Dynamical Localization of DivL and PleC in the Asymmetric Division Cycle of Caulobacter crescentus: A Theoretical Investigation of Alternative Models

The interplay of spatial organization and biochemistry in building blocks of cellular signalling pathways

Biochemical pathways and networks are central to cellular information processing. While a broad range of studies have dissected multiple aspects of information processing in biochemical pathways, the effect of spatial organization remains much less understood. It is clear that space is central to intracellular organization, plays important roles in cellular information processing and has been exploited in evolution; additionally, it is being increasingly exploited in synthetic biology through the development of artificial compartments, in a variety of ways. In this paper, we dissect different aspects of the interplay between spatial organization and biochemical pathways, by focusing on basic building blocks of these pathways: covalent modification cycles and two-component systems, with enzymes which may be monofunctional or bifunctional. Our analysis of spatial organization is performed by examining a range of 'spatial designs': patterns of localization or non-localization of enzymes/substrates, theoretically and computationally. Using these well-characterized in silico systems, we analyse the following. (i) The effect of different types of spatial organization on the overall kinetics of modification, and the role of distinct modification mechanisms therein. (ii) How different information processing characteristics seen experimentally and studied from the viewpoint of kinetics are perturbed, or generated. (iii) How the activity of enzymes (bifunctional enzymes in particular) may be spatially manipulated, and the relationship between localization and activity. (iv) How transitions in spatial organization (encountered either through evolution or through the lifetime of cells, as seen in multiple model organisms) impacts the kinetic module (and pathway) behaviour, and how transitions in chemistry may be impacted by prior spatial organization. The basic insights which emerge are central to understanding the role of spatial organization in biochemical pathways in both bacteria and eukaryotes, and are of direct relevance to engineering spatial organization of pathways in bottom-up synthetic biology in cellular and cell-free systems.

Reciprocal control of motility and biofilm formation by the PdhS2 two-component sensor kinase of Agrobacterium tumefaciens

A core regulatory pathway that directs developmental transitions and cellular asymmetries in Agrobacterium tumefaciens involves two overlapping, integrated phosphorelays. One of these phosphorelays putatively includes four histidine sensor kinase homologues, DivJ, PleC, PdhS1 and PdhS2, and two response regulators, DivK and PleD. In several different alphaproteobacteria, this pathway influences a conserved downstream phosphorelay that ultimately controls the phosphorylation state of the CtrA master response regulator. The PdhS2 sensor kinase reciprocally regulates biofilm formation and swimming motility. In the current study, the mechanisms by which the A. tumefaciens sensor kinase PdhS2 directs this regulation are delineated. PdhS2 lacking a key residue implicated in phosphatase activity is markedly deficient in proper control of attachment and motility phenotypes, whereas a kinase-deficient PdhS2 mutant is only modestly affected. A genetic interaction between DivK and PdhS2 is revealed, unmasking one of several connections between PdhS2-dependent phenotypes and transcriptional control by CtrA. Epistasis experiments suggest that PdhS2 may function independently of the CckA sensor kinase, the cognate sensor kinase for CtrA, which is inhibited by DivK. Global expression analysis of the pdhS2 mutant reveals a restricted regulon, most likely functioning through CtrA to separately control motility and regulate the levels of the intracellular signal cyclic diguanylate monophosphate (cdGMP), thereby affecting the production of adhesive polysaccharides and attachment. We hypothesize that in A. tumefaciens the CtrA regulatory circuit has expanded to include additional inputs through the addition of PdhS-type sensor kinases, likely fine-tuning the response of this organism to the soil microenvironment.

Stochastic modeling and simulation of reaction-diffusion system with Hill function dynamics

Background

Stochastic simulation of reaction-diffusion systems presents great challenges for spatiotemporal biological modeling and simulation. One widely used framework for stochastic simulation of reaction-diffusion systems is reaction diffusion master equation (RDME). Previous studies have discovered that for the RDME, when discretization size approaches zero, reaction time for bimolecular reactions in high dimensional domains tends to infinity.

Results

In this paper, we demonstrate that in the 1D domain, highly nonlinear reaction dynamics given by Hill function may also have dramatic change when discretization size is smaller than a critical value. Moreover, we discuss methods to avoid this problem: smoothing over space, fixed length smoothing over space and a hybrid method.

Conclusion

Our analysis reveals that the switch-like Hill dynamics reduces to a linear function of discretization size when the discretization size is small enough. The three proposed methods could correctly (under certain precision) simulate Hill function dynamics in the microscopic RDME system.

Spatiotemporal Models of the Asymmetric Division Cycle of Caulobacter crescentus

The spatial localization of proteins within the cytoplasm of bacteria is an underappreciated but critical aspect of cell cycle regulation for many prokaryotes. In Caulobacter crescentus-a model organism for the study of asymmetric cell reproduction in prokaryotes-heterogeneous localization of proteins has been identified as the underlying cause of asymmetry in cell morphology, DNA replication, and cell division. However, significant questions remain. Firstly, the mechanisms by which proteins localize in the organelle-free prokaryotic cytoplasm remain obscure. Furthermore, how variations in the spatial and temporal dynamics of cell fate determinants regulate signaling pathways and orchestrate the complex programs of asymmetric cell division and differentiation are subjects of ongoing research. In this chapter, we review current efforts in investigating these two questions. We describe how mathematical models of spatiotemporal protein dynamics are being used to generate and test competing hypotheses and provide complementary insight about the control mechanisms that regulate asymmetry in protein localization and cell division.

Core-oscillator model of Caulobacter crescentus

The gram-negative bacterium Caulobacter crescentus is a powerful model organism for studies of bacterial cell cycle regulation. Although the major regulators and their connections in Caulobacter have been identified, it still is a challenge to properly understand the dynamics of its circuitry which accounts for both cell cycle progression and arrest. We show that the key decision module in Caulobacter is built from a limit cycle oscillator which controls the DNA replication program. The effect of an induced cell cycle arrest is demonstrated to be a key feature to classify the underlying dynamics.

A stochastic spatiotemporal model of a response-regulator network in the Caulobacter crescentus cell cycle

The asymmetric cell division cycle in Caulobacter crescentus is controlled by an elaborate molecular mechanism governing the production, activation and spatial localization of a host of interacting proteins. In previous work, we proposed a deterministic mathematical model for the spatiotemporal dynamics of six major regulatory proteins. In this paper, we study a stochastic version of the model, which takes into account molecular fluctuations of these regulatory proteins in space and time during early stages of the cell cycle of wild-type Caulobacter cells. We test the stochastic model with regard to experimental observations of increased variability of cycle time in cells depleted of the divJ gene product. The deterministic model predicts that overexpression of the divK gene blocks cell cycle progression in the stalked stage; however, stochastic simulations suggest that a small fraction of the mutants cells do complete the cell cycle normally.

Bistability of a coupled Aurora B kinase-phosphatase system in cell division

Aurora B kinase, a key regulator of cell division, localizes to specific cellular locations, but the regulatory mechanisms responsible for phosphorylation of substrates located remotely from kinase enrichment sites are unclear. Here, we provide evidence that this activity at a distance depends on both sites of high kinase concentration and the bistability of a coupled kinase-phosphatase system. We reconstitute this bistable behavior and hysteresis using purified components to reveal co-existence of distinct high and low Aurora B activity states, sustained by a two-component kinase autoactivation mechanism. Furthermore, we demonstrate these non-linear regimes in live cells using a FRET-based phosphorylation sensor, and provide a mechanistic theoretical model for spatial regulation of Aurora B phosphorylation. We propose that bistability of an Aurora B-phosphatase system underlies formation of spatial phosphorylation patterns, which are generated and spread from sites of kinase autoactivation, thereby regulating cell division.