Modeling

For any detection system, its sensitivity and specificity are of great importance. Ideally one should determine those parameters from repeated experiments, but to shortening 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 Monto-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 bind to TALE are tallied with the number of negative DNA bind.

A 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. About 45% of the space counting from left are designed DNA loading zone, where only DNA will be placed there. The remaining of the space will be allocated to TALEs where initially only TALES present. DNA moves from its current square to its neighbouring squares, one square at a time, whose probability are set in such a way so that moving from left to right is favoured. When a DNA enters a square occupied by TALE, it will have a probability of binding to TALE thus saturating the TALE (no longer binds), whose probability determined by its type (positive or negative). After certain amount of time increments the total number of positive and negative DNA bind to TALE are tallied, from which sensitivity and specificity can be calculated.

What did it show?

Currently our model only supports probability of binding of positive DNA to be one and that of negative DNA to be zero. Other than that a scaled down model is deployed with interactivities enables for you to have a feel of what it do. Note that it requires installation of third-party software, Mathematica Player, provided by Wolfram Inc., free of charge.

The positive DNA’s are colored red, that of negative green, TALEs are black and after binding (i.e. saturation) they turn to 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 and takes while to show the results. The sliders under “display 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 “Play”.

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 “fair” 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.