The growth rate of senile plaques is determined by the competition between the rate of deposition of free Aß aggregates into plaques and the autocatalytic production of free Aß aggregates.

The formation of amyloid beta (Aß) deposits (senile plaques) is one of the hallmarks of Alzheimer's disease (AD). This study investigates what processes are primarily responsible for their formation. A model is developed to simulate the diffusion of amyloid beta (Aß) monomers, the production of free Aß aggregates through nucleation and autocatalytic processes, and the deposition of these aggregates into senile plaques. The model suggests that efficient degradation of Aß monomers alone may suffice to prevent the growth of senile plaques, even without degrading Aß aggregates and existing plaques. This is because the degradation of Aß monomers interrupts the supply of reactants needed for plaque formation. The impact of Aß monomer diffusivity is demonstrated to be small, enabling the application of the lumped capacitance approximation and the derivation of approximate analytical solutions for limiting cases with both small and large rates of Aß aggregate deposition into plaques. It is found that the rate of plaque growth is governed by two competing processes. One is the deposition rate of free Aß aggregates into senile plaques. If this rate is small, the plaque grows slowly. However, if the rate of deposition of Aß aggregates into senile plaques is very large, the free Aß aggregates are removed from the intracellular fluid by deposition into the plaques, leaving insufficient free Aß aggregates to catalyze the production of new aggregates. This suggests that under certain conditions, Aß plaques may offer neuroprotection and impede their own growth. Additionally, it indicates that there exists an optimal rate of deposition of free Aß aggregates into the plaques, at which the plaques attain their maximum size.

Effects of Time-Dependent Adenosine Triphosphate Consumption Caused by Neuron Firing on Adenosine Triphosphate Concentrations in Synaptic Boutons Containing and Lacking a Stationary Mitochondrion.

The precise mechanism behind the supply of adenosine triphosphate (ATP) to approximately half of the presynaptic release sites in axons that lack a stationary mitochondrion is not fully understood. This paper presents a mathematical model designed to simulate the transient ATP concentration in presynaptic en passant boutons. The model is utilized to investigate how the ATP concentration responds to increased ATP demand during neuronal firing in boutons with a stationary mitochondrion and those without one. The analysis suggests that neuron firing may cause oscillations in the ATP concentrations, with peak-to-peak amplitudes ranging from 0.06% to 5% of their average values. However, this does not deplete boutons lacking a mitochondrion of ATP; for physiologically relevant values of model parameters, their concentration remains approximately 3.75 times higher than the minimum concentration required for synaptic activity. The variance in average ATP concentrations between boutons containing a stationary mitochondrion and those lacking one ranges from 0.3% to 0.8%, contingent on the distance between the boutons. The model indicates that diffusion-driven ATP transport is rapid enough to adequately supply ATP molecules to boutons lacking a stationary mitochondrion.

Numerical modeling of senile plaque development under conditions of limited diffusivity of amyloid-ß monomers.

This paper introduces a new model to simulate the progression of senile plaques, focusing on scenarios where concentrations of amyloid beta (Aß) monomers and aggregates vary between neurons. Extracellular variations in these concentrations may arise due to limited diffusivity of Aß monomers and a high rate of Aß monomer production at lipid membranes, requiring a substantial concentration gradient for diffusion-driven transport of Aß monomers. The dimensionless formulation of the model is presented, which identifies four key dimensionless parameters governing the solutions for Aß monomer and aggregate concentrations, as well as the radius of a growing Aß plaque within the control volume. These parameters include the dimensionless diffusivity of Aß monomers, the dimensionless rate of Aß monomer production, and the dimensionless half-lives of Aß monomers and aggregates. A dimensionless parameter is then introduced to evaluate the validity of the lumped capacitance approximation. An approximate solution is derived for the scenario involving large diffusivity of Aß monomers and dysfunctional protein degradation machinery, resulting in infinitely long half-lives for Aß monomers and aggregates. In this scenario, the concentrations of Aß aggregates and the radius of the Aß plaque depend solely on a single dimensionless parameter that characterizes the rate of Aß monomer production. According to the approximate solution, the concentration of Aß aggregates is linearly dependent on the rate of monomer production, and the radius of an Aß plaque is directly proportional to the cube root of the rate of monomer production. However, when departing from the conditions of the approximate solution (e.g., finite half-lives), the concentrations of Aß monomers and aggregates, along with the plaque radius, exhibit complex dependencies on all four dimensionless parameters. For instance, under physiological half-life conditions, the plaque radius reaches a maximum value and stabilizes thereafter.

Modelling fuel oil transformation on geographically different seacoasts and assessing their self-cleansing capacity.

The present paper considers the results of long-term (up to 17 years) in situ and laboratory research carried out on oiled French, Spanish, and Russian seacoasts. The objective of this research is to quantify the influence of geographical factors on the rates of natural transformation of the heavy fuel oil stranded ashore and to develop an empirical statistical model in order to evaluate the self-cleansing capacity of the coastal environment. In a number of field campaigns, 363 samples of weathered oil slicks and tar balls have been collected and analysed with the use of thin-layer chromatography combined with optical and gravimetric methods. The results obtained have been subjected to multiple nonlinear regression analyses. It has been shown that heavy fuel oil natural attenuation is more active in continental or estuarine environments influenced by nutrient-rich freshwater runoff and characterised by a higher number of sunny days, solar irradiation, and large temperature fluctuations. On the oceanic coasts, especially in sectors with low hydrodynamic energy, these processes take more time. The resulting model allows for the identification and mapping of the most vulnerable seacoasts, characterised by a low potential to degrade oil pollution. This information may be used in the contingency plans in order to optimise clean-up techniques and associated costs.

Numerical and Analytical Simulation of the Growth of Amyloid-ß Plaques.

Numerical and analytical solutions were employed to calculate the radius of an amyloid-ß (Aß) plaque over time. To the author's knowledge, this study presents the first model simulating the growth of Aß plaques. Findings indicate that the plaque can attain a diameter of 50 µm after 20 years of growth, provided the Aß monomer degradation machinery is malfunctioning. A mathematical model incorporates nucleation and autocatalytic growth processes using the Finke-Watzky model. The resulting system of ordinary differential equations was solved numerically, and for the simplified case of infinitely long Aß monomer half-life, an analytical solution was found. Assuming that Aß aggregates stick together and using the distance between the plaques as an input parameter of the model, it was possible to calculate the plaque radius from the concentration of Aß aggregates. This led to the "cube root hypothesis," positing that Aß plaque size increases proportionally to the cube root of time. This hypothesis helps explain why larger plaques grow more slowly. Furthermore, the obtained results suggest that the plaque size is independent of the kinetic constants governing Aß plaque agglomeration, indicating that the kinetics of Aß plaque agglomeration is not a limiting factor for plaque growth. Instead, the plaque growth rate is limited by the rates of Aß monomer production and degradation.

Lewy body radius growth: The hypothesis of the cube root of time dependency.

This paper presents a model for the growth of Lewy bodies (LBs), which are pathological hallmarks of Parkinson's disease (PD). The model simulates the growth of classical LBs, consisting of a core and a halo. The core is assumed to comprise lipid membrane fragments and damaged organelles, while the halo consists of radiating alpha-synuclein (α-syn) fibrils. The Finke-Watzky model is employed to simulate the aggregation of lipid fragments and α-syn monomers. Analytical and numerical exploration of the governing equations yielded approximate solutions applicable for larger times. The application of these approximate solutions to simulate LB radius growth led to the discovery of the cube root hypothesis, which posits that the LB radius is proportional to the cube root of its growth time. Sensitivity analysis revealed that the LB radius is unaffected by the kinetic rates of nucleation and autocatalytic growth, with growth primarily regulated by the production rates of lipid membrane fragments and α-syn monomers. The model indicates that the formation of large LBs associated with PD is dependent on the malfunction of the machinery responsible for the degradation of lipid membrane fragments, α-syn monomers, and their aggregates.

ATAT: Automated Tissue Alignment and Traversal in Spatial Transcriptomics with Self-Supervised Learning.

Spatial transcriptomics (ST) has enhanced RNA analysis in tissue biopsies, but interpreting these data is challenging without expert input. We present Automated Tissue Alignment and Traversal (ATAT), a novel computational framework designed to enhance ST analysis in the context of multiple and complex tissue architectures and morphologies, such as those found in biopsies of the gastrointestinal tract. ATAT utilizes self-supervised contrastive learning on hematoxylin and eosin (H&E) stained images to automate the alignment and traversal of ST data. This approach addresses a critical gap in current ST analysis methodologies, which rely heavily on manual annotation and pathologist expertise to delineate regions of interest for accurate gene expression modeling. Our framework not only streamlines the alignment of multiple ST samples, but also demonstrates robustness in modeling gene expression transitions across specific regions. Additionally, we highlight the ability of ATAT to traverse complex tissue topologies in real-world cases from various individuals and conditions. Our method successfully elucidates differences in immune infiltration patterns across the intestinal wall, enabling the modeling of transcriptional changes across histological layers. We show that ATAT achieves comparable performance to the state-of-the-art method, while alleviating the burden of manual annotation and enabling alignment of tissue samples with complex morphologies.

Magnetostatic response and field-controlled haloing in binary superparamagnetic mixtures.

Nowadays, magnetoresponsive soft materials, based not simply on magnetic nanoparticles but rather on multiple components with distinct sizes and magnetic properties in both liquid and polymeric carriers, are becoming more and more widespread due to their unique and versatile macroscopic response to an applied magnetic field. The variability of the latter is related to a complex interplay of the magnetic interactions in a highly nonuniform internal field caused by spatial inhomogeneity in multicomponent systems. In this work, we present a combined analytical and simulation study of binary superparamagnetic systems containing nanoclusters and dispersed single-domain nanoparticles in both liquid and solid carrier matrices. We investigate the equilibrium magnetic response of these systems for wide ranges of concentrations and interaction energies. It turns out that, while the magnetization of a binary solid can be both above and below that of an ideal superparamagnetic gas, depending on the concentration of the dispersed phase and the interparticle interactions, the system in a liquid carrier is highly magnetically responsive. In liquid, a spatial redistribution of the initially homogeneously dispersed phase in the vicinity of the nanocluster is observed, an effect that is reminiscent of the so-called haloing effect previously observed experimentally on micro- and milliscales.