In multicellular organisms, secreted ligands selectively activate, or “address,” specific target cell populations to control cell fate decision-making and other processes. Key cell-cell communication pathways use multiple promiscuously interacting ligands and receptors, provoking the question of how addressing specificity can emerge from molecular promiscuity. To investigate this issue, we developed a general mathematical modeling framework based on the bone morphogenetic protein (BMP) pathway architecture. We find that promiscuously interacting ligand-receptor systems allow a small number of ligands, acting in combinations, to address a larger number of individual cell types, each defined by its receptor expression profile. Promiscuous systems outperform seemingly more specific one-to-one signaling architectures in addressing capacity. Combinatorial addressing extends to groups of cell types, is robust to receptor expression noise, grows more powerful with increasing receptor multiplicity, and is maximized by specific biochemical parameter relationships. Together, these results identify fundamental design principles governing cell addressing by ligand combinations.
Communication systems such as email enable individuals to address messages to specific recipients and groups of recipients. In biological systems, it is crucial to activate the right cells at the right time. Addressing is essential for targeted cell-cell communication by allowing signals to activate specific cell types or defined groups of cell types. Uncovering how signaling pathways enable different types of addressing is critical for understanding natural developmental programs and predictively controlling pathway activation of target cell types for regenerative medicine or clinical applications. However, the principles that enable cell-cell communication systems to address biological messages have generally remained unclear.
The simplest conceivable realization of addressing would use specific, one-to-one interactions between ligands and cognate receptors. This architecture is conceptually straightforward, has been implemented synthetically in the SynNotch system, and is extendable, as new orthogonal ligand-receptor pairs can provide additional communication channels without disturbing existing ones. Despite the simplicity of a one-to-one addressing system, most natural cell-cell communication systems instead employ an interconnected, many-to-many architecture. Pathways such as bone morphogenetic protein (BMP), Wnt, Notch, Eph-Ephrin, and fibroblast growth factor (FGF) exhibit promiscuous interactions among their multiple ligand and receptor variants. However, these ligand and receptor combinations may activate similar downstream targets. These observations provoke the questions of whether and how molecular promiscuity enables addressing, and what advantages it could have over the one-to-one architecture.
Promiscuous ligand-receptor interactions in the BMP pathway may allow combinatorial addressing.
The BMP pathway provides an ideal system to study these questions. BMP plays diverse roles in most tissues and has demonstrated therapeutic potential. In addition, the BMP pathway shows a high degree of promiscuous interactions between its ligands and receptors. In mammals, the pathway comprises more than 10 distinct ligand variants as well as 4 type I and 3 type II receptor variants. Signaling complexes, comprising a ligand dimer with two type I and two type II receptor subunits, phosphorylate SMAD1/5/8 effectors, which translocate to the nucleus and act as transcription factors to control the expression of target genes. Individual cells often co-express multiple receptor variants and are exposed to multiple ligands, suggesting that the pathway could function combinatorially.
Previous observations suggest that BMP ligands could show addressing capacity. For example, during neural tube development, different BMP ligands direct distinct dorsal interneuron identities, with each ligand showing specific effects on a subset of interneuron identities but not others. In this way, different ligands appear to address specific progenitors. Moreover, cells also appear to selectively respond to specific ligand combinations in other developmental contexts, and receptor expression patterns can modulate the cellular response.
Recently, mathematical modeling, together with in vitro experiments, showed that competitive formation of distinct BMP signaling complexes with different ligands and receptors effectively generates a set of “computations,” in which pathway activity depends on the relative concentrations and identities of multiple ligands. These computations comprise distinct response functions, including additive and ratiometric responses as well as balance and imbalance detection responses that are maximal or minimal, respectively, at defined ligand ratios. Further, the pathway can perform different computations on the same ligands depending on the combinations of receptors expressed by individual cells. In other words, these results suggest the possibility that different ligand combinations could selectively activate, or address, particular cell types based on their receptor expression profiles. Using combinations of ligands to activate specific cell types, promiscuous ligand-receptor interactions may in fact produce additional orthogonal communication channels compared to a one-to-one scheme. In a spatial context, this type of combinatorial addressing could further enable morphogenetic gradients of multiple ligands to activate distinct cell types at specific locations within a tissue.
To understand the principles that govern combinatorial addressing systems, we developed a minimal mathematical model that accounts for promiscuous ligand-receptor interactions, independently representing both the affinities for forming each ligand-receptor signaling complex and their enzymatic activities for activating the pathway. Using a computational optimization approach, we found that promiscuous ligand-receptor interactions generate an extensive repertoire of orthogonal communication channels, exceeding the number possible with the same number of ligands and receptors interacting in a one-to-one fashion. Modest increases in the number of receptor variants substantially increase the number and orthogonality of these addressing channels. Furthermore, the promiscuous architecture allows ligand combinations to address not only individual cell types but also more complex groups of cell types. Finally, using an information theoretic framework, we showed how specific biochemical features, such as anti-correlations between affinity and activity parameters, maximize the information content that can be transmitted through promiscuous ligand-receptor interactions, providing a design principle for building synthetic addressing systems out of promiscuously interacting ligands and receptors.
As an initial test of whether the BMP pathway could allow addressing, we analyzed the ability of mixtures of ligands at specific concentrations, or ligand words, to preferentially activate, or address, specific cell types in cell culture, where “cell type” here and throughout the paper refers to a group of cells sharing a common receptor expression profile. (An overview of addressing terminology is provided in Box 1.) To read out pathway activity, we used a transcriptional fluorescent reporter for Smad1/5/8 containing BMP response elements from the Id1 promoter. We stably integrated the reporter into three cell lines with different receptor expression profiles, then analyzed their responses to a range of BMP ligand combinations by flow cytometry 24 hours after ligand addition.
