Team:Tsinghua-A/Proof
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How to quantify channel capacity of gene regulatory networks?
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Do our circuits work?
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How well do circuits perform as evaluated by channel capacity?
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What can the result teach us?
- Inspirations for Synthetic Biology Engineering
- Highlighting the biological significance of dimerization
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.
Yes, they do sense the input level of Dox concentration. The transfer curves of all seven groups are illustrated below. All values are in logarithm space. Note that for the convenience of plotting, the points where Dox=0 are plotted at Dox=0.01. (or the point will fly out far to negative infinity)
In the leftmost figure, EBFP2 without intein sequence show relatively low affinity and thus low expression level. Nevertheless, their leakage level is low as well, and Dox induction leads to approximately fold change. As for the middle and right figures, both split EBFP2 with intein and intact EBFP2 have about fold change when induced by Dox, but split EBFP2 have lower leakage level.
Meanwhile, if one half of EBFP is driven by constitutive promotor CMV, the leakage level remains the same but the induced multiple suffers. This is expected beforehand because with one constitutively-expressed part, the circuit can only sense the input with one half of the split proteins, thus becoming slightly less inducible.
Normalizing the curves lead to more interesting discoveries. Even though TRE-EBFP2N + CMV-EBFP2C leads to poor fold change, the transfer curve is significantly steeper when the dimerization process is reversible. This means better switch-like properties. With the presence of intein, the effect is weaker but still visible.
Normalize transfer curves to the range of 0 to 1, we can find that the shapes are different. Lines representing split proteins are later to rise and steeper.
If we normalize the initial EBFP2 level to 1, split EBFP2 with intein displays better properties than the other two settings. From fig. we can clearly see that it has the highest multiple among the three, even significantly higher than that of the intact EBFP2. The result shows that split proteins, with high binding affinity, can defeat original undivided proteins for their low leakage level and high induced multiples, that is, high sensibility to inputs.
Seven circuits are evaluated in our experiment. Calculated channel capacities are displayed in fig.
Come on, this not as dizzying as it is at the first glance. Let’s look at it step by step.
When both promotors are TREs, both split parts are inducible, and channel capacity is relatively higher than that of channels with un-inducible CMVs. In the absence of intein, the two peptides find it hard to dimerize, giving rise to low channel capacity.
Upon addition of intein sequence, the binding process becomes irreversible since the two halves assemble into one intact protein through splicing. As a consequence, channel capacity greatly increases. Double-inducible group with two TRE promotors still win the competition speaking of channel capacity.
Comparing three inducible groups leads to the conclusion, that splitting leads to decrease in channel capacity, but adding intein sequence to peptides rescue the effect, elevating the channel capacity to even higher level.
For synthetic biologists, it is crucial and challenging to construct AND gate. Split up a regulatory protein such as transcription factor, express two halves independently, and an AND gate is born.
Nonetheless, the act of splitting up can bring about unexpected side effects. Gene regulatory circuits are highly dependent on quantitative properties, its complexity and nonlinearity contributing to hard-to-predict behaviors of biological systems. Once an important part in the system is chopped up, who knows what will happen next?
Our program quantitatively studies the behavior of such systems. Splitting up changes the circuit’s output-input function, alleviates leakage phenomenon, improving switch-like property, and increases fold change when induced by circuit inputs. Moreover, we use channel capacity from information theory to describe how well can they transmit signals. We find adding intein sequence tremendously beneficial in that it shifts the channel capacity to a higher level, thus ameliorating uncertainty.
When it comes to designing logic gates, our findings can lead the way. Not only can splitting achieve logic gate effect, but also can it improve sensibility to inputs and defend the system against detrimental interferences of noise when intein is added. Future work shall benefit from this fundamental investigation of basic synthetic biology blocks.
Dimerization is only too common in cells. Monomers assembly into dimers for further functions all the time, some interactions strong, some interactions weak. Function-less newborn peptides piece together and get to work, forming so-called tertiary structure; activated kinases reach each other and mutually phosphorylate; transcription factors, when forming homo- or hetero-dimers according to different stoichiometry, leads to varied downstream responses and distinct cellular fates…
Yes, we know which proteins dimerize. We understand how proteins dimerize as well, by interaction of domains like leucine zippers and so forth. But why? What is the point of dimerization?
Previous researches have underlined the important advantages of dimerization, including differential regulation, specificity, facilitated proximity and so on. [citation needed] The influence of dimerization in noise propagation is hardly touched due to the difficulty in controlling experiment variables. Synthetic biology provides powerful tools to carry out experiments otherwise impossible in designed systems. This is exactly what we do.
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.
