Biophysical Reports

For decades, the photon counting histogram (PCH) was used as the sole method to quantify fluorophore numbers in a diffraction-limited focal volume. This technique combines spatial excitation profiles, and the distribution of photon counts to register the photon emission statistics of individual fluorophores. However, this approach has not yet been transferred to widefield fluorescent imaging due to the lack of fast and single photon sensitive camera sensors which can capture the photon emission statistics of a single fluorophore. Here, we explore avenues towards quantitative analysis of the active fluorophore number by leveraging recent advancements in single photon avalanche diode (SPAD) array technology. Binary exposures of a SPAD array can be synchronized with picosecond laser pulses to measure the PCH in a widefield setting. Then, by modeling the statistical relationship between the active fluorophore number and the PCH in a region of interest following a laser pulse, we can perform Bayesian inference of this number. The model is demonstrated experimentally by counting quantum dots and various numbers of fluorescent dye molecules bound to DNA origamis. We find that this method has several important applications in widefield microscopy, including enhanced localization microscopy and constrained fitting of multiple unresolvable fluorescent emitters.

The spatial resolution of optical imaging systems is fundamentally restricted by the diffraction limit. However, in widefield live-cell microscopy, the achievable resolution is further constrained by the specimen motion, which indicates the existence of a fundamental spatio-temporal resolution trade-off between signal accumulation during the full frame integration and the resulting motion blur. To improve the fidelity with which moving objects can be imaged, a quantitative understanding of this spatio-temporal trade-off is necessary. Here, we present a systematic analysis of motion-induced resolution dynamics measured with spectral signal-to-noise ratio (SSNR). We developed a simulation framework which models the image formation of objects undergoing arbitrary motion, to evaluate the degradation of the spatial resolution under translational and rotational dynamics. Our results demonstrate that for translating objects, the spatial resolution is anisotropically reduced as a function of the orientation of the object relative to the motion vector, leading to the spectral signal-to-noise ratio degrading by up to 50% and the resolution by up to 40% for a 90{degrees} change in the motion direction. Furthermore, we show that for rotational motion, conventional radially averaged metrics such as the Fourier Ring Correlation are not able to quantify the effects of angular blur. On the other hand, the SSNR is able to accurately quantify this degradation. These findings underscore the necessity of an object-oriented imaging approach, in which acquisition parameters such as exposure time are tuned to specific biological spatio-temporal characteristics to optimize the trade-off between motion blur and spatial fidelity.

Quantum effects in biology are unavoidable at the molecular scale; the unresolved question is whether they can remain functionally relevant across the timescale gap between femtosecond molecular dynamics and microsecond-to-millisecond biological function. Here we formalize this mismatch as an equilibrium-to-functionality gap and use tubulin as a stringent open-system test case. We combine secular Lindblad, Redfield, and hierarchical equations of motion (HEOM) treatments to quantify decoherence, non-perturbative relaxation, and the physical amplification required for functional relevance. Equilibrium dephasing yields a conservative [Formula] fs at 310 K, with a generic protein-bath baseline of {approx} 13 fs. A completed 30 ps HEOM trajectory for the full 1JFF tryptophan network shows distributed non-Markovian relaxation, with terminal purity Pur = 0.210 and stretched-exponential exponent {beta}KWW {approx} 0.44, confirming that Redfield is useful as a short-time perturbative comparator but not quantitatively interchangeable with HEOM in this intermediate-coupling regime. We introduce a coherence-utility criterion [U] = [K]{tau}coh/{tau}func, separating required amplification from empirically bounded gain. A thermodynamic uncertainty relation closure shows that neural-scale cascade amplification would require Pmin [~] 10-7 W, about five orders of magnitude above the local microtubule GTP budget. Frohlich pumping is found to be linewidth-gated rather than generically micron-scale; ordered-water cavity QED and geometric subradiance remain experimentally testable but severely constrained candidates. The result is not a model of consciousness, but a reproducible physical benchmark framework for evaluating biological quantum-coherence claims under explicit open-system, energetic, and experimental constraints. Six falsifiable experimental programmes are prioritized, and the full computational framework is released with a validation ledger, cryptographic audit trail, and living supplementary material. O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=107 SRC="FIGDIR/small/724047v1_ufig1.gif" ALT="Figure 1"> View larger version (20K): org.highwire.dtl.DTLVardef@19e4f42org.highwire.dtl.DTLVardef@65a719org.highwire.dtl.DTLVardef@1bd63beorg.highwire.dtl.DTLVardef@df77d8_HPS_FORMAT_FIGEXP M_FIG O_FLOATNOGraphical abstract.C_FLOATNO Equilibrium tubulin coherence lies in the femtosecond regime, while functional neural timescales lie in the millisecond regime. Frohlich pumping, QED-cavity protection, and geometric subradiance remain experimentally discriminable non-equilibrium candidates requiring independently bounded amplification. C_FIG FundingThis research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. Versioned computational scope of this releaseThis manuscript reports the theoretical framework, calibrated equilibrium baseline, Redfield/HEOM validation ledger, stratified Bayesian evidence synthesis, classical comparators, and falsifiable experimental design. The release-specific reproduction audit, including the current validation-check total and the SHA-256 fingerprints of the binary production artefacts (.npz, .pkl), is documented in LIVING_SI.md and outputs_data/raw_json/structur al/validation_report.json. A completed 30 ps HEOM production trajectory has been validated on constrained hardware; the master dataset contains the full 8-site population trajectory. A summary of those results is provided in [§]2.2.5. All claims made below are restricted to the numerical and theoretical evidence reported in this manuscript and its associated repository artefacts. The public repository ships the calibrated phenomenological baseline for accessibility; the HEOM production artefacts serve as the non-perturbative validation benchmark. All source figure outputs associated with this release are maintained in the public repository under outputs_data/figures_final/.

Following ER Ca2+ depletion, Ca2+ release-activated Ca2+ (CRAC) channels are activated by STIM1 at ER-plasma membrane junctions. The restricted localization and low conductance of the CRAC channel (<40 fS) precludes single-channel recordings, limiting studies of CRAC channel gating. Here we describe an optical approach to characterize the gating of HaloTag-fused Orai1 channels labeled with JF646-BAPTA, a Ca2+-sensitive fluorescent dye. While Ca2+ influx through single channels generates fluorescence fluctuations, identifying true gating events is complicated by stochastic transitions of JF646-BAPTA to a non-fluorescent state. To overcome this, we combine TIRF microscopy with whole-cell voltage clamp to control the driving force for Ca2+ entry. We show the open channel intensity at -100 mV reflects Ca2+ saturation of the dyes on each channel, while the closed-channel intensity is defined by the fluorescence at +30 mV, where influx is absent. True gating events can be identified from transitions between the open- and closed-channel levels, distinguishing them from transitions to a non-fluorescent state. We describe the gating behavior of CRAC channels activated by STIM1 after store depletion. Dwell time distributions indicate at least two open and closed states with durations of 0.1 to several seconds, with most channels having an open probability of [&ge;]0.7. We also detect silent channels that colocalize with STIM1 but show no activity over tens of seconds, a population that would be undetectable by whole-cell electrophysiology alone. This method offers an approach to explore CRAC channel gating mechanisms and may be applicable to other Ca2+- permeable channels not amenable to patch-clamp techniques.

Characterizing conformational transitions between distinct structural states is essential for understanding protein function but remains challenging due to the timescale limitations of atomistic molecular dynamics. While coarse-grained models like Martini accelerate sampling, classical elastic-network or G[o]-like restraints often trap proteins in a single energy basin, precluding the study of transition pathways between distinct functional states. Here, we present CTGoMartini, a comprehensive Python package designed to simulate protein conformational transitions using G[o]-Martini models in explicit membranes. CTGoMartini addresses key methodological limitations of existing approaches by redefining native contacts as a dedicated interaction type, thereby eliminating spurious protein aggregation artifacts in multi-copy simulations. The package implements both switching and multiple-basin approaches (Exponential and Hamiltonian mixing) to sample transitions between experimentally defined states. Furthermore, it integrates Hamiltonian replica exchange molecular dynamics (HREMD) with PyMBAR analysis, enabling efficient optimization of mixing parameters that govern barrier heights and relative state stabilities. We demonstrate the power of CTGoMartini through two biologically significant membrane protein systems: (1) capturing the inward-open to outward-open transition of the lipid transporter SPNS2, revealing the molecular mechanism of S1P translocation; and (2) elucidating how membrane surface tension and anionic lipids (POPA, PIP2) modulate the conformational equilibrium of the mechanosensitive ion channel TREK1. By streamlining model construction, simulation, and analysis, CTGoMartini offers an easy-to-use platform that connects static structural snapshots with their underlying dynamic functional mechanisms. TOC Graphic O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=118 SRC="FIGDIR/small/721921v1_ufig1.gif" ALT="Figure 1"> View larger version (26K): org.highwire.dtl.DTLVardef@75eb26org.highwire.dtl.DTLVardef@1a12accorg.highwire.dtl.DTLVardef@e927org.highwire.dtl.DTLVardef@1cb0dcd_HPS_FORMAT_FIGEXP M_FIG C_FIG

The optimization of mRNA-lipid nanoparticles (mRNA-LNPs) for therapeutic applications is limited in part by the inadequate characterization of mRNA payload heterogeneity. One current challenge is accurately measuring the number of mRNA copies within individual LNPs, where the standard method of intensity-based mRNA number determination is sensitive to fluorescent dye-dye interactions and heterogeneity of mRNA labeling. Here we present a single-particle microscopy method that combines direct counting of the mRNA copies per LNP with LNP size measurements. While confined in microwells, individual mRNA-LNPs are lysed to release their cargo and stained with a dye such that the number of mRNA molecules in each well can be directly counted using fluorescence microscopy. Since the method stains the mRNA cargo in situ, it enables characterization of LNPs formulated with therapeutic grade (e.g., unlabeled) mRNA. We applied this approach to two Onpattro(R)-based LNP formulations prepared using different formulation buffers, where the two formulations had different average mRNA copy number, particle size, and fraction of LNPs lacking mRNA. The ability to directly count the number of mRNA molecules in LNPs establishes a complimentary method to intensity-based mRNA number determination and supports the characterization and screening of clinically relevant LNP formulations.

Stimulated emission depletion (STED) microscopy is a super-resolution fluorescence imaging technique that achieves high spatial and temporal resolution by exploiting stimulated emission to induce fluorescence depletion (FD) and is expected to have substantial utility for imaging applications using fluorescent proteins. However, the compatibility of fluorescent proteins with STED microscopy systems has been understood primarily through empirical observations, and there is no established methodology for the rational selection of fluorescent proteins for STED microscopy. In this study, we systematically evaluated the compatibility of commonly used fluorescent proteins with STED microscopy systems by measuring FD properties using transient absorption spectroscopy and fluorescence dip spectroscopy, both of which are classified as two-color spectroscopy (TCS). Fluorescent proteins identified as compatible with the STED microscopy system based on the TCS measurements were employed for three-dimensional STED imaging of cellular samples expressing each protein. In all samples, three-dimensional spatial resolution was improved relative to confocal laser microscopy, with particularly marked improvements in z-axis resolution. These findings demonstrate that measurements of FD properties via TCS provide a robust approach for evaluating the compatibility of fluorescent proteins with the STED microscopy system and for selecting suitable fluorescent proteins for STED imaging.

The long non-coding RNA NEAT1 is a fundamental architect of nuclear condensates, specifically paraspeckles. While the scaffold-essential isoform NEAT1-2 has been extensively characterized, the function and dynamics of its shorter isoform, NEAT1-1, remain poorly understood. Investigating NEAT1-1 in live cells has been historically hindered by its genomic overlap with NEAT1-2. Traditional visualization study designs require either the genetic ablation of NEAT1-2, which disrupts paraspeckle integrity, or the use of bulky tandem tagging arrays, which can sterically hinder RNA folding and partitioning. Here, we implemented a non-invasive imaging strategy and performed diffusivity analysis of NEAT1-1 using the fluorescence light-up aptamer biRhoBAST. This small, high-affinity RNA tag enables high-contrast visualization of NEAT1-1 while preserving the structural integrity of both isoforms and their associated nuclear bodies. By combining imaging and fluorescence fluctuation spectroscopy, we provide characterization of NEAT1-1 within intact micro-and para-speckles. Our results reveal that NEAT1-1 is not purely sequestered within visible condensates; rather, a fraction exists in a distinct diffusive state within the nucleoplasm, likely as nanoscale complexes. These findings suggest that NEAT1-1 possesses a previously unrecognized regulatory role independent of the primary paraspeckle scaffold, offering new insights into the functional diversity of the lncRNA isoforms.

Along with the membrane potential and respiration, mitochondrial matrix volume is a critical parameter that determines mitochondrial function. Mitochondria undergo constant changes in matrix volume and cristae dynamics, and in processes that are critical for normal metabolic rates and pathophysiological responses. Changes in matrix volume cannot be easily measured by conventional fluorescence imaging techniques due to the size of the sub-organellar structures, which are below resolution. This challenge was successfully resolved in studies of isolated mitochondria with the use of scattered light. Here we use dark-field imaging, which relies on scattered light contrast, to measure matrix volume dynamics in living cells. We demonstrate that mitochondrial volume changes can be easily detected as changes in intensity of the scattered light following matrix volume modulation with K+ ionophores or by onset of the permeability transition. Specifically, we found that stimulation of K+ influx leads to increase of mitochondrial matrix volume while stimulation of K+ efflux leads to matrix shrinkage, and that activation of the permeability transition leads to high-amplitude mitochondrial swelling in wild-type but not in cells lacking subunit c of ATP synthase. These results directly demonstrate the dynamic nature of mitochondrial matrix volume and its link to physiological and pathological ion transport.

Proteins in solution adsorb to the corona of nanoparticles such as single-walled carbon nanotubes (SWCNTs), but these interactions are difficult to predict and analyze due to ambiguities in the structure of the latter. In this work, we employ ss(GT)15-DNA wrapped SWCNTs, a commonly used fluorescent sensor construct, to examine protein adsorption by quantifying binding dissociation constants and characterizing the corresponding photophysical effects. A library of 20 proteins are used to evaluate adsorption-induced changes in photoluminescence (PL) intensity ({Delta}I/I0) and emission wavelength upon solution phase binding. We find that 15 proteins produce monotonic dose-response behavior well described using a single-site Langmuir model. Alternatively, five proteins exhibited more complex, non-monotonic behavior consistent with a two-step binding model representing protein-protein interactions coupled to adsorption. The study reveals that metalloproteins, which comprised 12 of the 20 proteins in the library, induced greater PL quenching compared with metal-free proteins for this system, with maximum binding-associated quenching ({Delta}I/I0) of 94% for metalloproteins versus 20% for metal-free proteins. For metalloproteins, we introduce a proximity-based quenching framework in which protein size provides a coarse proxy for cofactor-SWCNT separation, offering a mechanistic interpretation of the observed quenching variation across proteins. Together, these results establish the use of metal coordination sites, such as those in metalloproteins, to assist the transduction of certain nanoparticle fluorescent sensors, helping with sensor probe design and interpretation in biological environments.

A major challenge in neuroscience is to predict how currents in nanodomains affect voltage and ionic concentrations. Cable and Rall theory provide analytic current-voltage relations by neglecting concentration gradients, and the impact of concentration gradients is usually studied numerically with the Poisson-Nernst-Planck (PNP) model. A precise quantitative understanding of the combined dynamics remains limited because analytic current-voltage-concentration relations are missing. In this work we derive such relations using a novel approach based on cross-diffusion equations. For narrow cylindrical domains, we derive time-dependent and steady-state expressions that explicitly show how currents affect voltage and ionic concentrations. We find that the influx of only one ion can significantly change the concentrations of all the other ions even if no channels for these ions are present. After a current injection we compute a biphasic voltage transient where the small-time asymptotic corresponds to the steady-state solution of the cable equation. We show that the accuracy of cable theory prediction for the voltage depends on how the current is distributed among the various ions. Finally, we develop an iterative method to accurately compute steady-state profiles for voltage and concentrations using first-order results by subdividing a cylinder into small segments.

We introduce a workflow to identify oligomeric structures that are recorded with single-molecule localization microscopy (SMLM) under cryogenic conditions. Typically, these oligomers are assumed to consist of protomers arranged as equilateral two-dimensional polygons and every protomer is labeled with a dye molecule for visualization. Unlike previous work, we consider scenarios in which the sample plane has an unknown orientation relative to the focal plane. Our contribution is a high-precision plane-fitting algorithm to determine the sample plane, combined with geometrical transformations and two circle-fitting algorithms to identify the oligomeric structures. Our simulations on synthetic data demonstrate that the proposed workflow achieves high accuracy in estimating both the unknown tilted plane and the oligomer size.

Cytoplasmic mechanical properties are often treated as constant background parameters, yet whether they change systematically during development remains unclear. Here, we directly measured cytoplasmic mechanics during early embryogenesis of Caenorhabditis elegans by establishing active microrheology using micrometer-sized magnetic droplets. Active microrheology revealed a progressive decrease in creep compliance from the 1-cell to the 8-cell stage, indicating a progressive stiffening of the local cytoplasmic environment during development. This decrease persisted even when cytokinesis was inhibited, demonstrating that it cannot be explained solely by geometric changes associated with cell division. Passive microrheology using 40-nm fluorescent beads showed a consistent decrease in probe mobility over development. Together, these results demonstrate that cytoplasmic mechanical properties undergo a gradual, developmentally programmed change during embryogenesis that cannot be explained by cell division-associated geometry alone.

GPCR oligomerization has been reported for decades, yet its extent and functional relevance in living cells remain unresolved because existing approaches, often done in bulk, are poorly account for local receptor density, a major determinant of intermolecular interactions. Here, we establish a generic quantitative imaging framework that links spatially resolved FRET measurements describing protein oligomerization to local membrane protein in living cells. Using automated high-throughput analysis of fluorescence images, the method generates large density-resolved datasets that enable direct quantification of receptor oligomerization parameters, including apparent affinity, oligomerization state, and monomer/dimer populations at the submicrometer scale. Applied to class A GPCRs in HEK293 cells, the approach reveals receptor-specific density-dependent equilibria between monomers and dimers over physiologically relevant expression ranges, with no evidence for stable higher-order oligomers under basal conditions. The receptors studied exhibit distinct apparent affinities for dimerization, ranging from predominantly monomeric to dynamic monomer-dimer equilibria, indicating that local membrane density strongly influences receptor organization and that it is receptor dependent. The agreement between our measurements and low-density single-molecule studies further suggests that previously reported higher-order oligomers may partly reflect density-driven receptor proximity effects. By bridging single-molecule and ensemble measurements within a unified quantitative framework, this work reconciles conflicting observations in the GPCR oligomerization literature and provides a broadly applicable strategy for investigating membrane protein organization in living cells. SignificanceGPCR oligomerization in living cells is strongly influenced by the local protein density, yet most approaches do not quantitatively account for this parameter. Here, we introduce a quantitative high-throughput imaging framework that directly relates membrane protein local density to local oligomerization state in living cells. Applied to distinct GPCRs over physiologically relevant density ranges, the method reveals distinct density-dependent monomer-dimer equilibrium and apparent affinities for self-association. These results help reconcile longstanding discrepancies, where distinct oligomerization states have been measured depending on experimental conditions. More broadly, this work establishes local membrane protein density as a key determinant of membrane protein organization, and provides a quantitative framework applicable to membrane protein complexes in their native cellular context.

Ultraviolet (UV) radiation induces DNA damage associated with cancer and aging, yet the sequence dependence of UV absorption remains to be investigated. Here, we present a systematic study of the UV absorption spectra of DNA based on all-electron Hartree-Fock calculations. We analyze all possible sequences up to four base pairs, as well as longer randomized sequences and genomic nullomers - motifs which are missing in a given genome. We observe a pronounced sequence dependence: cytosine- and guanine-rich motifs exhibit significantly enhanced absorption, whereas adenine-thymine-rich sequences absorb up to four times less in the mid-UV range. Notably, the human genome is biased toward adenine-thymine-rich sequences, giving it an increased susceptibility to UV-induced damage. In addition, we introduce a computational framework enabling spectral calculations of large DNA and RNA fragments, opening the door to large-scale optical analyses.

Developing parsimonious, mechanism-aware quantitative models that predict how biological effectiveness changes with different modifiers remains, in general, an unsolved problem. Advances in radiobiological research have created a large knowledge base of first-principles mechanistic models of radiation response that, in principle, could accurately predict radiosensitivity across different experimental and clinical conditions. However, in practice these mechanistic models come with an overabundance of parameters, the majority of which are practically unidentifiable and, moreover, likely unnecessary if one simply wishes to predict how radiosensitivity changes for some specific modifier of interest. Nevertheless, determining which few details in the full mechanistic model are relevant for a given purpose, as well as how to remove any other extraneous details, remains a highly non-trivial task. In this study, we demonstrate the potential of model reduction, starting from a detailed mechanistic description, as a systematic strategy for deriving parsimonious, experimentally falsifiable radiobiological descriptors. As a proof-of-concept demonstration, we apply the Manifold Boundary Approximation Method (MBAM) to a Mechanistic Model of DNA Repair and Survival (MEDRAS), for the problem of cell survival prediction following an acute exposure. Our findings reveal that the complete MEDRAS model for an arbitrary mixed-quality exposure can be structurally simplified to a reduced three-parameter model for an effective uniform-quality, named MEDRAS-LPL. Additional MBAM analysis on MEDRAS-LPL identifies two boundaries in parameter space, corresponding to sparsely ionizing and densely ionizing radiation. Mapping of MEDRAS-LPL parameter space on to effective LQ space further demonstrates that parameters close to the sparsely ionizing boundary line up with expectations from the theory of dual radiation, while parameters close to the densely ionizing boundary line up with expectations from a purely linear model based on a target-theory description. Moreover, our formalism predicts enhanced synergistic interactions between sparsely ionizing and densely ionizing radiation beyond the Zaider Rossi model (ZRM) paradigm, in line with empirical observations. The results highlight the potential for using reduced-order models not only for predictive applications but also for generating novel hypotheses that can inform future experimental designs and optimization strategies in radiobiology.

The Poisson-Nernst-Planck (PNP) system is an accurate model of electrodiffusion of ionic species. It is commonly used in situations where nanoscale resolution is required, for instance close to ion channels in the membranes of biological cells. The inherent stiffness of the equations has made them challenging to solve and has limited the applicability of the system. In particular, the time step required for stable solutions has typically needed to be very short (nanoseconds), which makes simulations on the time scale of an action potential (milliseconds) difficult. Recently, it has been observed that avoiding operator splitting and instead solving the concentration equations and the electrostatic equation in a coupled manner relaxes the time-step limitation considerably. However, no theoretical explanation of this observation has been provided. Here, we aim to explain why the coupled scheme allows much larger time steps. We illustrate the mechanism by considering special cases that define necessary, but not sufficient, conditions for stability. We also show that these conditions remain relevant for the fully coupled PNP model in 3D.

1Correlations between cellular variables, such as gene-expression levels, provide insights into regulatory mechanisms. We focus here on correlations between mRNA and protein levels and re-examine previously derived analytical predictions. We test this prediction on single-cell E. coli data and see substantial disagreement. We hypothesize that this discrepancy arises from the assumption of constant cell volume and develop a theoretical framework for mRNA-protein correlations in growing and dividing cells. Within this framework, we derive an analytical expression for mRNA- protein correlations and show that explicit incorporation of growth and division substantially alters these correlations. The resulting relation is invariant to upstream transcriptional dynamics, and we validate it using stochastic simulations across multiple gene-regulatory architectures. Finally, we show that the derived predictions are consistent with the E. coli data.

Quantum kernel methods offer a potential advantage for classification tasks in high-dimensional feature spaces, yet their practical benefit critically depends on how input features are prepared. We compare five dimensionality reduction strategies--principal component analysis (PCA), Gaussian random projection (RP Gaussian), sparse random projection (RP Sparse), partial least squares (PLS), and uniform manifold approximation and projection (UMAP) -- as pre-processing steps for quantum kernel support vector machines (SVMs) applied to trabecular bone classification from synthetic micro-computed tomography (micro-CT) data. Using a custom procedural generator based on Gaussian random field zero-crossings, we produced 500 synthetic trabecular bone volumes with controlled morphometric properties such as bone volume fraction (BV/TV), trabecular thickness (Tb.Th), number (Tb.N) and spacing (Tb.Sp). Texture features extracted from grayscale slices are reduced to 8-dimensional quantum circuit inputs via each method, then classified using both classical radial basis function (RBF)-SVMs and quantum kernel SVMs with ZZ feature maps on a statevector simulator, both evaluated with 5 x 5 repeated stratified cross-validation (25 folds). Our results show that UMAP is the only reduction method where the quantum kernel remains competitive with the classical baseline. Under repeated cross-validation, UMAP showed a +0.032 accuracy gap favouring the quantum kernel (Dietterich 5 x 2 CV p = 0.177); however, validation on 10 fully independent datasets--each with independently generated samples, separate reduction fits, and separate kernel matrices -- reversed the sign to -0.030 (paired t-test p = 0.123; Wilcoxon p = 0.193; quantum wins 3/10 datasets), indicating that the apparent advantage was likely inflated by fold dependence. Nevertheless, UMAPs gap remains small and non-significant in both analyses, whereas all linear methods (PCA, RP Gaussian, PLS) show substantial quantum deficits of -0.090 to -0.116 across BV/TV classification, with PCA and PLS remaining significant under corrected tests (5 x 2 CV p = 0.004 and p = 0.007 respectively). We additionally evaluate quantum kernel ridge regression for continuous morphometric prediction, finding that ZZ quantum kernels fail uniformly at regression (negative R2 for all methods except PLS at 4 qubits), suggesting that the ZZ kernel captures decision boundaries but not smooth metric structure. These findings provide practical guidance for feature engineering in near-term quantum machine learning pipelines and demonstrate that the choice of dimensionality reduction can determine whether quantum kernels remain competitive with classical baselines.

Atomic force microscopy (AFM) enables nanometre-scale, label-free imaging of biomolecules and surfaces under near-native conditions, yet quantitative analysis of AFM data remains limited compared to other bioimaging modalities. This limitation largely arises from the absence of open, automated tools capable of addressing AFM-specific artefacts, data formats, and topographical outputs. Here, we present the latest version of TopoStats, an open-source Python package for automated and quantitative AFM image analysis, developed as a deep-learning enabled advancement of our original TopoStats software to support more complex samples and richer molecular characterisation. The pipeline integrates all key processing stages, including image flattening and noise correction, object detection and segmentation, morphometric feature extraction, and strand tracing with topological classification. Designed for accessibility and reproducibility, TopoStats adheres to the FAIR for Research Software (FAIR4RS) principles and provides configurable workflows adaptable to diverse biological samples. Combining high-resolution AFM and our analysis pipeline allows the quantification of subtle structural changes within a heterogeneous sample set, revealing properties not accessible with other structural biology techniques. We demonstrate the effectiveness of our pipeline to differentiate between plasmids with both different topology and sequence, by extracting meaningful quantitative descriptors that distinguish the samples with statistical significance. Collectively, these developments establish TopoStats as a versatile framework for high-throughput, quantitative AFM analysis, advancing AFM from a fundamentally qualitative visualisation technique toward a quantitative analytical tool.