Modelling

The questions which the modelling team set out to answer were inspired by the questions the biologists were asking in the wetlab. As we scrutinized how our reporters, detector, and other biological devices could merge together in our sensor, we realized these modular protein components could be assembled in numerous combinations. We’d would have to determine their optimal configuration for integration in the prototype.

To reduce the number of wet lab experiments to build our sensor, we followed a two-pronged modelling approach to find preliminary answers to these questions. Initially, we used spatial models in Autodesk Maya, where we assembled 3D protein structures to gain an intuitive understanding of the assembly of our sensor proteins. Finally, we deployed a quantitative Mathematica prototype model to test how amounts of target DNA versus detector proteins would influence sensitivity on our lateral flow strip.

Quantitative:

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For any detection system, the sensitivity and specificity are of great importance. Ideally, one should determine those parameters from repeated experiments, but to shorten the development time and to provide some insight on directions of further improvements, we seek to develop a model describing the behaviour of the system, from which the sensitivity and specificity can be theoretically obtained.

How did we do this?

A simple 2D Monte-Carlo method was used for the simulation of DNA moving along the strip and bind to TALE. At the end of the simulation the number of positive DNA binding to the TALE are tallied with the number of negative DNA that bind.

A 2D region of the test strip, viewed from the top, was partitioned into a grid of squares such that a single TALE (0.1 nm by 0.1 nm by 0.1 nm) will be occupying a single square. Initially, about 45% of the spaces counting from the left are designated the DNA loading zone, where only the DNA will be placed. The remaining spaces will be initially allocated for TALEs to be present. DNA then moves from its current square to its neighbouring squares, one square at a time, whose probabilities are set in such a way so that moving from left to right is favoured. When DNA enters a square occupied by a TALE, the probability of binding to that TALE is determined by whether the DNA is positive or negative. If binding occurs, the TALE becomes saturated and additional DNA cannot bind. After some time, the number of TALEs bound by a positive DNA are tallied against the number of TALEs bound by a negative DNA, from which sensitivity and specificity can be calculated.

What did it show?

Currently, our model only supports probability of positive DNA binding equalling one and that of negative DNA equalling zero. In addition, a downscaled model is deployed enabling the user to interact with what the model has processed. Please note that this requires installation of third-party software: Mathematica Player provided by Wolfram Inc. free of charge.

The positive DNA's are colored red, negative DNA is green, TALEs are black and after binding (i.e. saturation) they turn blue. The sliders under "global settings"€ are parameters needed before the simulation runs. Given that a simulation can take 30 seconds to complete, they should not be changed frequently as it will take longer to show the results. The sliders under "€œdisplay settings"€ are parameters needed after the simulation runs. Their responses are much faster and are best played by clicking on the plus sign to the right and hit "€œPlay".

Link to Quantitative Model

In addition to deploying the model on the webpage we had also investigated the effects of changing the ratios between positive and negative DNA, and the number of TALEs available. For 5 levels of each of those parameters, 3 runs were conducted since the method is stochastic, resulting a total of 125 experiments. They are summarized in the graph below.

From the graph we clearly see that not much TALE or DNA is required to have enough DNA bind to TALE, such that the signal cascade starting from the TALE can be read on the strip. Thus we have some theoretical evidence that our constructs will work the way they are designed. Also note that this experiment is not designed for specificity and sensitivity because of the simplicity of the binding probabilities chosen. We do acknowledge that as percentage of positive DNA increases, the total binding number will also increase, so it is not a "€œfair" comparison of performance of various levels of percentage of positive DNA. But for the purpose of ensuring the signals will be large enough to be read, this suffices.

What to be done?

In the future the model will be expanded to include parameters changing the probability of binding to TALE for both the positive and negative DNA. After which more experiments will be run to investigate the effects of those probabilities upon the sensitivity and specificity of the strip. We wish to conclude from those experiments, what is the bare minimal amount of TALE required on the strip, such that it gives good enough sensitivity and specificity for all possible ranges of probability of binding. This will in turn translate to the concentration of TALE needed, an important design parameter concerning the strip.