Whole-Body Physiologically-Based Pharmacokinetic Modeling of GalNAc conjugated siRNAs

doi:10.21203/rs.3.rs-4691195/v1

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Whole-Body Physiologically-Based Pharmacokinetic Modeling of GalNAc conjugated siRNAs

https://doi.org/10.21203/rs.3.rs-4691195/v1

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Introduction
N-Acetyl-galactosamine small interfering RNAs (GalNAc-siRNA) is an emerging class of drugs due to their durable knockdown of disease related proteins. Conjugation onto GalNAc allows for target specific uptake into hepatocytes via the Asia Glycoprotein Receptor (ASGPR). With a transient plasma exposure combined with a rapid liver uptake and prolonged half-life in the liver, GalNAc-siRNA exhibits distinct disposition characteristics. Therefore, we aimed to develop a generic GalNAc-siRNAs Whole-Body Physiological-Based Pharmacokinetic-Pharmacodynamic (WB-PBPK-PD) model for the means of describing the pharmacokinetic-pharmacodynamic (PK-PD) relationship and overall tissue distribution.
Methods
For model development a reference data set was compiled from published studies on GalNAc-siRNAs with different stabilization chemistry and different target proteins in mice. The WB-PBPK model structure leveraged the PK-Sim default implementation for large molecules, e.g., including the two-pore-formalism, included in the open-source platform Open System Pharmacology Suite. Specification of intracellular dynamics and efficacy was further implemented to describe mRNA and downstream protein expression of target protein.
Results
Overall, the generic implementation described the observed data within a 2-fold difference across all studies adopting a mix of global and compound specific parameters. The analysis identified significant compound variabilities, e.g., endosomal stability, with direct consequences for the pharmacological effect. Additionally, the model identified knowledge gaps in mechanistic understanding related to extravasation and overall tissue distribution.
Conclusion
The presented study provides a generic WB-PBPK-PD model for the investigation of GalNAc-siRNAs implemented in an open-source platform.

siRNA

Physiologically based pharmacokinetic modeling

PK-Sim

ASGPR

RISC

RNAi is a natural regulatory defense mechanism for invasion of exogenous genes but has also become a mechanism of drug action with several marketed products [1]. An example of such drug modality is the double stranded small interfering RNA (siRNA) that regulates expression of target genes. siRNAs consist of a sense strand and an antisense strand. To exert target gene regulation siRNA form RNA Induced Silencing Complex (RISC) by loading the sense strand into a member of the Argonaute protein family; Argonaute 2 (Ago2), in the cell cytosol [1]. From a series of events the RISC cleaves the warranted mRNA sequence giving diminished protein translation and target gene expression. The target specificity of siRNAs make them well suited drug candidates for a variety of diseases, even what earlier has been considered as untreatable diseases[2] .

However, siRNAs are large (< 16 kDa) and negatively charged biological molecules that are efficiently eliminated via endogenous nucleases. As a result, they suffer from poor drugability properties like short circulation time in plasma and limited potential for passive cell membrane translocation. Several strategies have successfully been developed to address these aspects. Enhanced stabilization chemistry (ESC) and Advanced ESC (ADV ESC) strategies, via addition of phosphorothioate linkages amongst other, are used to reduce vulnerability for cleavage by nucleases so to increase the overall stability and prolong the duration of effect [3].

A successful strategy for increased liver tissue uptake is to target the Asia Glycoprotein Receptor (ASGPR) which is expressed abundantly by hepatocytes. ASGPR substrate specificity is achieved adding multivalent tris N-acetylgalactosamine (GalNAc)₃ by direct conjugation to the siRNA (GalNAc-siRNA). After endosomal uptake of the GalNAc-siRNA-ASGPR complex, spontaneous GalNAc-siRNA cleavage occurs, and a fraction of the free siRNA escapes endosomal degradation to be released intracellularly. Target gene downregulation can be maintained up to several months although the plasma half-life is very short (< 1h). Givosiran, GIIVALRII®, for the treatment of acute hepatic porphyria (AHP) was the first GalNAc conjugated siRNA to reach market approval in 2019 [4]. Since Givosiran in 2019, three GalNAc conjugated siRNAs have been marketed, Lumasiran, Inclisiran, and Vutrisiran [5] and several products are currently in late-stage development[6].

Although insights and understanding of the mechanisms of therapeutic GalNAc-siRNA have increased, many aspects remain to understand the pharmacokinetic-pharmacodynamics (PK-PD) relationship, complex cellular actions, and systemic disposition. To address these questions, multiscale modeling approaches, e.g., physiological based pharmacokinetic (PBPK) models, can be applied to help identify and quantify specific processes and determinants involved. Especially since plasma concentrations are a poor surrogate for GalNAc-siRNAs concentrations in the biophase at the target and are not readily applicable for establishment of traditional PK-PD and dose-response relationships. In 2018, Ayyar et al. published a minimal PBPK (mPBPK) model that aimed to characterize the disposition of GalNAc-siRNAs in several species [7]. The liver was described by higher details than other organs including a mechanistic implementation of the ASGPR mediated uptake process. However, empirical implementations of extravasation, unspecific tissue partitioning and distribution to other organs were adopted to capture the observed rapid plasma disappearance and dynamics in liver tissue accumulation. A higher level of physiological and mechanistic relevant representations of these processes would increase confidence in pre-clinical to clinical translations in the development of new siRNA modalities. The two-pore formalism anticipates that continued and fenestrated endothelium contain small (rs = 4.4 nm) and large pores (rs = 22.85 nm) through which molecules extravasate. Therapeutic GalNAc-siRNAs are highly charged duplexes of 21–23 nucleotides, approximately 7.5 nm in length [8–11] and approximately 1 nm in radii [11] and could consequently be subject to small pore extravasation resistance. The two-pore formalism for extravasation of large molecules has previously been implemented in the open source whole-body PBPK (WB-PBPK) model PK-Sim which has been evaluated for several species [12].

The aim of this study is to develop a generic WB-PBPK-PD model for GalNAc-siRNAs, including the two-pore formalism for extravasation, liver disposition via ASGPR and endosomal trafficking as well as mRNA silencing and downstream target protein effects, by leveraging established models. No WB-PBPK-PD model has previously been reported to our knowledge.

Materials

For model development and qualification, a data set from the literature was compiled and digitized via computer digitization (WebPlotDigitizer, version 4.6). The data was extracted as mean values, so the estimated model parameters should be regarded as approximate and suitable for their intended purpose. For characterization on distribution, uptake and elimination, data on GalNAc-siRNAs targeting anti thrombin (ALN-AT3 (Fitusiran)[7, 13] and SIAT-2 [14]), transthyretin protein (SITTR-1/SITTR-2) [14], factor IX (siF9-1 and siF9-2)[3] and factor VII (siF7-1, siF7-2 and siF7-3) were used. Besides different target specificity, the GalNAc-siRNAs possessed two different stabilization designs, ESC and advanced ESC, allowing determination of compound specific PBPK-PD parameters. The data further comprised liver mRNA levels for each compound included as well as time course data of the downstream effect on target protein for ALN-AT3 and SITTR1. A liver tissue density of 1 mg/ml was assumed for converting the concentrations of Ago2 loaded sense strand and liver mRNA from weight-based to volume-based measurements An overview of compounds and data included in this study together with relevant information is summarized in Table 1.

Table 1

Summary of the published data on the GalNAc-siRNAs and their measurements included in the model development of the presented WB-PBPK-PD model.
Compound	Target	Design	Administration/Dose	Measurement	Reference
ALN-AT3 (Fitusiran Phase III)	Anti Thrombin	ESC^a	SC^b 1–5 mg/kg	Plasma, Liver, Liver mRNA, Serum Anti Thrombin	Sehgal et al., 2015; Nair et al. 2017
SIAT-2 (Investigational)	Anti Thrombin	Assumed ESC^a	SC^b 2.5–25 mg/kg	Plasma, Liver, Liver mRNA, RISC^d	Nair et al. 2017
siF7-1 (Investigational)	Coagulation Factor VII	ESC^a	SC^b 2.5 mg/kg	Liver, Liver mRNA, RISC^d	Brown et al. 2020
siF7-2/siF7-3 (Investigational)	Coagulation Factor VII	Advanced ESC^a	SC^b 0.75, 1 mg/kg	Liver, Liver mRNA, RISC^d	Brown et al. 2020
siF9-1 (Investigational)	Coagulation Factor IX	ESC^a	SC^b 2.5 mg/kg	Liver, Liver mRNA, RISC^d	Brown et al. 2020
siF9-2 (Investigational)	Coagulation Factor IX	Advanced ESC^a	SC^b 0.75 mg/kg	Liver, Liver mRNA, RISC^d	Brown et al. 2020
SITTR-1/SITTR-2 (Investigational)	Transthyretin Protein	ESC^a	SC^b 0.5, 1.5 mg/kg SC^b, IV^c 10 mg/kg	Plasma, Liver, liver, mRNA (SC), Serum Transthyretin Protein,	Nair et al. 2017 ; Brown et al. 2020
a: Enhanced Stabilization Chemistry; b: Subcutaneous; c: Intra Venous; d: RNA Indiced Silencing Complex

Model Development and Software

The presented WB-PBPK-PD model was developed and validated as an extension to the generic model for proteins and large molecules implemented in the open source platform Open Systems Pharmacology Suite, PK-Sim®/MoBi®, Version 11.2 (https://www.open‐systems‐pharmacology.org/)[12]. The implementation involves the two-pore-formalism for extravasation and elimination from vascular endothelial endosomes. In brief, this WB-PBPK model includes individually represented 15 individually represented tissue compartments connected by blood flows. Each tissue compartment is further subdivided into compartments representing the vascular space, interstitial space, endothelial endosomes, and the intracellular space. Lymphatic drainage from the interstitial space as well as endosomal uptake was included as per the default implementation while passive intracellular uptake was set to zero. Renal elimination was included as passive glomerular filtration parameterized according to the default implementation and the physiological database. Model parameter optimization was accomplished using the Levenberg-Marquardt or the Monte Carlo algorithm included in software.

Extravasation model

The exchange of GalNAc-siRNA between the plasma and the interstitial compartment in each organ represented in the model was described as an organ specific flux rate, $\:{J}_{vi},org$ (amount per time) according to the two-pore formalism theory (Eq. 1) [12].

$\:{J}_{vi},org=fu\:·\left(\begin{array}{c}{J}_{L,\:\:org}·\left(1-{\sigma\:}_{Lorg}\right)·{C}_{vorg}+P{S}_{Lorg}·\left({C}_{vorg}-\frac{{C}_{iorg}}{{K}_{ivorg}}\right)·\frac{{{P}_{e}}_{Lorg}}{{e}^{{{P}_{e}}_{Lorg}}-1}+\:\:\\\:{J}_{S,\:\:org}·\left(1-{\sigma\:}_{Sorg}\right)·{C}_{vorg}+P{S}_{Sorg}·\left({C}_{vorg}-\frac{{C}_{iorg}}{{K}_{ivorg}}\right)·\frac{{{P}_{e}}_{Sorg}}{{e}^{{{P}_{e}}_{Sorg}}-1}\end{array}\right)$

Eq. 1

In brief, J_vi depends on the plasma and interstitial concentration (C_v and C_i), the transcapillary fluid flow rate (J), the fraction of unbound drug in plasma (fu), partition coefficient between interstitial space and plasma (K_iv), the reflection coefficients (σ), Peclet number (P_e) and product of permeability and surface area (PS) for the large (L) and small (S) pores for in each organ (org). The pore permeability is calculated from the free diffusion coefficient of the solute, the ratios of the effective pore areas available for restricted diffusion through circular holes, the total cross sectional pore areas, the effective thickness of the endothelial membrane and the capillary surface area. Further details on the implementation of large molecule disposition in PK-Sim® see Niederalt et al. 2018 [12].

ASGPR Mediated Uptake by TMDD Model

Specification of siRNA and ASGPR/RISC dynamics, e.g., binding, internalization, recycling, as well as downstream translation was further implemented in MoBi by a target mediated drug disposition (TMDD) model approach. The TMDD model was originally developed by Kzryzanski et al including a receptor turnover on the cell surface, complex binding/dissociation, and internalization of the bound complex [15]. The model was further modified by Ayyar et al. 2018 by partitioning GalNAc dissociation from the receptor in the endosome, recycling of the free receptor from the endosome to cell surface, endosomal receptor degradation and escape of siRNA loading into Ago2 and form RISC [7]. In the current model Equations 2–4 were used to calculate the kinetics in free total receptor concentration in the interstitial compartment (A_free) accounting for the recycle of the receptor to the cell surface membrane (Eq. 2), the concentration of the free GalNAc-siRNA in the interstitial compartment (D_free) (Eq. 3) and the endosomal concentration of the ASGPR-GalNAc-siRNA complex (DA) (Eq. 4),

$\:\frac{d{A}_{free}}{dt}={k}_{syn}-{k}_{deg}\:·{A}_{free}-{k}_{on}\:·{D}_{free}\:\times\:R+{k}_{off}\:·DR+{k}_{recycle}·{A}_{endosme}$	Eq. 2
$\:\frac{d{D}_{free}}{dt}=\:-{k}_{on}\:·{D}_{free}\:·{R}_{free}+{k}_{off}\:·DA$	Eq. 3
$\:\frac{dDA}{dt}=\:{k}_{on}\:·{D}_{free}\:·{A}_{free}-{k}_{off}\:·DA-{k}_{int}·DA$	Eq. 4

where k_syn is the zero-order synthesis rate constant of the ASGPR, k_deg is the first-order elimination rate constant of ASGPR, k_on is the first-order binding rate constant, k_off is the first-order dissociation rate constant of the GalNAc-siRNA, k_int is the first-order internalization rate constant (elimination of the drug-receptor complex) and k_recycle is the first order recycle rate constant of the free receptor concentration in the endosome (A_endosome) that recycles back to the cell membrane. ASGPR mediated uptake parameters were based on values reported from Ayyar et al. 2018 and were fixed prior to simulation or estimated during simulation as depicted in Table 2. For full TMDD model description see supplementary 1 and for full model see attached model file WB-PBPK-PD_ALN-AT3_1mg_kg_Case_Example.

Table 2

Summary of the ASGPR TMDD model parameters and global WB-PBPK-PD parameter values and their references
ASGPR TMDD Parameters
Parameter (Unit)	Description	Value	Reference
R_tot (µmol/l)	Total ASGPR density	11.7	Estimated
k_on (l/nmol/h)	Association rate constant between GalNAc-siRNA and ASGPR	0.09	Estimated
k_off (1/h)	Dissociation rate constant between GalNAc-siRNA and ASGPR	11.0	Esimated
k_degA (1/h)	Degradation rate constant of ASGPR in cytoplasm	1.53	Schwartz et al., 1982 [17]
k_deg (1/h)	Degradation rate constant of ASGPR on hepatocyte	2.08	Estimated
k_syn (1/h)	Synthesis rate constant of ASGPR	24.3	k_syn =R_tot · k_deg
k_int (1/h)	Internalization rate constant of GalNAc-siRNA-ASGPR complex	4.30	Estimated
k_cle (1/h)	Cleavage rate constant of GalNAc-siRNA in endosome	1.32	Prakash et al., 2014 [18]
k_rec (1/h)	Recycling rate constant of ASGPR	13.8	Schwartz et al., 1982 [17]
k_degC (1/h)	siRNA degradation rate constant in cytoplasm	0.10^a	Fixed
RISC_tot (moly/l)	Total RISC concentration	0.0003	Wang et al., 2012 [19]
k_on.RISC (l/nmol/h)	Association rate constant of siRNA antisense strand and RISC	1.55	Estimated
K_off.RISC (1/h)	Dissociation rate constant of siRNA antisense strand and RISC	1·10^− 7	Barlett and Davis 2006. [20]
k_DR (1/h)	Degradation rate constant of RISC complex	0.0036	Estimated
Global PBPK Parameters
Parameter (Unit)	Description	Value	Reference
Radius Solute (nm)	Hydrodynamic radius of GalNAc-siRNA	1.85·10^− 3	Estimated
ka (1/h)	Absorption rate constant	0.63	Estimated
fu	Fraction of free GalNAc-siRNA in plasma	0.96	Estimated
k_uptake (1/min)	Global endosomal uptake rate in remaining tissue	61.7	Estimated
k_recycling (1/min)	Global endosomal recycling rate constant in remaining tissue	2.24	Estimated
k_kiduptake (1/min)	Kidney endosomal uptake rate constant in remaining tissue	68.0	Estimated
k_kidrecycling (1/min)	Kidney endosomal recycling rate constant in remaining tissue	12.01	Estimated
k_RNase (1(h)	RNase degradation rate constant	0.012	Estimated
RNase (µmol/l)	Ribonuclease concentration in remaining tissue	0.04	Estimated
a: Fixed to literature value to avoid overparameterization, Ayyar et al., 2018.

Pharmacodynamics

The pharmacodynamics of RISC induced mRNA silencing and target protein knockdown was described as relative change from base line (mRNA₀ and Protein₀). The rate of RISC induced mRNA silencing was modelled with an indirect stimulatory response model (IDR) (Eq. 5).

$\:\frac{dmRNA}{dt}={k}_{deg.mRNA}\:·\:\left(mRN{A}_{0}\:-\left(1+\frac{{S}_{max}*CRISC}{S{C}_{50}+CRISC}\right)·mRNA\right)$

Eq. 5

Where k_deg.mRNA represents the degradation rate constant of the target mRNA; mRNA₀ is the baseline value of mRNA equal to 1; CRISC is the concentration of the siRNA induced RISC formation; S_max describes the maximum effect induced and SC₅₀ is the concentration required to produce half the maximum effect. The knockdown of target protein was regulated in response to the mRNA level relative to mRNA baseline (mRNA₀) (Eq. 6).

$\:\frac{dProtein}{dt}={k}_{deg.protein}·\:{\left(\frac{mRNA}{mRN{A}_{0}}\right)}^{y}·Protein$

Eq. 6

where k_deg.protein represents the degradation rate constant of the target protein and γ is the Hill coefficient describing the slope of the drug response concentration curve.

The endogenous homeostasis of the drug response variables, mRNA and target protein, was described by a turnover model characterized by a zero-order synthesis rate constant k_syn and a first order degradation rate constant k_deg. Thus, the following initial condition for the IDR describing mRNA and target protein at baseline would be:

$$\:{k}_{syn.mRNA}={k}_{degmRNA}\bullet\:mRN{A}_{0}$$

$$\:{k}_{syn.protein}={k}_{degProtein}\bullet\:Protei{n}_{0}$$

As the pharmacodynamics were described as relative change to baseline the absolute value for mRNA₀ and Protein₀ was set to 100%. As a consequence, k_syn and k_deg correlated with a fixed factor of 100.

Model Strategy and Assumptions

The general model strategy was to leverage the previously described WB-PBPK model for large molecules and the ASGPR TMDD model to establish a WB-PBPK-PD model[7]. First, PK-Sim® was used to establish the generic structure for the WB-PBPK model for a GalNAc-siRNA molecule. The “Model for proteins and large molecules” was selected to include the size dependent two-pore formalism for extravasation and endothelial endosomal clearance. A first-order input function to central venous plasma was included to simulate systemic drug appearance after intravenous (IV) and subcutaneous (SC) drug administration. The PBPK model was exported to MoBi® where additional elements were added to accommodate for investigation of general disposition processes, ASGPR mediated liver uptake and downstream PD effects. The generic implementation for endosomal clearance in PK-Sim® was disabled and replaced with a first-order metabolic reaction in all organs except the liver. The ASGPR system was added to the endosomal sub-compartment in the liver compartment (liver zonation was not included) with uptake from the interstitial compartment and endosomal escape to the intracellular compartment. Finally, a first-order metabolic reaction was included in plasma compartments to allow for investigation of potential siRNA plasma degradation. Initial parameter values were informed by compound characteristics, the default settings in PK-Sim® and as reported in the ASGPR studies [16–20]. In accordance with previous investigations, the influence of plasma protein binding (PPB) on disposition processes was assumed to be negligible [21]. An iterative model development strategy was then applied comparing simulation output to compiled reference data. The approach adopted an iterative increase in deviation from the legacy models and flexibility in terms of compound specific parameter estimation. Due to model differences in structure and parameterization deviations from legacy implementations were expected. Similarly, compound differences were also expected. For example, the degradation rate may differ between GalNAc-siRNA sequence and chemical stabilization method which also may influence effective bioavailability after SC administration [22]. Likewise, endosomal degradation and endosomal release into the cytoplasm are believed to be sequence/formulation specific [3, 23].

Uptake into cells was assumed to be mediated by ASGPR and was hence restricted to the liver [16]. It was anticipated that when ASGPR is cleaved from the siRNA in the endosome, ASGPR is recycled quickly to the cell surface membrane and only a small fraction of free ASGPR is degraded in the cell cytosol. The ASGPR PK parameters were adopted from Ayyar et al. 2018 or optimized when appropriate, see Table 1. Equally, it was assumed that the receptor kinetics is mainly driven by the GalNAc ligand except for the internalization rate of the ASGPR-GalNAc-siRNA complex that was assumed to be dependent on the physio chemical properties of the siRNA [24]. We anticipated that 1% or less of the unconjugated siRNA would escape into the cytoplasm to induce RISC formation and exhibit mRNA cleavage [22]. Further, it was anticipated that the duration of mRNA cleavage would depend on the RISC formation and the dissociation from the RISC will not influence the PK-PD relationship. We assumed that the intracellular stability affected the duration of effect [3, 14].

Because of incomplete data, certain processes had to rely on a subset of compounds, assuming their similarity across all. Systemic, kidney and liver disposition processes as well as the link between these were established by compounds with plasma, kidney, and liver tissue data. The fraction escaping endosomal degradation and siRNA-RISC complex kinetics was informed by compounds with liver tissue and siRNA-RISC complex measurements. Compounds with siRNA-RISC, mRNA and downstream protein expression were used to inform PD. The Pharmacodynamics were characterized after establishment of the siRNA disposition and siRNA-RISC complex dynamics. Investigated compounds with respective available data is summarized in Table 1.

Model Evaluation

The model was subject to a sensitivity analysis to identify PBPK-specific sensitive parameters impacting the PK and PD. The sensitivity analysis was conducted according to PK-Sim® [25] and performed in R (http://www.r-project.org), R studio [26]. The sensitivity analysis calculates the relative impact for a given PK parameter to changes in different input parameters with a variation of 10%. The sensitivity of a PK parameter was calculated as the ratio of the relative change of the PK parameter and the relative variation of the input parameter as in Eq. 7:

$\:{S}_{ij}=\frac{\varDelta\:P{K}_{j}}{\varDelta\:{p}_{i}}·\frac{{p}_{i}}{P{K}_{j}}$

Eq. 7

Where $\:\varDelta\:P{K}_{j}$; is the change of the PK parameter, $\:\varDelta\:{p}_{i}$; is the change of the input parameter, $\:P{K}_{j}$; is the value of the PK parameter and $\:{p}_{i}$; is the value of the input parameter. According to WHO guidelines sensitivities were evaluated as being high (absolute value ≥ 0.5), medium (absolute value ≥ 0.2 but less than 0.5) or low (absolute value ≥ 0.1 but < 0.2 [27]. Parameters with a sensitivity < 0.1 were considered to have insignificant influence on the evaluated PK parameter. The PK parameter evaluated was exposure calculated as area under the curve simulated from time 0h to 1000h (AUC_{0 − 1000h}).

Overall, the WB-PBPK-PD successfully characterized the PK-PD relationship of GalNAc-siRNAs. Furthermore, the presented model identified compound specific PBPK parameters and shed light on the knowledge gaps of the GalNAc-siRNAs biodistribution.

The generic two pore formalism could not be readily employed to describe the extravasation of investigated GalNAc-siRNAs. By this parameterization the molecules were restricted to plasma, see figure S1 in Supplementary 2, prolonging the circulation time, while limiting ASGPR mediated uptake and failing to capture the fast onset in liver concentrations and the accumulation in kidney. To satisfactory characterize the extravasation of GalNAc-siRNAs by the two-pore formalism the radius solute calculated by PK-Sim® [12] was decreased by a 100-fold to a value of 1.85·10^− 3nm. In addition, to accurately describe plasma PK, the model further identified a necessity to introduce general tissue distribution, in our case accommodated for as unspecific first-order endosomal uptake from and recycling to plasma. Uptake and recycling rate constants (k_up and k_rec) were globally estimated to 61.7 1/min and 2.24 1/min, respectively.

On top of the manipulation of the radius solute, and implementation of general tissue distribution, some adjustments of the previously reported TMDD ASGPR model parameters were performed to accurately describe the ASGPR mediated uptake and intracellular liver mechanisms across all doses. The receptor density (R_tot), association rate constant between ASGPR and GalNAc (k_on), dissociation rate constant of ASGPR-GalNAc complex (k_off) and internalization rate constant of complex bound ASGPR-GalNAc-siRNA (k_int) were all estimated during Levenberg-Marquardt parameter optimization. The remaining ASGPR TMDD model parameters were achieved from the literature. See Table 2 for all ASGPR related parameters and how they were achieved.

The model successfully characterized the short half-life of the plasma concentrations as shown in Fig. 1. The model further identified a plasma degradation rate k_RNase of 0.011/h for all GalNAc-siRNAs included in the model and a subcutaneous absorption rate of 1.1 1/h for all subcutaneous administered GalNAc-siRNAs. The bioavailability (F) was estimated as a compound specific parameter across doses, with the exception of SIAT-2 for which a dose specific F for the highest dose (25 mg/kg) where needed in order to capture observations (Table 3). Overall, the bioavailability showed non-linearity across all compounds, see Table 3. Besides the bioavailability, the free fraction of GalNAc-siRNA in plasma was estimated to a value of 0.96.

Table 3

Summary of compound specific WB-PBPK-PD parameters
Parameter	Description	ALN-AT3/ SIAT-2^a (1–25 mg/kg) ESC^e	SITTR-1/2^b (0.5–10 mg/kg) ESC^e	siF7-1^c (2.5 mg/kg) ESC^e	siF7-2/3^c (0.75-1 mg/kg) ADV ESC^f	siF9-1^d (2.5 mg/kg) ESC^e	siF9-2^d (0.75 mg/kg) ADV ESC^f
Compound Specififc PBPK Parameters
F (%)	Bioavailabiltiy	0.40/0.98	0.64	0.068	0.20	0.064	0.14
k_degendosome (1/h)	Endosomal degradation rate for siRNA	0.012	0.042	0.0010	0.0063	0.0066	0.0042
f_escape (%)	Fraction of antisense strand escaping from the endosome to induce RISC formation	0.068				0.23
Pharmacodynamic Parameters
S_max	Maximum stimulation of mRNA degradation	17.8	96.2	96.2		34.5
SC₅₀ (nmol/l)	RISC loaded siRNA at half maximal stimulation	2.47	3.61	3.61		1.01
Gamma	Gamma coefficient for target protein knockdown	1.32	0.52	0.52		9.38
k_deg.mRNA (1/h)	Degradation rate constant for mRNA	0.02	0.006	0.006		0.01
k_deg.Protein (1/h)	Degradation rate target for protein	0.20	0.47	0.47		0.23
a: GalNAc-siRNA targeting Anti Thrombin; b: GalNAc-siRNA targeting Transthyretin Protein; c: GalNAc-siRNA targeting Coagulation Factor VII; d: GalNAc-siRNA targeting Coagulation Factor IX; e: Enhanced Stabilization Chemistry; f: Advanced Enhanced Stabilization Chemistry

The endosomal degradation/escape rate (k_endosome) were found to be highly influential on the extended half-life in the liver endosomes and was therefore estimated separately for each compound, see Table 3. By individually estimating k_endosome for each compound the TMDD ASGPR model accurately described the liver half-life across all compounds, as shown in Fig. 2. As expected, we observed that GalNAc-siRNA formulated with Adv ESC showed a tendency towards a lower endosomal degradation rate compared to its corresponding GalNAc-siRNAs, targeting the same protein, but formulated with ESC instead, see Table 2. The intracellular degradation in the cytoplasm k_cytoplasm was fixed to a value of 0.1 1/h as previously reported in the literature to avoid overparameterization.

Overall, the ASGPR TMDD model succeeded in describing the siRNA induced RISC formation within a 2-fold across all compounds, as depicted in Fig. 3, with the exception of siF9-1 being slightly underpredicted and siF7-1/2 being slightly overpredicted. The key model parameters involved in the intracellular liver concentration affecting the RISC formation, were k_DR and the fraction of free sense strand loading into Ago2 protein (f_escape). The fraction escaping endosomal degradation, was estimated as a global parameter 6.4·10^− 4 except for sif9-1/2, which was described by an individual estimate, 2.5·10^− 3, to adequately describe observations. The remaining model parameters involved in RISC (k_{on_RISC,} k_{off_RISC} and k_DR) were estimated as global parameters, see Table 2.

The characterization of the kidney distribution was informed by the data from GalNAc-siRNAs targeting transthyretin protein, SITTR-2 10 mg/kg (SC and IV) and was captured successfully as shown in Fig. 4. Distribution kinetics into renal tissue were described by unspecific endosomal trafficking (k_up = 68.0 1/min and k_rec = 12.0 1/min). Renal elimination was implemented as passive filtration of unbound drug via glomerular filtration rate into urine.

PK-PD Relationship

The gene silencing of the target mRNA was successfully characterized by an indirect response model within a 2-fold across all compounds, see Fig. 5. After optimized PK parameters, PD parameters previously estimated for ALN-AT3 were initially applied to the model [7]. Yet, the PD parameters required optimization across all compounds to fully capture observations see Table 3. See figure S5 and S6 in supplementary 1 for estimation of mRNA silencing and downstream effect on target protein on previously reported PD parameters. The PD parameters were estimated individually for each compound regardless of formulation strategy. Overall, PD parameters (SC₅₀, k_deg.mRNA and k_deg.Protein) showed similarities across compounds with SC₅₀ going from 1.07–2.61 nmol/l, k_deg.mRNA 0.006–0.04 1/h and k_deg.Protein estimated within a 2-fold variation going from 0.14–0.47 1/h. S_max depicted a higher variation between compounds with a 5-fold variation going from 17.8–96.2.

The downstream effect on the target protein was captured well for ALN-AT3 based on the response of the mRNA levels uplifted with an estimated Hill coefficient of 1.32 to account for the greater reduction in protein levels than the corresponding mRNA. The knockdown of target protein for SITTR-1 (0.5–1.5 mg/kg) were informed by mRNA silencing levels of SITTR-2 (10 mg/kg). The model successfully captured the abrupt mRNA silencing for SITTR-2 (10 mg/kg) which successfully informed the downstream effect on SITTR-1 (1.5 mg/kg) with SITTR-1 (0.5 mg/kg) being vaguely overpredicted with a mutual estimated Hill coefficient of 0.52.

Sensitivity analysis

A sensitivity analysis was performed to determine which model parameters would be most influential of the total liver tissue concentration, RISC formation and downstream effect of the target protein described as the changes to the AUC_{0 − 1000h} for each output. The most influential parameters for AUC_{0 − 1000h} and respective sensitivity coefficients are shown in Fig. 7.

Overall, the sensitivity analysis revealed that the exposure in plasma, liver and kidney and RISC formation, showed low sensitivity towards changes of k_uptake, the GFR and free fraction of the siRNA in plasma. Moreover, the sensitivity analysis showed that the total liver tissue concentrations displayed high sensitivity towards changes in k_endsome and medium sensitivity towards changes in k_int, k_on, k_off and R_tot. The AUC_{0 − 1000h} of the kidneys showed high sensitivity towards changes of kidney tissue distribution k_uptakeo and k_recycling. Likewise, liver and kidney AUC_{0 − 1000h} showed medium sensitivity towards ASGPR TMDD model parameters as shown in Fig. 7. For the RISC formation the f_escape was the most influential parameter and the second most influential parameter was the k_DR. The AUC_{0 − 1000h} of the RISC formation, did also show medium sensitivity towards changes in the R_tot, but minimum sensitivity towards changes of the k_int, k_on and k_off. Likewise, the RISC formation the mRNA and downstream effect of the target protein showed high sensitivity towards changes in k_DR and f_escape while the mRNA silencing showed low sensitivity towards ASGPR TMDD model parameters. Finally, the mRNA showed high sensitivities towards changes in S_max and SC₅₀ whereas downstream effect on the target protein showed medium sensitivity towards changes in S_max and SC₅₀ but high sensitivity in changes of gamma. Sensitivity coefficients are summarized in Fig. 7.

GalNAc-siRNAs with selective silencing off disease related proteins and target specific uptake in the liver is to this date the most successful RNAi drug modality[1]. The most unique feature for this novel drug class is the PK-PD relationship and quantifications of intra cellular traffic (liver uptake, RISC formation, intracellular concentrations etc.) and target tissue distribution is therefore warranted.

In this study we present a generic WB-PBPK-PD model describing plasma PK, ASGPR mediated liver disposition and PD. The model was informed by observation of 10 GalNAc-siRNAs in mice and leveraged previously established models for PK, TMDD and PD[7]. The presented WB-PBPK-PD model highlights some remaining knowledge gaps of the GalNAc-siRNAs complex cellular kinetics and biodistribution.

Overall, the presented WB-PBPK-PD model characterized the PK-PD relationship well across all compounds. The final model adopts a generic structure and parameterization according to the legacy WB-PBPK model [12] and ASGPR TMDD model [7] with only a few modifications and compound specific parameters.

At first, we identified that the generic two-pore formalism theory was inadequate in explaining the extravasation of GalNAc-siRNAs. To capture the observed extravasation via the two-pore formalism, the radius solute needed to be set significantly lower than reported values (1.8–2.4 nm) to reduce the resistance for epithelial translocation. There are several theoretical explanations for this discrepancy. First, although experimentally values are similar those calculated based on molecular weight (1.85 nm), it is possible that the effective hydrodynamic radius solute is smaller [28–31]. Another potential mechanism for enhanced extravasation of the GalNAc-siRNAs could involve uptake through binding and co-transportation with plasma proteins, such as α2-macroglobulin. This subtype of macroglobulin, α2-macroglobulin, undergoes passive filtration from plasma to the interstitial space [32]. From the interstitium it is subsequently cleared by the low-density lipoprotein receptor related protein (LRP1) via endocytic uptake in the liver [33, 34]. Potentially, α2-macroglobulin bound siRNA could also confound the bioassays for siRNA concentration determination. Moreover, extracellular RNA has been shown to induce vessel permeability via elevation of flux and disintegration of tight junctions [35]. This together with observed, accumulation of unconjugated siRNAs occurring throughout the body, e.g. kidney, intestines, or gland tissue, in addition to the liver indicate that the enhanced extravasation process is to some extent regulated by basal functionalities and general RNA characteristics rather than specific processes [36, 37]. This theory is further supported by the presented model where general tissue distribution was needed to capture observed plasma profiles.

Yet another physiological function of potential relevance for the siRNA extravasation is the negatively charged glycocalyx, a sugar coat attached to the apical surface of vascular endothelial cells [38]. There are several indications that an interaction between the GalNAc linker and the glycocalyx could serve as an extravasation enhancer. For instance, glycocalyx mimicking nano particles preferably absorbs into different tissues, likely due to interaction with other sugar moieties from the glycocalyx [38]. Interactions between different sugar moieties (glycans, glycolipids and glycoproteins) with glycocalyx have also been observed for Human immunodeficiency viruses (HIV) to enhance its entry into cell hosts [39]. These explanations support a possible theory of GalNAc-Glycocalyx interaction being responsible for the fast extravasation rather than the hydrodynamic size of the siRNA itself. In summary, this study highlights the importance of RNA/siRNA/GalNAc-siRNAs extravasation for tissue accumulation and further insights into this process may open new possibilities for tissue targeting.

The final model was able to accurately describe the liver exposure and downstream effects for all included compounds and investigated doses (Fig. 2, 3, 6). Saturation of ASGPR-mediated uptake, which limited liver exposure, was described by the model at higher doses (> 5 mg/kg) in accordance with observation. Model performance was comparable to the reported legacy models while some of the ASGPR related parameters were reoptimized from previously reported values such as the receptor density, k_on, k_off and k_deg. The need for re-estimation of parameters is not unexpected. Differences between general model structures and parameterization alter relative and absolute compartment concentrations that drive binding processes and flows. These optimizations were conducted using a middle-out approach, comparing simulation outputs with available reference concentrations. For instance, to adequately describe observed levels and dose non-linearities in liver exposure, the receptor density in the current model (13.4 µmol/l) was estimated to a higher value than what was estimated and utilized by the other legacy PBPK models (0.633 µmol/l [7] ,0.647 µmol/l [16]). Given that both models show good performance these values should be regarded as model specific ASGPR capacities rather than explicit receptor abundances. In addition, as previously mentioned additional liver uptake could be present either via the previously mentioned α2-macroglobulin-LRP1 mediated uptake or via macrophage Kupffer cells [40]. However, macrophage uptake in vivo has so far only shown modest effectiveness in vivo [41]. To perform optimally, a small increase in internalization rate applied (k_int = 3.58 1/h) compared to the legacy model (k_int = 2.4 1/h). The value of k_int used in the legacy model was originally determined via a murine model, testing the liver uptake of GalNAc-interleukin-2 [42]. Later Nie et al. showed that a hydrophilic linker onto the GalNAc tended to have a lower steric hindrance for effective ASGPR recognition [24]. It is commonly known that siRNAs are hydrophilic molecules [22, 31] and that interleukins are prone to be hydrophobic[43]. Therefore, we find it reasonable that the k_int is estimated to a higher value than what has previously been reported.

Overall, the model described the liver dynamics well across all compounds and doses (Fig. 5, 6). The half-life of the GalNAc-siRNA in liver was determined by the endosomal degradation rate k_endosome which also described the release rate into the cytoplasm. However, despite that the k_endosome being individually estimated for each compound, the initial liver concentrations of siF7-1 (2.5 mg/kg) were slightly underpredicted and the liver concentrations for siF7-2/3 (0.75 and 1 mg/kg) were vaguely overpredicted. Neither siF7-1 (2.5 mg/kg), siF7-2/3 (0.75 and 1 mg/kg) had included plasma concentrations in the analysis.

From a previously published mPBPK-PD model, it was stated that plasma concentrations would carry little information for the assessment of GalNAc-siRNA liver exposure [7]. However, plasma is essential for bioavailability assessments which ultimately determine the effective dose reaching the systemic circulation and consequently also the liver. This analysis indicates high compound variability and non-linearities in bioavailability which support inclusion of plasma measurements to gain insights on this matter. Another relevant point is the unknown influence of the plasma PK by the different stabilization designs. A previously published mPBPK model showed, that clinical plasma PK is dose proportional and is not affected by different stabilization designs, see Sten et al. for more details [44]. Nevertheless, the difference between ADV ESC vs. ESC were not included in the previous mPBPK model, as in the current model, and therefore we cannot completely exclude if ADV ESC vs. ESC would have an impact on the plasma pk and eventually the liver tissue concentration.

The model further characterized the RISC formation across all compounds. However, the RISC formation on siF7-1 (2.5 mg/kg) and siF7-3 (1 mg/kg) were slightly overpredicted compared to the additional compounds in the analysis yet still estimated within a 2-fold. The k_endosome also represented the release rate of the free siRNA from the endosome to the cytoplasm thus indirectly influencing the RISC dynamics as well. Improved results could have been achieved with independently described processes, however this was not investigated in this study. The level of created RISC is highly dependent on the amount of free siRNA escaping endosomal degradation into the cytosol, in the model determined by the parameter f_escape. Previous models have assumed the level of siRNA escaping from the endosomal compartment loading into Ago2 protein to 1% escape [7]. The iterative model development indicated that performance increased with a lower level of escape and hence this parameter was estimated for optimal results. We also identified that the escape level was similar between all compounds except siF9-1/2, leading to a shared parameter estimate for all compounds except siF9-1/2. Both estimates were less than 1% which are in line with reported estimates [23, 45]. Lastly, the sensitivity analysis revealed that the RISC AUC_{0 − 1000h} showed high sensitivity towards changes in k_DR. It is possible that estimating k_DR as compound specific parameter would improve the RISC estimation as seen in previously published mPBPK to accurately describe downstream effect [23]. However, that was not the case in our model and could possibly be due to sparse data informing the RISC formation predictions.

In general, the model described the mRNA silencing and the downstream effect of target protein well across all compounds except for the SITTR-1 0.5 mg/kg being slightly overpredicted. In general, SITTR-1/SITTR-2 were the only compounds included in the analysis to which RISC formation reference data was not available. It cannot be excluded if the uncertainties in the protein downstream effect is due to lack of RISC data since the sensitivity analysis confirmed that RISC formation and the protein knockdown is highly correlated by both being sensitive to f_escape but also k_DR. Nevertheless, the model still serves as a powerful tool for PD predictions with limited RISC reference data. The PD parameters showed similarity to previously estimated PD parameters with only a few exceptions. The Hill coefficient for SITTR-1/2 was estimated to a value below 1 as the only compound in the analysis. In short terms, the Hill coefficient is a standard parameter that describes the drug sensitivity. Often a Hill coefficient < 1 indicates that the drug response is less sensitive to changes in drug concentrations and produces shallower drug response curves [46]. However, in this context a Hill coefficient < 1 does not necessarily mean that SITTR-1/2 drug effect are less sensitive to changes in drug concentrations compared to other GalNAc-siRNAs. The low value of the Hill coefficient is potentially a compensation of the steep drug response curve of silenced mRNA produced by SITTR-2 10 mg/kg, that informed the estimation of the downstream effect on the target protein by SITTR-1 (0.5 mg/kg). Another reason for the uncertainties in the estimation of the downstream effect could be attributed to overpredicted liver concentrations of SITTR-1 (0.5) hence their bioavailability was informed by the plasma concentration of SITTR-2 (10 mg/kg with) with an estimated bioavailability of 63%. Once again, this analysis supports the importance of plasma concentrations to establish PK-PD relationship of GalNAc-siRNAs but still works as a reliable framework to characterize PK-PD relationship for GalNAc-siRNAs.

We present a generic GalNAc-siRNA WB-PBPK-PD model implemented in the open-source platform MoBi. This comprehensive model encompasses all necessary elements to describe physiologically-based systemic and liver disposition, including ASGPR-mediated liver uptake and RISC-induced mRNA silencing and protein reduction. As a result, the model is readily applicable for characterizing novel GalNAc-siRNAs in drug development and for hypothesis-driven investigations to elucidate specific disposition mechanisms. This model thus serves as a powerful tool for more effective development of GalNAc-siRNA therapeutics, ultimately advancing new RNAi treatments for patients.

Author Contribution

"Emilie Kirstine Langeskov Salim, Erik Sjögren and Kim Kristensen wrote the main manuscript text and Emilie Kirstine Langeskov Salim prepared figures 1-7 and tables 1-3. All authors reviewed the manuscript."

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No competing interests reported.

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Whole-Body Physiologically-Based Pharmacokinetic Modeling of GalNAc conjugated siRNAs

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\(\:\frac{d{A}_{free}}{dt}={k}_{syn}-{k}_{deg}\:·{A}_{free}-{k}_{on}\:·{D}_{free}\:\times\:R+{k}_{off}\:·DR+{k}_{recycle}·{A}_{endosme}\)	Eq. 2
\(\:\frac{d{D}_{free}}{dt}=\:-{k}_{on}\:·{D}_{free}\:·{R}_{free}+{k}_{off}\:·DA\)	Eq. 3
\(\:\frac{dDA}{dt}=\:{k}_{on}\:·{D}_{free}\:·{A}_{free}-{k}_{off}\:·DA-{k}_{int}·DA\)	Eq. 4