Overview

Background

In our design, after having designed the flip flop, the device can remember the information of its state, the next step is to transform the state into an actual function. To achieve this transformation, we first needed a “reader” to read out the current state. At this point the control unit comes into play. A control unit is a DNA sequence with recombinase sites whose expression is controlled by recom-binase and RDF by reversing or deleting a promoter and/or a terminator. To make the control unit reliable and predictable, we first need to be able to predict the behaviors of its “building blocks” (or “elements” in electrical engineering), from which we weave our engineer’s perspective into the biolog-ical system. However, we need to make some adaptations and adjustments to these “elements” to make them usable.

Control Unit

Intention of the Model

In this model, we aim to describe the sequence modification process of the control unit sequence with recombination sites. Different recombinases are expressed in series to alter the direction of terminators between corresponding recombination sites on the control unit circuit. The combination of unidirectional terminators in different directions (reverse or foward) determines the state of RNA polymerase flux, thus controlling expression of the downstream gene.

Though we have done simulation of recombinase dynamics in the previous section, it is necessary to consider two key concepts of biological processes:

1. population behavior 2. stochastic process

The reason for modeling cell population behavior is that deployment of synthetic bacterial devices would certainly involve populations of cells. Furthermore, we demonstrate our design through continuous imaging of entire cell cultures. This is a theory-experiment interaction procedure. The reason for stochastic modeling is self-evident. Cellular biological processes, especially gene expression, are innately noisy and stochastic.[^Footnote1] Previous work has demonstrated the effectiveness of the integration of population-level dynamics and stochastic cellular responses to inputs.[^Footnote2]It is important to explain how stochastic single-cell responses affect overall population-level distributions and behavior.

This section describes a Markov model of recombinase-based DNA flipping and a Gillespie stochastic simulation method[^Footnote3] to observe theoretical sequence state evolution. We will focus on our demonstration design, which can be generalized to other designs.

Biological Basis

The control units are implemented experimentally by transforming a plasmid into an E. coli. This plasmid has similar structure as the reporter plasmid in the previous section. However, in this situation the sequence fragments being inverted are terminators. Using experimentally screened uni-directional terminators, the transcription or polymerase flux[^Footnote4] can be precisely controlled. The figure below illustrates the result of the design software. （超链接到software）

Clock

Intention of the Model

We attempts to develop a framework of biological sequential circuits that are programmable. The envisioned circuit is capable of both storing states in DNA and automatically running a series of instructions in a specific order. According to our design, our bio-flip-flop has two promoters, each triggered by an inducing signal. Therefore, if we would like to build an automatic triggering system for the bio-flip-flop, we need at least two signals in our clock. It is then self-evident to incorporate the classic structure in synthetic biology: the repressilator.

This model serves as a proof of concept for such implementation. We first constructed an ordinary differential equation (ODE) system to describe the repressilator, then we used two repressor proteins expressed by the repressilator to regulate the two promoters. Finally we adjusted parameters and gave a simulation result as a proof of the possibility of repressilator-driven bio-flip-flop.

Biological Basis and Assumptions

The repressilator is a synthetic genetic regulatory network consisting of a ring-oscillator with three genes, each expressing a protein that represses the next gene in the loop.[^Footnote1] This network was designed from scratch to exhibit a stable oscillation which is reported via the expression of green fluorescent protein, and hence acts like an electrical oscillator system with fixed time periods. The repressilator consists of three genes connected in a feedback loop, such that each gene represses the next gene in the loop, and is repressed by the previous gene.



We decided to implement our repressilator-triggered bio-flip-flop with two repressor proteins regulating the two promoters’ transcription. The basis of ODE system construction is illustrated as follows:



The upper promoter (X) is \(P_{LtetO}\) and is repressed by tetR protein. The lower promoter (Y) is \(P_{R}\) and is repressed by cI protein.Simulation of bio-flip-flop starts at a later time than repressilator because the expression levels of the repressor proteins at the beginning is not high enough.

Equations and Parameters

Repressilator

The following table lists the reactions in the repressilator network. X, Y, Z represent LacI, TetR and cI mRNAs, and PX, PY, PZ represent the corresponding proteins.



Calculation of degradation rates are described as follows: \[ k_{dmRNA} = \frac{ln(2)}{\tau_{mRNA}} \] \[ k_{dprot} = \frac{ln(2)}{\tau_{protein}} \] \(\tau_{mRNA}\) and \(\tau_{protein}\) are half lives of mRNA and protein. Calculation of maximum transcription rate: \[ a_{tr} = 60(ps_a - ps_0) \] \(ps_a\) is “tps active” and \(ps_0\) is “tps_repressive”. Calculation of translation rate: \[ k_{tl} = \frac{eff}{t_{ave}} \] \(eff\) is translation efficiency and \(t_{ave}\) is average mRNA life time. \(t_{ave} = \frac{\tau_{mRNA}}{ln(2)}\)

Transcription in bio-flip-flop

The transcription kinetics in the bio-flip-flop were modified to be repressed by repressors. These can be described by the following equations:

Simulation Results

We conducted our simulation using Tellurium[^Footnote3], a Python-based simulation platform. We first adjusted the parameters protein half life and mRNA half life (equivalently transcription and translation of repressor proteins) to adjust oscillation period as the one observed in the experiment. (此处链接到clock实验)



Then we incorporate the bio-flip-flop into the model, and we got the following simulation results:



In this simulation experiment, the flip-flop lost approximately 10% of its initial state after two trigger signal groups.

Overview

Background

In our design, after having designed the flip flop, the device can remember the information of its state, the next step is to transform the state into an actual function. To achieve this transformation, we first needed a “reader” to read out the current state. At this point the control unit comes into play. A control unit is a DNA sequence with recombinase sites whose expression is controlled by recom-binase and RDF by reversing or deleting a promoter and/or a terminator. To make the control unit reliable and predictable, we first need to be able to predict the behaviors of its “building blocks” (or “elements” in electrical engineering), from which we weave our engineer’s perspective into the biolog-ical system. However, we need to make some adaptations and adjustments to these “elements” to make them usable.