| Citation: |
Jong Hyuk Byun, Anna Park, Il Hyo Jung. RECEPTOR-MEDIATED ENDOCYTOSIS MODELING OF ANTIBODY-DRUG CONJUGATES TO THE RELEASED PAYLOAD WITHIN THE INTRACELLULAR SPACE CONSIDERING TARGET ANTIGEN EXPRESSION LEVELS[J]. Journal of Applied Analysis & Computation, 2020, 10(5): 1848-1868. doi: 10.11948/20190232
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RECEPTOR-MEDIATED ENDOCYTOSIS MODELING OF ANTIBODY-DRUG CONJUGATES TO THE RELEASED PAYLOAD WITHIN THE INTRACELLULAR SPACE CONSIDERING TARGET ANTIGEN EXPRESSION LEVELS
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Abstract
An antibody-drug conjugate (ADC) is one of the effective treatment modalities designed as a targeted therapy for treating tumors. Certain ADCs such as brentuximab vedotin are known to kill negative tumor cells indirectly via membrane permeability and bystander-killing effect and to kill positive tumor cells directly. In this study, we propose a mathematical model to describe the ADC-receptor endocytosis mechanism and to predict payloads over a time profile more accurately, while considering target antigen-positive (Ag+)/negative (Ag–) cells. We discuss how the target-antigen expression levels derived using a ratio of Ag+ to Ag– cells determine the payload release in the intracellular space. The model is aimed at capturing the amount of the payloads based on the target expression levels with the total number of cells fixed. The results indicate that (i) the profile of the total payloads over a time within the intracellular space is less influenced by the target expression levels after a time period, but the slope at the growth phase in which the payload increases is determined by the target expression levels, (ii) the change in the area under the curve of the total intracellularly released payload with a change in the ratio of Ag+ to Ag– cells is more significant due to the initial ADC injection, (iii) the fluctuations in the released payloads within the Ag+ cells increase as the target expression levels decrease, unlike in the case of Ag– cells or extracellular space. In addition, the time $ t_{max} $ that corresponds to the maximum payload concentration $ C_{max} $ is shifted towards the right as the target-antigen levels decrease, and it is strengthened by an increase in the initial free ADCs. The proposed model may reduce the discrepancy between the experiment and the model in the prediction of payloads over time profile. -
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References
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Jong Hyuk Byun, Anna Park, Il Hyo Jung. RECEPTOR-MEDIATED ENDOCYTOSIS MODELING OF ANTIBODY-DRUG CONJUGATES TO THE RELEASED PAYLOAD WITHIN THE INTRACELLULAR SPACE CONSIDERING TARGET ANTIGEN EXPRESSION LEVELS[J]. Journal of Applied Analysis & Computation, 2020, 10(5): 1848-1868. doi: 10.11948/20190232
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- Figure 1. Mechanism of action of ADCs. After ADCs bind to the target antigens, the ADC-target complex undergoes internalization (endocytosis) and is subsequently degraded by lysosomes. Some of the intracellular release payloads in the cytosol permeate into the extracellular spaces and then enter into the cytosol of neighboring tumor cells. Some neighboring cells are Ag– cells that are subject to bystander killing. A specific target antigen is indicated by a red triangle.
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Figure 2. (a) Control (
$ C_0 = 0 $ ) on the left panel and ADC administration of 2.5 mg/kg and 10 mg/kg at the center and right, respectively. As the value of$ \beta $ is small, the free ADC disposition occurs slowly. We assume that the ADC disposition occurs only through the endocytosis mechanism. (b) Log-scale along the Y-axis is used to present the initial dynamics. -
Figure 3. Control on the right panel and ADC administrations of 10 mg/kg and 2.5 mg/kg on the left and center panels, respectively.
$ C_{int, p} $ represents the concentration of the released payload in the Ag+ cells. Fluctuations increase as$ \beta $ decreases. Furthermore, the time$ t_{max} $ corresponding to the maximum concentration$ C_{max} $ is gradually shifted to the right as$ \beta $ decreases and$ C_0 $ increases. -
Figure 4. Control on the right panel and ADC administration of 10 mg/kg and 2.5 mg/kg on the left and center panels, respectively.
$ C_{int, n} $ represents the concentration of the released payload in the Ag– cells. This is related to the bystander-killing effect. The slope in the time phase during which the payload increases and the equilibrium points depend on the value of$ \beta $ . -
Figure 5. Control on the right panel and ADC administration of 10 mg/kg and 2.5 mg/kg on the left and center panel, respectively. The intracellularly released payloads are
$ C_{int, p}+C_{int, n} $ . Equilibrium points are independent of$ \beta $ , but the slope in the time phase during which the payload increases depends on the value of$ \beta $ . In addition, this is effect becomes more apparent as$ C_0 $ increases. -
Figure 6. (a) AUC of the payloads over
$ \beta $ profile within Ag+ cells. The relation is proportional to and independent of the amount of$ C_0 $ . The ratio is measured by$ \frac{AUC_{c_{int, p}}}{AUC_{c_{int, p}|_{\beta = 1}}}. $ (b) AUC of the payloads over$ \beta $ profile in Ag– cells. The relation is roughly inversely proportional, and$ C_0 $ has a lower influences on it. The shrinkage ratio is determined using$ \frac{AUC_{c_{int, n}}}{AUC_{c_{int, n}|_{\beta = 0.1597}}}. $ -
Figure 7. (a) Profile of the AUC of the payloads within intracellular space over
$ \beta $ . The ratio is measured using$ \frac{AUC_{c_{int, p}+c_{int, n}}}{AUC_{c_{int, p}+c_{int, n}|_{\beta = 1}}}. $ (b) Profile of AUC over$ \tilde R_0 $ . The shrinkage ratio is determined as$ \frac{AUC_{c_{int, p}+c_{int, n}}}{AUC_{c_{int, p}+c_{int, n}|_{\tilde R_0 = 833}}}. $ The greater the initial$ C_0 $ , the greater the shrinkage owing to the values of$ \beta $ and$ \tilde R_0 $ . -
Figure 8. (a) Slope of the intracellular payloads depends on
$ \beta $ , but the equilibrium points are independent of$ \beta $ . (b) If$ C_0 $ is small, then$ t_{max} $ is shifted to the right, and the change in the slope due to$ \beta $ is small. (c)$ k = $ influx/efflux is investigated. From this and Fig. 7(a), the influence of the change in$ k $ is predicted to be greater than that of$ \beta $ . -
Figure 9.
$ k = k_{in}/k_{out} $ . As$ k $ increases, the concentrations of$ C_{int, p} $ ,$ C_{int, n} $ , and the intracellular payload increase. We perform a simulation to determine the relation between$ k $ ,$ \beta $ , and$ AUC $ for two initial ADC concentrations. The impact of the permeability is crucial for the ADC efficacy related to the bystander killing as well as direct killing. As$ \beta $ increases, the intracellularly released payload is slightly increased, but this is hardly observed when the initial ADC concentration is low. (a)$ \frac{C_{int, p}}{C_{int, p}|_{k = 50, \beta = 1}} $ ,$ C_0 = 2.5mg/kg $ . (b)$ \frac{C_{int, p}}{C_{int, p}|_{k = 50, \beta = 1}} $ ,$ C_0 = 10mg/kg $ . (c)$ \frac{C_{int, n}}{C_{int, n}|_{k = 50, \beta = 0}} $ ,$ C_0 = 2.5mg/kg $ . (d)$ \frac{C_{int, n}}{C_{int, n}|_{k = 50, \beta = 0}} $ ,$ C_0 = 10mg/kg $ . (e)$ \frac{C_{int, p}+C_{int, n}}{C_{int, p}+C_{int, n}|_{k = 50, \beta = 1}} $ ,$ C_0 = 2.5mg/kg $ . (f)$ \frac{C_{int, p}+C_{int, n}}{C_{int, p}+C_{int, n}|_{k = 50, \beta = 1}} $ ,$ C_0 = 10mg/kg $ .