Dose and DNA damage modelling of diffusing alpha-emitters radiation therapy using Geant4.

PURPOSE: Diffusing alpha-emitters radiation therapy (DaRT) is a brachytherapy technique using α-particles to treat solid tumours. The high linear energy transfer (LET) and short range of α-particles make them good candidates for the targeted treatment of cancer. Treatment planning of DaRT requires a good understanding of the dose from α-particles and the other particles released in the 224Ra decay chain. METHODS: The Geant4 Monte Carlo toolkit has been used to simulate a DaRT seed to better understand the dose contribution from all particles and simulate the DNA damage due to this treatment. RESULTS: Close to the seed α-particles deliver the majority of dose, however at radial distances greater than 4 mm, the contribution of ß-particles is greater. The RBE has been estimated as a function of number of double strand breaks (DSBs) and complex DSBs. A maximum seed spacing of 5.5 mm and 6.5 mm was found to deliver at least 20 Gy RBE weighted dose between the seeds for RBEDSB and RBEcDSB respectively. CONCLUSIONS: The DNA damage changes with radial distance from the seed and has been found to become less complex with distance, which is potentially easier for the cell to repair. Close to the seed α-particles contribute the majority of dose, however the contribution from other particles cannot be neglected and may influence the choice of seed spacing.

Asymptotic analysis of particle cluster formation in the presence of anchoring sites.

The aggregation or clustering of proteins and other macromolecules plays an important role in the formation of large-scale molecular assemblies within cell membranes. Examples of such assemblies include lipid rafts, and postsynaptic domains (PSDs) at excitatory and inhibitory synapses in neurons. PSDs are rich in scaffolding proteins that can transiently trap transmembrane neurotransmitter receptors, thus localizing them at specific spatial positions. Hence, PSDs play a key role in determining the strength of synaptic connections and their regulation during learning and memory. Recently, a two-dimensional (2D) diffusion-mediated aggregation model of PSD formation has been developed in which the spatial locations of the clusters are determined by a set of fixed anchoring sites. The system is kept out of equilibrium by the recycling of particles between the cell membrane and interior. This results in a stationary distribution consisting of multiple clusters, whose average size can be determined using an effective mean-field description of the particle concentration around each anchored cluster. In this paper, we derive corrections to the mean-field approximation by applying the theory of diffusion in singularly perturbed domains. The latter is a powerful analytical method for solving two-dimensional (2D) and three-dimensional (3D) diffusion problems in domains where small holes or perforations have been removed from the interior. Applications range from modeling intracellular diffusion, where interior holes could represent subcellular structures such as organelles or biological condensates, to tracking the spread of chemical pollutants or heat from localized sources. In this paper, we take the bounded domain to be the cell membrane and the holes to represent anchored clusters. The analysis proceeds by partitioning the membrane into a set of inner regions around each cluster, and an outer region where mean-field interactions occur. Asymptotically matching the inner and outer stationary solutions generates an asymptotic expansion of the particle concentration, which includes higher-order corrections to mean-field theory that depend on the positions of the clusters and the boundary of the domain. Motivated by a recent study of light-activated protein oligomerization in cells, we also develop the analogous theory for cluster formation in a three-dimensional (3D) domain. The details of the asymptotic analysis differ from the 2D case due to the contrasting singularity structure of 2D and 3D Green's functions.

Diffusion in Porous Rock Is Anomalous.

Molecular diffusion of chemical species in subsurface environments─rock formations, soil sediments, marine, river, and lake sediments─plays a critical role in a variety of dynamic processes, many of which affect water chemistry. We investigate and demonstrate the occurrence of anomalous (non-Fickian) diffusion behavior, distinct from classically assumed Fickian diffusion. We measured molecular diffusion through a series of five chalk and dolomite rock samples over a period of about two months. We demonstrate that in all cases, diffusion behavior is significantly different than Fickian. We then analyze the results using a continuous time random walk framework that can describe anomalous diffusion in heterogeneous porous materials such as rock. This methodology shows extreme long-time tailing of tracer advance as compared to conventional Fickian diffusion processes. The finding that distinct anomalous diffusion occurs ubiquitously implies that diffusion-driven processes in subsurface zones should be analyzed using tools that account for non-Fickian diffusion.

Exploring the Synthesis of Self-Organization and Active Motion.

Proteins, genetic material, and membranes are fundamental to all known organisms, yet these components alone do not constitute life. Life emerges from the dynamic processes of self-organization, assembly, and active motion, suggesting the existence of similar artificial systems. Against this backdrop, our Perspective explores a variety of chemical phenomena illustrating how nonequilibrium self-organization and micromotors contribute to life-like behavior and functionalities. After explaining key terms, we discuss specific examples including enzymatic motion, diffusiophoretic and bubble-driven self-propulsion, pattern-forming reaction-diffusion systems, self-assembling inorganic aggregates, and hierarchically emergent phenomena. We also provide a roadmap for combining self-organization and active motion and discuss possible outcomes through biological analogs. We suggest that this research direction, deeply rooted in physical chemistry, offers opportunities for further development with broad impacts on related sciences and technologies.

Quantification of diffusion coefficients of commonly used high-intensity sweeteners through mucin.

Low- and no-calorie sweeteners reduce the amount of carbohydrates in foods and beverages. However, concerns about taste perception surrounding the role of non-nutritive sweeteners in the oral cavity remain unanswered. One of the parameters that influences taste perception is the diffusion coefficient of the sweetener molecules inside the mucin layer lining the mouth. This study investigated the impact of diffusion coefficients of common high-intensity sweeteners on taste perception focusing on the sweeteners' diffusion through mucin. Transwell Permeable Support well plates were used to measure diffusion coefficients of samples that were collected at specific intervals to estimate the coefficients based on concentration measurements. The diffusion coefficients of acesulfame-K, aspartame, rebaudioside M, sucralose, and sucrose with and without NaCl were compared. We found that different sweeteners show different diffusion behavior through mucin and that the presence of salt enhances the diffusion. These findings contribute insights into the diffusion of high-intensity sweeteners, offer a way to evaluate diffusion coefficients in real-time, and inform the development of products with improved taste profiles.

Vesicle and reaction-diffusion hybrid modeling with STEPS.

Vesicles carry out many essential functions within cells through the processes of endocytosis, exocytosis, and passive and active transport. This includes transporting and delivering molecules between different parts of the cell, and storing and releasing neurotransmitters in neurons. To date, computational simulation of these key biological players has been rather limited and has not advanced at the same pace as other aspects of cell modeling, restricting the realism of computational models. We describe a general vesicle modeling tool that has been designed for wide application to a variety of cell models, implemented within our software STochastic Engine for Pathway Simulation (STEPS), a stochastic reaction-diffusion simulator that supports realistic reconstructions of cell tissue in tetrahedral meshes. The implementation is validated in an extensive test suite, parallel performance is demonstrated in a realistic synaptic bouton model, and example models are visualized in a Blender extension module.

Travelling waves for a fast reaction limit of a discrete coagulation-fragmentation model with diffusion and proliferation.

We study traveling wave solutions for a reaction-diffusion model, introduced in the article Calvez et al. (Regime switching on the propagation speed of travelling waves of some size-structured myxobacteriapopulation models, 2023), describing the spread of the social bacterium Myxococcus xanthus. This model describes the spatial dynamics of two different cluster sizes: isolated bacteria and paired bacteria. Two isolated bacteria can coagulate to form a cluster of two bacteria and conversely, a pair of bacteria can fragment into two isolated bacteria. Coagulation and fragmentation are assumed to occur at a certain rate denoted by k. In this article we study theoretically the limit of fast coagulation fragmentation corresponding mathematically to the limit when the value of the parameter k tends to + ∞ . For this regime, we demonstrate the existence and uniqueness of a transition between pulled and pushed fronts for a certain critical ratio θ ⋆ between the diffusion coefficient of isolated bacteria and the diffusion coefficient of paired bacteria. When the ratio is below θ ⋆ , the critical front speed is constant and corresponds to the linear speed. Conversely, when the ratio is above the critical threshold, the critical spreading speed becomes strictly greater than the linear speed.

The Influence of the Variable Wettability Characteristics of Layers on the Transport of Nanoparticles in the Context of Drug Delivery in Skin Structures.

The rapid development of nanotechnology has offered the possibility of creating nanosystems that can be used as drug carriers. The use of such carriers offers real opportunities for the development of non-invasive drug delivery through skin structures. However, in addition to the ability to create suitable nanocarriers, it is also necessary to know how they move through dermal layers. The human skin consists of layers with different wettability characteristics, which greatly complicates how introduced substances move through it. In this work, an experimental study of the diffusion process of nanoparticles through partitions with different wettability properties was carried out. Conventional diffusion tests using Franz chambers were used for this purpose. We quantified how the wettability of the barrier, the number of layers, and their mutual configuration affect the transport of nanoparticles. Based on the results, an analysis of the phenomena taking place, depending on the wettability of the partition, was carried out. A model relationship was also proposed to determine the effective diffusion coefficient, taking into account the influence of the wettability and porosity of the barrier.

Hydrodynamic Radii of Intrinsically Disordered Proteins: Fast Prediction by Minimum Dissipation Approximation and Experimental Validation.

The diffusion coefficients of globular and fully unfolded proteins can be predicted with high accuracy solely from their mass or chain length. However, this approach fails for intrinsically disordered proteins (IDPs) containing structural domains. We propose a rapid predictive methodology for estimating the diffusion coefficients of IDPs. The methodology uses accelerated conformational sampling based on self-avoiding random walks and includes hydrodynamic interactions between coarse-grained protein subunits, modeled using the generalized Rotne-Prager-Yamakawa approximation. To estimate the hydrodynamic radius, we rely on the minimum dissipation approximation recently introduced by Cichocki et al. Using a large set of experimentally measured hydrodynamic radii of IDPs over a wide range of chain lengths and domain contributions, we demonstrate that our predictions are more accurate than the Kirkwood approximation and phenomenological approaches. Our technique may prove to be valuable in predicting the hydrodynamic properties of both fully unstructured and multidomain disordered proteins.

Investigations on the Diffusion Behavior of Smoke-Associated Aroma Compounds into the Sausage Matrix as Affected by Casing, Caliber, and Packaging.

The aim of the study was to investigate how smoke-associated flavoring substances behave during storage in Frankfurter-type sausages. The diffusion behavior of seven selected aroma substances in the sausage matrix and the influence of the packaging and the casing were examined over a storage period of 28 days. The sausages were cut into uniformly thick layers at defined time intervals and examined by headspace-solid phase microextraction-gas chromatography-mass spectrometry. In general, three different groups could be distinguished: (1) even distribution over the entire product on the first day after smoking; (2) clear concentration gradient from outside to inside on the first day of storage, which leveled out until day 28 of storage; and (3) a clear concentration gradient that remained present throughout the storage period. In addition, only small effects were found in the distribution of flavorings between two types of packaging, selected casing, or different calibers.

Organic-solvent ditch overlap in reversed-phase liquid chromatography: A molecular dynamics simulation study in cylindrical 6-12 nm-diameter pores.

Mass transport through the mesopore space of a reversed-phase liquid chromatography (RPLC) column depends on the properties of the chromatographic interface, particularly on the extent of the organic-solvent ditch that favors the analyte surface diffusivity. Through molecular dynamics simulations in cylindrical RPLC mesopore models with pore diameters between 6 and 12 nm we systematically trace the evolution of organic-solvent ditch overlap due to spatial confinement in the mesopore space of RPLC columns for small-molecule separations. Each pore model of a silica-based, endcapped, C18-stationary phase is equilibrated with two mobile phases of comparable elution strength, namely 70/30 (v/v) water/acetonitrile and 60/40 (v/v) water/methanol, to consider the influence of the mobile-phase composition on the onset of organic-solvent ditch overlap. The simulations show that, as the pore diameter decreases from 9 to 6 nm, the bonded-phase density extends and compacts towards the pore center, which leads to increased accumulation of organic-solvent excess and thus enhanced organic-solvent diffusivity in the ditch. Because the acetonitrile ditch is more pronounced than the methanol ditch, acetonitrile ditch overlap sets in at less severe spatial confinement than methanol ditch overlap. The pore-averaged methanol and acetonitrile diffusivities are considerably raised by ditch overlap in the 6 nm-diameter pore, but also benefit from the ditch (without overlap) in the 7 to 12 nm-diameter pores, whereby local and pore-averaged effects are generally larger for acetonitrile than methanol.

Correlative single molecule lattice light sheet imaging reveals the dynamic relationship between nucleosomes and the local chromatin environment.

In the nucleus, biological processes are driven by proteins that diffuse through and bind to a meshwork of nucleic acid polymers. To better understand this interplay, we present an imaging platform to simultaneously visualize single protein dynamics together with the local chromatin environment in live cells. Together with super-resolution imaging, new fluorescent probes, and biophysical modeling, we demonstrate that nucleosomes display differential diffusion and packing arrangements as chromatin density increases whereas the viscoelastic properties and accessibility of the interchromatin space remain constant. Perturbing nuclear functions impacts nucleosome diffusive properties in a manner that is dependent both on local chromatin density and on relative location within the nucleus. Our results support a model wherein transcription locally stabilizes nucleosomes while simultaneously allowing for the free exchange of nuclear proteins. Additionally, they reveal that nuclear heterogeneity arises from both active and passive processes and highlight the need to account for different organizational principles when modeling different chromatin environments.

Variable Non-Gaussian Transport of Nanoplastic on Supported Lipid Bilayers in Saline Conditions.

Nanoplastic-lipid interaction is vital to understanding the nanoscale mechanism of plastic adsorption and aggregation on a lipid membrane surface. However, a single-particle mechanistic picture of the nanoplastic transport process on a lipid surface remains unclear. Here, we report a salt-dependent non-Gaussian transport mechanism of polystyrene particles on a supported 1-palmitoyl-2-oleoyl-glycero-3-phosphocholine (POPC) lipid bilayer surface. Particle stickiness on the POPC surface increases with salt concentration, where the particles stay longer at the surface and diffuse to shorter distances. Additionally, a non-Gaussian diffusion state dominates the transport process at high salt concentrations. Our current study provides insight into the transport mechanism of polystyrene (PS) particles on supported lipid membranes, which is essential to understanding fundamental questions regarding the adsorption mechanisms of nanoplastics on lipid surfaces.

Role of tumbling in bacterial scattering at convex obstacles.

Active propulsion, as performed by bacteria and Janus particles, in combination with hydrodynamic interaction results in the accumulation of bacteria at a flat wall. However, in microfluidic devices with cylindrical pillars of sufficiently small radius, self-propelled particles can slide along and scatter off the surface of a pillar, without becoming trapped over long times. This nonequilibrium scattering process has been predicted to result in large diffusivities, even at high obstacle density, unlike particles that undergo classical specular reflection. Here, we test this prediction by experimentally studying the nonequilibrium scattering of pusherlike swimmers in microfluidic obstacle lattices. To explore the role of tumbles in the scattering process, we microscopically tracked wild-type (run and tumble) and smooth-swimming (run only) mutants of the bacterium Escherichia coli scattering off microfluidic pillars. We quantified key scattering parameters and related them to previously proposed models that included a prediction for the diffusivity, discussing their relevance. Finally, we discuss potential interpretations of the role of tumbles in the scattering process and connect our work to the broader study of swimmers in porous media.

In situ pulmonary mucus hydration assay using rotational and translational diffusion of gold nanorods with polarization-sensitive optical coherence tomography.

Significance: Assessing the nanostructure of polymer solutions and biofluids is broadly useful for understanding drug delivery and disease progression and for monitoring therapy. Aim: Our objective is to quantify bronchial mucus solids concentration (wt. %) during hypertonic saline (HTS) treatment in vitro via nanostructurally constrained diffusion of gold nanorods (GNRs) monitored by polarization-sensitive optical coherence tomography (PS-OCT). Approach: Using PS-OCT, we quantified GNR translational (DT) and rotational (DR) diffusion coefficients within polyethylene oxide solutions (0 to 3 wt. %) and human bronchial epithelial cell (hBEC) mucus (0 to 6.4 wt. %). Interpolation of DT and DR data is used to develop an assay to quantify mucus concentration. The assay is demonstrated on the mucus layer of an air-liquid interface hBEC culture during HTS treatment. Results: In polymer solutions and mucus, DT and DR monotonically decrease with increasing concentration. DR is more sensitive than DT to changes above 1.5 wt. % of mucus and exhibits less intrasample variability. Mucus on HTS-treated hBEC cultures exhibits dynamic mixing from cilia. A region of hard-packed mucus is revealed by DR measurements. Conclusions: The extended dynamic range afforded by simultaneous measurement of DT and DR of GNRs using PS-OCT enables resolving concentration of the bronchial mucus layer over a range from healthy to disease in depth and time during HTS treatment in vitro.

Size-dependent steady state saturation limit in biomolecular transport through nuclear membranes.

The nucleus preserves the genomic DNA of eukaryotic organisms and maintains the integrity of the cell by regulating the transport of molecules across the nuclear membrane. It is hitherto assumed that small molecules having a size below the passive permeability limit are allowed to diffuse freely to the nucleus while the transport of larger molecules is regulated via an active mechanism involving energy. Here we report on the kinetics of nuclear import and export of dextran molecules having a size below the passive permeability limit. The studies carried out using time-lapse confocal fluorescence microscopy show a clear deviation from the passive diffusion model. In particular, it is observed that the steady-state concentration of dextran molecules inside the nucleus is consistently less than the concentration outside, in contradiction to the predictions of the passive diffusion model. Detailed analysis and modeling of the transport show that the nuclear export rates significantly differ from the import rates, and the difference in rates is dependent on the size of the molecules. The nuclear export rates are further confirmed by an independent experimental study where we observe the diffusion of dextran molecules from the nucleus directly. Our experiments and transport model would suggest that the nucleus actively rejects exogenous macromolecules even below the passive permeability limit. This result can have a significant impact on biomedical research, especially in areas related to targeted drug delivery and gene therapy.

stDiff: a diffusion model for imputing spatial transcriptomics through single-cell transcriptomics.

Spatial transcriptomics (ST) has become a powerful tool for exploring the spatial organization of gene expression in tissues. Imaging-based methods, though offering superior spatial resolutions at the single-cell level, are limited in either the number of imaged genes or the sensitivity of gene detection. Existing approaches for enhancing ST rely on the similarity between ST cells and reference single-cell RNA sequencing (scRNA-seq) cells. In contrast, we introduce stDiff, which leverages relationships between gene expression abundance in scRNA-seq data to enhance ST. stDiff employs a conditional diffusion model, capturing gene expression abundance relationships in scRNA-seq data through two Markov processes: one introducing noise to transcriptomics data and the other denoising to recover them. The missing portion of ST is predicted by incorporating the original ST data into the denoising process. In our comprehensive performance evaluation across 16 datasets, utilizing multiple clustering and similarity metrics, stDiff stands out for its exceptional ability to preserve topological structures among cells, positioning itself as a robust solution for cell population identification. Moreover, stDiff's enhancement outcomes closely mirror the actual ST data within the batch space. Across diverse spatial expression patterns, our model accurately reconstructs them, delineating distinct spatial boundaries. This highlights stDiff's capability to unify the observed and predicted segments of ST data for subsequent analysis. We anticipate that stDiff, with its innovative approach, will contribute to advancing ST imputation methodologies.

A Refined Thin-Film Model for Drug Dissolution Considering Radial Diffusion - Simulating Powder Dissolution.

PURPOSE: We aim to present a refined thin-film model describing the drug particle dissolution considering radial diffusion in spherical boundary layer, and to demonstrate the ability of the model to describe the dissolution behavior of bulk drug powders. METHODS: The dissolution model introduced in this study was refined from a radial diffusion-based model previously published by our laboratory (So et al. in Pharm Res. 39:907-17, 2022). The refined model was created to simulate the dissolution of bulk powders, and to account for the evolution of particle size and diffusion layer thickness during dissolution. In vitro dissolution testing, using fractionated hydrochlorothiazide powders, was employed to assess the performance of the model. RESULTS: Overall, there was a good agreement between the experimental dissolution data and the predicted dissolution profiles using the proposed model across all size fractions of hydrochlorothiazide. The model over-predicted the dissolution rate when the particles became smaller. Notably, the classic Nernst-Brunner formalism led to an under-estimation of the dissolution rate. Additionally, calculation based on the equivalent particle size derived from the specific surface area substantially over-predicted the dissolution rate. CONCLUSION: The study demonstrated the potential of the radial diffusion-based model to describe dissolution of drug powders. In contrast, the classic Nernst-Brunner equation could under-estimate drug dissolution rate, largely due to the underlying assumption of translational diffusion. Moreover, the study indicated that not all surfaces on a drug particle contribute to dissolution. Therefore, relying on the experimentally-determined specific surface area for predicting drug dissolution is not advisable.

Transfer of polarity information via diffusion of Wnt ligands in C. elegans embryos.

Different signaling mechanisms concur to ensure robust tissue patterning and cell fate instruction during animal development. Most of these mechanisms rely on signaling proteins that are produced, transported, and detected. The spatiotemporal dynamics of signaling molecules are largely unknown, yet they determine signal activity's spatial range and time frame. Here, we use the Caenorhabditis elegans embryo to study how Wnt ligands, an evolutionarily conserved family of signaling proteins, dynamically organize to establish cell polarity in a developing tissue. We identify how Wnt ligands, produced in the posterior half of the embryos, spread extracellularly to transmit information to distant target cells in the anterior half. With quantitative live imaging and fluorescence correlation spectroscopy, we show that Wnt ligands diffuse through the embryo over a timescale shorter than the cell cycle, in the intercellular space, and outside the tissue below the eggshell. We extracted diffusion coefficients of Wnt ligands and their receptor Frizzled and characterized their co-localization. Integrating our different measurements and observations in a simple computational framework, we show how fast diffusion in the embryo can polarize individual cells through a time integration of the arrival of the ligands at the target cells. The polarity established at the tissue level by a posterior Wnt source can be transferred to the cellular level. Our results support a diffusion-based long-range Wnt signaling, which is consistent with the dynamics of developing processes.

Dynamic structure of E. coli cytoplasm: supramolecular complexes and cell aging impact spatial distribution and mobility of proteins.

Protein diffusion is a critical factor governing the functioning and organization of a cell's cytoplasm. In this study, we investigate the influence of (poly)ribosome distribution, cell aging, protein aggregation, and biomolecular condensate formation on protein mobility within the E. coli cytoplasm. We employ nanoscale single-molecule displacement mapping (SMdM) to determine the spatial distribution of the proteins and to meticulously track their diffusion. We show that the distribution of polysomes does not impact the lateral diffusion coefficients of proteins. However, the degradation of mRNA induced by rifampicin treatment leads to an increase in protein mobility within the cytoplasm. Additionally, we establish a significant correlation between cell aging, the asymmetric localization of protein aggregates and reduced diffusion coefficients at the cell poles. Notably, we observe variations in the hindrance of diffusion at the poles and the central nucleoid region for small and large proteins, and we reveal differences between the old and new pole of the cell. Collectively, our research highlights cellular processes and mechanisms responsible for spatially organizing the bacterial cytoplasm into domains with different structural features and apparent viscosity.