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1. Biological Networks across Scales—The Theoretical and Empirical Foundations for Time-Varying Complex Networks that Connect Structure and Function across Levels of Biological Organization

   Paul Bogdan, Gustavo Caetano-Anolles (May 2021, Integrative and comparative biology)

   Many biological systems across scales of size and complexity exhibit a time-varying complex network structure that emerges and self-organizes as a result of interactions with the environment. Network interactions optimize some intrinsic cost functions that are unknown and involve for example energy efficiency, robustness, resilience, and frailty. A wide range of networks exist in biology, from gene regulatory networks important for organismal development, protein interaction networks that govern physiology and metabolism, and neural networks that store and convey information to networks of microbes that form microbiomes within hosts, animal contact networks that underlie social systems, and networks of populations on the landscape connected by migration. Increasing availability of extensive (big) data is amplifying our ability to quantify biological networks. Similarly, theoretical methods that describe network structure and dynamics are being developed. Beyond static networks representing snapshots of biological systems, collections of longitudinal data series can help either at defining and characterizing network dynamics over time or analyzing the dynamics constrained to networked architectures. Moreover, due to interactions with the environment and other biological systems, a biological network may not be fully observable. Also, subnetworks may emerge and disappear as a result of the need for the biological system to cope with for example invaders or new information flows. The confluence of these developments renders tractable the question of how the structure of biological networks predicts and controls network dynamics. In particular, there may be structural features that result in homeostatic networks with specific higher-order statistics (e.g., multifractal spectrum), which maintain stability over time through robustness and/or resilience to perturbation. Alternative, plastic networks may respond to perturbation by (adaptive to catastrophic) shifts in structure. Here, we explore the opportunity for discovering universal laws connecting the structure of biological networks with their function, positioning them on the spectrum of time-evolving network structure, that is, dynamics of networks, from highly stable to exquisitely sensitive to perturbation. If such general laws exist, they could transform our ability to predict the response of biological systems to perturbations—an increasingly urgent priority in the face of anthropogenic changes to the environment that affect life across the gamut of organizational scales. 

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2. Strong and weak environmental perturbations cause contrasting restructure of ant transportation networks

   https://doi.org/10.1098/rspb.2024.2342  

   Piross, Imre Sándor; Lecheval, Valentin; Powell, Scott; Donaldson-Matasci, Matina C; Robinson, Elva_J H (April 2025, Proceedings of the Royal Society B: Biological Sciences)

   Dynamic transportation networks are embedded in all levels of biological organization. Ever-growing anthropogenic disturbances and an increasingly variable climate highlight the importance of understanding how these networks restructure under environmental perturbations. Polydomous wood ants provide a convenient model system to study the resilience of self-organizing multi-source, multi-sink transportation networks. We used 10 years of longitudinal empirical data on both unperturbed and experimentally manipulated colony networks to develop and validate a comprehensive dynamic simulation model to study network restructuring after resource removal. We performed simulation experiments to study the effects of excluding food sources with varying importance, either temporarily or permanently, imitating pulse and press perturbations of the networks. We found that removing heavily used resources, corresponding to a strong targeted perturbation, persistently decreased network efficiency, unlike random or weak perturbations. We also found that strong perturbations had excessively adverse effects on robustness and function, reducing the networks’ ability to withstand potential future perturbations. When transportation networks develop around the efficient use of a few key resources, they may be unable to quickly recover from the loss of these through self-organized restructuring. Our findings highlight the importance of considering the interaction of perturbation strength and network structure in studying transportation network dynamics. 

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3. Resolving the Rules of Robustness and Resilience in Biology Across Scales

   https://doi.org/10.1093/icb/icab183  

   Crespi, Erica; Burnap, Robert; Chen, Jing; Das, Moumita; Gassman, Natalie; Rosa, Epaminondas; Simmons, Rebecca; Wada, Haruka; Wang, Zhen Q; Xiao, Jie; et al (August 2021, Integrative and Comparative Biology)

   Abstract Why do some biological systems and communities persist while others fail? Robustness, a system's stability, and resilience, the ability to return to a stable state, are key concepts that span multiple disciplines within and outside the biological sciences. Discovering and applying common rules that govern the robustness and resilience of biological systems is a critical step toward creating solutions for species survival in the face of climate change, as well as the for the ever-increasing need for food, health, and energy for human populations. We propose that network theory provides a framework for universal scalable mathematical models to describe robustness and resilience and the relationship between them, and hypothesize that resilience at lower organization levels contribute to robust systems. Insightful models of biological systems can be generated by quantifying the mechanisms of redundancy, diversity, and connectivity of networks, from biochemical processes to ecosystems. These models provide pathways towards understanding how evolvability can both contribute to and result from robustness and resilience under dynamic conditions. We now have an abundance of data from model and non-model systems and the technological and computational advances for studying complex systems. Several conceptual and policy advances will allow the research community to elucidate the rules of robustness and resilience. Conceptually, a common language and data structure that can be applied across levels of biological organization needs to be developed. Policy advances such as cross-disciplinary funding mechanisms, access to affordable computational capacity, and the integration of network theory and computer science within the standard biological science curriculum will provide the needed research environments. This new understanding of biological systems will allow us to derive ever more useful forecasts of biological behaviors and revolutionize the engineering of biological systems that can survive changing environments or disease, navigate the deepest oceans, or sustain life throughout the solar system. 

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4. The effective graph reveals redundancy, canalization, and control pathways in biochemical regulation and signaling

   https://doi.org/10.1073/pnas.2022598118  

   Gates, Alexander J.; Brattig Correia, Rion; Wang, Xuan; Rocha, Luis M. (March 2021, Proceedings of the National Academy of Sciences)

   null (Ed.)

   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. 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. 

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5. Analyzing Emergence in Biological Neural Networks Using Graph Signal Processing

   https://doi.org/10.1201/9781003160816-10  

   Schultz, Kevin; Villafañe-Delgado, Marisel; Reilly, Elizabeth P.; Saksena, Anshu; Hwang, Grace M. (January 2022, Emergent Behavior in System of Systems Engineering)

   Rainey, Larry B.; Holland, O. Thomas (Ed.)

   Biological neural networks offer some of the most striking and complex examples of emergence ever observed in natural or man-made systems. Individually, the behavior of a single neuron is rather simple, yet these basic building blocks are connected through synapses to form neural networks, which are capable of sophisticated capabilities such as pattern recognition and navigation. Lower-level functionality provided by a given network is combined with other networks to produce more sophisticated capabilities. These capabilities manifest emergently at two vastly different, yet interconnected time scales. At the time scale of neural dynamics, neural networks are responsible for turning noisy external stimuli and internal signals into signals capable of supporting complex computations. A key component in this process is the structure of the network, which itself forms emergently over much longer time scales based on the outputs of its constituent neurons, a process called learning. The analysis and interpretation of the behaviors of these interconnected dynamical systems of neurons should account for the network structure and the collective behavior of the network. The field of graph signal processing (GSP) combines signal processing with network science to study signals defined on irregular network structures. Here, we show that GSP can be a valuable tool in the analysis of emergence in biological neural networks. Beyond any purely scientific pursuits, understanding the emergence in biological neural networks directly impacts the design of more effective artificial neural networks for general machine learning and artificial intelligence tasks across domains, and motivates additional design motifs for novel emergent systems of systems. 

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