Team:Munich/Model

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Model

Introduction

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We developed A generic square placeholder image with rounded corners in a figure. to enable RNA export out of mammalian cells for minimal invasive longterm monitoring.

Incorporating the feedback given by Prof. Hohendorf, we developed an in-silico model for calculating the amount of obtainable RNA based on the experimental setup to account for the various factors involved. The image above shows some of these factors.
Therefore, we explored the influences of parameters such as cell number, cellular RNA levels, RNA to binding protein affinity, or binding protein export to create this model. We then developed the following rearrangeable formula, which allows for specific optimizations to the experiment at hand.

When applied, one can estimate the number of cells required to produce a detectable signal. The accuracy of this estimation was then experimentally tested by comparing the formula's results to our own data. The cell number detection limit predicted by our model correlated with the experimental data from a cell titration experiment.
The model can now be used to determine whether ALiVE would be suited for one's needs.

Formula Overview

RNAO = Ncells * RNAC * Dbound(NBP, RNAC, KD) * EBP * T(t, tM) * Dvol * η

RNAO: Total amount of extracted RNA
Ncells: Number of cells
RNAC: Average amount of RNA of interest per cell
NBP: RNA binding proteins per cell
Dbound(NBP, RNAC, KD): Fraction of RNA bound to RNA binding protein
EBP: Fraction of RNA binding protein exported
T(t, tM): Time(t)- and time-since-last-medium-change(tM)-dependant medium satuation function
Dvol: Fraction of Volume used
η: Fraction of signal retrieved by measurement after preparation

Assumptions

We assumed the following:
  • All the factors are directly proportional to the RNA output
  • RNAC and NBP are constant for a specific cell line
  • EBP is constant for a specific adapter-marker (Gag for VLPs, CD63 for Exosomes) couple
  • Dvol and η are constant for the experimental setup
  • Dbound needs to be derived from the KD formula
  • T levels off

Parameter Determination

Prior knowlegde

Dvol

The Fraction of Volume used was Dvol=1 in our case, since we took all of the sample at the beginning of each assay and later accounted for steps where we used less than the full volume.

Ncells

We used the number of cells at confluency for the respective well format, if the cells were seeded as suggested.
Most of the model data was obtained from 6-well plate wells, resulting in Ncells=1,2*106 for these data points.

η

The fraction of signal retrieved by measurement after preparation is the product of all quantified assay efficiencies, especially the vesicle purification (determined by HiBiT-Assay) and an estimated error. We assumed η=0.4 overall.

HiBiT-Assay

To assess and quantify the amount of exosomal and VLP marker in the supernatant above the cells and in the cells themselves we used Promega's Nano-Glo® HiBiT Extracellular Detection System. It provides the LgBiT and the substrate that the HiBiT tag on CD63 or Gag needs to luminesce. Two measurements are made on the same sample: One with unlysed supernatant and another one with detergent- and heat-treated supernatant. The signal coming from untreated supernatant provides information about how much tagged protein was not packaged into vesicles, thus determining the leakage of the system. The detergent- and heat-treatment ruptures the vesicles, allowing the LgBiT access to all HiBiT-molecules in the sample, therefore providing information about the total content of CD63-HiBiT and Gag-HiBiT. Cells can also be lysed in order to solubilize the cytosolic, exosomal and VLP markers not secreted yet. With a HiBiT standard curve, the measured RLU signal is then converted into pure HiBiT equivalents that we assumed to be the best possible approximation for the quantity of the target molecule, since there is exactly one HiBiT domain on each protein-of-interest.

NBP

The RNA binding proteins per cell were determined by dividing the cellular HiBiT-signal by the number of cells. NBP=2,4*109 was determined as mean for the exosomes, NBP=3,7*108 for the VLPs.

EBP

The fraction of RNA binding protein exported was computed by dividing the difference between the lysed supernatant and the unlysed supernatant signal (resulting in the HiBiT signal originating from intact vesicles) by the sum of the lysed supernatant and cell signal (total HiBiT signal). It was found that EBP=0,02 for exosomes and EBP=0,45 for VLPs.

RT-qPCR

The RNA in the vesicles was isolated either by a PEG-based precipitation and phenol-chloroform extraction for exosomes or a viral RNA extraction-specific protocol for VLPs. Cellular RNA was extracted via the TRIzolTM reagent. The samples were then reverse transcribed into cDNA and a qPCR was carried out to precisely quantify the FLuc transcript content of exosomes and VLPs. For more elaborate applications, the transcript-of-interest would be quantified with this method. The relative CT-value detected by the qPCR-maschine can be converted into absolute copy numbers by using a standard curve of known copy numbers. To get increase the precission of the value, a noRT control copy number is subtracted from the reverse-transcribed copy number.

RNAC

The average amount of RNA of interest per cell is calculated by dividing the mRNA of interest copy number of extracted cells by the number of cells. Our best RT-qPCR result for FLuc-mRNA without export (to not falsify the result by said export) showed RNAC=3,3*104

RNAO

The total amount of extracted RNA also needs to be measured as a reference. The value is the number of transcripts of the extracted vesicles. For some examples, look at the section below

Complex parameters

Dbound(NBP, RNAC, KD)

To get the fraction of RNA bound to RNA binding protein
Dbound(NBP, RNAC, KD) = (0,5*(-√(POTENZ(RNAC)-(2*RNAC*(NBP-KD))+POTENZ(NBP+KD)2 ))+(RNAC+NBP+KD)))/RNAC,
Afree = Atotal/AB and Bfree = Btotal/AB were put into KD = (Afree*Bfree)/AB, with Atotal representing RNAC and Btotal representing NBP. The resulting formula was solved for AB and divided by Atotal to obtain Dbound. The only parameter, that was not already determined is the KD. From literature KD=1*10-11 was obtained for the RNA binding protein L7Ae(Schroeder et al. 2010).

T(t, tM)

The time(t)- and time-since-last-medium-change(tM)-dependant medium satuation function was proposed and designed to account for satuation states of the RNA in the cells and the vesicles in the medium. These satuation states are theorized to result from constant growth with each generation decaying over time, modeled as a factor to multiply RNAC. This factor for each of the two layers fl = Σi=0tl (1-a)i = (1-(1-a)tl+1)/a is dependent on the parameter a representing the specific decay rate for the RNA or vesicle respectively. After rescaling the factors and multiplying them with each other, we arrive at the following final formula:
T(t, tM) = (1-(1-aRNA)t+1)*(1-(1-avesicle)t-tM+1)*TMax
As the parameters in this formula were hard to measure, they were fitted based on our data. aRNA was

Validation and Range of uncertainty

To validate our model, we rearranged the formula to calculate the cell number.

Ncells = RNAO / (RNAC * Dbound(NBP, RNAC, KD) * EBP * T(t, tM) * Dvol * η)

 N_cellsomRNAcmRNA/cellD_boundBP_ET(t, t_M)Dvoleta
Exo Minimum Cells851,174482306478100.000,0033111,112662563210,020,44352452838060810,4
VLP Minimum Cells30,2754578514225100.000,0033111,112662563210,450,55419550667410210,4

We decided to desire a yield of 100000 RNA molecules for a clean and reliable readout, although this is above the detection limit of qPCR.
t=72 and tM=48 were assumed as this were the prefered settings of the cell titration assay we performed to check the numbers obtained from the above calculations. Besides the resulting cell numbers and RT-qPCR copy numbers (omRNA), you can see the model applied to the different conditions with the resulting predicted transcript number (omRNA*). This additional information was not generated for fun but to estimate the error of the model.

 NcellsomRNA omRNA*N_cellscmRNA/cellD_boundBP_ET(t, t_M)Dvoleta DeviationABS Deviation
TitExo_SN125.000,00966.712,46 2.937.118,1325.000,0033.111,111,000,020,441,000,40 0,670,67
TitExo_SN212.500,00428.546,79 1.468.559,0612.500,0033.111,111,000,020,441,000,40 0,710,71
TitExo_SN36.250,00235.834,36 734.279,536.250,0033.111,111,000,020,441,000,40 0,680,68
TitExo_SN43.125,00124.509,18 367.139,773.125,0033.111,111,000,020,441,000,40 0,660,66
TitExo_SN51.562,50110.154,58 183.569,881.562,5033.111,111,000,020,441,000,40 0,400,40
TitExo_SN6781,2574.214,07 91.784,94781,2533.111,111,000,020,441,000,40 0,190,19
TitExo_SN7390,6360.506,59 45.892,47390,6333.111,111,000,020,441,000,40 -0,320,32
TitExo_SN8195,3177.629,42 22.946,24195,3133.111,111,000,020,441,000,40 -2,382,38
TitVLP_SN125.000,0027.136.224,28 82.575.134,3625.000,0033.111,111,000,450,551,000,40 0,670,67
TitVLP_SN212.500,0023.970.752,32 41.287.567,1812.500,0033.111,111,000,450,551,000,40 0,420,42
TitVLP_SN36.250,0012.586.309,84 20.643.783,596.250,0033.111,111,000,450,551,000,40 0,390,39
TitVLP_SN43.125,007.882.675,82 10.321.891,803.125,0033.111,111,000,450,551,000,40 0,240,24
TitVLP_SN51.562,502.582.841,55 5.160.945,901.562,5033.111,111,000,450,551,000,40 0,500,50
TitVLP_SN6781,252.119.567,10 2.580.472,95781,2533.111,111,000,450,551,000,40 0,180,18
TitVLP_SN7390,631.080.091,83 1.290.236,47390,6333.111,111,000,450,551,000,40 0,160,16
TitVLP_SN8195,31306.911,71 645.118,24195,3133.111,111,000,450,551,000,40 0,520,52

The sample name is made to display the corresponding conditions with
  • "Tit" refering to the titration assay
  • "Exo" and "VLP" to the respective vesicle type
  • "SN" to the supernatant (containing the vesicles but no cells)
  • the number indicating the dilution factor with "1" referring to conditions seeded with the suggested cell number, "2" 1/2 of the suggested cell number, "3" 1/4 up to "8" being 1/128 of the suggested cell number

Detection Limit

When looking at the exosomal samples, one can clearely see the predicted cell number as well as the required 100000 copy numbers located between "TitExo_SN5" and "TitExo_SN6", proving the prediction correct.
For VLPs, it is a bit less obvious, both of the values are below the sample with the minimal pipettable cell number, "TitVLP_SN8", indicating the predictions approximate correctness.

Deviation

The last two columns show the deviation of our predicted results from the measured values. The maximum error of our model (taking the maximum of the last column) is around 2.4. This number is quite high but still in the right order of magnitude. It is also the only deviation above 0.71, so it can be attributed to errors resulting from the low cell number.
The mean deviation is only around 23% making the model fairly accurate over all.

Conclusion

Incorporating the feedback given by Prof. Hohendorf, we decided to create an in-silico model to predict the outcome of ALiVE experiments. This allowed us to predict the minimum number of cells needed for a detectable signal that we were in fact able to validate. We were event able to show the models high accurecy.