skip to main content

Title: The effective graph reveals redundancy, canalization, and control pathways in biochemical regulation and signaling
The ability to map causal interactions underlying genetic control and cellular signaling has led to increasingly accurate models of the complex biochemical networks that regulate cellular function. These network models provide deep insights into the organization, dynamics, and function of biochemical systems: for example, by revealing genetic control pathways involved in disease. However, the traditional representation of biochemical networks as binary interaction graphs fails to accurately represent an important dynamical feature of these multivariate systems: some pathways propagate control signals much more effectively than do others. Such heterogeneity of interactions reflects canalization—the system is robust to dynamical interventions in redundant pathways but responsive to interventions in effective pathways. Here, we introduce the effective graph, a weighted graph that captures the nonlinear logical redundancy present in biochemical network regulation, signaling, and control. Using 78 experimentally validated models derived from systems biology, we demonstrate that 1) redundant pathways are prevalent in biological models of biochemical regulation, 2) the effective graph provides a probabilistic but precise characterization of multivariate dynamics in a causal graph form, and 3) the effective graph provides an accurate explanation of how dynamical perturbation and control signals, such as those induced by cancer drug therapies, propagate in biochemical pathways. more » Overall, our results indicate that the effective graph provides an enriched description of the structure and dynamics of networked multivariate causal interactions. We demonstrate that it improves explainability, prediction, and control of complex dynamical systems in general and biochemical regulation in particular. « less
Authors:
; ; ;
Award ID(s):
1735095
Publication Date:
NSF-PAR ID:
10294321
Journal Name:
Proceedings of the National Academy of Sciences
Volume:
118
Issue:
12
Page Range or eLocation-ID:
e2022598118
ISSN:
0027-8424
Sponsoring Org:
National Science Foundation
More Like this
  1. Iakoucheva, Lilia M. (Ed.)
    The complexity of biological processes such as cell differentiation is reflected in dynamic transitions between cellular states. Trajectory inference arranges the states into a progression using methodologies propelled by single-cell biology. However, current methods, all returning a best trajectory, do not adequately assess statistical significance of noisy patterns, leading to uncertainty in inferred trajectories. We introduce a tree dimension test for trajectory presence in multivariate data by a dimension measure of Euclidean minimum spanning tree, a test statistic, and a null distribution. Computable in linear time to tree size, the tree dimension measure summarizes the extent of branching more effectively than globally insensitive number of leaves or tree diameter indifferent to secondary branches. The test statistic quantifies trajectory presence and its null distribution is estimated under the null hypothesis of no trajectory in data. On simulated and real single-cell datasets, the test outperformed the intuitive number of leaves and tree diameter statistics. Next, we developed a measure for the tissue specificity of the dynamics of a subset, based on the minimum subtree cover of the subset in a minimum spanning tree. We found that tissue specificity of pathway gene expression dynamics is conserved in human and mouse development: several signalmore »transduction pathways including calcium and Wnt signaling are most tissue specific, while genetic information processing pathways such as ribosome and mismatch repair are least so. Neither the tree dimension test nor the subset specificity measure has any user parameter to tune. Our work opens a window to prioritize cellular dynamics and pathways in development and other multivariate dynamical systems.« less
  2. Martin, Allan R. (Ed.)
    Cellular differentiation is a tightly regulated process under the control of intricate signaling and transcription factors interaction network working in coordination. These interactions make the systems dynamic, robust and stable but also difficult to dissect. In the spinal cord, recent work has shown that a network of FGF, WNT and Retinoic Acid (RA) signaling factors regulate neural maturation by directing the activity of a transcription factor network that contains CDX at its core. Here we have used partial and ordinary (Hill) differential equation based models to understand the spatiotemporal dynamics of the FGF/WNT/RA and the CDX/transcription factor networks, alone and in combination. We show that in both networks, the strength of interaction among network partners impacts the dynamics, behavior and output of the system. In the signaling network, interaction strength determine the position and size of discrete regions of cell differentiation and small changes in the strength of the interactions among networking partners can result in a signal overriding, balancing or oscillating with another signal. We also show that the spatiotemporal information generated by the signaling network can be conveyed to the CDX/transcription network to produces a transition zone that separates regions of high cell potency from regions of cellmore »differentiation, in agreement with most in vivo observations. Importantly, one emerging property of the networks is their robustness to extrinsic disturbances, which allows the system to retain or canalize NP cells in developmental trajectories. This analysis provides a model for the interaction conditions underlying spinal cord cell maturation during embryonic axial elongation.« less
  3. Many tissues undergo a steady turnover, where cell divisions are on average balanced with cell deaths. Cell fate decisions such as stem cell (SC) differentiations, proliferations, or differentiated cell (DC) deaths, may be controlled by cell populations through cell-to-cell signaling. Here, we examine a class of mathematical models of turnover in SC lineages to understand engineering design principles of control (feedback) loops, that may operate in such systems. By using ordinary differential equations that describe the co-dynamics of SCs and DCs, we study the effect of different types of mutations that interfere with feedback present within cellular networks. For instance, we find that mutants that do not participate in feedback are less dangerous in the sense that they will not rise from low numbers, whereas mutants that do not respond to feedback signals could rise and replace the wild-type population. Additionally, we asked if different feedback networks can have different degrees of resilience against such mutations. We found that all minimal networks, that is networks consisting of exactly one feedback loop that is sufficient for homeostatic stability of the wild-type population, are equally vulnerable. Mutants with a weakened/eliminated feedback parameter might expand from lower numbers and either enter unlimited growth ormore »reach an equilibrium with an increased number of SCs and DCs. Therefore, from an evolutionary viewpoint, it appears advantageous to combine feedback loops, creating redundant feedback networks. Interestingly, from an engineering prospective, not all such redundant systems are equally resilient. For some of them, any mutation that weakens/eliminates one of the loops will lead to a population growth of SCs. For others, the population of SCs can actually shrink as a result of “cutting” one of the loops, thus slowing down further unwanted transformations.« less
  4. Kamoun, Sophien (Ed.)
    Plant protein kinases form redundant signaling pathways to perceive microbial pathogens and activate immunity. Bacterial pathogens repress cellular immune responses by secreting effectors, some of which bind and inhibit multiple host kinases. To understand how broadly bacterial effectors may bind protein kinases and the function of these kinase interactors, we first tested kinase–effector (K-E) interactions using the Pseudomonas syringae pv. tomato–tomato pathosystem. We tested interactions between five individual effectors (HopAI1, AvrPto, HopA1, HopM1, and HopAF1) and 279 tomato kinases in tomato cells. Over half of the tested kinases interacted with at least one effector, and 48% of these kinases interacted with more than three effectors, suggesting a role in the defense. Next, we characterized the role of select multi-effector–interacting kinases and revealed their roles in basal resistance, effector-triggered immunity (ETI), or programmed cell death (PCD). The immune function of several of these kinases was only detectable in the presence of effectors, suggesting that these kinases are critical when particular cell functions are perturbed or that their role is typically masked. To visualize the kinase networks underlying the cellular responses, we derived signal-specific networks. A comparison of the networks revealed a limited overlap between ETI and basal immunity networks. In addition,more »the basal immune network complexity increased when exposed to some of the effectors. The networks were used to successfully predict the role of a new set of kinases in basal immunity. Our work indicates the complexity of the larger kinase-based defense network and demonstrates how virulence- and avirulence-associated bacterial effectors alter sectors of the defense network.« less
  5. Abstract

    Understanding global communications among cells requires accurate representation of cell-cell signaling links and effective systems-level analyses of those links. We construct a database of interactions among ligands, receptors and their cofactors that accurately represent known heteromeric molecular complexes. We then develop CellChat, a tool that is able to quantitatively infer and analyze intercellular communication networks from single-cell RNA-sequencing (scRNA-seq) data. CellChat predicts major signaling inputs and outputs for cells and how those cells and signals coordinate for functions using network analysis and pattern recognition approaches. Through manifold learning and quantitative contrasts, CellChat classifies signaling pathways and delineates conserved and context-specific pathways across different datasets. Applying CellChat to mouse and human skin datasets shows its ability to extract complex signaling patterns. Our versatile and easy-to-use toolkit CellChat and a web-based Explorer (http://www.cellchat.org/) will help discover novel intercellular communications and build cell-cell communication atlases in diverse tissues.