After developing the mathematical model and thinking about the equations we developed our model in Matlab, which can be used to perform other experiments with different values or light pulses. In Matlab we performed different experiments in order to see how our biological decoder would react to different light pulses and to try different ideas.

Constitutive level: Zero input response

Before studying saturation when light pulses were given, we must take in advice that first level (producing A, B, C and D), starts expressing from minute 0. Activation of next level is directly proportional to the amount of those proteins that were produced firstly, as they are binding domains of secondly activated constructions. Thus, more expression will be obtained as more binding domains are synthetized.

Inputs used in our circuit are determined by the value of two variables: color and time. Distinguish different colors is easy due to their different wavelength, resulting in the stimulation of different photoreceptors that regulate each switch. But how can our genetic constructions assign an order to inputs of the same colors?

Recombinases are the biological elements which grant memory to AladDNA. These enzymes work as excisionases and integrases, cutting the gen which is surrounded by recognition sites specific for those recombinases. In our model this excision has been represented by the change from g+ to g-, referring to the capability of the gen for being translated.

In our device, recombinases used are BxB1 and θC31. They are produced with the first input:

Both second levels have the recognition sites for recombinases produced in the analogous level. Thus, enzymes firstly produced recombinate the option which has not been activated. When the second input is introduced, production in the second level will not be possible, as genetic codes have been flipped. In other words, if the second light is a different color, it will only mean production regulated by switches of the final level, resulting in a circuit that reminds which was the first input.

As we explain in the biochemical reactions section, when recombinases are produced they instantaneously dimerize, and two dimmers will be needed to recombinate each gene. The duration of this process will determine the moment when it will be save to give the second input.

Firstly, we will plot the results of a single red input in order to appreciate the curve described by g+ in the analogous level. Gene copy number used for this performance is of a single copy.

On the other hand, the moment when recombinases switch off gH+, gI+ and gJ+, is approx. the minute 280, as we can see in the graphic below:

In order to prove recombinases efficiency, we will simulate two followed inputs of different colors. If they work, the expected result is that there is no expression of that genes later, when the other light is given.

As we guessed, no expression of the second level is produced after a previous input of 280 minutes, which is the time that ensure us the end of recombinases action.

Different vectors can be used to introduce our genetic constructions in the cell. The amount of gene’s copies varies in each kind of plasmid, and this is a critical parameter. There will be a trade-off between the amount of genes expressing enzymes, and the number of genes that those will have to recombinate.

We performed simulations with different values of gene copy numbers relying on some vectors typically used to transform E.coli.

Values considered for this parameter were:

gin=[1,5,10,17,400,600]; %Initial amount of genes

From 1 to 17 copies:

With more genes, there is more basal expression of recombinases, but also of those genes that BxB1 and θc31 must recombinate. Moreover, levels of basal expression of the analogous recombinases will also increase. This is the reson of the decay in gE+, which is more abrupted as the gene copy numer rises. That basal recombination is undesired, because the amount of binding domain produced also decays, as we can appreciate in the second group of curves (E). However, with 5 copies the difference is positive, but this arise does not persist when the number of copies keeps on increasing.

Graphic above suggests that recombinases efficiencyis not affected by the numer of copies, because they can get the same result (g+  0) in the same time. Then, if increasing the number of copies means less amount of expression and it makes no difference in recombinases efficiency, these results suggest that low numbers of copies are more suitable to get the desired behavior.

Results with 400 and 600 copies support that higher amounts of copies induce more basal expression of recombinases, which leads in an undesired behaviour of our circuit:

No protein production is appreciated. Looking closer to the first 100 minutes of simulation:

Basal expression of both recombinases is so high that even when light is still off, they are produced in enough quantities to totally switch off production in the second level.

We knew from literature, that changes induced by light are instantaneous. However, there are several differences between switching on and off these switches. For example, if we had implemented a red toggle switch, we would be able to ensure the stop of production using far red light, whereas dark periods induce a slower decay.

This means that although light irradiation is stopped, the presence of photosensible elements may will decrease slowly, and production will not occur only when light is given. In other words: production will not be totally over light control.

In order to ensure this coordination between light and presence of active elements, we suggested our wet lab mates tagging PhyB and ePDZ, they may will be degraded fast enough to minimize their presence when light has been eliminated. This is the reason why B and D have higher degradation rates than other proteins.

So, if dark periods mean loss of activators, pauses between first and second inputs should be as short as they can be, in order to maximize production. The shorter pause possible, is a no-pause, i.e continuous irradiation.

Firstly, we will compare production of alpha with different pauses between both red inputs, in order to analyze the influence of the dark period length. We implemented in Matlab a for loop to facilitate the comparison:

pause_dur=[0,2,30,60,80,100]; % vector containing different duration of pauses.

Here we plot the results. All time axis are expressed in minutes.

Fixing our attention in alpha:

It is clear that production decays with the increase of the pause between inputs. In other words, production is increased with more irradiation. Then, combinations of the same color repeated (red_red and blue_blue), will provide better results if they are one single pulse instead of two.

From conclusions extracted above, we will assume that both pulses must be continuously given, with no pause between them. Furthermore, in combinations red_blue and blue_red, there will be a necessary condition that ensures waiting time enough in order to let recombinases finish their work. The duration of this period was estimated before, concluding that 280 minutes of simulation were enough in order to give the second pulse. In summary:

Another criteria which may be useful, is the moment when production reaches its plateau. This leads in abundance of binding domains required by next level. Output amounts are directly proportional to the presence of those binding domains. From saturation experiments we determined that since production begins, it reached its maximum 250 minutes later. As second level expression arises after an initial pause of 250 minutes, the absolute time will be:

Our first idea was comparing three kinds of structure:

- Both inputs with the same length.

- First input longer than the second one.

- Second input longer than the first one.

Inputs introduced in Matlab in order to test each possibility, and results obtained were:

input_red =[zeros(251,1);red_intensity*ones((2750/2)+500,1) ;zeros(length(input_t)-(2750/2)-500-251,1)];

input_blue=[zeros(251+(2750/2)+500,1); blue_intensity*ones((2750/2)-500,1) ;zeros(100,1)];

input_red =[zeros(251,1);red_intensity*ones((2750/2)-500,1) ;zeros(length(input_t)-(2750/2)+500-251,1)];

input_blue=[zeros(251+(2750/2)-500,1); blue_intensity*ones((2750/2)+500,1) ;zeros(100,1)];

In simulations performed above, the expected output was β, and the third scenario is that one which gets higher levels of its expression. Then, the second input must be longer that the first one. If we optimize this condition, our aim in following simulations will be to find the first and second inputs as short and as long as they can be, respectively.

Since necessary condition is achieved in (t_max.BD > 280 min), theoretically, the best option would be giving the second input in minute 500. However, we will simulate different scenarios in order to test which one gets the best result. As the order of inputs is red_blue, the expected output is β.

In graphics below prove recombinases condition is achieved, but not max BD production:

Outputs amounts obtained:

Maximum BD production is achieved, and also is action of recombinases:

Outputs produced:

If we give time enough for recombinases to actuate, giving the second input at minute 280, but we do not stop production of the BD until it reaches its maximum (t1st input=500 minutes), there will be an overlap between pulses, but both conditions are accomplished as well.

Comparing the production of all products in each of the three last simulations:

The third option presents the worst results of all. As irradiation with both lights is more prolonged, more undesired outputs are produced.

Between the first and the second option, the main difference is between the production of alpha and gamma in the first case, and the production of Omega in the second one. At the end, ratios achieved in both cases:

Ratio beta versus alpha is higher if the second input begins just after recombinases work, i.e minute 280.

Although the logical structure of inputs would be one after another, we found interesting the idea of simulate some unusual conditions such as two inputs partial or totally simultaneous, or sequences with three structure color1_color2_color1.

Three pulses are not valid to obtain just one output and consequently, this combination should be avoided if only one output is wanted, because the presence of all which is produced and its possible intake, may have negative consequences.

However, if multiple production is desired, this kind of sequence permits the production of two outputs in different proportions, which could be useful in situations such as obtention of products which need a “helper” compound.

input_red =[zeros(251,1);red_intensity*ones(2750,1); zeros(100,1)];

input_blue=[zeros(251,1);blue_intensity*ones(1375,1) ;zeros(1475,1)];

input_red =[zeros(251,1);red_intensity*ones(2750,1); zeros(100,1)];

input_blue=[zeros(1626,1);blue_intensity*ones(1375,1) ;zeros(100,1)];

input_red =[zeros(251,1);red_intensity*ones(1375,1); zeros(1475,1)];

input_blue=[zeros(251,1);blue_intensity*ones(2750,1); zeros(100,1)];

input_red =[zeros(1626,1);red_intensity*ones(1375,1); zeros(100,1)];

input_blue=[zeros(251,1);blue_intensity*ones(2750,1); zeros(100,1)];

With this sequences we can produce majorly 2 outputs, or three with one of those three majorly produced. This sequence offers the possibility of multiple production, combining the effect of different compounds, which could be useful in scenarios as the production of multivitamin complex.

Using information recovered from simulations described, we were able to determine light sequences that obtained ratios of nearly 100, being the desired output the one majorly produced with a great difference. In summary, these are the relations between inputs and outputs that describe AladDNA’s performance:

Output alpha:

Output beta:

Output gamma:

Output Omega:

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