Potential role of a bistable histidine kinase switch in the asymmetric division cycle of Caulobacter crescentus

Computational modeling of unphosphorylated CtrA:Cori binding in the Caulobacter cell cycle

In the alphaproteobacterium, Caulobacter crescentus, phosphorylated CtrA (CtrA∼P), a master regulatory protein, binds directly to the chromosome origin (Cori) to inhibit DNA replication. Using a mathematical model of CtrA binding at Cori site [d], we provide computational evidence that CtrA_U can displace CtrA∼P from Cori at the G1-S transition. Investigation of this interaction within a detailed model of the C. crescentus cell cycle suggests that CckA phosphatase may clear Cori of CtrA∼P by altering the [CtrA_U]/[CtrA∼P] ratio rather than by completely depleting CtrA∼P. Model analysis reveals that the mechanism allows for a speedier transition into S phase, stabilizes the timing of chromosome replication under fluctuating rates of CtrA proteolysis, and may contribute to the viability of numerous mutant strains. Overall, these results suggest that CtrA_U enhances the robustness of chromosome replication. More generally, our proposed regulation of CtrA:Cori dynamics may represent a novel motif for molecular signaling in cell physiology.

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.

Noise control for molecular computing

Synthetic biology is a growing interdisciplinary field, with far-reaching applications, which aims to design biochemical systems that behave in a desired manner. With the advancement in nucleic-acid-based technology in general, and strand-displacement DNA computing in particular, a large class of abstract biochemical networks may be physically realized using nucleic acids. Methods for systematic design of the abstract systems with prescribed behaviours have been predominantly developed at the (less-detailed) deterministic level. However, stochastic effects, neglected at the deterministic level, are increasingly found to play an important role in biochemistry. In such circumstances, methods for controlling the intrinsic noise in the system are necessary for a successful network design at the (more-detailed) stochastic level. To bridge the gap, the noise-control algorithm for designing biochemical networks is developed in this paper. The algorithm structurally modifies any given reaction network under mass-action kinetics, in such a way that (i) controllable state-dependent noise is introduced into the stochastic dynamics, while (ii) the deterministic dynamics are preserved. The capabilities of the algorithm are demonstrated on a production-decay reaction system, and on an exotic system displaying bistability. For the production-decay system, it is shown that the algorithm may be used to redesign the network to achieve noise-induced multistability. For the exotic system, the algorithm is used to redesign the network to control the stochastic switching, and achieve noise-induced oscillations.

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.

Modeling Asymmetric Cell Division in Caulobacter crescentus Using a Boolean Logic Approach

Caulobacter crescentus is a model organism for the study of asymmetric division and cell type differentiation, as its cell division cycle generates a pair of daughter cells that differ from one another in their morphology and behavior. One of these cells (called stalked) develops a structure that allows it to attach to solid surfaces and is the only one capable of dividing, while the other (called swarmer) develops a flagellum that allows it to move in liquid media and divides only after differentiating into a stalked cell type. Although many genes, proteins, and other molecules involved in the asymmetric division exhibited by C. crescentus have been discovered and characterized for several decades, it remains as a challenging task to understand how cell properties arise from the high number of interactions between these molecular components. This chapter describes a modeling approach based on the Boolean logic framework that provides a means for the integration of knowledge and study of the emergence of asymmetric division. The text illustrates how the simulation of simple logic models gives valuable insight into the dynamic behavior of the regulatory and signaling networks driving the emergence of the phenotypes exhibited by C. crescentus. These models provide useful tools for the characterization and analysis of other complex biological networks.

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.

A cell cycle kinase with tandem sensory PAS domains integrates cell fate cues

All cells must integrate sensory information to coordinate developmental events in space and time. The bacterium Caulobacter crescentus uses two-component phospho-signalling to regulate spatially distinct cell cycle events through the master regulator CtrA. Here, we report that CckA, the histidine kinase upstream of CtrA, employs a tandem-PAS domain sensor to integrate two distinct spatiotemporal signals. Using CckA reconstituted on liposomes, we show that one PAS domain modulates kinase activity in a CckA density-dependent manner, mimicking the stimulation of CckA kinase activity that occurs on its transition from diffuse to densely packed at the cell poles. The second PAS domain interacts with the asymmetrically partitioned second messenger cyclic-di-GMP, inhibiting kinase activity while stimulating phosphatase activity, consistent with the selective inactivation of CtrA in the incipient stalked cell compartment. The integration of these spatially and temporally regulated signalling events within a single signalling receptor enables robust orchestration of cell-type-specific gene regulation.

The membrane-bound kinase CckA controls the activity of the Caulobacter crescentus master regulator CtrA, which in turn coordinates asymmetric cell division. Here, the authors show that CckA contains two sensory domains that have distinct sensitivities to fluctuations in cyclic-di-GMP concentration and subcellular niche.

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

Cell-fate asymmetry in the predivisional cell of Caulobacter crescentus requires that the regulatory protein DivL localizes to the new pole of the cell where it up-regulates CckA kinase, resulting in a gradient of CtrA~P across the cell. In the preceding stage of the cell cycle (the "stalked" cell), DivL is localized uniformly along the cell membrane and maintained in an inactive form by DivK~P. It is unclear how DivL overcomes inhibition by DivK~P in the predivisional cell simply by changing its location to the new pole. It has been suggested that co-localization of DivL with PleC phosphatase at the new pole is essential to DivL's activity there. However, there are contrasting views on whether the bifunctional enzyme, PleC, acts as a kinase or phosphatase at the new pole. To explore these ambiguities, we formulated a mathematical model of the spatiotemporal distributions of DivL, PleC and associated proteins (DivJ, DivK, CckA, and CtrA) during the asymmetric division cycle of a Caulobacter cell. By varying localization profiles of DivL and PleC in our model, we show how the physiologically observed spatial distributions of these proteins are essential for the transition from a stalked cell to a predivisional cell. Our simulations suggest that PleC is a kinase in predivisional cells, and that, by sequestering DivK~P, the kinase form of PleC enables DivL to be reactivated at the new pole. Hence, co-localization of PleC kinase and DivL is essential to establishing cellular asymmetry. Our simulations reproduce the experimentally observed spatial distribution and phosphorylation status of CtrA in wild-type and mutant cells. Based on the model, we explore novel combinations of mutant alleles, making predictions that can be tested experimentally.

Dynamical modeling of the cell cycle and cell fate emergence in Caulobacter crescentus

The division of Caulobacter crescentus, a model organism for studying cell cycle and differentiation in bacteria, generates two cell types: swarmer and stalked. To complete its cycle, C. crescentus must first differentiate from the swarmer to the stalked phenotype. An important regulator involved in this process is CtrA, which operates in a gene regulatory network and coordinates many of the interactions associated to the generation of cellular asymmetry. Gaining insight into how such a differentiation phenomenon arises and how network components interact to bring about cellular behavior and function demands mathematical models and simulations. In this work, we present a dynamical model based on a generalization of the Boolean abstraction of gene expression for a minimal network controlling the cell cycle and asymmetric cell division in C. crescentus. This network was constructed from data obtained from an exhaustive search in the literature. The results of the simulations based on our model show a cyclic attractor whose configurations can be made to correspond with the current knowledge of the activity of the regulators participating in the gene network during the cell cycle. Additionally, we found two point attractors that can be interpreted in terms of the network configurations directing the two cell types. The entire network is shown to be operating close to the critical regime, which means that it is robust enough to perturbations on dynamics of the network, but adaptable to environmental changes.

Identification of essential alphaproteobacterial genes reveals operational variability in conserved developmental and cell cycle systems

The cell cycle of Caulobacter crescentus is controlled by a complex signalling network that co-ordinates events. Genome sequencing has revealed many C. crescentus cell cycle genes are conserved in other Alphaproteobacteria, but it is not clear to what extent their function is conserved. As many cell cycle regulatory genes are essential in C. crescentus, the essential genes of two Alphaproteobacteria, Agrobacterium tumefaciens (Rhizobiales) and Brevundimonas subvibrioides (Caulobacterales), were elucidated to identify changes in cell cycle protein function over different phylogenetic distances as demonstrated by changes in essentiality. The results show the majority of conserved essential genes are involved in critical cell cycle processes. Changes in component essentiality reflect major changes in lifestyle, such as divisome components in A. tumefaciens resulting from that organism's different growth pattern. Larger variability of essentiality was observed in cell cycle regulators, suggesting regulatory mechanisms are more customizable than the processes they regulate. Examples include variability in the essentiality of divJ and divK spatial cell cycle regulators, and non-essentiality of the highly conserved and usually essential DNA methyltransferase CcrM. These results show that while essential cell functions are conserved across varying genetic distance, much of a given organism's essential gene pool is specific to that organism.