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

Biomolecular neural networks (BNNs) offer a promising framework for implementing advanced computation in living cells, but their performance in vivo is fundamentally constrained by competition for cellular resources. In this work, we develop a mathematical and computational framework to analyze how shared translational resources (i.e., competition for ribosomes) affect protein neural networks implemented via molecular sequestration. Focusing on classification tasks, we show that ribosome competition primarily induces a rescaling of the neural networks effective weights, while preserving the shape of the decision boundary under identical mRNA-ribosome affinities. However, when these affinities are heterogeneous, limited resources lead to a bounded bending of the decision boundary, generating a well-defined uncertainty region. Importantly, classification remains reliable outside this region. Then, we extend our analysis from a perceptron to a multi-layer architectures (MLP), and illustrate that robustness to resource competition is maintained for an MLP with 2 nodes in the hidden layer. To our knowledge, this is the first protein-level neural-network circuit design shown to tolerate competition for translational resources without auxiliary insulation or feedback control.