Yang-Yu Liu

Control Principles of Complex Networks

A reflection of our ultimate understanding of a complex system is our ability to control its behavior. Typically, control has multiple prerequisites: It requires an accurate map of the network that governs the interactions between the systems components, a quantitative description of the dynamical laws that govern the temporal behavior of each component, and an ability to influence the state and temporal behavior of a selected subset of the components. With deep roots in nonlinear dynamics and control theory, notions of control and controllability have taken a new life recently in the study of complex networks, inspiring several fundamental questions: What are the control principles of complex systems? How do networks organize themselves to balance control with functionality? To address these here we review recent advances on the controllability and the control of complex networks, exploring the intricate interplay between a systems structure, captured by its network topology, and the dynamical laws that govern the interactions between the components. We match the pertinent mathematical results with empirical findings and applications. We show that uncovering the control principles of complex systems can help us explore and ultimately understand the fundamental laws that govern their behavior.

Universality of human microbial dynamics

The recent realization that human-associated microbial communities play a crucial role in determining our health and well-being1,2 has led to the ongoing development of microbiome-based therapies3 such as fecal microbiota transplantation4,5. Thosemicrobial communities are very complex, dynamic6 and highly personalized ecosystems3,7, exhibiting a high degree of inter-individual variability in both species assemblages8 and abundance profiles9. It is not known whether the underlying ecological dynamics, which can be parameterized by growth rates, intra- and inter-species interactions in population dynamics models10, are largely host-independent (i.e. “universal”) or host-specific. If the inter-individual variability reflects host-specific dynamics due to differences in host lifestyle11, physiology12, or genetics13, then generic microbiome manipulations may have unintended consequences, rendering them ineffectual or even detrimental. Alternatively, microbial ecosystems of different subjects may follow a universal dynamics with the inter-individual variability mainly stemming from differences in the sets of colonizing species7,14. Here we developed a novel computational method to characterize human microbial dynamics. Applying this method to cross-sectional data from two large-scale metagenomic studies, the Human Microbiome Project9,15 and the Student Microbiome Project16, we found that both gut and mouth microbiomes display pronounced universal dynamics, whereas communities associated with certain skin sites are likely shaped by differences in the host environment. Interestingly, the universality of gut microbial dynamics is not observed in subjects with recurrent Clostridium difficile infection17 but is observed in the same set of subjects after fecal microbiota transplantation. These results fundamentally improve our understanding of forces and processes shaping human microbial ecosystems, paving the way to design general microbiome-based therapies18.

On the Origins and Control of Community Types in the Human Microbiome

Microbiome-based stratification of healthy individuals into compositional categories, referred to as “enterotypes” or “community types”, holds promise for drastically improving personalized medicine. Despite this potential, the existence of community types and the degree of their distinctness have been highly debated. Here we adopted a dynamic systems approach and found that heterogeneity in the interspecific interactions or the presence of strongly interacting species is sufficient to explain community types, independent of the topology of the underlying ecological network. By controlling the presence or absence of these strongly interacting species we can steer the microbial ecosystem to any desired community type. This open-loop control strategy still holds even when the community types are not distinct but appear as dense regions within a continuous gradient. This finding can be used to develop viable therapeutic strategies for shifting the microbial composition to a healthy configuration.

Systems Pharmacology and Rational Polypharmacy: Nitric Oxide−Cyclic GMP Signaling Pathway as an Illustrative Example and Derivation of the General Case

Impaired nitric oxide (NO˙)-cyclic guanosine 3, 5-monophosphate (cGMP) signaling has been observed in many cardiovascular disorders, including heart failure and pulmonary arterial hypertension. There are several enzymatic determinants of cGMP levels in this pathway, including soluble guanylyl cyclase (sGC) itself, the NO˙-activated form of sGC, and phosphodiesterase(s) (PDE). Therapies for some of these disorders with PDE inhibitors have been successful at increasing cGMP levels in both cardiac and vascular tissues. However, at the systems level, it is not clear whether perturbation of PDE alone, under oxidative stress, is the best approach for increasing cGMP levels as compared with perturbation of other potential pathway targets, either alone or in combination. Here, we develop a model-based approach to perturbing this pathway, focusing on single reactions, pairs of reactions, or trios of reactions as targets, then monitoring the theoretical effects of these interventions on cGMP levels. Single perturbations of all reaction steps within this pathway demonstrated that three reaction steps, including the oxidation of sGC, NO˙ dissociation from sGC, and cGMP degradation by PDE, exerted a dominant influence on cGMP accumulation relative to other reaction steps. Furthermore, among all possible single, paired, and triple perturbations of this pathway, the combined perturbations of these three reaction steps had the greatest impact on cGMP accumulation. These computational findings were confirmed in cell-based experiments. We conclude that a combined perturbation of the oxidatively-impaired NO˙-cGMP signaling pathway is a better approach to the restoration of cGMP levels as compared with corresponding individual perturbations. This approach may also yield improved therapeutic responses in other complex pharmacologically amenable pathways.

Inferring human microbial dynamics from temporal metagenomics data: Pitfalls and lessons

The human gut microbiota is a very complex and dynamic ecosystem that plays a crucial role in health and well‐being. Inferring microbial community structure and dynamics directly from time‐resolved metagenomics data is key to understanding the community ecology and predicting its temporal behavior. Many methods have been proposed to perform the inference. Yet, as we point out in this review, there are several pitfalls along the way. Indeed, the uninformative temporal measurements and the compositional nature of the relative abundance data raise serious challenges in inference. Moreover, the inference results can be largely distorted when only focusing on highly abundant species by ignoring or grouping low‐abundance species. Finally, the implicit assumptions in various regularization methods may not reflect reality. Those issues have to be seriously considered in ecological modeling of human gut microbiota.

Impacts of network topology on the performance of a Distributed Algorithm Solving Linear Equations

Recently a distributed algorithm has been proposed for multi-agent networks to solve a system of linear algebraic equations, by assuming each agent only knows part of the system and is able to communicate with nearest neighbors to update their local solutions. This paper investigates how the net- work topology impacts exponential convergence of the proposed algorithm. It is found that networks with higher mean degree, smaller diameter, and homogeneous degree distribution tend to achieve faster convergence. Both analytical and numerical results are provided.

Controlling microbial communities: a theoretical framework

Microbes comprise nearly half of all biomass on Earth. Almost every habitat on Earth is teeming with microbes, from hydrothermal vents to the human gastrointestinal tract. Those microbes form complex communities and play critical roles in maintaining the integrity of their environment or the well-being of their hosts. Controlling microbial communities can help us restore natural ecosystems and maintain healthy human microbiota. Yet, our ability to precisely manipulate microbial communities has been fundamentally impeded by the lack of a systematic framework to control them. Here we fill this gap by developing a control framework based on the new notion of structural accessibility. This framework allows identifying minimal sets of “driver species” through which we can achieve feasible control of the entire microbial community. We numerically validate our control framework on large microbial communities, and then we demonstrate its application for controlling the gut microbiota of gnotobiotic mice infected with Clostridium difficile and the core microbiota of the sea sponge Ircinia oros.Microbial communities perform key functions for the host they associate with or the environment they reside in. Our ability to control those microbial communities is crucial for maintaining or even enhancing the well-being of their host or environment. But this potential has not been fully harvested due to the lack of a systematic method to control those complex microbial communities. Here we introduce a theoretical framework to rigorously address this challenge, based on the new notion of structural accessibility. This framework allows the identification of minimal sets of “driver species” through which we can achieve feasible control of the entire community. We apply our framework to control the core microbiota of a sea sponge and the gut microbiota of gnotobiotic mice infected with C. difficile. This control-theoretical framework fundamentally enhances our ability to effectively manage and control complex microbial communities, such as the human gut microbiota. In particular, the concept of driver species of a microbial community holds translational promise in the design of probiotic cocktails for various diseases associated with disrupted microbiota.

Revealing complex ecological dynamics via symbolic regression

Complex ecosystems, from food webs to our gut microbiota, are essential to human life. Understanding the dynamics of those ecosystems can help us better maintain or control them. Yet, reverse-engineering complex ecosystems (i.e., extracting their dynamic models) directly from measured temporal data has not been very successful so far. Here we propose to close this gap via symbolic regression. We validate our method using both synthetic and real data. We firstly show this method allows reverse engineering two-species ecosystems, inferring both the structure and the parameters of ordinary differential equation models that reveal the mechanisms behind the system dynamics. We find that as the size of the ecosystem increases or the complexity of the inter-species interactions grow, using a dictionary of known functional responses (either previously reported or reverse-engineered from small ecosystems using symbolic regression) opens the door to correctly reverse-engineer large ecosystems.

Controllability in an islet specific regulatory network identifies the transcriptional factor NFATC4, which regulates Type 2 Diabetes associated genes

Probing the dynamic control features of biological networks represents a new frontier in capturing the dysregulated pathways in complex diseases. Here, using patient samples obtained from a pancreatic islet transplantation program, we constructed a tissue-specific gene regulatory network and used the control centrality (Cc) concept to identify the high control centrality (HiCc) pathways, which might serve as key pathobiological pathways for Type 2 Diabetes (T2D). We found that HiCc pathway genes were significantly enriched with modest GWAS p-values in the DIAbetes Genetics Replication And Meta-analysis (DIAGRAM) study. We identified variants regulating gene expression (expression quantitative loci, eQTL) of HiCc pathway genes in islet samples. These eQTL genes showed higher levels of differential expression compared to non-eQTL genes in low, medium, and high glucose concentrations in rat islets. Among genes with highly significant eQTL evidence, NFATC4 belonged to four HiCc pathways. We asked if the expressions of T2D-associated candidate genes from GWAS and literature are regulated by Nfatc4 in rat islets. Extensive in vitro silencing of Nfatc4 in rat islet cells displayed reduced expression of 16, and increased expression of four putative downstream T2D genes. Overall, our approach uncovers the mechanistic connection of NFATC4 with downstream targets including a previously unknown one, TCF7L2, and establishes the HiCc pathways’ relationship to T2D.Network medicine: Identifying the controlling pathways of Type 2 DiabetesGenes that structurally control regulatory networks uncover the pathways driving complex diseases. Amitabh Sharma of Brigham and Women’s Hospital and his colleagues constructed a tissue-specific gene regulatory network derived from human pancreatic islets and determined the genes that control the network, using the concept of “control centrality.” Pathways with high control centrality were significantly more associated with Type 2 Diabetes (T2D) than pathways with lower control centrality, and harbored loci that significantly affected gene expression (eQTLs) related to glucose levels. In vitro knockdown of NFATC4, jointly identified by control centrality and eQTL analysis, verified its downstream influence on genes known to be associated with T2D. Controllability in biological networks may help us pinpoint influential pathways as well as key regulators of many other complex diseases.

Link Prediction through Deep Learning

Inferring missing links or predicting future ones based on the currently observed network is known as link prediction, which has tremendous real-world applications in biomedicine1,2, e-commerce3, social media4 and criminal intelligence5. Numerous methods have been proposed to solve the link prediction problem6–8. Yet, many of these existing methods are designed for undirected networks only. Moreover, most methods are based on domain-specific heuristics9, and hence their performances differ greatly for networks from different domains. Here we developed a new link prediction method based on deep generative models10 in machine learning. This method does not rely on any domain-specific heuristic and works for general undirected or directed complex networks. Our key idea is to represent the adjacency matrix of a network as an image and then learn hierarchical feature representations of the image by training a deep generative model. Those features correspond to structural patterns in the network at different scales, from small subgraphs to mesoscopic communities11. Conceptually, taking into account structural patterns at different scales all together should outperform any domain-specific heuristics that typically focus on structural patterns at a particular scale. Indeed, when applied to various real-world networks from different domains12–16, our method shows overall superior performance against existing methods. Moreover, it can be easily parallelized by splitting a large network into several small subnetworks and then perform link prediction for each subnetwork in parallel. Our results imply that deep learning techniques can be effectively applied to complex networks and solve the classical link prediction problem with robust and superior performance.