Team:AFCM-Egypt/Model
Modeling
Mathematical Modeling of platform-responsiveness "Math never lies"
Mathematical modelling is a powerful tool for verifying and evaluating synthetic biology solutions…….. In this mathematical model, we will consider the effect of the introduction of TMP, Riboswitch, and Toehold Switch into the system. We believe this model was able to Increase the expression and effectiveness of the vaccine, provide an auto-regulatory function to the platform and provide methods for the termination of the vaccine.
Our Circuit design
| TMP | ToeHoldOn | Antibody | ChimVac |
|---|---|---|---|
| 1 | 0 | 0 | 0 |
| 1 | 1 | 1 | 0 |
| 1 | 1 | 0 | 0 |
| 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 1 |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 1 |
| 0 | 0 | 0 | 0 |
The truth tables briefly illustrates the logic gates used in our design that’s diagramed using logisim tool software. It represents the decision made in the whole system which consists of 2 AND gates and finally, OR gates.
| Parameter | Symbol | Unit | Description | Estimation |
| syn_mRNA1 | Co | molL-1min-1 | Synthesis rate of the DD-MS2 | 7.58e-06 |
| syn_mRNA2 | C1 | molL-1min-1 | Synthesis rate of Toeholdon | 7.20e-06 |
| syn_mRNA3 | C2 | molL-1min-1 | Synthesis rate of VLPvac | 8.76e-06 |
| syn_Pep | C3 | min-1 | Synthesis rate of the protein | 2.07e-05 |
| deg_Pep | d1 | min-1 | Degradation rate of the protein | 5.38e-3 |
| Pep1max | µo | molL-1 | Maximal protein concentration factor | 4.87e-10 |
| Pep2max | µ1 | molL-1 | Maximal protein concentration factor | 1.11e-05 |
| Kleak | Ko | molL-1min-1 | Basal leakiness transcription rate | 8.96e-06 |
| Kleak1 | K1 | molL-1min-1 | Basal leakiness transcription rate | 2.08e-06 |
| deg_mRNA | do | min-1 | Degradation rate of the mRNA | 0.1386 |
| state1 | Lo | dimensionless | The state of the input | 0 or 1 |
| state2 | L1 | dimensionless | The state of the input | 0 or 1 |
Equations of AND gate
(Co) represents the synthesis rate of the DD-MS2 related to the state of the input1, (do) represents the degradation rate of mRNA so, it is to acquire the safety which Riboswitch fused with destabilizing domain (DD) that is controllable by TMP administration that acts as small molecule inhibitor to inhibit transcription if the circuit is uncontrollable, (C3) represents the rate of the protein , (d1) represents the degradation rate of the protein, mRNA2 and (C1) represents the synthesis rate of Toeholdon related to the state of the input.2 which ToeholdOnmotif switch upstream to vaccine that bind miRNA indicating increased tumor growth in order to remove the inhibitory effect of Riboswitch to make more copies of transcripts to combat cancer cells, (µo, µ1) represents the maximum concentration factor of the proteins ,(C2) represents the synthesis rate of the VLPvac and the expression of the vaccine depend on absence of TMP and removing the inhibitory effect of Riboswitches or binding of miRNA to upstream Toehold switch.
Simulation
Equations of NOT gate
(Co) represents the synthesis rate of the DD-MS2, (do) represents the degradation rate of mRNA so, it is to acquire the safety which Riboswitch fused with destabilizing domain (DD) that is controllable by TMP administration that acts as small molecule inhibitor to inhibit transcription if the circuit is uncontrollable, (C3) represents the rate of the protein , (d1) represents the degradation rate of the protein, mRNA2 and (C1) represents the synthesis rate of Toeholdon which ToeholdOnmotif switch upstream to vaccine that bind miRNA indicating increased tumor growth in order to remove the inhibitory effect of Riboswitch to make more copies of transcripts to combat cancer cells, (µo) represents the maximum concentration factor of the protein, Kmax represents the Maximal repression capacity, and the expression of the vaccine depend on absence of TMP and removing the inhibitory effect of Riboswitches or binding of miRNA to upstream Toehold switch. *The higher upper bound of 𝑃𝑒𝑝𝑚𝑎𝑥 is to ensure that the estimated mRNA level is settled at the same order of magnitude of the protein level.
Simulation
Equations of OR gate
(Co) represents the synthesis rate of the DD-MS2 related to the state of the input1, (do) represents the degradation rate of mRNA so, it is to acquire the safety which Riboswitch fused with destabilizing domain (DD) that is controllable by TMP administration that acts as small molecule inhibitor to inhibit transcription if the circuit is uncontrollable, (C3) represents the rate of the protein , (d1) represents the degradation rate of the protein, mRNA2 and (C1) represents the synthesis rate of Toeholdon related to the state of the input.2 which ToeholdOnmotif switch upstream to vaccine that bind miRNA indicating increased tumor growth in order to remove the inhibitory effect of Riboswitch to make more copies of transcripts to combat cancer cells, (µ) represents the maximum concentration factor of the proteins ,(C2) represents the synthesis rate of the VLPvac and the expression of the vaccine depend on absence of TMP and removing the inhibitory effect of Riboswitches or binding of miRNA to upstream Toehold switch.
Simulation
Dynamics of Riboswitches
This year the team designed 2 Riboswitches:
dCas13-L7Ae fused by Gly Ser linker: that has an inhibitory effect on the transcription by binding to its kink-turn. It is cell specific design by binding to mRNA of PD-L1 which has an immune evasion role in the cancerous environment especially TLCs.
DD-MS2: which is dependent on TMP to be administered in uncontrolled cases to stabilize DD therefore, inhibiting the circuit via binding of MS2 to its small nuclear ribonucleoprotein (snRNP)
| Parameter | Symbol | Unit | Description | Estimation |
| mRNA1on | O | mRNA | the number of mRNA1on | 1 |
| MS2 | A | protein | the number of MS2 | 1 |
| mRNA2off | B | mRNA | the number of mRNA2off | 1 |
| mRNA2on | T | mRNA | the number of mRNA2on | 1 |
| PP7 | R | protein | the number of PP7 | 1 |
| mRNA3on | Q | mRNA | the number of mRNA3on | 1 |
| mRNA3off | M | mRNA | the number of mRNA3off | 1 |
| mRNA1off | V | mRNA | the number of mRNA1off | 1 |
| dmRNA1on | min-1 | cleavage rate of dmRNA1on | 0.104 | |
| dmRNA2on | min-1 | cleavage rate of dmRNA2on | 0.1386 | |
| dmRNA3on | min-1 | cleavage rate of dmRNA3on | 0.197 | |
| dmRNA1off | min-1 | cleavage rate of dmRNA1off | 0.085 | |
| dmRNA2off | min-1 | cleavage rate of dmRNA2off | 0.073 | |
| dmRNA3off | min-1 | cleavage rate of dmRNA3off | 0.015 | |
| dMS2 | peptide chain*min-1 | degradation rate of MS2 | 1.67*10-3 | |
| dPP7 | peptide chain*min-1 | degradation rate of PP7 | 1.67*10-3 | |
| pMS2 | min-1 | translation rate of MS2 | 27.660 | |
| pPP7 | min-1 | translation rate of PP7 | 11.277 | |
| Cr1 | min-1 | transcription rate of mRNA1 | 14.400 | |
| Cr2 | min-1 | transcription rate of mRNA2 | 0.144 | |
| Cr3 | min-1 | transcription rate of mRNA3 | 2.400 | |
| k1 | dimensionless | constant of the second order reaction MS2 and mRNA2off | 6*10-6 | |
| k2 | dimensionless | constant of the second order reaction MS2 and mRNA3on | 7.22*10-6 | |
| k3 | dimensionless | constant of the second order reaction PP7 and mRNA1on | 6.8*10-6 |
Equations of Riboswitch
Simulation in the level of mRNA
Simulation in the level of protein
In-silico thermodynamic modeling of Toehold switches
After designing the 2 toehold switches in our circuit to construct an environment-sensitive system, we modeled the structural stability using NUPACK that predicts secondary structures of single stranded RNA with mean free energy (MFE).
Minimal Free Energy (MFE) Difference:
The binding of the toehold switch to the trigger must be preferable to both the toehold switch and the trigger in their unbound states. A metric for quantifying the favorability and spontaneity of binding is the change in Gibbs free energy (G). Because a lower G in the bound state indicates higher favorability, it has to be lower than the total of G in the toehold and G in the trigger in the unbound state.
MFE = ΔGbound - (ΔGtoehold + ΔGtrigger)
Toehold degrader switch:
Unbound state:
Bound state:
MFE = ΔGbound - (ΔGtoehold + ΔGtrigger)
MFE = -51.80 - (-27.20 -4.80) = -19.8 which indicates a high stability of the bound state between toehold degrader and miRNA(trigger)
Toehold On switch:
Unbound state:
MFE = ΔGbound - (ΔGtoehold + ΔGtrigger)
MFE = -45.40 - (-24.40 -1.90) = -19.1 which indicates a high stability of the bound state between toehold degrader and miRNA (trigger)
Mathematical Modeling of Apoptotic cell population
In order to simulate the dynamics of apoptotic cell population of Hbax we used a system of ODEs and fitted parameters based of previous experimental data which can initiate a cascades of activation of apoptosis proteins results in the activation of ATR and p53 proteins. As a response to the DNA damage, the proapoptosis proteins, such as Bax and Bak, will be activated, leading to the opening of mitochondrial permeability transition pore. This triggers the release of cytochrome c from mitochondria into the cytosol. On the other hand, the antiapoptosis protein, such as Bcl-2, will inhibit the release of cytochrome c. Cytochrome c will bind with Apaf-1 and activate caspase 9. Activated caspase 9 will then cleave and activate downstream caspases, such as caspase 3, which is also known as the apoptosis executor protein.
| Parameter | Unit | Estimation |
| Bax | molL-1min-1 | [0-1] |
| Bid | molL-1min-1 | [0-1] |
| tBid | molL-1min-1 | 0 |
| Casp3 | min-1 | [0-1] |
| Casp3* | min-1 | 0 |
| APOP | molL-1 | 0 |
| granB* | molL-1 | 0 |
| P53* | molL-1min-1 | 0 |
| BCl2 | molL-1min-1 | [0-1] |
| Casp8* | min-1 | 0 |
| Casp9* | dimensionless | 0 |
| Casp10* | dimensionless | 0 |
| K1 | 𝜇M−1s−1 | 1 |
| K2 | 1 s−1 | 1 |
| K3 | 𝜇M−1s−1 | 1 |
| K4 | 1 s−1 | 1 |
| K5 | 𝜇M−1s−1 | 1 |
| K6 | 1 s−1 | 1 |
| K7 | 𝜇M−1s−1 | 1 |
| K8 | 1 s−1 | 1 |
| K9 | 𝜇M−1s−1 | 1 |
| K10 | 1 s−1 | 1 |
| K11 | 𝜇M−1s−1 | 1 |
| K12 | 𝜇M−1s−1 | 1 |
| K13 | 1 s−1 | 1 |
| K14 | 1 s−1 | 1 |
| K15 | 𝜇M−1s−1 | 10 |
| K16 | 1 s−1 | 0.5 |
| K17 | 𝜇M−1s−1 | 1 |
| K18 | 1 s−1 | 1 |
| K19 | 𝜇M−1s−1 | 1 |
| K20 | 𝜇M−1s−1 | 1 |
| K21 | 𝜇M−1s−1 | 1 |
| K22 | 𝜇M−1s−1 | 1 |
| K23 | 𝜇M−1s−1 | 1 |
| K24 | 𝜇M−1s−1 | 1 |
Equation of Apoptotic cell population
Simulation
References:
Melisa Hendrata, Janti Sudiono, "A Computational Model for Investigating Tumor Apoptosis Induced by Mesenchymal Stem Cell-Derived Secretome", Computational and Mathematical Methods in Medicine, vol. 2016, Article ID 4910603, 17 pages, 2016. https://doi.org/10.1155/2016/4910603
Modeling the immune response of the vaccine
Immune validation and computational simulation of the immune-specific interaction potential according to the amount of antigen introduced were performed to estimate the number of vaccine injections required along a period of 6 months.
