Bayes-PD: Exploring a Sequence to Binding Bayesian Neural Network model trained on Phage Display data

TL;DR

Bayes-PD addresses learning from noisy phage display data to predict protein–target binding affinities by integrating a Bayesian neural network within a loop that simulates the experimental selection and its noise. It combines sequence embeddings from a lightweight protein language model, Poissonized count modeling to reflect sampling, and a CNN-based Bayesian predictor trained with stochastic variational inference, yielding calibrated uncertainty and explainable attributions. The approach demonstrates meaningful alignment with actual binding measurements, shows generalization to generated sequences, and provides uncertainty-aware criteria to guide experimental prioritization. This framework offers a principled, scalable means to extract reliable sequence–binding insights from noisy phage display data and to inform design decisions in protein engineering.

Abstract

Phage display is a powerful laboratory technique used to study the interactions between proteins and other molecules, whether other proteins, peptides, DNA or RNA. The under-utilisation of this data in conjunction with deep learning models for protein design may be attributed to; high experimental noise levels; the complex nature of data pre-processing; and difficulty interpreting these experimental results. In this work, we propose a novel approach utilising a Bayesian Neural Network within a training loop, in order to simulate the phage display experiment and its associated noise. Our goal is to investigate how understanding the experimental noise and model uncertainty can enable the reliable application of such models to reliably interpret phage display experiments. We validate our approach using actual binding affinity measurements instead of relying solely on proxy values derived from 'held-out' phage display rounds.

Figures (21)

• Figure 1: Schematic of a selection step in phage display.
• Figure 2: Phage display Poisson model. Unsequenced rate of occurrence $\Lambda^N_i$ stands for the parameters of our Poisson law at the relevant experimental population size, before downscaling to obtain the sequenced rate of occurrence $\lambda^N_i$ which is measured (sequenced).
• Figure 3: Correlation plots with the dissociation constant test set (A) for$\mathbf{target_1}$: Correlation with model prediction. Error bars on predicting binding probability (y axis) are estimated errors from N samples of the models while the actual dot markers represent the estimated mean from that same sampling. Error bars on $K_{d}$ are uncertainty from curve fitting. (B) : Correlation with raw Selectivities (Exp 1-6). Error bars on selectivity are estimated from counting noise following $\frac{\Delta s}{s} = \frac{1}{\sqrt{C_i^N}} +\frac{1}{\sqrt{C_i^{N+1}}}+\mathcal{O}(C_{tot}^N)$. Error bars on $K_{d}$ are uncertainty from curve fitting. 95% Confidence intervals on correlation are based on 97.5% and 2.5% percentiles of N samples of the model compared to N Gaussian samples of the $K_{d}$ values. (In our case, N = 1000).
• Figure 4: Integrated Gradient bayesian explanation of a sequence. Dash line is a visual representation of the end of the sequence: sequences are batched at prediction time and thus need padding.
• Figure 5: Error handling possibilities within the Bayesian model. (A): Error handling based on relative standard deviation. (B): Error handling based on AUC Mean metric