Team:TECHNION-ISRAEL/Assay Model

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Our Model

Tolerance Assay Model



The purpose of our model

We set out to model the interaction between our engineered model cell lines (HPC-7 /HEK293 cells presenting antigen) and an immature B cell model (WEHI-231 naturally presenting IgM). We chose to model this interaction because data and protocols for this kind of assay are scarce or non-existent. It was our goal to produce valuable information, which would be incorporated into our wet-lab experiment, in an attempt to define more concretely the necessary conditions and concentrations for our assay.


What our model does

Our model simulates receptor induced apoptosis in heterogeneous mammalian cell co-culture. Given initial conditions by the user, our model predicts the rate at which the cells within the system will die. While seemingly a simple task, due to the variable nature of cells and receptor presentation combined with non-binary signaling, the system is very complex. Determining the optimal initial concentrations of each cell line as well as the necessary transfection efficiency would require tens of experiments and weeks of work. Using our model, researchers may narrow down the ranges of the aforementioned parameters, saving valuable time and money.


Assumptions

  1. The growth rate of HEK293 cells is similar to the growth rate of WEHI cells
  2. WEHI-231 cells undergo apoptosis as a result of interaction with antigen presenting HEK/HPC cells
  3. Kapop > Ka

In order to accurately model our system, we designed a kinetic model based on the following equations:




Eq. 1: Chemical equations describing the system




Eq. 2: Set of three ODEs describing the interactions within the system


Where:

  • H represents our model cell lines HEK293/HPC-7
  • W represents the WEHI cells
  • H-W represents HEK cells bound to WEHI cells
  • KH is the proliferation rate constant of HEK/HPC cells
  • ᵞH is the death rate constant of HEK/HPC cells
  • KW is the proliferation rate constant of WEHI cells
  • ᵞW is the death rate constant of WEHI cells
  • Ka is the binding rate constant for combination of HEK and WEHI to form H-W
  • Kd is the rate constant for disassociation of H-W to form HEK and WEHI
  • Kapop is the rate constant for the apoptosis of WEHI cells as a result of binding HEK cells

The equations were solved by MATLAB and the simulation was done using the following values for constants and initial concentrations:


Chart 1 – values of constants and initial concentrations

Constants and Initial Conc. Value (arbitrary units)
[HEK/HPC]0 4
[WEHI]0 6
KH 1
ᵞH 0.09
KW 1
ᵞW 0.01
Ka 2
Kd 0.06
Kapop 3

The ratios between the constants were defined based on the ratios found in relevant literature [1] [2] .
The initial concentrations were determined based on a co-culture experiment that we conducted. In this experiment we aimed to test the viability of HEK cells that were not transfected with the assay plasmid, and thus don't induce apoptosis, and WEHI cells, in co-culture. Different ratios of [WEHI]:[HEK/HPC] cells were tested and the optimal ratio was found to be 6:4 for [WEHI]:[HEK/HPC] respectively.


Results and Analysis




Figure 1: The model simulation results - when using the constants as listed in Chart 1


As can be seen in figure 1, our model is in line with our expectations. We can see that the WEHI cells undergo apoptosis as a result of co-culture with the antigen displaying HEK/HPC cells, and in direct response to the increase of H-W complexes.
In order to further characterize our system, we tested our model using different constants and cell ratios. We discovered that setting the value of Ka equal to KH yields a second behavioral regime in the model (figure 2):




Figure 2: The model simulation results when Ka=KH


For this value of Ka, and for a wide range of smaller values, the same behavior was observed. We can conclude that when Ka is higher than KH, at least 50% of HEK cells must bind WEHI cells in order to reduce the amount of WEHI cells to a negligible level.


We also found that our model is robust and shows the same behavior for a wide range of initial concentration ratios- a decrease in WEHI cells to near zero. For example, setting the ratio of [WEHI]:[HEK/HPC-7] to 4:6 yielded the following graph (figure 3):




Figure 3: The model simulation results for the initial concentrations [WEHI]:[HEK/HPC] ratio of 4:6


As the model predicted excellent results using a [WEHI]:[HEK] ratio of 6:4, we conducted the tolerance assay experiment using this ratio. Our Results established our model’s assumptions and demonstrated a qualitatively equivalent outcome.




  1. Rudich, S. M., et al. "Anti-IgM-mediated B cell signaling. Molecular analysis of ligand binding requisites for human B cell clonal expansion and tolerance." Journal of Experimental Medicine 168.1 (1988): 247-266.
  2. Molina-Peña, Rodolfo, and Mario Moisés Álvarez. "A simple mathematical model based on the cancer stem cell hypothesis suggests kinetic commonalities in solid tumor growth." PloS one 7.2 (2012): e26233.
My First Website

Department of Biotechnology & Food Engineering
Technion – Israel Institute of Technology
Haifa 32000, Israel

    • igem.technion.2017@gmail.com