MS09 - OTHE-05

Design Principles of Biological Networks

Friday, July 18 at 4:00pm

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Kishore Hari and Pradyumna Harlapur (Postdoctoral Research Fellow, Center for Theoretical Biological Physics), Pradyumna Harlapur, PhD Candidate, Dept. of BioEngineering, Indian Institute of Science

Description:

Gene regulatory networks (GRNs) are networks of interacting genes and regulatory elements that govern the expression of genes in a cell and, hence, the decisions they make when undergoing a biological process. GRNs take a holistic approach by incorporating the relevant regulatory elements governing cellular processes, allowing researchers to model and estimate complex biological processes' properties accurately. Studies of these networks have identified 'design principles' that influence their function, and these common patterns have been observed across contexts and shown to lead to behaviors like robustness, adaptability, and plasticity. The rise of high-throughput data has also led to the development of GRN inference tools, which incorporate various modalities of gene regulation, leading to the creation of detailed, context-specific GRNs. This progress motivates the renewed importance of studying such networks to better understand how various processes are coordinated and carried out in the cell and how any divergence from normal behavior can be corrected using the insights gained from studying such networks. In this mini-symposium, we gather a group of scientists studying the design principles of biological networks across diverse contexts to encourage discussions about identifying, analyzing, and controlling such design patterns, thereby advancing research and discovery in network biology.

Claus Kadelka

Iowa State University

"Biological networks operate closer to the edge of chaos than recently proposed"

Since Kauffman introduced Boolean networks to study gene regulatory networks, they have been successfully used to model various biological networks such as cancer signaling pathways and T-cell differentiation. Due to their finite size, Boolean networks eventually exhibit periodic behavior, and the attracting states in a biological Boolean network correspond to phenotypes or cell types. Traditional stability measures, such as the Derrida value or network and basin coherence, quantify the resilience of network dynamics to perturbations of any random state in the network, yet real-world systems typically rest at an attracting state. To address this, we introduce attractor coherence, a metric that quantifies how likely the perturbation of a network attractor causes the system to transition to another attractor. A comparison of attractor coherence and conventional basin coherence in expert-curated Boolean biological network models reveals substantial and systematic differences. Through extensive simulations of random network ensembles, we demonstrate that increased canalization not only boosts the number of fixed‐point attractors but also magnifies the gap between basin and attractor‐focused stability. Similarly, networks with higher fractions of frozen nodes exhibit larger discrepancies between the coherence measures. These findings highlight the importance of attractor‐centric metrics for accurately assessing the phenotype robustness in biological networks.

Chandrakala Meena

Indian Institute of Science Education and Research Pune

"Emergent stability in complex biological systems"

First, I will discuss briefly the general dynamical framework to analyze the macroscopic behaviour of biological systems using their microscopic components—network topology and dynamics and then the identification of emergent dynamical states using the dynamical framework. Then, I will present analytical approaches to predict the stability of emergent steady states in complex biological systems, ranging from ecological, and cellular to brain networks. Complex systems are often described by interaction graphs, where the dynamical state is captured by the activities of all nodes, for example, the excitation of neurons in brain networks or the expression levels of genes in subcellular interactions. To capture the system’s stability, we perturb its dynamical states from their fixed-point steady states and analyze its response to the perturbation, such as a local spike in neuronal activity or a sudden increase in the expression of one or several genes. A system is considered stable if the perturbation decays; otherwise, it loses stability and may transition to an entirely new state. The system’s response to perturbations is encoded within its stability matrix - the Jacobian, but retrieving this information is challenging due to the scale and diversity of these systems, their broad parameter space, and their nonlinear interaction dynamics. To address this complexity, we develop the dynamic Jacobian ensemble, which provides a systematic framework for investigating the fixed-point dynamics of a wide range of graph-based nonlinear interaction models, including social, biological, chemical, and technological systems. These Jacobians reveal universal scaling patterns, where structure and dynamics are intricately connected. Further, to predict system stability, we develop some stability classifiers that are based on Jacobian ensembles and the Gershgorin Disk Theorem. These stability classifiers capture the influence of both network topology and dynamics, enabling the prediction and classification of large complex systems into stable, unstable, or sensitively stable categories.

Jordan C Rozum

Pacific Northwest National Lab

"Redundant structures and robust dynamics in biomolecular networks"

Cells must cope with noisy, dynamic, and spatially heterogeneous environments. They must balance robustness with adaptability in the biomolecular networks that govern their behavior. For instance, cyanobacteria adapt their metabolism to changing nutrient and light conditions, while phages that infect these organisms carry auxiliary metabolic genes (AMGs) that hijack adaptive responses, ostensibly to promote viral replication. Using a flux network model, we showed how AMGs in a particular host-pathogen system come in two types: those that limit host growth by reconfiguring metabolic fluxes to favor phage production, and those for which the host metabolism can robustly compensate without affecting host-phage biomass trade-offs. More broadly, we and others have observed a high level of redundancy in metabolic networks. For instance, we have shown that key pathways and subsystems can be extracted even after removing over 90% of the connections between metabolic reactions. Indeed, many metabolic genes and reactions, across organisms, are not essential for survival and growth. This robustness is present directly in the metabolism, even before accounting for the substantial redundancy in regulatory and signaling networks that modulate it. In a wide variety of cell process models, it is exceedingly difficult to alter long-term behavior via large transient perturbations. Using novel mathematical and computational techniques, we ascribe this phenomenon to canalization, or buffering of environmental fluctuations, in both the local regulatory logic and the global regulatory topology.

Pradyumna Harlapur

Indian Institute of Science

"Characterizing Regulatory Interactions and Dimensionality in Gene Networks Driving Cell-Fate Choices"

Cell-fate decisions involve coordinated genome-wide expression changes, typically leading to a limited number of phenotypes. Although often modeled as simple toggle switches, these rather simplistic representations often disregard the complexity of regulatory networks governing these changes. Here, we unravel design principles underlying complex cell decision-making networks in multiple contexts. We show that the emergent dynamics of these networks are consistently low-dimensional, as quantified by the variance explained by principal component 1 (PC1). This low dimensionality in phenotypic space arises from extensive feedback loops in these networks arranged to effectively enable the formation of two teams of mutually inhibiting nodes (Hari*, Harlapur* et al. iScience 2025). We use team strength as a metric to quantify these feedback interactions and show its strong correlation with PC1 variance. We then examined how biological networks are organized with specific topologies that allow them to remain sparse while effectively coordinating decision-making under various levels of coherent interactions (i.e., structural balance). We found that networks with low coherence needed higher densities to show coordinated expression profiles. The balance between sparsity and coordinated control highlights the role of network architecture in ensuring stable and robust phenotypic outcomes, providing new insights into how GRNs guide cellular behavior precisely yet adaptable. These results shed light on how, despite being very sparse, the networks that govern various cellular decisions follow certain basic design principles to ensure the expression between the nodes involved is well coordinated.

#SMB2025 Follow

Annual Meeting for the Society for Mathematical Biology, 2025.