Simulation of <i>E. coli</i> Gene Regulation including Overlapping Cell Cycles, Growth, Division, Time Delays and Noise

<div><p>Due to the complexity of biological systems, simulation of biological networks is necessary but sometimes complicated. The classic stochastic simulation algorithm (SSA) by Gillespie and its modified versions are widely used to simulate the stochastic dynamics of biochemical reaction systems. However, it has remained a challenge to implement accurate and efficient simulation algorithms for general reaction schemes in growing cells. Here, we present a modeling and simulation tool, called ‘<i>GeneCircuits</i>’, which is specifically developed to simulate gene-regulation in exponentially growing bacterial cells (such as <i>E. coli</i>) with overlapping cell cycles. Our tool integrates three specific features of these cells that are not generally included in SSA tools: 1) the time delay between the regulation and synthesis of proteins that is due to transcription and translation processes; 2) cell cycle-dependent periodic changes of gene dosage; and 3) variations in the propensities of chemical reactions that have time-dependent reaction rates as a consequence of volume expansion and cell division. We give three biologically relevant examples to illustrate the use of our simulation tool in quantitative studies of systems biology and synthetic biology.</p></div

The parameters used in the metabolic system.

<p>The parameters used in the metabolic system.</p

The fluctuation of the metabolite concentration due to the gene position of the enzyme on the chromosome.

<p>(A) The biological model with the balanced flux of metabolite M2. There are two enzymes, A and B, and three metabolites, M1, M2 and M3. M1 can be taken up from the surroundings. Enzyme A and enzyme B can catalyze the input flux and output flux of metabolite M2, respectively. In this figure, we use “i” and “t” to represent the starting point of chromosome replication and termination, respectively. (B) If two enzymes have the same gene position on the chromosome, the average rate of the input flux and output flux are equal. The fluctuation of M2 concentration is only due to the replication of the genes and bacterial volume growth. The insert illustrates the gene dosage. (C) The model of unbalanced flux of M2. There is a long distance between the gene positions of two enzymes on the chromosome. (D) The difference in the temporal expression of two enzymes caused the inequality of the average input and output flux and enhanced the fluctuation of M2 concentration. The insert shows the gene dosage of A (green curve) and B (red curve).</p

Bi-stable system in a double-negative feedback loop.

<p>(A) A schematic illustration of a double-negative feedback loop is shown. Protein A acts as a repressor of gene B, and protein B represses the expression of gene A. (B) For the parameters given in the model, the system is bi-stable. (C) Two lineage trees (left and right) describe the distribution dynamics for the expression of Genes A and B. The color bar represents the concentration of the protein, and each bar represents the profile of one protein of one bacterium during one cell cycle. For the unsynchronized initial states, the lineage trees of the expression of Gene A and B display inverse correlations.</p

Schematic diagram of the software architecture.

<p>(A) The tool contains three logical levels: the interface level, explanation level and calculation level. The interface level is an editor to build biological models and integrate necessary information and parameters. The explanation level is a complier to understand the user’s biological model and translate it into the mathematical model. The calculation level is a computational element to calculate the model and return the results. (B) The interface of building the model and setting parameters. With a user-friendly interface, the tool provides an instant visual bio-model building environment. For user convenience, <i>GeneCircuits</i> chose standard icons to present biological elements. For example, a gene icon is represented by a set of standard sub-symbols, including two regulatory domains (white square), one mRNA (hollow parallelogram) and one corresponding protein (solid red rounded quadrilateral). Users can define the various roles of each element in the system. Based on the Petri net representation, each reaction has a horizontal line, which is a representation of the reaction. By double-clicking this horizontal line, users can set up parameters of the reaction. (C) The user interface for setting parameters.</p

Simulation of a negative auto-regulation system with or without time delay.

<p>(A) When the simulation of the system without time delay is performed, the curves from the deterministic equations and the classic Gillespie method are smooth and approximately equal. The protein (monomer) copy number of a time series is generated from the deterministic equations (ODE, yellow curve), the classic Gillespie method (Gillespie, blue curve) and our stochastic algorithm (<i>GeneCircuits</i>, red curve). The curve of <i>GeneCircuits</i> is slightly higher than those of the two other simulations. (B) Oscillations in the protein concentration are induced at a longer time delay (1000 seconds).</p

Additional file 1: of PU.1 controls the expression of long noncoding RNA HOTAIRM1 during granulocytic differentiation

Figure S1. Arsenic trioxide had minimal effect on the expression levels of HOTAIRM1 and PU.1. Table S1: Primers for RT-qPCR. Table S2: Primers for ChIP-qPCR. (DOCX 35 kb

GSEA of the THP1r2<i>Mtb</i>-induced signature using transcriptomes from patients with other inflammatory or pathological conditions.

1<p><i>Staph</i>: <i>Staphylococcus aureus</i> infection, Liver-transplant: liver-transplant undergoing immunosuppressive therapy, Melanoma: metastatic melanoma, SLE: systemic lupus erythematosus, JIA: systemic juvenile idiopathic arthritis.</p>2,3<p>The same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0038367#pone-0038367-t001" target="_blank">Table 1</a>.</p

Experimental design for detecting host transcriptional responses to different <i>Mtb</i> W-Beijing strains.

<p>Genetic diversity of W-Beijing family strains, as revealed by SNPs-based genotyping (see our recent work <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0038367#pone.0038367-Mestre1" target="_blank">[16]</a> for details). In brief, 48 SNPs were characterized by sequencing 22 genes (being involved in DNA repair, replication, and recombination) in 58 W-Beijing isolates plus one non-W-Beijing isolate (Myc2). Each node represents one genotype (the same SNPs profile), with the node area proportional to the population size (the number of W-Beijing isolates in it was indicated on the left). Strains from the corresponding node used for the THP-1 infection in this study (e.g., R1.4 from Bmyc10) were indicated on the right. Lab strain H37Rv, which was also recruited for the THP-1 infection, was not shown here.</p

GSEA of the THP1r2<i>Mtb</i>-induced signature using transcriptome data from human tuberculosis patients.

1<p>Traning set: all the donors, which were defined as PTB, LTB or healthy, were recruited from London, UK. Test set: all the donors were from London UK. Validation set: all the donors were from Cape Town, South Africa. Test set_seperated: purified neutrophils, monocytes, CD4⁺ T cells, and CD8⁺ T cells from both PTB and healthy controls. Longitudinal study: PTB patients before drug treatment, 2 months after drug treatment, and 12 months after drug treatment.</p>2<p>Group-group contrasted and ranked by LIMMA-based method.</p>3<p>(+) NES for positive correlation, (−) NES for negative correlation.</p>4<p>Significance of correlation, an FDR of 0.05 or lower was accepted as statistically significant for NES (“Positive” or “Negative”), otherwise “Null”. See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0038367#pone.0038367.s007" target="_blank">Figures S7</a>,S8,S9 for plot graph of each group comparison. See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0038367#pone.0038367.s010" target="_blank">Figure S10</a> for CPP-SOM graph of expression data of each donor.</p