A physiologically-based pharmacokinetic model to describe antisense oligonucleotide distribution after intrathecal administration

Abstract

Antisense oligonucleotides (ASOs) are promising therapeutic agents for a variety of neurodegenerative and neuromuscular disorders, e.g., Alzheimer’s, Parkinson’s and Huntington’s diseases, spinal muscular atrophy (SMA) and amyotrophic lateral sclerosis (ALS), caused by genetic abnormalities or increased protein accumulation. The blood–brain barrier (BBB) represents a challenge to the delivery of systemically administered ASOs to the relevant sites of action within the central nervous system (CNS). Intrathecal (IT) delivery, in which drugs are administered directly into the cerebrospinal fluid (CSF) space, enables to bypass the BBB. Several IT-administered ASO therapeutics have already demonstrated clinical effect, e.g., nusinersen (SMA) and tofersen (ALS). Due to novelty of IT dosing for ASOs, very limited pharmacokinetic (PK) data is available and only a few modeling reports have been generated. The objective of this work is to advance fundamental understanding of whole-body distribution of IT-administered ASOs. We propose a physiologically-based pharmacokinetic modeling approach to describe the distribution along the neuroaxis based on PK data from non-human primate (NHP) studies. We aim to understand the key processes that drive and limit ASO access to the CNS target tissues. To elucidate the trade-off between parameter identifiability and physiological plausibility of the model, several alternative model structures were chosen and fitted to the NHP data. The model analysis of the NHP data led to important qualitative conclusions that can inform projection to human. In particular, the model predicts that the maximum total exposure in the CNS tissues, including the spinal cord and brain, is achieved within two days after the IT injection, and the maximum amount absorbed by the CNS tissues is about 4% of the administered IT dose. This amount greatly exceeds the CNS exposures delivered by systemic administration of ASOs. Clearance from the CNS is controlled by the rate of transfer from the CNS tissues back to CSF, whereas ASO degradation in tissues is very slow and can be neglected. The model also describes local differences in ASO concentration emerging along the spinal CSF canal. These local concentrations need to be taken into account when scaling the NHP model to human: due to the lengthier human spinal column, inhomogeneity along the spinal CSF may cause even higher gradients and delays potentially limiting ASO access to target CNS tissues.

Appendix

All models analyzed consist of a system of ordinary differential equations (ODEs) that are parameterized in terms of amounts. As defined in the equations below and in accordance with the schematics presented in Fig. 1, the amount of ASO in region $i$ (e.g., CSF or tissue type) and specific location $l$ is denoted by variable $A_{i}^{l}$ that has units of mass (e.g., ng).

The two model modifications presented here share the same equations and parameter definitions but differ in the number of parameters to be estimated. Model 1 contains 32 parameters to be estimated, whereas in Model 2, the number of parameters to be estimated is reduced to 21 respectively. The following parameter values of Model 1 are lumped into single values in Model 2:

$$\begin{gathered} k_{1}^{LT} = k_{1}^{TC} = k_{1}^{CP} = k_{1}^{PD} = k_{up} , \hfill \\ k_{1}^{TL} = k_{1}^{CT} = k_{1}^{PC} = k_{1}^{DP} = k_{down} , \hfill \\ k_{21}^{L} = k_{21}^{T} = k_{21}^{C} = k_{21}^{S} \,{\text{and}} \hfill \\ k_{31}^{P} = k_{31}^{B} = k_{31}^{H} = k_{31}^{X} = k_{31}^{Br} . \hfill \\ \end{gathered}$$

The following equations define the CNS structure in both models:

$$\frac{{dA_{1}^{L} }}{dt} = - \left( {k_{14}^{S} + k_{12}^{L} + k_{1}^{LT} } \right)A_{1}^{L} + k_{21}^{L} A_{2}^{L} + k_{1}^{TL} A_{1}^{T} ,$$

(A1)

$$\frac{{dA_{2}^{L} }}{dt} = k_{12}^{L} A_{1}^{L} - k_{21}^{L} A_{2}^{L} - k_{deg} A_{2}^{L} ,$$

(A2)

$$\frac{{dA_{1}^{T} }}{dt} = - \left( {k_{14}^{S} + k_{12}^{T} + k_{1}^{TC} + k_{1}^{TL} } \right)A_{1}^{T} + k_{1}^{LT} A_{1}^{L} + k_{21}^{T} A_{2}^{T} + k_{1}^{CT} A_{1}^{C} ,$$

(A3)

$$\frac{{dA_{2}^{T} }}{dt} = k_{12}^{T} A_{1}^{T} - k_{21}^{T} A_{2}^{T} - k_{deg} A_{2}^{T} ,$$

(A4)

$$\frac{{dA_{1}^{C} }}{dt} = - \left( {k_{14}^{S} + k_{12}^{C} + k_{1}^{CP} + k_{1}^{CT} } \right)A_{1}^{C} + k_{1}^{TC} A_{1}^{T} + k_{21}^{C} A_{2}^{C} + k_{1}^{PC} A_{1}^{P} ,$$

(A5)

$$\frac{{dA_{2}^{C} }}{dt} = k_{12}^{C} A_{1}^{C} - k_{21}^{C} A_{2}^{C} - k_{deg} A_{2}^{C} ,$$

(A6)

$$\begin{gathered} \frac{{dA_{1}^{P} }}{dt} = - \left( {k_{14}^{B} + k_{13}^{P} + k_{13}^{B} + k_{13}^{H} + k_{1}^{PC} + k_{1}^{PD} } \right)A_{1}^{P} + k_{1}^{DP} A_{1}^{D} + k_{1}^{CP} A_{1}^{C} \hfill \\ + \;k_{31}^{P} A_{3}^{P} + k_{31}^{B} A_{3}^{B} + k_{31}^{H} A_{3}^{H} , \hfill \\ \end{gathered}$$

(A7)

$$\frac{{dA_{3}^{P} }}{dt} = k_{13}^{P} A_{1}^{P} - k_{31}^{P} A_{3}^{P} - k_{deg} A_{3}^{P} ,$$

(A8)

$$\frac{{dA_{3}^{B} }}{dt} = k_{13}^{B} A_{1}^{P} - k_{31}^{B} A_{3}^{B} - k_{deg} A_{3}^{B} ,$$

(A9)

$$\frac{{dA_{3}^{H} }}{dt} = k_{13}^{H} A_{1}^{P} - k_{31}^{H} A_{3}^{H} - k_{deg} A_{3}^{H} ,$$

(A10)

$$\frac{{dA_{1}^{D} }}{dt} = - \left( {k_{14}^{B} + k_{13}^{X} + k_{1}^{DP} } \right)A_{1}^{D} + k_{1}^{PD} A_{1}^{P} + k_{31}^{X} A_{3}^{X} ,$$

(A11)

$$\frac{{dA_{3}^{X} }}{dt} = k_{13}^{X} A_{1}^{D} - k_{31}^{X} A_{3}^{X} - k_{deg} A_{3}^{X} .$$

(A12)

Systemic part equations:

$$\begin{gathered} \frac{{dA_{4} }}{dt} = k_{14}^{S} \left( {A_{1}^{L} + A_{1}^{T} + A_{1}^{C} } \right) + k_{14}^{B} \left( {A_{1}^{P} + A_{1}^{D} } \right) - k_{4} A_{4} - k_{45} A_{4} + \hfill \\ k_{54} A_{5} - k_{46} A_{4} + k_{64} A_{6} , \hfill \\ \end{gathered}$$

(A13)

$$\frac{{dA_{5} }}{dt} = k_{45} A_{4} - k_{54} A_{5} - k_{5} A_{5} ,$$

(A14)

$$\frac{{dA_{6} }}{dt} = k_{46} A_{4} - k_{64} A_{6} - k_{6} A_{6} .$$

(A15)