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Team:Tsinghua-A/Model
From 2013.igem.org
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Overview
The expression of interacting genes depends on the structure of gene regulatory networks (GRN). In order to figure out optimal biological networks that can particularly function reliably when faced with fluctuation of DNA template amount (copy number), it is important to do some simulations in advance to narrow the screening scope. Therefore, it would be easier for us to search for adaptive and robust networks in wet lab and theoretically discuss certain functional regulatory motifs that are significant in showing adaptation. In our project, we abstractly analyzed gene regulatory network topologies and computed all possible three-node network structures by enumeration. We modeled, synthesized, tested and made comparisons, and finally screened 3 optimal network structures out of 19683 network structures, which show great adaptation to copy number. In order to verify the correctness of our screening process, we introduced an optimal testing case and simulated to check the results. Based on our screening results, we analyzed and concluded 9 core motifs that may be essential to adaptation. We respectively simulated these motifs and tried to explain their characters via mathematical proof. Finally we figured out a general rule of artificially constructing an adaptive network by combining core motifs.
Construction of Networks And Description Mathematical Description -- ODE Equations
We based on the Michealis-Menten Equations to describe the kinetics of gene regulatory networks, and simulated some basic modules of regulatory edges such as Mutual-activation, Mutual-inhibition, Activation with negative feedback, Inhibition with positive feedback, Self-activation and Self-inhibition.
Picture: simulation result
Picture: 4 sketches representing 4 modules
Note1:
(1) Possible regulatory edges among three-node network topologies
(2) Illustrative examples of three-node network topologies
(3) D
(4)
The simulation result indicates that networks involving Mutual-activation and Self-activation are generally instable, which may lead to infinite increase of molecule number. On contrary, negative feedback is always favorable to stability, such as Activation with negative feedback (contains 1 edge as feedback) and Self-inhibition (contains 1 edge as feedback). Interestingly, although Mutual-inhibition contains 2 edges as negative feedback, it may results in strong self-activation and switch between two stable states.
In our project, we aimed at all three-node network structures which contain 4 nodes (1 input node, 2 regulatory nodes and 1 output node) and vast possible regulatory edges among them. So we combined these basic modules above to construct networks.
Picture: some sketch maps of network structures like bellows:
Note2:
(1) Possible regulatory edges among three-node network topologies
(2) Illustrative examples of three-node network topologies
The ODE Equations involve two 4*4 matrices to bring in the activating effect and inhibitive effect respectively, and a column vector for self-decomposition.
In our wet lab part, we constructed plasmids in ** (need particular cell type), so we made some adjustment in our design for a better realization in experiment:
We fixed two certain edges (Input inhibits A, A inhibits output) because in the***(need explanation from wet lab)
We chose relative parameters close to the actual experiments in our simulation, such as b and K .
Picture: some sketch map of network structures like bellows:
Note3:
(1) Possible regulatory edges among nodesthree-node network topologies
(2) Illustrative examples of three-node network topologies
Basic Function Analysis -- Massive Parallel Data Processing
The ideal network in our project must be sensitive to the input signal and be able to distinguish the low input and high input from each other. So we expected that the target structure should have a low-input-low-output and high-input-high-output character. Besides, it should avoid ambiguous interim region between low input and high input.
Picture: a curve added index descriptions like bellow:
Note4:
(1) The input-output curve of functional networks
We firstly raised two basic indexes, High-low Ratio and Interim Slope to evaluate the performance of all three-node network structures. To each structure, we scanned the value of input ranging from 1 to 1000 and recorded the corresponding output.
Graph: like bellow:
