The Journal of Physical Chemistry B

Lipid nanoparticles (LNPs) are a leading drug delivery platform for mRNA or other nucleic acid-based therapeutics. LNP platforms are typically composed of ionizable aminolipids, phospholipids, sterols, and lipids tagged with polyethylene glycol. The ionizable aminolipids are typically cationic at low pH, allowing them to encapsulate negatively charged mRNA. The pH at which the ionizable head groups change charge states, the apparent pKa, is crucial to understand the characteristics and formulation of LNP. However, this is difficult to measure as the apparent pKa differs from the pKa of the aminolipids in bulk solution due to the complex chemical and charge environment. In this study, we use molecular dynamics (MD) simulations with alchemical free energy perturbation to calculate the pKa shift as a function of lipid composition, treating LNP-like and vesicle-like environments. Our results show that the pH-dependent structure of the systems affects the trends in pKa shifts in complex ways, driven by factors including surface electrostatics and lipid internalization. Our all-atom simulation protocol allows us to efficiently estimate the apparent pKa of LNP-like models formed with novel ionizable aminolipids and estimate how it will change with composition.

Amyloid {beta}-protein (A{beta}), which is known for its role in Alzheimer's disease (AD), is also involved in several physiological functions. Of the two predominant isoforms, A{beta}40 and A{beta}42, the latter is more aggregation-prone and more active in health and disease. In the brain, A{beta} interacts with free lipids, which may affect its assembly pathways. Here, thioflavin T (ThT) fluorescence spectroscopy is combined with molecular dynamics (MD) to investigate A{beta}40 and A{beta}42 co-assembly with free dimyristoylphosphatidylcholine (DMPC) and DMPC/cholesterol (CHOL) lipids. ThT measurements at several protein-to-lipid (PL) ratios show isoform- and lipid composition-dependent kinetics of A{beta} fibril formation with clear isoform-dependent lipid effects at a PL ratio of 1:5. Early co-assembly stages of six A{beta}40/A{beta}42 with DMPC and DMPC/CHOL lipids at this PL ratio are then examined by MD. MD results indicate that lipids alter the secondary structure more and interact more avidly with A{beta}40 than with A{beta}42. In turn, A{beta}40 increases the planar order of lipid bicelles more than A{beta}42. Unlike A{beta}40, A{beta}42 decreases the nematic order of CHOL. In DMPC/CHOL lipids, A{beta}42 but not A{beta}40 exhibits two A{beta}-lipid interaction modes associated with mutually exclusive A{beta}42-lipid and A{beta}42-A{beta}42 interactions. Our MD findings provide a plausible explanation for an experimentally observed increase in the lag time for A{beta}40 fibril formation in DMPC lipids and even more so in DMPC/CHOL lipids that contrasts with much smaller effects of lipids on A{beta}42 fibril formation and offer additional atomistic-level insights into A{beta} co-assembly with lipids amenable to experimental testing.

Biomolecular condensates are condensed assemblies of biomolecules that form through the process of liquid phase separation. Condensates in biology typically function as membraneless organelles, providing compartmentalization in the absence of a dividing lipid membrane. The molecular make-up of different condensates includes diverse multivalent proteins and nucleic acids as the primary drivers, many of them including significant fractions of intrinsically disordered regions (IDRs). To date, the sequence to phase separation relationship of IDRs has focused largely on one protein at a time, studying single-component condensate formation, or single-component partitioning into condensates. The co-phase separation and mixing of two or more IDRs is considerably more complex as both sequences can vary widely in their self- and cross-interactions, as well as their relative abundance in solution. It is unclear that a rule which predicts how a single sequence behaves will also predict what happens when two sequences are mixed. In this study, we disentangle the influence of sequence from that of composition using a set of 18 LAF-1 RGG variants that keep the same length and amino-acid composition and change only the order of the residues. This lets us vary charge patterning and, to a lesser extent, hydropathy patterning while keeping protein composition fixed. By themselves, the sequences phase separation and single-chain compaction are controlled by their degree of charge and hydropathy patterning. Within single-component condensed phases, each sequence adopts a more extended conformational ensemble, due to a more favorable, selfsolvated environment. We find that mixing two IDRs together into a condensate causes this universal scaling behavior to break, impacted by the relative interactions of the two components and overall composition of the slab. We find two different qualitative behaviors, one characterized by cooperative co-condensation when both sequences are subcritical, and the other by scaffold-client behavior when one sequence is supercritical. The scaffold-client systems generally show a high degree of demixing, while the co-condensing systems are generally quite well-mixed in the dense phase. This is surprising because even in cases where both partners have significantly different patterning parameters, they still mix. Thus, the descriptor that predicts a sequence's behavior alone can help indicate whether it will mix with or separate from a second component, but it does not fully determine the outcome on its own.

Simulations have emerged as a pillar in biophysics to understand behavior at the molecular scale, in particular for proteins such as intrinsically disordered proteins. These often show transient folding with long-lived states that are challenging to efficiently sample using conventional simulations. Here, we show that Hamiltonian replica-exchange at the level of hydrogen bonds can be used to systematically explore the conformational landscape of proteins. Investigating the IM30 protein, a partially alpha helical protein, under the PLUM coarse-grain force-field, we show that this approach straightforwardly allows characterization of local helix stability, which would be otherwise hard to obtain. For instance, we show that some regions of the conserved coiled-coil structure are less stable than others. By combining the different replicas with principal component analysis, we are able to dissect the conformational landscape of the IM30 protein. Taken together, this indicates that enhanced sampling remains an important part of simulations, allowing insights that cannot be easily obtained in traditional simulations.

Phase separating biopolymers are often described by the sticker-spacer model, which accounts for non-attractive linkers that connect discrete attractive moieties. "Associative polymer" theories describe these systems as two coexisting fluids of stickers and spacers, respectively. In such theories the stickers and spacers are decoupled in the sense that sticker binding does not affect spacer conformations or vice versa. Informed by coarse-grained simulations, we develop a phenomenological mean-field theory to determine the microscopic coupling between the sticker and spacer degrees of freedom. Accounting for linkers connecting adjacent spacers introduces free energy contributions due to conformational entropy of the spacer and the binding combinatorics of the stickers. These contributions have opposite dependencies on spacer length because longer spacers allow a greater volume to search for binding partners but incur a greater entropy cost upon bond formation. The length dependent terms from these contributions cancel leaving a length-independent elastic term arising from the fact that a small amount of spacer stretching lowers the free energy by increasing the number of possible binding partners. The cancellation of spacer length from the theory justifies the decoupling approximation and supports mean-field treatments of heterogeneous spacers.

Enzymes are central to biological function, catalyzing the chemical transformations that sustain metabolism, signalling, molecular transport, and cellular regulation. Understanding their catalytic activity requires connecting molecular structure and conformational dynamics to measurable reaction kinetics. Classical Michaelis--Menten kinetics describes turnover through a dominant catalytic pathway approaching a single saturation limit, whereas conformational-selection, induced-fit, allosteric, and dynamic-disorder models account for additional complexity arising from conformational exchange and heterogeneous catalytic states. Experimental studies further reveal concentration-dependent changes in pathway usage, cooperative or sigmoidal responses, transitions between distinct turnover regimes, and intermittent single-molecule activity. These behaviours are typically treated within separate kinetic descriptions, leaving their mechanistic relationship within a common physical picture incompletely resolved. Here, we formulate a minimal conformational free-energy landscape with interconverting enzyme states and competing catalytic routes to examine whether these apparently distinct kinetic signatures can arise from a shared physical mechanism. In this framework, substrate availability and conformational barriers redistribute catalytic flux between slower and faster pathways, thereby altering both pathway occupancy and turnover times. Stochastic Gillespie simulations together with deterministic mean-first-passage-time analysis show that different parameter regimes generate low- and high-turnover states, concentration-dependent kinetic crossovers, burst--halt intermittency consistent with single-molecule observations, and effectively Michaelis--Menten-like or sigmoidal allosteric-like responses. The same underlying landscape can therefore produce qualitatively different kinetic behaviours depending on how conformational exchange and substrate capture partition catalytic flux. It also explains how finite substrate windows can mask underlying bimodal behaviour. These results provide a physically interpretable framework linking conformational dynamics, pathway selection, and experimentally observed enzyme kinetics.

Deep learning co-folding and docking models accurately predict ligand binding poses at orthosteric sites yet systematically underperform at allosteric pockets. Here, we demonstrate that this accuracy gap reflects a fundamental biophysical property of local energy landscape topology specifically, the magnitude of frustration quenching upon ligand binding rather than an intrinsic algorithmic defect. By evaluating leading co-folding and docking paradigms across curated benchmarks and large-scale uncurated datasets, we show that AI prediction success strongly tracks frustration quenching which the degree to which ligand binding relieves local energetic strain to form a steep energy funnel. Topologically, frustration-weighted residue interaction networks reveal that orthosteric pockets act as high-betweenness communication hubs embedded within contiguous, minimally frustrated pathways. In contrast, allosteric sites reside in low-betweenness peripheral regions with fragmented frustration profiles, presenting flatter, entropy-dominated landscapes that challenge structure prediction algorithms. Comparing generative diffusion with single-shot regression demonstrates that multi-pose sampling capacity is required to cross energy barriers and discover the frustration funnel, whereas joint receptor-ligand coordinate co-adaptation governs local optimization within the funnel. Collectively, this study reframes the allosteric "blind spot" as a quantitative property of energy landscape architecture rather than a defect of any specific predictive framework. We demonstrate that frustration quenching magnitude and structural network centrality serve as physical descriptors that define the intrinsic limits of AI performance, reframing AI accuracy from a benchmark metric into a physics-grounded quantitative reporter of macromolecular binding landscape architecture.

Fluorescent base analogues have proven to be valuable probes of RNA structure. Pyrrolocytosine (pC), an analogue of cytosine, exhibits highly environment-sensitive fluorescence within RNA and is strongly quenched in hydrogen-bonded contexts. In this work, we incorporated pC into the aptamer domain of the B. subtilis guanine riboswitch to determine if this quenching mechanism could allow for sensing of RNA-small molecule interactions. We utilized complementary fluorescence spectroscopy methods to under-stand the functional impacts and ligand-sensitivity of pC substitutions distal to and within the binding pocket. We found that pC substitution within a static structural region exhibits the expected ligand-independent fluorescence properties. When placed in the ligand binding pocket, pC exhibits a moderately decreased affinity for the ligands guanine (G) and hypoxanthine (Hx) while maintaining high specificity for G. We found that pC behaves as a turn-off sensor, with distinct changes in fluorescence upon G or Hx binding. These differences are dependent on the number of hydrogen bonds formed with pC and are resolvable in both time-dependent and steady-state fluorescence measurements. Our results show that pC can be used to study RNA-small molecule interactions and can discriminate between similar ligands even when they have identical binding modes.

Liquid-liquid phase separation (LLPS) driven by intrinsically disordered protein regions underlies the formation of membraneless organelles. The role of these structures in cell biology is an active area of research, yet their physical understanding remains less developed than that of protein assemblies with well-defined, rigid tertiary structures. The amino acid composition of disordered regions, particularly the abundance of charged residues, is known to modulate phase behavior. These factors govern accessible conformations, the assembly of compact sticker clusters, and the porosity of the resulting polymer networks. In contrast, the spatial distribution of side-chain volumes remains a comparatively understudied sequence determinant. Here, we employ a model that captures the patterning of side-chain volumes and interaction strengths without specifying chemical identity to show how sequence blockiness modulates the phase-nucleation propensity, connectivity, and compactness of polypeptide-like polymer assemblies. Using a library of polymers with identical composition but permuted residue arrangements, we show that clustering of bulky residues generates cooperative sticker domains and identify the threshold blockiness required to stabilize polymer networks. Coarse-grained simulations and mean-field theory reveal that this effect arises from an interplay among steric repulsion, solvent entropy, and higher-valency interactions, whereby blocky patterns promote the formation of multi-node percolated networks. Segregation of stickers and spacers is therefore one of the sequence parameters governing LLPS which may be useful for interpreting the evolution of disordered protein sequences, high-throughput proteome screening, and engineering of stimuli-responsive biomaterials. These rules may be exploited to predetermine condensate stability, viscoelasticity, and molecular exchange rates without altering chemical functionality.

The development of NIR fluorescent dyes with favorable optical properties is of great importance especially for applications within the field of optical imaging. In this study, we report the design, synthesis and photophysical characterization of novel BODIPY-Xanthene hybrid dyes obtained via Knoevenagel condensation between an asymmetrical BODIPY core and the functionalized xanthene aldehydes intermediates. The synthesized dyes ex-hibit absorption (667 nm) and emission bands (720-722 nm) within the NIR region. Detailed UV-Vis and fluo-rescence studies were performed and molar extinction coefficients and stokes shifts also calculated. Moreover, findings highlighting the influence of structural modifications on the optical behavior of the hybrid dyes and their potential utility in optical imaging applications are reported.

The prevailing view holds that simpler animate beings predating the dawn of cellular life once existed, yet they have long since vanished from the present-day Earth. Our hypothesis posits that these animate beings persist to this day. To this end, we devised a long-term experiment spanning over a decade, keeping Staphylococcus aureus (S. aureus) within a sealed aqueous system of pure water. The findings illustrated that, upon the complete cell death (CCD) of the S. aureus, as cellular remnants progressively succumbed to dissolution, the aqueous solution underwent self-purification, bringing forth a class of lipid bilayer membrane microspheres containing RNA and proteins. These structures maintained long-term sustainable stability within the thermodynamic storm of water molecules and underwent dynamic size fluctuations over time - collectively exhibited phenomena indicative of being "alive". This study reveals that the cell, upon complete cell death, undergoes reversion to a living entity simpler than the cell itself - the Meta Body (MB). The discovery of MB opens an entire re-conceptualization of what death ultimately brings.

Nanoplastic contamination is increasingly recognized as a biochemical stressor, yet the molecular determinants governing how polymer fragment size dictates protein-level interactions remain poorly understood. Here, we combine molecular docking and all-atom molecular dynamics simulations to characterize the interaction of polyethylene (PE) oligomers of increasing length (n = 3, 5, 7, and 14 repeat units) with human catalase, a tetrameric heme enzyme central to cellular antioxidant defense. Single-chain simulations reveal that short PE fragments (3-, 5-, and 7-mer) migrate from an initial domain-connector pose toward a heme-proximal, previously characterized inhibitor-binding site, whereas the 14-mer remains kinetically confined to a peripheral surface site, implicating short-chain PE as a potential catalase inhibitor. In multichain corona systems, backbone dynamics show a non-monotonic, chain-length-dependent destabilization, with the 3- and 5-mer inducing the greatest structural perturbation and the 14-mer best preserving native-like dynamics despite forming an extensive, percolating surface network across all four subunits. MM-PBSA free energy decomposition identifies van der Waals interactions as the dominant thermodynamic driver of binding, while electrostatic surface mapping indicates that cationic surface patches instead govern long-range spatial targeting of PE chains. These findings establish a framework linking nanoplastic fragment size to protein-level toxicity, with direct implications for assessing the biochemical risk of environmentally weathered polyethylene.

Aromatic side chains carry the optical and redox chemistry of peptides, and lengthening one is widely expected to extend its conjugation and narrow its HOMO-LUMO gap. We test that expectation with plane-wave density functional theory on 22 isolated neutral peptides NH2-(X)n-COOH (X = Phe, Tyr, Trp, Cys; n = 1 to 5, and n = 10 for Cys and Trp). The gap does narrow, at the same rate for all three aromatic residues, i.e., -0.17 to -0.18 eV per residue, even though benzene, phenol and indole are very different chromophores. Residue-resolved projections reveal why: nothing delocalises. Every aromatic frontier orbital is 97 to 100 % confined to a single residue and the HOMO participation number saturates at one ring. Each residue instead keeps its own local gap: for Trp it is invariant to within 0.03 eV over n = 2 to 10, while over that same span the global gap falls by 1.19 eV. The global gap is therefore an extreme-value functional of the residue site energies, gap(n) =<g_f>-{Delta}(n), whose alignment penalty accounts for the entire effect: the polar backbone generates a monotonic internal electrostatic ramp that leaves the two gap edges at opposite ends of the chain, 32 [A] apart. We set out the resulting design rules for peptide-based bio-organic semiconductors.

Understanding how conformational dynamics regulate protein complex assembly remains a central challenge in molecular systems biology. Here, we develop a multiscale modeling framework that integrates all-atom molecular dynamics (MD) simulations with rule-based kinetic modeling to investigate the formation of the PP1-GADD34-eIF2 complex, a critical regulator of the integrated stress response. Using umbrella sampling, we compute the potential of mean force (PMF) for key interactions, revealing strong thermodynamic driving forces for eIF2 binding ({Delta}G = -89.5 kJ/mol, KD {approx} 0.07 fM) and moderate affinity for PP1-GADD34 association ({Delta}G = -40.7 kJ/mol, KD {approx} 0.138 M). These energetics inform a PySB-based model that incorporates GADD34's folding state as a continuous variable ({varphi}), linking conformational transitions to holoenzyme assembly and activity. Simulations show that catalytic efficiency is maximized when GADD34 folding free energy is 20 kJ/mol and {varphi} = 0.9, reflecting a highly ordered state stabilized by actin and PP1 binding. Comparative analysis of energy-constrained and optimized parameter regimes reveals that folding-dependent assembly enhances both eIF2 dephosphorylation and information transmission, with channel capacities increasing from <0.002 bits to >5.5 bits. These results demonstrate how conformational regulation encodes system-level function and underscore the utility of multiscale models in bridging molecular energetics with dynamic biochemical control.

G protein-coupled receptors (GPCRs) represent the largest membrane protein family in the human body and the major targets of FDA-approved medications. Unlike some other physiological proteins, GPCRs are highly plastic and often exist as collections of conformational ensembles in the environment to exert their function. Therefore, understanding how a GPCR adopts different conformational ensembles in response to ligands and signaling partners is essential for drug development. 19F-NMR has emerged as one of the most promising tools in this regard; however, a well-established 19F-labeling system is still lacking, including an effective 19F probe that meets both environmental susceptibility and NMR sensitivity requirements, even though progress has been made dramatically in recent years. Thus, this manuscript reports a novel conformational probe (4-(bromomethyl)-ethoxy-2-(trifluoromethyl)benzene, BTMB) that offers paramount benefits for future GPCR conformational dynamics studies. To rationalize the mechanism behind BTMB's superiority for future probe development, we performed MD simulations, referenced to the current state-of-the-art probe, BTFMA. Our study suggests that the spatial proximity of aromatic residues significantly influences the chemical shift dispersion and linewidths of related 19F-probe-profiled conformational states, as well as the rigidity and compactness of -CF3 in the target protein.

Proteolysis-targeting chimeras (PROTACs) are large, flexible molecules that frequently extend beyond conventional drug-like chemical space, including Lipinski's rule-of-five boundaries. Their membrane permeability has often been linked to molecular chameleonicity and the ability to adopt compact conformations with reduced polar surface exposure; however, the underlying conformational determinants remain unclear. Here, we investigated 20 PROTACs spanning distinct passive-permeability classes using enhanced-sampling molecular dynamics (ES-MD). All permeability classes accessed compact states with low radius of gyration (Rg) and polar surface area (PSA), indicating that compact-state accessibility alone does not distinguish permeable from non-permeable PROTACs. We therefore introduce maximum ring size (MRS), defined as the size of the largest intramolecular hydrogen-bonded ring, as a metric for identifying compact conformations stabilized by long-range intramolecular hydrogen bonding. Like the other descriptors examined, MRS neither separates nor ranks the permeability classes, but helps locate folded states in the large ensemble. Representative compact conformations from selected highly permeable, moderately permeable, and non-permeable compounds were subsequently examined by all-atom unbiased MD in water and chloroform. The highly permeable PROTAC held a closed-flat ensemble in both environments, but in two structurally distinct arrangements, whereas the other two redistributed across heterogeneous ensembles. Passive diffusion therefore appears to depend on the population, stability, and environment-dependent persistence of permeable-like states rather than on compactness alone.

P-type ATPases maintain cellular metal homeostasis by coupling ATP hydrolysis to the active translocation of ions across biological membranes. Within this superfamily, P1B -type ATPases play a central role in the transport and detoxification of transition metals such as Cu+ and Ag+. Despite the availability of several crystallographic structures for bacterial ATPases, molecular determinants governing ion selectivity, coordination dynamics, and transport efficiency are not yet fully resolved, particularly for plant homologs, whose conformational landscapes have not been explored in detail at atomistic resolution. In this study, we combine molecular dynamics (MD) simulations with enhanced sampling through metadynamics to characterize the conformational dynamics and ion-binding mechanisms of representative heavy-metal P-type ATPases. By comparing bacterial and plant homologs in phosphorylated and dephosphorylated states, we examine how phosphorylation is associated with changes in structural plasticity, channel accessibility and ion coordination environments. The simulations indicate phosphorylation-dependent rearrangements of the cytosolic domains and transmembrane helices, which may alter access to the metal-binding pathway. Enhanced sampling identifies distinct conformational basins and possible transition pathways along functionally relevant collective variables, allowing characterization of the free-energy landscape associated with ion displacement within the transmembrane region. Together, these results provide an atomistic perspective on the relationship between metal coordination and protein conformational dynamics. Overall, our findings support a model in which phosphorylation state, structural dynamics, and local coordination environments collectively contribute to the differential behavior of metal ions in P1B -type ATPases.

Nanoplastic interactions with cell membranes can influence particle uptake, translocation, and biological effects, making their molecular description important for assessing the environmental and biological consequences of plastic pollution. However, molecular simulations generally represent nanoplastics using monodisperse polymer chains, whereas nanoplastics formed by environmental degradation are polydisperse. Here, we construct 4 nm polyethylene terephthalate (PET), polyethylene (PE), and polystyrene (PS) nanoparticles with lognormal molecular-weight distributions reported for degraded polymers, and with melt-like chain packing and entanglement. Using Martini coarse-grained molecular dynamics, we simulate their interactions for 10 microseconds with three lipid bilayers of increasing complexity. PE and PS insert rapidly and remain largely intact, whereas PET remains surface-associated and progressively releases individual chains. Fluid, polyunsaturated lipid environments undergo greater deformation and promote substantially more chain release, up to 56% of the chains for PET and 43% for PS. Release begins with the shortest chains and progressively extends to longer chains, while semicrystalline PE remains largely intact. In contrast, a size-matched monodisperse PS particle releases no chains and minimally perturbs the membrane. These results identify the molecular-weight distribution as a key determinant of nanoplastic-membrane interactions, and indicate that uniform model particles underestimate the release of polymer chains into biological membranes.

Force spectroscopy enables direct investigation of the interplay between free energy and transition kinetics in proteins and nucleic acids. However, multi-domain proteins often display multiple intermediate structures with diverse stabilities and kinetics, making equilibrium conditions difficult to achieve and out-of-equilibrium experiments challenging to interpret. We introduce a single-molecule force spectroscopy assay using periodic forces and high-resolution magnetic tweezers to bridge different stabilities, selectively enhance intermediate populations, and rigorously analyze multi-domain protein folding kinetics at quasi-equilibrium. By applying well-defined periodic square force functions with tunable steady states, we first validate our framework on the two-state folder {lambda}6-85, demonstrating that periodic force experiments can reproduce equilibrium kinetics. Extending this approach to the multi-domain protein mimic (Protein L), we show that tuning force, frequency, and amplitude enhances populations of distinct intermediate states. Finally, we dissect the entangled states of the hybrid two-domain protein {lambda}-L, where a 100-fold difference in domain kinetics precludes equilibrium analysis, by expanding from a two-state to a three-state periodic force protocol to direct intermediate populations. Our assay and analysis framework open new possibilities for deciphering complex multi-domain folds and their multi-dimensional folding pathways.

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(N3) 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.