resource competition

This work explores the integration of machine learning (ML) and mechanistic models (MM). While ML has demonstrated remarkable success in data-driven modeling across engineering, biology, and other scientific fields, MM remain essential for their interpretability and capacity to extrapolate beyond observed conditions based on established principles such as chemical kinetics and physiological processes. However, MM can be labor-intensive to construct and often rely on simplifying assumptions that may not fully capture real-world complexity. It is thus desirable to combine MM and ML approaches so as to enable more robust predictions, enhanced system insights, and improved handling of sparse or noisy data. A key challenge when doing so is ensuring that ML components do not disregard mechanistic information, potentially leading to overfitting or reduced interpretability. To address that challenge, this paper introduces the idea of Partially Uncertain Model Structures (PUMS) and investigates conditions that discourage the ML components from ignoring mechanistic constraints. This work also introduces the concept of embedded Physics-Informed Neural Networks (ePINNs), which consist of two loss-sharing neural networks that seamlessly blend ML and MM components. This work arose in the study of the context problem in synthetic biology. Engineered genetic circuits may exhibit unexpected behavior in living cells due to resource sharing. To illustrate the advantages of the ePINNs approach, this paper applies the framework to a gene network model subject to resource competition, demonstrating the effectiveness of this hybrid modeling approach in capturing complex system interactions while maintaining physical consistency.

Understanding how opposing regulatory factors shape gene expression is essential for understanding complex biological systems. A motivating observation, drawn from cancer epigenetics, is that removing an activating factor can sometimes lead to higher, not lower, expression of a gene that is also subject to a repressing factor. Prior theoretical work explained this counterintuitive behavior by competition of repressors and activators for genomic binding sites. However, it has been difficult to test this directly in natural systems, where layers of regulation obscure causal relationships. This paper introduces a fully synthetic, tunable genetic platform in a prokaryotic model system that reconstitutes this competition mechanism in a controlled and isolated setting. The genetic platform contains a target gene with binding sites for both an activator and a repressor, together with separate overlapping decoy binding sites for the same regulators. Activator and repressor functions are implemented using CRISPRa and CRISPRi, which permit independent control of regulator expression levels, design of the binding sites, and modulation of the binding affinities. Using this minimal system, we demonstrate that increasing activator expression level can reduce expression of the target gene when both regulators are present, consistent with the hypothesis that additional activator molecules displace the repressor from decoy sites, which becomes available to repress the target. By demonstrating how competition for genomic binding sites can invert expected regulatory responses, this synthetic framework provides a system for understanding similar paradoxical behaviors in natural regulatory networks and establishes a foundation for future studies in more complex mammalian contexts.

In the context of epigenetic transformations in cancer metastasis, a puzzling effect was recently discovered, in which the elimination (knock-out) of an activating regulatory element leads to increased (rather than decreased) activity of the element being regulated. It has been postulated that this paradoxical behavior can be explained by activating and repressing transcription factors competing for binding to other possible targets. It is very difficult to prove this hypothesis in mammalian cells, due to the large number of potential players and the complexity of endogenous intracellular regulatory networks. Instead, this paper analyzes this issue through an analogous synthetic biology construct which aims to reproduce the paradoxical behavior using standard bacterial gene expression networks. The paper first reviews the motivating cancer biology work, and then describes a proposed synthetic construct. A mathematical model is formulated, and basic properties of uniqueness of steady states and convergence to equilibria are established, as well as an identification of parameter regimes which should lead to observing such paradoxical phenomena (more activator leads to less activity at steady state). A proof is also given to show that this is a steady-state property, and for initial transients the phenomenon will not be observed. This work adds to the general line of work of resource competition in synthetic circuits.

Synthetic gene circuits require cellular resources, which are often limited. This leads to competition for resources by different genes, which alter a synthetic genetic circuit's behavior. However, the manner in which competition impacts behavior depends on the identity of the "bottleneck" resource which might be difficult to discern from input-output data. In this paper, we aim at classifying the mathematical structures of resource competition in biochemical circuits. We find that some competition structures can be distinguished by their response to different competitors or resource levels. Specifically, we show that some response curves are always linear, convex, or concave. Furthermore, high levels of certain resources protect the behavior from low competition, while others do not. We also show that competition phenotypes respond differently to various interventions. Such differences can be used to eliminate candidate competition mechanisms when constructing models based on given data. On the other hand, we show that different networks can display mathematically equivalent competition phenotypes.

We develop and analyze a general model for large-scale simultaneous mRNA translation and competition for ribosomes. Such models are especially important when dealing with highly expressed genes, as these consume more resources. For our model, we prove that the compound system always converges to a steady-state and that it always entrains or phase locks to periodically time-varying transition rates in any of the mRNA molecules. We use this model to explore the interactions between the various mRNA molecules and ribosomes at steady-state. We show that increasing the length of an mRNA molecule decreases the production rate of all the mRNAs. Increasing any of the codon translation rates in a specific mRNA molecule yields a local effect: an increase in the translation rate of this mRNA, and also a global effect: the translation rates in the other mRNA molecules all increase or all decrease. These results suggest that the effect of codon decoding rates of endogenous and heterologous mRNAs on protein production might be more complicated than previously thought.