A modular view of the diversity of cell-density-encoding schemes in bacterial quorum-sensing systems

Abstract

Certain environmental parameters are accessible to cells only indirectly and require an encoding step for cells to retrieve the relevant information. A prominent example is the phenomenon of quorum sensing by microorganisms, where information about cell density is encoded by means of secreted signaling molecules. The mapping of cell density to signal molecule concentration and the corresponding network modules involved have been at least partially characterized in many bacteria, and vary markedly between different systems. In this study, we investigate theoretically how differences in signal transport, signal modification, and site of signal detection shape the encoding function and affect the sensitivity and the noise characteristics of the cell-density-encoding process. We find that different modules are capable of implementing both fairly basic as well as more complex encoding schemes, whose qualitative characteristics vary with cell density and are linked to network architecture, providing the basis for a hierarchical classification scheme. We exploit the tight relationship between encoding behavior and network architecture to constrain the network topology of partially characterized natural systems, and verify one such prediction by showing experimentally that Vibrio harveyi is capable of importing Autoinducer 2. The framework developed in this research can serve not only to guide reverse engineering of natural systems but also to stimulate the design of synthetic systems and generally facilitate a better understanding of the complexities arising in the quorum-sensing process because of variations in the physical organization of the encoder network module.

Figure 1

Cell-density-encoding schemes in bacterial quorum-sensing systems. (A) Cells encode information about the cell density into the SM concentration and decode it to control a target response. (B) The quorum-sensing network can be divided into an encoder module (EM, left) and a decoder module (DM, right). The EM produces SMs (diamonds) at rate π inside the cell (volume V_c), which are exchanged (θ_diff) with the environment (volume V_e) and are degraded both intra- and extracellular (λ_c, λ_e). The concentration of the SM detected by the receptor (diamond surrounded by a bold red line) determines the encoding behavior of the system. The DM transduces the signal from the receptor to regulate target gene expression. (C) Different encoding schemes. Left: abstract representation of EM shown in (B): intracellular encoding with diffusive SMs (A_c, A_e). Subscripts c and e denote cellular and extracellular concentrations, respectively. Middle: molecules A are actively exported (θ_out) and modified (γ) into molecules B, which are again imported (θ_in). [B_c] is detected by the receptor. Right: molecules A are modified during export (θ_γ) into molecules B. The extracellular concentration [B_e] is detected by the receptor. To see this figure in color, go online.

Figure 2

Diversity of encoder architectures. By combining different basic processes (transport, modification, receptor location, and specificity) in all possible ways, one can build 116 different feedforward encoder architectures, which are summarized schematically by a network diagram that comprises all architectures considered. The different molecular species (X = A, B) represent the nodes of the encoding module. The arrows describe the processes of structural or state conversion of these species.

Figure 3

Encoder characteristics and definition of basic encoder classes. (A) Every EM has a characteristic sensitivity, noise, and [SM] profile. Noise can be determined from stochastic simulations (dots) and approximated analytically (lines). The shaded area in the [SM] profile denotes the magnitude of the noise. These profiles define four basic encoder classes schematically represented by icons derived from their sensitivity profiles and are ordered from left to right according to increasing encoding range. (B) Prototype networks (“core motifs”) define the encoding behavior. White ovals denote cells. Red diamonds mark the site where SMs are detected; double arrows denote bidirectional SM flow, directed arrows denote unidirectional SM export. A key feature of the low-pass architecture shown on the right is that it detects modified SMs. This is visualized by including an additional diamond. To see this figure in color, go online.

Figure 4

Decomposition of complex encoding architectures. (A) Sensitivity profiles (blue, solid line) generated by four-node networks showing ultrasensitive (ε > 1) and inverted sensitivity (ε < 0) regimes. The dashed and dashed-dotted, green, blue, and red lines show the basic profiles from which the complex encoding behavior can be derived. (B) and (C) Origins of encoding complexity: decomposition of complex networks into basic networks (top). Networks with modification (dark gray arrow) during import (B) can be decomposed into pairs of two-node networks with intracellular SM production (gray arrow marked with π). Networks with extracellular modification (C) can be decomposed into one two-node network with intracellular and one with extracellular SM production. Complex networks sense the modified SMs (red diamonds) either intracellular or extracellular. In the first two-node network the extracellular SM concentration determines the behavior, the second network senses the same concentration as the complex four-node network. Bottom: the overall sensitivity characteristics (novel icons, “+” and “-“ denoting ultra- and negative sensitivity, respectively) follow from a superposition of the underlying basic encoder profiles (icons as defined in Fig. 3). To see this figure in color, go online.

Figure 5

Taxonomic scheme for classifying encoding architectures into distinct encoder classes based on their sensitivity profiles. The connections illustrate the hierarchical relationship between functional and nonfunctional quorum-sensing systems, basic and derived encoder classes. The Venn diagram orders all 116 encoding architectures into nine distinct encoder classes denoted as BP (band-pass), LP (low-pass), ID (ideal), NF (nonfunctional), MP (multipass), BPU (band-pass ultrasensitive), LPU (low-pass ultrasensitive), IDU (ideal ultrasensitive), NS (negative sensitivity), and INV (inverted).

Figure 6

AI-2 import in V. harveyi. (A) Whether V. harveyi is able to internalize AI-2 molecules or not (circled arrow marked with question mark) can be predicted from its encoder profile. A low-pass profile implies the capacity for import, an ideal profile suggests that such a capacity is lacking. (B) The form of the AI-2 encoder sensitivity profile for V. harveyi derived from data in a previous study (26) is qualitatively compatible with the behavior of a low-pass encoder. This implies the presence of an uptake mechanism for AI-2 molecules in V. harveyi. (C) Schematic representation of the heterologous lsrKR-based P_lsr::lacZ reporter system in V. harveyi. (D) Histograms showing β−galactosidase activity (as a measure of P_lsr::lacZ expression) of AI-2-producing V. harveyi wild-type cells, the nonproducing mutant (ΔluxS) and the nonproducing mutant after external addition of AI-2 (20 μM).