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Model

Overview

SPIDEY SPIDEY

1- Mathematical modeling

Overview

As we aim to develop a reliable cell-mediated therapeutic approach for rheumatoid arthritis, we have formulated three main mathematical models. These models simulate the kinetics of our therapeutic systems.

These models rely on sets of ordinary differential equations (ODEs) that include different populations of our therapeutic approach while retrieving their parameter values from experimental literature data, in addition to manipulating them to fit into our designed system when interpreting the resulting graphs.

These models are designed to serve as modular platforms for future iGEM teams working on cell-based therapy in general or engineered stem cell-based therapy specifically in order to simulate the kinetics of the engineered receptor and subsequently the cellular interactions between the different parts of the system and to make a contributable usage of estimated parameter values.

These models have also benefited our team in directing the project design, as they helped us understand the kinetics of our parts and devices as well as make comparisons between different parts based on parts measurements. The designed models serve as a significant contribution to our project and for the future iGEM teams.

Model 1: Binding between the engineered Receptor on Stem Cell and BCR on autoreactive B-cell

Description:

In this model, we simulate the kinetics of binding between the engineered Syn-notch receptor on the engineered mesenchymal stem cells and the B-cell receptor (BCR) on the autoreactive B-cells in rheumatoid arthritis. This model depends on a set of 4 equations (ODEs) that illustrate the binding kinetics. This model is considered modular and useful in determining the most suitable type of receptor according to the most representative parameter values that can result in high-affinity binding between both cells, as shown in figures (1),(2).

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Fig 1. Represents the binding between syn-notch receptors on mesenchymal stem cells and BCR on autoreactive B-cells.

The populations in this system are 4 main populations that are described through the binding of the external domain of the Syn-notch receptor (L) on MSC (S) to the B-cell receptor of autoreactive B-cells (B), which is determined by the concentration of both injected MSC and the already present autoreactive B-cells in the body.

We used different parameters that describe the binding of mesenchymal stem cells to autoreactive B-cell (B-cell receptor to synNotch receptor on MSC). Through binding, the internal domain of the syn-notch will activate a specific genetic circuit that is responsible for the production of modified exosomes containing a specific cargo. This cargo consists of a Crispr Cas12k system, preceded by a synthetic safety switch for controlled regulation of the Crispr mRNA translation, called (DART-VADAR switch). In addition, these exosomes are capable of producing MCP/ADAR enzymes upon endocytosis inside the target auto-reactive B-cells and are conditionally released in case the Cas12k system is successfully produced and translated.

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Fig 2. Represents the system kinetics of the engineered receptor on MSC and its binding to the autoreactive B-cell.

Abbreviations of the model 1:

MSCs Mesenchymal stem cells
ADAR Adenosine deaminase acting on RNA
BCR B-cell receptor
CCP1/External domain Cyclic citrullinated peptide
Cas12K Crispr cas system 12K
L External domain of Syn-notch receptor
S Mesenchymal stem cells
B B-cell receptor

Parameters:

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 [-]

Assumptions:

  • The presence of BCR on the surface of autoreactive B-cells and the increased expression of the external domain of Syn-notch receptors will lead to increased proliferation of MSC.

  • The unbound autoreactive B-cells concentration will definitely decrease upon binding with MSC .

  • The basal activity of the Syn-notch receptor is assumed to be zero.

  • A higher binding affinity implies a lower dissociation rate. [5]

Equation (1):

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This part of our sets of equations describes MSC from being injected up until their activation inside the body. Accordingly, the activation of the stem cells is dependent on the binding between the external domain of the Syn-Notch receptor presented on MSC and the BCR, depending on their rates of expression (k1), and it is degraded by the reciprocal rate of degradation (k2). [1]

Equation (2):

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This equation represents the number of engineered receptors presented on the surface of the MSC. This depends on the rate of formation of the Syn-Notch receptor and their surface expression on the MSC, which is (k3). The expression decreases by the rate of inhibition of the receptor expression or its binding to BCR, which is described as (k4).

Equation (3):

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This ODE represents the number of autoreactive B-cells that significantly decrease once binding occurs between autoreactive B-cells and MSC at rate (k4) to form a binding state, in addition to being decreased based on the reciprocal rate of degradation of autoreactive B-cells (k5).

Equation (4):

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The fourth equation represents the net result of the previously explained set of reactions to finally form a binding complex (BS) consisting of both CCP1 of the Syn-Notch receptor on the surface of MSC and BCR on the surface of autoreactive B-cells . This process is dependent on the rate of formation (k4) as well as the rate at which the binding complex dissociates (k8).

Model 1 Plotting:

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Graph 1. Represents the binding between CCP1 of Syn-Notch receptors on MSC (represented by the blue line) and the BCR of autoreactive B-cells (represented by the orange line) and the binding state (represented by the green line), as shown in the graph, once the engineered MSC is administered to the body and increases in concentration, it binds to the BCR, which appears to be decreasing. therefore, increasing the binding complex until it reachs the steady state after about (7.5) time units.

How did this model direct the project design?

In order to choose the most suitable type of external domain of the Syn-Notch receptor that could be used in our design. We modeled three different types of external domains by using docking scores that determine the binding affinity between the external domain and BCR. So the comparison is held between the three types of external domains, as shown in the next table, based on the assumption that is supported by the experimental literature data that higher binding affinity implies a lower dissociation rate.

1- CILP of Syn-Notch receptor docking score = -242.04 , K8 = 0.0567 (The dissociation occurs spontaneously after the binding as the binding complex units decreased from 1200 to 600 within about 12.5 time units) 2-CV of Syn-Notch receptor docking score = -160.74 , K8 = 0.138 (The dissociation occurs spontaneously after the binding as the binding complex units decreased from 1000 to 200 within about 12.5 time units)
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Graph 2. Represents the interaction between CILP as the external domain of Syn-Notch receptors on MSC (represented by the blue line) and BCR of autoreactive B-cell (represented by the orange line) and the binding state (represented by the green line).
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Graph 3. Represents the interaction between CV as the external domain of Syn-Notch receptors on MSC (represented by the blue line) and BCR of autoreactive B-cell (represented by the orange line) and the binding state (represented by the green line).
3-CCP1 of syn-notch receptor: docking score = -298.80 , K8 =0.001 ( Binding complex = 1400 units reaching the steady state after about (7.5) time units)
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Graph 1. Represents the interaction between CCP1 as the external domain of Syn-Notch receptors on MSC (represented by the blue line) and the BCR of autoreactive B-cells (represented by the orange line) and the binding state (represented by the green line).

As there are different types of external domains that could be used in our design, we made this comparison between the most suitable ones based on literature in order to direct our design into the most suitable type and to understand the kinetics of this part.

  • We modeled the kinetics of the CILP external domain of the Syn-Notch receptor to explain the binding affinity between it and BCR. Depending on the result of the docking score, it’s concluded that it wasn’t stable and the dissociation occurs spontaneously after the binding as binding complex units decreased from 1200 to 600 within about 12.5 time units.

  • We modeled the kinetics of the CV external domain of the Syn-Notch receptor to explain the binding affinity between it and BCR. Depending on the result of the docking score, it’s concluded that it wasn’t stable and the dissociation occurs spontaneously after the binding as binding complex units decreased from 1000 to 200 within about 12.5 time units.

  • We modeled the kinetics of the CCP1 external domain of the Syn-Notch receptor to explain the binding affinity between it and BCR. Depending on the result of the docking score, it’s concluded that it was stable, with a binding complex of 1400 units reaching the steady state after about (7.5) time units, which is the most suitable type in our condition.

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

This model gave us the feature of modifying the external domain of the engineered receptors to bind to BCR. We compared different types of external domains ( CCP1, CILP, and CV) by the ODEs based on our parameter values, resulting in choosing the most suitable type of external domain, which is CCP1 in our design, so this model is considered to be modular. The model provides necessary equations for binding and interaction at the cellular and molecular levels.

Future teams can use these designed ODEs and benefit from our iterations and estimated parameter values to fit into their designs and allow them to compare the affinity between different external domains.

In order to make this model accessible to everyone, we have constructed an online interface which is user-friendly and allows the user to edit the parameter values based on the measurements of their parts and devices to fit into their designs, as shown in figures (3),(4) and acts as a pre-wet lab tool that can direct their project designs and compare different external domains of different engineered receptors. Click Here to access the tool.

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Fig 3.Shows an example where to put parameter values and how to get your model
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Fig 4.Shows the interface for our binding model

References of The Binding Model:

  • León-Triana O, Sabir S, Calvo GF, Belmonte-Beitia J, Chulián S, Martínez-Rubio Á, Rosa M, Pérez-Martínez A, Ramirez-Orellana M, Pérez-García VM. CAR T cell therapy in B-cell acute lymphoblastic leukaemia: Insights from mathematical models. Communications in Nonlinear Science and Numerical Simulation. 2021 Mar 1;94:105570.
  • Ghorashian S, Kramer AM, Onuoha S, Wright G, Bartram J, Richardson R, Albon SJ, Casanovas-Company J, Castro F, Popova B, Villanueva K. Enhanced CAR T cell expansion and prolonged persistence in pediatric patients with ALL treated with a low-affinity CD19 CAR. Nature medicine. 2019 Sep;25(9):1408-14.
  • 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.
  • Fulcher DA, Basten A. B cell life span: a review. Immunology and cell biology. 1997 Oct;75(5):446-55.
  • Manuel Alejandro Marín-López, Joan Planas-Iglesias, Joaquim Aguirre-Plans, Jaume Bonet, Javier Garcia-Garcia, Narcis Fernandez-Fuentes, Baldo Oliva, On the mechanisms of protein interactions: predicting their affinity from unbound tertiary structures, Bioinformatics, Volume 34, Issue 4, February 2018, Pages 592–598, https://doi.org/10.1093/bioinformatics/btx616


Model 2: Modeling of internal domain activation and exosomes secretion and its effect on autoreactive B cells level

Description:

In this model, we simulate the kinetics and activity of the internal domain (ZF21.16 VP64) of the Syn-Notch receptor in comparison to other receptors on MSC upon binding of BCR to the receptors, as shown in the previous model. This binding between the external domain and BCR will lead to activation of the internal domain, which results in transcription factor activation that acts on (ZF21.16 minCMV) promoter that controls the expression of our internal circuit.

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Fig 5. Describes the system kinetics upon activation of the internal domain in which the transcription factor (VP64) activates the promoter (ZF21.16 minCMV) that is responsible for expression of our circuit and the cargo which is regulated by DART-V-ADAR switch.

The populations in this system are 5 populations in which the main one is the internal domain activation of the receptor (ID) that leads to the activation of the transcription factor VP64 which transfers from cytoplasm to the nucleus to stimulate the activity of (ZF21.16 minCMV) promoter, which initiates the transcription of our specific genetic circuit as shown in figures (5),(6).

In addition to the populations mentioned in the previous model, we add a new population to model the secreted modified exosomes with specific cargo (EE) that enter the targeted autoreactive B-cell and become fully activated when the DART-V-ADAR switch identifies its complementary mRNA of the ACPA variable region. This activation leads to the release of the Cas12K system, which inactivates the BAFF-R gene (which is essential for B-cell survival) and cause apoptosis of autoreactive B-cells that produce ACPA, Eventually decreasing the number of viable autoreactive B-cells as shown in graph (5).

Based on the results in model (1), the population that characterizes the external domain of the Syn-Notch receptor (S) is responsible for activating the internal domain (ID).

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Fig 6. Represents the system kinetics of the internal domain activation upon interaction between stem cells and B-cells and formation of the engineered exosomes including our cargo.

Abbreviations of the model 2:

ACPA Anti-citrullinated protein antibodies
ZF21.16 VP64 Name of the internal domain of the Syn-Notch receptor
VP64 Transcription factor
BAFF-R B-cell activating factor receptor
ID Internal domain of syn-notch
EE Exosomes with the cargo

Parameters:

Parameters overview:

The parameters describe the level of expression of the internal domain of the Syn-Notch receptor: Predicting its effect on the level of production of our exosomes carrying the specific cargo.

The parameters values were retrieved from literature experimental data and were manipulated to fit the equation. In comparison between different groups, the parameters were also modified and manipulated based on literature experimental data.

In addition to parameters of the previous model , these are the values of the additional parameters.

Description Value Units Reference
K9 Formation rate of transcription factor VP64 0.1 day-1 × cell-1 [1],[2]
K10 Rate of secretion of modified exosomes from MSCs 1450 days/cell [3]
K11 The initial number of modified exosomes existing in targeted autoreactive B-cell 1 -- [4]
GR Growth rate of modified exosomes 0.036 days [5]
RD Degradation rate of modified exosomes 0.0689 days [4]
A Activation rate of the conditioned system 0.1 day-1 × cell-1 [-]

Assumptions:

  • The plotted exosomes are those who have only been directed towards autoreactive B-cells.

  • The exosomes production will begin upon internal domain activation and lasts after the activation

  • The activity of the internal domain is dependent on the activation of the external domain of the Syn-Notch receptor. Therefore, it’s assumed that (S) = (ID)

Equation (1):

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This part describes the production of the modified exosomes that are initiated by activating the internal domain of Syn-Notch receptors (ZF21.16-VP64).

The equation represents the number of modified exosomes being exist and have the cargo reaching the autoreactive B-cell which depends on, the rate of formation of transcription factor VP64 (k9), which triggers the expression of the circuit and rate of secretion of modified exosmes in term of (k10). In addition to assuming the initial number of modified exosomes that are secreted from MSCs as (k11) because the number of modified exosomes decreases till they reach the targeted autoreactive B-cells, we used an exponential function to calculate the exponential growth rare and degradation rate of modified exosomes in a given set of parameters in terms of (GR and RD) respectively. In addition to, the activation rate of our conditioned system at (A) that is activated to synchronize production of our engineered exosomes to internal domain activation, to finally model the decrease of autoreactive B-cells by increasing our modified exosomes.[4]

Equations (2,3,4,5):

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These equations represent the kinetics of the binding state between Syn-Notch receptor and BCR (as illustrated in the binding model) that leads to activation of the internal domain.

Model 2 Plotting:

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Graph 4. Represents the relation between the internal domain of the Syn-Notch (represented as red line) and production of exosomes with specific cargo (represented as blue line) as the production of the engineered exosomes is initiated once the internal domain is activated.
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Graph 5. Represents the effect of production of modified exosomes from the engineered stem cell on autoreactive B-cells level (as the expression of modified exosmes increases the level of autoreactive B-cells decreases).

How did this model direct the project design?

In order to choose the most suitable type of receptor that could be used in our project, we modeled four different types of receptors.The parameters of every type based on literature data were manipulated to fit into the design. The results were plotted, as shown in the next table, that directed us to choose Syn-Notch receptor as it has a specific transcription factor activation for exosomes production.

1- Chimeric antigen receptor (No inducible exosome production ) k9=0.007 2- Receptors Activated Solely by Synthetic Ligands (RASSLs) (low transcription factor specificity) k9= 0.02
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Graph 6. Represents the activation of the internal domain of CAR does not significantly affect the release of the exosomes.
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Graph 7. Represents the activation of the internal domain of RASSLs and does not specifically affect expression of engineered exosomes.
3- Antibody scaffold receptor (No inducible exosome production ) K9=0.002 4- Syn-Notch receptor (specific transcription factor activation for exosome production ) K9= 0.1
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Graph 8. Represents the activation of the internal domain of CAR that does not significantly affect the expression of engineered exosomes.
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Graph 4. Represents the relation between the activation of the internal domain of the Syn-Notch (represented as red line) and production of exosomes with specific cargo (represented as blue line) as the production of the engineered exosomes is initiated once the internal domain is activated.

  • We modeled the kinetics of chimeric antigen receptor (CAR) to explain production of engineered exosomes from MSC, but it’s concluded that it wasn’t efficient as there’s no signal of exosomes production as shown in the graph (6) because its internal domain couldn’t be modified to be used in MSC and its internal domain (endodomain) can only transmit activation signal to T-cells once a specific antigen bind to the external domain of CAR as it doesn’t offer inducible expression if the exosomes releasing circuit which is supported by literature experimental data. [6]

  • We modeled the kinetics of Receptors Activated Solely by Synthetic Ligands (RASSLs) to explain production of engineered exosomes from MSC as shown in the graph (7), but it was insignificant as the internal domain transcription factor activates a lot of pathways so it will not be specific to activate our internal circuit which is supported by literature experimental data. [7]

  • We modeled the kinetics of Antibody scaffold receptor ( Example for it third generation of CAR receptors ) to explain production of engineered exosomes from MSC as shown in the graph (8), but it was insignificant as the internal domain of CAR (CD3 zeta) can only transmit activation signal to T-cells once a specific antigen bind to the external domain of CAR which is supported by literature experimental data. [8]

Exosomes production modeling iterations:

As our cargo will be loaded to the secreted exosomes, we have made 3 iterations to finally reach the optimum condition that could be used in the wet lab.

1- Booster gene with unconditioned release K10=1450 2- No booster genes with conditioned release K10=1150
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Graph 9. Represents the relation between the activation of the internal domain of the Syn-Notch (represented as red line) and production of exosomes with specific cargo (represented as blue line) as the production of the engineered exosomes is not related to activation of the internal domain.
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Graph 10. Represents the relation between the activation of the internal domain of the Syn-Notch (represented as red line) and production of exosomes with specific cargo (represented as blue line) as the production of the engineered exosomes is initiated once the internal domain is activated.
3- Booster gene with conditioned release K10=1450
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Graph 4. Represents the relation between the activation of the internal domain of the Syn-Notch (represented as red line) and production of exosomes with specific cargo (represented as blue line) as the production of the engineered exosomes is initiated once the internal domain is activated.

  • The First condition: We modeled the kinetics of using booster genes to amplify the exosome production, we first decided to use it in an unconditioned release that produces exosomes continuously in order to have a high yield of exosomes[9]. But it was not related to activation of Syn-Notch receptors so exosomes production was not conditioned and can cause overregulation as it is not controlled as shown in graph (9).

  • The Second condition: No booster gene added to our circuit but the exosome production will be conditioned to activation of Syn-Notch receptors. So exosomes production will not be high as needed as shown in graph (10).

  • The Third condition: It was found to be the most suitable one. As there is a booster gene added to our circuit, that will increase the exosomes production about 1.2 times the traditional release without booster genes which is supported by literature data [9], In addition to adding an conditioned release that produces exosomes related to activation of Syn-Notch receptors, So it is conditioned production as shown in graph (4).

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

This model allowed us to modify the internal domain of different types of receptors to activate the internal circuit for production of the engineered exosomes, it gave us the feature of comparing four types of signals produced through different types of internal domains to determine which one is more efficient for producing the engineered exosomes levels. The model provides the needed equations (ODEs) for modeling internal domain activation and internal circuit transcription.

Future teams can use these designed ODEs and benefit from our iterations and estimated parameter values to fit into their design and allow them to compare the affinity between different internal domains of different receptors and do their own iterations for exosome production as we did to fit into their designs based on what we have designed.

In order to make this model accessible by everyone, we have constructed an online tool or interface which is user-friendly and allows the user to edit the parameter values based on the measurements of their parts and devices to fit into their designs as shown in figures (7),(8) and acts as a pre-wet lab tool that can direct their project designs and comparing different internal domains of different engineered receptors and models the kinetics of the internal circuit and exosomes production. Click Here to access the tool.

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Fig 7.Shows an example where to put parameter values and how to get your model
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Fig 8.Shows the interface for our exosomes production model

References of The Exosomes Production Model:

  • Théry, C., L. Zitvogel, and S. Amigorena, Exosomes: composition, biogenesis and function.Nature Reviews Immunology, 2002. 2: p. 569.
  • Christianson, H.C., et al., Cancer cell exosomes depend on cell-surface heparan sulfate proteoglycans for their internalization and functional activity.2013. 110(43): p. 17380-17385.
  • Yukawa, H., et al., Imaging of angiogenesis of human umbilical vein endothelial cells by uptake of exosomes secreted from hepatocellular carcinoma cells.Scientific Reports, 2018. 8(1): p. 6765.
  • Sun, H., 2019. Exosome-Based Early Detection of Cancer and Parkinson’s Disease (Doctoral dissertation, UC Santa Cruz).
  • Cai, J., et al., Differential Expression of Methionine Adenosyltransferase Genes Influences the Rate of Growth of Human Hepatocellular Carcinoma Cells.1998. 58(7): p. 1444-1450.
  • M. Sadelain, et al., “The basic principles of chimeric antigen receptor design,” Cancer Discov 3(4):388-398, 2013.
  • Scearce-Levie K, Coward P, Redfern CH, Conklin BR. Engineering receptors activated solely by synthetic ligands (RASSLs). Trends Pharmacol Sci. 2001 Aug;22(8):414-20. doi: 10.1016/s0165-6147(00)01743-0. PMID: 11479004.
  • Wu L, Wei Q, Brzostek J, Gascoigne NRJ. Signaling from T cell receptors (TCRs) and chimeric antigen receptors (CARs) on T cells. Cell Mol Immunol. 2020 Jun;17(6):600-612. doi: 10.1038/s41423-020-0470-3. Epub 2020 May 25. PMID: 32451454; PMCID: PMC7264185.
  • Zhang, R., Bu, T., Cao, R. et al. An optimized exosome production strategy for enhanced yield while without sacrificing cargo loading efficiency. J Nanobiotechnol 20, 463 (2022). https://doi.org/10.1186/s12951-022-01668-3


Model 3: Immunomodulatory effect of injected MSCs on rheumatoid arthritis vs current medication.

Description

The destruction that happens in the joints of RA patients is caused by ACPA and some proinflammatory cytokines such as TNF and IL-6 that are mediated by proinflammatory macrophages (M1) have a bad effect on the patient. [1]

So in this model we will be monitoring the impact of injected stem cells on the body by observing the rise in levels of anti-inflammatory macrophages (M2) through transformation of M1 to M2, In the other hand decrease ACPA produced from autoreactive B-cells that plays the main role in RA patients as shown in model 2.

The model contains 5 populations that describe the effect of injected engineered MSCs and their binding to BCR on the surface of autoreactive B-cells. This continues until the production of our engineered exosomes which enter autoreactive B-cells and activation of their cargo. This cargo consists of a Crispr Cas12k system, preceded by a synthetic safety switch for controlled regulation of the Crispr mRNA translation, called the DART-VADAR switch. This leads to apoptosis of autoreactive B-cells that produce ACPA, resulting in decrease in the number of ACPA and proinflammatory macrophages and returning anti-inflammatory macrophages (M2) to their normal level. The five populations are mesenchymal stem cells (S), ACPA from autoreactive B-cells (D), resting macrophage (Mr), proinflammatory macrophages (M1), and anti-inflammatory macrophages (M2).

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Fig 9. Shows the effect of MSC on decreasing ACPA and increasing level of M2.

Abbreviations of the model 3:

TNF Tumor necrosis factor
IL-6 Interleukin 6
M1 Proinflammatory macrophages
M2 Anti-inflammatory macrophages
Mr Resting macrophages

Parameters:

Description Value Units Reference
KC1 Rate of formation of stem cells 0.69 day-1 × cell-1 [2]
KC2 Rate of interaction between stem cells and anti-inflammatory macrophages 0.046 day-1 × cell-1 [4]
KC3 Rate of interaction between stem cells and proinflammatory macrophages 0.5 day-1 × cell-1 [-]
KC4 Rate of degradation of stem cells 0.1 day-1 × cell-1 [2]
KC5 Degradation rate of autoreactive B-cells by proinflammatory macrophages 0.1 day-1 × cell-1 [3]
KC6 Elimination rate of damaged autoreactive B-cells by proinflammatory macrophages 0.05 day-1 × cell-1 [4]
KC7 Elimination rate of damaged cells by anti-inflammatory macrophages 0.0125 day-1 × cell-1 [4]
KC8 Rate of formation of resting macrophages 1.0115 day-1 × cell-1 [-]
KC9 Rate of activation of resting macrophages to proinflammatory macrophages 0.12 day-1 × cell-1 [4]
KC10 Rate of activation of resting macrophages to anti-inflammatory macrophages 0.017 day-1 × cell-1 [4]
KC11 Degradation rate of resting macrophages 0.003 day-1 × cell-1 [4]
KC13 Rate of damage from proinflammatory macrophages by the cytokines 0.001 day-1 × cell-1 [-]
KC14 Rate of change of proinflammatory macrophages to anti-inflammatory macrophages 0.11 day-1 × cell-1 [4]
KC15 Degradation rate of proinflammatory macrophages 0.06 day-1 × cell-1 [4]
KC16 Degradation rate of anti-inflammatory macrophages 0.05 day-1 × cell-1 [4]
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Fig 10. Shows the system kinetics from injecting MSC till the level of M2 increases and apoptosis of autoreactive B-cells which produce ACPA .

Equation (1):

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This equation describes formation of stem cells that increases at rate (KC1) and decreases by interaction with anti-inflammatory macrophages and proinflammatory macrophages at rates (KC2 and KC3) respectively, in addition to degradation rate of the stem cells (KC4) [5]

Equation (2):

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The second ODE describes ACPA from autoreactive B-cells that decreased through interaction with the proinflammatory macrophages at rate (KC5) and elimination of dead cells from either anti or pro inflammatory macrophages at rate (KC6 and KC7) respectively.

Equation (3):

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The third equation describes the normal level of macrophages as resting macrophages. These resting macrophages increase through formation rate (KC8), which is responsible for increasing the number of resting macrophages. However, they also decrease through their transformation into pro and anti-inflammatory macrophages at rates (KC9 and KC10) respectively. Additionally, the level of the resting macrophages decreases due to the degradation rate(KC11).

Equation (4):

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The fourth ODE describes proinflammatory macrophages, which increases in the concentration through the transformation of resting macrophages to proinflammatory macrophages at a rate of (KC9) .However, their concentration decreases through several mechanisms:

  • The interaction between proinflammatory macrophages and stem cells (represented at a rate of KC3) leads to a decrease in free proinflammatory macrophages.

  • Proinflammatory macrophages are damaged when exposed to cytokines (at a rate of KC13).

  • Transformation of proinflammatory macrophages to anti-inflammatory macrophages at a rate of KC14.

  • Natural degradation of proinflammatory macrophages at a rate of KC15.

Equation (5):

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The fifth ODE describes anti-inflammatory macrophages as their concentration increases through:

  • Transformation of resting macrophages to anti-inflammatory macrophages at rate (KC10).

  • Transformation of proinflammatory macrophages to anti-inflammatory macrophages at rate (KC14).

  • Interaction between stem cells and proinflammatory macrophages at rate (KC3) that will leave a space for anti-inflammatory macrophages to increase in number.

In the other hand the concentration of anti-inflammatory macrophages decreases through:

  • The interaction between anti-inflammatory macrophages and the stem cells (represented at rate KC2) will lead to decrease free anti-inflammatory macrophages.

  • Natural degradation of proinflammatory macrophages at rate KC16.

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Graph 11. Represents the immunomodulatory effect of MSCs, as once injected, there’s an increase in anti-inflammatory macrophage concentration.

MSCs vs Methotrexate effect on anti-inflammatory macrophages :

1- Methotrexate KC2= 0.066 2- Stem cells KC2= 0.046
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Graph 12. Represents the anti-inflammatory effect of methotrexate, which is currently used in the treatment of RA, as it leads to an increase in the concentration of anti-inflammatory macrophages.
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Graph 11. Represents the immunomodulatory effect of MSCs, as once injected, there’s an increase in anti-inflammatory macrophage concentration.

We compared the effect of methotrexate and our engineered MSC on the level of anti-inflammatory macrophages. We conclude that the engineered MSC showed a higher concentration of anti-inflammatory macrophages than methotrexate, which is used nowadays in RA treatment, as it increases the degradation of M1 [6]. This conclusion supported our design and showed the benefit of the immunomodulatory effect of MSCs.

References of The Immunomodulatory Model:

  • Chauhan K, Jandu JS, Goyal A, Al-Dhahir MA. Continuing Education Activity. StatPearls [Internet]; Treasure Island (FL): StatPearls Publishing: Mountain View, CA, USA. 2021.
  • Johnston, M.D.; Edwards, C.M.; Bodmer, W.F.; Maini, P.K.; Chapman, S.J. Examples of mathematical modeling: Tales from the crypt. Cell Cycle 2007, 6, 2106–2112
  • Russo, C.D.; Lagaert, J.-B.; Chapuisat, G.; Dronne, M.-A. A mathematical model of inflammation during ischemic stroke. ESAIM Proc. 2010, 30, 15–33.
  • Alqarni, A.J.; Rambely, A.S.; Hashim, I. Dynamic Modelling of Interactions between Microglia and Endogenous Neural Stem Cells in the Brain during a Stroke. Mathematics 2020, 8, 132.
  • Awrejcewicz J, editor. Symmetry in Modeling and Analysis of Dynamic Systems. MDPI-Multidisciplinary Digital Publishing Institute; 2022 Jun 22, Pages 64–77.
  • Lo, S.Z., Steer, J.H. & Joyce, D.A. Tumor necrosis factor-alpha promotes survival in methotrexate-exposed macrophages by an NF-kappaB-dependent pathway. Arthritis Res Ther 13, R24 (2011). https://doi.org/10.1186/ar3248


In-Silico Simulations

To enable our SUPER-Cells to specifically identify and target the Anti-Citrullinated Peptide Antibody (ACPA) present on the surface of auto-reactive B-cells, it was essential to model the interactions between the ACPA and its different targets. Understanding this relation can allow us to identify the best possible candidate that can enable our cells to efficiently identify only the auto-reactive cells while sparing the body’s normal immune cells.

That’s why we had to conduct docking and molecular dynamics simulations between the ACPA and some of its known targets in order to choose the top-ranking protein in terms of structural stability and binding affinity, which can significantly enhance the specificity of our cells.

Molecular Docking simulations of our receptor’s interactions:

We performed our docking simulations using the HDOCK server developed by Huang Lab. These simulations were conducted between the ACPA as the main target, in association with 3 different proteins that are known to be targeted by the autoantibody. These proteins are:

  • The Citrullinated Vimentin (CV).

  • The Cartilage Intermediate Layer Protein (CILP).

  • The Cyclic Citrullinated Peptide (CCP1).

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Fig 11,12,13. Demonstrate the 3D structure of the proteins after completing the docking simulations. These structures were visualized using the PyMOL Molecular Visualization System. (A) ACPA-CV, (B) ACPA-CILP, (C) ACPA-CCP1
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Fig 14. Plotting the results of the molecular docking simulations of the 3 complexes

The docking results concluded that the highest docking score was found between the ACPA and CCP1, with a score of (-298.80), closely followed by the ACPA-CILP complex with a score of (-242.04), and the lowest score was between the ACPA and CV with a score of (-160.74).

These docking simulations were followed by subjecting our proteins to molecular dynamics simulations to analyze their interactions at the atomic and molecular levels, as well as visualizing the energy changes of the binding process.

Molecular Dynamics (MD) Simulations:

Using the AMBER Molecular Dynamics Package on Google Colab, we’ve performed molecular dynamics simulations on all of the aforementioned complexes to test their stability in a perturbed environment, similar to what they would encounter within the cellular settings.

ACPA-CCP1:

The ACPA-CCP1 simulations showed the best results in terms of structural stability and flexibility. After 4 nanoseconds of simulation, the Root Mean Square Deviation (RMSD) was between 1.5-2.5 Å, which means that the deviation between the atoms of both proteins was minimal, indicating stability of the binding between the 2 proteins. The value of the Root Mean Square Fluctuation (RMSF) also ranged between 2-3 Å, which also indicates minimal fluctuation in the position of each of the residues forming the structure of each protein.

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Fig 15. A display of the MD results of the ACPA-CCP1 Complex

ACPA-CV:

As for the ACPA-CV complex, the MD results weren’t as good as with the ACPA-CCP1 Complex. It showed an RMSD value that fluctuated between 2 up to 4 Å, showing more deviation between the position of atoms in the 2 proteins and indicating less stable binding than the ACPA-CCP1 complex. The RMSF calculations were also slightly higher than the ACPA-CCP1 complex, fluctuating between 1-4 Å.

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Fig 16. A display of the MD results of the ACPA-CV Complex

ACPA-CILP:

Finally, the results of the ACPA-CILP showed constant increase in the RMSD value, reaching up to 7 Å. This indicates more deviation in the positions of the molecules that construct both proteins, resulting in a less stable binding process compared to the other two complexes.

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Fig 17. A display of the MD results of the ACPA-CILP Complex

All of these simulations have directed our modeling process towards using the CCP1 protein, as it showed the highest docking score, in addition to being the most stable structure when bound with the ACPA, compared to the other proteins.

The simulation of the behavior of the 3 aforementioned complexes was important to determine the best protein that can effectively identify and bind with the ACPA receptor of Auto-reactive B-cells. The selected protein can then be integrated into the design of our Syn-Notch receptor, which can significantly improve the specificity of our approach, while maintaining the stability and flexibility of the binding between the 2 structures. This ensures a high level of specificity of our receptor, which is very important as this represents one of the safety measures of our system that allows for precise and specific targeting of the ACPA-presenting B-cells while avoiding normal B-cells.

CD19-CD19 Ligand:

As a proof-of-concept of our approach, our wet lab work was conducted through the binding between the CD19 receptor of B-cells and the CD19-ligand that is integrated in the structure of the Syn-Notch receptor. This is due to the fact that to work with ACPA-presenting cells, we would have to extract them from samples of RA patients, so we decided to test the validity of our approach before proceeding to the next phase.

We’ve also performed docking and MD simulations for the CD19-CD19 Ligand to analyze the binding between them, as well as ensuring the stability of their structures within a simulation of a physiological system. The docking score between the 2 structures was -311.10. However, when the structures were submitted for MD simulations, their RMSD reached a value of 5 Å, as well as the values of their RMSF.

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Fig 18. The 3D structure of the docking between the CD19 and the CD19 Ligand, visualized using PyMOL
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Fig 19. A display of the MD results of the CD19-CD19 Ligand Complex

Role of Directed Evolution in our project:

To improve the features of the proteins used in our project, we turned to the concept of directed evolution, where random mutations can be applied to protein residues in order to direct the protein into expressing better features. The impact of these mutations is then measured in relation to their surrounding residues, and on the protein structure as a whole.

Using an online tool called EVcouplings, we subjected our proteins to generate mutant variants at different positions of the protein. The effect of these mutations is then measured independently, as well as on the global protein structure, which is called epistatic fitness. Both these parameters correspond to the overall evolutionary fitness of the formed mutant variants, which contributes to improving their functions.

Herein, we’re presenting the mutational landscape that was generated by EVcouplings for the proteins that are most important in the performance and safety of our therapeutic approach. We’ve chosen to apply these mutations to 4 proteins that are implemented in different aspects of the therapeutic pathway. These include:

  • CD19 Ligand: as it is involved in the primary step of recognizing the auto-reactive B-cells.

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    Fig 20. Depicts the mutational landscape of the CD19 Ligand, generated by the EVcouplings software. It shows that the mutant variant associated with the highest epistatic fitness was (P152S), while the highest independent score was related to the (P162G).

  • The (CD63-L7Ae) loading system: which is designed for loading our therapeutic cargo in the exosomal delivery system once the recognition process is achieved. Afterwards, these exosomes start delivering our cargo to the auto-reactive cells to terminate their activity.

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    Fig 21. Depicts the mutational landscape of the CD63-L7Ae, generated by the EVcouplings software. It shows that the mutant variant associated with the highest epistatic fitness was (N117K), while the highest independent score was related to the (L18N).

  • The therapeutic cargo itself: represented in the CRISPR/Cas12k system: whose role is to target the B-cell Activating Factor Receptor (BAFF-R) gene which is essential for the survival and differentiation of B-cells. This results in initiating an apoptotic response that destroys the auto-reactive cells.

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    Fig 22. Depicts the mutational landscape of the Cas12k, generated by the EVcouplings software. It shows that the mutant variant associated with the highest epistatic fitness was (A8C), while the highest independent score was also related to the (A8C).

  • Our (DART-VADAR) safety switch: this safety system is designed so that our CRISPR/Cas12k cargo can only perform its action within auto-reactive B-cells, further improving the specificity and safety of our approach.

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    Fig 23.Depicts the mutational landscape of the ADAR enzyme, generated by the EVcouplings software. It shows that the mutant variant associated with the highest epistatic fitness was (Q173E), while the highest independent score was also related to the (A182G).

For more details about the specific role of each component in approach, kindly refer to the project description and design pages.

References of the in-silico simulations:

  • Schrödinger L, DeLano W. PyMOL [Internet]. 2020. Available from: http://www.pymol.org/pymol.
  • Hopf TA, Green AG, Schubert B, Mersmann S, Schärfe CPI, Ingraham JB, et al. The EVcouplings Python framework for coevolutionary sequence analysis. Bioinformatics. 2019 May 1;35(9):1582–4.
  • D.A. Case, H.M. Aktulga, K. Belfon, I.Y. Ben-Shalom, J.T. Berryman, S.R. Brozell, D.S. Cerutti, T.E. Cheatham, III, G.A. Cisneros, V.W.D. Cruzeiro, T.A. Darden, N. Forouzesh, G. Giambaşu, T. Giese, M.K. Gilson, H. Gohlke, A.W. Goetz, J. Harris, S. Izadi, S.A. Izmailov, K. Kasavajhala, M.C. Kaymak, E. King, A. Kovalenko, T. Kurtzman, T.S. Lee, P. Li, C. Lin, J. Liu, T. Luchko, R. Luo, M. Machado, V. Man, M. Manathunga, K.M. Merz, Y. Miao, O. Mikhailovskii, G. Monard, H. Nguyen, K.A. O’Hearn, A. Onufriev, F. Pan, S. Pantano, R. Qi, A. Rahnamoun, D.R. Roe, A. Roitberg, C. Sagui, S. Schott-Verdugo, A. Shajan, J. Shen, C.L. Simmerling, N.R. Skrynnikov, J. Smith, J. Swails, R.C. Walker, J. Wang, J. Wang, H. Wei, X. Wu, Y. Wu, Y. Xiong, Y. Xue, D.M. York, S. Zhao, Q. Zhu, and P.A. Kollman (2023), Amber 2023, University of California, San Francisco.
  • Yan Y, Tao H, He J, Huang S-Y. The HDOCK server for integrated protein-protein docking. Nat Protoc. 2020 May;15(5):1829–52.