) 17.3 4.42 5.72 2.59 270mg Q2W (15.2, 20.5) (3.44, 5.78) (4.44, 7.26) (1.93, 3.61) 17.2 4.56 5.67 2.66 540mg Q1M (15.2, 20.0) (3.61, 5.88) (4.48, 7.15) (1.99, 3.67) 10.4 3.22 3.27 1.56 540mg Q3M (8.03, 12.4) (2.28, 4.09) (2.22, 4.37) (0.92, 2.18) 5.27 2.32 1.54 0.81 540mg Q6M (3.31, 6.95) (1.29, 3.33) (0.77, 2.32) (0.15, 1.49) Abbreviation: Q1W= once every week; Q2W= once every two weeks; Q1M= once every month; Q3M= once every two months; Q6M= once every six months. a Summarized from 200 virtual clinical trials which were simulated to predict lumbar spine and total hip BMD responses in 1000 patients.

7.1.2. Effect of Body Weight on Drug Exposure and BMD Responses Body weight was identified as a covariate on the clearance and volumes of distribution of blosozumab and so body weight differences could lead to different drug exposure profiles and possibly BMD responses. Model simulation was performed to evaluate if dose adjustments by body weight was necessary.

Simulations were generated to evaluate the drug exposure at steady state and BMD responses for patients with different body weights (30, 50, 70,

90, and 110kg). For each combination of body weight and dose regimen, simulations were conducted in 200 virtual patients with the final PK and BMD models. Simulations showed that the exposure difference between the patients weighing 30kg and 110kg were approximately two-fold in the five different treatment regimens explored (135mg Q1W, 270mg Q2W, 540mg Q1M,

540mg Q3M, 540mg Q6M) (Table 14). Figure 23 illustrates the steady-state blosozumab concentration profiles for various dose regimens stratified by body weight. According to this simulation, in the 135mg Q1W, 270mg Q2W and 540mg Q1M regimens, patients across the wide range of body weight will have at least 50% of target neutralization throughout the treatment duration

(Figure 23). For the regimens with shorter dosing intervals (135mg Q1W and

270mg Q2W), patients across all body weight will have at least 80% of target neutralization throughout the treatment duration (Figure 23). Therefore, 135mg

Q1W, 270mg Q2W and 540mg Q1M regimens, were expected to consistently maintain target engagement across different body weights and dose adjustments were not necessary. Fixed-dose blosozumab was predicted to perform well across body weight in regimens with smaller dosing intervals.

Consequently, the predicted differences of BMD responses in both lumbar

spine and total hip are the smallest across 30- to 110-kg body weight in regimens with the smaller dosing intervals (135mg Q1W, 270mg Q2W and

540mg Q1M regimens) (Figure 23).

Table 14 Comparison of simulated steady state blosuzumab exposure stratified by body weight following 1 year treatment of blosozumab administered subcutaneously.

Median (90% Prediction Interval) a Cav,ss (nM) Body weight 30kg 50kg 70kg 90kg 110kg 334 282 249 211 171 135mg Q1W (191, 575) (158, 506) (127, 439) (100, 405) (69.5, 342) 332 288 247 205 169 270mg Q2W (188, 568) (166, 517) (134, 464) (97.2, 386) (72.5, 335) 296 253 216 181 146 540mg Q1M (177, 509) (148, 467) (122, 383) (105, 346) (77.8, 288) 91.7 73.4 60.2 49.5 41.7 540mg Q3M (54.4, 144) (45.2, 117) (38.0, 94.7) (30.1, 79.7) (24.7, 63.3) 46.2 37.5 30.3 25.3 20.7 540mg Q6M (28.0, 73.2) (22.7, 58.6) (18.5, 48.0) (15.5, 40.7) (11.8, 32.0) a Simulated and summarized with the final population PK model in 1000 virtual patients. Since body weight was identified to be covariate for saturable clearance and central volume, the simulation was conducted for patients with different body weight.

Abbreviation: Q1W= once every week; Q2W= once every two weeks; Q1M= once every month; Q3M= once every two months; Q6M= once every six months; TE=target engagement. With the final population PK model, for each combination of body weight and dose regimen, simulations with 1-year treatment of blosozumab administered subcutaneously were conducted in 1000 virtual patients to achieve steady state. The medians were presented. Horizontal lines were blosozumab concentrations associated

with 50%, 80%, or 90% target engagement (based on the dissociation coefficient (KD= 21.4nM).

Figure 23 Simulated median (90% PI) (A) blosozumab serum concentration at steady state and (B) lumbar spine and (C) total hip BMD response as percent change from baseline (%CFB) following various regimens of 1-year treatment of blosozumab administered subcutaneously and 1-year follow-up stratified by body weight

7.2. Extended Bone Remodeling Model Simulations We simulated the different blosozumab dosing regimens to investigate how the bone biomarker responses relate to BMD changes. By altering the doses and dosing frequencies, how will the drug exposure change and how will BMD responses be affected? Based on the observed P1NP responses that showed attenuated responses after repeated dosing56–58,107; will a longer dosing interval improve the recovery of the bone formation by allowing time for the

ROB pool to build up and mitigate the attenuation of P1NP response during treatment period? To answer these questions, we simulated 135mg Q1W,

270mg Q2W, 540mg Q1M of blosozumab administered subcutaneously which were predicted to give similar drug exposure. The doses considered were practical, meaning it can potentially be manufactured into a viable medical product with suitable delivery device, and were within range of the doses tested clinically and did not show any safety concerns (the largest dose studied clinically was 1100mg IV single dose blosozumab in study 2) . 540mg Q3M and 540mg Q6M were also investigate to evaluate how a longer dosing interval at a fixed-dose affected the biomarker and BMD responses. Figure 24 shows the predicted drug exposure, biomarker and BMD responses following one-year treatment of 135mg Q1W, 270mg Q2W, 540mg Q1M, 540mg Q3M and 540mg Q6M.

7.2.1. Effect of Dosing Interval on Drug Exposure and BMD Responses 135mg Q1W, 270mg Q2W and 540mg Q1M performed similarly in terms of BMD responses. Predicted lumbar spine change from baseline were

25.9%, 26.1% and 23.3% while total hip BMD change from baseline were

7.72%, 7.81% and 7.11% at one year after 135mg Q1W, 270mg Q2W and

540mg Q1M respectively (Table 15). Figure 24 (C) shows that 540mg Q3M and 540mg Q6M dose regimen did not allay the attenuation in the P1NP response in subsequent doses, refuting the hypothesis that a longer dosing interval will counter the development of tolerance in the P1NP response, at least in the dosing regimens investigated in the simulation. P1NP response after the first 540mg dose increased more than 150% followed by a decrease towards pretreatment baseline with a small overshoot during the first dosing interval. Repeat doses failed to achieve the same level of P1NP response and the responses were lower in magnitude compared with the first dose. Another observation was that repeated dosing alters the steady-state magnitude of the

P1NP responses. The initial maximum magnitude of P1NP responses after

135mg Q1W, 270mg Q2W and 540mg Q1M were 148%, 153% and 176%, respectively. The maximum response declined thereafter and reached a steady level by about 9 months and the maximum P1NP responses were 34.3%,

34.0% and 28.7%, respectively, at steady state. The 540mg Q3M and 540mg

Q6M regimens, because of the greater intervals between doses, had greater fluctuations in the P1NP responses. Between each dosing intervals there were extended periods where the P1NP responses were below the pretreatment baseline levels. At each dosing event, the P1NP responses increased and quickly dissipated, producing sharp spikes in the P1NP profiles, but the general P1NP profile remained largely below the pretreatment baseline levels.

Similarly, the maximum P1NP responses at repeated doses attained a steady state level by about 12 months of continuous treatment. The maximum P1NP responses after initial dose declined from 176% to 88.1% and 133%, following

540mg Q3M and 540mg Q6M doses, respectively. This is an interesting observation and suggests that the longer dosing interval can retain a much higher maximum P1NP response in repeat doses. However, more frequent dosing can maintain better bone formation activities and keep the P1NP responses largely above the pretreatment baseline level. It also suggests that the systems need an even longer interval (more than 6 months) of recovery for the P1NP response to return to its pretreatment level. Nevertheless, the anti- sclerostin therapy can drive bone formation activities in all the dosing regimens investigated here and initiate BMD accretion.

Figure 24 (E) shows that the lumbar spine BMD change from baseline response dropped from 18.3% (540mg Q1M) to 8.63% and 4.91% for 540mg

Q3M and 540mg Q6M, respectively (Table 15). Similarly, Figure 24 (F) shows that the total hip BMD change from baseline response dropped from

5.97% (540mg Q1M) to 2.88% and 1.56% for 540mg Q3M and 540mg Q6M, respectively (Table 15). The model predictions suggest that more frequent dosing is required for the maintenance of the BMD response despite observation of tolerance response in the bone formation marker. It is attractive and scientifically logical to employ a longer dosing interval to counter the attenuation of the bone formation response by allowing time for new osteoblast recruitment and maturation. However, based on systematic analysis of the model, a more frequent dosing regimen is predicted to be more preferable and provided more optimal efficacy response.

Table 15 Summary of bone remodeling model predicted mean BMD change from baseline following 1 year of blosozumab treatment administered subcutaneously

Lumbar Spine Total Hip Year 1 Year 2 Year 1 Year 2 135mg Q1W 19.4 6.58 6.28 3.72 270mg Q2W 19.5 6.73 6.33 3.80 540mg Q1M 18.3 6.19 5.97 3.49 540mg Q3M 8.63 2.75 2.88 1.49 540mg Q6M 4.91 2.03 1.56 1.09 Abbreviation: Q1W= once every week; Q2W= once every two weeks; Q1M= once every month; Q3M= once every three months; Q6M= once every six months.

A B

C D

E F

Abbreviation: BMD: bone mineral density CTX=serum type 1 C-terminal procollagen; P1NP=serum type-1 procollagen N-terminal; Q1W= once every week; Q2W= once every two weeks; Q1M= once every month; Q3M= once every two months; Q6M= once every six months; %CFB=percent change from pretreatment baseline. Figure 24 Prediction of (A) blosozumab concentration and (B) unbound sclerostin (C) P1NP, (D) CTX, (E) lumbar spine BMD and (F) total hip BMD following various dose regimens of blosozumab administered subcutaneously

7.2.2. Duration of Precursor Osteoblast Suppression and Replenishment The Q6M dosing regimen predicted that the P1NP levels did not return to baseline between doses (Figure 24 (C)); thereby suggesting that a longer interval, more than six months, between doses would be required for the preosteoblast pool to be replenished and P1NP level to return to pretreatment levels. Simulation of 540mg Q1M, Q3M, Q6M, Q9M (once every nine months), Q12M (once every year) and Q18M (once every one-and-a-half year) was performed to estimate the duration needed for the ROB to be replenished and P1NP levels to return to pretreatment levels. Figure 25 (A) showed that the P1NP levels will take more than 18 months to return to baseline following one dose of anti-sclerostin antibody treatment. The simulated preosteoblast number decreased as anti-sclerostin therapy was administered. The precursor pool then slowly replenished itself taking more than 18 months to return to baseline level (Figure 25 (B)). The decrease in the precursor pool was about

28.0% after the first dose. Shorter dosing interval regimens continue to deplete the precursor pool before the system was able to recover. With the repeated dosing, precursor pool continued to decrease and reached steady state level by about 12 months. The precursor pool decreased to about -69.5% in the 540mg

Q1M regimen. Regimens with intervals longer than one month showed more fluctuations and the steady-state precursor pools fluctuated between -51.8% and -39.0% for 540mg Q3M, -40.0% and -19.9% for 540mg Q6M, -34.8% and

-11.6% for 540mg Q9M, -32.1% and -7.00% for 540mg Q12M, and -14.5% and -2.91% for 540mg Q18M.

A B

Abbreviation: CTX=serum type 1 C-terminal procollagen; P1NP=serum type-1 procollagen N-terminal; Q1M= once every month; Q3M= once every two months; Q6M= once every six months. Q9M= once every nine months; Q12M= once every twelve months; Q18M= once every eighteen months; ROB=responding osteoblast; %CFB=percent change from pretreatment baseline.

Figure 25 Prediction of (A) P1NP and (B) ROB following various dose regimens blosozumab treatment administered subcutaneously for 36 months

7.2.3. Long-Term Anti-Sclerostin Treatment The extended bone remodeling model predicted that P1NP response

achieved a steady level following about 12 months of repeated dosing; we

simulated a longer term treatment to investigate when the BMD responses

would attain steady state. Figure 26 shows the lumbar spine and total hip BMD

responses following 30 years of treatment followed by a 20-year observation

period. The model predicted that both lumbar spine and total hip BMD

responses would reach a plateau by about 5 and 15 years of 130mg Q1W

continuous treatment, respectively; treatment thereafter would maintain the

BMD responses at a steady-state. The predicted steady state lumbar spine

BMD responses were 21.9%, 21.8%, 19.0%, 6.95% and 4.22% and the steady

state total hip BMD responses were 13.6%, 13.5%, 11.4%, 3.55% and 2.21%

following 135mg Q1W, 270mg Q2W, 540mg Q1M, 540mg Q3M and 540mg

Q6M, respectively. The model also predicted that when sclerostin inhibition is removed after treatment discontinued, the duration needed for lumbar spine and total hip BMD to return to pretreatment baseline level after 135 mg Q1W discontinued were about 5 and 15 years. The duration to achieve steady state following treatment administration and return to baseline after treatment discontinued was affected by the treatment frequency. The turnover of lumbar spine and total hip BMD were different and unexpected BMD responses were predicted with different doses and dose frequencies (Figure 26).

Lumbar spine BMD had a higher turnover rate and achieved a higher response compared to total hip BMD and where steady state achieved post- treatment and the return to baseline post-treatment discontinuation were faster

(Figure 26). Interestingly, the model also predicted that the less frequent dosing regimens (Q1M, Q3M and Q6M) produced “overshoot” in lumbar spine BMD response in the first 2 years which then decreased to the steady state by the fifth year. After treatment discontinued, the BMD response returned towards pretreatment baseline in about 2 years. For the less frequent dosing regimens

(Q1M, Q3M and Q6M), the BMD response demonstrated a rebound that caused the BMD to dip below and subsequently return to pretreatment baseline (Figure 26 (A)). Total hip BMD, on the other hand, did not predict overshoot or rebound profiles following anti-sclerostin treatment. The different long-term BMD profiles at different skeletal sites, an unexpected model prediction, reflected the reality that different skeletal sites grow and respond to anti-sclerostin therapy differently. Correspondingly, observations of the rare sclerosteosis and van Buchem disease patients revealed that bone thickening, due to loss of sclerostin, is different at different skeletal sites. For

example, the skull of a van Buchem disease patient can weigh nearly four times that of normal skull122 while other skeletal sites have varying degrees of hyperostosis128,131,133.

The model predictions can have an impact on the design of clinical trials. The rate of bone turnover and the time to reach steady state for BMD increase in vertebral and non-vertebral skeleton are different as suggested by the model predictions; and therefore the fracture rates can also have temporal differences. For phase 3 clinical trials where fracture rate reductions are important clinical endpoints, vertebral and non-vertebral fracture rates may need different observation periods where the non-vertebral skeletal fracture might require a longer treatment and observation duration to attain differentiation with active comparator.

It should be noted that long-term observations of BMD responses after anti-sclerostin treatment are lacking, unsurprising since the anti-sclerostin treatment is a new therapy under clinical development, and these predictions will need to be validated when more information becomes available. Also note that the model did not account for the general bone loss associated with age and hormonal change due to menopause. Therefore, the actual BMD response may be lower and the return to pretreatment baseline level could be more rapid. Nonetheless, the model is useful to inform the general trend of BMD responses following long term usage and give an indication when steady state will be achieved, as well as the time required for treatment effect to be washed out after treatments stopped.

A B

Abbreviation: BMD: bone mineral density; Q1W= once every week; Q2W= once every two weeks; Q1M= once every month; Q3M= once every two months; Q6M= once every six months; %CFB=percent change from pretreatment baseline.

Figure 26 Prediction of (A) Lumbar Spine BMD and (B)Total Hip BMD following various dose regimens of blosozumab treatment administered subcutaneously for 30 years followed by 20 years observation

7.2.4. Dose-Response Curve of BMD improvement In vivo measurements of the sclerostin and bone biomarkers suggested

that the bone formation rate decreases with age and that different levels of

sclerostin can have different effects on the phenotypic expressions111. P1NP

levels are higher in younger subjects implying that bone formation processes

are more active in the young and possibly more susceptible to sclerostin

regulation. In addition, the different degrees of bone deformation in

sclerosteosis patients (no measurable sclerostin) and van Buchem disease

patients (a more benign condition of increased bone mass with reduced serum

sclerostin level) imply that the sclerostin effect is not an all-or-none response;

instead the levels can be controlled by varying levels of bone formation

activity. Fine-tuning of the levels of target inhibition, therefore, can potentially

be employed to titrate biomarker and BMD responses. Our model provides

the mathematical framework to measure changes in sclerostin levels and

quantitatively links it to the changes in the bone formation markers and BMD changes. This allows for precise calibration of dose and dosing frequencies which is crucial to optimize the benefits through computational modeling and simulations.

Dose-response relation for lumbar spine and total hip BMD percent change from pre-treatment baseline were mapped out for different blosozumab doses and dosing intervals (Figure 27 and Figure 28). The BMD responses were higher with more frequent dosing and all dose regimens attained steady- state levels by about 4 years of continuous treatment (Figure 27). The simulations suggested that a 2-year treatment instead of 1-year treatment might be a better observation duration for clinical investigation as the BMD responses continued to increase and can provide a better differentiation of the doses and against comparator. Simulations also suggest that the higher doses can be used to compensate for less frequent dosing. However, the doses will have to be increased more than dose-proportionally (i.e., two-fold increase in dosing interval demands a more than two-fold increase in dose amount to achieve the same drug exposure), due to the non-linear pharmacokinetics characteristics. For example, 135mg Q1W regimen attained a lumbar spine

BMD increase of 19.4% after 1 year treatment. To attain the same lumbar spine BMD responses with less frequent dosing, 296mg Q2W, 594mg Q1M,

2250mg Q3M and 4980mg Q6M regimens would be needed (Figure 28 (A)).

Similarly 135mg Q1W regimen attained a total hip BMD increase of 6.28% after 1 year treatment. To attain the same total hip BMD responses with less frequent dosing, 267mg Q2W, 573mg Q1M, 1850mg Q3M and 3700mg Q6M regimens would be needed (Figure 28 (B)).

Generally, the clinical efficacious dose regimens (e.g., 135mg Q1W,

270mg Q2W and 540mg Q1M) were at the steep slope of the curve and there was a potential to achieve higher BMD responses with higher doses (Figure

28). Given the non-linear PK and efficacy relationships, it is not possible to simply project efficacy responses for dose regimens that were not tested before. The model allowed us to explore different doses and to quantify the efficacy responses.

Dose (mg):

Abbreviation: BMD=bone mineral density; Q1M= once every month; Q3M= once every two months; Q6M= once every six months. Q12M= once every twelve months; %CFB=percent change from pretreatment baseline. Figure 27 Temporal responses of (A) lumbar spine and (B) total hip BMD following various dose regimens of blosozumab treatment administered subcutaneously for 10 years

Abbreviation: BMD=bone mineral density; Q1M= once every month; Q3M= once every two months; Q6M= once every six months. Q12M= once every twelve months; %CFB=percent change from pretreatment baseline.

Figure 28 Dose-Response relationship of (A) lumbar spine and (B) total hip BMD at 1 year following various dose regimens of blosozumab treatment administered subcutaneously. Left Panel: normal x-axis. Right Panel: logarithmic x-axis.

7.3. Comparison of Population PK-PD and Bone Remodeling Model George Box famously declared that, “Essentially, all models are wrong, but some are useful." 135. All models are simplifications of the reality and cannot possibly fully represent all the complexities in the underlying biological processes. However, these simple mathematical constructs can be useful and enable us to better understand the essential physiological pathways or answer critical questions that we have on hand. Two approaches, population

PK-PD and systems pharmacology models, were employed to characterize the kinetics of anti-sclerostin therapy, bone turnover markers and BMD responses.

In this section, we will compare the two models and discuss the strength and weaknesses of each model and demonstrate how these two models can be used to optimize dose regimens and investigate the impact of body weight on therapeutic outcomes.

To compare the two models, a wide range of dose and dosing interval regimens were simulated to evaluate the drug exposure and therapeutic outcomes at clinically relevant dose ranges as well as at high dose to probe the limits of the system. Blosozumab of doses 65mg, 95mg, 135mg, 270mg,

540mg, 810mg, 1080mg, 1620 mg, 2160mg and 3240mg administered subcutaneously at intervals of Q1W, Q2W, Q1M, Q3M and Q6M for one year and observed for an additional year were simulated and the predicted drug exposures and clinical outcomes compared. Figure 29 shows the PK profiles predicted using the population PK-PD and systems biology TMDD model respectively. Based on visual inspection of the PK profiles, the exposures generated by either model at all doses and dosing intervals were similar and

therefore using either model to predict drug exposures will likely yield similar results and conclusions.

(A) Population PK Model (B) Target-Mediated Drug Disposition Model

Abbreviation: Q1W= once every week; Q2W= once every two weeks; Q1M= once every month; Q3M= once every two months; Q6M= once every six months Note: (A) Simulations with 1-year treatment of blosozumab were conducted in 1000 virtual patients with the final PK model. The medians and 90% prediction intervals (shaded area) were presented. (B) Simulations with 1-year treatment of blosozumab were conducted with the TMDD model. Visual inspections of the profiles shows that drug exposure prediction using either model were similar.

Figure 29 Predicted blosozumab serum concentration using (A) population PK model and (B) TMDD model at various blosozumab regimens administered subcutaneously for 1 year

Different BMD responses in high doses of blosozumab subcutaneous administration, however, were predicted by the population PK-PD model and the extended-bone remodeling model (Figure 30 and Figure 31). Figure 30 (A) and

Figure 31 (A) showed that the maximum lumbar spine and total hip BMD responses, predicted by the population PK-PD model, reached their maximum of

19.3% (95% CI: 17.1%, 24.3%) and 6.46% (95% CI: 5.31%, 8.44%) increase following 1 year of 3240mg Q1W blosozumab treatment, respectively. The extended bone remodeling model, on the other hand, predicted much higher BMD responses following high doses of the blosozumab treatment (Figure 30 (B) and

Figure 31 (B)). The lumbar spine and total hip BMD, predicted by the extended bone remodeling model, achieved a maximum of 59.9% and 27.4% increase, respectively, following 1 year of 3240mg Q1W blosozumab treatment. The different BMD response predictions reflected the differences in the model assumptions and suggested that the two different models are useful to serve different purposes and answer different questions. Therefore, when making predictions using the different models, it is necessary to consider the models’ assumptions and understand the limitations and boundaries where the models are valid.

(A) Population PK-PD Model (B) Extended Bone Remodeling Model

Abbreviation: BMD=bone mineral density; Q1W= once every week; Q2W= once every two weeks; Q1M= once every month; Q3M= once every two months; Q6M= once every six months; CI=confidence interval. Note: (A) Simulations with 1-year treatment of blosozumab were conducted in 1000 virtual patients with the final PK-PD model. The medians and 90% prediction intervals (shaded area) were presented. (B) Simulations with 1-year treatment of blosozumab were conducted with the extended bone remodeling model. The population PK-PD model (A) predicted maximum median (95% CI) lumbar spine increase was 19.3% (17.1%, 24.3%) while the extended bone remodeling model predicted that the maximum lumbar spine BMD increase was 59.9% following 1 year of 3240mg Q1W blosozumab treatment.

Figure 30 Predicted lumbar spine BMD percent change from baseline using (A) population PK-PD model and (B) extended bone remodeling model at various blosozumab regimens administered subcutaneously for 1 year

(A) Population PK-PD Model (B) Extended Bone Remodeling Model

Abbreviation: BMD=bone mineral density; Q1W= once every week; Q2W= once every two weeks; Q1M= once every month; Q3M= once every two months; Q6M= once every six months; CI=confidence interval. Note: (A) Simulations with 1-year treatment of blosozumab were conducted in 1000 virtual patients with the final PK-PD model. The medians and 90% prediction intervals (shaded area) were presented. (B) Simulations with 1-year treatment of blosozumab were conducted with the extended bone remodeling model. The population PK-PD model (A) predicted maximum median (95% CI) total hip BMD increase was 6.46% (5.31%, 8.44%) while the extended bone remodeling model predicted that the maximum total hip BMD increase was 27.4% following 1 year of 3240mg Q1W blosozumab treatment.

Figure 31 Predicted total hip BMD percent change from baseline using (A) population PK-PD model and (B) extended bone remodeling model at various blosozumab regimens administered subcutaneously for 1 year

7.3.1. Discussions, Strengths and Limitations of Population PK-PD Model The population PK-PD model uses a pseudo-target engagement to link the drug exposure with the BMD responses (Section 3.2.4). The model parameter estimates were informed using the phase 2 blosozumab clinical trials and this limited the maximum response for lumbar spine and total hip

BMD to 20.5% and 9.27% increase from pretreatment baseline (Table 6). The model performed well, stable and reliable, within the boundaries of the drug exposures that were investigated in the phase 2 blosozumab trials (Section

4.5). The model can reasonably be used to predict dose regimens that were not studied before, but within the boundaries of drug exposure equivalent to

270mg Q2W. 270mg Q2W was the dose regimen with the largest drug exposure studied, and this regimen sets the limits for the BMD responses.

Qualifications of the PK-PD models were performed by inspecting the goodness-of-fit between the model predictions and observations, reviewing the residuals against the model predictions, and ensuring the fidelity of the models and observations was conserved through visual predictive checks. These were considered internal validation checks to ascertain the reliability and stability of the models, since the observations used for the checks were also used in the model building. External validation is encouraged but not necessary as per the

FDA guidelines136. Our PK-PD models adequately described the data and quantified the variability. The models were deemed to reliably and stably reproduce clinical trial observations and robust enough to predict for future trials.

Therefore, the population PK-PD model is useful for fine-tuning clinically relevant dose regimens and investigating dose and dosing

frequencies that are within the drug exposures tested clinically. In other words, the model simulation should only be used for interpolation of the dose regimens and trial designs. Extrapolation of the model beyond the drug exposure tested in the 2 blosozumab trial will need further examination and probably should not be used. The population PK-PD model is also useful for quantifying patient factors that affected the drug exposure and clinical outcomes. The nonlinear mixed-effect model utilized all patient-level data and quantified variability caused by patient factors as well as unidentified residual errors. By mathematically quantifying the covariate effects, we can then investigate the impact that these covariate effects have on the system. We determined that body weight has an effect on the clearance and distribution of blosozumab (Sections 4.3) and will demonstrate that the impact of body weight differences on drug exposures and clinical efficacies may not be clinically meaningful in the dose ranges that were suitable for further clinical investigations in later section (Section 7.1.2).

7.3.2. Discussions, Strengths and Limitations of the Extended Bone Remodeling Model The extended bone remodeling model linked drug exposure following anti-sclerostin treatment to unbound sclerostin levels which then affected the osteoblast and osteoclast interactions. The osteoblast and osteoclast numbers, reflected by the P1NP and CTX levels, then altered bone formation and destruction rates and drove the BMD responses (Section 5). The model successfully predicted the P1NP levels and adequately described the change in

CTX levels following anti-sclerostin treatment. The BMD predictions were consistent with the observations after anti-sclerostin treatment and the model

also satisfactorily defined an upper boundary of BMD increase that mimics the disease condition of sclerosteosis and van Buchem disease when there is a complete shutdown of sclerostin regulation (Section 6.4.3). This allows for the model to be used to investigate dose regimens beyond the drug exposures that were tested clinically and with confidence that the sclerostin regulation in the model was within clinically observable limits.

The extended bone remodeling model is useful to test a wide range of dose regimens including dose ranges that predict drug exposures beyond drug regimens that have been investigated clinically. For example, the extended bone remodeling model would be appropriate to investigate dose regimens that have drug exposures larger than 270mg Q2W 1-year blosozumab subcutaneous treatment, as simulations showed that the efficacy responses were not limited by the data used to inform the model parameters (Figure 30 and Figure 31). Also, since the extended bone remodeling model included physiological processes based on in vitro and preclinical knowledge, the model is also useful to probe the systems components and generate hypotheses for the mechanism of action of sclerostin regulation of bone homeostasis.

Figure 32 shows the predicted time profiles of various systems components in the extended bone remodeling model following increasing doses of Q1W subcutaneous blosozumab treatment. Figure 32 (A) shows that increasing the blosozumab dose increased the target neutralization of the unbound sclerostin. Even the smallest dose of 65mg Q1W neutralized the unbound sclerostin by more than 75% (Figure 32 (F)). Increasing the dose, thereafter, continued to improve the target neutralization, albeit marginally.

This suggests the system is sensitive to small changes in the sclerostin level.

At the four intersection points of sclerostin regulation included in the extended bone remodeling model ( 휋푆푅 , 휋푆퐵 , 휋푆퐿 , and 휋푆푂 ), the active osteoblast apoptosis (휋푆퐵 ) is the most affected by sclerostin levels with the greatest separation of the 휋푆퐵 levels with different blosozumab doses (Figure 32 (B-E)).

This implied that small changes in sclerostin level resulted in large responses in the 휋푆퐵 levels and that a large portion of the anti-sclerostin treatment was possibly accomplished by inhibiting the apoptosis of active osteoblasts, thus improving their survival and bone formation activities. As the model is built based on biological processes, when new knowledge grows, the model can be updated and improved.

A B C D E

F G H I J

Abbreviation: AOB=active osteoblast; BMD=bone mineral density CTX=serum type 1 C-

terminal procollagen; P1NP=serum type-1 procollagen N-terminal; 휋푆푅=activator function of sclerostin regulation on ROB maturation; 휋푆퐵=repressor function of sclerostin regulation on AOB apoptosis; 휋푆퐿=repressor function of sclerostin regulation on RANKL: levels; 휋푆푂=activator function of sclerostin regulation on OPG levels; %CFB=percent change from baseline. Notes: (A) shows the increased target neutralization with increasing blosozumab doses. Although the lowest dose of 65mg Q1W achieved more than 75% target neutralization (F), the sclerostin regulations at 휋푆푅, 휋푆퐵, 휋푆퐿, and 휋푆푂 were not at their maximum levels (B-E). Increasing blosozumab dose improved the target neutralization marginally but resulted in greater sclerostin regulations (A-E). Osteoblast numbers (G), reflected by the P1NP %CFB, and osteoclast numbers (H), reflected by the CTX %CFB, continued to increase in their level of responses with increasing doses, even though the level of sclerostin changed marginally. Similarly lumbar spine (I) and total hip (J) BMD continues to increase with increasing doses. Simulation results suggested that the system was very sensitive to the sclerostin levels and small changes in the sclerostin levels can result in large changes in the bone cell interactions. Also, the survival of active osteoblast (휋푆퐵) (C) was most affected by the changes in the sclerostin level and increased sclerostin neutralization with higher blosozumab doses greatly decreased the rate of osteoblast apoptosis.

Figure 32 Predicted (A) sclerostin concentration, (B) 흅푺푹, (C) 흅푺푩, (D) 흅푺푳, (E) 흅푺푶, and (F) sclerostin, (G) P1NP, (H) CTX, (I) lumbar spine and (J) total hip BMD percent change from baseline following Q1W blosozumab regimens of various doses administered subcutaneously for one year followed by one year observation

Nevertheless, there are limitations in using and interpreting the extended bone remodeling model. The extended bone remodeling model is a complex systems biology model with many parameters. As the individual components that formed the full model may not be practically measured in clinical trials, many of these parameter estimates were fixed to arbitrary constants or preclinical experimental values in an attempt to combine the different networks signals and cellular interactions into a coherent bone remodeling mathematical model. Despite the arbitrary assignment and fixing parameter estimates per the original Lemaire et al. model for some of model components, the model demonstrated predictive power by successfully replicated anti-sclerostin therapy trials and sclerostin knock-out disease state.

The predictive capability of a systems biology model is a more important model evaluation criterion compared to identifying specific model subcomponents for complex systems biology models 137.

There are improvements to be made to the model as we gain better understanding of the physiological mechanisms governing bone metabolism.

The bone resorption (CTX) response predictions by the model were more irregular with model predictions fluctuating widely between dosing intervals.

The model fitted and described satisfactorily the CTX responses following blosozumab treatment (Figure 17), but the prediction of the CTX responses following romosozumab were more irregular and less well defined (Figure

19). Nonetheless, prediction lines pass through most of the observations. This implies that the sclerostin effect on bone resorption may not have been fully captured in the model and needs further improvement when more information becomes available. The difference in CTX response between blosozumab and

romosozumab could possibly be due to differences in laboratory processing and assay methods of the samples, different subject populations as well as different time and season of sample collection. CTX levels were known to fluctuate based on daily circadian rhythm, seasonal changes as well as the age and level of physical activities of the patient127,138. This is unsurprising given that CTX is a marker of bone resorption and bone metabolism is affected by these factors. Furthermore, magnitude of CTX changes after anti-sclerostin treatment were smaller than the variability in CTX measurement as evident from the both blosozumab and romosozumab observations (Figure 17 and

Figure 19) and this variability posed a problem to accurately quantify the CTX profiles after antis-sclerostin treatment. Additionally, there are several methods of quantifying CTX levels. In phase 1 romosozumab trials, CTX was assayed using radioimmunoassay (RIA)55, while in the phase 2 romosozumab trials CTX was assayed using a commercial enzyme-linked immunosorbent assay (ELISA) kit139. More differences yet, serum CTX from blosozumab trials were analyzed using a different commercial ELISA kit57 from that of romosozumab trials. These factors could have contributed to the differences in the absolute CTX measurements and in turn account for the differences in the change from pre-treatment baseline values.

The biomarker responses after anti-sclerostin therapies are interesting.

Most other available osteoporosis treatments either increase or decrease both bone formation and bone resorption140. For example, teriparatide increased both P1NP and serum type 1 N-terminal procollagen (NTX). The bone formation marker, however, increased more than the bone resorption marker, resulting in an overall increase in bone mass. Similarly, alendronate decreased

both P1NP and NTX and depressed the overall level of bone remodeling resulting in a halt in bone loss. Anti-sclerostin treatments, however, demonstrated decoupled bone biomarker responses. P1NP levels increased rapidly following treatment and then quickly become attenuated; CTX levels, on the other hand, decreased initially and then rebounded beyond the pretreatment baseline levels; and thereafter fluctuated around the pretreatment baseline levels. The decoupled bone formation and bone resorption marker responses suggest that in addition to the bone remodeling regulation, sclerostin can also affect the bone modeling process.

Sclerostin and consequently, the wnt signaling pathway, are also involved in the bone modeling process. Bone modeling occurs mainly in the early growth period, and less throughout the human lifespan, during which the bone increases in mass and volume. Bone modeling also sculpts the bone into specific three-dimensional form by separating osteoblast and osteoclast actions at different bone surfaces (Figure 33). The turnover marker responses based on blosozumab and romosozumab suggest that anti-sclerostin therapy could possibly affect both the bone modeling and remodeling mechanisms16,141. Our model currently only describes the bone remodeling process and the interaction of the osteoblasts and osteoclasts. The model can be further improved to include the bone modeling pathway when more experimental data becomes available that can distinguish the different processes involved in bone metabolism.

A Bone Modeling B Bone Remodeling

Osteoclast Osteoblast New bone matrix Note: (A) Bone modeling is the process that accrues bone mass and volume and shapes the bone architecture. Bone formation and resorption are decoupled on different bone surfaces. (B) Bone remodeling is the process that maintains the bone mass and repairs the micro-fractures sustained in mechanical exertion. Bone resorption is tightly coupled with subsequent bone formation to maintain bone homeostasis.

Figure 33 Comparison of (A) bone modeling and (B) bone remodeling. Another limitation is that the model assumes that the system maintains steady state when there is no perturbation to the components. This assumption might be appropriate for the duration of a clinical trial when the BMD changes over the period of time are not significant. The rate of bone loss as a subject ages and estrogen levels changes over time will have to be accounted for if the observation period were to be extended. In the population PK-PD model, an empirical linear slope of bone loss was added and the estimated linear loss of lumbar spine and total hip BMD were 0.0121 g/cm2/year and 0.00780 g/cm2/year, respectively (Table 6). This translates to approximately 1-2%

BMD loss a year (Table 6). A next step towards improving the model will be to relate how age and hormonal changes in PMP women affects the bone cell interactions and incorporate it into the bone homeostasis model.

The Metrum group recently reported a similar effort where the action of sclerostin was added to a multi-scale bone physiology model102,142. Our

approach started with a minimal bone remodeling model and incorporated the target-mediated drug disposition of blosozumab and romosozumab with unbound sclerostin. The unbound sclerostin then activates or represses the specific pathways in the bone remodeling model, based on clinical and preclinical understanding of the sclerostin’s actions at those regulatory junctions.

The basic structure of bone cell interactions follows that of Lemaire and colleagues6. This model was used in developing models describing denosumab97,143, bisphosphonates97 and selective estrogen receptor modulator101. Using similar basic model structure has the advantage that these different models can potentially be combined to form a unifying model which can then be used to investigate different drug combinations.

The extended bone remodeling model was built from summary study- level data that were extracted from reported clinical trials. The model therefore lacked the finer resolution of a population PK-PD model, built from patient- level data that can quantify variability and identify important potential covariates that can impact drug exposure and efficacy outcomes. Therefore, the strength of the extended bone remodeling model is to screen for a large range of dose regimens and evaluate the biomarker and efficacy responses. A smaller subset of clinically meaningful dose regimens could then be screened and selected. These dose regimens could be further refined and impact of covariates evaluated using the population PK-PD model.

8. Summary and Conclusion Bone degeneration disease, such as osteoporosis, is an important global healthcare issue144,145. It is estimated that worldwide, one-third of elderly women over 50 years old suffer from osteoporosis36. In these patients with low bone mass, fracture risk increases significantly and these fractures have debilitating consequences on the sufferers which include pain, limited physical mobility and increased dependence on care-giving services. This healthcare issue is expected to grow with an aging population. The standard of care for osteoporosis currently is bisphosphonates which is effective but inconvenient to administer. Alendronate, for example, needs to be taken weekly on an empty stomach while standing or sitting146. Then, for the next half an hour, patients must stay upright and cannot consume food and water. In addition, there are other gastrointestinal side effects that can undermine the quality of life and treatment compliance. There are other antiresorptives available, such as denosumab, hormone replacement and selective estrogen receptor modulators, but concerns that antiresorptive treatments block the overall bone turnover and could lead to build-up of micro-fractures in bone architecture remain unaddressed. There is only one type of bone anabolic treatment available currently, teriparatide, and the use is limited to severe osteoporotic patients and limited to a maximum two years’ treatment. Therefore, there is a need to develop new bone anabolic treatment for better bone mass accretion, with more convenient treatment administration method and better adverse event profile.

Anti-sclerostin therapy is being actively pursued as a treatment for bone degenerative disease. This project aimed to utilize a model-based approach in

the development of the anti-sclerostin therapy to aid in understanding the mechanism of sclerostin action on bone formation activities as well as propose clinically meaningful dose regimens that can improve clinical outcomes.

In the first part, population PK-PD modeling was developed for blosozumab to integrate the vast clinical data collected in three phase 1 trials and one phase 2 trial. Model-based dose selection approach eliminates “best- guessing” untested dose regimens for future trials. Simulations based on the validated PK-PD model were performed to investigate drug exposures and dose response in a panel of different dose regimens. Different dosing frequencies that were not tested in previous trials were investigated. BMD responses in lumbar spine and total hip were simulated and the results suggested that 135mg Q1W, 270mg Q2W and 540mg Q1M frequencies were comparable in terms of their efficacy responses and could be investigated in future clinical trials. Nevertheless, the dose regimens will need to balance efficacy with the ease of administration to improve drug compliance and also to take safety and tolerability into consideration. Poor patient compliance was cited as the main reason for the poor outcome of fracture incidences in current available osteoporosis treatments in real world setting. The incidence of fractures in clinical observations were much higher compared to randomized controlled trials147. A convenient dosing regimen with fewer restrictions on intake instructions can potentially offer greater benefits to patients in the real world. Anti-sclerostin mAbs that are administered as SC injections without other dietary limitations and have a longer dosing interval offers exciting possibilities to fill this gap in current available osteoporosis treatments.

We demonstrated the use of PK-PD modeling by combining knowledge of blosozumab’s properties accrued over the four clinical studies exploring a wide range of doses, including IV and SC injections, and making predictions for potential effective dose regimens for phase 3 clinical investigations. We built a PK model that described the nonlinear kinetics in blosozumab and linked it to the lumbar spine and total hip BMD response. Because of the nonlinear kinetics displayed in the drug, dose proportionality is not guaranteed whereby a doubling of dose results in a doubling of exposure. Using the PK model, we were able to simulate and compare drug exposures in different dose regimens, within the drug exposure that was tested clinically, and make informed decisions about the exposure-response outcomes by maximizing the

BMD response while minimizing the variability. Many late-phase clinical trials fail because of ineffective dosage and regimen. Doses that are too high expose subjects to higher risk of adverse events while doses that are too low might be safe but ineffective. Appropriate dose selection for late-phase trial is crucial so that effective drugs can be thoroughly investigated with greater probability of success.

The second part of this project combined the publicly available information on clinical uses of anti-sclerostin therapies, blosozumab and romosozumab, to extend a systems model of bone remodeling and add sclerostin regulation of bone cell interaction. Bone turnover biomarkers and

BMD were incorporated into the model and the simulations of the biomarkers and BMD emulate the observations in anti-sclerostin mAbs clinical trials. The model predictions of different clinically meaningful dosing regimens were consistent with the population PK-PD model and dosing frequencies of Q1W,

Q2W and QM were predicted to yield similar favorable BMD responses.

Simulation experiments were performed to explore the effects of sclerostin regulation and predict the duration of the bone system to attain steady state, the duration of preosteoblast recovery and the duration of treatment effect washout. Such probing of the system, which is difficult to be performed clinically, but can be done readily in silico using our model, will be useful to map the characteristics of anti-sclerostin therapy and guide future investigations.

Our effort adds to the knowledge of the different mechanisms of bone formation and resorption regulation. Parameterization of the model with the basic bone remodeling model that other research groups worked on will also facilitate the future integration of the different drug models to form a unified model. The unified model can integrate various sources of knowledge and potentially be used to address questions about combination therapies where adding different drug treatment does not equal to a simple arithmetic addition of drug effects. For example, one might consider adding a combination of antiresorptive drug and anabolic drug to boost the BMD increase by targeting the two pathways of bone balance. However, adding bisphosphonate to teriparatide treatment did not result in better clinically significant BMD response148 and in some cases, the combination therapy fared worse than the using teriparatide alone83. Prior bisphosphonate treatment also attenuated the

BMD response in teriparatide treatment149,150. On the other hand, using denosumab and teriparatide together demonstrated better BMD responses than using either drug alone151,152. These suggest that the simpler reasoning of inhibiting bone resorption and stimulating bone formation without considering

the underlying mechanism of action will not be sufficient to help clinicians make decisions for better patient care. A unified bone systems biology model will allow us to investigate combination therapies in virtual population, based on knowledge and complexities of bone cell feedback and signaling loops that may be otherwise difficult to mentally process.

9. References

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10. Appendix

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Appendix A 10.1. Equations for the Extended Bone Remodeling model

The full set of equations and governing the kinetics of anti-sclerostin drug, sclerostin and bone remodeling activities are presented here:

The kinetics of serum sclerostin after anti-sclerostin treatment is represented by equations A1 to A4. The mechanics of bone remodeling involving osteoblasts and osteoclasts interactions and sclerostin regulation added are represented by equations A5 to A7.

Details and model assumptions are discussed in Section 5.

푑(퐴 ) 푠.푐. = −푘푎 ∙ 퐴 + 퐷표푠푒 A1 푑푡 푠.푐. 푠.푐.

푑(퐶푡표푡푎푙) 퐴푠.푐. 퐴푡 푆푐푙푡표푡푎푙 ∙ 퐶 = 퐼푛(푡) + 푘푎 ∙ − (푘 + 푘23) ∙ 퐶푠푒푟푢푚 + 푘32 ∙ − 푘푖푛푡 ∙ ( ) A2 푑푡 푉 푉 퐾퐷 + 퐶 푑(퐴 ) 푡 = 푘 ∙ 퐶 ∙ 푉 − 푘 ∙ 퐴 A3 푑푡 23 32 푡

푑(푆푐푙푡표푡푎푙) 푆푐푙푡표푡푎푙 ∙ 퐶 = 푘푠푦푛 − 푘푑푒푔 ∙ 푆푐푙푡표푡푎푙 − (푘푖푛푡 − 푘푑푒푔) ∙ ( ) A4 푑푡 퐾퐷 + 퐶 푑(푅푂퐵) 퐷퐵 = 퐷푅 ∙ 휋퐶 − 휋푆푅 ∙ ∙ 푅푂퐵 A5 푑푡 휋퐶 푑(퐴푂퐵) 퐷퐵 = 휋푆푅 ∙ ∙ 푅푂퐵 − 푘퐵 ∙ 휋푆퐵 ∙ 퐴푂퐵 A6 푑푡 휋퐶 푑(퐴푂퐶) = 퐷퐶 ∙ 휋 − 퐷퐴 ∙ 휋 ∙ 퐴푂퐶 푑푡 퐿 퐶 A7

푑(퐸푓푓푒푐푡퐿푆) = 푘푒0 ∙ (퐴푂퐵 − 퐸푓푓푒푐푡 ) A8 푑푡 ,퐿푆퐵푀퐷 퐿푆 훾푘푖푛,퐿푆퐵푀퐷 푑(퐿푆퐵푀퐷) 퐸푓푓푒푐푡퐿푆 = 푘푖푛퐿푆퐵푀퐷 ∙ ( ) − 푘표푢푡퐵푀퐷 ∙ 퐿푆퐵푀퐷 A9 푑푡 퐴푂퐵푏 푑(퐸푓푓푒푐푡퐻퐼푃) = 푘푒0 ∙ (퐴푂퐵 − 퐸푓푓푒푐푡 ) A10 푑푡 퐻퐼푃퐵푀퐷 퐻퐼푃 푑(퐻퐼푃퐵푀퐷) 퐸푓푓푒푐푡 훾푘푖푛퐻퐼푃퐵푀퐷 = 푘푖푛퐻퐼푃퐵푀퐷 ∙ ( ) − 푘표푢푡퐿푆퐵푀퐷 ∙ 퐻퐼푃퐵푀퐷 A11 푑푡 퐴푂퐵푏 where 푘푠푦푛 = 푘푑푒푔 ∙ 푆푐푙0 A12

퐷퐴 ∙ 휋푐,푠푠 퐷퐶 = ∙ 퐴푂퐶푠푠 A13 휋퐿,푠푠 ∙ 휋푆퐶,푠푠

푘표푢푡퐿푆퐵푀퐷 = 푘푖푛퐻퐼푃퐵푀퐷 A14

푘표푢푡퐻퐼푃퐵푀퐷 = 푘푖푛퐻퐼푃퐵푀퐷 A15 156

퐴푂퐶 + 푓0 ∙ 퐶푠 휋퐶 = A16 퐴푂퐶 + 퐶푠 푘 퐾푃퐿 ∙ 휋 ∙ 퐴푂퐶 휋 = 3 × 푃 퐿 푘 푘 푘 4 (1 + 1 ∙ 푂푃퐺 + 3 ∙ 푅퐴푁퐾) A17 푘2 푘4 푃푇퐻 휋 = 푃 푃푇퐻 + 푃푠 A18

훽푂푅 휋 = 푆푅 푆푐푙 (1 + ) A19 훿푂푅

훽푂퐵 ∙ 푆푐푙 휋푆퐵 = 1 + A20 (푆푐푙 + 훿푂퐵)

훽푅퐴푁퐾퐿 ∙ 푆푐푙 휋푆퐿 = 1 + A21 (푆푐푙 + 훿푅퐴푁퐾퐿) 훽 휋 = 푂푃퐺 푆푂 푆푐푙 (1 + ) A22 훿푂푃퐺

2 (퐶푡표푡푎푙 − 푆푐푙푡표푡푎푙 − 퐾퐷) + √(퐶푡표푡푎푙 − 푆푐푙푡표푡푎푙 − 퐾퐷) + 4 × 퐾퐷 ∙ 퐶푡표푡푎푙 퐶 = A23 2

푆푐푙 = 푆푐푙푡표푡푎푙 − 퐶푝푙푥 A24

푆푐푙 ∙ 퐶 퐶푝푙푥 = 푡표푡푎푙 A25 퐾퐷 + 퐶 퐾푃퐿 ∙ 휋 ∙ 퐴푂퐵 푅퐴푁퐾퐿 = 휋 × 푃 푆퐿 푘 푘 A26 (1 + 1 ∙ 푂푃퐺 + 3 ∙ 푅퐴푁퐾) 푘2 푘4 퐾푃푂 ∙ 푅푂퐵 푂푃퐺 = 휋푆푂 × A27 (푘푂 ∙ 휋푃)

The initial conditions for the differential equations are summarized in Table 16.

157

Table 16 Initial Conditions for Differential Equations A1 to A7

Symbol Description Value amount of drug in subcutaneous injection 퐴 0 푠.푐. depot compartment total concentration of drug in serum/central 퐶 0 푡표푡푎푙 compartment amount of drug in tissue/peripheral 퐴 0 푡 compartment total concentration of sclerostin in 푆푐푙 0.259 nMa 푡표푡푎푙 serum/central compartment 2 퐷푅 ∙ 휋푐,푠푠 푅푂퐵 responding osteoblast 퐷퐵 ∙ 휋푆푅,푠푠 퐷푅 ∙ 휋푐,푠푠 퐴푂퐵 active osteoblast 푘퐵 ∙ 휋푆퐵,푠푠 퐴푂퐶 active osteoclast 9.127 x 10-4 pMb transit compartment for osteoblast action on 퐷푅 ∙ 휋푐,푠푠 퐸푓푓푒푐푡퐿푆 lumbar spine BMD formation 푘퐵 ∙ 휋푆퐵,푠푠 퐿푆퐵푀퐷 lumbar spine BMD 1 transit compartment for osteoblast action on 퐷푅 ∙ 휋푐,푠푠 퐸푓푓푒푐푡퐻퐼푃 total hip BMD formation 푘퐵 ∙ 휋푆퐵,푠푠 퐻퐼푃퐵푀퐷 total hip BMD 1 a fixed to average baseline value of sclerostin measurement from blosozumab studies b fixed to value per Lemaire et al., 20046

158

Appendix B 10.2. Derivation of the Quasi-Equilibrium Target-Mediated Drug Disposition for Anti-Sclerostin Therapy and Unbound Sclerostin

Target-mediated drug disposition can be described with a system of five differential equations (B1 to B5) based on mass balance of unbound drug in site of administration and serum, unbound drug in tissue, unbound target in serum and drug target-complex in serum153,154.

푑(퐴 ) 퐷표푠푒 푠.푐. = −푘푎 ∙ 퐴 + 푠.푐. B1 푑푡 푠.푐. 퐹 푑(퐴) = 퐼푛(푡) + 푘푎 ∙ 퐴 − (푘 + 푘 ) ∙ 퐶 ∙ 푉 + 푘 ∙ 퐴 − 푘 ∙ 퐶 ∙ 푉 ∙ 푆푐푙 + 푘 푑푡 푠.푐. 23 32 푡 표푛 표푓푓 B2 ∙ 퐶푝푙푥 ∙ 푉 푑(퐴 ) 푡 = 푘 ∙ 퐶 ∙ 푉 − 푘 ∙ 퐴 B3 푑푡 23 32 푡 푑(푆푐푙) = 푘 − 푘 ∙ 푆푐푙 − 푘 ∙ 퐶 ∙ 푆푐푙 + 푘 ∙ 퐶푝푙푥 B4 푑푡 푠푦푛 푑푒푔 표푛 표푓푓 푑(퐶푝푙푥) = 푘 ∙ 퐶 ∙ 푆푐푙 − (푘 + 푘 ) ∙ 퐶푝푙푥 B5 푑푡 표푛 표푓푓 푖푛푡

The binding and unbinding of drug to the unbound sclerostin occurs at a much rapid rate compared to the serum kinetics of the drug and unbound sclerostin such that the binding process could be considered to be in a quasi-

equilibrium state and the binding and unbinding constants (푘표푛 푎푛푑 푘표푓푓) were

replaced by a dissociation constant (퐾퐷 ). The total sclerostin is the sum of unbound sclerostin and the drug-sclerostin complex and therefore 푆푐푙 =

푆푐푙푡표푡푎푙 − 퐶푝푙푥.

퐶 ∙ 푆푐푙 퐾퐷 퐾퐷 = where, 퐶 + 푆푐푙 ↔ 퐶푝푙푥 퐶푝푙푥 퐶 ∙ (푆푐푙푡표푡푎푙 − 퐶푝푙푥) 퐾 = 퐷 퐶푝푙푥

푆푐푙푡표푡푎푙 ∙ 퐶 B6 퐶푝푙푥 = 퐾퐷 + 퐶

159

For subsequent manipulation, equation B2 was first changed from amount of drug to concentration of drug in the serum by dividing both sides of the equation by 푉.

푑(퐶) 퐴푠.푐. 퐴푡 B7 = 퐼푛(푡) + 푘푎 ∙ − (푘 + 푘 ) ∙ 퐶 + 푘 ∙ − 푘 ∙ 퐶 ∙ 푆푐푙 + 푘 ∙ 퐶푝푙푥 푑푡 푉 23 32 푉 표푛 표푓푓

Serum drug and drug complex concentration can be simplified to total drug concentration by adding equations B7 and B5.

푑(퐶 + 퐶푝푙푥) 퐴푠.푐. 퐴푡 = 퐼푛(푡) + 푘푎 ∙ − (푘 + 푘 ) ∙ 퐶 + 푘 ∙ − 푘 ∙ 퐶푝푙푥 푑푡 푉 23 32 푉 푖푛푡 푑(퐶푡표푡푎푙) 퐴푠.푐. 퐴푡 = 퐼푛(푡) + 푘푎 ∙ − (푘 + 푘 ) ∙ 퐶 + 푘 ∙ − 푘 푑푡 푉 23 푠푒푟푢푚 32 푉 푖푛푡 푆푐푙 ∙ 퐶 B8 ∙ ( 푡표푡푎푙 )

퐾퐷 + 퐶

Similarly, serum unbound sclerostin and drug complex concentration can be simplified to total sclerostin concentration by adding equations B4 and

B5.

푑(푆푐푙 + 퐶푝푙푥) = 푘 − 푘 ∙ 푆푐푙 − 푘 ∙ 퐶푝푙푥 푑푡 푠푦푛 푑푒푔 푖푛푡 푑(푆푐푙 ) 푡표푡푎푙 = 푘 − 푘 ∙ (푆푐푙 − 퐶푝푙푥) − 푘 ∙ 퐶푝푙푥 푑푡 푠푦푛 푑푒푔 푡표푡푎푙 푖푛푡 푑(푆푐푙 ) 푡표푡푎푙 = 푘 − 푘 ∙ 푆푐푙 − (푘 − 푘 ) ∙ 퐶푝푙푥 푑푡 푠푦푛 푑푒푔 푡표푡푎푙 푖푛푡 푑푒푔 푑(푆푐푙푡표푡푎푙) 푆푐푙푡표푡푎푙 ∙ 퐶 B9 8 = 푘 − 푘 ∙ 푆푐푙 − (푘 − 푘 ) ∙ ( ) 푑푡 푠푦푛 푑푒푔 푡표푡푎푙 푖푛푡 푑푒푔 퐾 + 퐶 퐷

The serum drug concentration can be solved with the total drug concentration and the total sclerostin concentration in the quadratic equation

B10.

퐶 = 퐶푡표푡푎푙 − 퐶푝푙푥

푆푐푙푡표푡푎푙 ∙ 퐶 퐶 = 퐶푡표푡푎푙 − ( ) 퐾퐷 + 퐶 2 퐶 − (퐶푡표푡푎푙 − 푆푐푙푡표푡푎푙 − 퐾퐷) ∙ 퐶푠푒푟푢푚 − 퐾퐷 ∙ 퐶푡표푡푎푙 2 (퐶푡표푡푎푙 − 푆푐푙푡표푡푎푙 − 퐾퐷) + √(퐶푡표푡푎푙 − 푆푐푙푡표푡푎푙 − 퐾퐷) + 4 × 퐾퐷 ∙ 퐶푡표푡푎푙 퐶 = B10

160

In summary, the quasi-steady state target-mediated drug disposition model is described by equations B1, B8, B3, B9 and B10.

푑(퐴푠.푐.) B1 = −푘푎 ∙ 퐴 + 퐷표푠푒 푑푡 푠.푐. 푠.푐. 푑(퐶 ) 퐴 퐴 B8 푡표푡푎푙 = 퐼푛(푡) + 푘푎 ∙ 푠.푐. − (푘 + 푘 ) ∙ 퐶 + 푘 ∙ 푡 − 푘 푑푡 푉 23 푠푒푟푢푚 32 푉 푖푛푡 푆푐푙 ∙ 퐶 ∙ ( 푡표푡푎푙 ) 퐾퐷 + 퐶 푑(퐴푡) B3 = 푘 ∙ 퐶 ∙ 푉 − 푘 ∙ 퐴 푑푡 23 32 푡 푑(푆푐푙푡표푡푎푙) 푆푐푙푡표푡푎푙 ∙ 퐶 B9 = 푘푠푦푛 − 푘푑푒푔 ∙ 푆푐푙푡표푡푎푙 − (푘푖푛푡 − 푘푑푒푔) ∙ ( ) 푑푡 퐾퐷 + 퐶 (퐶 − 푆푐푙 − 퐾 ) + √(퐶 − 푆푐푙 − 퐾 )2 + 4 × 퐾 ∙ 퐶 B10 퐶 = 푡표푡푎푙 푡표푡푎푙 퐷 푡표푡푎푙 푡표푡푎푙 퐷 퐷 푡표푡푎푙 2

161

Appendix C

10.3. Derivation of RANK-RANK-OPG regulation (흅푳) in Bone Remodeling Model as Described by Lemaire et al, 2004.

For the complete discussion, assumptions and derivation of the

RANKL-RANK-OPG regulation (휋퐿), reader is referred to the original bone remodeling model publication by Lemaire and colleagues (2004)6.

A simplified discussion on the important aspects of the RANKL-

RANK-OPG regulation is reproduced here to improve the understanding of the bone remodeling model.

The kinetics of RANKL (L), OPG (O), RANK (K), OPG-RANKL complex (OL) and RANK-RANKL (KL) complex are described in equations

C1 to C4 based on the binding reactions as follows:

and

Note that the concentration of RANK was fixed, based on the assumption that the osteoclast precursors (where RANK is expressed as a surface receptor) are in constant supply and not limited.

푑(푂) = 푝푂 − 푘 ∙ 푂 ∙ 퐿 + 푘 ∙ 푂퐿 − 푑 C1 푑푡 1 2 푂 푑(퐿) = 푝퐿 − 푘 ∙ 푂 ∙ 퐿 + 푘 ∙ 푂퐿 − 푘 ∙ 퐾 ∙ 퐿 + 푘 ∙ 퐾퐿 − 푑 C2 푑푡 1 2 3 4 푂 푑(푂퐿) = 푘 ∙ 푂 ∙ 퐿 + 푘 ∙ 푂퐿 C3 푑푡 1 2 푑(퐾퐿) = 푘 ∙ 퐾 ∙ 퐿 − 푘 ∙ 퐾퐿 C4 푑푡 3 4

162

The production of OPG was assumed to be a first order reaction and depended on the concentration of ROB and the intrinsic rate of OPG production (퐾푃푂 ) by 퐾푃푂 × 푅푂퐵. Additionally, PTH inhibits the OPG production and this was implemented by an inverse relationship with PTH

1 occupancy (휋푃) by 푝푂 ≈ (Equation C5). 휋푃

퐾푃푂 푝푂 = ∙ 푅푂퐵 C5 휋푃

The production of RANKL was more complex as it is an osteoblast surface molecule and therefore RANKL concentration was limited by the number and surface carrying capacity of osteoblasts. The process involving

RANKL production is described in equation C6. To restrict the RANKL

production, RANKL turnover (푝퐿 − 푑퐿) was limited such that production rate of RANKL (푝퐿) was proportional to and not exceed the ratio of total RANKL concentration (퐿 + 푂퐿 + 퐾퐿) and the maximum surface carrying capacity of

퐿+푂퐿+퐾퐿 osteoblasts (퐾푃퐿 ∙ 퐴푂퐵) by . 퐾푃퐿 represents the maximum number of 퐾푃퐿×퐴푂퐵

RANKL molecule per osteoblast. Additionally, PTH up-regulates RANKL production and this was implemented by 퐾푃퐿 × 휋푃 × 퐴푂퐵, where increasing

PTH increased the value of the denominator and therefore decreased the value

퐿+푂퐿+퐾퐿 퐿+푂퐿+퐾퐿 of but increased the RANKL production 푝퐿 ∙ (1 − ). 퐾푃퐿∙휋푃∙퐴푂퐵 퐾푃퐿∙휋푃∙퐴푂퐵

퐿 + 푂퐿 + 퐾퐿 푝퐿 − 푑퐿 = 푝퐿 ∙ (1 − ) C6 퐾푃퐿 ∙ 휋푃 ∙ 퐴푂퐵

Note that the level of PTH was kept constant in our analysis and 휋푃 did not affect the overall OPG or RANKL levels with respect to anti-sclerostin treatment.

163

By evaluating equations C1 to C6 at steady state, the steady state concentration of RANKL and OPG can be derived as per equation C7 and C8.

퐾푃퐿 ∙ 휋 ∙ 퐴푂퐵 퐿 = 푃 푘 푘 C7 (1 + 1 ∙ 푂 + 3 ∙ 퐾) 푘2 푘4 퐾푃푂 ∙ 푅푂퐵 푂 = C8 (푘푂 ∙ 휋푃)

The RANK-RANKL-OPG axis of osteoblast-osteoclast interaction

(휋퐿) (Equation C9), based on receptor occupancy of RANK-RANKL, was evaluated at steady state since it was assumed that the binding reaction was much faster than the other model components.

퐾퐿 휋 = 퐿 퐾 푘 ∙ 퐾 ∙ 퐿 C9 = 3 푘4 ∙ 퐾 푘 퐾푃퐿 ∙ 휋 ∙ 퐴푂퐵 = 3 × 푃 푘 푘 푘4 (1 + 1 ∙ 푂 + 3 ∙ 퐾) 푘2 푘4

164

Appendix D 10.4. Berkeley Madonna Code for the Extended Bone Remodeling Model.

METHOD RK4

STARTTIME = 0 STOPTIME= 2*365*24 + 782 ; Enter the time of last observation in hours (e.g., 1 year = 8736 hours) DT = 0.1;0.02 DTOUT = 0.1

;----- Define the Blosozumab regimens -----; Dose = 270 ; Enter dose in mg (e.g., 270mg) Dose_Interval = 336 ; Enter dosing interval in hours (e.g., 2 weeks = 336 hours) Dose_End = 8736 ; Enter the time of last dose in hours (e.g., 1 year = 8736 hours) Dose_Route = 1 ; Enter the administration route (i.e., 1 = subcutaneous, 2 = intravenous)

; Set up dose according to the dosing options DD1 = Dose*1E6/150 * (pulse(1,0,Dose_Interval) - pulse(1,Dose_End+Dose_Interval,Dose_Interval)) DSC1 = IF Dose_Route = 1 THEN DD1*FM ELSE 0 DIV1 = IF Dose_Route = 2 THEN DD1 ELSE 0

;----- initial estimates -----; R0 = (DR*Pic0^2)/(DB*PiSr0) ;pM - baseline ROB (Responding Osteoblast) B0 = (DR*Pic0)/(kB*PiSb0) ;pM - baseline AOB (Active Osteoblast) C0 = 9.127e-4 ;pM - baseline AOC (Active Osteoclast) PTH0 = 3.6*14 ;pmol - baseline PTH amount PTHConc0 = 3.6 ;pM - baseline PTH concentration RANK0 =10 ;pmol - baseline RANK LSBMD0 = 1 ;nil - baseline Lumbar Spine BMD HPBMD0 = 1 ;nil - baselineTotal Hip BMD

;------Parameter estimates ------;

; cellular interaction Cs = 0.005 ;pM - value of C to get half differentiation flux DA = 0.0533046 ;1/h - rate of osteoclast apoptosis caused by TGF-b dsB =0.01*0.7/24 ;1/h - differentiation of responding osteoblast DC = DA*Pic0*C0/(PiL0) ;pM/h - differentiation rate of osteoclast precursor DR = 2.91667E-6 ;pM/h - differentiation rate of osteoblast progenitors f0 = 0.05 ;nil - fixed proportion IL = 0 ;pM/h - rate of administration of RANKL IO = 0 ;pM/h - rate of administration of OPG Ip = 0 ;pM/h - rate of administration of PTH RANK = 10 ;pM - fixed concentration of RANK k1 = 0.01/24 ;1/pM/h - rate of OPG-RANKL binding k2 = 10/24 ;1/h - rate of OPG-RANKL unbinding k3 = 0.00058/24 ;1/pM/h - rate of RANK-RANKL binding k4 = 0.017/24 ;1/h - rate of RANK-RANKL unbinding k5 = 0.02/24 ;1/pM/h - rate of PTH binding with its receptor k6 = 3/24 ;1/h - rate of PTH unbinding kB =7.875e-4 ;1/h - rate of elimination of active osteoblast

165

KPL = 3E6 ;pmol/pmol cell - maximum number of RANKL attached on each cell surface kO = 0.35/24 ;1/h - rate of elimination of OPG KPO = 2E5/24 ;pmol/day/pmol cell - minimal rate of production of OPG per cell kp = 86/24 ;1/h - rate of elimination of PTH rL = 1000/24 ;pM/h - rate of RANKL production and elimination Sp = kp*PTH0 ;pM/h - rate of synthesis of systemic PTH f0s = 0.431421 ;nil - proportionaility constant

; blosozumab-sclerostin V1 = 2520 ;ml - blosozumab Central Volume of Distribution CL = 8.82 ;ml/h - blosozumab Clearance V2 = 1440 ;ml - blosozumab peripheral Volume of Distribution KA = 0.00697 ;1/h - blosozumab rate of absorption Q = 16.8 ;ml/h - blosozumab intercompartmental clearance FM = 0.691 ;fraction - blosozumab absolute bioavailability KSYN =KDEG*Scl0 ;pmol/h - rate of sclerostin production KDEG =1.5313 ;1/h - rate of sclerostin elimination KINT = 0.0272139 ;pmol/h - rate of drug-sclerostin complex elimination

KSS =0.36164 ;pmol/h - rate of drug-sclerostin complex elimination Scl0 = 0.2594 ;nM - baseline unbound sclerostin level

; sclerostin effect on bone remodeling EmaxPiSr =10.9085 ;nil - maximum effect of sclerostin on osteoblast maturation Sc50r = 0.198425 ;pmol/ml - potency of sclerostin on osteoblast maturation EmaxPiSb = 5.13131 ;nil - maximum effect of sclerostin on osteoblast apoptosis Sc50b = 0.0153283 ;pmol/ml - potency of sclerostin on osteoblast apoptosis EmaxPiSL = 1.77016 ;nil - maximum effect of sclerostin RANKL level Sc50L =0.0691952 ;pmol/ml- potency of sclerostin on RANKL level EmaxPiSO =1.80461 ;nil - maximum effect of sclerostin OPG level Sc50O = 0.0179259 ;pmol/ml- potency of sclerostin on OPG level

; BMD kinLSBMD = 0.0769255 ;1/h - lumbar spine BMD production rate kinHPBMD = 0.0714122 ;1/h - total hip BMD production rate KDELAY1= 7.18514e-5 ;1/h - transduction rate of AOB effect on lumbar spine BMD KDELAY2= 2.82831e-5 ;1/h - transduction rate of AOB effect on total hip BMD kinLSBMDgam = 0.495861 ;1/h - exponent of AOB effect on lumbar spine BMD koutLSBMDgam = 0.191044 ;1/h - exponent of AOC effect on lumbar spine BMD kinHPBMDgam = 0.451389 ;1/h - exponent of AOB effect on total hip BMD koutHPBMDgam = 0.0266692 ;1/h - exponent of AOC effect on total hip BMD

DB= f0*dsB PicS1= (CS1+f0*Cs)/(CS1+Cs) PiLS1=(k3/k4) *PiSLS1 * (1+IL/rL) * (KPL*PiP*BS1) / (1 +(k1/k2)*OS1 + (k3/k4)*RANK)

LS1 = (KPL*PiP*BS1) / (1 + (k3*RANK/k4) + (k1*OS1/k2))*PiSLS1 OS1 = (KPO*RS1/(kO*PiP))*PiSOS1 166

K20 = CL/V1 K23 = Q/V1 K32 = Q/V2

PiSrS1 = EmaxPiSr/(1+(SCLS1/Sc50r)) PiSbS1 = 1+EmaxPiSb*SCLS1/(SCLS1+Sc50b) PiSLS1 = 1+EmaxPiSL*SCLS1/(SCLS1+Sc50L) PiSOS1 = EmaxPiSO/(1+(SCLS1/Sc50O))

koutLSBMD = kinLSBMD/LSBMD0/168 koutHPBMD = kinHPBMD/HPBMD0/168

BeffLSBMDS1 = (TR1S1/B0)^kinLSBMDgam CeffLSBMDS1 = (CS1/C0)^koutLSBMDgam BeffHPBMDS1 = (TR2S1/B0)^kinHPBMDgam CeffHPBMDS1 = (CS1/C0)^koutHPBMDgam

;----- steady state computation -----; PiC0 = (C0+f0*Cs)/(C0+Cs) PiL0 =(k3/k4) * PiSL0 * (KPL*PiP0*B0) / (1 +(k1/k2)*OPG0 + (k3/k4)*RANK0) PiP0 = (Pd + P0)/(Pd + Ps) RANKL0 = (KPL*PiP0*B0) / (1 + (k3*RANK0/k4) + (k1*OPG0/k2))*PiSL0 OPG0 = (KPO*R0/(kO*PiP0)) * PiSO0

PiSr0 = EmaxPiSr/(1+(Scl0/Sc50r)) PiSb0 = 1+EmaxPiSb*Scl0/(Scl0+Sc50b) PiSL0 = 1+EmaxPiSL*Scl0/(Scl0+Sc50L) PiSO0 = EmaxPiSO/(1+(Scl0/Sc50O))

;----- derived parameters computation -----;

PiP = (Pd + P0)/(Pd + Ps) Pd = Ip/kp P0 = Sp/kp Ps = k6/k5

;----- differential equations -----; d/dt(PTH) = Sp - kp*PTH INIT PTH = PTH0 d/dt(X1S1) =-KA*X1S1 + DSC1 INIT X1S1 = 0 d/dt(X2S1) = KA*X1S1-(K20+K23)*CPS1*V1+K32*X3S1- KINT*X4S1*CPS1*V1/(KSS+CPS1) + DIV1 INIT X2S1 = 0 d/dt(X3S1) = K23 *CPS1*V1-K32*X3S1 INIT X3S1 = 0 d/dt(X4S1) = (KSYN) - KDEG*X4S1 + (KDEG-KINT)*X4S1*CPS1/(KSS+CPS1) INIT X4S1 = Scl0 d/dt(RS1) = DR*PicS1 - DB*RS1*PiSrS1/(PicS1) INIT RS1 = R0 d/dt(BS1) = DB*RS1*PiSrS1/(PicS1) - kB*PiSbS1*BS1 INIT BS1 = B0 d/dt(CS1) = DC*PiLS1 - DA*PicS1*CS1 INIT CS1 = C0 d/dt(TR1S1) = KDELAY1*(BS1 - TR1S1) INIT TR1S1 = B0 167

d/dt(LSBMDS1) = (kinLSBMD/168)*BeffLSBMDS1 - koutLSBMD*CeffLSBMDS1* LSBMDS1 INIT LSBMDS1 = LSBMD0 d/dt(TR2S1) = KDELAY2*(BS1 - TR2S1) INIT TR2S1 = B0 d/dt(HPBMDS1) = (kinHPBMD/168)*BeffHPBMDS1 - koutHPBMD*CeffHPBMDS1* HPBMDS1 INIT HPBMDS1 = HPBMD0

;----- for plotting purposes -----;

PTHConc = PTH/14 DAY = TIME/24 WEEK = TIME/168 MONTH = TIME/((13/3)*168)

TCPS1 = X2S1/V1 ; Total drug concentration CPS1 = (0.5*(X2S1/V1-X4S1-KSS)+0.5*SQRT((X2S1/V1-X4S1- KSS)^2+4*KSS*X2S1/V1)) ; Unbound drug concentration TSCLS1 = X4S1 ; Total sclerostin concentration SCLS1 = TSCLS1 - CPLXS1 ; Unbound sclerostin concentration CPLXS1 = TSCLS1*CPS1/(KSS+CPS1) ; Drug-sclerostin complex concentration P1NPS1_PCFB = (BS1/B0-1)*100 ; Percent change in P1NP CTXS1_PCFB = (CS1/C0-1)*100 ; percent change in CTX TSCLS1_PCFB = (TSCLS1/Scl0-1)*100 ; percent change in total sclerostin SCLS1_PCFB = (SCLS1/Scl0-1)*100 ; percent change in unbound sclerostin LSBMDS1_PCFB = (LSBMDS1/LSBMD0-1)*100 ; percent change in lumbar spine BMD HPBMDS1_PCFB = (HPBMDS1/HPBMD0-1)*100 ; percent change in total hip BMD

168