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. 2024 Jul 19;45(4-6):190–200. doi: 10.1002/bdd.2398

Model‐based interspecies interpretation of botulinum neurotoxin type A on muscle‐contraction inhibition

Hyo‐jeong Ryu 1,2, Seongsung Kwak 1, Misun Park 1, Hwi‐yeol Yun 2,3,✉
PMCID: PMC11687410  PMID: 39031599

Abstract

Botulinum neurotoxins (BoNTs) are commonly used in therapeutic and cosmetic applications. One such neurotoxin, BoNT type A (BoNT/A), has been studied widely for its effects on muscle function and contraction. Despite the importance of BoNT/A products, determining the blood concentrations of these toxins can be challenging. To address this, researchers have focused on pharmacodynamic (PD) markers, including compound muscle action potential (CMAP) and digit abduction scoring (DAS). In this study, we aimed to develop a probabilistic kinetic‐pharmacodynamic (K‐PD) model to interpret CMAP and DAS data obtained from mice and rats during the development of BoNT/A products. The researchers also wanted to gain a better understanding of how the estimated parameters from the model relate to the bridging of animal models to human responses. We used female Institute of Cancer Research mice and Sprague‐Dawley (SD) rats to measure CMAP and DAS levels over 32 weeks after administering BoNT/A. We developed a muscle‐contraction inhibition model using a virtual pharmacokinetic (PK) compartment combined with an indirect response model and performed model diagnostics using goodness‐of‐fit analysis, visual predictive checks (VPC), and bootstrap analysis. The CMAP and DAS profiles were dose‐dependent, with recovery times varying depending on the administered dose. The final K‐PD model effectively characterized the data and provided insights into species‐specific differences in the PK and PD parameters. Overall, this study demonstrated the utility of PK‐PD modeling in understanding the effects of BoNT/A and provides a foundation for future research on other BoNT/A products.

Keywords: botulinum neurotoxin type A, kinetic‐pharmacodynamic (K‐PD) model, muscle‐contraction inhibition, pharmacodynamic, pharmacokinetic

This study addresses the challenges in evaluating botulinum neurotoxin type A (BoNT/A) efficacy and understanding species‐specific responses. By developing a kinetic‐pharmacodynamic (K‐PD) model, it interprets muscle function data from animal studies, offering insights into BoNT/A effects and potential applications in humans. This approach enhances translational relevance and may improve therapeutic outcomes for conditions involving muscle spasticity.

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1. INTRODUCTION

Botulinum neurotoxins (BoNTs) are produced by the anaerobic bacterium Clostridium botulinum and related species, representing the most well‐known protein neurotoxins discovered thus far (Poulain & Popoff, 2019). Among them, BoNT type A (BoNT/A) stands out as the initial and widely accepted serotype for both clinical and cosmetic applications (Tsui, 1996). Its therapeutic action arises from its ability to specifically block the release of acetylcholine at the neuromuscular junction (NMJ), leading to a reduction in muscle contraction. The first reported clinical usage of BoNT/A was in the treatment of strabismus as an alternative to surgical intervention (Scott, 1980). Since then, its therapeutic applications have expanded to include various conditions associated with muscle spasticity (Guida et al., 2018; Jankovic, 2004).

During the discovery and development phases of BoNT products, researchers investigated extensively its in vivo pharmacological effects. Key indicators, such as compound muscle action potential (CMAP) and digit abduction score (DAS), are commonly used to assess these effects. CMAP is used to measure electrical changes in the hind limb muscles of mice, providing insights into overall muscle activity. By recording and analyzing these changes, researchers can evaluate the impact of BoNTs on muscle function and contraction (Pollari et al., 2018; Rummel, 2013). Additionally, DAS is a valuable tool for assessing the localized muscle‐weakening efficacy of BoNTs. Following the injection of BoNT into the hind limb muscles of mice, the DAS assay measures the extent of muscle weakening by evaluating the digit abduction response. This assessment aids researchers in understanding the specific muscle groups affected and the effectiveness of BoNT in inducing localized muscle paralysis (Broide et al., 2013; Weisemann et al., 2016). Using both CMAP and DAS, researchers have gained a comprehensive understanding of the pharmacological effects of BoNT, enabling them to further refine and optimize its development for therapeutic applications.

From a pharmacometrician’s perspective, CMAP and DAS can serve as valuable pharmacodynamic (PD) markers or indicators for evaluating the pharmacological effects of BoNT products. During the discovery and development stages, these markers exhibit time‐dependent variations that can be quantitatively interpreted using appropriate mathematical models. However, quantifying the blood concentration of BoNTs is challenging because of the small volumes injected into local tissues. Consequently, regulatory agencies have approved BoNT products based on limited pharmacokinetic (PK) data (Kang et al., 2021; Ravichandran et al., 2006; United States Food and Drug Administration, 2009, 2010, 2011). This lack of PK data complicates pharmacometric research, including the prediction of exposure–response relationships. To address these challenges, the kinetic‐pharmacodynamic (K‐PD) model, also known as the kinetic drug action model, offers an alternative approach. The K‐PD model establishes a connection between virtual pharmacokinetic (PK) and pharmacodynamic (PD) compartments. The virtual PK parameters were defined in reverse through curve fitting of observed values from the pharmacodynamic compartment (González‐Sales et al., 2017; Jacqmin et al., 2007; Kang et al., 2021; Pillai et al., 2004).

Understanding the precise effects of BoNT/A across species is crucial for optimizing its therapeutic applications and development. The ability to translate findings from one species to another allows researchers to predict how the neurotoxin would behave in humans based on animal model studies. For instance, despite animal testing, species‐specific differences in the NMJ have led to challenges in predicting the effective dosage for humans so far. In animal models, the action duration of BoNT/A and the degree of muscle paralysis can differ significantly from those observed in humans, which can complicate the estimation of safe exposure levels and the duration of therapeutic effects in clinical settings. A notable example has been the discrepancy observed in the potency of BoNT/A and the duration of activity between rodent models and human, which necessitate careful consideration of species‐specific responses to refine dosing strategies and to predict long‐term outcomes more accurately (Aoki, 2001; Eleopra et al., 2004). However, directly translating findings from one species to another remains challenging because of inherent physiological variations between species, such as differences in NMJ morphology, muscle fiber type composition, and toxin sensitivity. Successfully addressing such challenges could facilitate the development of more effective and safer botulinum neurotoxin products for human use.

This study aimed to achieve two primary objectives. First, a probabilistic K‐PD model capable of effectively interpreting biological activity data (such as CMAP and DAS) collected from mice and rats during the development of BoNT products. Second, to gain a more comprehensive understanding of the relationship between model‐estimated parameters, thereby offering deeper insights into the connection between animal models and human response.

2. MATERIALS AND METHODS

2.1. CMAP and DAS measurements in ICR mice and SD rats

Six‐week‐old female Institute of Cancer Research (ICR) mice and Sprague‐Dawley (SD) rats were obtained from Orient Bio, Inc. (Seongnam‐si) and were housed in a controlled environment with a 12 h light/dark cycle at 23 ± 3°C, relative humidity of 55 ± 15%, and provided ad libitum access to food and water.

On the day of BoNT/A administration (day 0), 75 mg kg−1 ketamine hydrochloride and 10 mg kg−1 xylazine were administered intraperitoneally to each animal to induce anesthesia. The CMAP was measured in anesthetized mice on day 0 to determine the baseline value for each animal. Subsequently, BoNT/A was administered to the right gastrocnemius. Based on the median effective dose value of BoNT/A (11.9 U kg−1) following intramuscular injection (Kim et al., 2013), BoNT/A (NEWLUX® 100 U, NEWMECO Corp) was administered 0.4, 1.2, 4, 12, and 40 U kg−1 to female ICR mice and SD rats (n = 5 mice and n = 6 rats per group). Furthermore, dose levels of 40 U kg−1 or less were selected in accordance with the 3 Rs principles (Replacement, Reduction, and Refinement) to reduce the number of animals used in the study and to minimize the incidence of death and unnecessary pain resulting from the administration of BoNT exceeding 40 U kg−1 (Hubrecht & Carter, 2019; Torii et al., 2015). CMAP and DAS were measured at 0, 1, 3, and 7 weeks and then weekly from 2 to 32 weeks after administration (Table S1). DAS evaluation was first performed on the test animals on all scoring days, followed by CMAP measurements. CMAP and DAS measurements were discontinued once the animals recovered from the treatment, as indicated by the CMAP and DAS values of the treated leg returning to baseline levels.

CMAP measurements were performed on the gastrocnemius area of the hind legs using a Nicolet Viking Quest device (Viasys Healthcare Inc., Tokyo, Japan). Only animals that showed a CMAP amplitude greater than 40 mV before the start of treatment (day 0) were used in this experiment. The 40 mV threshold was selected based on preliminary experiments, which demonstrated that the value effectively distinguished between background noise and meaningful physiological responses. Using this threshold ensured that only animals with a sufficiently strong baseline response were included, thus minimizing variability and ensuring more reliable results. The CMAP value was measured from day 1 following injection of BoNT/A, and the efficacy of each dose level was compared (Sakamoto et al., 2009; Torii et al., 2010). A drop in amplitude on the BoNT/A‐injected ipsilateral leg indicated direct inhibition of muscle contraction caused by nerve impulse blockage. Two blinded experimenters performed DAS measurements, and a score was assigned using a 5‐point scale, with 0 indicating normal and 4 indicating the most significant reduction in digit abduction and leg extension (Aoki, 2001; Broide et al., 2013). All experiments were conducted after receiving approval from the Institutional Animal Care and Use Committee of Medytox Inc. (Approval No. A‐2017‐003 and A‐2019‐004; Approval Dates, 25 August 2017, and 25 April 2019).

2.2. Collection for human CMAP and DAS results

CMAP and DAS results from humans were explored through a systematic literature review using databases (e.g., PubMed) and keywords (botulinum neurotoxin A, CMAP, and humans). Nevertheless, an extensive systematic literature review was performed, and there were no suitable previous reports on DAS. However, in the case of CMAP, electrophysiological analysis is commonly conducted to assess the duration of clinical effects following BoNT/A injections in humans. This approach is widely accepted as it reliably evaluates neuromuscular function (Eleopra et al., 2004, 2020; Hamjian & Walker, 1994; Kessler & Benecke, 1997; Sloop et al., 1996). Therefore, electrophysiological techniques measuring changes in CMAP amplitude over time were used for this purpose. The CMAP values measured in humans after BoNT/A injections in this study were obtained from the literature (Eleopra et al., 1998).

2.3. Establishment of muscle‐contraction inhibition model using virtual PK concept

We established a muscle‐contraction inhibition model using a virtual PK compartment (Figure 1). Muscle‐contraction inhibition modeling was conducted using the nonlinear mixed effects modeling (NONMEM) tool version 7.4 (ICON PLC, Dublin, Ireland) with the assistance of Pirana version 3.0.0 (Princeton) and Perl‐speaks‐NONMEM version 4.9.0 (Husargatan). Statistical and graphical analyses were performed using R version 4.3.1 (Welthandelsplatz, Vienna), R Studio (version 2023.09.0 +463), and GraphPad Prism (version 8.0.2).

FIGURE 1.

FIGURE 1

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Model structure. *Compound muscle action potential (CMAP) is used only in humans.

We combined the virtual PK model in parallel with the indirect response (IDR) model to explain the muscle‐contraction inhibition effects of BoNT/A, which can be described using the PD indicators CMAP and DAS following intramuscular injection. We described the inhibition pattern of muscle contraction following intramuscular injection of BoNT/A using differential equations. Equation (1) assumes that BoNT/A delivered through a virtual PK compartment after intramuscular injection inhibits muscle contraction. Thus, the efficiency and rate of inhibition of muscle contraction by BoNT/A were assumed to be generated by the virtual PK compartment. As mentioned in the Introduction, in the K‐PD model, in cases where drug concentration data are either unavailable or insufficient, all PK functions can be implied by the virtual infusion rate rather than typical PK parameters, such as clearance, volume of distribution, absorption rate constant, and bioavailability, where A (1) and KDE represent the quantity of BoNT/A and the degradation rate constant in the virtual PK compartment, respectively. The products of A (1) and KDE represent the virtual infusion rate from the virtual PK compartment to the PD compartment, CMAP, and DAS, respectively. Equations (2) and (3) represent CMAP and its counteractive counterpart, DAS, respectively, using the general E max equations to describe muscle contraction.

In summary, in the final muscle‐contraction inhibition model, BoNT/A flowed into the PD compartment at a virtual infusion rate that was the product of A (1) and KDE. Subsequently, BoNT/A within the PD compartment inhibited muscle contraction, as described by CMAP and DAS. However, in humans with only CMAP measurement data, the virtual PK compartment was exclusively combined with the PD compartment of CMAP.

dA(1)dt=−KDE·A (1)

Here, A (1) represents the drug amount in the virtual PK compartment, while KDE stands for the degradation rate constant within the same virtual PK compartment. Together, A (1) and KDE define the virtual infusion rate.

dA(2)dt=Kin·1−Emax×(KDE·A(1))EDK50+(KDE·A(1))−Kout·A (2)
dA(3)dt=Kin·1+Emax×(KDE·A(1))EDK50+(KDE·A(1))−Kout·A (3)

Equation (2) describes the effect compartment for CMAP, where A (2) denotes the amount of BoNT/A influencing CMAP. Equation (3) models the effect compartment for DAS, where A (3) represents the amount of BoNT/A affecting DAS. In both equations, the parameters K in and K out are the input and output rate constants for these effect compartments. The E max represents the maximum effect of BoNT/A, while EDK 50 is the rate that produces 50% of this maximum effect. The response in both the CMAP and DAS compartments is influenced by the virtual infusion rate, which is given by KDE · A (1).

2.4. Model diagnostics and evaluation

We conducted a goodness‐of‐fit (GOF) analysis of the final muscle‐contraction inhibition model and examined it with respect to both mouse and rat data for CMAP and DAS, along with a human study focusing on CMAP. Additionally, we performed a visual predictive check (VPC) to assess the final muscle‐contraction inhibition model. Using the final muscle‐contraction inhibition model, we generated 1000 simulation replicates of the original dataset, enabling us to compute the fifth, median, and 95th percentiles of the simulation results for comparison with the observed CMAP and DAS in the simulated CMAP and DAS. Furthermore, bootstrap analysis was performed to evaluate the internal model, and the final muscle‐contraction inhibition model was compared with the 95% confidence intervals in the bootstrap analysis.

3. RESULTS

3.1. CMAP profiles in ICR mice, SD rats, and humans

We observed time‐dependent changes in the CMAP levels in mice, rats, and humans following BoNT/A injection. The CMAP patterns after BoNT/A injection are shown in Figures 2, 3, 4. In general, the minimum CMAP values were observed in both mice and rats 3 days after injection, whereas in humans, this occurred 7 days after injection. Mice in the 0.4 U kg−1 group exhibited complete recovery at approximately 28 days after injection, while the 1.2, 4, and 12 U kg−1 groups showed full recovery at approximately 42, 70, and 91 days, respectively (Figure 2). In rats, the 0.4 U kg−1 group reached full recovery approximately 49 days after injection, the 1.2 U kg−1 group reached full recovery approximately 70 days after injection, and the 4, 12, and 40 U kg−1 groups at 126, 140, and 224 days after injection, respectively (Figure 3). However, following a 0.04 U kg−1 injection in humans, recovery to approximately half of the basal CMAP value was observed at approximately 90 days (Figure 4). The CMAP values in mice and rats exhibited a dose‐dependent decrease, with no significant difference in the time required to reach the minimum CMAP value. In contrast, the time to achieve CMAP measurement recovery was approximately 1.78 times longer in rats than in mice in the 0.4 U kg−1 group, about 1.7 times longer in the 1.2 and 4 U kg−1 groups, and approximately 1.5 times longer in the 12 U kg−1 group (Table S2). Mice have a higher metabolic rate compared with rats, which leads to a more rapid reduction in the activity and efficacy of BoNT/A. Furthermore, the metabolism and excretion of BoNT/A has been influenced by enzymatic degradation in subcutaneous tissues and specific excretion routes. The quantity of the enzymes and the structural properties of tissues are dependent on body size, with smaller animals such as mice having higher relative enzyme activity and distinct tissue structures compared with larger animals such as rats. Such size‐dependent differences impact the infusion rate and overall PK of BoNT/A, resulting in more rapid degradation and clearance of the toxin in mice (Puente & López‐Otín, 2004).

FIGURE 2.

FIGURE 2

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Compound muscle action potential (CMAP)–time profiles following botulinum neurotoxin type A (BoNT/A) injection and visual check prediction (VPC) results in the mouse model. (a) BoNT/A 0.4 U kg−1, (b) BoNT/A 1.2 U kg−1, (c) BoNT/A 4 U kg−1, (d) BoNT/A 12 U kg−1. Black point, observed CMAP value; Gray shade, 90% simulation intervals; Blue line, observed median value; Red line, simulated median value.

FIGURE 3.

FIGURE 3

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Compound muscle action potential (CMAP)–time profiles following botulinum neurotoxin type A (BoNT/A) injection and visual check prediction (VPC) results in the rat model. (a) BoNT/A 0.4 U kg−1, (b) BoNT/A 1.2 U kg−1, (c) BoNT/A 4 U kg−1, (d) BoNT/A 12 U kg−1, (e) BoNT/A 40 U kg−1. Black point, observed CMAP value; Gray shade, 90% simulation intervals; Blue line, observed median value; Red line, simulated median value.

FIGURE 4.

FIGURE 4

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Compound muscle action potential (CMAP)–time profiles following botulinum neurotoxin type A (BoNT/A) 0.04 U kg−1 injection and visual check prediction (VPC) results for the human model. Black point, observed CMAP value; Gray shade, 90% simulation intervals; Blue line, observed median value; Red line, simulated median value.

3.2. DAS profiles in ICR mice and SD rats

We observed changes in DAS over time in both mice and rats, and DAS values exhibited a dose‐dependent increase. The DAS patterns after BoNT/A injection are shown in Figures 5 and 6. In all BoNT/A dose groups, the mice reached their maximum DAS values approximately 2 days after injection, whereas the rats reached their maximum DAS values approximately 3 days after injection, with no significant difference. The mice in the 1.2 U kg−1 dosage group recovered approximately 8.9 days after injection, whereas those in the 4, 12, and 40 U kg−1 dosage groups recovered approximately 19.1, 23.8, and 45.7 days, respectively (Figure 5). In contrast, the rats in the 1.2 U kg−1 dosage group took approximately 22.2 days to recover, while the 4, 12, and 40 U kg−1 dosage groups required approximately 30.3, 43.2, and 65.3 days, respectively, to recover (Figure 6). The recovery times for DAS measurements in rats were approximately 2.49 times longer in the 1.2 U kg−1 dose group, 1.59 times longer in the 4 U kg−1 dose group, 1.82 times longer in the 12 U kg−1 dose group, and 1.43 times longer in the 40 U kg−1 dose group than in mice (Table S2). Due to their higher metabolic rate, mice experience a more rapid decline in BoNT/A activity and effectiveness compared with rats. BoNT/A metabolism and excretion occur through enzymatic activity in the dermal tissues and via excretion routes, both of which are size‐dependent processes influenced by the quantity of enzymes present and the structural composition of the tissues. Consequently, the factors can affect the infusion rate and ultimately contribute to the observed differences in recovery times between mice and rats (Puente & López‐Otín, 2004).

FIGURE 5.

FIGURE 5

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Digit abduction score (DAS)–time profiles following botulinum neurotoxin type A (BoNT/A) injection and visual check prediction (VPC) results in the mouse model. (a) BoNT/A 1.2 U kg−1, (b) BoNT/A 4 U kg−1, (c) BoNT/A 12 U kg−1, (d) BoNT/A 40 U kg−1. Black point, observed DAS value; Gray shade, 90% simulation intervals; Blue line, observed median value; Red line, simulated median value.

FIGURE 6.

FIGURE 6

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Digit abduction score (DAS)–time profiles following botulinum neurotoxin type A (BoNT/A) injection and visual check prediction (VPC) results in the rat model. (a) BoNT/A 0.4 U kg−1, (b) BoNT/A 1.2 U kg−1, (c) BoNT/A 4 U kg−1, (d) BoNT/A 12 U kg−1, (e) BoNT/A 40 U kg−1. Black point, observed DAS value; Gray shade, 90% simulation intervals; Blue line, observed median value; Red line, simulated median value.

3.3. Muscle‐contraction inhibition modeling for CMAP and DAS

We applied the datasets for CMAP and DAS in mice, rats, and humans to our novel muscle‐contraction inhibition modeling system. Our final muscle‐contraction inhibition model best described the inhibition of muscle contraction based on the CMAP and DAS time profiles, indicating a combination of the modified IDR model with a virtual PK compartment. The estimated parameters are listed in Table 1. In the BoNT/A administration groups, as BoNT/A was directly injected into the muscles, which are the response sites for CMAP and DAS, KDE was estimated to have low values of 0.0886, 0.0773, and 0.00925 days−1 in mice, rats, and humans, respectively. In the E max formula for the CMAP compartment, which reflects the product of A (1) and KDE, representing the virtual infusion rate into the CMAP and DAS compartments from the virtual PK compartment, the EDK 50 was 1.07, 6.19, and 0.00938 U day−1 in mice, rats, and humans, respectively. The EDK 50 in the DAS compartment was 17.8 and 43.3 U day−1 in mice and rats, respectively. EDK 50 is a parameter that defines the infusion rate, causing a 50% inhibition coefficient, which represents in vivo efficacy. The fact that the EDK 50 in the DAS compartment was higher than that in the CMAP compartment indicates that a larger quantity of BoNT/A is required in the DAS compartment to inhibit muscle contraction.

TABLE 1.

Parameter estimates and bootstrap validation results across species.

Species Mice Rats Humans
Parameter Estimate (%RSE) Inter‐individual variability (%RSE) Bootstrap median (2.5%–97.5% percentile) Estimate (%RSE) Inter‐individual variability (%RSE) Bootstrap median (2.5%–97.5% percentile) Estimate (%RSE) Inter‐individual variability (%RSE) Bootstrap median (2.5%–97.5% percentile)
KDE (day−1) 0.0886 (3.8%) ‐ 0.0887 (0.0826–0.0968) 0.0773 (4.1%) 12.4% (31.6%) 0.0771 (0.0706–0.0834 0.00925 (28.2%) ‐ 0.00924 (0.00439–0.01474)
E max _CMAP (mol) 1.04 (1.2%) ‐ 1.04 (1.02–1.09) 0.94 (1.3%) ‐ 0.94 (0.92–0.97) 1 FIX ‐ ‐
EDK 50 _CMAP (U day−1) 1.07 (5.8%) ‐ 1.07 (0.92–1.22) 6.19 (7.9%) ‐ 6.25 (5.41–7.24) 0.00938 (27.5%) ‐ 0.00935 (0.00449–0.01439)
K in _CMAP (day−1) 365 (11.8%) ‐ 355 (282–455) 217 (5.4%) ‐ 217 (195–251) 255 (1.8%) 3.2% (24.9%) 262 (245–502)
Base_CMAP 98.4 (1.0%) 8.5% (14.9%) 98.4 (96.1–100.6) 91.9 (1.6%) 7.6% (10.9%) 92.0 (89.0–95.0) 100 (0.0%) ‐ 99.98 (99.94–100.04)
E max _DAS (mol) 3000 (0.1%) ‐ 3000 (2998–3000) 2870 (11.8%) ‐ 2947 (2848–2999) ‐ ‐ ‐
EDK 50 _DAS (U day−1) 17.8 (20.3%) ‐ 17.9 (12.4–23.8) 43.3 (17.0%) ‐ 43.7 (31.0–64.1) ‐ ‐ ‐
K in _DAS (day−1) 0.0054 (13.6%) 34.4% (14.9%) 0.0054 (0.0041–0.0069) 0.00289 (8.9%) ‐ 0.00287 (0.00233–0.00388) ‐ ‐ ‐
K out _DAS (day−1) 2.76 (17.3%) ‐ 2.73 (2.27–3.94) 2.04 (21.8%) ‐ 2.06 (1.58–2.91) ‐ ‐ ‐
Additive error_CMAP 7.11 (3.8%) ‐ ‐ 7.73 (7.0%) ‐ ‐ 12.1 (12.7%) ‐ ‐
Additive error_DAS 0.379 (4.1%) ‐ ‐ 0.489 (5.5%) ‐ ‐ ‐ ‐ ‐
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Abbreviations: BASE_CMAP, baseline value for CMAP; CMAP, compound muscle action potential; DAS, digit abduction score; EDK 50 _CMAP, rate that produces 50% of CMAP maximum effect; EDK 50 _DAS, rate that produces 50% of DAS maximum effect; E max _CMAP, maximum effect of botulinum neurotoxin type A (BoNT/A) influencing CMAP; E max _DAS, maximum effect of BoNT/A influencing DAS; KDE, degradation rate constant; K in _CMAP, input rate constant influencing CMAP; K in _DAS, input rate constant influencing DAS; K out _DAS, output rate constant influencing DAS.

VPC plots with 95% prediction intervals using the final muscle‐contraction inhibition model are shown in Figures 2, 3, 4, 5, 6. The VPC plots showed that most of the values were within the 95% prediction interval of the simulated data. These results suggest that the muscle‐contraction inhibition model demonstrated adequate predictive performance in explaining muscle contraction inhibition in the CMAP and DAS data. These values closely resembled those generated from 1000 bootstrap replications, indicating a high level of precision in the final muscle‐contraction inhibition model, as shown in Table 1. Basic GOF plots for the final muscle‐contraction inhibition model are shown in Figures S1–S5. Both individual and population predictions were uniformly distributed along the identity line, indicating a strong model fit.

4. DISCUSSION

Given the unavailability of time‐course plasma concentration data for BoNT/A, alternative approaches must be considered to link exposure to biological markers or clinical indicators during drug discovery and development. We created a mathematical model to explain the inhibitory effect of BoNT/A on muscle contraction when injected into the muscle when PK data were unavailable. We attempted to integrate the virtual PK component of the K‐PD model with the PD component of the IDR model in a parallel manner. BoNT/A works indirectly by inhibiting the release of acetylcholine, which subsequently reduces muscle contraction (Scott, 1980). Therefore, the IDR model was deemed appropriate to capture this indirect mechanism. Direct response models were considered but found inadequate to describe the delayed onset and prolonged duration of BoNT/A’s effects. The IDR model, capable of accounting for the delay between drug administration and the observed pharmacological effect, offered a more accurate representation (Table S3). Furthermore, in the final muscle‐contraction inhibition model, we considered substantial inter‐individual variability (IIV) in the CMAP and DAS profiles of mice with base and K in omega. For rats, we considered KDE and base omega (Figures 2 and 5, and Figures 3 and 6, respectively). Additionally, for humans, we considered K in omega to account for significant IIV in the final muscle‐contraction inhibition model using CMAP profiles (Figure 4). Throughout the model development process, the IIV of various parameters was considered for different species; however, it had minimal impact on the reduction in the objective function value. Our ultimate muscle‐contraction inhibition model effectively described the inhibitory effects of CMAP and DAS on muscle contraction. Initially, our final muscle‐contraction inhibition model estimated that the virtual infusion rate was slow for the mouse, rat, and human data. Furthermore, the virtual PK parameters were accurately predicted and consistently estimated during curve fitting using CMAP and DAS as dependent variables for mice and rats and CMAP for humans. During multiple NONMEM runs, virtual PK parameters were consistently estimated. Furthermore, our findings showed that as body weight increased, the virtual infusion rate decreased (Figure 7). Botulinum toxin is a large protein with numerous linear and conformational epitopes, which are susceptible to protease degradation. These proteases show interspecies differences, with lower levels in mice, rats, and humans in descending order, leading to a reduced metabolic rate of proteases in the same sequence. Hence, it was inferred that the virtual infusion rate slowed as the body weight increased (Puente & López‐Otín, 2004; Ravichandran et al., 2006). This inverse relationship between body weight and KDE suggests that larger animals require a lower virtual infusion rate to achieve PD effects comparable to those of smaller animals. To address this, our model adjusts the KDE based on body weight, ensuring more accurate predictions across different species. Despite KDE being a single parameter in our model, its estimation encompasses the complexities arising from both continuous and categorical PD variables, such as CMAP and DAS. As mentioned in the introduction, our K‐PD model offers a unique solution to cases where traditional pharmacokinetic parameters are lacking or insufficient. By utilizing the virtual infusion rate derived from A (1) and KDE, we effectively capture the drug distribution dynamics within the neural tissue and its subsequent effects on CMAP and DAS. While KDE is a single parameter, its inclusion accounts for the intricate interplay between drug distribution kinetics and PD responses. This parameterization allows us to streamline the modeling process without sacrificing the model’s ability to accurately represent the observed data. To ensure the robustness and reliability of our KDE estimate, we conducted thorough validation and sensitivity analyses, including evaluating the Relative Standard Error (RSE%) and performing bootstrap analysis. Our results indicated low RSE% values for KDE across different species: 3.8% for mice, 4.1% for rats, and 28.2% for humans, demonstrating high stability. Furthermore, the bootstrap analysis with 1000 replicates confirmed consistent KDE estimates with narrow confidence intervals (mice: KDE = 0.0886 days⁻1, 95% confidence interval: 0.0826–0.0968; rats: KDE = 0.0773 days⁻1, 95% confidence interval: 0.0706–0.0834; humans: KDE = 0.00925 days⁻1, 95% confidence interval: 0.00439–0.01474). These findings affirm the KDE parameter’s robustness in our model. In summary, the inclusion of KDE as a single parameter in our model strikes a balance between complexity and simplicity, enabling us to capture the essential dynamics of drug distribution and PD responses in a robust and reliable manner. This approach is validated through sensitivity analyses and bootstrap methods, confirming the robustness and reliability of the KDE parameter. Consequently, our model accurately captures the dynamics of drug distribution and pharmacodynamic responses, facilitating reliable interspecies translation.

FIGURE 7.

FIGURE 7

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The relationship of KDE parameters across species. KDE, degradation rate constant.

Consequently, we concluded that the residence time of BoNT/A within the muscle may vary among species. Upon examining the CMAP patterns after actual BoNT/A injections, we confirmed a delayed onset of the muscle contraction inhibitory effect in humans compared with that in mice and rats (Figures 2, 3, 4). Specifically, the minimum CMAP values were observed 3 days after injection in both mice and rats, whereas in humans, this occurred 7 days after injection (in‐house results). This demonstrates a clear delayed onset in humans compared with rodents. Additionally, the K in for the CMAP compartment was 365 days−1 for mice, 217 days−1 for rats, and 255 days−1 for humans, whereas the base values were 98.4, 91.9, and 100 for mice, rats, and humans, respectively. Although the K in values show differences of over 100 days across species, the variations reflect species‐specific physiological characteristics (Puente & López‐Otín, 2004). The similarity in base values across species indicates that the initial response to BoNT/A and the overall trend in CMAP responses are comparable. Considering the over 6 month dosing intervals and the prolonged effects of BoNT/A, these differences in K in values are not clinically significant and do not affect the overall pattern of CMAP responses. Thus, despite the numerical differences, the trends in the rate of CMAP responses elicited by BoNT/A are similar, supporting the use of these values for interspecies comparison. Considering that the virtual infusion rate decreases with an increase in body weight, this phenomenon must be taken into account for interspecies translation. Specifically, while K in and base values suggest that the response initiation time is consistent, the decreasing virtual infusion rate implies that larger species may have a slower toxin distribution rate. Therefore, for accurate interspecies translation, it is crucial to consider both the consistent K in and base values and the varying virtual infusion rate when modeling BoNT/A PK across different species. This ensures a comprehensive understanding of how the drug distributes and acts in species of varying sizes.

This study had several limitations. First, our conceptualization for model development was specific to the BoNT/A product NEWLUX®. However, to ensure broader applicability, we conducted a literature review to collect human clinical data for comparison purposes. We made an effort to focus on BoNT/A products similar to NEWLUX® to ensure consistency in the BoNT type. It is important to note that while our model provides valuable insights into PD responses, interspecies translation may be affected by the inherent differences in BoNT/A products. Therefore, the applicability of our muscle‐contraction inhibition model to other BoNT/A products remains uncertain. Second, we only used a single dose of CMAP as a PD marker in humans. However, if muscle‐contraction inhibition had been tested at various doses and different levels of biological markers related to muscle‐contraction inhibition had been obtained, we may have been able to develop a more robust model.

In summary, we developed a mathematical model to elucidate the muscle‐contraction inhibition effect using datasets derived from mice and rats, incorporating measurements of CMAP and DAS. In addition, human data comprising CMAP measurements were included in our analysis. This study proposes a valuable approach for PK‐PD modeling of BoNT/A and highlights its potential applications.

CONFLICT OF INTEREST STATEMENT

The authors declare that they have no conflicts of interest. H.‐j.R., S.K., and M.P. are employees of Medytox Inc.

Supporting information

Supporting Information S1

BDD-45-190-s001.docx (1.2MB, docx)

ACKNOWLEDGMENTS

The authors gratefully acknowledge the financial support received for this research from the following sources: Chungnam National University; Institute of Information and Communications Technology Planning and Evaluation grant funded by the government of the Republic of Korea (MSIT; No. RS‐2022‐00155857; Artificial Intelligence Convergence Innovation Human Resources Development [Chungnam National University]); the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT; No. RS‐2023‐00278597, NRF‐2022R1A2C1010929, and NRF2022R1A5A7085156); and the Korea Environmental Industry & Technology Institute (KEITI) through the Core Technology Development Project for Environmental Diseases Prevention and Management (2021003310001), funded by the Korea Ministry of Environment.

Ryu, H.‐j. , Kwak, S. , Park, M. , & Yun, H.‐y. (2024). Model‐based interspecies interpretation of botulinum neurotoxin type A on muscle‐contraction inhibition. Biopharmaceutics and Drug Disposition, 45(4-6), 190–200. 10.1002/bdd.2398

DATA AVAILABILITY STATEMENT

The data underlying this article will be made available upon reasonable request from the corresponding authors.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Supporting Information S1

BDD-45-190-s001.docx (1.2MB, docx)

Data Availability Statement

The data underlying this article will be made available upon reasonable request from the corresponding authors.

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