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Our proposed method is entirely derived through the high-order system of differential equations. Lee et al. derived multiple states of the molecular network describing homeostasis via a set of differential equations [258]. Gao and Miele developed an underlying stochastic differential equation [223] for modeling transcriptional dynamics in a multi-cell population. Chipman et al. derived simulation models to estimate candidate GRNs in sample-and-hold switch data [136]. It includes two equations consisting of a transcription law and a translation law. The two equations are weighted, with one element in the equation chosen at random, which determines the weight to be equal to one or the other of the governing exponents. We focused on a single equation, which could be associated with a random sequence of activations with this random selection of equal weights. We applied this weighting for the RNA expression states in the Gillespie algorithm.

The biological process of gene expression is influenced by various factors such as the binding of transcription factors to DNA, methylation of DNA, chromatin remodeling, or assembly of protein complexes that together influence ribonucleic acid expression. Likewise, the biological process of protein synthesis is also influenced by various factors affecting different steps in the protein translation process, including the selection of optimal start codons, the translation rates, and the degradation of messenger ribonucleic acids (mRNAs). The change in protein concentration affects the biological processes of protein synthesis, turnover, and degradation. When simulating the concentration of proteins, we considered these factors to be minimal with modifications to the simulation time step. It therefore reflects the connections within a process of the biological network, although this can be improved. Currently, we simulate the protein expression process but have as yet employed few components (protein, translation, transcription); however, in the near future, the connection to molecular networks via the translation and transcription processes should become important. d2c66b5586

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