HUMAN PRACTICES
Model
In the first part of the experimental design, in order to avoid the simultaneous occurrence of a large number of enzymes with conflicting functions, we plan to adopt the dynamic regulation method and let thioesterase and hydroxylase be expressed in cells first. With the aim of achieving periodic alternating expression, in other words, the TesA gene, P450 gene, FadD gene, and WS gene can carry out periodic oscillations with opposite phases and robustness.
Such gene oscillators would involve a wealth of dynamic behavior[1]. This requires a series of models to provide predictions in order to satisfy the kinetic rate of the reaction mechanism, which is sufficient to disrupt the steady state and that the generation and consumption interaction reactions occur on appropriate time scales that allow the network to generate oscillations. We will establish the model of the gene oscillation through mathematical modeling to test the theory and envisage the component selection.
The ordinary differential model is utilized to establish the gene expression simulation prediction so as to assist the design of the gene oscillator. We performed simulations of related gene networks, including promoter selection, whole-gene pathway simulation, and metabolic pathway simulation[2]. It has played a certain reference role for us to select the appropriate components, and check whether our gene circuit theoretically conforms to the mathematical theoretical model.
Figure 1 Modeling ideas and model overview
In the third part of the experiment, we will face the problems such as cell culture and culture medium replacement. In the terms of the cell culture, changes in nutrient solution concentration cannot be ignored. We measure the nutrient solution weight by mass.
Cells cause nutrient fluid changes by absorbing nutrient growth and metabolism. Cells grow, and the absorption of nutrients causes a decrease in the cell culture medium[3]. At the same time, cells discharge waste to increase the quality of nutrient solution. With appropriate simplifying assumptions, you can get the relationship of nutrient solution quality and change, and thus the replacement of nutrient solution rate is reasonably chosen to grow the cells. Usually, it is more convenient to culture cells in days as time units, so the discrete-time model —— difference equation model is discussed here [4].
We hope to master the appropriate time for the replacement of culture medium so as to better culture cells.
Reviewing the articles, we found that there are many mathematical models which can predict the dynamics of gene networks, ranging from Boolean networks to large-scale discrete stochastic simulations. After careful deliberations, we chose the most common model type: coupled nonlinear ordinary differential equations (Odes)[5], which integrates a combination of Hill functions, Mie equations, and exponential decay to pattern the dynamics of gene products. But these models usually use the quasi-steady state assumption (QSSA) and ignore reactions occurring on fast time scales. Apart from that, these approximations do not include the inherent randomness associated with the finite number of molecular constituent reactions. Therefore, we utilized stochastic simulations to address the lack of randomness[6]. These types of models are usually Langevin-type stochastic [7] differential equations or discrete stochastic simulations, such as the Gillespie algorithm.
In the mathematical model of the project, we established the mathematical model of gene oscillator dynamics. These models usually involve the use of nonlinear dynamics, parameter tuning, and attempts to more accurately describe the theoretical basis of circuit dynamics. Ultimately, we hope that mathematical models of gene regulation will provide predictive tools for synthetic biology and tools for gene circuits needed in industry and biomedicine.
Before discussing how to model synthetic genetic oscillators, the most basic biochemical processes need to be patterned, such as gene expressions, protein formation, and how they are regulated intracellularly. The modeling begins with the most basic biochemical processes that regulate gene expression at the transcriptional level, the basic processes that occur during protein production, and the decay of proteolytic processes[8].
Based on what we want to analysis in the part of the third exipriment, the cell culture data concerned makes the following simplified assumptions[9]:
Building synthetic circuits begin with matching promoters to transcription factors, components of the transcriptional machinery. For a regulated promoter, the activity of a gene depends on the concentration of transcription factors available to activate or repress the gene and their binding probability. If the concentrations of DNA and TF are constant, then we can write the following set of chemical reactions.
Where P, Ou, and Ob are the concentrations of TF monomer, TF dimer, unbound operator, and bound operator, respectively, and the forward and reverse reaction rate constants are shown. The total concentration of DNA is constant so that Ou+ Ob =N. Solving for Ou gives us:
Vu is defined as the rate when the promoters are not bonded, Vb is defined as the rate after bonding, then the total rate of the reaction is:
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Figure 2 The transcriptional unit is abstracted as gene 1 and gene 2
The left panel shows the gene circuit we designed, and the right panel shows the two-gene oscillator abstracted from the model.
The upstream elements (GFP, pleD) are recognized as gene A, and the downstream C-DI-GMP, etc. as gene B in figure (1), constructing a set of negative feedback circuits consisting of two genes in order to conceive a gene oscillator. Since the production of each protein in the loop is not depend linearly on the other protein, the ODE should be modeled as follows.
First, Matlab's SimBiology toolbox is used to verify the basic circuit:
Figure 3 The surface of the Matlab's SimBiology toolbox
We used ODE45, the Runge-Kutta algorithm, to solve the established ordinary differential equations.
Figure 4 The algorithm we solve the problem is ODE45
Finally, it appears that the protein transcription and translation curve conform to the theory. The accuracy of the model basis is proved.
We used Matlab to solve the gene oscillator model, finding that the parameters would affect the oscillation period and whether the oscillation decays. In order to make the oscillations periodic and robust, a proper choice of the parameters (and corresponding components) is important.
As shown in the figure, when the transcription rate or translation rate is increased, the oscillator oscillates steadily and periodically.
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Figure 5 The results shows the oscillation and the rate
The solution results not only verify that our gene circuit theory meets up with a mathematical theoretical model with high accuracy. Meanwhile, It also helps us to select the components that stabilize the oscillation range and prove it through later experiments.
The modeling results of cell growth fitting, nutrient solution consumption quality under normal growth, and the addition of accelerated cell growth factor are as follows:
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Figure 6 Results of cell culture medium concentration changes