Team:Tsinghua-A/Measurement
Traditionally, we evaluate the impacts of noise using variance-related statistics, such as coefficient of variance. These quantities can only describe how concentrated the output is around the mean value, but cannot tell us how well we can infer one of the correlated random variables from the other. Channel capacity makes a better criteria of noise because it more scientifically depicts the information dissemination process.
We measured channel capacity of the part BBa K1061013. We quantify the properties of TRE promotor.
The link is:
http://parts.igem.org/Part:BBa_K1061013
Our Improvement
Purpose
Channel capacity evaluates correlation between input and output signals. For instance, if channel capacity is larger than 1 bit, the part can decern between high and low inputs, and vice versa. By assessing this novel quantity, we through light on how much information can a inducible promotor pass on. The measuring and calcualtion methods can be applied to more promotors in the future.
Results
Using EBFP2 as reporter, we measure channel capacity of a simple circuit driven by TRE to be 0.5259, with standard deviation of 0.0058.
Methods
We transfect HEK-293 human cells with our plasmid constructions as described in the form [ref: table]. Different concentrations of Dox are applied to cell culture at the same time.
Transfected cells are cultured for 48 hours before performing flow cytometry, long enough for protein expression level to achieve steady state. FACS examination measures florescent intensity emitted by each cell, from which we obtain a large sample of florescent protein expression level, tens of thousands of cells for each experiment group.
Data collected from flow cytometry are later analyzed on computers. We estimated probability density function (p.d.f.) from data using kernel density estimation, a nonparametric statistics method. Given high and low Dox concentration input, cells exhibit different probability distributions, as illustrated in the example below [ref: fig].
What we have in hand is the conditional distribution $p\left( {Y\left| {X = x} \right.} \right)$ , given a known level of input $x$ . In order to calculate mutual information $I\left( {X;Y} \right) = \iint {p\left( {x,y} \right){{\log }_2}\frac{{p\left( {x,y} \right)}}{{p\left( x \right)p\left( y \right)}}dxdy}$ and estimate channel capacity, which is $C = \sup I\left( {X;Y} \right)$ , we need to find the input distribution $p\left( X \right)$ and joint distribution $p\left( {X,Y} \right)$ that optimizes the equation. $p\left( X \right)$ , however, is not known in the first place. We first randomly pick a stochastic vector as the initial input distribution and then use an optimization algorithm to iterate the function and maximize $I\left( {X;Y} \right)$ . The final result is the channel capacity.
