Home
Team
Project
Human Practices
Wet Lab
Model Safety Sustainability

Model

Mathematical model

Overview

In order to simulate the kinetics of our therapeutic platform, we used mathematical modeling in order to understand the different relations between our parts through formulating four main mathematical models.

These models are based on different sets of ordinary differential equations (ODEs) containing different populations of the designed approach. The parameters’ values were retrieved from experimental literature data; these values were manipulated to fit into our formulated ODEs.

We aimed at providing these models as modular platforms for future iGEM teams working on similar designs specifically to simulate the kinetics of binding cascades between the ligand and the designed receptor. The parameter values for these reactions can be easily altered according to each teams’ unique set of designs. Moreover, our team has constructed 2 software tools that ease the usage of the designed models in simulating the designed circuits. These tools are available on the team's software Gitlab page via this link:



These models have also directed the flow of our project’s design as they helped us in understanding the kinetics of our parts. They also allowed us to make comparisons between different parts to choose the most suitable of which based on parts measurements. Therefore, these models have a significant contribution to the progress of our own project and for future iGEM teams.

Three models describe parts’ function and activity, while the last model describes cells’ behavior and interaction. Our models for this year include:

  1. The binding model of the vascular endothelial growth factor (VEGF) and its receptors.
  2. An Internal domain activation model for production of the yes-associated protein 1 (YAP-1).
  3. Protein specific mRNA switch activation.
  4. Fibroblasts’ behavior and interactions

Model 1 : Binding system between VEGF and VEGFR chains

Description

We simulated the kinetics of Vascular endothelial growth factor (VEGF) and its receptor by ODEs [1]. The receptor is composed of the 2 different chains: VEGFR-1 and VEGFR-2. Firstly, the ligand binds to VEGFR-2 because the binding affinity of VEGFR-2 to its ligand is higher compared to that of VEGFR-1 [2]. Eventually, this binding dimerizes the receptor chains leading to activation of the internal domain parts which consists of Tobacco Etch Virus (TEV) protease. This protease cleaves at its own cleavage sites on the internal domain chains to release the d-Cas9 system.

Assumptions

  1. It is assumed that the initial population of Vascular endothelial growth factor (VEGF) is 1. To model the binding capacity at conctant rate of VEGF concentration.

  2. It was found that the binding affinity of VEGFR2 to its ligand has higher affinity compared to that of VEGFR1. [2]

  3. it is assumed that the higher binding affinity reflects a higher and stable dimerization rate. As higher and stable dimerization mediates higher internal domain activity.
For more details about the equations Click Here

Index

This model is concised into 7 equations that describe the binding kinetics of VEGF initially to VEGFR2, then binding of this (VEGF - VEGFR2) complex to VEGFR1 to form (VEGFR2-VEGF-VEGFR1) complex. Sequentially, the complex initiates the dimerization of the receptor’s chains to activate the TEV protease that releases the d-Cas9 system.

This system is composed of 7 main populations:

  1. VEGFR2
  2. Complex of VEGF and VEGFR2
  3. VEGFR1
  4. Complex of (VEGF-VEGFR2) and VEGFR1
  5. Dimerization
  6. TEV protease
  7. d-Cas9 system

Abbreviations of model 1

A Vascular endothelial growth factor
R2 Vascular endothelial growth factor receptor 2 (VEGFR2)
R2A Complex of VEGF and VEGFR2
R1 Vascular endothelial growth factor receptor 1 (VEGFR1)
R2AR1 Complex of (VEGF-VEGFR2) and VEGFR1
D Dimerization process of VEGFR chains
TEV Tobacco etch virus protease
V1 MESA VEGFR1 modular extracellular sensor architecture
V2 MESA VEGFR2 modular extracellular sensor architecture
C d-Cas9 system

Parameters

Description Value Unit Reference
K1 Rate of binding between vascular endothelial growth factor (VEGF) to VEGFR2. 0.9 M−1 s−1 [3]
K2 Rate of binding between (VEGF-VEGFR2) complex to (VEGFR1). 4.4 M−1 s−1 [3]
K3 Dimerization rate of VEGFR chains. 2.1 cm2 mol−1 s− 1 [1]
K5 Cleavage rate of TEV protease to release d-Cas9 system. 1 units [4]
K6 Rate of activation of d-Cas9 system. 0.01 s−1 [-]
RD1 Rate of dissociation of (VEGF-VEGFR2) complex. 1 s−1 [3]
RD2 Rate of dissociation of (VEGFR2-VEGF-VEGFR1) complex. 0.00132 s−1 [3]
d1 Rate of degradation of VEGFR2. 0.1 s−1 [3]
d2 Rate of degradation of (VEGF-VEGFR2) complex 0.5 s−1 [3]
d3 Rate of degradation of VEGFR1. 0.09 s−1 [3]
d4 Rate of degradation of (VEGFR2-VEGF-VEGFR1) complex. 0.1 s−1 [3]
d5 Degradation rate of TEV protease. 0.01 s−1 [4]
d6 Degradation rate of the d-Cas9 system 0.05 s−1 [5]

Equations

Equation (1)

Figure (1) describes equation (1).

Fig 1. Illustrates the kinetics of VEGF binding to VEGFR2 and their dissociation.

The first equation describes free VEGFR-2 (R2) which decreases upon:

  1. Binding of VEGF (A) to VEGFR2 (R2) at rate (K1).
  2. Degradation of free VEGFR2 (R2) at rate (d1).

Moreover, they increase in case of :

  1. Dissociation of VEGF-VEGFR2 (R2A) complex at rate (RD1).

Equation (2)

Figure (2) describes equations (2,3,4 and 5).

Fig 2. Illustrates the kinetics of (VEGF-VEGFR2) complex and its binding to VEGFR1 and their dissociation. In addition to the dimerization process of the 2 chains of the receptor.

In this equation describes VEGF-VEGFR2 complex (R2A) which decreases upon:

  1. Dissociation of the binding complex VEGF-VEGFR2 (R2A) at rate (RD1).
  2. Binding of VEGF-VEGFR2 (R2A) complex to VEGFR1 (R1) receptor at rate (K2).
  3. Degradation of VEGF-VEGFR2 (R2A) complex at rate (d2).

Moreover, they increase in case of :

  1. Binding of VEGF (A) to VEGFR2 (R2) at rate (K1).
  2. Dissociation of the binding complex VEGFR2-VEGF-VEGFR1 (R2AR1) at rate (RD2).

Equation (3)

This ODE describes free VEGfR-1 (R1) which decrease upon:

  1. Binding of VEGF-VEGFR2 (R2A) complex to VEGFR1 (R1) at rate (K2).
  2. Degradation of free VEGFR1 at rate (d3).

On the other hand, they increase in case of:

  1. Dissociation of VEGFR2-VEGF-VEGFR1 (R2AR1) complex at rate (RD2).

Equation (4)

The fourth equation describes VEGFR2-VEGF-VEGFR1 complex (R2AR1) which decrease upon:

  1. Dissociation of VEGFR2-VEGF-VEGFR1 (R2AR1) complex at rate (RD2).
  2. Degradation of VEGFR2-VEGF-VEGFR1 (R2AR1) complex at rate (d4).

In contrast, they increase in cases of :

  1. Binding of VEGF-VEGFR2 (R2A) complex to VEGFR1 (R1) at rate (K2).

Equation (5)

This equation describes the receptor dimerization process at rate (K3). This process vanishes by degradation of the binding complex VEGFR2-VEGF-VEGFR1 (R2AR1) at rate (d4).(As shown in Graph (2))

Equation (6)

Figure (3) describes equations (6 and 7).

Fig 3. Illustrates the activation of TEV protease and its action on specific cleavage site (TCS) for releasing d-Cas9 system and its activation.

The sixth equation describes TEV protease activation upon dimerization of VEGFR chains at a rate of (K3). However, this activity is decreased by TEV protease degradation rate at (d5).(As shown in Graph (2) )

Equation (7)

The seventh equation describes TEV protease activation sequelae in which the free d-Cas9 system (C) increases in response to the TEV protease action on the specific cleavage sites at the receptor’s internal domain (TCS1 and TCS2) at rate of (K5). The activation of the d-Cas9 system depends on the assembly of the d-cas9 N-terminal and C-terminal at rate (K6). Nevertheless, d-Cas9 activity decreases by the d-Cas9 system degradation rate (d6). ( As shown in Graph (3) )

Model (1) plotting:

Graph 1. Illustrates the decreasing of VEGFR2 (R2) (Red line) upon binding of VEGF (A) to form VEGF-VEGFR2 complex (R2A) (Yellow line) which increases till its binding to VEGFR1 (R1), which decreases once binding happens ( Black line). To finally form a binding complex (R2AR1) (Blue line).

Graph 2. Shows the dimerization level (Blue line) that reaches steady state upon binding of VEGF to its receptor to activate TEV protease (Red line) to release d-Cas9 system.

.

Graph 3. Demonstrates the released d-Cas9 system that activation reaches its peak at (60) unit time, upon activation of TEV protease.

How did this model affect the project design?

First iteration:

This model directed our project design as it was used to make a comparison between 2 types of receptors (homodimer receptor and heterodimer receptor). As concluded from this model, the activation of the TEV protease depends on the dimerization rate of the receptor’s two chains which mainly relies on the binding rate [2]. thus, we held a comparison between both receptor forms as shown in the next table:

  1. Homodimer receptor (receptor composed of 2 same chains which are VEGFR1).
  2. Heterodimer receptor (receptor composed of 2 different chains which are VEGFR2 and VEGFR1).

1- Homodimer receptor ( VEGFR1- VEGFR1 ) 2- Heterodimer receptor ( VEGFR2- VEGFR1 )

Graph 4. Illustrates the decreasing of free VEGFR (Black line) upon binding of VEGF to one of the receptor chains to form (RA) complex (Yellow line), the (RA) complex directly binds to the other chain of the receptor to final form a binding complex (RAR) (Blue line) that reachs 0.2.

As Illustrated in graph (1). The decreasing of VEGFR2 (Red line) upon binding of VEGF (A) to form VEGF-VEGFR2 complex (R2A) (Yellow line) which increases till its binding to VEGFR1 (R1), which decrease once the binding happend ( Black line). To finally form a binding complex (R2AR1) (Blue line) that reachs 0.4.

Graph 5. Shows the dimerization level (Blue line) that reaches steady state upon binding of VEGF to its receptor to activate TEV protease (Red line) to release d-Cas9 system.

As Illustrated in graph (2). The dimerization level (Blue line) that reaches steady state upon binding of VEGF to its receptor to activate TEV protease (Red line) to release d-Cas9 system.

Graph 6. Demonstrates the released d-Cas9 system that activation reaches its peak at (50) unit time, upon activation of TEV protease.

.

As Illustrated in graph (3). The released d-Cas9 system that activation reaches its peak at (60) unit time, upon activation of TEV protease.

It was concluded that the binding state of the heterodimer receptor is higher than homodimer receptor. As shown in Graphs (1,4)..

Sequentially, Sequentially, the dimerization level in the heterodimer receptor is higher which reflects higher activation of the receptor internal domain including TEV protease and d-Cas9 system, as shown Graphs (2,5)..

Second iteration:

The second reason for choosing to use the heterodimer receptor form instead of the homodimer form receptors was concluded by testing the receptor’s basal activity through measuring the d-Cas9 system activity in absence of the VEGF Ligand (OFF STATE):

  1. Heterodimer receptor internal domain composed of 2 chains
    (VEGFR2 connected to N terminal of TEV and d-Cas9 while VEGFR1 connected to C terminal of TEV and d-Cas9).

  2. V1 MESA receptor internal domain composed of 2 chains
    (1st chain : VEGFR1 connected to complete form of d-Cas9, 2nd chain :composed of complete form of TEV protease).

  3. V2 MESA receptor internal domain composed of 2 chains
    (1st chain :VEGFR2 connected to complete form of d-Cas9, 2nd chain :composed complete form of TEV protease).

we compared d-Cas9 activity depending on TEV protease activity in off state for each of the previous conditions as shown in the next table.

1-Heterodimer receptor

Graph 7. Illustrates basal activity of the d-Cas9 system of our heterodimer receptor.

2-V1 MESA receptor (VEGFR1) 3-V2 MESA receptor (VEGFR2)

Graph 8. Demonstrates basal activity of the d-Cas9 system of V1 MESA receptor.

Graph 9. Shows basal activity of the d-Cas9 system of V2 MESA receptor.

Through analyzing the results of the previous models:

  1. The heterodimer receptor shows the lowest basal activity in the off state of the receptor as the activity of the d-Cas9 reaches its peak at 45 time units that reflects the activity of TEV protease, by help of experimental literature [2]. So we choose the heterodimer receptor for our design.

  2. V1 MESA receptor (VEGFR1) shows high basal activity in the off state of the receptor , compared to the heterodimer receptor. As the activity of the d-Cas9 reaches its peak at 45 time units that reflects the activity of TEV protease, by help of experimental literature [6].

  3. V2 MESA receptor (VEGFR2) shows the highest basal activity in the off state , compared to the heterodimer receptor. As the activity of the d-Cas9 reaches its peak at 45 time units that reflects the activity of TEV protease, by help of experimental literature [6].

Conclusion

The heterodimer receptor is the most suitable choice as it has higher binding state upon interaction with the VEGFR ligand. It was also proven to have low basal activity in the off state compared to V1 and V2 MESA receptors.

Graph 10. Compares between the binding state of homodimer and heterodimer receptors.

Graph 11. Shows the basal activity of different receptors.

Model (1) References

1- Mac Gabhann F, Popel AS. Dimerization of VEGF receptors and implications for signal transduction: a computational study. Biophys Chem. 2007 Jul;128(2-3):125-39. doi: 10.1016/j.bpc.2007.03.010. Epub 2007 Mar 24. PMID: 17442480; PMCID: PMC2711879.

2- Baeumler TA, Ahmed AA, Fulga TA. Engineering Synthetic Signaling Pathways with Programmable dCas9-Based Chimeric Receptors. Cell Rep. 2017 Sep 12;20(11):2639-2653. doi: 10.1016/j.celrep.2017.08.044. PMID: 28903044; PMCID: PMC5608971.

3- White C, Rottschäfer V, Bridge LJ. Insights into the dynamics of ligand-induced dimerisation via mathematical modelling and analysis. J Theor Biol. 2022 Apr 7;538:110996. doi: 10.1016/j.jtbi.2021.110996. Epub 2022 Jan 24. PMID: 35085533.

4- Paththamperuma C, Page RC. Fluorescence dequenching assay for the activity of TEV protease. Anal Biochem. 2022 Dec 15;659:114954. doi: 10.1016/j.ab.2022.114954. Epub 2022 Oct 18. PMID: 36265691; PMCID: PMC9662696.

5- Sreekanth V, Zhou Q, Kokkonda P, Bermudez-Cabrera HC, Lim D, Law BK, Holmes BR, Chaudhary SK, Pergu R, Leger BS, Walker JA, Gifford DK, Sherwood RI, Choudhary A. Chemogenetic System Demonstrates That Cas9 Longevity Impacts Genome Editing Outcomes. ACS Cent Sci. 2020 Dec 23;6(12):2228-2237. doi: 10.1021/acscentsci.0c00129. Epub 2020 Nov 18. PMID: 33376784; PMCID: PMC7760466.

6- Schwarz KA, Daringer NM, Dolberg TB, Leonard JN. Rewiring human cellular input-output using modular extracellular sensors. Nat Chem Biol. 2017 Feb;13(2):202-209. doi: 10.1038/nchembio.2253. Epub 2016 Dec 12. PMID:27941759.

Model 2 : The activaton model of the d-Cas9 system for production of intrinsic YAP-1 ( yes associated protein )

Description

We simulated the kinetics and the sequel of activity of the internal domain upon dimerization of the 2 separate chains of VEGFR, activating Tobacco Etch Virus (TEV) protease which releases both N-terminal and C-terminal of d-Cas9 system which leads to their assembly and activation [1]. The d-Cas9 system is loaded with 3 different transcription activators (VP64, GAL4 and CMV trans-enhancer) to show the optimum level of YAP-1 [2], resulting in optimum proliferation and differentiation of stem cells.

Fig 4. Illustrates the interaction between the 3 transaction activators (VP64 , GAL4 and CMV trans-enhancer).

Fig 5. Illustrates the transcrption of YAP-1.

Assumptions

  1. It is assumed that the normal YAP-1 production from the stem cells is Zero. to ensure that the transcription level of YAP-1 is affected only by our transcription activators and not biased by the normal YAP-1. [1]



For more details about the equations Click Here

Index

This system consists of 5 ODEs. It is starts by releasing and activating the d-Cas9 system, loaded with 3 different transcription activators (VP64, GAL4 and CMV trans-enhancer) which induces the YAP-1 transcription.

In addition to the population mentioned in model (1), the activation level of the different transcription activators and YAP-1 transcription used in this model are based on the results of model (1). So the activation of the external domain till production of YAP-1 is sequential .

Abbreviations of model 2

C d-Cas9 system
VP VP64 transcription activator
GAL GAL4 transcription activator
CMV CMV trans-enhancer
YAP Yes associated proteins-1

Parameters

Description Value Unit Reference
K7 Rate of activation of CMV trans-enhancer for transcription of YAP. 5.4 s−1 [3]
K8 Rate of activation of VP64 transcription activator for transcription of YAP. 1.8 s−1 [4]
K9 Rate of activation of GAL4 transcription activator for transcription of YAP. 1.3 s−1 [3]
d7 Degradation rate of CMV trans-enhancer. 0.15 s−1 [3]
d8 Degradation rate of VP64 transcription activator. 0.2 s−1 [4]
d9 Degradation rate of GAL4 transcription activator. 0.05 s−1 [3]
d10 Degradation rate of YAP 3.3 s−1 [5]

Equations

Equation (1)

Figure (6) describes equations (1, 2, 3 and 4).

Fig 6. Illustrates the activation kinetics the 3 transaction activators (VP64 , GAL4 and CMV trans-enhancer) loaded on the d-Cas9 system for initiating transcrption of YAP-1.

The first equation describes the cytomegalovirus (CMV) trans-enhancer activation. This activation depends on releasing of the d-Cas9 system, yielding increase in transcrption level of YAP-1 at the rate (K7). Moreover, its activity is decreased by degradation of CMV trans-enhancer at rate (d7).

Equation (2)

This ODE describes the activation level of VP64. When the d-cas9 system is released , VP-64 is turned on leading to increase the transcrption level of YAP-1 at rate (K8). This activation is decreased by degradation of VP-64 at rate (d8).

Equation (3)

This equation describes GAL4 activation level. Upon releasing of d-Cas9 system, GAL4 is stimulated, meanwhile Increasing the transcrption level of YAP-1 at rate (K9), respectively. In contrast, this activation is decreased by degradation of GAL-4 at rate (d9)

Equation (4)

The fourth equation in that model describes YAP-1 production that determined by activation rates of CMV trans-enhancer , VP64 and GAL4 transcription activators at rate (K7 , K8 and K9) respectively. In contrast, the YAP-1 concentration is decreased by degradation of YAP-1 at rate (d10).

Equation (5,6,7,8,9,10,11)

These equations represent the binding kinetics of VEGF to its receptor and the dimerization process for activating the internal domain parts till releasing of the d-Cas9 system.

Model (2) plotting:

Graph 12. Illustrates the relation between activation levels of different transcriptional activators (CMV trans-enhancer , VP64 and GAL4) for Increasing the transcription level of YAP-1 (Black line).

How did this model direct the project design and system action?

In order to choose the optimum level of YAP-1 transcrption for proliferation and regeneration of the stem cells [2], we held a comparison between 3 different transcription activators ( CMV trans-enhancer , VP64 and GAL4) showing different levels of YAP-1 based on parameter values supported by literature experimental date [3] as shown in the following table :

1- CMV trans-enhancer shows high expression level of YAP-1, reaching 13800 at 65 time units 2- VP64 transcription activator shows very low expression level of YAP-1 , reaching 1150 at 55 time units.

Graph 13. Demonstrates the relation between activation level of CMV trans-enhancer (Blue line) for increasing the transcription level of YAP-1 (Black line).

Graph 14. shows the relation between activation level of VP64 transcription activator (Yellow line) for increasing the transcription level of YAP-1 (Black line).

3- GAL4 transcription activator shows low expression level of YAP-1, reaching 2500 at 75 time units. 4- The 3 transcription activators Integrated design shows the optimum level of YAP-1, reaching 17000 at 65 time units.

Graph 15. Illustrates the relation between activation level of GAL4 transcription activator (Red line) for increasing the transcription level of YAP-1 (Black line).

As Illustrated in graph (12). The relation between activation levels of different transcriptional activators (CMV trans-enhancer , VP64 and GAL4) for increasing the transcription level of YAP-1 (Black line).

As there are different types of transcription activators that can be used, as mentioned in the previous table :

  1. We modeled the kinetics of CMV trans-enhancer for YAP-1 production. The transcription level was not satisfactory even showing high YAP-1 expression reaching its peak at 65 time units. As shown in graph (13)

  2. Also, we modeled VP64 transcription activator kinetics for YAP-1 transcription. The result shows the lowest transcription level for YAP-1 , reaching its peak at 55 time units. Conclusively, the time needed to reach the peak of expression was better; however, its activation level for YAP-1 was not satisfying to reach our target. As shown in graph (14)

  3. Moreover, we modeled the kinetics of GAL4 transcription activator for YAP-1 transcription. The report illustrates low transcription level of YAP-1 , achieving its peak at 75 time units, which will reach YAP-1 full generation later than other models. Even its concentration was not enough to reach our target. As shown in graph (15)

  4. Additionally, we modeled the kinetics of the 3 transcription activators integrated together (CMV trans-enhancer, VP64 and GAL4) in our design for transcription of YAP-1, to get the high benefit from each transcription activator, considered in time of activation for each one to have transcription of YAP-1 for long time comparing to each one separate. The result shows high expression of YAP1- to reach its peak at 65 unit time which is better in time needed to reach the peak of expression and the full regeneration. so we choose the integrated design for our project.As shown in graph (12)

Conclusion

Through the previous modeled transcrption activator the integrated design of the 3 transcription activators ( VP64 ,GAL4 and CMV trans-enhancer ) shows the optimum transcrption level of YAP-1

Graph 16. Shows YAP-1 production level under effect of different transcription activators.

How is this model considered to be modular and useful for others?

Model 1 and 2 gave an advantage to compare between different binding states according to the type of the receptor for a specific ligand. that leads to activation of the internal domain, the internal domain composed of d-Cas system loaded with different transcrption avtivators . Also this model compares between the different transcription activators (CMV trans-enhancer, VP64 and GAL4) for reaching the optimum transcrption level of the desired protein depending on ODEs based on estimated parameter values. Thus, this model is considered to be modular.

Future teams can use these designed ODEs to simulate binding of different receptors and ligands. In addition to testing the same or different transcription activators’ activity for their desired protein by estimating parameter values to fit their design.

In order to make these ODEs and the models accessible for iGEM teams, we have made a user-friendly online interface tool to allow the users to edit the parameter values for their aimed receptor binding and the transcription activator. For accessing our tool Click Here.

Model (2) References:

1- Ma, D., Peng, S. & Xie, Z. Integration and exchange of split dCas9 domains for transcriptional controls in mammalian cells. Nat Commun 7, 13056 (2016). https://doi.org/10.1038/ncomms13056

2- Goodman CA, Dietz JM, Jacobs BL, McNally RM, You JS, Hornberger TA. Yes-Associated Protein is up-regulated by mechanical overload and is sufficient to induce skeletal muscle hypertrophy. FEBS Lett. 2015 Jun 4;589(13):1491-7. doi: 10.1016/j.febslet.2015.04.047. Epub 2015 May 8. PMID: 25959868; PMCID: PMC4442043.

3- Xu X, Gao J, Dai W, Wang D, Wu J, Wang J. Gene activation by a CRISPR-assisted trans enhancer. Elife. 2019 Apr 11;8:e45973. doi: 10.7554/eLife.45973. PMID: 30973327; PMCID: PMC6478495.

4- Morita S, Horii T, Kimura M, Hatada I. Synergistic Upregulation of Target Genes by TET1 and VP64 in the dCas9-SunTag Platform. Int J Mol Sci. 2020 Feb 25;21(5):1574. doi: 10.3390/ijms21051574. PMID: 32106616; PMCID: PMC7084704.

5- LeBlanc L, Ramirez N, Kim J. Context-dependent roles of YAP/TAZ in stem cell fates and cancer. Cell Mol Life Sci. 2021 May;78(9):4201-4219. doi: 10.1007/s00018-021-03781-2. Epub 2021 Feb 13. PMID: 33582842; PMCID: PMC8164607.

Model 3: MMP-9 specific mRNA switch : YAP-1 conditioned translation in target cells

Description

We simulated the kinetics and activity of matrix metalloproteinase 9 (MMP-9) specific mRNA switch, which is activated upon binding of MMP-9 to their nanobody-1 from the cap side and nanobody-3 from MS2 aptamer side , which leads to changing the switch into circular form for initiating the translation of YAP-1 in the targeted cells [3]. As shown in figure (7)

We prevent the switch’s basal activity through adding hammerhead ribozyme (HHR) to our design. In presence of HHR, the HHR undergoes self-cleavage which cleaves the following poly-A tail forbidding the poly-A tail to bind with the mRNA cap in absence of MMP-9 allowing proper switch on-off state transition. However, in absence of HHR, no cleavage will happen which means the presence of poly-A tail, permitting switch’s basal activity [3].

Fig 7. Illustrates the switch circularization through 4 steps

Assumptions

  1. We assumed that the unbounded MMP-9 will eventually decrease. Because the switch activation will contribute in healing process upon production of YAP-1 which decreases MMP-9 production.

  2. It is assumed that the degradation rate of HHR is zero, to ensure that HHR will do its function before its degradation.

  3. The dissociation rate between MMP-9 and their Nanobodies assumed to be zero. This is to reach the optimum level of YAP-1 translation to induce the healing process without being interrupted by the dissociation rate.

  4. we neglected the basal activity that may be due to cross talk between different MMPs.



For more details about the equations Click Here

Index

This system consists of 8 ODEs. The MMP-9 (MMP) binds to nanobody-1 (RA1) and nanobody-3 (RA3) to form a binding complex (CO). This combination promotes switch circularization (CF) in presence of MS2 aptamers (MS) that maintains its stability and HHR to control basal activity of poly-A tail (PA) for production the only desired amount of YAP-1 (YAP).

Abbreviations of model 3

MMP Matrix metalloproteinase 9
RA1 Free MMP9-nanobody-1
RA3 Free MMP9-nanobody-3
CO Binding complex of MMP with both RA1 and RA3
CF Circular form of the switch
MS MS2 aptamers
PA Poly-A tail
HHR Hammerhead ribozyme
YAP Yes associated protein-1 (YAP-1)

Parameters

Description Value Unit Reference
K10 Rate of expression of MMP-9 in wound site to represent their concentration 0.046 s−1 [1]
K11 Rate of binding between MMP-9 and nanobody-1. 0.00041 s−1 [2,8]
K12 Activation rate of poly-A tail to initiate circularization of the switch. 0.001 s−1 [3]
K13 Cleavage rate of HHR to separate poly-A tail. 0.1 s− 1 [4]
K14 Rate of circularization of the switch. 10 s−1 [-]
K15 Activation rate of MS2 aptamer. 0.0017 s−1 [3]
K19 Rate of binding between MMP-9 and nanobody-3. 0.00038 s−1 [2,8]
d11 Degradation rate of MMP-9. 0.1 s−1 [6]
d12 Degradation rate of nanobody-1. 0.02 s−1 [8]
d13 Degradation rate of the binding complex. 0.0001 s−1 [8]
d14 Degradation rate of the circulating form of the switch. 0.4 s−1 [-]
d15 Degradation rate of MS2 aptamer. 0.01 s−1 [3]
d19 Degradation rate of nanobody-3. 0.04 s−1 [8]
d10 Degradation rate of YAP. 3.3 s−1 [5]

Equations

Equation (1)

Fig 8. Illustrates the kinetics of MMP9 and its binding to MMP9-Nanobody to form the binding complex

The first equation describes the decrease in free MMP-9 level. This is due to:

  1. Binding of free MMP-9 to nanobody-1 (RA1) at rate (K11).
  2. Binding of free MMP-9 to nanobody-3 (RA3) at rate (K19).
  3. Degradation of MMP-9 at rate (d11).

In contrast, they increase in cases of :

  1. Formation rate of MMP-9 upon injury at rate (K10) so it will finally reflect the concentration of MMP.

Equation (2)

This equation describes the decrease in the number of free nanobody-1 (RA1). This is due to:

  1. Binding of free MMP-9 to nanobody-1 (RA1) at rate (K11).
  2. Degradation of nanobody-1 at rate (d12).

Equation (3)

This ODE describes the decrease in the number of free nanobody-3 (RA2) . This is due to:

  1. Binding of free MMP-9 to nanobody-3 (RA3) at rate (K19).
  2. Degradation of nanobody-3 (RA3) at rate (d19).

Equation (4)

Fig 9. Illustrates the kinetics of switch circularization

This equation describes the number of binding complexes that have been obtained from MMP-9 binding to nanobody-1 (RA1) and nanobody-3 (RA3) at the same time at rates (K11 and K19) simultaneously. In addition to the degradation rate of these binding complexes at rate (d13).

Equation (5)

The fifth equation describes the switch’s ability to circularize which happens once the MMP-9 binds to both nanobody-1 (RA1) and nanobody-3 (RA3) at the same time at rates (K11 and K19) simultaneously. Moreover, the activity of MS2 aptamers increases at rate (K15) upon binding of MMP-9 to their nanobodies to maintain the switch stability.

In addition to the degradation of the switch circular form at rate (d14). This occurred to initiate the YAP-1 translation without basal activity of the switch.

In case of absence of HHR the switch will have the ability to circulate by the aid of poly-A tail at rate (K12) in presence or absence of MMP-9.

Equation (6)

Fig 10. Illustrates the kinetics of HHR to cleave the poly-A tail

The sixth equation describes MS2 aptamer activity that increases upon binding of free MMP-9 to both nanobody-1 (RA1) and nanobody-3 (RA3) at the same time at rates (K11 and K19) simultaneously. For maintaining the switch stability that happens after the switch circularization at rate (K15). In addition to the degradation of the switch circular form at rate (d14) and degradation of the MS2 aptamer at rate (d15).

Equation (7)

This ODE describes the poly-A tail activity that vanishes by HHR cleavage rate through cleaving specific cleavage sites before PA at rate (K13). In addition to the degradation of the switch circular form at rate (d14).

Equation (8)

The eighth equation describes the YAP-1 translation which depends on:

  1. Formation rate of MMP-9 upon injury at rate (K14)
  2. Binding of free MMP-9 to nanobody-1 (RA1) at rate (K11).
  3. Binding of free MMP-9 to nanobody-3 (RA3) at rate (K19).
  4. The switch circularization at rate (K14).

Moreover, the degradation rate of YAP-1 at rate (d10).

Model (3) plotting:

Graph 17. Illustrates the relation between decreasing free MMP-9 (Blue line) upon their binding to nanobody-1 (orange line) and nanobody-3 (Red line) at the same time, which results in forming a binding complex ( Green line).

Graph 18. Shows the relation between circularization form activity of our switch (Yellow line) and their ability for YAP-1 production (Black line).

we concluded that the activation of our conditioned switch through presence of MMP-9 results in changing the switch into its circular form for translation of the YAP-1 in the targeted cells [7].

How did this model direct the project design ?

In order to choose the most suitable ligand that binds to our nanobodies to activate our switch, we have compared 3 different MMPs that are found in the wound site ( MMP-1 , MMP-2 and MMP-9).the comparison held according to MMPs docking score results and their concentration at the onset of injury [1]. As shown in the next table :

1- MMP-1 docking score with nanobody-1 is -276.9, ( K11 = 0.00033) and nanobody-3 is -265.74 ( K19 = 0.00032). In addition, it has low formation rate in the wound site (K10 = 0.00046). . 2- MMP-2 docking score nanobody-1 is -240.83, ( K11 = 0.000291) and nanobody-3 is -241.75 ( K19 = 0.000292). In addition, it has moderate formation rate in the wound site (K10 = 0.005).

Graph 19. Illustrates the relation between decreasing free MMP-1 (Blue line) upon their binding to nanobody-1 (orange line) and nanobody-3 (Red line) at the same time, which results in forming a binding complex ( Green line).

Graph 20. Demonstrates the relation between decreasing free MMP-2 (Blue line) upon their binding to nanobody-1 (orange line) and nanobody-3 (Red line) at the same time, which results in forming a binding complex ( Green line).

3- MMP-9 docking score with nanobody-1 is -335.83, ( K11 = 0.00041) and with nanobody-3 is (K19 = 0.00038). In addition, it has the highest formation rate in the wound site (K10 = 0.046).

As Illustrated in graph (17). The relation between decreasing free MMP-9 (Blue line) upon their binding to nanobody-1 (orange line) and nanobody-3 (Red line) at the same time, which results in forming a binding complex ( Green line).

  1. MMP-1 shows the lowest binding affinity to the nanobodies according to their docking score, that reachs 200 at (11) unit time which implies long time for binding. In addition, it has low concentration in the wound site [1].

  2. MMP-2 shows high binding affinity to the nanobodies according to their docking score which is not sufficient , that reachs 550 at (4) unit time which implies satisfactory time for binding, but it has moderate concentration in the wound site [1].

  3. MMP-9 shows the highest binding affinity to the nanobodies according to their docking score which is sufficient, that reachs 700 at (3.5) unit time which implies satisfactory time for binding. In addition, it has high concentration in the wound site [1].

How did the project design affects model kinetics ?

The first design of the switch did not include the HHR part, so we modeled the parts as it was (As shown in figure (11)). After further searching, we found that presence of poly-A tails increases basal activity of the switch (which impair the on and off state) that can initiate translation of YAP-1 in absence of MMP-9 which is supported by literature experimental data [3]. So we have changed our design to add an HHR part for safe conditioned production of YAP-1, as shown in the next figures with and without basal activity of the switch.

Fig 11. Illustrates the kinetics of switch circularization without HHR

Fig 12. Illustrates the kinetics of switch circularization after modification with HHR

1- Without HHR. 2- With HHR.

Graph 21. Illustrates the presence of basal activity of the switch through the ability of the switch to circulate (Yellow line) resulting in production of YAP-1 (Black line).

Graph 22. Shows the absence of basal activity of the switch through the inability of the switch to circulate (Yellow line) resulting in zero production of YAP-1 (Black line).

The comparison between presence and absence of HHR part shows:

  1. We modeled our switch design without the presence of HHR that shows activation of the switch with help of basal activity of the poly-A tail. (As shown in graph (21))

  2. After that ,We modeled the kinetics of HHR to cleave specific cleavage sites in the genetic circuit, these cleavage sites located before Poly-A tail to prevent activation of the switch in absence of MMP-9 for safe production of YAP-1.
    So the basal activity of the switch is zero. (As shown in graph (22))

How is this model considered to be modular and useful for others?

This model allowed to compare between different substances based on their binding abilities to the nanobodies of the translation initiation device switch (TID). These substances' binding abilities were determined by their concentration and docking score. It can also model the change of the switch linear form to a circular form for starting translation of the desired protein.

Future teams can use these designed ODEs for comparing different substances binding states to the TID switch nanobodies that affect the circularization process of the switch and the translation of their desired protein.

In order to make these ODEs and the models accessible for iGEM teams, we have made a user-friendly online interface tool to allow the users to edit the parameter values for their aimed protein translation. For accessing our tool Click Here.

Model (3) References:

1- Carlton M, Voisey J, Parker TJ, Punyadeera C, Cuttle L. A review of potential biomarkers for assessing physical and psychological trauma in paediatric burns. Burns Trauma. 2021 Feb 9;9:tkaa049. doi: 10.1093/burnst/tkaa049. PMID: 33654699; PMCID: PMC7901707.

2- Lee DW, Kochenderfer JN, Stetler-Stevenson M, Cui YK, Delbrook C, Feldman SA, Fry TJ, Orentas R, Sabatino M, Shah NN, Steinberg SM. T cells expressing CD19 chimeric antigen receptors for acute lymphoblastic leukaemia in children and young adults: a phase 1 dose-escalation trial. The Lancet. 2015 Feb 7;385(9967):517-28.

3- Shao, J., Li, S., Qiu, X. et al. Engineered poly(A)-surrogates for translational regulation and therapeutic biocomputation in mammalian cells. Cell Res 34, 31–46 (2024). https://doi.org/10.1038/s41422-023-00896-y

4- Kawamura, Kunio & Ogawa, Mari & Konagaya, Noriko & Maruoka, Yoshimi & Lambert, Jean-François & Ter-Ovanessian, Louis & Vergne, Jacques & Herve, Guy & Maurel, Marie-Christine. (2022). A High-Pressure, High-Temperature Flow Reactor Simulating the Hadean Earth Environment, with Application to the Pressure Dependence of the Cleavage of Avocado Viroid Hammerhead Ribozyme. Life. 12. 1224. 10.3390/life12081224.

5- LeBlanc L, Ramirez N, Kim J. Context-dependent roles of YAP/TAZ in stem cell fates and cancer. Cell Mol Life Sci. 2021 May;78(9):4201-4219. doi: 10.1007/s00018-021-03781-2. Epub 2021 Feb 13. PMID: 33582842; PMCID: PMC8164607.

6- Hahn-Dantona E, Ruiz JF, Bornstein P, Strickland DK. The low density lipoprotein receptor-related protein modulates levels of matrix metalloproteinase 9 (MMP-9) by mediating its cellular catabolism. J Biol Chem. 2001 May 4;276(18):15498-503. doi: 10.1074/jbc.M100121200. Epub 2001 Feb 2. PMID: 11279011.

7- Goodman CA, Dietz JM, Jacobs BL, McNally RM, You JS, Hornberger TA. Yes-Associated Protein is up-regulated by mechanical overload and is sufficient to induce skeletal muscle hypertrophy. FEBS Lett. 2015 Jun 4;589(13):1491-7. doi: 10.1016/j.febslet.2015.04.047. Epub 2015 May 8. PMID: 25959868; PMCID: PMC4442043.

8- Shin YJ, Park SK, Jung YJ, Kim YN, Kim KS, Park OK, Kwon SH, Jeon SH, Trinh le A, Fraser SE, Kee Y, Hwang BJ. Nanobody-targeted E3-ubiquitin ligase complex degrades nuclear proteins. Sci Rep. 2015 Sep 16;5:14269. doi: 10.1038/srep14269. PMID: 26373678; PMCID: PMC4571616.

Model 4: MSCs’ effect on fibroblasts activity in wound healing

Description

When burn injuries take place, a breaking of skin integrity and soft tissue occurs. This results in the activation of different inflammatory cells within the wound site, in addition to the release of cytokines and growth factors, which trigger fibroblastic activity to start the healing process. This activity will be decreased by time due to the effect of different inflammatory cells and it will form a weak scar. But in extensive wounds like burns, scars are formed due to prolonged fibroblast activity [2]. [2].

This is what we targeted in model 4: the effect of mesenchymal stem cells (MSCs) in modulating the fibroblastic activity for extensive scar prevention [3]. Under modulation of MSCs, we simulate the kinetics and the activity of fibroblasts (proliferative, migratory and active forms) in producing extracellular matrix and collagen for wound healing.

For more details about the equations Click Here

Index

This system consists of 3 populations : Firstly, the proliferation of fibroblasts (PF). Secondly, its transformation to migratory fibroblasts (MF). Thirdly, when reaching the wound site, its transformation to active fibroblast (AF) to start wound healing. The three populations will be regulated by MSCs [3].

Abbreviations of model 4

PF Proliferative fibroblast
MF Migratory fibroblasts
AF Activated fibroblasts

Parameters

Description Value Unit Reference
K16 Proliferation rate of proliferative fibroblasts. 0.49 day [4]
K17 Proliferation rate of migratory fibroblasts. 0.6 day [4]
K18 Proliferation rate of activated fibroblasts. 0.3 day [4]
V1 Transformation rate of the 3 types of fibroblasts. 0.6 day [4]
V2 Rate of interaction of MSCs to fibroblasts. 0.7 day−1 x cell−1 [4]
V3 Baseline proliferation of Activated fibroblasts. 0.1 units/day [4]
d15 Degradation rate of the 3 types of fibroblasts (PF , MF and AF). 0.1 day [4]
d16 Rate at which inflammatory cells destroy the proliferative fibroblasts. 0.4 day [4]
d17 Rate at which inflammatory cells destroy the migratory fibroblasts 0.5 day [4]
d18 Rate at which inflammatory cells destroy the activated fibroblasts. 0.4 day [4]
N Activity of the inflammatory cells. 0.4 units [4]

Fig 13. Illustrates the interactions between MSCs and fibroblasts.Also, It illustrates the interactions between each other.

Fig 14. Illustrates the normal destruction of fibroblasts by inflammatory cells.

Equations

Equation (1)

The first equation clarifies the kinetics of the proliferative fibroblast activation through:

  1. Increasing their number (under the effect of cytokines and growth factors in the wound site) through:
    Their proliferation at rate ( K16).
  2. Decreasing their number through:
    Their degradation at rate (d15)
    Their transformation to migratory fibroblasts at rate (V1)
    The effect of different inflammatory cells at rate (d16)
    The interaction rate of MSCs for their modulation at rate (V2).

Equation (2)

The second equation describes the kinetics of the migratory fibroblast activation by:

  1. Increasing their number through:
    Their proliferation at rate (K17)
    The transformation of proliferative fibroblast (PF) to migratory fibroblast at rate (V1).
  2. Decreasing their number through:
    Their degradation at rate (d15)
    Their transformation to activated fibroblasts at rate (V1)
    The effect of different inflammatory cells at rate (d17)
    Interaction rate of MSCs for their modulation at rate (V2) .

Equation (3)

The third equation describes the kinetics of the activated fibroblast activation by :

  1. Increasing their number through:
    Their proliferation at rate (K18)
    The transformation of migratory fibroblast (MF) to activated fibroblast (AF) at rates (V1)
    Their baseline activity in prolonged inflammation at rate (V3).
  2. Decreasing their number through:
    Their degradation at rate (d15)
    The effect of different inflammatory cells at rate (d18)
    The interaction rate of MSCs for their modulation at rate (V2).

Model (4) plotting:

Graph 23. shows the increase in activated fibroblasts concentration until they eventually decrease with having low basal activity. Therefore, preventing scars formation.

Activity of fibroblasts during inflammatory response with MSCs VS without MSCs

1- With MSCs (V2=0.7) 2- without MSCs (V2=0)

As Illustrated in graph (23), The usage of MSCs increases the activated fibroblasts and allowed them to decrease with lower basal activity. Therefore, preventing scars formation

Graph 24. Demonstrates that withous MSCs, the concentration of activated fibroblasts have lower levels and have a prolonged basal activity that contributes in scars formation (Black line).

We compared the activity of fibroblasts in 2 different conditions :

  1. In presence of MSCs, it was found that MSCs modulated the inflammatory response and increased the activity of fibroblasts until they restore their levels with lower basal activity [3,5].
  2. Without MSCs, the activity of fibroblasts had lower levels which results in delayed wound healing and forms weak new collagen that encourages the activity of the fibroblasts to be prolonged as they have a higher and prolonged basal activity [2,4]. Thus, the wound will heal with extensive scar.

Conclusion

The presence of MSCs had higher activated fibroblasts with minimum basal activity as it contributed in restoring the normal activity of fibroblasts, aiming for normal wound healing with minimal scar formation.

Graph 25. Represent the relation between fibroblast activity in presence and absence of MSCs.

Model (4) References:

1- Schultz GS, Chin GA, Moldawer L, et al. Principles of Wound Healing. In: Fitridge R, Thompson M, editors. Mechanisms of Vascular Disease: A Reference Book for Vascular Specialists [Internet]. Adelaide (AU): University of Adelaide Press; 2011. 23.

2- Ma Y, Liu Z, Miao L, Jiang X, Ruan H, Xuan R, Xu S. Mechanisms underlying pathological scarring by fibroblasts during wound healing. Int Wound J. 2023 Aug;20(6):2190-2206. doi: 10.1111/iwj.14097. Epub 2023 Feb 1. PMID: 36726192; PMCID: PMC10333014.

3- Wu, S.; Sun, S.; Fu, W.; Yang, Z.; Yao, H.; Zhang, Z. The Role and Prospects of Mesenchymal Stem Cells in Skin Repair and Regeneration. Biomedicines 2024, 12, 743. https://doi.org/10.3390/biomedicines12040743

4- Segal RA, Diegelmann RF, Ward KR, Reynolds A. A differential equation model of collagen accumulation in a healing wound. Bull Math Biol. 2012 Sep;74(9):2165-82. doi: 10.1007/s11538-012-9751-z. Epub 2012 Jul 19. PMID: 22810171.

5- Zupan J. Mesenchymal Stem/Stromal Cells and Fibroblasts: Their Roles in Tissue Injury and Regeneration, and Age-Related Degeneration [Internet]. Biochemistry. IntechOpen; 2021. Available from: http://dx.doi.org/10.5772/intechopen.100556

jump to top to select Drylab or logic gates