A Mathematical Model of In Vitro Cellular Uptake of Zoledronic Acid and Isopentenyl Pyrophosphate Accumulation
The mevalonate pathway is an attractive target for many areas of research, such as autoimmune disorders, atherosclerosis, Alzheimer’s disease and cancer. Indeed, manipulating this pathway results in the alteration of malignant cell growth with promising therapeutic potential. There are several pharm...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-06-01
|
| Series: | Pharmaceutics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1999-4923/14/6/1262 |
| _version_ | 1827657468344270848 |
|---|---|
| author | Elena Lo Presti Laura D’Orsi Andrea De Gaetano |
| author_facet | Elena Lo Presti Laura D’Orsi Andrea De Gaetano |
| author_sort | Elena Lo Presti |
| collection | DOAJ |
| description | The mevalonate pathway is an attractive target for many areas of research, such as autoimmune disorders, atherosclerosis, Alzheimer’s disease and cancer. Indeed, manipulating this pathway results in the alteration of malignant cell growth with promising therapeutic potential. There are several pharmacological options to block the mevalonate pathway in cancer cells, one of which is zoledronic acid (ZA) (an N-bisphosphonate (N-BP)), which inhibits the farnesyl pyrophosphate (FPP) synthase enzyme, inducing cell cycle arrest, apoptosis, inhibition of protein prenylation, and cholesterol reduction, as well as leading to the accumulation of isopentenyl pyrophosphate (IPP). We extrapolated the data based on two independently published papers that provide numerical data on the uptake of zoledronic acid (ZA) and the accumulation of IPP (Ag) and its isomer over time by using in vitro human cell line models. Two different mathematical models for IPP kinetics are proposed. The first model (Model 1) is a simpler ordinary differential equation (ODE) compartmental system composed of 3 equations with 10 parameters; the second model (Model 2) is a differential algebraic equation (DAE) system with 4 differential equations, 1 algebraic equation and 13 parameters incorporating the formation of the ZA+enzyme+Ag complex. Each of the two models aims to describe two different experimental situations (continuous and pulse experiments) with the same ZA kinetics. Both models fit the collected data very well. With Model 1, we obtained a prevision accumulation of IPP after 24 h of 169.6 pmol/mgprot/h with an IPP decreasing rate per (pmol/mgprot) of ZA (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>k</mi><mrow><mi>X</mi><mi>G</mi><mi>Z</mi></mrow></msub></semantics></math></inline-formula>) equal to 13.24/h. With Model 2, we have comprehensive kinetics of IPP upon ZA treatment. We calculate that the IPP concentration was equal to 141.6 pmol/mgprot/h with a decreasing rate/percentage of 0.051 (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>k</mi><mrow><mi>X</mi><mi>G</mi><mi>U</mi></mrow></msub></semantics></math></inline-formula>). The present study is the first to quantify the influence of ZA on the pharmacodynamics of IPP. While still incorporating a small number of parameters, Model 2 better represents the complexity of the biological behaviour for calculating the IPP produced in different situations, such as studies on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>γ</mi><mi>δ</mi></mrow></semantics></math></inline-formula> T cell-based immunotherapy. In the future, additional clinical studies are warranted to further evaluate and fine-tune dosing approaches. |
| first_indexed | 2024-03-09T22:45:32Z |
| format | Article |
| id | doaj.art-7594aa5f491643cc8859700c218fd03f |
| institution | Directory Open Access Journal |
| issn | 1999-4923 |
| language | English |
| last_indexed | 2024-03-09T22:45:32Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Pharmaceutics |
| spelling | doaj.art-7594aa5f491643cc8859700c218fd03f2023-11-23T18:30:53ZengMDPI AGPharmaceutics1999-49232022-06-01146126210.3390/pharmaceutics14061262A Mathematical Model of In Vitro Cellular Uptake of Zoledronic Acid and Isopentenyl Pyrophosphate AccumulationElena Lo Presti0Laura D’Orsi1Andrea De Gaetano2CNR-IRIB (Institute for Biomedical Research and Innovation), National Research Council, Via Ugo La Malfa 153, 90146 Palermo, ItalyCNR-IASI BioMatLab (Institute of Analysis, Systems and Computer Science), National Research Council, Via dei Taurini 19, 00185 Rome, ItalyCNR-IRIB (Institute for Biomedical Research and Innovation), National Research Council, Via Ugo La Malfa 153, 90146 Palermo, ItalyThe mevalonate pathway is an attractive target for many areas of research, such as autoimmune disorders, atherosclerosis, Alzheimer’s disease and cancer. Indeed, manipulating this pathway results in the alteration of malignant cell growth with promising therapeutic potential. There are several pharmacological options to block the mevalonate pathway in cancer cells, one of which is zoledronic acid (ZA) (an N-bisphosphonate (N-BP)), which inhibits the farnesyl pyrophosphate (FPP) synthase enzyme, inducing cell cycle arrest, apoptosis, inhibition of protein prenylation, and cholesterol reduction, as well as leading to the accumulation of isopentenyl pyrophosphate (IPP). We extrapolated the data based on two independently published papers that provide numerical data on the uptake of zoledronic acid (ZA) and the accumulation of IPP (Ag) and its isomer over time by using in vitro human cell line models. Two different mathematical models for IPP kinetics are proposed. The first model (Model 1) is a simpler ordinary differential equation (ODE) compartmental system composed of 3 equations with 10 parameters; the second model (Model 2) is a differential algebraic equation (DAE) system with 4 differential equations, 1 algebraic equation and 13 parameters incorporating the formation of the ZA+enzyme+Ag complex. Each of the two models aims to describe two different experimental situations (continuous and pulse experiments) with the same ZA kinetics. Both models fit the collected data very well. With Model 1, we obtained a prevision accumulation of IPP after 24 h of 169.6 pmol/mgprot/h with an IPP decreasing rate per (pmol/mgprot) of ZA (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>k</mi><mrow><mi>X</mi><mi>G</mi><mi>Z</mi></mrow></msub></semantics></math></inline-formula>) equal to 13.24/h. With Model 2, we have comprehensive kinetics of IPP upon ZA treatment. We calculate that the IPP concentration was equal to 141.6 pmol/mgprot/h with a decreasing rate/percentage of 0.051 (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>k</mi><mrow><mi>X</mi><mi>G</mi><mi>U</mi></mrow></msub></semantics></math></inline-formula>). The present study is the first to quantify the influence of ZA on the pharmacodynamics of IPP. While still incorporating a small number of parameters, Model 2 better represents the complexity of the biological behaviour for calculating the IPP produced in different situations, such as studies on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>γ</mi><mi>δ</mi></mrow></semantics></math></inline-formula> T cell-based immunotherapy. In the future, additional clinical studies are warranted to further evaluate and fine-tune dosing approaches.https://www.mdpi.com/1999-4923/14/6/1262zoledronic acidgamma-delta T cellsimmunotherapyisopentenyl pyrophosphateATRAIDpharmacodynamics |
| spellingShingle | Elena Lo Presti Laura D’Orsi Andrea De Gaetano A Mathematical Model of In Vitro Cellular Uptake of Zoledronic Acid and Isopentenyl Pyrophosphate Accumulation Pharmaceutics zoledronic acid gamma-delta T cells immunotherapy isopentenyl pyrophosphate ATRAID pharmacodynamics |
| title | A Mathematical Model of In Vitro Cellular Uptake of Zoledronic Acid and Isopentenyl Pyrophosphate Accumulation |
| title_full | A Mathematical Model of In Vitro Cellular Uptake of Zoledronic Acid and Isopentenyl Pyrophosphate Accumulation |
| title_fullStr | A Mathematical Model of In Vitro Cellular Uptake of Zoledronic Acid and Isopentenyl Pyrophosphate Accumulation |
| title_full_unstemmed | A Mathematical Model of In Vitro Cellular Uptake of Zoledronic Acid and Isopentenyl Pyrophosphate Accumulation |
| title_short | A Mathematical Model of In Vitro Cellular Uptake of Zoledronic Acid and Isopentenyl Pyrophosphate Accumulation |
| title_sort | mathematical model of in vitro cellular uptake of zoledronic acid and isopentenyl pyrophosphate accumulation |
| topic | zoledronic acid gamma-delta T cells immunotherapy isopentenyl pyrophosphate ATRAID pharmacodynamics |
| url | https://www.mdpi.com/1999-4923/14/6/1262 |
| work_keys_str_mv | AT elenalopresti amathematicalmodelofinvitrocellularuptakeofzoledronicacidandisopentenylpyrophosphateaccumulation AT lauradorsi amathematicalmodelofinvitrocellularuptakeofzoledronicacidandisopentenylpyrophosphateaccumulation AT andreadegaetano amathematicalmodelofinvitrocellularuptakeofzoledronicacidandisopentenylpyrophosphateaccumulation AT elenalopresti mathematicalmodelofinvitrocellularuptakeofzoledronicacidandisopentenylpyrophosphateaccumulation AT lauradorsi mathematicalmodelofinvitrocellularuptakeofzoledronicacidandisopentenylpyrophosphateaccumulation AT andreadegaetano mathematicalmodelofinvitrocellularuptakeofzoledronicacidandisopentenylpyrophosphateaccumulation |