Physiologically Based Pharmacokinetic Modeling of 3 HIV Drugs in Combination and the Role of Lymphatic System after Subcutaneous Dosing. Part 2: Model for the Drug-combination Nanoparticles

Abstract

We previously developed a mechanism-based pharmacokinetic (MBPK) model to characterize the PK of a lymphocyte-targeted, long-acting 3 HIV drug-combination nanoparticle (DcNP) formulation of lopinavir, ritonavir, and tenofovir. MBPK describes time-courses of plasma drug concentration and has provided an initial hypothesis for the lymphatic PK of DcNP. Because anatomical and physiological interpretation of MBPK is limited, in this Part 2, we report the development of a Physiologically Based Pharmacokinetic (PBPK) model for a detailed evaluation of the systemic and lymphatic PK of drugs associated with DcNP. The DcNP model is linked to the PBPK model presented earlier in Part 1 to account for the disposition of released free drugs. A key feature of the DcNP model is the uptake of the injected dose from the subcutaneous site to the adjacent lymphoid depot, routing through the nodes within and throughout the lymphatic network, and its subsequent passage into the blood circulation. Furthermore, the model accounts for DcNP transport to the lymph by lymphatic recirculation and mononuclear cell migration. The present PBPK model can be extended to other nano-drug combinations that target or transit through the lymphatic system. The PBPK model may allow scaling and prediction of DcNP PK in humans.

Introduction

The development of new drug combinations and delivery strategies are set to optimize HIV prevention and therapy.^1,2 To improve adherence, resistance, pill fatigue, and accessibility in disadvantaged countries, which could lead to a viral rebound and transmission, there is growing willingness and acceptance in people living with HIV to switch to a long-acting therapy.^3,4 Long-acting (LA) drugs are generally already approved “short-acting” drugs that are rendered long-acting through pharmaceutical reformulation or they are loaded in implants and patches.^5,6 The intramuscular LA-injectable formulation CABENUVA (ViiV Healthcare, UK) has just been approved as a once-a-month LA treatment to replace the combination antiretroviral therapy (cART) regimen in patients who are virologically stable and suppressed. CABENUVA maintenance consists of separate injections of two nanoformulations of cabotegravir and rilpivirine, which form two separate local depots with very slow and continuous drug release into the plasma. Several other LA HIV formulations are in development aiming at elongate duration, waiving lead-in dosing, reducing the number of injections, or obtaining a better targeting of the lymphatic system.

Among emerging LA injectables, there is one novel platform that combines 3 to 4 different antiretrovirals in one injectable, referred to as Targeted Long-Acting Antiretroviral Therapy (TLC-ART), which was developed in our laboratory.^7–9 TLC-ART consists of incorporating antiretrovirals into lipid excipients to form Drug-combination Nanoparticles (DcNP), which are suitable for lymphatic uptake and depot in the lymph nodes cells.¹⁰ The current lead triple-drug-combination DcNP formulation, namely TLC-ART 101, contains two hydrophobic protease inhibitors (PI) − lopinavir (LPV, logP = 4.4) and ritonavir (RTV, logP = 5.0) and a hydrophilic nucleotide reverse transcriptase inhibitor – tenofovir (logP = −1.6). Even though the combination lopinavir-ritonavir is now a second-line therapy and not reccomended any longer to treat adults, it still has scope for disadvantaged areas and pediatrics. Nonetheless, TLC-ART 101 has served as a proof-of-work formulation to demonstrate the ability to co-formulate different drugs in one nanoparticle and getting long-acting and targeting features for all drugs. It also has a demonstrated flexibility to swap all three antivirals in the nanoformulation for other more recent agents and still retain the desirable LA properties in preclinical studies.^7–9 In fact, a single SC injection of TLC-ART 101 sustains pharmacologically relevant concentrations of all three antiretrovirals in both plasma and mononuclear cells in blood and lymph nodes, for at least two weeks in nonhuman primates (NHP). In contrast, when the same triple-drug combination was given in suspension as a free-drug mixture, plasma drug concentrations became undetectable within 1 to 2 days after injection.

The TLC-ART pharmacokinetics (PK) was investigated thoroughly, especially by the creation of two mechanism-based models (MBPK). We observed in NHP that a single SC injection of TLC-ART produced, not only a prolonged plasma antiretroviral drug concentration over time, but also displayed a characteristic undulating pattern, which suggests a multiphasic absorptive system of DcNP. To elucidate the complex presystemic absorption kinetics, we developed in succession MBPK1 and MBPK2 models to capture and investigate the DcNP PK. MBPK1 focused on modeling the presystemic or lymphatic “first-pass” transit of DcNP; it featured three distinct transit routes through the lymphatics with varying kinetic delays, which provided an explaination of the the observed undulating plasma concentration-time profiles typical of TLC-ART formulations.^7,14 The later addition of PK data from an intravenous TLC-ART 101 study prompted a refinement of MBPK1 to MBPK2.¹⁰ Comparison of the IV and SC dataset revealed that SC bioavailability of TLC-ART 101 was incomplete due to lymphatic trapping of DcNP, and first-pass release of free drug. Trapping of DcNP further explained the observed enhancement of drug concentration in lymph node mononuclear cell (LNMC) following the SC route of administration.^11,15 Summarizing, our previous investigations revealed three governing mechanisms for TLC-ART targeted LA properties¹⁰: (i) preferential lymphatic uptake of DcNP from the SC injection site; (ii) formation of drug depot in transiting lymph nodes; and (iii) drugs associated with DcNP remain reasonably stable as they circulate in the lymph and blood.

As compartmental models, MBPK models lack the important details about anatomy and physiology that can be used for proper NHP-to-human scaling, particularly for the pivotal lymphatic system. In this Part 2 report, we describe the construction of a physiologically based pharmacokinetic (PBPK) model to better interpret the fate of lymphatic-targeting DcNP. We divided our model development into two phases: (i) modeling of the systemic distribution and clearance of DcNP, and (ii) modeling of the presystemic processes including DcNP uptake from the SC injection site, sequestration in adjacent lymphoid tissue, and transit through the network of regional lymph nodes. PBPK models are particularly suited for interspecies scaling to support the first-in-human investigation and later-stage clinical studies in special populations, such as dosing proposals in pediatric patients. Given the complexity of DcNP disposition, allometric scaling of conventional compartmental model parameters for human predictions is fraught with difficulties. PBPK modeling appears to be the most logical next step in preparation for the clinical transition of TLC-ART development.

Methods

Nanoparticle Formulation and Experimental Protocol

The present dataset was previously used for the mechanism-based pharmacokinetic (MBPK2) modeling¹⁰; hence, only the essential experimental details are summarized herein. Briefly, 8 non-human primates (pig-tailed macaque, Macaca nemestrina) were given a single SC injection of TLC-ART 101. Each injection was given in 2 or 4 divided boluses (<60 sec for each) at symmetrical locations about 1-inch lateral from the midline in the upper mid-scapular area between shoulder blades. The SC injection site in the upper back was chosen as being practically convenient and deemed to be the best site to achieve a widespread whole-body DcNP distribution within the lymphatic system. Each ensuing pharmacokinetic study consisted of serial blood sampling over 2 weeks (336 h) yielding a rich sample set of plasma and peripheral blood mononuclear cells (PBMC). In another set of macaques, groups of animals were euthanized at 24, 96, and 336 h (N=3 at each time) followed by necropsy to collect visceral tissues including kidneys, spleen, liver, and lymph nodes from cervical, hilar, axillary, mesenteric, and inguinal regions. Homogenates from tissues and lymph nodes were prepared and drug concentrations measured, as reported before.¹⁶ Lymph node mononuclear cells (LNMC) were isolated from both the left and right axillary node only at 24 and 192 h, as reported before.¹⁶ Construction of the DcNP systemic submodel required PK data obtained with intravenous (IV) TLC-ART 101, while we employed the SC experiments to inform the presystemic portion of the model. We had previously described an IV TLC-ART 101 study in two macaques.¹⁰ All NHP studies were conducted under a protocol approved by the University of Washington Institutional Animal Care and Use Committee (IACUC). Animals were housed and cared for by the Washington National Primate Research Center (WaNPRC) according to standard operating procedures.

For laboratory-scale production of the Drug-combination Nanoparticles (DcNP), GMP-grade lopinavir (LPV), ritonavir (RTV), and tenofovir (TFV, as PMPA form) were dispersed in DSPC and DSPE-PEG2000. First, hydrophobic LPV and RTV were dissolved together with DSPC and DSPE-PEG2000 in ethanol. Then, TFV dissolved in carbonate buffer was added to the mixture dropwise. The ethanol-carbonate buffer solution was subjected to spray drying. The resulting powder – comprising of the 3 APIs and 2 lipidic excipients – was reconstituted with sterile physiological saline (see more details in¹³). The resulting suspension underwent particle size reduction via homogenization to yield an average diameter of 52.4 ± 9.1 nm as measured by photon correlation spectroscopy. The final suspended nanoparticles possess a slightly negative Z-potential and appear oblate in shape.¹³ The final injectable suspension, herein referred to as TLC-ART 101, contains a fixed drug molar ratio of 4:1:5 (LPV:RTV: TFV); the molar ratio of total drugs-to-lipids was 1:9. For the SC injections, doses of 25 mg/kg LPV, 7.2 mg/kg RTV and 14.2 mg/kg TFV were dissolved in suspension in a 10-ml volume of injectate.

PBPK Modeling Approach

Construction of the DcNP PBPK model followed a stacked-layer approach illustrated in Fig. 1 as a 3D scheme, where each layer represents a distinct segment of the PBPK model. From the top: (i) DcNP SC submodel dealing with absorption of DcNP from the SC injection site to the adjacent lymphoid tissue compartments that serve as deposits and sorting centers; (ii) DcNP systemic submodel representing the whole-body lymphatic network linked to the blood circulatory network of organs and tissues; and (iii) the free drug submodel accounting for free drug released from DcNP, as it was presented in Part 1. As mentioned in the Introduction, the salient PK mechanisms DcNP featured in the present PBPK model were informed by our earlier MBPK modeling efforts.^7,10,14 In brief,¹⁰ upon injection, all three antivirals are 100% associated with DcNP in the formulation. This condition was tested and found to be the best at fitting our data in vivo.¹⁰ The DcNP dose is absorbed exclusively into the lymphatic capillaries and eventually routed through the network of regional lymph nodes. Within each regional lymph node, DcNP is taken up by the residing cells, mainly lymph node mononuclear cells (LNMC). In the nodes, release of free drug is assumed to occur either spontaneously in the sinusoidal fluid or via intracellular degradation of DcNP. A fraction of the absorbed DcNP dose eventually reaches the blood circulation for distribution among the systemic organs and tissues. During the systemic phase, DcNP can release the payload as free drugs or itself eliminate. The free drugs in turn follow their native PK (e.g., TFV eliminates through renal clearance). Thus, the three layers in the model scheme of Fig. 1 are connected via unidirectional drug fluxes from top to bottom. Construction of the top and middle DcNP layers relied on data from two major TLC-ART 101 preclinical studies: the middle submodel structure was mainly identified with data from the IV study in NHP, and the top submodel structure was identified with data from the SC study in NHP. Relevant details on DcNP submodels are presented in the next two sections; supplemental information is also available in the Appendix.

Figure 1.

3D configuration of the PBPK model for the drug-combination nanoparticles (DcNP) in non-human primates. Top layer: submodel describing the absorption of DcNP from the subcutaneous (SC) injection site to the Adjacent Lymphoid Tissues (ALTs). ALTs represent the local lymphatic uptake into lymphatics and near nodes. They serve as a local depot for subsequent forwarding of the dose to the lymphatic network. Middle layer: submodel representing the further distribution of the absorbed DcNP from the ALTs to the network of regional lymph nodes (lfet, in organge). Once a fraction of the dose gets to the blood (upper orange arrow), DcNP distributes and eliminates in the connected systemic PBPK (right, in black). Some DcNP can penetrate RES organs and recirculate to the lymphjatic model (lymphatic recirculation, lower orange arrow). The inset scheme from the blood pool displays the mononuclear cell transport via migration of DcNP between blood (PBMC) and lymph nodes (LNMC) and PBMC. Lower layer: submodel of the free drugs. Once the drug detaches from the DcNP, it follows its free drug disposition, which was modeled and described in Part 1. From top to bottom, fluxes of drugs connect the layers. Absorptive fluxes via lymph flow connect the top with the middle DcNP layers; between the DcNP and free submodels, fluxes of drug released from DcNP via drug dissociation in fluids and intracellular degradation. Models built based on non-human primate data (SC and IV experiments).

DcNP Systemic Submodel

The systemic whole-body submodel for DcNP describes the distribution and disposition of DcNP once they get in the blood from the lymphatic system. The systemic submodel is depicted in Fig. 2 (right portion). It is in effect a plasma circulatory model as DcNP size is not expected to be taken up into red blood cells. Blood volumes V_b and blood flows Q_b values for the typical 10 kg NHP can be found in Part 1 tables; they were converted here to plasma volumes V_P and plasma flow Q_P according to the respective formulae V_P = V_B·(1-H) and Q_P = Q_B·(1-H), with H = 0.41 as the NHP hematocrit. There are two types of organs when modeling the distribution of DcNP: RES organs, i.e., those containing the reticuloendothelial system (RES) vs. the non-RES organs.

Figure 2.

Detailed 2D prospective of the DcNP PBPK model layers of Fig. 1. In blue, the DcNP SC submodel. In orange, the whole-body lymphatic network within the Systemic DcNP submodel. In grey, the vascular portion of the PBPK model. Within the vascular system, light blue shading denotes organs of the Reticuloendothelial System (RES). DcNP administered as a series of SC sub-injections in the upper back of a typical NHP is expected to be taken up by ALTs, which serve as a depot for DcNP release into the upper and lower lymphatic systems. As DcNP move through the regional nodes (cervical, axillary, mesenteric, and inguinal), a portion is taken up by the LNMC, while the rest of the dose is borne by the collective lymph flows to the thoracic duct, which is then emptied into the blood circulation (left-right human lymphatic asymmetry ignored). Within the blood circulation, DcNP is preferentially taken into RES-containing organs which allows access back to the lymphatics for recirculation. DcNP flow straight through non-RES organs. Free drug is released from DcNP via spontaneous dissociation in all fluid spaces or flow streams, or via intracellular particle degradation. The red dotted arrows denote exchange of DcNP between LNMC and PBMC migrated into the proximity of individual lymph node.

DcNP averages 52 nm in its largest dimension, so DcNP is not expected to cross the capillary endothelium into the interstitium of most tissues or organs as endothelial pore transport is generally limited to particles with diameters less than 12 nm.^17–19 Hence, during its passage through most organs, DcNP would be restricted to within the capillary plasma stream; we refer to these as being “general” or non-RES organs. This assumption was confirmed in a previous whole-body imaging study after IV injection of similarly formulated gadolinium (Gd)-tagged DcNP in rats, which showed that Gd distribution was confined to the vascular spaces.²⁰ The general organs scheme is shown in Fig. A1 of the Appendix. The rate equation for the general organ is:

$$V_{P,cap}\frac{d{c}_{P,cap}^{\mathit{\text{DcNP}}}}{dt}=Q_P\left(c_A^{\mathit{\text{DcNP}}}-c_{P,cap}^{\mathit{\text{DcNP}}}\right)-k_{\mathit{\text{diss}}}{V}_{P,cap}{c}_{P,cap}^{\mathit{\text{DcNP}}}$$ (1)

with V_P,cap as plasma capillary space volume for the organ, c_A as the feeding plasma artery concentration, and c_P,cap as DcNP concentration in the emergent venous plasma. Drugs carried by DcNP are expected to continuously release from DcNP via dissociation in the capillary plasma space denoted by rate constant k_diss. Such spontaneous off-loading process should occur in all biological fluid spaces; hence, k_diss was assumed to be the same across all body fluid locations, including plasma, lymph, and organ or tissue interstitial spaces. k_diss was initially set to a value obtained from equilibrium dialysis experiments; later, we found it was necessary to adjust its estimation through regression to improve the model fit of the data. The other free drug release mechanism that can conceivably occur is through degradation of the nanoparticles after their internalization into RES cells and mononuclear cells (see later).

Kidneys, liver, and spleen are RES-containing organs. RES is comprised of phagocytic cell types capable of internalizing foreign particles. Also, large fenestrae or rectangular clefts/slits characterize the blood capillary endothelium in the liver (sinuses), spleen (splenic sinuses), and kidneys (glomerulus only), which allow convective transport of colloids from the capillary lumen into the interstitial space. Accordingly, we divided the RES organs into 3 sub-spaces (see scheme in Fig. A1 in the Appendix): namely, microvascular space (sinuses or capillary space), interstitial space (IS), and cell compartment (cell). To represent the movement of drugs from blood to the RES interstitium, we modeled the extravasion of DcNP by a unidirectional flux of DcNP from the vascular lumen to IS (“slit flux”). Extravasation was predicted in-silico using the slit theory for large molecules (see derivation in Appendix, Section 2A). Once translocated into the IS, DcNP should undergo uptake by specialized RES cells, e.g., Kupffer cells in the liver. Parameters for tissue cells entry and exit, k_in,organ and k_out,organ, respectively, were conceived as first-order rate constants to represent the combination of DcNP uptake, cellular trafficking, and recycling back to the IS. Once inside the cytosol, DcNP were assumed to be in part processed resulting in the liberation of free drug as denoted by the rate constant k_deg, which was initially set equal to the dissociation k_diss, and later adjusted by regression. Next, we describe modeling of the liver as an exemplary RES organ for DcNP distribution after IV administration and invite the reader to consult spleen and kidney model details in Appendix 1A.

Liver Model.

Liver sinusoids lack an organized basal lamina and have large, open fenestrae or slits with diameters ranging from 100 to 150 nm. The fenestrae occupy 20% of the sinusoidal surface and are arranged in groups referred to as “sieve plates”. Plasma fluid partitions readily between the sinusoidal lumen and the liver interstitial space (space of Disse). Hence, the fenestrae facilitate the access and exposure of macromolecules (e.g., lipoproteins) and particulates (e.g., liposomes, nanoparticles) to hepatocytes and Kupffer cells. Although endocytic transport of nanoparticles across sinusoidal endothelium could exist, we assume that convection dominates the extravasation process. Exchange across the sinusoidal membrane of hepatocytes is described by transport parameters — ${k_{in,liv}}^{\mathit{\text{DcNP}}}$ and ${k_{out,liv}}^{\mathit{\text{DcNP}}}$ for cell entry and exit, respectively. Once inside the cells, DcNP can undergo degradation (k_deg) or possibly routed toward biliary excretion CL_DcNP. Under these assumptions, we formulated the following rate equations for the liver:

$$\begin{gathered} V_{P,\mathit{\text{sin}},lv}\frac{d{c}_{sin,lv}^{\mathit{\text{DcNP}}}}{dt}=J_{\mathit{\text{portal}}}^{\mathit{\text{DcNP}}}+\left(Q_{P,lvA}\cdot c_A^{\mathit{\text{DcNP}}}\right)-\left(Q_{P,lvV}-Q_{L,lv}\right)\cdot c_{sin,lv}^{\mathit{\text{DcNP}}} \\ -k_{\mathit{\text{diss}}}\cdot V_{P,sin,lv}\cdot c_{sin,lv}^{\mathit{\text{DcNP}}}-Q_{\mathit{\text{slit}},lv}\cdot c_{sin,lv}^{\mathit{\text{DcNP}}} \end{gathered}$$ (2a)

$$\begin{gathered} V_{\mathit{\text{Disse}}}\frac{d{c}_{\mathit{\text{Disse}}}^{\mathit{\text{DcNP}}}}{dt}=Q_{\mathit{\text{slit}},lv}\cdot c_{sin,lv}^{\mathit{\text{DcNP}}}-k_{in,lv}^{\mathit{\text{DcNP}}}\cdot V_{\mathit{\text{Disse}}}{c}_{IS,lv}^{\mathit{\text{DcNP}}}+k_{out,lv}^{\mathit{\text{DcNP}}}\cdot V_{\mathit{\text{cell}},lv}\cdot c_{\mathit{\text{cell}},lv}^{\mathit{\text{DcNP}}} \\ -k_{\mathit{\text{diss}}}\cdot V_{\mathit{\text{Disse}}}\cdot c_{\mathit{\text{Disse}}}^{\mathit{\text{DcNP}}}-Q_{L,lv}\cdot c_{\mathit{\text{Disse}}}^{\text{DcNP}}\cdot \left(1-{\sigma }_L\right) \end{gathered}$$ (2b)

$$\begin{gathered} V_{\mathit{\text{cell}},lv}\frac{d{c}_{\mathit{\text{cell}},lv}^{\mathit{\text{DcNP}}}}{dt}=k_{in,lv}^{\mathit{\text{DcNP}}}\cdot V_{\mathit{\text{Disse}}}\cdot c_{\mathit{\text{Disse}}}^{\mathit{\text{DcNP}}}-k_{out,lv}^{\mathit{\text{DcNP}}}\cdot V_{\mathit{\text{cell}},lv}\cdot c_{\mathit{\text{cell}},lv}^{\mathit{\text{DcNP}}} \\ -k_{deg}\cdot V_{\mathit{\text{cell}},lv}\cdot c_{\mathit{\text{cell}},liv}^{\mathit{\text{DcNP}}}-C{L}_{\mathit{\text{DcNP}}}\cdot c_{\mathit{\text{cell}},lv}^{\mathit{\text{DcNP}}} \end{gathered}$$ (2c)

Subscripts designated the subspace location within the organ; superscripts identified the drug in DcNP. J_portal was the influx of DcNP via the portal blood flow. Given that in our model we included spleen and small and large intestine as portal organs, J_portal consisted of:

$$J_{\mathit{\text{portal}}}^{\mathit{\text{DcNP}}}=Q_{P,sp}\cdot c_{cap,sp}^{\mathit{\text{DcNP}}}+Q_{P,si}\cdot c_{cap,si}^{\mathit{\text{DcNP}}}+Q_{P,li}\cdot c_{cap,li}^{\mathit{\text{DcNP}}}$$ (2d)

with sp, si, and li denoting spleen, small and large intestine. Logically, venous outflow from the liver (lvV) equals the sum of portal flows plus liver artery (lvA) flow, Q_P,lvV = Q_P,lvA.+ Q_P,sp + Q_P,si + Q_P,li; Q_L,lv as the lymph flow from the liver to the thoracic duct. σ_L is the lymphatic reflection coefficient set at 0.3²¹ (so 1 - σL = 0.7). Q_slit,lv was the extravasation flow of DcNP calculated using the slit theory in the Appendix. ${k_{in,liv}}^{\mathit{\text{DcNP}}}$ and ${k_{out,lv}}^{\mathit{\text{DcNP}}}$ were estimated by means of regression.

Lymphatic System in the Systemic DcNP Submodel.

We employed here the same whole-body lymphatic network as described in Part 1 for the free drug model and presented here in Fig. 2 (left portion). Once DcNP reach the blood circulation, their large particle size prevents them from entering the interstitial spaces of most organs or tissues, except for the RES organs which allowed convection of DcNP across their vascular endothelium. Therefore, lymphatic recirculation of DcNP from the organ blood is limited to the liver and kidneys, which accounts for >50% of the lymph flow into the thoracic duct. As per Part 1, the contribution of the spleen to the total lymphatic drainage is minor and therefore ignored. Furthermore, in the absence of complete clarity about the simian lymphatic anatomy, we decided to ignore the anatomical asymmetry in lymph drainage flow between the left and right upper quadrant known to exist in humans. Hence, in the present model scheme right and left side drainage from the cervical and axillary regional nodes are both directed into the thoracic duct. In effect, for IV administration of TLC-ART 101, we expect no uptake of DcNP into all the regional nodes that were sampled because no RES organs drain to the regions singled out in this study. Instead, nodes would be exposed only to free drugs released from DcNP or DcNP transport via mononuclear cell migration (see later). So the contribution of the lymphatic recirculation of DcNP through lymph formation in RES organ can be seen in the thoracic duct equation (IV case):

$$\begin{gathered} V_{td}\frac{d{c}_{td}^{\mathit{\text{DcNP}}}}{dt}=Q_{L,kid}\cdot c_{lS,kid}^{\mathit{\text{DcNP}}}\cdot \left(1-{\sigma }_L\right)+Q_{L,lv}\cdot c_{\mathit{\text{Disse}}}^{\mathit{\text{DcNP}}}\cdot \left(1-{\sigma }_L\right) \\ -Q_{td}\cdot c_{td}^{\mathit{\text{DcNP}}}-k_{\mathit{\text{diss}}}\cdot V_{td}\cdot c_{td}^{\mathit{\text{DcNP}}} \end{gathered}$$ (3)

with td for the thoracic duct as the body lymph collector and Q_L,organ for the lymphatic outflow from the contributing organs. Eq. 3 was informed by the IV administration of TLC-ART 101.

Mononuclear Cell Migration.

We suggested the possibility of direct exchange of DcNP between blood and the lymph node bypassing the lymphatic recirculation. This direct passage could occur through migration of specialized immune cells, such as the peripheral blood mononuclear cells (PBMC). In fact, the majority of mononuclear cells in lymph nodes come directly from the blood through lymphocyte migration across the walls of specialized postcapillary venules which are located in the paracortex (T-lymphocyte areas) of the node, also called high endothelial venules (HEV). HEV serves as an efficient portal that enables T-cells to circumvent long migration distances through the lymphatic recirculation and access lymph nodes rapidly to maintain close surveillance and promptly set off a needed response to an antigen. Note that because less than 10% of the lymphocytes arrive in lymph nodes through carriage by lymph flow from the organs, we decided to ignore such a migration contribution.^22–24 Because DcNP are known to concentrate in mononuclear cells likely via endocytosis or transcytosis uptake, a significant supply of DcNP to lymph nodes may be mediated by cell trafficking that is especially of importance following an IV administration. Thus, in our model, we assume that the trafficking of PBMC in and out of the lymph nodes allows the exchange of DcNP-drug between blood and LNMC (“blood-lymph barrier”). Using the rate constants representing blood monocyte exchange with nodes previously reported by Ganusov et al.,²⁵ we modeled DcNP exchange between PBMC and LNMC. The model depicted in Fig. A2 in the Appendix represents the blood-lymph node transport of DcNP mediated by the exchange of mononuclear cells via the lymph-plasma barrier. The PBMC-to-lymph node rate constant k_in,migr,i, embodies the region or location-specific time-delay in cell migration into the nodes in a manner presumably driven by local immune requirements. Because the mean estimated residence times of T-cells in superficial and visceral lymph nodes were found to be similar (9.9 h),²⁵ the exit rate constant from LNMC k_out,migr, was set to a uniform value across nodes. The PBMC equation is given by:

$$\begin{gathered} V_{\mathit{\text{PBMC}}}\frac{d{c}_{\mathit{\text{PBMC}}}^{\mathit{\text{DcNP}}}}{dt}=k_{in,\mathit{\text{PBMC}}}^{\mathit{\text{DcNP}}}\cdot V_P\cdot c_P^{\mathit{\text{DcNP}}}-k_{out,\mathit{\text{PBMC}}}^{\mathit{\text{DcNP}}}\cdot V_{\mathit{\text{PBMC}}}\cdot c_{\mathit{\text{PBMC}}}^{\mathit{\text{DcNP}}}-k_{deg}\cdot V_{\mathit{\text{PBMC}}}\cdot c_{\mathit{\text{PBMC}}}^{\mathit{\text{DcNP}}} \\ -\sum _i{k}_{in,\mathit{\text{migr}},i}\cdot V_{\mathit{\text{PBMC}}}\cdot c_{\mathit{\text{PBMC}}}^{\mathit{\text{DcNP}}}+\sum _i{k}_{out,\mathit{\text{migr}}}\cdot V_{\mathit{\text{LNMC}},i}\cdot c_{\mathit{\text{LNMC}},i}^{\mathit{\text{DcNP}}} \end{gathered}$$ (4)

V_PBMC is the PBMC volume set at 1% of the whole blood volume. $k_{in,\mathit{\text{PBMC}}}^{\mathit{\text{DcNP}}}$ and $k_{out\text{,}\mathit{\text{PBMC}}}^{\mathit{\text{DcNP}}}$ are the DcNP influx-and-efflux rate constants between PBMC and plasma ($k_{in,\mathit{\text{PBMC}}}^{\mathit{\text{DcNP}}}$ was initially set to PBMC in vitro uptake rates to guide regression). The subscript “i” denotes the lymphatic region (cervical, hilar, axillary, mesenteric and inguinal). It should be noted that PBMC is featured as a distinct cellular compartment within the circulating venous plasma. Migration parameters were identified by the IV administration of TLC-ART 101.

DcNP SC Submodel

According to the scheme depicted in Fig. 1, the top layer was the submodel representing the absorption of DcNP from the SC space. As further elaborated in Fig. 2, the presystemic absorption pathways consisted of: (i) SC injection site compartment which accommodated the input dose; (ii) two adjacent-to-injection lymphoid tissue (ALT) compartments serving to relay the DcNP SC dose to the upper and lower lymphatic system; (iii) lymph flow paths connecting ALTs to regional lymph nodes compartments (dashed arrows in Fig. 2); (iv) the parallel set of regional nodes; and (v) collection of lymph out-flows from the regional nodes into the thoracic duct and subsequent dump of DcNP into the venous pool. SC submodel parameters are reported in Table 1 and A1 in the Appendix. The SC dose transfer from SC to ALT was described in flow terms Q_ALT1 and Q_ALT2 as:

$$V_{SC}\frac{d{c}_{SC}^{\mathit{\text{DcNP}}}}{dt}=-Q_{ALT1}{c}_{SC}^{\mathit{\text{DcNP}}}-Q_{ALT2}{c}_{SC}^{\mathit{\text{DcNP}}}$$ (5)

with the uptake rate to the two ALTs split equally as $Q=0.5{k_{sc}}^{\mathit{\text{DcNP}}}\cdot V_{SC};V_{SC}$ denoted the SC injection site and it was posed equal to the injection volume of 10 ml, and ${k_{sc}}^{\mathit{\text{DcNP}}}$ was estimated from the SC absorption data obtained in an earlier ICG-tagged nanoparticle imaging study in mice.¹⁰ ALTs represented a modeling maneuver to reconcile our observations of the rapid disappearance of DcNP suspension from the SC injection site and relatively slow uptake into the regional nodes. It posits an in-between compartment that would buffer the fast DcNP uptake from the SC injection site into the lymphatics without overwhelming the regional lymph nodes. We assumed the two ALTs have structures similar to lymph nodes as depicted in Fig. A1 in the Appendix, i.e., it consists of a sinusoid and cellular space. Accordingly, the mass transport equations for ALT1 were:

$$\begin{array}{l}{F}_{\mathit{\text{sin}}}\cdot V_{ALT1}\frac{d{c}_{ALT1,\mathit{\text{sin}}}^{\mathit{\text{DcNP}}}}{dt}\\ =Q_{ALT1}{c}_{SC}^{\mathit{\text{DcNP}}}-Q_{Sc,cer}\cdot c_{ALT1,\mathit{\text{sin}}}^{\mathit{\text{DcNP}}}-Q_{Sc,axi}\cdot c_{ALT1,\mathit{\text{sin}}}^{\mathit{\text{DcNP}}}\\ -k_{in,\mathit{\text{cell}}}^{\mathit{\text{DcNP}}}\cdot F_{\mathit{\text{sin}}}\cdot V_{ALT1}\cdot c_{ALT1,sin}^{\mathit{\text{DcNP}}}+k_{out,\mathit{\text{cell}}}^{\mathit{\text{DcNP}}}\cdot F_{\mathit{\text{cell}}}\cdot V_{ALT1}\cdot c_{ALT1,\mathit{\text{cell}}}\end{array}$$ (6a)

$$\begin{gathered} F_{\mathit{\text{cell}}}\cdot V_{\text{ALT1}1}\frac{d{c}_{ALT\text{1,}\mathit{\text{cell}}}^{\mathit{\text{DcNP}}}}{dt}=k_{in\text{,}\mathit{\text{cell}}}^{\mathit{\text{DcNP}}}\cdot F_{sin}\cdot V_{ALT1}\cdot c_{ALT\text{1,}sin}^{\mathit{\text{DcNP}}}-k_{out\text{,}\mathit{\text{cell}}}^{\mathit{\text{DcNP}}}\cdot F_{\mathit{\text{cell}}}\cdot V_{ALT1}\cdot c_{ALT1,\mathit{\text{cell}}}^{\mathit{\text{DcNP}}} \\ -k_{deg}\cdot F_{\mathit{\text{cell}}}\cdot V_{ALT1}\cdot c_{ALT1,\mathit{\text{cell}}}^{\mathit{\text{DcNP}}} \end{gathered}$$ (6b)

As mentioned, ALT1 is the source buffer for the upper lymphatic system distribution, therefore forwarding part of the dose to the cervical and axillary regions. For ALT2 equations refer to Appendix. The ALT-to-regional flows, namely Q_sc,cer and Q_sc,ax, were extrapolated from previously reported disappearance kinetics of subcutaneously injected ¹³¹I-albumin site factoring in the anatomical distances between the NHP back and each regional basin.^26–30 ALT’s volumes V_ALT were assumed to be 5% (1.8 ml) of the total lymphatic system volume, like the ratio of skin-to-body weight. Fs are volumetric fractions of the sinusoid and cellular space as reported in lymph nodes.³¹ The sinus-to-cell exchange rate constants — $k_{in,\mathit{\text{cell}}}^{\mathit{\text{DcNP}}}$ and $k_{out\text{,}\mathit{\text{cell}}}^{\mathit{\text{DcNP}}}$ were set initially equal to the LNMC/PBMC influx and efflux rate constants and later regressed to achieve a better fit of the data, if necessary.

Table 1.

Key Pharmacokinetic Parameter Estimates for the DcNP Portion of the Whole-body PBPK Model.

DcNP Systemic Submodel	Lopinavir	Ritonavir	Tenofovir
kdiss (1/min)a	0.030	0.061	1.0 × 10−4
kdeg (1/min)a	12 × 10−4	12 × 10−4	1.0 × 10−4
kin,liver (1/min)b	0.90	0.90	0.90
kout,liver (1/min)b	0.0011	0.0011	0.0011
kin,spleen (1/min)b	0.90	0.90	0.90
kout,spleen (1/min)b	0.0011	0.0011	0.0011
kin,kidney (1/min)b	0.90	0.90	0.90
kout,kidney (1/min)b	0.0011	0.0011	0.0011
kin,PBMC (1/min)b	7.0 × 10−4	7.0 × 10−4	0.8 × 10−5
kout,PBMC (1/min)b	1.0 × 10−4	1.0 × 10−4	5.0 × 10−4
CLDCNP (ml/min)b	0.60	0.60	0.010
kin_migr,i (1/min)c	35–320 × 10−4	35–320 × 10−4	35–320 × 10−4
kout_migr (1/min)	34 × 10−4	34 × 10−4	34 × 10−4
DcNPSC Submodel	Lopinavir	Ritonavir	Tenofovir
ksc (1/min)	33 × 10−4	33 × 10−4	33 × 10−4
kdiss (1/min)a	0.030	0.061	1.0 × 10−4
kdeg (1/min)a	12 × 10−4	12 × 10−4	1.0 × 10−4
kinATL1,LNMC (1/min)d	0.011	0.011	0.16 × 10−4
koutATL1,LNMC (1/min)d	11 × 10−5	18 × 10−5	0.50 × 10−3
kin,LNMC (1/min)	7.0 × 10−4	7.0 × 10−4	0.80 × 10−5
kout,LNMC (1/min)	1.0 × 10−4	1.0 × 10−4	5.0 × 10−4

All regression estimates had precision CV<40%. More PBPK parameter estimates are presented in Table A1 in the Appendix. Note that in the text all DcNP parameters have ‘DcNP’ superscripts to distinguish them from parallel free drug processes.

^aParameter from pooled regression of IV and SC experiments.

^bParameter from regression of IV experiments.

^cGiven as range across the sampled regions (minimum: hilar nodes; maximum: axillary nodes), see Appendix for individual node values.

^dParameter from regression of SC experiments.

As an example, the rate equations for the axillary lymph node are presented below:

$$\begin{gathered} F_{sin}\cdot V_{LN}\frac{d{c}_{LN,sin}^{\mathit{\text{DcNP}}}}{dt}=Q_{sc,axi}\cdot c_{ALT1,sin}^{\mathit{\text{DcNP}}}-Q_{axi}\cdot c_{LN,sin}^{\mathit{\text{DcNP}}}-k_{in,\mathit{\text{LNMC}}}^{\mathit{\text{DcNP}}}\cdot F_{sin}\cdot V_{LN}\cdot c_{LN,sin}^{\mathit{\text{DcNP}}} \\ +k_{out,\mathit{\text{LNMC}}}^{\mathit{\text{DcNP}}}\cdot F_{\mathit{\text{LNMC}}}\cdot V_{LN}\cdot c_{LN,\mathit{\text{LNMC}}}^{\mathit{\text{DcNP}}}-k_{\mathit{\text{diss}}}\cdot F_{sin}\cdot V_{LN}\cdot c_{LN,sin}^{\mathit{\text{DcNP}}} \end{gathered}$$ (7a)

$$\begin{gathered} F_{\mathit{\text{LNMC}}}\cdot V_{LN}\frac{d{c}_{LN,\mathit{\text{LNMC}}}^{\mathit{\text{DcNP}}}}{dt}=k_{in,\mathit{\text{LNMC}}}^{\mathit{\text{DcNP}}}\cdot F_{sin}\cdot V_{LN}\cdot c_{LN,sin}^{\mathit{\text{DcNP}}}-k_{out,\mathit{\text{LNMC}}}^{\mathit{\text{DcNP}}}\cdot F_{\mathit{\text{LNMC}}}\cdot V_{LN}\cdot c_{LN,\mathit{\text{LNMC}}}^{\mathit{\text{DcNP}}} \\ -k_{deg}\cdot F_{\mathit{\text{LNMC}}}\cdot V_{LN}\cdot c_{LN,\mathit{\text{LNMC}}}^{\mathit{\text{DcNP}}}+k_{in,\mathit{\text{migr}},ax}\cdot V_{\mathit{\text{PBMC}}}\cdot c_{\mathit{\text{PBMC}}}^{\mathit{\text{DcNP}}} \\ -k_{out,\mathit{\text{migr}}}\cdot F_{\mathit{\text{LNMC}}}\cdot V_{LN}\cdot C_{LN,\mathit{\text{LNMC}}}^{\mathit{\text{DcNP}}}\cdot \end{gathered}$$ (7b)

Note that Eq. 7b for the lymph node LNMC fraction includes terms that encompass DcNP-drug exchange via the trafficking of PBMC into regional lymph nodes. A remainder pathway was also conceived for mass balance accounting (Fig. 2), which is arbitrarily assumed to arise from ALT2. In fact, if a fraction of the dose crossing the lymphatyic system is not gauged by set of nodes we collected, we could miss it. The remainder pathway features a series of delay compartments that helped to better fit the slow terminal phase which was evident in the plasma concentration-time profiles (see Appendix, Section 3A for Equations).

The complete thoracic duct equation below shows the collection of DcNP-enriched lymph from the SC injection and subsequent emptying into the plasma; it is composed of Eq. 3 recirculation terms plus the fluxes coming from each contributing regional node and the remainder lymphatic pathway (SC case):

$$\begin{gathered} V_{TD}\frac{d{c}_{TD}^{\mathit{\text{DcNP}}}}{dt}=Q_{L,kid}\cdot c_{IS,kid}^{\mathit{\text{DcNP}}}\cdot \left(1-{\sigma }_L\right)+Q_{L,lv}\cdot c_{\mathit{\text{Disse}}}^{\mathit{\text{DcNP}}}\cdot \left(1-{\sigma }_L\right)-Q_{td}\cdot c_{td}^{\mathit{\text{DcNP}}} \\ -k_{\mathit{\text{diss}}}\cdot V_{TD}\cdot c_{td}^{\mathit{\text{DcNP}}}+Q_{cer}\cdot c_{cer,sin}^{\mathit{\text{DcNP}}}+Q_{axi}\cdot c_{axi,sin}^{\mathit{\text{DcNP}}}+Q_{me}\cdot c_{me.sin}^{\mathit{\text{DcNP}}} \\ +Q_{ing}\cdot c_{ing,sin}^{\mathit{\text{DcNP}}}+C{L}_w{w}_4 \end{gathered}$$ (8)

, with CL_w, and w₄ as the parameters representing flux coming from the last of the delay compartments in the remainder pathway (see Appendix, Section 3A).

Parameter Estimation And Sensitivity Analysis

Model assembly along with parametric estimation was implemented in MATLAB (Release 2020a, The MathWorks, MA). The parameters estimated through regression included the rate constants for dissociation of free drugs from DcNP in circulating plasma and interstitial or lymphatic fluid k_diss, for intracellular degradation of the particle with subsequent liberation of drugs k_deg, for cellular uptake and release of DcNP in tissue $k_{in,\mathit{\text{organ}}}^{\mathit{\text{DcNP}}}$ and $k_{out,\mathit{\text{organ}}}^{\mathit{\text{DcNP}}}$, and plasma-to-PBMC exchange of DcNP $k_{in,\mathit{\text{PBMC}}}^{\mathit{\text{DcNP}}}$ and $k_{out,\mathit{\text{PBMC}}}^{\mathit{\text{DcNP}}}$ These parameters were estimated by regression fit of the model to the time-course of total drug concentrations in plasma, tissues, and lymph node homogenates from IV experiments with TLC-ART 101. Since we had just the total (free plus DcNP-associated) drug concentration measurements, to ensure identifiability of k_diss and k_deg we guided their regression search by setting the initial guess estimates to values derived from in vitro experiments. k_diss was set to the dissociation rate observed during equilibrium dialysis of DcNP; k_deg was set equal to k_diss in absence of experimental information. SC data were further leveraged to identify additional parameters for the absorption phase: LNMC uptake and release kinetic parameters $k_{in,\mathit{\text{cell}}}^{\mathit{\text{DcNP}}}$ and $k_{out\text{,}\mathit{\text{cell}}}^{\mathit{\text{DcNP}}}$ in ALTs, and the delayed kinetics in the remainder pathway.

Goodness of regression fit was evaluated by visual inspection of the model predicted time course of drug concentrations vs. the observed data. Then an analysis of the weighted residual was carried out (not shown). The overall goodness-of-fit was measured by the R-squared metric and deemed acceptable when R² >0.85.

Model estimates were then subjected to structural sensitivity analysis; only local sensitivity analysis was feasible as global sensitivity analysis was too onerous to attempt due to the rather complex structure of the model. More details are presented in Appendix 4A. As a form of validation, the present model (built upon single-dosing) was challenged in its ability to predict time course of plasma drug concentrations for an unpublished multiple-dosing study in NHP where TLC-ART 101 was given weekly or biweekly (data in preparation to be published).

Results

The present PBPK model was able to adequately account for the time-course of drug concentrations in plasma, PBMC, critical organ/tissue (liver, kidney, and spleen), and regional lymph nodes (homogenate and LNMC), achieving R²>0.86 in all cases. Visual comparisons of model predictions versus observed data are presented in Figs. 3 and 4 (and Fig. A6). The available preclinical dataset was sufficiently diverse and rich to allow reasonably good model regression fits and afford satisfactory estimation of the unknown adjustable parameters with reasonable precision (CV<40%).

Figure 3.

PBPK model fit to observed plasma and mononuclear cell (PBMC and LNMC) data for a single SC Dose of TLC-ART 101 in non-human primates: Lopinavir (25 mg/kg), Ritonavir (7.2 mg/kg), and Tenofovir (14.1 mg/kg). Upper Panel: Model predicted (solid) vs. observed plasma concentration-time points (white circles) for each antiviral over 2-week course of study. For lopinavir, we reported its 0–24 h profile as an insert. Mid Panel: Peripheral Blood Mononuclear Cells (PBMC) model predicted (solid) vs. observed PBMC time points (white down-pointing triangles) for each antiviral over 2 weeks; Lower Panel: Model predictions for axillary Lymph Node Mononuclear Cells (LNMC) (solid) vs. observed data at 24 and 192 hr for each drug (white squares). Model predicted time-courses of total drug concentration (DcNP-associated plus free) are plotted as solid lines. Model-predicted free drug concentration-time courses are plotted as dashed lines. In cells, free drug concentrations represent those of the active TFV diphosphate (TFV-dp).

Fig. 4.

PBPK model fit to observed lymph node data for a single SC Dose of TLC-ART 101 in non-human primates: Lopinavir (25 mg/kg), Ritonavir (7.2 mg/kg), and Tenofovir (14.1 mg/kg). First Panel: model prediction of DcNP in the subcutaneous injection site for each antiviral throughout the 2-week course of study. ALTs stand for Adjacent-to-Injection Lymphoid Tissues: ALT1 relay the dose to the upper lymphatic system (cervical and axillary regions), and ALT2 relay the dose to the lower lymphatic system (mesenteric and inguinal regions). Mid Panels: Model predicted (solid) vs. observed lymph node tissue homogenates time points collected at 24, 96, and 336 h for each drug (white squares with a cross). Model predictions of total drug concentrations for LNMC in solid black lines are based on sub-division of the node into the sinus and cell compartments. Grey dashed lines represent model predictions of free drug concentrations (TFV as TFV-dp) in LNMC of each node region. Bottom Panel: Model predictions of the time course of thoracic duct drug concentrations for each drug: solid lines represent the total drug concentration (DcNP-associated plus free), and dashed lines represent the free drug.

Systemic Pharmacokinetics of DcNP

Distribution.

Insights into the distribution of DcNP in NHP tissues were garnered mostly through the IV study. Modeling of organ distribution was guided mainly by the hypothesis that during passage through general organs DcNP are restricted to the blood capillary space, whereas they can get across the vascular endothelium within RES organs and allow their penetration into RES parenchyma. Based upon these assumptions, the systemic distribution model was able to provide a good fit of the observed data for all three antiretrovirals in both plasma and RES organs after IV injection of TLC-ART 101 (R²>0.88, Fig. A4 in Appendix). Sensitivity analysis on the final IV model revealed that a key parameter is the dissociation k_diss governing the stability of drugs association with circulating nanoparticles. Also, after IV injection plasma PK of DcNP was largely controlled by events in the liver, namely the parameters for liver cells uptake and intracellular degradation parameters, $k_{in,lv}^{\mathit{\text{DcNP}}}$ and k_deg (Fig. A1). This result was not surprising as the liver is estimated to harbor 90% of the functioning cells for the entire RES.³² In comparison, the liver’s influence on the DcNP PK was much attenuated following SC administration, in which case the absorption process and transit through the lymphatic system had more control over the systemic PK (See later). Interestingly, the same estimates of k_in and k_out (0.9/min and 0.0011/min, respectively, Table 1) applied across RES tissues and across drugs, suggesting an apparent kinetic similarity in transport of DcNP within the RES tissues.

Drug Release from DcNP.

We conceived of two modes by which the antiviral drugs can be liberated from DcNP: spontaneous dissociation in fluid medium denoted by k_diss, and degradation of the nanoparticles by intracellular mechanisms denoted by k_deg. Estimates of k_diss for the two PIs were similar in magnitude — 0.03 and 0.06/min for LPV and RTV (and very close to in vitro dialysis rates), respectively, while it was much lower for TFV 1.0 × 10⁻⁴ (Table 1). A lower spontaneous dissociation rate of TFV from DcNP in body fluids was consistent with our previous notion that TFV is rendered very stable in vivo when formulated in DcNP.¹⁰ Degradation should occur within the cellular compartments of RES organs, in PBMC, and LNMC. Just as in the case of dissociation, the degradation parameter k_deg was 12 × 10⁻⁴/min for PIs versus 1.0 × 10⁻⁴/min for TFV, a 12-fold slower degradation process for TFV (Table 1). This result suggests that the cellular processing rate of DcNP may vary depending on the associated drug.

DcNP and Drug Elimination.

There are two possible ways drugs associated with DcNP can be eliminated: after their release from DcNP to then follow the elimination fate of individual free drug (i.e., PIs via metabolism and TFV via renal excretion, see Part 1); and via biliary excretion of DcNP in the liver. To evaluate the disposition fate of the DcNP dose quantitatively, we performed a single dose simulation of the IV systemic submodel over a very long period (6 months); the simulations revealed that for all three antivirals more than 90% of the dose was eliminated as free drug following its release from DcNP. Regarding the mode of release, 70% of the DcNP dose degraded intracellularly, while 20% was released through dissociation, mostly in the plasma. Less than 10% of the dose underwent an unspecific excretion from the liver (see CL_DcNP reported in Table 1), the addition of which improved the model fit only in the IV case.

PBMC Concentrations.

In PK studies of HIV therapy and prevention, drug concentrations in PBMC are taken as a biomarker for achieving effective levels at the target lymphocytes. Data from the IV study were used to identify the kinetic parameters for plasma-PBMC exchange of DcNP-associated drugs: $K_{in,\mathit{\text{PBMC}}}^{\mathit{\text{DcNP}}}$ and $K_{out,\mathit{\text{PBMC}}}^{\mathit{\text{DcNP}}}$. For PIs, $k_{in,\mathit{\text{PBMC}}}^{\mathit{\text{DcNP}}}$ was generally higher than $k_{out,\mathit{\text{PBMC}}}^{\mathit{\text{DcNP}}}$, indicating a net transport of DcNP into the cells, whereas for TFV, it was the opposite (Table 1). PBMC transport parameters estimated from the IV study applied well to modeling for the SC route. As shown in Fig. 3, model predictions of PBMC concentrations over time matched the observed data well with a high R²>0.91. In addition, PBMC-derived transport parameter estimates also apply well to DcNP exchange between lymph node sinus and LNMC as we got acceptable model predictions of LNMC data at the two available time-points (Fig. 3). We also introduced the novel concept of a supplemental source of DcNP for the LNMC owing to a likely migration of PBMC (carrying DcNP) into the regional lymph nodes, thus becoming LNMC. Without this additional mechanism, the PBPK model prediction was not able to match the lymph node data from the IV study: there was a gross underprediction by two orders of magnitude. The incorporation of Ganusov’s lymphocyte migration model into our system helped to shift more DcNP from the systemic circulation to the lymph nodes. In summary, our semi-empirical static cell-trafficking modeling strategy worked well in affording a satisfactory model fit of both the PBMC and LNMC data.

Subcutaneous Pharmacokinetics of DcNP

In our earlier MBPK modeling, we showed that plasma PK of TLC-ART 101 following a SC injection was largely governed by first-pass sequestration and transit of DcNP through the lymphatic system.¹⁰ As depicted in Fig. 2, the lymphatic first-pass consisted of a multi-step process starting with DcNP uptake from the SC injection site into the surrounding lymphatic basins (ALTs), followed by distribution into regional nodes throughout the body. As evidenced by the good model fit (R²>0.9) to the available lymph node homogenate and isolated mononuclear cell data shown in Fig. 3 (axillary LNMC) and Fig. 4 (homogenate and LNMC for the rest of the nodes), the proposed design of the lymphatic system worked well in describing the sequential transfer of the injected dose from SC site to the lymphatic system and then onto the circulating blood.

Dose Uptake and Routing to Regional Nodes.

Following a relatively fast and complete uptake of DcNP from the SC injection site, the dose was postulated to drain into two local lymphatic basins referred to as Adjacent Lymphatic Tissues (ALT1 and ALT2), which in turn route the collected amount of DcNP into the upper and lower lymphatic system, respectively. From the sensitivity analysis, ALT parameters were key in influencing thoracic duct and plasma AUCs (Fig. A3); their regression estimates confirmed the rate-limiting role of ALTs in the presystemic absorption kinetics of DcNP. Consisting of depot kinetics, k_in,ALTs were much higher than k_out,ALTs (Table 1). While k_ALTs were ini tially set equal to mononuclear cells uptake rates $k_{in,\mathit{\text{LNMC}}}^{\mathit{\text{DcNP}}}$, major adjustment was observed during regression; final regression estimates of the uptake rate constant for the PIs were about 15-folds higher than the initial guess estimate, while the upward adjustment for TFV was about 2-folds. On the contrary, upon regression k_out,ALTs were reduced by 11-folds compared to k_out,LNMCs for PIs, while it was relatively unchanged for TFV. This suggested that the ALTs have a higher holding capacity than a typical visceral node region, serving as a critical controller of the long-acting plasma kinetics. Interestingly, previously noted differences in mononuclear cell transport parameters between PIs and TFV are also observed for the ALT parameters. Model simulations focused on the early part of the SC absorption phase showed that an entire dose left the SC injection site by day 2 (Fig. 4), while ALTs still held 24% of PI doses at 2 weeks after injection (12% in each ALT). By running model simulations further out beyond 2 weeks, PIs in the ALT depot finally emptied out after 18 weeks from the injection. In the case of TFV, similar disappearance kinetics from the SC injection site was observed, whereas ALTs emptied of TFV after 10 days after injection while maintaining a long-acting feature in the plasma due to TFV stability in the particle (Fig. 4).

Distribution in the Lymphatic System.

ALT depots served to relay the absorbed dose to the rest of the lymphatic regions in the body. Earlier on, we did consider the scenarios where the dose was introduced directly into the regional lymph node compartments from the SC injection site; in that scenario, the predictions were unacceptably high compared to the observed lymph node concentrations (except for the pulmonary hilar region). This led to our working hypothesis that an intermediary arrangement (as depicted in Fig. 2) is needed between the SC injection site and the regional nodes to accommodate to asynchronous PK of DcNP at the injection site and the regional lymph nodes.

According to our modeling, antiviral distribution into the lymphatic system had multiple contributors. Following an IV injection, drug concentration in nodes come from the recirculating free drug (25%) and DcNP borne by migrating PBMC (75%). On the other hand, following an SC injection, lymph nodes received majority of the drug as DcNP from the SC injection site via the SC lymphatic network (90%), PBMC-to-LNMC migration as DcNP (5%), and lymphatic recirculation via RES organs as free drugs (<5%). By comparing node homogenate concentrations between IV and SC concentration at 96 h after dosing (Fig. A5 in Appendix), a generally equal-to-higher lymphatic concentration was achieved after SC than IV administration. Especially noteworthy was the spike in drug concentrations and node-to-plasma ratio observed in the axillary nodes for all three antivirals compared to the other sampled nodes (Fig. A5), which is likely due to the proximity of the axilla to the injection site and consistent with our idea of regionality discussed in Part 1.

PK of DcNP-Associated and Free Drug Species.

The measured drug concentrations in the plasma, tissues and cells from the TLC-ART 101 studies were the total concentrations of DcNP-associated and free species. Presently, the two species are not separable or distinguishable analytically, so we had to resort to model predictions of individual drug species as depicted in Figs. 3 and 4. Computing the AUC (to infinity) ratio of the predicted free drug time-courses to the total fitted time-course for each drug following SC administration, free LPV constituted in average 22% of total plasma LPV, free RTV was 35% of total plasma RTV, and free TFV was 6.5% of total plasma TFV (Table 2). Analyzing the release fluxes over time, the free drug species in the plasma, after a SC administration, mostly came from intracellular degradation of DcNP in the lymphatic system with a lesser contribution of DcNP dissociation in the plasma. RES organ contribution in increasing the free levels in the plasma, in the SC case, was not significant. In PBMC, free drugs derived mostly from internal DcNP degradation, along with a minor contribution from equilibration of free drugs between plasma and PBMC. PBMC-to-plasma AUC ratios of the free drugs ranged between 0.34 to 1.1 for PIs, while it was 0.49 for TFV. Free drugs in LNMC almost entirely came from local degradation of DcNP (>98%) rather than from lymphatic recirculation. As reported in Table 2, the free LPV LNMC-to-plasma AUC ratio spanned from 2.4 (hilar node) to 3.6 (axillary node). Free RTV in LNMC was 5 to 7.2-fold higher than plasma. Free TFV was 1.2 (hilar) and 3.4 (axillary) higher in LNMC than plasma (Table 2). In comparing concentrations of the free species in mononuclear cells, the LNMC-PBMC ratio revealed that PI had to 4.5- to 10-fold higher free drug concentrations in LNMC than in PBMC. Also, intracellular concentration of TFV-dp active metabolite was 4.3- to 13-fold higher in LNMC than PBMC (Table 2). In summary, according to our modeling predictions, a constant and enhanced lymphatic targeting could be achieved also for the DcNP-unbound species.

Table 2.

Free drug exposure following a single SC administration of TLC-ART 101 as predicted by the PBPK model and expressed in terms of AUC_0-inf ratio.

	Free plasma/Total plasma	Free PBMC/Free plasma	Free LNMC/Free plasma	Free LNMC/Free PBMC
Lopinavir	22%	0.34	2.4–3.6	6.8–10
Ritonavir	35%	1.1	5.0–7.2	4.5–6.5
Tenofovir	6.5%	0.49a	1.2–3.4a	4.3–13b

Free: drugs released from DcNP by dissociation and degradation of DcNP. Ranges as min-max; min is hilar region; max is axillary region. Total = free + associated.

^a(TFV + TFV-monophosphate + TFV-diphosphate)/TFV.

^bTFV-diphosphate/TFV-diphosphate.

Discussion

Herein, we have presented a novel whole-body PBPK model for the lipid nanoparticle system carrying a combination of LPV-RTV and TFV intended for HIV long-acting therapy. The modeling effort has proven valuable in improving our biological understanding of DcNP disposition in the NHP and guiding the early phases of clinical development of TLC-ART 101 within the regulatory framework. The model will serve also as a tool to support the further development of DcNP-based new formulations given the demonstrated DcNP flexibility of swapping or adding new drugs.^7,9,12,33

The final PBPK model for each of the antiviral drugs in TLC-ART 101 consists of three distinct components or submodels. The first is the subcutaneous submodel (DcNP SC submodel, Fig. 1) that tracks DcNP absorption from the SC injection site to the adjacent lymphoid tissues (ALT) which serves as a depot in relaying the injected dose to regional lymph nodes. After traversing a large part of the lymphatic network, drugs associated with the nanoparticles are emptied into the blood circulation; by this point, DcNP have entered the second component of the PBPK model — the Systemic submodel, which features systemic distribution of DcNP into RES organs and subsequent processing including clearance through degradation and excretion as well as return to the lymphatics. The third submodel (bottom layer of the 3D model in Fig. 1) accounts for the disposition of free drugs liberated from DcNP either through spontaneous dissociation and intracellular degradation of the nanoparticles. The free drug submodel was presented in Part 1. The three PBPK layers were constructed in sequence: beginning with the free drug submodel based on data gathered from the studies with the free drug mixture (Part 1), then the systemic submodel based upon data collected from the IV DcNP study, and finally the subcutaneous submodel (along with parts of the lymphatics) that utilize datasets from both IV and SC studies. The modeling exercise managed to leverage all the available preclinical data in constructing a powerful in-silico tool that offers an integrative understanding of the biological fate of DcNP and predictions on the product’s clinical utilization and performance.

Our knowledge regarding the PK of TLC-ART 101 and more generally that of DcNP was gained through a stepwise process. We began with a series of PK experiments in NHP that led to the development of mechanism-based compartmental models (i.e., the MBPKs),^7,10,14 through which we arrived at the crucial working hypothesis that DcNP form a drug depot in the lymphatic system rather than in the injection site as it is featured in most of the long-acting injectables in development (e.g., ref³⁴). We previously conducted a fluorescence-imaging study with indocyanine green (ICG) tagged lipid nanoparticles (i.e., labeled empty DcNP) in mice to provide detailed information on the distributive kinetics of DcNP across the lymphatic network following SC injection in the hind paw (ref³⁵ and unpublished material). Injected ICG-DcNP were quickly and exclusively taken up by lymphatics. Over 24 h, gradual and eventual complete disappearance of fluorescence at the SC site was observed along with the appearance of fluorescence first in nearby nodes (i.e., popliteal, and sciatic) and then upstream successively in the ileac, lumbar, and axillary lymph nodes. This sequestration-release process occurs sequentially along the vertical chain of nodes to the collecting thoracic duct, where fluorescence was first detected only after a few hours after SC injection. This study led to the idea of a sequential transport of the dose from one node to the next along a chain. Hence, if ICG-DcNP in the mouse serves as a reasonable model for passage of DcNP through the lymphatics of NHP, uptake and distribution of DcNP along the lymphatic network should be quick and efficient, at least initially adjacent to the injection site. However, in higher mammals, where the lymphatic architecture is in the form of a complex network, mouse model is a rather simplistic reference. In view of this physiologic reality, we decided to adopt a physiological approach in modeling the transit of DcNP through the lymphatic system as a parallel set of linear or sequential nodal pathways which suits the typical PBPK compartmental design. Future refinement of this aspect of our PBPK model may be necessary for its application to other similar nanoparticle drug delivery system.

There are several modeling constraints, simplifications, and assumptions worth mentioning. We elected to go with a simple, single-step process for uptake of DcNP from the subcutaneous injection site based on the earlier ICG-DcNP imaging-data; the same was assumed in the earlier MBPK2 modeling.¹⁰ The SC space is a very complex environment, with oncotic and convective flows balancing the interstitial fluid volume and solute content. When an abrupt injection inserts an external volume, homeostatic forces act to restore the interstitial environment. The many factors affecting local absorption are generally due to extracellular matrix hindrance, external forces (e.g., operator massaging), and nanoparticle properties. The dynamics of such a system is too convoluted to be modeled by a bottom-up approach at this stage. As a result, we elected to represent the absorptive step by an empirical first-order kinetic description extracted from the ICG-fluorescence imaging data.

Yet another limitation is the creation of a buffer or depot region adjacent to the injection site, namely the Adjacent Lymphoid Tissues (ALTs). Given that uptake of DcNP from the SC injection site to the surrounding lymphoid tissue was facile and complete, we needed to invoke a mechanism to withhold the dose for a gradual release to the rest of the lymphatic network over a long period. Otherwise, lymph flow-mediated delivery of the dose would have overwhelmed the regional nodes resulting in node concentrations that are well above their observed values. The ALT constructs likely correspond to physiological realities. The skin holds a very rich surface lymphatic network that could distribute the DcNP dose across the entire back of the NHP (especially after 4 sub-injections, see Methods). In addition, the effect of post-injection massaging and gravity would further facilitate the spread of the dose to a large area well beyond the local injection site. Furthermore, it is known that in order to present foreign antigens to naive T cells, dendritic cells migrate from inflamed or injured peripheral tissues to the closest draining lymph nodes through afferent lymphatic vessels.³⁶ Hence, another possible mechanism contributing to the substantial ALT accumulation could be that nanoparticles are taken up by dendritic cells at injection sites and trafficked into local lymph nodes. Empirically, we propose dividing the proximate lymphatic depot into the upper-trunk adjacent lymphoid tissue (ALT1) and the lower-trunk adjacent lymphoid tissue (ALT2), as depicted in Fig. 2. The creation of ALTs as a metering mechanism for whole-body lymphatic distribution was the only hypothesis that is physiologically sound and could fit the data. Interestingly, the only regional nodes that did not need the buffering by an adjacent lymphoid reservoir were the pulmonary hilar nodes. Hilar nodes are located deep in the chest cavity, which is easy to spot at necropsy, but they might just serve to receive the lung lymphatic drainage. Because, according to our modeling, hilar nodes did not need any direct mass transfer from the injection site, they might be useful for comparison to other nodes receiving such a contribution. The last empirical aspect of the model was the lymphatic remainder pathway featuring a delayed flux from ALT2 directly to the thoracic duct; it serves to account for prolonged drug residence or sequestration in the lymphatics and to complete dose bioavailability. Four delay compartments were needed for a total delay of 160 h, which contributed to the long-acting PK of all three antivirals. This is similar to the strategy we adopted for our previous MBPK models, where the slowest first-pass lymphatic transit featured a total delay of 150–200 h for the three antivirals.^7,10,14

The modeling assumptions described above are subject to further investigation. One conceivable approach is to tag DcNP (empty or drug-loaded) with 111-indium, which would allow real-time PET imaging to investigate absorption from the SC injection site, uptake of nanoparticles into adjacent, superficial lymphatic network, the pattern of further spread to the network of regional nodes in both the lower and upper trunk, and locations of the residual drug that constitutes the postulated remainder pathway. We should also examine different SC locations and routing of the injected dose when given in the back, belly or thigh of the macaques. Abdomen and thigh administrations will be particularly relevant for self-injections. Different locations of SC injection may provide a fuller appreciation of routing through the lymphatic network and a better approach to modeling the network structure.

One important insight gained from our modeling effort was the revelation of an alternate source of nanoparticle delivery to the lymph nodes, i.e., contribution by mononuclear cell trafficking between blood and lymph nodes. Lymphocyte homing to the secondary lymphoid organs is a well-known process initiated by the rolling of lymphocytes on high endothelial venules (HEV) of lymph nodes. This process is followed by chemokine expression in high endothelial cells, tight biding of lymphocytes to high endothelial cells via integrins, and extravasation into cortex of the lymph nodes. This immunological route of entry or re-entry into the nodes assumes prominence especially after an IV injection of DcNP as reported by several tagged T-cells experiments^37–41; these cells are capable of engulfing DcNP in the blood plasma and transporting them to the nodes, thus potentially impacting the drug fluxes. Without accounting for this route of monocyte-mediated transport after an IV injection of DcNP, our model under-predicted drug distribution into lymph nodes by at least two orders of magnitude, but was less sensitive during SC. The inclusion of a monocyte migration model elaborated by Ganusov et al. was a simple but effective means to improve modeling of the lymph node data after IV DcNP administration in the healthy NHP. If the investigator’s focus is on IV administration of lymphocyte-targeting formulations, the present PBPK model could benefit from a fuller elaboration of mononuclear cell migration and turnover kinetics at the lymph nodes, especially regarding the impact of HIV infection (and perhaps other diseases involving lymph nodes). Butcher et al. offer an excellent review on the mechanisms controlling the migration and tissue localization of lymphocytes throughout their life cycle,⁴² which might spark ideas for further modeling effort.

Interesting points can be inferred by analyzing the regression estimates presented in Table 1. Some parameters, especially characterizing DcNP-drug transport in RES cells (e.g., k_in,liver), worked very well by assuming uniform values across drugs. However, when dealing with DcNP stability and mononuclear cell transport kinetics, there were clear differences between PIs and TFV. We indeed expected a difference in the drug dissociation rate from the nanoparticles — k_diss, for which TFV we found to be more stable in vivo than PIs.¹⁰ However, it was not anticipated that such a difference would also exist for those parameters representing cell membrane transport in PBMC and LNMC, and degradation inside all the cells. DcNP-associated drug uptake rate constant into PBMC from the plasma $k_{in,\mathit{\text{PBMC}}}^{\mathit{\text{DcNP}}}$ was around 10 times higher for PIs than TFV. Also, the degradation rate inside the cells, k_deg, was found to be drug dependent. It should be noted that ks are apparent parameters embodying several mechanisms. For example, the PBMC uptake parameter represents the overall kinetics of nanoparticle translocation across the membrane barrier, which includes multiple steps of membrane attachment, endocytosis, and early endosome trafficking. The degradation parameter is a simplistic representation of very complex intracellular processing of lipid nanoparticles, which likely follows a cascade of cellular processes which have yet to be elucidated (e.g., lysosome fusion). In summary, across-drug differences or similarities in the parameter estimates at the cellular level might indicate drug-dependent mechanisms for membrane trafficking and intracellular degradation; in general, TFV seems to be more stable or inert than PIs when subject to various cellular actions. Based upon molecular modeling, TFV could develop a hydrogen bond with the DSPE-PEG₂₀₀₀ excipient, thereby stabilizing its hydrophilic molecule in the DcNP in vivo both in extra- and intra-cellular environments.^10,13 Still another hypothesis is that, during DcNP passage through the liver, the nanoparticle-associated PIs might somehow interact with the CYP enzymes thereby facilitating their release. This could explain the PIs’ shorter terminal half-life in the IV study and much higher liver CL (see Table 1). On the other hand, TFV not being a CYP substrate, nor it can be exctreted or transported via OATs in the kidneys, when in the nanoparticle-associated form, it tends to persist in circulation. Overall, while our modeling hypotheses require confirmation by further investigations, it is a pharmaceutical novelty for drugs with poor PK characteristics, such as TFV, to be improved (i.e., rendered longer acting) via stabilization by its incorporation into DcNP. Based on the formulated-in-DcNP TFV encouraging results, we recently proposed the idea of formulating remdesivir in DcNP for an outpatient long-acting therapy against SARS-CoV2 infection.³³

Our model-based prediction of the time-course of drug concentrations in the mononuclear cell populations allows one to evaluate whether efficacious antiviral levels are achievable in the biophase with TLC-ART 101. Levels of free drugs (dashes in Figs. 3 and 4) were predicted to be in the range of reported in vitro EC₅₀s¹¹ for all three antivirals in combination for the entire 2 weeks. Model simulations over many weeks showed that all three antivirals tended to accumulate in LNMC over that in plasma and PMBC. LNMC-to-PBMC ratios of the free drugs were over 4 at most for all three antivirals, which indicates the unique ability of SC DcNP to enrich drug delivery to the HIV sanctuary sites in the lymphatic system. In fact, it suggests that, for this delivery technology, PBMC may under-represent drug delivery to LNMC and that biopsy of lymph nodes and LNMC analysis may be necessary to obtain an accurate assessment of DcNP targeted drug delivery potential. Equally important, dissociated concentrations of TFV in the kidneys were about 1 μg/ml (Fig. A6), which are well below the reported 30 μg/ml level associated cytotoxicity⁴³; hence, renal toxicity of TFV encapsulated in DcNP may not be of clinical concern. Furthermore, dissociated TFV levels in the liver were quite stable at 10 μg/ml for the entire two weeks (Fig. A6), which suggests the potential for a sustained anti-hepatitis potential (EC_50,HBV = 1.5 μg/ml⁴⁴) and development of a LA therapy against chronic HBV (see ref⁴⁵ for a review about the need of a LA therapy in HBV).

Finally, the model presented here is amenable to inter-species scaling towards designing an appropriate human dose regimen for early phase clinical development. We are planning for a first-in-human study and a suitable dose is sought that is firstly safe and perhaps effective. The PBPK model is the best approach to translate NHP PK into a human projection, both in healthy adults and special populations. Some caveats are warranted. Modeling of lymphatic first-pass that invoked several empirical constructs will still need verification or elaboration before the PBPK model can provide a fully a priori projection in humans. Until then, assumptions such as similar mononuclear uptake of DcNP between NHP and humans will be taken; furthermore, we will use scaling equations for physiological parameters relative to the lymphatic system (see Perelson’s equations⁴⁶). As discussed in Part 1, the human lymphatic system may be more complex than NHP as it relates to drug disposition, but hopefully, there is enough of a human representation in the current PBPK modeling. Also, physiological differences between NHP and human exists in CYPs abundancy and activity, thus likely involving the PIs PK. Nonetheless, the PBPK approach and our modeling design allow for an easy inclusion of these differences. Beyond scaling, once the model is proven valid given the first human plasma and PBMC data, it can be harnessed to project tissue and lymphatic concentrations where lymph node biopsies might not be feasible. The present model is therefore poised for predictive optimization of the PK characteristics of new DcNP-based formulations loaded with a desirable or novel combination of antivirals in humans to facilitate their clinical development.