Team:HIT-Harbin/project/model

    Staphylococcus aureus AgrA, the transcriptional component of a quorum sensing system and global regulator of virulence that upregulates secreted virulence factors and down-regulates cell wall-associated proteins, can bind in both the P2 and P3 promoter regions of the agr locus.

    The structure of AgrA, described by online software PDB (Protein Data Bank), has ten β strands arranged into three antiparallel β sheets and a small α helix. The sheets are arranged roughly parallel to each other in an elongated β-β-β sandwich. A hydrophobic five-stranded β sheet (sheet 2: β3-β7) is at the center of the domain with two smaller amphipathic β sheets (sheet 1: β1-β2 and sheet 3: β8-β10) positioned on either side.

    AgrC belongs to the histidine protein kinase (HPK) family and in particular to the HPK10 subfamily of QS peptide HPKs, which are predicted to consist of six or seven N-terminal transmembrane segments and a C-terminal cytoplasmic kinase domain.

    The 3D structures of HPK10 kinases have not been determined, but topology modeling using different prediction methods has indicated that AgrC has either five or six transmembrane segments. We have tried many different tools for modeling the structure of AgrC.

    Fig.2 shows the predicted topology of AgrC using the MEMSAT3 program, which indicates six transmembrane helices (18-24 amino acid sequence domains), three extracellular loops, with high probability of N-terminal in the cytoplasmic by TMHMM program.

The Mathematical Model

    The detecting system can sense the existence of S.aureus by responding to the AIPs secreted only from S.aureus, accelerating the production of Lux I, which releases signal protein AHL into the environment (Fig. 3). We have constructed a set of ordinary differential equations to mathematically analyze this novel genetic circuit. Considering that the system is quite complicated, we make several reasonable assumptions to simplify it.

(1) In order to simulate the detecting part separately, we neglect the mechanism of AIPs production by S.aureus, watching the AIPs dynamic variation directly.

(2) The population consists of a number (n) of cells with a cytoplasmic volume (v), and is located in a medium with activating AIPs concentration of P, neglecting inhibiting AIPs.

(3) All reactions are modeled by mass action principles, except transcription which obeys saturation kinetics, and all variables are explained in Table 1.

(4) There is no delay in synthesis of either substance, subjecting to degradation all the time.

    We set up 5 ODEs (ordinary differential equations) in our model to describe the detecting circuit, the interaction between AIP and AgrC, the AgrA phosphorylation process, the Lux I synthesis in response to phosphorylated AgrA binding to the promoter. The parameters are defined when necessary and all described in Table 2.

    P is a special variable. In this model, we cannot predict the AIP’s variation, for the reason of the killing system having a negative effect of S.aureus population, which determines the concentration of AIP directly. The following figure shows all the substances levels in response to the concentration of AIP Fig. 4. It can be concluded that the phosphorylated AgrA (Api) and unphosphorylated AgrA would be at stable levels after a certain concentration of AIP. Besides, Lux I is on the increase via adding AIP in the whole environment, which is identical to the next part.

    In this section, we analyze the substances level with time passing, by control AIP be at a high level (P=0.8). As shown in Fig. 5, Lux I would stay at a stable level when AIP be controlled as a constant value, which is the most important output of this model. So we can make bold prediction that the whole system would be at stable state, including detecting and killing parts.

    The variation of unphosphorylated AgrA (A) shown in the figure is corresponding to biological mechanism (the green line). Until the complex between AgrC and AIP (Ccp) reaches threshold value, level of unphosphorylated AgrA would not stop increase at top speed.

    As far as possible, parameter values are based on present publications on the agr system and on biological plausibility. The degradation rates for all components were equally set.

    In summary, the protein structure prediction model of AgrA and topology analysis of membrane protein AgrC are conforming to the expected function, which also need further validation in the lab. The mathematical model of this system is part of a complete gene circuit. But under the reasonable assumption, we conclude some valuable information from the output of ODEs, of which the most important is all the substances would stay at a stable level when AIP be controlled as a constant value.

Reference

[1] Erik G., Patric N., Stefan K., Stanffan A., Characterizing the Dynamics of the Quorum-Sensing System in Staphylococcus aureus. J Mol Microbiol Biotechnol 2004; 8: 232-242.

[2] Sidote D.J., Barbieri C.M., Wu T., Stock A.M., Structure of the Staphylococcus aureus AgrA LytTR Domain Bound to DNA Reveals a Beta Fold with a Novel Mode of Binding. Structure 2008; 16: 727-735.

[3] Rasmus O.J., Klaus W., Simon R.C., Weng C.C., Paul W., Differential Recognition of Staphylococcus aureus Quorum-Sensing Signals Depends on Both Extracellular Loops 1 and 2 of the Transmembrane Sensor AgrC. J. Mol. Biol. 2008; 381: 300– 309.