Untangling the Hairball: Fitness-Based Asymptotic Reduction of Biological Networks

Processes in DNA damage response from a whole-cell multi-omics perspective

Technological advances have made it feasible to collect multi-condition multi-omic time courses of cellular response to perturbation, but the complexity of these datasets impedes discovery due to challenges in data management, analysis, visualization, and interpretation. Here, we report a whole-cell mechanistic analysis of HL-60 cellular response to bendamustine. We integrate both enrichment and network analysis to show the progression of DNA damage and programmed cell death over time in molecular, pathway, and process-level detail using an interactive analysis framework for multi-omics data. Our framework, Mechanism of Action Generator Involving Network analysis (MAGINE), automates network construction and enrichment analysis across multiple samples and platforms, which can be integrated into our annotated gene-set network to combine the strengths of networks and ontology-driven analysis. Taken together, our work demonstrates how multi-omics integration can be used to explore signaling processes at various resolutions and demonstrates multi-pathway involvement beyond the canonical bendamustine mechanism.

Arnold tongue entrainment reveals dynamical principles of the embryonic segmentation clock

Living systems exhibit an unmatched complexity, due to countless, entangled interactions across scales. Here, we aim to understand a complex system, that is, segmentation timing in mouse embryos, without a reference to these detailed interactions. To this end, we develop a coarse-grained approach, in which theory guides the experimental identification of the segmentation clock entrainment responses. We demonstrate period- and phase-locking of the segmentation clock across a wide range of entrainment parameters, including higher-order coupling. These quantifications allow to derive the phase response curve (PRC) and Arnold tongues of the segmentation clock, revealing its essential dynamical properties. Our results indicate that the somite segmentation clock has characteristics reminiscent of a highly non-linear oscillator close to an infinite period bifurcation and suggests the presence of long-term feedbacks. Combined, this coarse-grained theoretical-experimental approach reveals how we can derive simple, essential features of a highly complex dynamical system, providing precise experimental control over the pace and rhythm of the somite segmentation clock.

Latent space of a small genetic network: Geometry of dynamics and information

The high-dimensional character of most biological systems presents genuine challenges for modeling and prediction. Here we propose a neural network-based approach for dimensionality reduction and analysis of biological gene expression data, using, as a case study, a well-known genetic network in the early Drosophila embryo, the gap gene patterning system. We build an autoencoder compressing the dynamics of spatial gap gene expression into a two-dimensional (2D) latent map. The resulting 2D dynamics suggests an almost linear model, with a small bare set of essential interactions. Maternally defined spatial modes control gap genes positioning, without the classically assumed intricate set of repressive gap gene interactions. This, surprisingly, predicts minimal changes of neighboring gap domains when knocking out gap genes, consistent with previous observations. Latent space geometries in maternal mutants are also consistent with the existence of such spatial modes. Finally, we show how positional information is well defined and interpretable as a polar angle in latent space. Our work illustrates how optimization of small neural networks on medium-sized biological datasets is sufficiently informative to capture essential underlying mechanisms of network function.

Predictive landscapes hidden beneath biological cellular automata

To celebrate Hans Frauenfelder's achievements, we examine energy(-like) "landscapes" for complex living systems. Energy landscapes summarize all possible dynamics of some physical systems. Energy(-like) landscapes can explain some biomolecular processes, including gene expression and, as Frauenfelder showed, protein folding. But energy-like landscapes and existing frameworks like statistical mechanics seem impractical for describing many living systems. Difficulties stem from living systems being high dimensional, nonlinear, and governed by many, tightly coupled constituents that are noisy. The predominant modeling approach is devising differential equations that are tailored to each living system. This ad hoc approach faces the notorious "parameter problem": models have numerous nonlinear, mathematical functions with unknown parameter values, even for describing just a few intracellular processes. One cannot measure many intracellular parameters or can only measure them as snapshots in time. Another modeling approach uses cellular automata to represent living systems as discrete dynamical systems with binary variables. Quantitative (Hamiltonian-based) rules can dictate cellular automata (e.g., Cellular Potts Model). But numerous biological features, in current practice, are qualitatively described rather than quantitatively (e.g., gene is (highly) expressed or not (highly) expressed). Cellular automata governed by verbal rules are useful representations for living systems and can mitigate the parameter problem. However, they can yield complex dynamics that are difficult to understand because the automata-governing rules are not quantitative and much of the existing mathematical tools and theorems apply to continuous but not discrete dynamical systems. Recent studies found ways to overcome this challenge. These studies either discovered or suggest an existence of predictive "landscapes" whose shapes are described by Lyapunov functions and yield "equations of motion" for a "pseudo-particle." The pseudo-particle represents the entire cellular lattice and moves on the landscape, thereby giving a low-dimensional representation of the cellular automata dynamics. We outline this promising modeling strategy.

Numerical Parameter Space Compression and Its Application to Biophysical Models

Physical models of biological systems can become difficult to interpret when they have a large number of parameters. But the models themselves actually depend on (i.e., are sensitive to) only a subset of those parameters. This phenomenon is due to parameter space compression (PSC), in which a subset of parameters emerges as "stiff" as a function of time or space. PSC has only been used to explain analytically solvable physics models. We have generalized this result by developing a numerical approach to PSC that can be applied to any computational model. We validated our method against analytically solvable models of a random walk with drift and protein production and degradation. We then applied our method to a simple computational model of microtubule dynamic instability. We propose that numerical PSC has the potential to identify the low-dimensional structure of many computational models in biophysics. The low-dimensional structure of a model is easier to interpret and identifies the mechanisms and experiments that best characterize the system.

φ-evo: A program to evolve phenotypic models of biological networks

Molecular networks are at the core of most cellular decisions, but are often difficult to comprehend. Reverse engineering of network architecture from their functions has proved fruitful to classify and predict the structure and function of molecular networks, suggesting new experimental tests and biological predictions. We present φ-evo, an open-source program to evolve in silico phenotypic networks performing a given biological function. We include implementations for evolution of biochemical adaptation, adaptive sorting for immune recognition, metazoan development (somitogenesis, hox patterning), as well as Pareto evolution. We detail the program architecture based on C, Python 3, and a Jupyter interface for project configuration and network analysis. We illustrate the predictive power of φ-evo by first recovering the asymmetrical structure of the lac operon regulation from an objective function with symmetrical constraints. Second, we use the problem of hox-like embryonic patterning to show how a single effective fitness can emerge from multi-objective (Pareto) evolution. φ-evo provides an efficient approach and user-friendly interface for the phenotypic prediction of networks and the numerical study of evolution itself.