Investigating Endogenous Opioids Unravels the Mechanisms Behind Opioid-Induced Constipation, a Mathematical Modeling Approach
Abstract
1. Introduction
2. Results
2.1. 5HT Has a Positive Cooperative Effect on cAMP Accumulation
Species (Reaction Network) | Species (COPASI) | Initial Concentration in μM | Source |
---|---|---|---|
5HT | 5HT | Model Calibration Appendix A.2 | |
5HTIN | 5HT_IN | Model Calibration Appendix A.2 | |
5HTR4 | 5HTR4 | [31] | |
AC | AC | Model Calibration Appendix A.2 | |
5HTR4:5HT | 0 | ||
AC:ALPHA_S_GTP | 0 | ||
AC:ALPHA_I_GTP | 0 | ||
ALPHA_S_GDP | 0 | ||
ALPHA_I_GDP | 0 | ||
ALPHA_S_GDP_BG_S | 0.05 | Model Calibration Appendix A.2 | |
ALPHA_I_GDP_BG_I | 0.05 | Model Calibration Appendix A.2 | |
ALPHA_S_GTP | 0 | ||
ALPHA_I_GTP | 0 | ||
BG_S | 0 | ||
BG_I | 0 | ||
MOR | MOR | [31] | |
MOR:OL | 0 | ||
OL | OL | 0 | |
OL_Blood | 0 |
Parameter | Description | Value | Source |
---|---|---|---|
Endogenous serotonin (in EC cell) synthesis rate constant | ms−1 | Model calibration Appendix A.3 | |
Endogenous serotonin (in EC cell) release rate constant | 0.001 ms−1 | Calculated from [14] | |
Endogenous serotonin (in EC cell) degradation rate constant | 0.01 ms−1 | Model calibration Appendix A.3 | |
Cellular serotonin degradation rate constant | 0.01 ms−1 | Model calibration Appendix A.3 | |
Reuptake of intracellular serotonin into EC cell rate constant | ms−1 | Model calibration Appendix A.3 | |
Endogenous 5HT binding to 5HTR4 | M−1·ms−1 | Model calibration Appendix A.3 | |
Endogenous 5HT unbinding from 5HTR4 | ms−1 | Model calibration Appendix A.3 | |
Rate at which administered opioid reaches the desired tissue via the blood | ms−1 | Estimated from [32] | |
rate at which opioid in the desired tissue is metabolized | ms−1 | Estimated from [32] | |
Rate at which opioid in the blood stream is eliminated | ms−1 | Estimated from [32] | |
Rate at which opioid binds to MOR | varying for opioids | Calculated from different sources Appendix A.3 | |
Rate at which opioid unbinds from MOR | varying for opioids | Calculated from different sources Appendix A.3 | |
Rate at which subunint is activated | 0.2 M−1·ms−1 | Calculated from [33] | |
Rate at which and reform into G protein complex | 0.033 M−1·ms−1 | Calculated from [33] | |
Rate at which the GTP is hydrolyzed into a GDP | ms−1 | Calculated from [34] | |
Rate at which AC and form a complex | M−1·ms−1 | [35] | |
Rate at which AC and form a complex | M−1·ms−1 | [35] | |
rate at which dissociates from AC | ms−1 | Model calibration Appendix A.3 | |
rate at which dissociates from AC | ms−1 | Model calibration Appendix A.3 |
2.2. The Activation of the Opioid Pathway Inhibits cAMP Accumulation
2.3. cAMP Accumulation Drastically Decreases upon Acute Treatment with Opioids
2.4. cAMP Shows Differences in Recovery Times
2.5. Modulating Opioid Degradation Is an Alternative Approach to Improving the cAMP Recovery
3. Discussion
4. Methods and Materials
4.1. Reaction Network
4.2. Software and Model Implementation
4.3. Mapping AC Activity to cAMP Production
4.4. In Silico Protonation of Endomorphin-2
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
Appendix A.1. Reaction Parameters
Receptor Density | Fitted (k1, k2, , n) | (nM) | (%) |
---|---|---|---|
5730 | (0.1, 1.0, 2.1, 1.96) | 1.37 | 38 |
9510 | (0.0065, 14.14, 13.5, 2.44) | 1.7 | 46 |
19,840 | (0.018, 2.97, 6.2, 2.09) | 1.49 | 58 |
31,100 | (0.007, 50.25, 25.99, 2.24) | 1.59 | 69 |
Appendix A.2. Initial Conditions
- We calibrated the initial concentration of AC, such that the AC activity is around 40%. It was shown by Das et al. that the baseline muscle contraction is in the human colon is around 40% [12].
- We calibrated the initial concentrations of 5HT and 5HTIN such that 5HTIN is smaller than 5HT as estimated in [29].
- We calibrated the initial concentration of the receptor species MOR and 5HTR4 to that given in [31]. We calibrated the initial concentration of both and to ensure an approximate maximum AC activity of 40%.
Appendix A.3. Parameter Settings
- Synthesis of 5HTIN was calibrated using the COPASI sliders to ensure that the concentration ratio of 5HTIN and 5HT was greater than 1 as estimated in [29].
- We calibrated and to ensure a ratio greater than 1 for 5HTIN and 5HT.
- We calibrated to ensure a particular clearance time.
- We calibrated the binding and unbinding rate for 5HT to ensure an of around 0.05 M, as implemented in Das et al.
- We calculated the binding and unbinding rates using values from available resources (see Table 4).
- We calibrated the reaction rates for , , and , such that the maximum amplitude of AC was capped at 40%, as suggested in Das et al.
Appendix A.4. Stoichiometric Matrix
Appendix A.5. Choice of Recovery Treshold
Treshold | Morphine (d) | Methadone (d) | Fentanyl (d) | Endomorphin-2 (h) |
---|---|---|---|---|
50% | 6.162 | 4.446 | 4.177 | 6.191 |
57.5% | 6.539 | 4.781 | 4.454 | 6.191 |
65% | 6.891 | 5.117 | 4.705 | 6.191 |
72.5% | 7.318 | 5.563 | 4.957 | 6.191 |
80% | 7.796 | 5.982 | 5.259 | 6.191 |
Appendix A.6. Effects of Varying 5HT Reuptake Rates on cAMP Recovery
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Compartment | i | |
---|---|---|
Serotonin Pathway () | 1 | * |
2 | IN | |
3 | IN | |
4 | ||
5 | IN | |
6 | ||
7 | ||
8 | ||
9 | ||
10 | ||
11 | ||
12 | ||
Opioid Pathway () | 1 | |
2 | ||
3 | ||
4 | ||
5 | ||
6 | ||
7 | ||
8 | ||
9 | ||
10 | ||
Competing Pathway () | 1 | see Equation (2) |
2 | ||
3 |
Drug | (nM) | Simulations | Reference |
---|---|---|---|
Morphine | 76.08 ± 9.19 [36] | 6.7 [37] | |
Methadone | 41.92 ± 28.31 [38] | 8.7 ± 0.13 | 7.5 [37] |
Fentanyl | 0.57± 0.12 [39] | 10.04 ± 0.03 | 8.9 [40] |
Endomorphin-2 | 2.33 ± 0.19 [20] | 9.43 ± 0.01 | 8.42 [23] |
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Coomber, C.; Chewle, S.; Secker, C.; Fackeldey, K.; Weber, M.; Winkelmann, S.; Schütte, C.; Sunkara, V. Investigating Endogenous Opioids Unravels the Mechanisms Behind Opioid-Induced Constipation, a Mathematical Modeling Approach. Int. J. Mol. Sci. 2025, 26, 6207. https://doi.org/10.3390/ijms26136207
Coomber C, Chewle S, Secker C, Fackeldey K, Weber M, Winkelmann S, Schütte C, Sunkara V. Investigating Endogenous Opioids Unravels the Mechanisms Behind Opioid-Induced Constipation, a Mathematical Modeling Approach. International Journal of Molecular Sciences. 2025; 26(13):6207. https://doi.org/10.3390/ijms26136207
Chicago/Turabian StyleCoomber, Celvic, Surahit Chewle, Christopher Secker, Konstantin Fackeldey, Marcus Weber, Stefanie Winkelmann, Christof Schütte, and Vikram Sunkara. 2025. "Investigating Endogenous Opioids Unravels the Mechanisms Behind Opioid-Induced Constipation, a Mathematical Modeling Approach" International Journal of Molecular Sciences 26, no. 13: 6207. https://doi.org/10.3390/ijms26136207
APA StyleCoomber, C., Chewle, S., Secker, C., Fackeldey, K., Weber, M., Winkelmann, S., Schütte, C., & Sunkara, V. (2025). Investigating Endogenous Opioids Unravels the Mechanisms Behind Opioid-Induced Constipation, a Mathematical Modeling Approach. International Journal of Molecular Sciences, 26(13), 6207. https://doi.org/10.3390/ijms26136207