Sequestration-based Protein Neural Networks Tolerate the Effects of Shared Translational Resources

Biochemical neural networks offer a promising framework for implementing advanced computation in living cells, yet how competition for shared cellular resources shapes their behavior remains poorly characterized. In this work, we develop a resource-aware mathematical framework to analyze how competition for ribosomes affects protein neural networks implemented via molecular sequestration in bacterial systems. Focusing on classification tasks, we show that when all mRNA species share identical ribosome-binding affinities, competition induces a uniform rescaling of the network's effective weights, reducing the output magnitude while preserving the geometry of the decision boundary. When these affinities differ, competition introduces curvature in the decision boundary, transforming a linear classifier into a nonlinear one through resource coupling. This curvature is constrained to a well-defined region of the input space whose extent is determined by the degree of variability in the binding affinities, making the effect both predictable and, potentially, exploitable for design. Next, we numerically extend our analysis from a single perceptron to multi-layer architectures with two hidden-layer nodes and show that, for both closed and non-convex decision boundaries, resource competition preserves the boundary geometry in the homogeneous-affinity case, while in the heterogeneous case, curvature distortions from hidden-layer nodes propagate and compose at the output within a bounded uncertainty region. Finally, we incorporate growth-mediated feedback into the framework and show that the structural form of the activation function and decision boundary is preserved. Overall, our results provide a quantitative basis for understanding how translational resource competition shapes the behavior of protein-level molecular classifiers.