Figure 1.
Phase variation of type 1 fimbriae expression in E. coli.
Type 1 fimbriae phase variation is controlled by the invertible DNA element, fimS, which contains the promoter for the genes encoding structural fimbriae subunits (including fimA and fimH) and is flanked by two inverted repeat sequences: IRL and IRR. (In this diagram, IRL is the inverted version of IRR.) When the switch is in the ON position, transcription of structural fim genes can be initiated because the promoter is in the appropriate orientation. However, when the switch is inverted into the OFF position, the promoter points in the opposite direction and so no longer supports the expression of fimbriae components—leading to their rapid degradation. The ON-to-OFF inversion of the switch is mediated by recombinases FimE and FimB, while the OFF-to-ON events are mediated by FimB.
Table 1.
Abstraction methods used by reb2sac in the analysis of the fim circuit switch model.
Figure 2.
Type 1 fimbriae genetic regulatory network—the fim switch circuit.
Structural fimbriae subunits are encoded by fimA and other downstream genes, which are transcribed when the fim switch is in the ON position (as shown here – also see Figure 1). Recombinases and
bind to
/
and invert the switch with different rates (
is strongly biased in the ON-to-OFF direction, while
is close to fair). A small protein,
, acts in a temperature-dependent manner and represses the expression of the two recombinases.
stimulates and inhibits switching based on its occupancy of three
sites, while its expression is also repressed by
.
is required for any observable phase variation as it plays a structural role during switching through its ability to produce sharp bends in the DNA.
Figure 3.
Detailed model subnetwork of FimB and FimE regulation.
Here, is the promoter for fimB and
is the promoter for fimE . Each
represents a transcriptionally active configuration, while
corresponds to the transcriptionally silent complex.
Figure 4.
Detailed fim switch configuration model.
Here, abstracts the free form of the regulatory protein binding sites in fimS. Complex species
through
represent the various states of the fimS DNA element given in Table 6. An abstracted species, switch, captures the switching events.
Table 2.
Comparison of ON-to-OFF switching probability estimates in minimal medium.
Table 3.
Simulation time comparison between detailed and abstracted models.
Figure 5.
Graph-based model representation of FimB and FimE regulation subnetwork.
A reaction connected to a species with a double arrow designates a reversible reaction. Species connected to a reaction with letters, r, p, or m corresponds to a reactant, a product, or a modifier for that reaction – respectively – as defined in the SBML standard [156]. A mathematical expression inside a reaction node provides the kinetic reaction rate function for that reaction. (A) Detailed model; and (B) Abstracted model.
Figure 6.
Reaction scheme for fim switch ON-to-OFF inversion through state 6.
In this state, 1 molecule of , 1 molecule of
, and 3 molecules of
occupy available binding sites in the switch DNA region—leading to the corresponding switching event. (A) Detailed model; and (B) Abstracted model. (See Text S1 for further detail.)
Figure 7.
Regulation of the ON-to-OFF fim circuit switching probability via temperature control.
The detailed model was used to evaluate ON-to-OFF switching probabilities over one cell generation at the three temperature points (,
, and
), where experimental measurements had been made previously [30]. Calculations were repeated using the abstracted model at these and seven additional temperature points (
,
,
,
,
,
, and
) – all in minimal medium. Here, (A) Wild-type (
and
) ON-to-OFF switching probability per cell per generation is plotted versus temperature; and (B) Same, but for
-only mediated switching, where further points (
,
,
,
,
,
,
, and
) were added to increase resolution around the physiological temperature peak. (Error bars in (A) and (B) indicate 95% confidence interval.)
Figure 8.
Role of FimB in the temperature control mechanism of the total ON-to-OFF fim switching probability.
The total ON-to-OFF switching probability of two in silico generated mutants: one—overproducing (at twice the wild-type level), and the other—a
knockout (no ON-to-OFF
activity). These are compared with the wild-type system behavior using their respective abstracted models at the same 10 temperature points (see Figure 7A). Here, (A) The total ON-to-OFF switching probability per cell per generation in minimal medium is plotted versus temperature. For numerical comparison, each case also includes three points computed directly via the detailed model. (Error bars indicate 95% confidence interval); and (B) The ratio of the total ON-to-OFF switching probability in each of the mutants to the total ON-to-OFF switching probability of the wild-type is plotted versus temperature.
Table 4.
Temperature-dependent rate constants and parameters in the FimB and FimE regulation module.
Table 5.
Temperature-independent rate constants and parameters in the FimB and FimE regulation module.
Table 6.
Configuration of fimS DNA element for the ON-to-OFF switching.
Table 7.
Concentration of Lrp at various temperatures.
Figure 9.
High-level workflow of reb2sac automated model abstraction engine.
The engine automatically generates an abstracted model by taking as inputs a detailed interaction-based model and, optionally, various targets and tolerances that can help set and adjust the level of abstraction. A list of available abstraction methods (which include graph-theoretical interaction-network analysis tools, dynamic reaction-level approximations, etc.) is sequentially checked and, if appropriate, the method is applied to the original detailed model—transforming it accordingly. This procedure is then repeated using the next method until the list of available methods is exhausted. (See Refs. [63],[64] for further description and explanation.)