Analytical solution of fuzzy heat problem in two-dimensional case under Caputo-type fractional derivative.

This work aims to investigate the analytical solution of a two-dimensional fuzzy fractional-ordered heat equation that includes an external diffusion source factor. We develop the Sawi homotopy perturbation transform scheme (SHPTS) by merging the Sawi transform and the homotopy perturbation scheme. The fractional derivatives are examined in Caputo sense. The novelty and innovation of this study originate from the fact that this technique has never been tested for two-dimensional fuzzy fractional ordered heat problems. We presented two distinguished examples to validate our scheme, and the solutions are in fuzzy form. We also exhibit contour and surface plots for the lower and upper bound solutions of two-dimensional fuzzy fractional-ordered heat problems. The results show that this approach works quite well for resolving fuzzy fractional situations.

Evaluation of the DGT passive samplers for integrating fluctuating concentrations of pharmaceuticals in surface water.

Diffusive gradients in thin films (DGTs) have been well-documented for the measurement of a broad range of organic pollutants in surface water. However, the performance has been challenged by the inherent periodic concentration fluctuations for most organic pollutants. Therefore, there is an urgent need to assess the true time-weighted average (TWA) concentration based on fluctuating concentration profiles. The study aimed to evaluate the responsiveness of DGT and accuracy of TWA concentrations, considering various concentration fluctuating scenarios of 20 pharmaceuticals in surface water. The reliability and accuracy of the TWA concentrations measured by the DGT were assessed by comparison with the sum of cumulative mass of DGT exposed at different stages over the deployment period. The results showed that peak concentration duration (1-5 days), peak concentration fluctuation intensity (6-20 times), and occurrence time of peak concentration fluctuation (early, middle, and late stages) have minimal effect on DGT's response to most target pharmaceutical concentration fluctuations (0.8 < CDGT/CTWA < 1.2). While the downward-bent accumulations of a few pharmaceuticals on DGT occur as the sampling time increases, which could be accounted for by capacity effects during a long-time sampling period. Additionally, the DGT device had good sampling performance in recording short fluctuating concentrations from a pulse event returning to background concentrations with variable intensity and duration. This study revealed a satisfactory capacity for the evaluation of the TWA concentration of pharmaceuticals integrated over the period of different pulse deployment for DGT, suggesting that this passive sampler is ideally suited as a monitoring tool for field application. This study represents the first trial for evaluating DGT sampling performance for pharmaceuticals with multiple concentration fluctuating scenarios over time, which would be valuable for assessing the pollution status in future monitoring campaign.

Application of diffusive gradient in thin films probes to monitor trace levels of labile methylmercury in freshwaters.

This study aimed to optimize the methods for sampling and analyzing methylmercury (MeHg) concentrated within diffusive gradients in thin films (DGT) and its application to different water bodies. We explored the elution solution for MeHg, comprised of 1.13 mM thiourea and 0.1M HCl, optimizing its volume to 50 mL. In addition, we found that it is necessary to analyze the entire extraction solution after adjusting its pH, to ensure completion of the ethylation reaction. The DGT samplers were deployed in two distinct aquatic environments (i.e., Okjeong Lake and Nakdong River) for up to 6 weeks, and this study demonstrated to predict the time-weighted average concentration with a diffusion coefficient of 7.65 × 10-6 cm2 s-1 for MeHg in the diffusive gel. To assess the diffusive boundary layer (DBL) effects, the DGT samplers with different agarose diffusive gel thickness were deployed. The mass of MeHg accumulated in the DGT resin at a given time decreased with increasing diffusive gel thickness, because of creating longer diffusion pathways within thicker gels. The labile MeHg concentration estimated by the DGT in Okjeong Lake and Nakdong River are found in the range of 61-111 and 55-105 pg L-1, respectively, which were found to be similar to the grab sampling data. Additionally, this study evaluated depth-dependent MeHg in Okjeong Lake. The vertical profile results showed that the concentration of MeHg at the depth of 2.3 and 15.7 m are about 1.5 and 4.6 times of the DGT installed at 0.3 m of the surface layer, respectively, suggesting potential mercury methylation in deep waters. These findings have practical implications for predicting bioavailability, assessing risks, and formulating strategies for water body management and contamination remediation.

GLDM: hit molecule generation with constrained graph latent diffusion model.

Discovering hit molecules with desired biological activity in a directed manner is a promising but profound task in computer-aided drug discovery. Inspired by recent generative AI approaches, particularly Diffusion Models (DM), we propose Graph Latent Diffusion Model (GLDM)-a latent DM that preserves both the effectiveness of autoencoders of compressing complex chemical data and the DM's capabilities of generating novel molecules. Specifically, we first develop an autoencoder to encode the molecular data into low-dimensional latent representations and then train the DM on the latent space to generate molecules inducing targeted biological activity defined by gene expression profiles. Manipulating DM in the latent space rather than the input space avoids complicated operations to map molecule decomposition and reconstruction to diffusion processes, and thus improves training efficiency. Experiments show that GLDM not only achieves outstanding performances on molecular generation benchmarks, but also generates samples with optimal chemical properties and potentials to induce desired biological activity.

MAM-E: Mammographic Synthetic Image Generation with Diffusion Models.

Generative models are used as an alternative data augmentation technique to alleviate the data scarcity problem faced in the medical imaging field. Diffusion models have gathered special attention due to their innovative generation approach, the high quality of the generated images, and their relatively less complex training process compared with Generative Adversarial Networks. Still, the implementation of such models in the medical domain remains at an early stage. In this work, we propose exploring the use of diffusion models for the generation of high-quality, full-field digital mammograms using state-of-the-art conditional diffusion pipelines. Additionally, we propose using stable diffusion models for the inpainting of synthetic mass-like lesions on healthy mammograms. We introduce MAM-E, a pipeline of generative models for high-quality mammography synthesis controlled by a text prompt and capable of generating synthetic mass-like lesions on specific regions of the breast. Finally, we provide quantitative and qualitative assessment of the generated images and easy-to-use graphical user interfaces for mammography synthesis.

A Study of the Drift Phenomena of Gate-Functionalized Biosensors and Dual-Gate-Functionalized Biosensors in Human Serum.

In this paper, we study the drift behavior of organic electrochemical transistor (OECT) biosensors in a phosphate-buffered saline (PBS) buffer solution and human serum. Theoretical and experimental methods are illustrated in this paper to understand the origin of the drift phenomenon and the mechanism of ion diffusion in the sensing layer. The drift phenomenon is explained using a first-order kinetic model of ion adsorption into the gate material and shows very good agreement with experimental data on drift in OECTs. We show that the temporal current drift can be largely mitigated using a dual-gate OECT architecture and that dual-gate-based biosensors can increase the accuracy and sensitivity of immuno-biosensors compared to a standard single-gate design. Specific binding can be detected at a relatively low limit of detection, even in human serum.

A psycholinguistic study of intergroup bias and its cultural propagation.

Intergroup bias is the tendency for people to inflate positive regard for their in-group and derogate the out-group. Across two online experiments (N = 922) this study revisits the methodological premises of research on language as a window into intergroup bias. Experiment 1 examined (i) whether the valence (positivity) of language production differs when communicating about an in- vs. out-group, and (ii) whether the extent of this bias is influenced by the positivity of input descriptors that were initially presented to participants as examples of how an in-group or out-group characterize themselves. Experiment 2 used the linear diffusion chain method to examine how biases are transmitted through cultural generations. Valence of verbal descriptions were quantified using ratings obtained from a large-scale psycholinguistic database. The findings from Experiment 1 indicated a bias towards employing positive language in describing the in-group (exhibiting in-group favoritism), particularly in cases where the input descriptors were negative. However, there was weak evidence for increased negativity aimed at the out-group (i.e., out-group derogation). The findings from Experiment 2 demonstrated that in-group positivity bias propagated across cultural generations at a higher rate than out-group derogation. The results shed light on the formation and cultural transmission of intergroup bias.

A hard sphere model for single-file water transport across biological membranes.

We use Gürsey's statistical mechanics of a one-dimensional fluid to find a formula for the P f / P d ratio in the transport of hard spheres across a membrane through a narrow channel that can accommodate molecular movement only in single file. P f is the membrane permeability for osmotic flow and P d the permeability for exchange across the membrane in the absence of osmotic flow. The deviation of the ratio from unity indicates the degree of cooperative transport relative to ordinary diffusion of independent molecules. In contrast to an early idea that P f / P d must be equal to the number of molecules in the channel, regardless of the physical nature of the interactions among the molecules, we find a functional dependence on the fractional occupancy of the length of the channel by the hard spheres. We also attempt a random walk calculation for P d individually, which gives a result for P f as well when combined with the ratio.

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.

Biomolecular Interaction Analysis Quantification with a Low-Volume Microfluidic Chip and Particle Diffusometry.

Microfluidic techniques are widely applied in biomolecular analysis and disease diagnostic assays. While the volume of the sample that is directly used in such assays is often only femto-to microliters, the "dead volume" of solutions supplied in syringes and tubing can be much larger, even up to milliliters, increasing overall reagent use and making analysis significantly more expensive. To reduce the difficulty and cost, we designed a new chip using a low volume solution for analysis and applied it to obtain real-time data for protein-protein interaction measurements. The chip takes advantage of air/aqueous two-phase droplet flow, on-chip rapid mixing within milliseconds, and a droplet capture method, that ultimately requires only 2 µL of reagent solution. The interaction is analyzed by particle diffusometry, a nonintrusive and precise optical detection method to analyze the properties of microparticle diffusion in solution. Herein, we demonstrate on-chip characterization of human immunodeficiency virus p24 antibody-antigen protein binding kinetics imaged via fluorescence microscopy and analyzed by PD. The measured kon and koff are 1 × 106 M-1 s-1 and 3.3 × 10-4 s-1, respectively, and agree with independent measurement via biolayer interferometry and previously calculated p24-antibody binding kinetics. This new microfluidic chip and the protein-protein interaction analysis method can also be applied in other fields that require low-volume solutions to perform accurate measurement, analysis, and detection.

Single-Molecule Diffusivity Quantification Unveils Ubiquitous Net Charge-Driven Protein-Protein Interaction.

Recent microscopy and nuclear magnetic resonance (NMR) studies have noticed substantial suppression of intracellular diffusion for positively charged proteins, suggesting an overlooked role of electrostatic attraction in nonspecific protein interactions in a predominantly negatively charged intracellular environment. Utilizing single-molecule detection and statistics, here, we quantify in aqueous solutions how protein diffusion, in the limit of low diffuser concentration to avoid aggregate/coacervate formation, is modulated by differently charged interactor proteins over wide concentration ranges. We thus report substantially suppressed diffusion when oppositely charged interactors are added at parts per million levels, yet unvaried diffusivities when same-charge interactors are added beyond 1%. The electrostatic attraction-driven suppression of diffusion is sensitive to the protein net charge states, as probed by varying the solution pH and ionic strength or chemically modifying the proteins and is robust across different diffuser-interactor pairs. By converting the measured diffusivities to diffuser diameters, we further show that in the limit of excess interactors, a positively charged diffuser molecule effectively drags along just one monolayer of negatively charged interactors, where further interactions stop. We thus unveil ubiquitous, net charge-driven protein-protein interactions and shed new light on the mechanism of charge-based diffusion suppression in living cells.

Development of a novel DGT passive sampler for measuring polycyclic aromatic hydrocarbons in aquatic systems.

Polycyclic aromatic hydrocarbons (PAHs) are priority pollutants and need to be measured reliably in waters and other media, to understand their sources, fate, behaviour and to meet regulatory monitoring requirements. Conventional water sampling requires large water volumes, time-consuming pre-concentration and clean-up and is prone to analyte loss or contamination. Here, for the first time, we developed and validated a novel diffusive gradients in thin-films (DGT) passive sampler for PAHs. Based on the well-known DGT principles, the sampler pre-concentrates PAHs with typical deployment times of days/weeks, with minimal sample handling. For the first time, DGT holding devices made of metal and suitable for sampling hydrophobic organic compounds were designed and tested. They minimize sorption and sampling lag times. Following tests on different binding layer resins, a MIP-DGT was preferred - the first time applying MIP for PAHs. It samples PAHs independent of pH (3.9 -8.1), ionic strength (0.01 -0.5 M) and dissolved organic matter < 20 mg L-1, making it suitable for applications across a wide range of environments. Field trials in river water and wastewater demonstrated that DGT is a convenient and reliable tool for monitoring labile PAHs, readily achieving quantitative detection of environmental levels (sub-ng and ng/L range) when coupled with conventional GC-MS or HPLC. ENVIRONMENTAL IMPLICATIONS: PAHs are carcinogenic and genotoxic compounds. They are environmentally ubiquitous and must be monitored in waters and other media. This study successfully developed a new DGT passive sampler for reliable in situ time-integrated measurements of PAHs in waters at the ng/L level. This is the first time to use passive samplers for accurate measurements of hydrophobic organic contaminants in aquatic systems without calibration, a big step forward in monitoring PAHs. The application of this new sampler will enhance our understanding of the sources, fate, behavior and ecotoxicology of PAHs, enabling improved environmental risk assessment and management of these compounds.

Label-Free Light Scattering Imaging with Purified Brownian Motion Differentiates Small Extracellular Vesicles in Cell Microenvironments.

Small extracellular vesicles (sEVs) are heterogeneous biological nanoparticles (NPs) with wide biomedicine applications. Tracking individual nanoscale sEVs can reveal information that conventional microscopic methods may lack, especially in cellular microenvironments. This usually requires biolabeling to identify single sEVs. Here, we developed a light scattering imaging method based on dark-field technology for label-free nanoparticle diffusion analysis (NDA). Compared with nanoparticle tracking analysis (NTA), our method was shown to determine the diffusion probabilities of a single NP. It was demonstrated that accurate size determination of NPs of 41 and 120 nm in diameter is achieved by purified Brownian motion (pBM), without or within the cell microenvironments. Our pBM method was also shown to obtain a consistent size estimation of the normal and cancerous plasma-derived sEVs without and within cell microenvironments, while cancerous plasma-derived sEVs are statistically smaller than normal ones. Moreover, we showed that the velocity and diffusion coefficient are key parameters for determining the diffusion types of the NPs and sEVs in a cancerous cell microenvironment. Our light scattering-based NDA and pBM methods can be used for size determination of NPs, even in cell microenvironments, and also provide a tool that may be used to analyze sEVs for many biomedical applications.

Modeling of brain efflux: Constraints of brain surfaces.

Fluid efflux from the brain plays an important role in solute waste clearance. Current experimental approaches provide little spatial information, and data collection is limited due to short duration or low frequency of sampling. One approach shows tracer efflux to be independent of molecular size, indicating bulk flow, yet also decelerating like simple membrane diffusion. In an apparent contradiction to this report, other studies point to tracer efflux acceleration. We here develop a one-dimensional advection-diffusion model to gain insight into brain efflux principles. The model is characterized by nine physiological constants and three efflux parameters for which we quantify prior uncertainty. Using Bayes' rule and the two efflux studies, we validate the model and calculate data-informed parameter distributions. The apparent contradictions in the efflux studies are resolved by brain surface boundaries being bottlenecks for efflux. To critically test the model, a custom MRI efflux assay measuring solute dispersion in tissue and release to cerebrospinal fluid was employed. The model passed the test with tissue bulk flow velocities in the range 60 to 190 [Formula: see text]m/h. Dimensional analysis identified three principal determinants of efflux, highlighting brain surfaces as a restricting factor for metabolite solute clearance.

Two-Photon Microscopy for the Study of Tendons.

Two-photon microscopy has emerged as a potent tool for evaluating deep tissue cells and characterizing the alignment of the extracellular matrix (ECM) in various biological systems. This technique relies on nonlinear light-matter interactions to detect two distinct signals: the second harmonic generated (SHG) diffusion signal, which facilitates the visualization of collagen fibers and their orientation, and the near-infrared excitation signal for imaging ultraviolet excited autofluorescence. SHG imaging proves especially effective in visualizing collagen fibers due to the non-centrosymmetric crystalline structure of fibrillar collagen I. Given that tendons are matrix-rich tissues with a limited number of cells, their high collagen content makes them ideal candidates for analysis using two-photon microscopy. Consequently, two-photon microscopy offers a valuable means to analyze and characterize collagen abnormalities in tendons. Its application extends to studying tendon development, injuries, healing, and aging, enabling the comprehensive characterization of tendon cells and their interactions with the ECM under various conditions using two-photon microscopy tools. This protocol outlines the use of two-photon microscopy in tendon biology and presents an adapted methodology to achieve effective imaging and characterization of tendon cells during development and after injury. The method allows the utilization of thin microscopic sections to create a comprehensive image of the ECM within tendons and the cells that interact with this matrix. Most notably, the article showcases a technique to generate 3D images using two-photon microscopy in animal models.

Radiopharmaceutical transport in solid tumors via a 3-dimensional image-based spatiotemporal model.

Lutetium-177 prostate-specific membrane antigen (177Lu-PSMA)-targeted radiopharmaceutical therapy is a clinically approved treatment for patients with metastatic castration-resistant prostate cancer (mCRPC). Even though common practice reluctantly follows "one size fits all" approach, medical community believes there is significant room for deeper understanding and personalization of radiopharmaceutical therapies. To pursue this aim, we present a 3-dimensional spatiotemporal radiopharmaceutical delivery model based on clinical imaging data to simulate pharmacokinetic of 177Lu-PSMA within the prostate tumors. The model includes interstitial flow, radiopharmaceutical transport in tissues, receptor cycles, association/dissociation with ligands, synthesis of PSMA receptors, receptor recycling, internalization of radiopharmaceuticals, and degradation of receptors and drugs. The model was studied for a range of values for injection amount (100-1000 nmol), receptor density (10-500 nmol•l-1), and recycling rate of receptors (10-4 to 10-1 min-1). Furthermore, injection type, different convection-diffusion-reaction mechanisms, characteristic time scales, and length scales are discussed. The study found that increasing receptor density, ligand amount, and labeled ligands improved radiopharmaceutical uptake in the tumor. A high receptor recycling rate (0.1 min-1) increased radiopharmaceutical concentration by promoting repeated binding to tumor cell receptors. Continuous infusion results in higher radiopharmaceutical concentrations within tumors compared to bolus administration. These insights are crucial for advancing targeted therapy for prostate cancer by understanding the mechanism of radiopharmaceutical distribution in tumors. Furthermore, measures of characteristic length and advection time scale were computed. The presented spatiotemporal tumor transport model can analyze different physiological parameters affecting 177Lu-PSMA delivery.

Modelling non-local cell-cell adhesion: a multiscale approach.

Cell-cell adhesion plays a vital role in the development and maintenance of multicellular organisms. One of its functions is regulation of cell migration, such as occurs, e.g. during embryogenesis or in cancer. In this work, we develop a versatile multiscale approach to modelling a moving self-adhesive cell population that combines a careful microscopic description of a deterministic adhesion-driven motion component with an efficient mesoscopic representation of a stochastic velocity-jump process. This approach gives rise to mesoscopic models in the form of kinetic transport equations featuring multiple non-localities. Subsequent parabolic and hyperbolic scalings produce general classes of equations with non-local adhesion and myopic diffusion, a special case being the classical macroscopic model proposed in Armstrong et al. (J Theoret Biol 243(1): 98-113, 2006). Our simulations show how the combination of the two motion effects can unfold. Cell-cell adhesion relies on the subcellular cell adhesion molecule binding. Our approach lends itself conveniently to capturing this microscopic effect. On the macroscale, this results in an additional non-linear integral equation of a novel type that is coupled to the cell density equation.

A rigorous theoretical and numerical analysis of a nonlinear reaction-diffusion epidemic model pertaining dynamics of COVID-19.

The spatial movement of the human population from one region to another and the existence of super-spreaders are the main factors that enhanced the disease incidence. Super-spreaders refer to the individuals having transmitting ability to multiple pathogens. In this article, an epidemic model with spatial and temporal effects is formulated to analyze the impact of some preventing measures of COVID-19. The model is developed using six nonlinear partial differential equations. The infectious individuals are sub-divided into symptomatic, asymptomatic and super-spreader classes. In this study, we focused on the rigorous qualitative analysis of the reaction-diffusion model. The fundamental mathematical properties of the proposed COVID-19 epidemic model such as boundedness, positivity, and invariant region of the problem solution are derived, which ensure the validity of the proposed model. The model equilibria and its stability analysis for both local and global cases have been presented. The normalized sensitivity analysis of the model is carried out in order to observe the crucial factors in the transmission of infection. Furthermore, an efficient numerical scheme is applied to solve the proposed model and detailed simulation are performed. Based on the graphical observation, diffusion in the context of confined public gatherings is observed to significantly inhibit the spread of infection when compared to the absence of diffusion. This is especially important in scenarios where super-spreaders may play a major role in transmission. The impact of some non-pharmaceutical interventions are illustrated graphically with and without diffusion. We believe that the present investigation will be beneficial in understanding the complex dynamics and control of COVID-19 under various non-pharmaceutical interventions.

Elzaki residual power series method to solve fractional diffusion equation.

The time-fractional order differential equations are used in many different contexts to analyse the integrated scientific phenomenon. Hence these equations are the point of interest of the researchers. In this work, the diffusion equation for a one-dimensional time-fractional order is solved using a combination of residual power series method with Elzaki transforms. The residual power series approach is a useful technique for finding approximate analytical solutions of fractional differential equations that needs the residual function's (n-1)α derivative. Since it is challenging to determine a function's fractional-order derivative, the traditional residual power series method's application is somewhat constrained. The Elzaki transform with residual power series method is an attempt to get over the limitations of the residual power series method. The obtained numerical solutions are compared with the exact solution of this equation to discuss the method's applicability and efficiency. The results are also graphically displayed to show how the fractional derivative influences the behaviour of the solutions to the suggested method.