Computational Modeling of Mechanical Systems: From Disordered Networks to Protein Allostery

Mechanical strain provides a unifying framework for connecting structure, dynamics, and function across scales; from engineered metamaterials to biological macromolecules. This dissertation establishes strain as a mechanistic bridge in proteins and leverages it for rational therapeutic design. We begin by optimizing two‑dimensional spring networks toward auxetic (negative Poisson's ratio) states, enriching them in acute, re‑entrant angles. These motifs simultaneously enable compression‑activated acoustic bandgaps, revealing a design principle, small‑angle enrichment, that achieves multiple functional goals through a single topological feature. Building on this, we introduce Collective Variable Free Energy Surface Tailoring (CV‑\\FEST): short unbiased simulations yield high‑dimensional structural descriptors, which Harmonic Linear Discriminant Analysis reduces to a few collective variables encoding dominant degrees of freedom. Targeted bond modifications then reshape the free energy landscape predictably, enabling control over responses like allostery or strain propagation. We apply this strain‑centric approach to the PDZ3 domain of PSD‑95. Atomistic strain tensors from molecular dynamics colocalize with evolutionarily conserved residues (from Statistical Coupling Analysis) and NMR‑perturbed sites, establishing strain as the physical link between sequence co‑evolution and functional mechanics. A strain-derived collective variable, captures the deformation coupling the ligand‑binding groove to a distal helix, and its free energy surface reproduces the experimentally observed discrete‑state switch, demonstrating strain's dual role as a diagnostic and design variable. The framework is extended to SARS‑CoV‑2 targets: in the RNA‑dependent RNA polymerase, remdesivir induces strain‑mediated active‑site destabilization consistent with delayed chain termination; in the main protease (Mpro), ebselen binds an allosteric site at the domain II–III interface, generating shear strain that constricts the catalytic cleft and inhibits function. Together, these results show that mechanical strain is a quantifiable, tunable descriptor for engineering both materials and proteins. By integrating topological optimization, data‑driven collective variables, and enhanced sampling, this work provides a general workflow for inverse design of adaptive systems and allosteric therapeutics. Future efforts will embed strain‑based coordinates into generative AI to automate the creation of structures, synthetic or biological, tailored to desired deformation and function.