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Mathematical model

overview

Tooltip on top First of all , the Model is an essential part of any project that aids in understanding parts function and kinetics and predicts their results depending on primary experimented parametric values for their specific differential equations. On the other hand, the project design may affect model results by integrating new parts that have a significant effect on the project.Moreover, these results help you in adding new conditions for fitting the new design. [5].

For our project this year, we have constructed 4 main models using Ordinary differential equations (ODEs). Three of them describe parts’ function and activity, while the last model describes cells’ behavior and their interaction based on assumptions that we have conducted by the aid of experimental literature. These models are:

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

NOTE

Take care while exploring our models 1 and 2 from the dimensions of our graphs considering the time frame and the population scale level , as they show a sequence in their actions and values for getting the most satisfactory prediction for our project results.

Model 1 : The binding model

Description

We simulate the kinetics of Vascular endothelial growth factor (VEGF) and its receptors by ODEs[1]. The receptor is composed of the 2 different chains: VEGFR-1 and VEGFR-2. Firstly, the ligand binds to VEGFR2 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 dCas-9 system.

This model is concised into 7 equations that describe the binding kinetics of VEGF initially to VEGFR-2, then binding of this (VEGF - VEGFR-2) complex to VEGFR-1 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 dCas-9 system.

This system is composed of 7 main population:

  1. VEGFR-2
  2. Complex of VEGF and VEGFR-2
  3. VEGFR-1
  4. Complex of (VEGF-VEGFR-2) and VEGFR-1
  5. Dimerization
  6. TEV protease
  7. dCas-9 system

Abbreviations of model 1

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
C dCas-9 system

Parameters

Description Value Units 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 [3]
K5 Cleavage rate of TEV protease to release dCas9 system. 1 units [4]
K6 Rate of activation of Cas9 system. 0.001 s−1 [-]
RD1 Rate of dissociation of (VEGF-VEGFR2) complex. 1 s−1 [3]
RD2 Rate of dissociation of (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 0.1 s−1 [3]
d3 Rate of degradation of VEGFR1. 0.09 s−1 [3]
d4 Rate of degradation of (VEGFR2-VEGF-VEGFR1) complex. 0.5 s−1 [3]
d5 Degradation rate of TEV protease activator. 0.01 s−1 [4]
d6 Degradation rate of the dCas9 system 0.05 s−1 [5]

Assumptions

  1. Vascular endothelial growth factor (VEGF) has constant value = 1.
  2. The binding affinity of VEGFR-2 to its ligand has higher affinity compared to that of VEGFR-1. [2]
  3. The higher binding affinity reflects higher and stable dimerization rate.

Equation (1)

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

  1. Binding of VEGF (A) to its receptor (R2) at rate (K1).
  2. Degradation of free receptor-2 (R2) at rate (d1).
Moreover, they increase in case of :
  1. Dissociation of (R2A) complex at rate (RD1).

Equation (2)

The second equation describes (VEGF-VEGFR2) complex (R2A) which decreases upon:

  1. Dissociation of the binding complex (R2A) at rate (RD1).
  2. Binding of (R2A) complex to (R1) receptor at rate (K2).
  3. Degradation of (R2A) complex at rate (d2).
Moreover, they increase in case of :
  1. Binding of VEGF (A) to its receptor (R2) at rate (K1).
  2. Dissociation of the binding complex (R2AR1) at rate (RD2).

Equation (3)

The third equation describes free receptors-1 (R1) which decrease upon:

  1. Binding of (R2A) complex to receptor (R1) at rate (K2).
  2. Degradation of free receptor-1 at rate (d3).
On the other hand, they increase in case of:
  1. Dissociation of (R2AR1) complex at rate (RD2).

Equation (4)

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

  1. Dissociation of (R2AR1) complex at rate (RD2).
  2. Degradation of (R2AR1) complex at rate (d4).
In contrast, they increase in cases of :
  1. Binding of (R2A) complex to receptor (R1) at rate (K2).

Equation (5)

The fifth equation describes the receptor dimerization process at rate (K3) as in graph(2). This process vanishes by binding complex (R2AR1) degradation at rate (d4).

Equation (6)

Thesixth equation describes TEV protease activation (as in graph (2) ) upon dimerization of VEGFR chains at a rate of (K3). This binding results in an increase of free TEV concentration. However, this concentration is decreased by normal TEV protease degradation rate at (d5).

Equation (7)

The seventh equationseventh equation describes TEV protease activation sequelae in which the free dCas-9 system concentration increases ( as in graph (3) ) in response to the protease action on cleavage specific sites at the receptor’s internal domain (TCS1 and TCS2) at rate of (K5). The activation of the dCas-9 system depends on the integration of the dcas-9 N-terminal and C-terminal at rate (K6). Nevertheless, dCas9 concentration decreases by the normal dCas-9 system degradation rate (d6).

Model (1) plotting:

How did this model affect the project design?

In order to choose the suitable VEGFR to reach the full activity of our internal domain parts, we noticed that TEV protease activity depends on the dimerization rate of the receptor’s chains.Dependently, this dimerization rate depends on the receptor-ligand binding state; thus, we held a comparison between the 2 forms of the receptor:

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

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

From the previous table, we can conclude that the binding affinity of the heterodimer receptor is higher and more stable than the homodimer receptor as in graphs(2,5). Sequentially, the dimerization level in the heterodimer receptor is higher which reflects higher activation of the receptor internal domain including TEV protease and dCas9- system as in graphs(3,6).

References

  • 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.
  • 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.
  • 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.
  • 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.
  • 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.

References

  • Silman AJ, MacGregor AJ, Thomson W, Holligan S, Carthy D, Farhan A, Ollier WE. Twin concordance rates for rheumatoid arthritis: results from a nationwide study. Br J Rheumatol. 1993 Oct;32(10):903-7.
  • Qiu M, Zhou XM, Liu L. Improved Strategies for CRISPR-Cas12-based Nucleic Acids Detection. J Anal Test. 2022;6(1):44-52. doi: 10.1007/s41664-022-00212-4. Epub 2022 Feb 28. PMID: 35251748; PMCID: PMC8883004.

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

Description

In this model, we simulate the kinetics and the sequel of activity of the internal domain upon dimerization of the 2 separate domains of vascular endothelial growth factor receptor (VEGFR), activating Tobacco Etch Virus (TEV) protease which releases both N-terminal and C-terminal of dCas9 system and leading to their binding and activation [1]. The dCas9 system is uploaded with 3 different transcription activators (VP46, GAL4 and CMV trans-enhancer) to show a satisfactory level of YAP-1 [2], resulting in optimum proliferation and differentiation of stem cells.[2]

In other words, this system consists of 5 populations. Briefly, our system started by releasing and activating the dCas9 system, uploaded with 3 different transcription activators (VP46, 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 activator and YAP-1 transcription used in that model based on the results of model (1). So the activation of the external domain till production YAP-1 is sequential .

Abbreviations of model 2

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

Parameters

Description Value Units Reference
K7 Rate of activation of CMV trans-enhancer for transcription of YAP. 5.4 M−1 s−1 [3]
K8 Rate of activation of VP64 transcription activator for transcription of YAP. 1.8 M−1 s−1 [4]
K9 Rate of activation of GAL4 transcription activator for transcription of YAP. 1.3 cm2 mol−1 s− 1 [3]
d7 Natural degradation rate of CMV trans-enhancer. 0.15 units [-]
d8 Natural degradation rate of VP64 transcription. 0.2 s−1 [-]
d9 Natural degradation rate of GAL4 transcription activator. 0.05 s−1 [-]
d10 Rate of dissociation of (VEGF-VEGFR1) complex. 3.3 s−1 [5]

Assumptions

  1. Basal activity of TEV protease is zero.
  2. Neglection of normal YAP production which is 600 [1] from the final result of it. [2]

Equation (1)

The first equation escribes the cytomegalovirus (CMV) trans-enhancer activation. This CMV trans-enhancer depends on the activation of the dCas-9 system, yielding the optimum level of YAP-1 at the rate (K7). Moreover, its activity is decreased by the normal CMV trans-enhancer degradation rate (d7).

Equation (2)

The second equation describes the activation level of VP64. When the dcas-9 system is activated , VP-64 is turned on leading to release of an optimum level of YAP-1 at rate (K8). This activation is decreased by normal VP-64 degradation rate (d8).

Equation (3)

The third equation describes GAL4 activation level. Upon activation of dCas-9 system, GAL4 is stimulated, meanwhile releasing optimum level of YAP-1 at rate (K9), respectively. In contrast, this activation is decreased by normal GAL-4 degradation rate (d9)

last equation

The last equation in that model describes YAP-1 transcription level that determined by activation rates of CMV trans-enhancer , VP64 and GAL4 transcription activators at rate (K7,K8 and K9) respectively. In contrast, this activation is decreased by normal GAL-4 degradation rate (d10).

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

These equations represent the kinetics of binding of VRGF to its receptor and the dimerization process for activating the internal domain parts till releasing of the dCas-9 system (d4).

Model (2) plotting:

Graph (7) Illustrates the relation between activation levels of different transcriptional activators (CMV trans-enhancer , VP64 and GAL4) for transcription for YAP-1 (d4).

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

In order to choose the most satisfactory level of YAP-1[2] production for proliferation and regeneration of the stem cells, 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 excremental date [3] as shown in the following table. This directed us to choose the integrated design of these 3 different transcription activators as this integrated design reaches the satisfactory level of YAP-1 in small time (20 unit time).

CMV trans-enhancer only which shows high expression level of YAP-1, but not the optimum level, reaching 12800 at 65 time units VP64 transaction activator only which shows very low expression level of YAP-1 , reaching 1050 at 55 time units.
GAL4 transcription activator that shows low expression level of YAP-1, reaching 2000 at 75 time units. Three transcription activator Integrated design which shows the optimum level of YAP-1, reaching 16000 at 65 time units.

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

  1. We modeled the kinetics of CMV trans-enhancer in YAP-1 transcription; the result was not satisfactory even showing high YAP-1 expression reaching 12800 at 65 time units as in graph (8).
  2. Also, we modeled the kinetics of the VP64 transcription activator in YAP-1 transcription. The result shows low YAP-1 expression, reaching 1050 at 55 time units. Conclusively, the time needed to reach the peak of expression was better and able to accomplish YAP-1 full generation; however, the concentration was not satisfying to reach our target as in graph (9). [2]
  3. Also, we modeled GAL4 transcription activator kinetics in YAP-1 transcription. The report illustrates very low YAP-1 expression , achieving 2000 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 in graph (10).
  4. Also, we modeled the kinetics of activation of (CMV trans-enhancer, VP64 and GAL4) transcription activator integrated together in our design for transcription of YAP, to get the high benefit from each transcription activator considered in time of activation for each one for transcription to have transcription of YAP for long time from each one separate. The result shows high expression of YAP to reach 16000 at 65 unit time which is better in time needed to reach the peak of expression and the full regeneration and its concentration is satisfactory to reach our target. so we choose the integrated design for our project as in graph (7).

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

This model gave an advantage to integrate and compare different transcription activators (CMV trans-enhancer, VP64 and GAL4) by ODEs based on our parameter values. Thus, this model is considered to be modular.

Future teams can use these designed ODEs for testing the same or different transcription activators’ activity for protein production and estimating parameter values to fit their design.

In order to make these ODEs and the model 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 transcription activator.

References

  • 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
  • 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.
  • 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.
  • 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.
  • 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 : a switch model illustrating YAP-1 regulation in the target cells

Description

In this model, we simulate the kinetics and activity of our MMP-9 specific mRNA switch, which is activated upon binding of matrix metalloproteinase 9 (MMP9) to its MMP9-nanobody through changing into circular form [1](as shown in figure ()) for initiating transcription of YAP-1 in the targeted cells.[1].We prevent the switch’s basal activity through adding hammerhead ribozyme (HHR)[1] to our design.[2]. In presence of HHR. the switch will not circularize except in the existence of MMP-9, forbidding the poly A tail to bind with the mRNA cap. Indeed, the HHR undergoes self-cleavage which cleaves the following poly A tail , allowing proper switch on-off state transition, respectively. However, in absence of HHR, no cleavage will happen which means the presence of poly A tail, permitting switch’s basal activity[1].

In other words, this system consists of 6 populations. Simply, the MMP-9 (MMP) binds to MMP9-nanobody (RA) to form a binding complex (CO). This combination promotes switch circulation (CF) in presence of poly A tail (PA) that maintains its stability and HHR to control basal activity of poly A tail for production of the only desired amount of (YAP).

Abbreviations of model 3

MMP Matrix metalloproteinase9
RA Free MMP9-nanobody
CO Binding complex of MMP-9 and RA
CF Circular form of the switch
PA Poly A tail
HHR Hammerhead ribozyme

Parameters

Description Value Units Reference
K11 Rate of binding between MMP-9 and MMP-9 nanobody. 0.9 M−1 s−1 [2]
K12 Rate activation of poly A tail to initiate and maintain the stability of the switch. 4.4 M−1 s−1 [1]
K13 Cleavage rate of HHR to separate poly A tail. 2.1 cm2 mol−1 s− 1 [3]
K14 Rate of circulation of the switch. 1 units [-]
K15 Activation rate of MS2 aptamer. 0.001 s−1 [1]
d11 Degradation rate of MMP-9. 1 s−1 [-]
d12 Degradation rate of MMP-9 nanobody. 0.00132 s−1 [-]
d13 Degradation rate of the binding complex. 0.1 s−1 [-]
d14 Degradation rate of the circulating form of the switch. 0.1 s−1 [-]
d10 Degradation rate of YAP. 3.3 s−1 [4]

Assumptions

  1. The unbounded MMP-9 will eventually decreases through activating our switch with production of YAP-1.
  2. Neglection of Hammerhead ribozyme (HHR) degradation rate.
  3. The dissociation rate between MMP-9 to its Nanobody assumed to be zero.

Equation (1)

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

  1. Binding of free MMP-9 to MMP-9 nanobody (RA) at rate (K11).
  2. Degradation of MMP-9 at rate (d11).
Moreover, they increase in case of :
  1. Formation rate of MMP-9 upon injury at rate (K10) so it will finally reflect the concentration of MMP.

Equation (2)

The second equation describes the decrease in the number of free MMP-9 nanobodies (RA) . This is due to:

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

Equation (3)

The third equation describes the number of binding complexes that have been obtained from MMP-9 binding to MMP-9 nanobody (RA) at rate (K11). In addition to the normal degradation rate of these binding complexes at rate (d13).

Equation (4)

The fourth equation describes the switch’s ability to circularize which happens once the MMP-9 binds to MMP-9 nanobody (RA) at rate (K11). By the aid of poly A tail at rate (K12) for maintaining the switch stability before the circulation. Once circulation is initiated:

  1. The HHR will perform self cleavage before poly A tail with a cleavage rate (K13).
  2. The activity of MS2 aptamers increases at rate (K15) upon binding of MMP-9 to its nanobody to maintain the switch stability.
In contrast, they increase in cases of :
  1. Binding of (R2A) complex to receptor (R1) at rate (K2).
In addition to the normal degradation of the switch circular form at rate (d14). This occurred to initiate the YAP-1 translation without basal activity of the switch.

Equation (5)

The fifth equation describes MS2 aptamer activity that increases upon binding of free MMP-9 nanobodies to MMP-9 at rate (K11) and maintains the switch stability that happens after the switch circulation at rate (K15). In addition to the normal degradation of the switch circular form at rate (d14) and degradation of MMP-9 at rate (d11).

Equation (6)

Thesixth equation describes the HHR function in decreasing the poly A tail activity before circulation. Through cleaving specific cleavage sites before PA at rate (K13). In addition to the normal degradation of the switch circular form at rate (d14).

Equation (7)

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

  1. Formation rate of MMP-9 upon injury at rate (K10).
  2. The binding of free MMP-9 nanobodies to MMP-9 at rate (K11).
  3. The switch circulation at rate (K14).
Moreover, the normal degradation rate of YAP-1 at rate (d10).

Model (3) plotting:

To sum up, the activation of our conditioned switch through presence of MMP-9 results in changing the switch into its circular form for transcription of the normal amount of YAP-1 in the targeted cells [5].

How did the project design affects model kinetics and activity ?

The first design of the switch did not include the hammerhead ribozyme (HHR) part, so we modeled the parts as it was. 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 transcription of YAP-1 in absence of MMP-9 to activate it which is supported by literature experimental data[1]. so we have changed our design to add an HHR part for safety conditioned production of YAP-1, as shown in the next figures with and without basal activity of the switch.

With HHR Without HHR

The comparison between presence and absence of HHR part shows:

  1. We modeled the kinetics of HHR to cleave specific cleavage sites in the genetic circuit if the circulation process is initiated, these cleavage sites located before Poly A tail to prevent activation of the switch in absence of MMP-9 for safety production of YAP-1. MMP-9 is responsible for activation of our switch.
    So the basal activity of the switch is zero as in graph (12).
  2. Before that , 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 in graph (13).

References

  • 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
  • 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.
  • 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.
  • 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.
  • 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.

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References

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Description Value Units Reference
K1 Rate of expression of external domain (CCP1) Syn-Notch receptor 0.001 day-1 × cell-1 [1]
K2 Reciprocal rate of degradation of MSCs 15 Days-1 [2]
K3 Rate of formation on Syn-Notch receptor on MSCs 0.033 Days-1 [1]
K4 Rate of the binding state between S and B 0.000411 day-1 × cell-1 [3]
K5 Reciprocal rate of degradation of autoreactive B-cell 30 Days [4]
K8 Rate of dissociation of the binding state 0.001 day-1 [-]

Introduction

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