Integrating molecular simulations with experimental characterization using a series alignment algorithm

Quantitative comparison between molecular simulations and experimental characterization is often complicated by systematic differences in accessible timescales and control parameters, such that exact matching in absolute units is not generally expected. We introduce a series alignment framework that enables order-preserving, quantitative matching between simulated and experimental observables without requiring one-to-one correspondence in time or temperature. The method formulates the comparison as a global optimization problem over a pairwise distance matrix and identifies an optimal monotonic mapping using dynamic programming. We demonstrate the approach in two case studies: quasi-elastic neutron scattering (QENS) of hydrated lysozyme aligned with molecular dynamics simulations across a range of temperatures and time-resolved small angle X-ray scattering (SAXS) and dynamic light scattering (DLS) measurements of nanoparticle assembly aligned with coarse-grained simulations. In both cases, the alignment reveals systematic offsets between experimental and simulated conditions while preserving physically meaningful trends. This work establishes series alignment as a general framework for integrating simulations with experimental characterization data.