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BMC Bioinformatics
2022 Nov 24;231:503. doi: 10.1186/s12859-022-05055-5.
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Reconstructing gene regulatory networks of biological function using differential equations of multilayer perceptrons.
Mao G
,
Zeng R
,
Peng J
,
Zuo K
,
Pang Z
,
Liu J
.
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BACKGROUND: Building biological networks with a certain function is a challenge in systems biology. For the functionality of small (less than ten nodes) biological networks, most methods are implemented by exhausting all possible network topological spaces. This exhaustive approach is difficult to scale to large-scale biological networks. And regulatory relationships are complex and often nonlinear or non-monotonic, which makes inference using linear models challenging.
RESULTS: In this paper, we propose a multi-layer perceptron-based differential equation method, which operates by training a fully connected neural network (NN) to simulate the transcription rate of genes in traditional differential equations. We verify whether the regulatory network constructed by the NN method can continue to achieve the expected biological function by verifying the degree of overlap between the regulatory network discovered by NN and the regulatory network constructed by the Hill function. And we validate our approach by adapting to noise signals, regulator knockout, and constructing large-scale gene regulatory networks using link-knockout techniques. We apply a real dataset (the mesoderm inducer Xenopus Brachyury expression) to construct the core topology of the gene regulatory network and find that Xbra is only strongly expressed at moderate levels of activin signaling.
CONCLUSION: We have demonstrated from the results that this method has the ability to identify the underlying network topology and functional mechanisms, and can also be applied to larger and more complex gene network topologies.
Fig. 1
Fully linked neural network. a Schematic diagram of the fully connected neural network training synthetic term f. b Three genes are used as an example to illustrate. The synthetic term π2
(π3
) of π2
(π3
) is evaluated by a fully connected network. π2
and π3
(wheat and light blue) can depend on all three variables: π3
, π2
and the input signal π1
Fig. 2
Time evolution process under noisy conditions. (1) Under the stimulus after adding Gaussian white noise to the input signal (the red line of Input), without any constraints on g2, the time evolution curves g3 and g2 obtained after training the NN, and the expression level of g3 (blue line) is the same as The target time progress value (targetβs blue dotted line) basically matches. (2) Cross-section information obtained by training a NN under noisy conditions. Three panels show the dependence of π3
, π2
on I, π3
or π2
with the other two variables fixed. (3) The regulatory network obtained from (2)
Fig. 3
Simulate regulator knockout. (1) The perturbed f function can be iterated to simulate the effect of mutants in which specific regulatory chains are deleted. For example, deletion of π3
βs modulating effect on π3
leads to an increase in π3
(from darker to brighter solid green lines), indicating self-inhibition (shown in the third panel). The difference in π2
levels is not important here (dotted line). A similar argument applies to the other three panel. (2) Describes the sensitivity of network sequence and adapt to the error. Pane shows the knockout technology through links, step 1 to 4 of the evolution process of the network topology. The minimum incoherent feed forward motif appears naturally (topology #4), before the network has too few links to adapt
Fig. 4
The AUROC and AUPR of GENIE3, BiXGBoost, SIGNET, GNIPLP, PoLoBag and our methods on DREAM4 InSilico_Size100 five networks
Fig. 5
E. coli network including 1484 genes. Each bar represents the performance of one method in which the abscissas are the corresponding AUROC (right) and AUPR (left) values
Fig. 6
the activin/gsc/Xbra system. The Activin gene was activated by the input signal of morphogenetic gradient (Bcd), so it began to imitate its gradient mode. The Activin gene activated Xbra gene and opened the positive feedback of Xbra gene at a certain threshold. The Activin gene activates the Goosecold gene, and when the concentration of the two genes accumulates high enough, it forces the Xbra gene down. However, the concentration is highest only on the left side, when the concentration of Goosecold gene is low and its inhibitory effect is low, so that Xbra gene reaches a stable state
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