In order to model IFFL's characteristics and its ability to encode and decode time-domain inputs relative to its alternative, Naive scheme, we developed system of Ordinary Differential Equations (ODE) to gain insight on parameters and their interactions leading to the behaviors of the output expressions. Then, we began implementing methods to assess IFFL's decoding ability under noise as means to develop a framework for acquiring relevant biological information in the time-domain. This step includes numerical computations of all possible concentration expression under different temporal structures of input that could be translated into vector analysis (heat map) to observing the behavior of variance under fixed temporal structures with respect to regions of parameter values as direct implication to noise response (illustrated using mesh and contour graphs). Overall, these methods support IFFL's ability to decode time-domain information much more accurately than its counterpart as well as having superior fidelity to noise response. With these findings, we hope that future iGEM team could develop IFFL systems that would be able to react to its input in an almost lossless manner.

Zhang et al. demonstrated that fundamental property of Incoherent Feedforward Loop(IFFL) can be used to exhibit temporal adaptation [1]. They further indicated this property could serve as the foundation for distinguishing input's temporal structure. To demonstrate this important ability, we built quantitative ordinary differential equations (ODE) model inspired by the generic model in Zhang's paper. Specifically, this model was meant to simulate the Temperature-Sensitive IFFL system developed by the wetlab team (Analysis of our model can be found here). Here, promoter inhibitor protein CI is quickly degraded at a specific temperature, which activates the production pathway for mf-Lon and m-Scarlet. The denominator seen under the production rate is intended to highlight leakiness in production even when there is a high concentration of CI, but this event is not observed during numerical testings due to low parameter values being used. These parameter values implemented for testing are derived and altered from MCMC and hard-coded values done in our chemically-induced model.

To assess Zhang's claim, we needed to come up with a system that serves as a counterpart to IFFL Decoder. The best way to measure the "distinguishability" performance was to take different types of inputs that encode information in the time domain and simulate these inputs being processed by the Decoder, which converts them into the amplitude domain. If inputs that are distinguishable in the time domain become outputs that are well-distinguishable in the amplitude domain, then we call that successful decoding. We did a computational experiment where we compared the use of our IFFL decoder against a “naive decoding circuit” (Above ODE) which consists of a gene that is activated by the input without any additional regulation. The naive decoding circuit represents the transfer of information from an endogenous biological signal into a synthetic circuit in the simplest possible way.

To compare the relative successful decoding of IFFL, we derived quantitative method of representing the difference between reporter's expression concentration decoded through different temporal inputs - call it on time or duration - with fixed off time as vector for both systems. This vector was calculated using the Euclidean distance among all points between the two concentration expressions, then a determining value was derived by taking the vector difference between Naive and IFFL. Finally, these values were organized in a "heat map", where the shadings in red represented relatively how much better IFFL was at decoding the input signal at that two specific different on time, and vice versa for the blue shadings. Overall, this assessment can be summed up as IFFL's relative "distinguishability" strength of time-domain inputs from amplitude-domain output.

With IFFL's ability to detect small variations in temporal structure from the input, we would expect that the system would be susceptible to noise. To test this hypothesis, we performed the following numerical testing for both IFFL and Naive model and compare the variance as direct translation to noise response. Gaussian noise with average value 0 and standard deviation of 0.1 was applied to the concentration of CI: Start with fixed value for off-on ratio, calculate all concentration expressions of m-Scarlet within a specific parameter region of m-Scarlet production rate. Variance is then taken for that specific off-on ratio, then on ratio is incremented, then off ratio is incremented as on ratio resets. Each variance for respective off-on ratio is the average variance of concentration expression as function for varying parameter value range of m-Scarlet production rate.

We believe that this is the appropriate method to assess the system's ability to respond to noise. Production rate of m-Scarlet was selected to be the changing parameter region since this is analogous to either changing values for degradation rate of mf-Lon or the induced degradation rate of m-Scarlet by the protease. The method not only covered output expressions in wide range of parameter regions, but it also guaranteed to illustrate output's behavior across all possible range of structural inputs.