A Mathematical Model of In Vitro Cellular Uptake of Zoledronic Acid and Isopentenyl Pyrophosphate Accumulation
Abstract
:1. Introduction
2. Materials and Methods
2.1. In Vitro Model Assay
2.2. Mathematical Model
2.3. Parameter Estimation
3. Results
3.1. Model 1, Continuous Experiment
3.2. Model 1, Pulse Experiment
3.3. Model 2, Continuous Experiment
3.4. Model 2, Pulse Experiment
3.5. Model Identifiability Analysis
4. Discussion and Conclusions
- (1)
- ZA is taken up by macrophages and osteoclast cells in endocytic vacuoles; acidification of vacuoles seems to be required to release it into the cytoplasm.
- (2)
- ZA inhibits FPP synthase in the mevalonate pathway through conformational changes in the enzyme upon binding of ZA.
- (3)
- A second conformational change after the binding of the second substrate, IPP, forms a tightly bound inhibition complex that provides further stabilisation of the FPPS and ZA complex [45].
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Variable | Unit | Meaning |
---|---|---|
Y | M | Pre-zoledronate concentration (zoledronate in medium) |
Z | pmol/mg prote | Zoledronate acid concentration (in adhered cells) |
G | pmol/mg prote | Isopentenyl pyrophosphate antigen concentration |
B | % | Percentage of bound enzyme |
U | % | Percentage of unbound enzyme |
Parameter | Unit | Kinetic Model | |
---|---|---|---|
Continuous | Pulse | ||
/h | 0.007 | 0.607 | |
/h | 0.004 | 0.029 | |
M | — | 0 | |
/h | 0.001 | 18.06 | |
pmol/mgprot/M | 25.46 | 14.91 | |
/h | 0 | 0 |
Parameter | Unit | Model 2 | |
---|---|---|---|
Continuous | Pulse | ||
pmol/mgprot/h | 141.7 | 22.18 | |
/h | 0.081 | 0 | |
/h/% | 0.051 | 0.224 | |
/h | 5.181 | 22.44 | |
pmol/mgprot | 27.32 | 0.988 | |
/(pmol/mgprot) | 1.806 | 0.017 | |
/h/(pmol/mgprot) | 0.099 | 0.150 | |
/h | 0.168 | 0.057 |
Parameter | Unit | Model 1 | |
---|---|---|---|
Continuous | Pulse | ||
pmol/mgprot/h | 169.7 | 6.466 | |
/h | 0.101 | 0 | |
/h | 13.25 | 2.391 | |
/h | 13.35 | 2.391 | |
pmol/mgprot | 12.71 | 2.704 | |
/pmol/mgprot | 0.195 | 0.377 |
Parameter [Unit] | SD | CV | LLC | ULC |
---|---|---|---|---|
[/h] | 0.001 | 19.30 | 0.004 | 0.0092 |
[pmol/mgprot/M] | 4.922 | 19.30 | 15.81 | 35.11 |
[/h] | 0.064 | 62.80 | −0.023 | 0.226 |
[/pmol/mgprot] | 0.258 | 146.3 | −0.330 | 0.683 |
[/h] | 0.051 | 63.10 | −0.019 | 0.181 |
[/h/%] | 0.525 | 1029 | −0.977 | 1.080 |
[/h/(pmol/mgprot)] | 0.051 | 459.7 | −0.791 | 0.988 |
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Lo Presti, E.; D’Orsi, L.; De Gaetano, A. A Mathematical Model of In Vitro Cellular Uptake of Zoledronic Acid and Isopentenyl Pyrophosphate Accumulation. Pharmaceutics 2022, 14, 1262. https://doi.org/10.3390/pharmaceutics14061262
Lo Presti E, D’Orsi L, De Gaetano A. A Mathematical Model of In Vitro Cellular Uptake of Zoledronic Acid and Isopentenyl Pyrophosphate Accumulation. Pharmaceutics. 2022; 14(6):1262. https://doi.org/10.3390/pharmaceutics14061262
Chicago/Turabian StyleLo Presti, Elena, Laura D’Orsi, and Andrea De Gaetano. 2022. "A Mathematical Model of In Vitro Cellular Uptake of Zoledronic Acid and Isopentenyl Pyrophosphate Accumulation" Pharmaceutics 14, no. 6: 1262. https://doi.org/10.3390/pharmaceutics14061262
APA StyleLo Presti, E., D’Orsi, L., & De Gaetano, A. (2022). A Mathematical Model of In Vitro Cellular Uptake of Zoledronic Acid and Isopentenyl Pyrophosphate Accumulation. Pharmaceutics, 14(6), 1262. https://doi.org/10.3390/pharmaceutics14061262