Year: 2026
Type: preprint
Abstract: Nucleic acid secondary structure thermodynamic models have great utility for the analysis and design of nucleic acid structures, devices, and systems, yet their complexity and piecemeal development over decades pose challenges to further innovation. Employing different functional forms for each loop type within a structure, existing nearest neighbor (NN) models necessitate numerous loop-specific dynamic programming recursions in order to calculate physical quantities of interest. Here, we derive and implement a new class of models based on transfer matrices, yielding a single functional form for the free energy of all loop types (as the trace of a matrix product) and a single dynamic programming recursion for calculating physical quantities of interest. This new class of models has additional attractive properties: 1) incorporating a subensemble of states describing proximal interactions within each loop, 2) approximating logarithmic entropic scaling for all closed loops, 3) offering the opportunity to model correlations between the subensembles of neighboring loops by generalizing transfer matrices to tensors, and 4) providing a basis for systematically adjusting the number of model parameters to enhance accuracy as new empirical data become available for parameter regression. We use literature experimental data to regress parameters for representative new transfer matrix models, observing accuracy as good as or better than that of existing NN models, yet using dramatically fewer parameters (e.g., dozens vs hundreds or thousands). For complex ensembles containing an arbitrary number of interacting nucleic acid strands totaling N nucleotides, the new single recursion leads to exact dynamic programs for calculating diverse physical quantities (including the partition function, equilibrium base-pairing probabilities, minimum free energy and suboptimal proxy structures, Boltzmann-sampled secondary structures, and gradient of the partition function) with O ( N 3 ) time complexity. The simplicity of the new partition function dynamic program enables overflow-safe partition function calculations using renormalization to achieve scalability for large complexes (e.g., 50,000 nt) as well as formulation using a global matrix multiplication primitive that facilitates GPU acceleration, yielding speedups of an order of magnitude relative to NN partition function algorithms for large complexes. The new class of transfer matrix and tensor models provides an elegant framework for future efforts to advance the accuracy, speed, and scope of computational nucleic acid analysis and design. Relevance to Life Sciences The programmable chemistry of nucleic acid base-pairing is central to the biological circuits that orchestrate life and to the emerging fields of molecular programming, nucleic acid nanotechnology, and synthetic biology. Mathematical Content This paper introduces the use of transfer matrices and tensor contraction to model nucleic acid secondary structure thermodynamics, providing an extensible framework for enhancing model fidelity as new experimental training data become available, and leading to dramatically simplified dynamic programming recursions that can be formulated linear algebraically for GPU acceleration.
Authors: Mark E. Fornace, Niles A. Pierce
Language: English
Subfield: Molecular Biology
Domain: Life Sciences
Open Access status: green
Funders: National Science Foundation, U.S. Department of Energy, National Energy Research Scientific Computing Center, Beckman Institute, California Institute of Technology, Office of Advanced Cyberinfrastructure, Division of Chemistry, Advanced Scientific Computing Research, Lawrence Berkeley National Laboratory
Awards: G1079818582, G1143651532, Software Elements: NUPACK: Molecular Programming in the Cloud, G122673668, G1286236842, G1453181110, G1555197637, G1677143136, G1787346651, G1799333409, G1863003419, Track 4: Advanced CI Coordination Ecosystem: Monitoring and Measurement Services, G1914717814, INSPIRE: Computational Parameterization of Nucleic Acid Secondary Structure Models, G216176624, G2260841242, G2514109075, G2946657097, G3136028036, G338811424, G3562386289, Track 1: ACCESS Resource Allocations Marketplace and Platform Services (RAMPS), G4010157413, G4021360626, G42916606, G4533910268, ACO: An Open CI Ecosystem to Advance Scientific Discovery (OpenCI), G4890976013, G5076365615, Track 3: COre National Ecosystem for CyberinfrasTructure (CONECT), G5094606986, G5367127336, G5449939725, G5464919783, G5754141309, NUPACK: New Capabilities for Nucleic Acid Analysis and Design, G7354628648, G7916508619, Track 2: Customized Multi-tier Assistance, Training, and Computational Help (MATCH) for End User ACCESS to CI, G8994211811
OpenAlex ID: W7220953800