Multivalent Surface Search Dynamics Shape Bacteriophage Adsorption Efficiency: A Stochastic Model of Tail Fiber Optimization

Abstract

Phages must locate and bind to bacterial surface receptors to initiate infection. Their tail fiber configuration critically influences this process. We develop a stochastic model describing surface search as a renewal process, incorporating attachment, detachment, and target-finding steps. Using both numerical simulations and analytical calculations, we quantify how tail fiber number, attachment-detachment rates, and geometric constraints impact the mean and the distribution of time to successful adsorption. Notably, the search efficiency shows a nonmonotonic dependence on tail fiber number, governed by a trade-off between binding stability and diffusion-mediated mobility. This optimum shifts depending on the effective bacterial density, target radius, and fiber reach. Short fiber reach imposes severe geometric constraints, reducing mobility at high tail fiber counts and leading to performance degradation. Our findings suggest that phage adsorption strategies are shaped by a balance between anchoring and exploration, with evolutionary implications for tail fiber design and infection efficiency.