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.

Why slow axonal transport is bidirectional - can axonal transport of tau protein rely only on motor-driven anterograde transport?

Slow axonal transport (SAT) moves multiple proteins from the soma, where they are synthesized, to the axon terminal. Due to the great lengths of axons, SAT almost exclusively relies on active transport, which is driven by molecular motors. The puzzling feature of slow axonal transport is its bidirectionality. Although the net direction of SAT is anterograde, from the soma to the terminal, experiments show that it also contains a retrograde component. One of the proteins transported by SAT is the microtubule-associated protein tau. To better understand why the retrograde component in tau transport is needed, we used the perturbation technique to analyze how the full tau SAT model can be simplified for the specific case when retrograde motor-driven transport and diffusion-driven transport of tau are negligible and tau is driven only by anterograde (kinesin) motors. The solution of the simplified equations shows that without retrograde transport the tau concentration along the axon length stays almost uniform (decreases very slightly), which is inconsistent with the experimenal tau concentration at the outlet boundary (at the axon tip). Thus kinesin-driven transport alone is not enough to explain the empirically observed distribution of tau, and the retrograde motor-driven component in SAT is needed.

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.

Effect of mitochondrial circulation on mitochondrial age density distribution.

Recent publications report that although the mitochondria population in an axon can be quickly replaced by a combination of retrograde and anterograde axonal transport (often within less than 24 hours), the axon contains much older mitochondria. This suggests that not all mitochondria that reach the soma are degraded and that some are recirculating back into the axon. To explain this, we developed a model that simulates mitochondria distribution when a portion of mitochondria that return to the soma are redirected back to the axon rather than being destroyed in somatic lysosomes. Utilizing the developed model, we studied how the percentage of returning mitochondria affects the mean age and age density distributions of mitochondria at different distances from the soma. We also investigated whether turning off the mitochondrial anchoring switch can reduce the mean age of mitochondria. For this purpose, we studied the effect of reducing the value of a parameter that characterizes the probability of mitochondria transition to the stationary (anchored) state. The reduction in mitochondria mean age observed when the anchoring probability is reduced suggests that some injured neurons may be saved if the percentage of stationary mitochondria is decreased. The replacement of possibly damaged stationary mitochondria with newly synthesized ones may restore the energy supply in an injured axon. We also performed a sensitivity study of the mean age of stationary mitochondria to the parameter that determines what portion of mitochondria re-enter the axon and the parameter that determines the probability of mitochondria transition to the stationary state. The sensitivity of the mean age of stationary mitochondria to the mitochondria stopping probability increases linearly with the number of compartments in the axon. High stopping probability in long axons can significantly increase mitochondrial age.

Mitochondrial transport in symmetric and asymmetric axons with multiple branching junctions: a computational study.

Mitochondrial aging has been proposed to be involved in a variety of neurodegenerative disorders, such as Parkinson's disease. Here, we explore the impact of multiple branching junctions in axons on the mean age of mitochondria and their age density distributions in demand sites. The study examined mitochondrial concentration, mean age, and age density distribution in relation to the distance from the soma. We developed models for a symmetric axon containing 14 demand sites and an asymmetric axon containing 10 demand sites. We investigated how the concentration of mitochondria changes when an axon splits into two branches at the branching junction. Additionally, we studied whether mitochondrial concentrations in the branches are affected by what proportion of mitochondrial flux enters the upper branch versus the lower branch. Furthermore, we explored whether the distributions of mitochondrial mean age and age density in branching axons are affected by how the mitochondrial flux splits at the branching junction. When the mitochondrial flux is unevenly split at the branching junction of an asymmetric axon, with a greater proportion of the flux entering the longer branch, the average age of mitochondria (system age) in the axon increases. Our findings elucidate the effects of axonal branching on the mitochondrial age.

Multicore-based ferrofluids in zero field: initial magnetic susceptibility and self-assembly mechanisms.

The necessity to improve magnetic building blocks in magnetic nano-structured soft materials stems from a fascinating potential these materials have in bio-medical applications and nanofluidics. Along with practical reasons, the interplay of magnetic and steric interactions on one hand, and entropy, on the other, makes magnetic soft matter fundamentally challenging. Recently, in order to tailor magnetic response of the magnetic particle suspensions, the idea arose to replace standard single-core nanoparticles with nano-sized clusters of single-domain nanoparticles (grains) rigidly bound together by solid polymer matrix - multicore magnetic nanoparticles (MMNPs). To pursue this idea, a profound understanding of the MMNP interactions and self-assembly is required. In this work we present a computational study of the MMNP suspensions and elucidate their self-assembly and magnetic susceptibility. We show that depending on the magnetic moment of individual grains the suspensions exhibit qualitatively distinct regimes. Firstly, if the grains are moderately interacting, they contribute to a significant decrease of the remanent magnetisation of MMNPs and as such to a decrease of the magnetic susceptibility, this way confirming previous findings. If the grains are strongly interacting, instead, they serve as anchor points and support formation of grain clusters that span through several MMNPs, leading to MMNP cluster formation and a drastic increase of the initial magnetic response. Both the topology of the clusters and their size distribution in MMNP suspensions is found to be notably different from those formed in conventional magnetic fluids or magnetorheological suspensions.

XANES/EXAFS and quantum chemical study of the speciation of arsenic in the condensate formed in landfill gas processing: Evidence of the dominance of As-S species.

The XANES/EXAFS data and quantum chemical simulations presented in this study demonstrate several features of the chemistry of arsenic compounds found in the condensates and solids generated in landfill gas (LFG) processing carried out for renewable natural gas (RNG) production. The XANES data show the decrease in the position of the absorption edge of As atoms, similar to that characteristic for sulfur-containing As solutes and solids. The EXAFS data show that the As-O and As-S distances in these matrixes are similar to those in thioarsenates. Quantum-chemical calculations demonstrated the close agreement between the experimental and modeled As-S and As-O distances determined for a range of methylated and thiolated arsenic solutes. These calculations also showed that the increase of the number of the As-S bonds in the coordination shell of arsenic is accompanied by a consistent decrease of the charges of As atoms. This decrease is correlated with the number of the As-S bonds, in agreement with the trend observed in the XANES data. These results provide insight into the intrinsic chemistry and reactivity of As species present in LFG matrixes; they may be helpful for the development of treatment methods to control arsenic in these systems.

Mitochondrial Transport in Symmetric and Asymmetric Axons with Multiple Branching Junctions: A Computational Study.

We explore the impact of multiple branching junctions in axons on the mean age of mitochondria and their age density distributions in demand sites. The study looked at mitochondrial concentration, mean age, and age density distribution in relation to the distance from the soma. We developed models for a symmetric axon containing 14 demand sites and an asymmetric axon containing 10 demand sites. We examined how the concentration of mitochondria changes when an axon splits into two branches at the branching junction. We also studied whether mitochondria concentrations in the branches are affected by what proportion of mitochondrial flux enters the upper branch and what proportion of flux enters the lower branch. Additionally, we explored whether the distributions of mitochondria mean age and age density in branching axons are affected by how the mitochondrial flux splits at the branching junction. When the mitochondrial flux is split unevenly at the branching junction of an asymmetric axon, with a greater proportion of the flux entering the longer branch, the average age of mitochondria (system age) in the axon increases. Our findings elucidate the effects of axonal branching on mitochondria age. Mitochondria aging is the focus of this study as recent research suggests it may be involved in neurodegenerative disorders, such as Parkinson's disease.

ATP diffusional gradients are sufficient to maintain bioenergetic homeostasis in synaptic boutons lacking mitochondria.

Previous work on mitochondrial distribution in axons has shown that approximately half of the presynaptic release sites do not contain mitochondria, raising the question of how the boutons that do not contain mitochondria are supplied with ATP. Here, we develop and apply a mathematical model to study this question. Specifically, we investigate whether diffusive transport of ATP is sufficient to support the exocytic functionality in synaptic boutons which lack mitochondria. Our results demonstrate that the difference in ATP concentration between a bouton containing a mitochondrion and a neighboring bouton lacking a mitochondrion is only approximately 0.4%, which is still 3.75 times larger than the ATP concentration minimally required to support synaptic vesicle release. This work therefore suggests that passive diffusion of ATP is sufficient to maintain the functionality of boutons which do not contain mitochondria.

DFT and ONIOM Simulation of 1,3-Butadiene Polymerization Catalyzed by Neodymium-Based Ziegler-Natta System.

Using modern methods of quantum chemistry, a theoretical substantiation of the high cis-stereospecificity of 1,3-butadiene polymerization catalyzed by the neodymium-based Ziegler-Natta system was carried out. For DFT and ONIOM simulation, the most cis-stereospecific active site of the catalytic system was used. By analyzing the total energy, as well as the enthalpy and Gibbs free energy of the simulated catalytically active centers, it was found that the coordination of 1,3-butadiene in the trans-form was more favorable than in the cis-form by 11 kJ/mol. However, as a result of π-allylic insertion mechanism modeling, it was found that the activation energy of cis-1,3-butadiene insertion into the π-allylic neodymium-carbon bond of the terminal group on the reactive growing chain was 10-15 kJ/mol lower than the activation energy of trans-1,3-butadiene insertion. The activation energies did not change when both trans-1,4-butadiene and cis-1,4-butadiene were used for modeling. That is, 1,4-cis-regulation was due not to the primary coordination of 1,3-butadiene in its cis-configuration, but to its lower energy of attachment to the active site. The obtained results allowed us to clarify the mechanism of the high cis-stereospecificity of 1,3-butadiene polymerization by the neodymium-based Ziegler-Natta system.

Absorption rate governs cell transduction in dry macroporous scaffolds.

Developing the next generation of cellular therapies will depend on fast, versatile, and efficient cellular reprogramming. Novel biomaterials will play a central role in this process by providing scaffolding and bioactive signals that shape cell fate and function. Previously, our lab reported that dry macroporous alginate scaffolds mediate retroviral transduction of primary T cells with efficiencies that rival the gold-standard clinical spinoculation procedures, which involve centrifugation on Retronectin-coated plates. This scaffold transduction required the scaffolds to be both macroporous and dry. Transduction by dry, macroporous scaffolds, termed "Drydux transduction," provides a fast and inexpensive method for transducing cells for cellular therapy, including for the production of CAR T cells. In this study, we investigate the mechanism of action by which Drydux transduction works through exploring the impact of pore size, stiffness, viral concentration, and absorption speed on transduction efficiency. We report that Drydux scaffolds with macropores ranging from 50-230 µm and with Young's moduli ranging from 25-620 kPa all effectively transduce primary T cells, suggesting that these parameters are not central to the mechanism of action, but also demonstrating that Drydux scaffolds can be tuned without losing functionality. Increasing viral concentrations led to significantly higher transduction efficiencies, demonstrating that increased cell-virus interaction is necessary for optimal transduction. Finally, we discovered that the rate with which the cell-virus solution is absorbed into the scaffold is closely correlated to viral transduction efficiency, with faster absorption producing significantly higher transduction. A computational model of liquid flow through porous media validates this finding by showing that increased fluid flow substantially increases collisions between virus particles and cells in a porous scaffold. Taken together, we conclude that the rate of liquid flow through the scaffolds, rather than pore size or stiffness, serves as a central regulator for efficient Drydux transduction.

Diversity of Structural, Dynamic, and Environmental Effects Explain a Distinctive Functional Role of Transmembrane Domains in the Insulin Receptor Subfamily.

Human InsR, IGF1R, and IRR receptor tyrosine kinases (RTK) of the insulin receptor subfamily play an important role in signaling pathways for a wide range of physiological processes and are directly associated with many pathologies, including neurodegenerative diseases. The disulfide-linked dimeric structure of these receptors is unique among RTKs. Sharing high sequence and structure homology, the receptors differ dramatically in their localization, expression, and functions. In this work, using high-resolution NMR spectroscopy supported by atomistic computer modeling, conformational variability of the transmembrane domains and their interactions with surrounding lipids were found to differ significantly between representatives of the subfamily. Therefore, we suggest that the heterogeneous and highly dynamic membrane environment should be taken into account in the observed diversity of the structural/dynamic organization and mechanisms of activation of InsR, IGF1R, and IRR receptors. This membrane-mediated control of receptor signaling offers an attractive prospect for the development of new targeted therapies for diseases associated with dysfunction of insulin subfamily receptors.

Dynein Dysfunction Prevents Maintenance of High Concentrations of Slow Axonal Transport Cargos at the Axon Terminal: A Computational Study.

Here, we report computational studies of bidirectional transport in an axon, specifically focusing on predictions when the retrograde motor becomes dysfunctional. We are motivated by reports that mutations in dynein-encoding genes can cause diseases associated with peripheral motor and sensory neurons, such as type 2O Charcot-Marie-Tooth disease. We use two different models to simulate bidirectional transport in an axon: an anterograde-retrograde model, which neglects passive transport by diffusion in the cytosol, and a full slow transport model, which includes passive transport by diffusion in the cytosol. As dynein is a retrograde motor, its dysfunction should not directly influence anterograde transport. However, our modeling results unexpectedly predict that slow axonal transport fails to transport cargos against their concentration gradient without dynein. The reason is the lack of a physical mechanism for the reverse information flow from the axon terminal, which is required so that the cargo concentration at the terminal could influence the cargo concentration distribution in the axon. Mathematically speaking, to achieve a prescribed concentration at the terminal, equations governing cargo transport must allow for the imposition of a boundary condition postulating the cargo concentration at the terminal. Perturbation analysis for the case when the retrograde motor velocity becomes close to zero predicts uniform cargo distributions along the axon. The obtained results explain why slow axonal transport must be bidirectional to allow for the maintenance of concentration gradients along the axon length. Our result is limited to small cargo diffusivity, which is a reasonable assumption for many slow axonal transport cargos (such as cytosolic and cytoskeletal proteins, neurofilaments, actin, and microtubules) which are transported as large multiprotein complexes or polymers.

Research of Mitochondrial Function, Structure, Dynamics and Intracellular Organization.

Mitochondria have been recognized as the energy (in the form of ATP)-producing cell organelles, required for cell viability, survival and normal cell function [...].

Microbiota-dependent proteolysis of gluten subverts diet-mediated protection against type 1 diabetes.

Diet and commensals can affect the development of autoimmune diseases like type 1 diabetes (T1D). However, whether dietary interventions are microbe-mediated was unclear. We found that a diet based on hydrolyzed casein (HC) as a protein source protects non-obese diabetic (NOD) mice in conventional and germ-free (GF) conditions via improvement in the physiology of insulin-producing cells to reduce autoimmune activation. The addition of gluten (a cereal protein complex associated with celiac disease) facilitates autoimmunity dependent on microbial proteolysis of gluten: T1D develops in GF animals monocolonized with Enterococcus faecalis harboring secreted gluten-digesting proteases but not in mice colonized with protease deficient bacteria. Gluten digestion by E. faecalis generates T cell-activating peptides and promotes innate immunity by enhancing macrophage reactivity to lipopolysaccharide (LPS). Gnotobiotic NOD Toll4-negative mice monocolonized with E. faecalis on an HC + gluten diet are resistant to T1D. These findings provide insights into strategies to develop dietary interventions to help protect humans against autoimmunity.