title: Logical-continuous modelling of post-translationally regulated bistability of curli fiber expression in Escherichia coli.
abstract: BACKGROUND
  Bacteria have developed a repertoire of signalling mechanisms that enable adaptive responses to fluctuating environmental conditions. The formation of biofilm, for example, allows persisting in times of external stresses, e.g. induced by antibiotics or a lack of nutrients. Adhesive curli fibers, the major extracellular matrix components in Escherichia coli biofilms, exhibit heterogeneous expression in isogenic cells exposed to identical external conditions. The dynamical mechanisms underlying this heterogeneity remain poorly understood. In this work, we elucidate the potential role of post-translational bistability as a source for this heterogeneity.
  
  
  RESULTS
  We introduce a structured modelling workflow combining logical network topology analysis with time-continuous deterministic and stochastic modelling. The aim is to evaluate the topological structure of the underlying signalling network and to identify and analyse model parameterisations that satisfy observations from a set of genetic knockout experiments. Our work supports the hypothesis that the phenotypic heterogeneity of curli expression in biofilm cells is induced by bistable regulation at the post-translational level. Stochastic modelling suggests diverse noise-induced switching behaviours between the stable states, depending on the expression levels of the c-di-GMP-producing (diguanylate cyclases, DGCs) and -degrading (phosphodiesterases, PDEs) enzymes and reveals the quantitative difference in stable c-di-GMP levels between distinct phenotypes. The most dominant type of behaviour is characterised by a fast switching from curli-off to curli-on with a slow switching in the reverse direction and the second most dominant type is a long-term differentiation into curli-on or curli-off cells. This behaviour may implicate an intrinsic feature of the system allowing for a fast adaptive response (curli-on) versus a slow transition to the curli-off state, in line with experimental observations.
  
  
  CONCLUSIONS
  The combination of logical and continuous modelling enables a thorough analysis of different determinants of bistable regulation, i.e. network topology and biochemical kinetics, and allows for an incorporation of experimental data from heterogeneous sources. Our approach yields a mechanistic explanation for the phenotypic heterogeneity of curli fiber expression. Furthermore, the presented work provides a detailed insight into the interactions between the multiple DGC- and PDE-type enzymes and the role of c-di-GMP in dynamical regulation of cellular decisions.
authors.affiliation: Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, Berlin, 14195, Germany. kaveh.yousef@fu-berlin.de.
authors.forename: Kaveh Pouran
authors.initials: KP
authors.lastname: Yousef
authors.affiliation: Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, Berlin, 14195, Germany. adam.streck@gmail.com.
authors.forename: Adam
authors.initials: A
authors.lastname: Streck
authors.affiliation: Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, Berlin, 14195, Germany. Christof.Schuette@fu-berlin.de.
authors.forename: Christof
authors.initials: C
authors.lastname: Schütte
authors.affiliation: Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, Berlin, 14195, Germany. siebert@mi.fu-berlin.de.
authors.forename: Heike
authors.initials: H
authors.lastname: Siebert
authors.affiliation: Faculty of Biology/Microbiology, Humboldt Universität zu Berlin, Chausseestraße 117, Berlin, 10115, Germany. Regine.hengge@hu-berlin.de.
authors.forename: Regine
authors.initials: R
authors.lastname: Hengge
authors.affiliation: Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, Berlin, 14195, Germany. vkleist@zedat.fu-berlin.de.
authors.forename: Max
authors.initials: M
authors.lastname: von Kleist
mesh_terms: D018441:Biofilms; D006152:Cyclic GMP / Q000031:analogs & derivatives / Q000378:metabolism; D004926:Escherichia coli / Q000166:cytology / Q000201:enzymology / Q000235:genetics* / Q000502:physiology*; D029968:Escherichia coli Proteins / Q000235:genetics / Q000378:metabolism; D005109:Extracellular Matrix / Q000378:metabolism; D015964:Gene Expression Regulation, Bacterial; D055786:Gene Knockout Techniques; D008957:Models, Genetic; D010641:Phenotype; D010727:Phosphoric Diester Hydrolases / Q000378:metabolism; D019761:Phosphorus-Oxygen Lyases / Q000378:metabolism; D014176:Protein Biosynthesis; D015398:Signal Transduction; D013269:Stochastic Processes
chemical_list: D029968:Escherichia coli Proteins; C062025:bis(3',5')-cyclic diguanylic acid; D010727:Phosphoric Diester Hydrolases; D019761:Phosphorus-Oxygen Lyases; C060720:diguanylate cyclase; D006152:Cyclic GMP