Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Interactions between cytosolic biomolecules and the bacterial inner membrane are fundamental to many cellular processes, yet directly measuring their binding kinetics in living cells remains challenging. Conventional two-dimensional single-molecule tracking analyses can be insufficient, particularly when membrane association does not markedly alter the diffusion rate. Here, we present a method to recover membrane interaction kinetics from three-dimensional single-molecule trajectories in rod-shaped bacteria. Using simulated 3D tracking data, we identify membrane-associated motion by quantifying how well short trajectory segments follow the circular curvature of the cell membrane. The resulting measure is further analyzed using a hidden Markov modeling framework, enabling robust discrimination between cytosolic and membrane-bound states and capturing the dynamics of state transitions without requiring diffusion-rate changes or direct colocalization with membrane markers. This work establishes a general framework for extracting membrane interaction kinetics from 3D single-molecule tracking data in live bacteria, and highlights the value of realistic microscopy simulations for quantitative interpretation and systematic bias assessment.

Digital holographic microscopy systems in a common-path configuration, compared to systems with a separate reference arm, offer a compact design and resistance to disturbances. They can operate with partially coherent illumination, reducing speckle noise. However, they are limited by the overlapping of the object beam and its laterally shifted replica. As a result, images from different regions of the object overlap on the detector, preventing imaging of dense samples. We present the wavelength-scanning replica-removal method, which solves this problem by enabling the separation of information from both replicas and thereby doubling the effective field of view (FOV). The wavelength-scanning multi-shear replica removal algorithm plays a key role in reconstructing the undisturbed phase from a series of holograms recorded with variable shears. The shear value is controlled by changing the illumination wavelength. This enabled the development of two measurement modes: time-domain wavelength scanning for high-quality imaging, and a single-shot mode with frame division into color channels to improve temporal resolution. The method was validated using resolution tests and biological samples - neurons and dynamic yeast cultures. By combining the advantages of the common-path configuration with dense-structure imaging and dynamic processes, the proposed method constitutes a versatile tool for quantitative phase microscopy.

Symptom propagation occurs when the symptoms of secondary cases are related to those of the primary case as a result of epidemiological mechanisms. Determining whether - and to what extent - symptom propagation occurs requires data-driven methods. Here we quantify the strength of symptom propagation as the increase in risk of a secondary case developing severe symptoms if the primary case has severe symptoms. We first used synthetic results to determine the data requirements to robustly estimate the strength of symptom propagation and to investigate the effect of severity-dependent reporting bias. Categorising symptom severity into two group (mild or severe; asymptomatic or symptomatic), our estimation requires only four summary statistics - the number of primary-secondary case pairs of each combination of symptom presentations. Our analysis showed that a relatively small number (100) of synthetic primary-secondary case pairs was sufficient to obtain a reasonable estimate of the strength of symptom propagation and 1,000 pairs meant errors were consistently small across replicates. Our estimates were robust to severity-dependent reporting bias. We also explored how symptom propagation can be separated from other individual-level factors affecting severity, using age dependence as an example. Although synthetic data generated from an age-structured model led to overestimations of the strength of symptom propagation, allowing disease severity to be age-dependent restored the accuracy of parameter estimation. Finally, we applied our methodology to estimate the strength of symptom propagation from three publicly available data collected during the COVID-19 pandemic with data on presence or absence of symptoms: England households, Israel households, and Norway contact tracing. Our age-free methodology indicated a 12-17% increase in the risk of being symptomatic if infected by someone symptomatic. Our positive estimates for the strength of symptom propagation persisted when applying our age-dependent methodology to the two household data sets with age-structured information (England and Israel). These findings demonstrate evidence for symptom propagation of SARS-CoV-2 and provide consistent estimates for its strength. Our synthetic data analysis supports the conclusion that these correlations are not a result of reporting bias or age-dependent effects. This work provides a practical tool for estimating the strength of symptom propagation that has minimal data requirements, enabling application across a wide range of pathogens and epidemiological settings.

Synchrony is a key mechanism that builds up the foundations of human interactions. Quantifying the level of physiological synchronization that occurs during dyadic exchanges is essential to fully comprehend social phenomena. We present a new index to characterize the coupling of complex physiological dynamics: the optimized Multichannel Complexity Index (opMCI). We validated this approach using synthetic time series of two coupled Henon Maps, with four different coupling levels in unidirectional and bidirectional manners. We demonstrated that the opMCI method allows to effectively discern between all coupling levels. Then, we applied the opMCI metric on heart rate variability data collected from 37 parent-infant dyads, during shared reading and playing activities, in the framework of the Shared Emotional Reading (SHER) project, with the aim of assessing the effects of early intervention in preterm babies. Two groups presented preterm infants: an intervention group, who participated in a two-month shared reading program, and a control group, who practiced shared play activities. A full-term group provided additional control data. The opMCI values were significantly higher for the intervention dyads with respect to the other groups during the shared reading task, showing that an early reading intervention program could increase parent-infant synchrony in preterm babies.

Single-molecule localization microscopy (SMLM) methods enable fluorescence imaging of biological specimens with nanometer-scale resolution. Although fluorophore localization precision is theoretically limited only by photon statistics, in practice the resolution of SMLM images is often degraded by physical drift of the sample and/or the microscope during data acquisition. At present, correcting this effect requires either specialized stabilization systems or computationally intensive post-processing, and established drift correction algorithms based on image cross-correlation suffer from limited temporal resolution. In this study we introduce COMET, a new method for SMLM drift estimation which achieves a substantially higher precision, accuracy, and temporal resolution compared with existing algorithmic approaches. We demonstrate that improved drift estimation translates directly into higher SMLM image resolution, limited by localization precision rather than drift artifacts. COMET is applicable to all types of SMLM data, operating directly on 2D or 3D localization datasets, and is readily integrated into analysis workflows. We benchmark its performance using both simulations and experiments, including STORM, MINFLUX, and Sequential OligoSTORM measurements, where long acquisition times make drift correction particularly challenging. COMET is published as an open-source, Python-based software project and is also available on open cloud-computing platforms.

Lightweight epidemic calculators are widely used for teaching and rapid scenario exploration, yet many omit the methodological detail needed for scientific reuse. We present a browser-native SIR calculator that exposes forward Euler and classical fourth-order Runge--Kutta (RK4) integration alongside epidemiologically interpretable outputs and a population-conservation diagnostic. The implementation is anchored to analytical properties of the deterministic SIR system, including the epidemic threshold, the peak condition, and the final-size relation. Benchmark experiments show that RK4 is essentially step-size invariant over practical discretizations, whereas Euler at a coarse one-day step overestimates peak prevalence by 3.97% and final size by 0.66% relative to a fine-step RK4 reference. These results demonstrate that browser-based tools can support publication-quality computational narratives when solver choice, diagnostics, and assumptions are treated as first-class outputs.

Spectral similarity is often judged with a single metric such as RMSE, yet this can be misleading: physically different errors can produce similar scores. This is a critical limitation for computational biomechanics, where spectral agreement underpins both model validation and machine-learning loss design. Here, we develop a multi-metric framework for objective spectral biofidelity and test whether it better captures meaningful disagreement across complex frequency-domain responses. We evaluated 12 complementary similarity metrics, including CORA and ISO/TS 18571, using controlled spectral perturbations that mimic common real-world deviations such as resonance shifts, localized spikes, and broadband tilts. We then applied the framework to an SBI-tuned finite-element middle-ear model to assess convergence with training dataset size and robustness to measurement noise across repeated stochastic runs. No single metric performed reliably across all distortion types. Shape-based metrics tracked resonance morphology but could miss vertical scaling, whereas MaxError remained important for narrowband anomalies that smoother metrics underweighted. CORA and ISO 18571 did not consistently outperform simpler metrics. Rank aggregation using Borda count provided a robust consensus across metrics, enabling objective identification of training-data saturation and noise thresholds beyond which similarity rankings became unstable. These results show that spectral biofidelity cannot be reduced to a single norm. A multi-metric consensus provides a clearer and more physically meaningful basis for comparing experimental and simulated spectra, and offers a more defensible foundation for data-fidelity terms in physics-informed and simulation-based machine learning.

Reverse correlation is a widely-used and well-established method for probing latent perceptual representations in which subjects render subjective preference responses to ambiguous stimuli. Stimuli are purposefully designed to have no direct relationship with the target representation (e.g., they are randomly-generated), a property which makes each individual stimulus minimally informative toward reconstructing the target, and often difficult to interpret for subjects. As a result, a large number of stimulus-response pairs must be gathered from a given subject in order for reconstructions to be of sufficient quality, making the task fatiguing. Recent work has demonstrated that the number of trials needed can be substantially reduced using a compressive sensing framework that incorporates the assumption that the target representation can be sparsely represented in some basis into the reconstruction process. Here, we introduce an alternative method that incorporates the sparsity assumption directly into stimulus generation, which holds promise not only for improving efficiency, but also for improving the interpretability of stimuli from subjects perspective. We develop this new method as a mathematical variation of the compressive sensing approach, before conducting one simulation study and two human subjects experiments to assess the benefits of this method to reconstruction quality, sample size efficiency, and subjective interpretability. Results show that sparse stimulus generation improves all three of these areas relative to conventional reverse correlation approaches, and also relative to compressive sensing in most conditions.

Conventional temporal interference stimulation (TI, TIS, or tTIS) leverages two pairs of electrodes to induce an interfering electrical field in the brain. Both computational and experimental studies show that TI can stimulate deep brain regions without significantly affecting shallow areas. While promising, optimization of the locations and dosages on these two pairs of electrodes for maximal focal modulation remains computationally challenging. We are the first to propose two arrays of electrodes instead of two or multiple pairs of electrodes to boost modulation focality. However, the optimization algorithm outputs too many electrodes with overlaps across two frequencies, making it difficult to implement in practice. Based on recent progress in developing multi-channel TI devices and computational work on TI optimization, here we again advocate two-array TI, but with solid software and hardware evidence to show the feasibility. Specifically, we show that the latest optimization algorithm for two-pair TI innately works for two-array TI with the fastest speed (under 30s) among all major algorithms. With a similar amount of electrodes, two-array TI could achieve better focality (3.03 cm) at the hippocampus even than TI using up to 16 pairs of electrodes (3.19 cm) that takes days to optimize. We also show a hardware implementation of two-array TI using 10 electrodes on our 8-channel TI device. We argue that two-pair TI is only preferred when one does not care about modulation focality and promote two-array TI for its advantages in focality and lower cost in terms of both optimization time and electrodes needed. We restate the focality-intensity tradeoff but in the context of TI and provide a first voxel-level map of achievable focality and modulation strength by TI in the MNI-152 head template. We hope this work will pave the way for future adoptions of two-array TI for more focal non-invasive deep brain stimulation.

In contemporary bio-imaging-based research, computer-based assessment is becoming crucial for the characterisation of biological structures, as it minimises the need for time-consuming human annotation, which is prone to human error. Furthermore, it allows for the use of optical techniques that use lower photon intensities, thereby reducing reliance on high-intensity excitation and mitigating adverse effects on their activities. This study details the development and evaluation of sophisticated deep-learning models for amoeba detection using phase-contrast imaging. Using a single-class annotated dataset comprising 88 images and 4,131 annotations, we developed nine object detection models based on Detectron 2 and six variants based on YOLO v10. The diversity of the dataset, acquired under varying setup parameters, facilitated a comprehensive evaluation of the strengths and limitations of each model. A comparative analysis of speed and accuracy was performed to identify the most efficient models for real-time detection, providing critical insights for future microscopic analyses.

The performance of a laser scanning microscope inevitably depends on the performance of the point detector. As laser scanning approaches aim to penetrate deeper in tissue, there is a commensurate need for detectors that can operate with high sensitivity, bandwidth, and dynamic range at near-infrared wavelengths where scattering is reduced. Here, we demonstrate that fiber optical parametric amplification can be used to boost low-power microscopy signals to levels that can be detected by near-infrared photodiodes without introducing prohibitive noise. We construct amplifiers that achieve >50 dB of parametric gain at wavelengths within the third near-infrared transparency window and have similar sensitivity to near-infrared photomultiplier tubes. Furthermore, these amplifiers outperform detection with a photodiode and subsequent electrical amplification, providing a factor of 10-100-fold improvement in sensitivity. We demonstrate amplifier bandwidths up to ~1.6 GHz, a factor of 10 faster than conventional detectors, including near-infrared photo-multiplier tubes, with sensitivity of ~8 nW (corresponding to ~20 photons/pixel). Finally, the increased performance of the optical amplifier is confirmed in diagnostic imaging experiments where >10x less power is required to achieve the same signal-to-noise ratio and contrast as images using electrical amplification. Accordingly, fiber optical parametric amplification is a new path forward for extending the performance of laser scanning microscopes in the near infrared.

The basic reproduction number of an infectious disease is known to depend on the structure of contacts between individuals in a population. This relationship has been explored mathematically through two well-known models: one which depends on a matrix of contact rates between different demographic groups, and another which depends on the variability of contact rates over the population. Here we introduce a model that combines and generalises these two approaches. We derive a formula for the basic reproduction number and validate it through comparisons to simulated outbreaks. Applying this method to contact survey data collected in Belgium between 2020 and 2022, we find that our model produces higher estimates of the basic reproduction number and larger relative changes over periods when social contact behaviour was changing during the COVID-19 pandemic. Our analysis suggests some practical considerations when using contact data in models of infectious disease transmission.

Fluorescent reporters such as fluorescent proteins or chemigenetic indicators are indispensable tools for studying biological processes using light microscopy. Choosing an appropriate fluorescent tag is a crucial step in experimental design not only for imaging but also for quantitative measurements such as fluorescence fluctuation spectroscopy. Two key parameters should be considered: Fluorescent brightness and photo-bleaching. Change to fluorescence intensity due to photobleaching is relatively easy to assess in different biological environments, while brightness is more elusive. Here, we develop and employ a fluorescence correlation spectroscopy (FCS) based excitation scan assay that determines fluorescent protein performance and validate it in tissue culture and zebrafish embryos. We employ our FCS pipeline to compare a set of 10 established fluorescent proteins as well as HALO and SNAP tags for both cellular imaging and measurements of diffusion dynamics with FCS. We show that mNeonGreen outperforms mEGFP in tissue culture and zebrafish embryos. We also compare StayGold variants against other green fluorescent proteins and chemigenetic reporters in tissue culture. Overall, we present a broadly applicable approach for determining fluorescent reporter brightness in the living system of interest.

Ultraweak photon emission is the spontaneous emission of extremely low levels of light from a broad range of biological systems. Recent studies have reported that UPE measured extracranially can serve as a potential non-invasive biomarker of brain activity. Here, we show that this interpretation suffers from serious problems. First, when observed under properly dark conditions, the UPE from the head is much weaker than what is reported in certain papers on brain UPE from human heads. Signals detected in these studies are overwhelmingly dominated by background light. Second, photons at wavelengths < 600 nm are strongly attenuated by scalp and skull tissues, and longer wavelengths fall largely outside the effective spectral sensitivity of the photomultiplier tubes (PMTs) used. As a consequence, even if UPE from the head is detected under properly background-free conditions, it is likely to be dominated by emission from the scalp rather than from the brain, certainly as long as PMTs are used. Our results emphasize the importance of careful experimental design to make genuine progress on this important question.

Understanding how cells migrate through confined environments is crucial for elucidating fundamental biological processes, including cancer invasion, immune surveillance, and tissue morphogenesis. The nucleus, as the largest and stiffest cellular organelle, often limits cellular deformability, making it a key factor in migration through narrow pores or highly constrained spaces. In this work, we introduce a geometric surface partial differential equation (GS-PDE) model in which the cell plasma membrane and nuclear envelope are described as evolving energetic closed surfaces governed by force-balance equations. We replicate the results of a biophysical experiment, where a microfluidic device is used to impose compressive stresses on cells by driving them through narrow microchannels under a controlled pressure gradient. The model is validated by reproducing cell entry into the microchannels. A parametric sensitivity analysis highlights the dominant influence of specific parameters, whose accurate estimation is essential for faithfully capturing the experimental setup. We found that surface tension and confinement geometry emerge as key determinants of translocation efficiency. Although tailored to this specific setup for validation purposes, the framework is sufficiently general to be applied to a broad range of cell mechanics scenarios, providing a robust and flexible tool for investigating the interplay between cell mechanics and confinement. It also offers a solid foundation for future extensions integrating more complex biochemical processes such as active confined migration.

Fourier ptychographic microscopy (FPM) uses sequential multi-angle illumination and iterative phase retrieval to recover a high-resolution complex image from a series of low-resolution brightfield and darkfield images. We present OpenFPM, an open-source FPM platform in which conventional and optomechanical hardware is replaced with compact, low-cost 3D printed components. Illumination, sample and objective positioning, and camera triggering are controlled using a Python-based interface on a Raspberry Pi microcomputer. With a 10 x /0.25 NA objective lens and 636 nm illumination, OpenFPM experimentally achieves amplitude and phase reconstructions with an effective synthetic NA of 0.90 over a 1 mm field-of-view. This platform gives researchers accessible and affordable hardware for developing and testing LED-array microscopy techniques for a range of biomedical imaging applications.

Atrial fibrillation (AF) promotes blood stasis and thrombus formation, most often within the left atrial appendage (LAA), and can lead to stroke or transient ischemic attack (TIA). Time-resolved contrast-enhanced computed tomography (4D CT) captures left atrial (LA) opacification and washout, but it does not directly provide quantitative stasis metrics such as blood residence time. Patient-specific computational fluid dynamics (CFD) can quantify LA/LAA residence time, yet routine clinical use is limited by computational cost and sensitivity to patient-specific boundary conditions. Here, we present two complementary approaches to infer time-resolved 3D residence time fields directly from contrast dynamics. First, a physics-informed neural network (PINN) treats contrast as a passive scalar and jointly reconstructs velocity and residence time by enforcing the incompressible Navier-Stokes equations and transport equations for contrast concentration and residence time in moving, patient-specific LA anatomies. Second, an indicator dilution theory (IDT) formulation computes voxelwise, time-resolved residence time maps from contrast time curves alone by constructing a PV-referenced impulse response and modeling transport with a tank-in-series model with spatially dependent parameters. Both methods are benchmarked against patient-specific CFD in six cases spanning diverse LA function, including three patients with TIA or thrombus in the LAA and three patients free of events. Both approaches reproduce expected spatial and temporal trends, with higher residence time in the distal LAA and higher LAA residence time in cases with TIA or thrombus. IDT demonstrates the closest agreement with CFD across the full range of residence times and produces maps in seconds, facilitating clinical translation. In contrast, the PINN additionally recovers phase-dependent atrial flow structures, but tends to smooth and underestimate the highest residence-time regions and requires hours of training. Together, these results support a scalable workflow in which IDT enables rapid stasis screening from contrast CT, and PINNs provide a complementary pathway for detailed, patient-specific hemodynamic inference when full-field flow information is needed.

Background: Accurate estimation of respiratory syncytial virus (RSV) disease burden is challenged by the imperfect testing performance that varies by clinical specimens, diagnostic tests, and timing of specimen collection. Although the use of multiple testing approaches (such as testing multiple clinical specimens or additional diagnostic tests) could increase the RSV detection, there is absence of a modelling framework to fully incorporate the complexity of heterogeneous diagnostic data. In this study, we proposed a novel Bayesian latent class model that accounted for heterogeneous data on the number of RSV tests and variable specimen collection time among individual patients, imperfect testing sensitivity and specificity of different combinations of clinical specimen and diagnostic test (i.e., testing approaches), and RSV seasonality. Methods: Using simulated datasets consisting of four different testing approaches that mimic real-world RSV epidemiologic characteristics in the UK under different sample size and testing practice scenarios, we assessed the model performance in estimating RSV disease burden as the annual RSV positive proportion in lower respiratory tract infection (LRTI) cases across three respiratory seasons (August 2021 to July 2024) in four adult age groups: 18 to 49 years, 50 to 64 years, 65 to 74 years and over 75 years. Results: We demonstrated that model performance increased substantially with increased sample size, achieving over 80% in accuracy at a sample size of 30,000 tests and 95% in accuracy at a sample size of 60,000 tests; by contrast, smaller sample size could lead to severe over-estimation of the RSV disease burden. In comparison with the existing approaches, both the naive model and the multiplier model systematically under-estimated the RSV disease burden regardless of sample size. The Bayesian model yielded more accurate estimates when the sample size reached 30,000 tests or more; its advantage over the other two models was even more pronounced if the number of testing approaches reduced to 3. Conclusion: The findings above suggest that the proposed Bayesian model provides a robust framework for estimating RSV burden by integrating complex, individual-level testing data when fitting with sufficient input data, offering a critical tool for generating more accurate RSV disease burden estimates to inform national immunisation policies.

Microscopy-based analysis of red blood cell (RBC) morphology is widely used to study phenotypes in sickle cell disease (SCD). Although AI models have been developed to automate classification, most are trained on pre-cropped single-cell images and thus struggle with full-scope microscopic images containing densely packed cells and diverse morphologies, which require both accurate detection and fine-grained classification. We propose an end-to-end computational framework to identify individual RBCs in full-scope microscopy images and classify them into five morphological categories: discocytes (DO), echinocytes (E), elongated and sickle-shaped cells (ES), granular cells (G), and reticulocytes (R). We first evaluate advanced detection-classification models, including You Only Look Once (YOLO) and Detection Transformers (DETR), and demonstrate that while these models effectively detect cells, their classification performance falls short of specialized classifiers trained on single-cell images, particularly for minority phenotypes. To address this limitation, we introduce a two-step framework in which a YOLO-based detector localizes and crops individual cells from full-scope images, followed by a fine-tuned DenseNet121 ensemble classifier that assigns each cell to one of the five morphological categories. The proposed framework achieves a detection-level F1-score of 0.9661 and a weighted-average classification F1-score of 0.9708, with an overall classification accuracy of 97.06%. Compared with the single-step YOLO26n baseline, the two-step pipeline yields a macro-average F1-score improvement of +0.1675, with particularly substantial gains for minority classes (E: +0.1623; G: +0.2774; R: +0.2603). Overall, this hybrid framework demonstrates a practical strategy for adapting fast, general-purpose detection models to domain-specific biomedical tasks by combining them with specialized classifiers, delivering both efficiency and high accuracy for scientific and clinical image analysis.

Infectious disease surveillance systems in tropical countries show that respiratory disease incidence generally manifests as year-round activity with weak fluctuations and irregular seasonality. Previously, using a ten-year time series of influenza-like illness (ILI) collected from outpatient clinics in Ho Chi Minh City (HCMC), Vietnam, we found a combination of nonannual and annual signals driving these dynamics, but with unknown mechanisms. In this study, we use seven stochastic dynamical models incorporating humidity, temperature, and school term to investigate plausible mechanisms behind these annual and nonannual incidence trends. We use iterated filtering to fit the models and evaluate the models by comparing how well they replicate the combination of annual and nonannual signals. We find that a model including specific humidity, temperature, and school term best fits our observed data from HCMC and partially reproduces the irregular seasonality. The estimated effects from specific humidity and temperature on transmission are nonlinearly negative but weak. School dismissal is associated with decreased transmission, but also with low magnitude. Under these weak external drivers, we hypothesize that stochasticity makes a strong sub-annual cycle more likely to be observed in ILI disease dynamics. Our study shows a possible mechanism for respiratory disease dynamics in the tropics. When the external drivers are weak, the seasonality of respiratory disease dynamics is prone to the influence of stochasticity.