Biophysical Journal

Adherent cells must continuously adapt to rapid environmental fluctuations to preserve mechanical integrity. However, conventional theoretical frameworks predominantly rely on quasi-static assumptions, thereby limiting their ability to capture the transient dynamics of cellular responses to high-rate perturbations, such as acute osmotic shocks. To address this limitation, we developed a biophysical model incorporating a Hill-type law that couples active cytoskeletal mechanics to cell-edge velocity, explaining the counterintuitive experimental observation that traction forces transiently decrease during rapid hypotonic swelling despite an increase in cell size. We further construct a kinematic-geometric phase diagram that connects classical quasi-static theories with our dynamic model. Moreover, we show that traction-force dynamics are sensitive to the loading rate and amplitude of osmotic shock. In addition, stiffness-associated simulations and supporting perturbation evidence suggest a cellular stiffness-associated recovery trend in which stiffer cells exhibit faster volume recovery driven by stronger recoil of hydrostatic pressure.

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.

Centrosome positioning is governed by mechanical interactions between the actin and microtubule cytoskeletons, yet the contribution of different actin architectures and their attachment to the cell membrane remains unclear. We use numerical simulations to study a centrosomal array of microtubules interacting with cortical, bulk, and centrosome-associated actin networks, including passive cross-linkers, motor proteins, and ERM-mediated coupling of actin to the cell membrane. We find that bulk and centrosome-associated actin alone are insufficient for robust centrosome centering, whereas sufficiently dense cortical actin promotes centering through steric interactions with growing microtubules. ERM-mediated attachment of cortical actin to the cell membrane enhances this effect, allowing stable centering at lower actin densities. In a two-centrosome system, microtubule interactions generate a spindle-like structure, while the organization of actin and its membrane attachment through ERM regulate centrosome separation. Antagonistic microtubule motors further limit centrosome separation and establish a finite spindle length. These results demonstrate that ERM-mediated coupling of actin to the cell membrane provides an important mechanical link between the actin cortex and microtubule-driven centrosome positioning, influencing both centrosome centering and spindle geometry.

Polyvalent-cation-induced condensation and reentrant transition in double-stranded DNA are classically described by backbone electrostatics. Whether the same principles govern single-stranded DNA, whose solvent-exposed bases can interact within and between chains to form complex phases, is unknown. Here, we employ simulations and experiments to show that the tetravalent cation spermine (Spm4+) drives two equilibrium transitions in poly(dT) and poly(dA). The onset of phase separation, resulting in thermodynamic equilibrium between the dispersed low-density phase and high density coacervate, occurs at a low sequence independent Spm4+ concentration and is primarily driven by charge balance between phosphate groups and Spm4+. Strikingly, the condensed phases are stabilized by at most 1.5 (poly dT) and 2.5 (poly dA) bridging Spm4+ per chain. The ssDNA chains condense to form fluid-like networks without chain collapse. The fluidity of chains in the dense phases is confirmed by fluorescence recovery after photobleaching experiments. Both simulations and experiments show that the range of spermine concentration over which phase coexistence persists is sequence dependent and nearly threefold wider in poly(dA). At higher sequence dependent spermine concentrations, a reentrant phase, characterized by dissolution of the coacervates, emerges. The transition to the reentrant phase occurs when the number of bridging Spm4+ molecules vanishes at high sequence dependent spermine concentration. The combination of experiments and simulations show that the two phase transitions in ssDNA are driven by an interplay of stacking and electrostatic interactions.

Clathrin-mediated endocytosis (CME) is the primary pathway for internalization of extracellular and membrane cargo in eukaryotic cells. It is characterized by a patch of the plasma membrane invaginating and pinching off to generate a cytoplasmic vesicle. Recently, experimental evidence has begun to accumulate in support of proteins assembling into liquid-like condensates at nascent CME sites, but potential functional consequences are not understood. Given that condensate capillary forces can influence membrane bending, we constructed complementary analytical and numerical model systems to probe the mechanical influence of a protein droplet on endocytosis. Model evaluations and analysis reveal that a droplet can regulate the progression of endocytosis by stalling invagination until the droplet grows past a threshold size. After the droplet-mediated brake is released, the droplet provides a force that can drive the membrane bud toward scission. Thus, we propose a ``mechanical timer'' mechanism as a function for protein phase separation in cellular membrane trafficking.

It is important to determine whether native state dynamics drive the misfolding and oligomerization of the prion protein, which are important events in prion disease, and how they are modulated by conformational conversion. Native (N) mouse prion protein (moPrP) is known to form small (OS) and large (OL) oligomers rich in {beta}-sheet, and in this study, photoinduced electron transfer-fluorescence correlation spectroscopy (PET-FCS) has been used to characterize intramolecular dynamics within individual monomeric units in both isolated OS and OL, as well as the diffusion properties of the oligomers. It is estimated that OS and OL comprise of about 15 and 55 monomeric units, respectively. Microsecond dynamics at each of the two regions that are the 1-3 and 2-3 interfaces of native protein are distinct in N, OS and OL, although they occur on very similar timescales. Analysis of the evolution of the distribution of diffusion times, determined using the maximum entropy method, indicates heterogeneity in the oligomerization reaction. Analysis of the change in the fluctuations which occur in two different timescales in the native state ensemble shows that they are damped more at the erstwhile 1-3 interface than the erstwhile 2-3 interface. The difference in the extent of damping at the erstwhile 1-3 and 2-3 interfaces can be explained on the basis of the structural changes known to occur across each region. The changes in dynamics occur concurrently in both regions, indicating that the structural changes accompanying conformational conversion also occur simultaneously during the oligomerization of moPrP.

Actin cross-linkers are essential modulators of the actin cytoskeleton, enabling structural diversity and dynamic remodeling. Among them, calcium/calmodulin-dependent protein kinase II (CaMKII) is unique in serving a dual role as a kinase and as a multivalent structural binder of actin in dendritic spines, where it plays a major role in supporting dendritic spine structure via its {beta} subunit. To understand the basis of the structural function of CaMKII, we quantified the morphology and mechanics of actin bundles formed by CaMKII and directly compared them with bundles assembled by the canonical bivalent cross-linkers -actinin and fascin. Using fluorescence microscopy, we measured contour length, straightness ratio, and persistence length across different cross-linker concentrations. Fascin generated progressively shorter, straighter, and stiffer bundles with increasing concentration, whereas -actinin bundles remained largely unchanged. In contrast, increasing CaMKII concentration reduced both bundle straightness and persistence length, revealing a unique concentration-dependent increase in bundle flexibility. To investigate the structural origins of these mechanical behaviors, we complemented the experiments with coarse-grained simulations of cross-linked actin bundles. Simulations revealed that CaMKII-generated bundles retained a substantially larger fraction of their curvature in their time-averaged configuration than bundles formed by -actinin or fascin, indicating that bundle mechanics are strongly influenced by organizational features beyond thermal bending fluctuations alone. CaMKII bundles displayed behavior consistent with additional structural complexity arising from their multivalent architecture and flexible linker domains. Together, our experimental and computational results identify CaMKII as a structurally and mechanically distinct actin cross-linker. We propose that the combination of multivalency and linker flexibility enables CaMKII to function as a molecular structural pivot, promoting flexible, adaptable actin assemblies that are mechanically compatible with the dynamic remodeling required for dendritic spine plasticity.

Cell membranes are decorated by dense, polymeric macromolecules such as proteins with bulky intrinsically disordered regions, glycosylated proteins, and glycopolymers. Experiments have illustrated that the curvature of cellular membranes, which plays a role in diverse biological processes, can be regulated by the local density of these membrane-tethered polymers and their response to environmental changes. However, the mechanisms underlying the feedback between solution conditions, membrane curvature, and the local density and molecular weight of membrane-tethered polymers remain largely unexplored. In this work, using a combination of theory and experiment, we show that the ionic strength of the surrounding solution and the degree of ionization both play important roles in regulating the conformation of the membrane-tethered polymers, which in turn influences their membrane curvature generation capabilities. Specifically, we show that for negatively charged, disordered proteins and glycans, the thickness of the polymer brush decreases with ionic strength but increases with grafting density and degree of ionization, resulting in enhanced sensitivity to membrane curvature and an amplified ability to drive membrane curvature at lower ionic concentrations. Our findings reveal a mechanism by which membrane-tethered polymers generate membrane curvature to minimize free energy, with the extent of curvature generation modulated by the polymer grafting density and layer thickness, as well as by the ionic strength of the surrounding solution. The implications of these findings are broad, suggesting that perturbations to biopolymer charge, such as sialylation of glycans and phosphorylation of disordered proteins, could actively modulate membrane curvature induction in diverse cellular processes from endocytosis to cell motility.

A cell's ability to maintain its volume is a prerequisite for its essential physiological functions. Changes in extracellular osmolarity induce the flux of water and solutes across the cell and nuclear membrane and, therefore, alters cell and nuclear volumes. Here, we investigated the equilibrium and dynamic volumetric responses of cells and nuclei in adherent human hepatoma (HepG2) cell monolayers using live three-dimensional imaging. Through image segmentation, 3D reconstruction, and volume rendering, precise cell and nuclear volumes were quantified. We found that during hypoosmotic stress, cells swell and lose osmolytes through active volume regulation, and nuclei undergo greater relative expansion than cells. During hyperosmotic stress, we found that both cells and nuclei shrink rapidly, develop irregular morphologies and undergo passive volume regulation. Furthermore, we explored the osmotic responses in these cells by restoring isosmotic conditions following osmotic stress and found that nuclei returned to volumes greater than their initial isosmotic volume, whereas cytoplasmic volume returned to a value below its initial isosmotic volume following swelling. By fitting coupled transport models water and solute permeability estimates for both cells and nuclei were made from their dynamic responses to different anisosmotic media with and without the presence of permeating solutes dimethyl sulfoxide and ethylene glycol. Together, these quantitative measurements of cell, cytoplasm, and nuclear volumetric responses and associated transport parameters have important implications for understanding cell physiology and the mechanism of osmoregulation.

Ion-pairs are central charged motifs that control the biological function of several proteins. Yet, the physical principles linked to the formation of ion-pairs during protein folding remain poorly understood. Here, we show that buried ion-pairs of de novo-designed helical bundle proteins reshape the folding pathways by introducing kinetic barriers that are overcome by a hydrophobic collapse linked to packing of the protein core. By combining protein design with co-translational folding studies, nuclear magnetic resonance (NMR) spectroscopy, and molecular dynamics simulations, we show that introduction of a buried ion-pair leads to a shifted folding transition that balances desolvation and electrostatic interactions within the protein and the bulk solvent. Moreover, we find that the folding pathway is sensitive to modifications in non-polar interactions and motifs that electrostatically shield the ion-pair from its surroundings. Our combined findings provide a blueprint for understanding how functional motifs affect protein folding and how mutation of charged networks alter the stability of proteins.

Many protein functions are coupled to proton transfer, yet the underlying mechanisms remain extremely difficult to resolve by experiment or conventional molecular dynamics (MD) simulations. The human voltage-gated proton channel HV1 (hHV1) plays key roles in human physiology, but how voltage and pH together drive its activation remains unresolved. Experimental structures of hHV1 are limited to the X-ray structure of a mouse chimera and NMR models of a truncated hHV1, both representing an intermediate resting state. Here we determine the activation pathway of hHV1, together with structural models of its resting and activated states, using an approach that integrates all-atom continuous constant-pH MD (CpHMD), weighted-ensemble (WE) path sampling, and AlphaFold modeling. Starting from an AlphaFold model selected for consistency with resting-state experimental data, over 100 s of simulations reveal a mechanism in which transmembrane voltage, assisted by proton titration, drives an outward displacement of the transmembrane segment S4 accompanied by a one-click reorganization of countercharge pairings. These events are enabled by a delicately balanced electrostatic landscape and pH-modulated breathing motions in the resting state that prime the channel for protonation-state switches upon voltage sensing, a principle that may underlie other proton-coupled voltage-gating processes. The simulations also uncover lipid-binding sites at which POPG selectively stabilizes the S4-up conformation, whereas POPE can stabilize either state. These predictions are validated against extensive electrophysiology, mutagenesis data, and new smFRET experiments, which support the one-click S4 displacement and the lipid effects. WE-CpHMD, implemented in the AMBER package, is applicable to other proton-coupled processes that remain elusive.

Cardiomyocyte contraction is essential for the pumping action of the heart and deteriorates after myocardial damage, either as a consequence of irreversible cardiomyocyte injury or stiffening of the extracellular matrix, a process described as fibrosis. Cell geometry and substrate stiffness not only influence sarcomere architecture and contractility, they also determine how much work the cardiomyocytes can transfer to their environment. Human induced pluripotent stem cell (hiPSC)-derived cardiomyocytes provide a model system to examine these effects in a controlled manner, enabling us to mimic key features of the cardiac environment in vitro. Here we show that geometric confinement and substrate stiffness influence different aspects of cardiomyocyte force generation. By combining traction force microscopy and live-cell imaging of hiPSC-derived cardiomyocytes on soft and patterned substrates, we find that geometric confinement leads to longer resting sarcomeres and more pronounced sarcomere shortening on substrates with both physiological (10 kPa) and fibrotic (30 kPa) stiffness. Interestingly, the substrate stiffness itself has little effect on resting sarcomere length, but influences the peak contractile stress. On 10 kPa substrates, confined cells generate higher peak contractile stresses than unconfined cells, whereas this difference is not observed at 30 kPa. Confinement also results in faster mechanical relaxation at 10 kPa, with no detectable difference at 30 kPa. The combination of defined cell geometry and physiological stiffness leads to longer resting sarcomere lengths, more pronounced sarcomere shortening, higher peak contractile stress, and faster relaxation, features associated with a more mature cardiomyocyte phenotype. These findings show that the mechanical consequences of cell geometry depend on substrate stiffness and, therefore, both aspects have to be considered when employing hiPSC-derived cardiomyocytes as a model system in mechanobiology research, disease modeling and drug testing.

Interpreting single-molecule force spectroscopy (SMFS) data from optical tweezers with steered molecular dynamics (SMD) is hindered by a severe timescale mismatch: SMD trajectories span nanoseconds to microseconds, while SMFS experiments unfold over milliseconds to seconds, forcing SMD to pull six to nine orders of magnitude faster than experiment and systematically distorting rupture forces, molecular pathways, and kinetic intermediates. We introduce force-probe coupled steered molecular dynamics (fp-SMD), which explicitly propagates the force probe (the optically trapped bead) alongside the biomolecule within a single classical Hamiltonian description of the coupled molecule-linker-bead system. A Predict-Correct Trajectory Propagation (PCTP) scheme resolves the resulting computational bottleneck by decoupling the fast molecular relaxation from the slow, macroscopic bead motion, using metadynamics and transition-state theory to identify the kinetically resolved molecular intermediate reached at each macroscopic time step. On the cholesterol-{beta}-cyclodextrin ({beta}-CD) host-guest complex, fp-SMD reproduces the experimental rupture-force histogram directly at matched conditions, without extrapolation from standard SMD. fp-SMD further resolves how applied force reshapes the molecular escape pathway itself--cholesterol dissociates via a high-angle route at low force and a direct, small-angle route at high force--providing, to our knowledge, the first direct structural evidence for force-induced pathway switching within small host-guest systems believed to underlie catch-slip bond behavior. fp-SMD/PCTP thus offers a general route to simulating force-probe-coupled biomolecular mechanics at experimentally relevant timescales.

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.

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.

Viral entry requires remodeling the host membrane with a short fusion peptide (FP) that anchors and deforms the target lipid bilayer. However, the contribution of the FP throughout the full fusion pathway remains unknown. Here, all-atom molecular dynamics simulations define the membrane- deformation mechanisms associated with two distinct insertion configurations of membrane-bound human parainfluenza virus type 3 (HPIV3) FP. Molecular simulations quantifying the linear response of curvature to the peptide are complemented with analyses of lipid organization and FP-lipid interactions to define the underlying membrane-deformation mechanisms. The surface-parallel FP configuration generates positive membrane curvature through deformation of the proximal leaflet, consistent with the classical hydrophobic insertion (wedging) mechanism. In contrast, the transmembrane FP configuration generates curvature through localized deformation of the distal leaflet, a distinct mechanism that would strongly influence later stages of fusion. Cryo-electron tomography shows that target membrane curvature at virus-host contact sites is consistent with the molecular dynamics prediction. In the absence of F-protein activation and FP insertion, the cryo-ET-determined curvature distribution shifts toward negative values, thereby isolating the role of the fusion protein in inducing early-stage curvature that enables the host and virus membranes to approach one another. Modeling key mutational changes isolates how aromatic and electrostatic interactions act together to promote curvature generation. Taken together, these findings establish FP insertion configuration as a determinant of productive membrane curvature across the full fusion pathway.

Light-gated K+ channelrhodopsins (KCRs) are recognized as an ideal neuronal silencing tool in optogenetics. KCRs contain functionally important residues for a light-driven H+ pump bacteriorhodopsin, but their roles have been unclear. Utilizing electrophysiological methods, we demonstrate that KCRs function as a light-driven H+ pump in the absence of K+. Transport experiments using pH electrodes further elucidated the function of the H+-pump, which operates even in the presence of K+. The hypothesis that the H+ pump exerts a blocking effect on K+ transport in KCRs has been postulated. Furthermore, we ascertained that there was conversion of KCRs from the H+ pump into the H+ channel by light, yet this conversion was never reversed. However, the addition of K+ resulted in the formation of the K+ channel. KCRs exhibit three distinct functional states, H+ pump, H+ channel, and K+ channel. These multifaceted functions are modulated by environmental ions and light.

Nanopore sensors have transformed single-molecule analysis, enabling real-time detection of biomolecules with unprecedented resolution. Understanding and modelling noise in nanopore sensing is essential to unlocking their full analytical potential. Although mechanistic models of nanopore noise exist, a rigorous statistical framework that characterises noise structure across diverse experimental conditions is still lacking. Here, we present a comprehensive empirical analysis of nanopore noise using twelve diverse experimental conditions acquired with different nanopores, analytes, and electronic recording systems. By employing multiple, mutually reinforcing statistical methods, we establish that nanopore noise is well described by a composite fractional model comprising multiple fractional Gaussian noise and fractional Brownian motion components. This finding is supported by confirmation of Gaussianity, rigorous interpretation of second-order exponents, multifractal analysis, and evidence that transient deviations are attributable to deterministic or experimental artefacts rather than alternative stochastic mechanisms. We further resolve quasi-deterministic structures, such as baseline trends and structural breaks, and demonstrate their separability from the underlying stochastic profile. Collectively, these results provide the first formal statistical validation of a composite fractional model for nanopore noise and establish a principled basis for noise reconstruction, realistic simulation, and statistically grounded algorithm design for nanopore sensing applications. This study provides the foundation for the creation of high-fidelity performance evaluation datasets for signal processing, and the controlled generation and augmentation of data for machine learning while maintaining statistical fidelity to experimental conditions.

Biofilm formation--the establishment of cellular communities within a self-secreted polymer matrix--is a behavior exhibited by almost all species of bacteria. Bacterial biofilms are well described as viscoelastic materials, with properties that grant physical advantages, such as elastic resilience and viscous adaptability. Additionally, many biofilm-forming species produce a subpopulation of highly resilient spores. In the model biofilm- and spore-forming species Bacillus subtilis, sporulation and matrix production are regulated by a common gene pathway, provoking the question of how sporulation influences biofilm viscoelastic properties. Investigating this point will facilitate the management of both salutary and deleterious biofilms, especially through manipulating their establishment and dispersion. Here, we investigate the interplay of sporulation and viscoelastic properties using rheological measurements of B. subtilis biofilms with varied matrix and spore production. We find that, to a significantly greater extent than matrix production, biofilm physical development is strongly altered by activation of sporulation through the spo0A regulation pathway. Spore-deficient strains initially establish physically robust biofilms with linear viscoelastic properties and recovery behavior distinct from spore-producing biofilms. However, spore-deficient biofilms fail to maintain their physical properties over time. In contrast, spore-producing wild-type and matrix-mutant biofilms exhibit more stable physical properties. Our results demonstrate that cell-level gene regulation is associated with macroscopic mechanical transitions in cellular communities, with sporulation granting not only a cellular-level survival advantage, but also greater community-level physical stability.

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.