Biology subjects

Kuznetsov, A. V.

Publications and source records attributed to Kuznetsov, A. V..

At least 19 recordsLinked to original sources

bioRxiv2026

Accumulated Cytotoxicity Induced by Islet Amyloid Polypeptide Oligomers in Type 2 Diabetes

Type 2 diabetes is characterized by the progressive aggregation of islet amyloid polypeptide (IAPP) within the islets of Langerhans, a process strongly implicated in beta-cell dysfunction and loss. Although oligomeric IAPP intermediates are widely considered the principal cytotoxic species, the relative contributions of the numerous biological and kinetic processes governing their formation, clearance, and conversion into fibrils remain poorly quantified. Here, a mathematical model of IAPP aggregation is developed that incorporates the physiology of beta-cell secretion and the microanatomy of the islet, including capillary-mediated clearance, enzymatic degradation, and the kinetics of oligomer and fibril formation within a well-mixed control volume. Building on the hypothesis that oligomers are the major cytotoxic species, the concept of accumulated cytotoxicity is introduced, defined as the time integral of the oligomer concentration, and a systematic sensitivity analysis of this quantity with respect to all model parameters is conducted. The results reveal a clear hierarchy: only two parameters, the basal rate of IAPP monomer secretion and the rate constant for spontaneous oligomer dissociation, exert a first-order influence on long-term accumulated cytotoxicity, with dimensionless sensitivities approaching +1 and -1, respectively, while the effects of all other parameters remain subordinate and diminish at long times. The model further shows that capillary clearance, owing to the physical exclusion of oligomers from fenestrated capillaries, selectively reduces fibril accumulation and amyloid deposition without affecting oligomer-mediated cytotoxicity, indicating that amyloid area fraction, a commonly used histological metric of disease severity, may not be a reliable surrogate for cytotoxic burden. At the highest secretion rate, the model predicts approximately 48% islet replacement by amyloid after 30 years, substantially below the >85% reported in some end-stage histological studies; this discrepancy is consistent with the omission of late-stage processes such as beta-cell death and release of intracellular IAPP from the present model. These findings identify monomer secretion and oligomer dissociation as potentially promising therapeutic targets for limiting cytotoxic damage in type 2 diabetes and provide a quantitative framework for evaluating candidate intervention strategies.

biophysics↗

bioRxiv2026

Investigating a Relation between Amyloid Beta Plaque Burden and Accumulated Neurotoxicity Caused by Amyloid Beta Oligomers

Alzheimers disease (AD) is characterized by the accumulation of amyloid-{beta} (A{beta}), yet the specific link between plaque burden and cognitive decline remains a subject of intense investigation. This paper presents a mathematical model that simulates the coupled dynamics of A{beta} monomers, soluble oligomers, and fibrillar species in the brain tissue. By modifying existing moment equations to include a dedicated conservation equation for A{beta} monomers, the model explores how various microscopic processes, such as primary nucleation, surface-catalyzed secondary nucleation, fibril elongation, and fragmentation, contribute to macroscopic disease progression. Central to this study is the concept of "accumulated neurotoxicity" as a surrogate marker of biological age, defined as the time-integrated concentration of soluble A{beta} oligomers. Unlike plaque burden, accumulated neurotoxicity cannot be reversed, and the harm it causes depends critically on the sequence of events that produced it. Numerical results demonstrate that while plaque burden and neurotoxicity both increase over time, their relationship is non-linear and highly sensitive to the efficiency of protein degradation machinery. Specifically, impaired degradation leads to a rapid advancement of biological age relative to calendar age. The model further identifies oligomer dissociation and fibril fragmentation as potential protective mechanisms that can counterintuitively reduce neurotoxic burden by diverting monomers away from the soluble oligomer pool. These findings provide a quantitative framework for understanding why individuals with similar plaque burdens may experience vastly different cognitive outcomes, underscoring the importance of targeting soluble oligomers early in therapeutic interventions.

biophysics↗

bioRxiv2026

Mathematical Modeling of AA Amyloidosis: Coupling SAA-HDL Binding Dynamics with Path-Dependent Renal Aging

AA amyloidosis is a severe complication of chronic inflammatory diseases characterized by fibrillar protein deposition in the kidneys, leading to progressive organ failure. This study presents a mathematical model that couples SAA-HDL binding dynamics with renal amyloid aggregation kinetics to investigate the pathogenesis of AA amyloidosis. Under normal physiological conditions, Serum Amyloid A (SAA) circulates predominantly bound to high-density lipoprotein (HDL), which acts as a chaperone-like carrier that can reduce SAA misfolding. However, during chronic inflammation, SAA production exceeds HDL binding capacity, resulting in an increased concentration of free SAA available for renal filtration. The model calculates free SAA concentration from reversible binding equilibrium and incorporates renal filtration, mesangial accumulation, and conversion to amyloid fibrils through primary nucleation and autocatalytic growth mechanisms. A central contribution of this work is the quantification of accumulated nephrotoxicity associated with AA oligomers, which may contribute to cumulative cytotoxic damage to mesangial and tubular cells over time. Because oligomers are continuously generated during ongoing aggregation, their toxic burden integrates across the entire duration of the disease. Combined nephrotoxic damage, encompassing oligomer-associated cellular injury and fibril-associated disruption of renal architecture, therefore reflects not merely the current disease state but the full inflammatory trajectory of the patient. This cumulative damage defines renal biological age, a measure of functional deterioration, a portion of which, attributable to accumulated nephrotoxicity, is assumed to be irreversible. Renal biological age is also path-dependent: two patients with identical present-day SAA levels may carry different renal damage burdens depending on the duration, timing, and severity of their prior inflammatory episodes. Sensitivity analysis reveals that HDL concentration and SAA cleavage rate are critical determinants of amyloid burden.

biophysics↗

bioRxiv2026

Hydrodynamic dispersion drives viral-cellular contact for gene delivery in porous media

Reactive biological processes often hinge on rare collisions between particles that occupy vastly different physical regimes, yet the transport physics that govern these encounters remain poorly understood. Biological cell-virus encounters offer a uniquely quantifiable instance of this general problem: collisions between particles whose transport is governed by entirely different physical mechanisms, yet whose interactions determine system-level function. In stagnant liquids, nanoscale viral vectors explore space only through slow Brownian diffusion, while microscale cells rapidly sediment, producing species separation that suppresses the virus-cell interaction interface. Here we show that liquid absorption into a dry, macroporous sponge enhances viral-cellular interactions by shifting the system into an advection-dispersion regime that circumvents this sedimentation-diffusion limit. By integrating experimental results with a multiscale simulation model, we demonstrate that the tortuous sponge porosity converts capillary-driven flow into convective mixing, driving orders-of-magnitude increases in viral-cellular collision rates. Coupling these dispersive transport dynamics with a probabilistic capture model reveals that hydrodynamic dispersion accounts for the multifold enhancement in viral-cellular transduction efficiency observed in porous sponges. These results provide a quantitative framework for emergent collision dynamics in complex porous media and establish a generalizable strategy to optimize active transport in spatiotemporally heterogeneous biological systems.

bioengineering↗

bioRxiv2025

Mathematical modeling of light chain aggregation and cardiac damage in AL amyloidosis

AL amyloidosis is a rapidly progressive disorder characterized by clonal plasma cell expansion, excessive production of light chains (LCs), and their misfolding into aggregation-prone monomers. These monomers assemble into oligomers and ultimately deposit as amyloid fibrils, particularly within cardiac tissue, where they contribute to myocardial stiffening and direct cardiotoxicity. A reduced-order mechanistic model is developed to describe LC secretion by a pathogenic plasma-cell clone, LC unfolding and aggregation, cardiac deposition, and the resulting myocardial injury during advanced cardiac AL amyloidosis. Simulations reveal pronounced nonlinear LC aggregation kinetics: oligomer concentrations remain low during the early part of the modeled terminal cardiac-progression interval and subsequently increase rapidly as autocatalytic conversion becomes dominant. When aggregation is assumed to occur within cardiac tissue, fibril deposition is approximately 30 times greater, and oligomer-induced cardiotoxicity is about five times higher, compared with aggregation occurring in the blood plasma. These differences stem from the smaller cardiac volume, which accelerates autocatalytic oligomer formation. A combined cardiac damage criterion, integrating both oligomer-induced cardiotoxicity and fibril-associated myocardial stiffening, was introduced and found to reach values approximately tenfold higher when LC aggregation occurs within cardiac tissue compared with aggregation in the blood plasma. This parameter may provide a candidate model-based measure of cardiac aging or disease severity. The model also predicts that therapeutic intervention markedly reduces, but does not eliminate cardiac injury, highlighting the importance of early treatment initiation in AL amyloidosis.

biophysics↗

bioRxiv2025

Does Human Transthyretin Aggregate in Blood Plasma or in Cardiac Tissue? A Mathematical Modeling Study

Transthyretin (TTR) amyloidosis is a progressive disease characterized by the destabilization of TTR tetramers, leading to monomer dissociation, oligomer formation, and fibril deposition in cardiac tissue. This study presents a mathematical model that captures the kinetics of TTR aggregation and deposition, integrating clinically relevant parameters to distinguish between scenarios of TTR aggregation in blood plasma and cardiac tissue. The governing equations are derived by applying conservation principles to the number of TTR tetramers, monomers, and oligomers within defined control volumes, such as the blood plasma or heart. The model predicts that the scenario with fibril accumulation within cardiac tissue better reflects the clinical progression of wild-type TTR amyloidosis, aligning with observed patient survival times and measured tetramer concentrations. In this scenario, the model successfully recapitulates published physiological data, accurately predicting a total plasma TTR concentration of approximately 25 mg/dL. Sensitivity analyses reveal that the rate of tetramer dissociation and the half-deposition time of TTR oligomers are key regulators of disease progression. Lower tetramer dissociation rates, mimicking the stabilizing effect of tafamidis, reduce fibril accumulation and biological aging. Conversely, faster oligomer deposition into fibrils leads to reduced oligomer concentrations but accelerated tissue fibril accumulation. The model predicts that, after five years of disease progression, the volumetric ratio of deposited TTR fibrils to baseline myocardial volume may reach 58% in the tissue aggregation scenario, compared to 10% when aggregation occurs in plasma. These predictions are consistent with clinical observations that link higher amyloid burden to increased mortality. Overall, the findings support a pathogenic mechanism in which TTR aggregation predominantly occurs in cardiac tissue, highlighting potential therapeutic targets to modulate disease progression. A correlation is proposed for estimating biological age in humans, which incorporates both calendar age and the volumetric ratio of deposited TTR fibrils to baseline myocardial volume.

biophysics↗

bioRxiv2025

Predicting Biological Age Using an Accumulated Neurotoxicity Biomarker for Amyloid Beta Oligomers

This study proposes using accumulated neurotoxicity, defined as the time integral of A{beta} oligomer concentration, as a biomarker for neuronal aging. A relationship between biological age and accumulated neurotoxicity is proposed. Numerical analysis guided the development of a new analytical solution linking the biological and calendar ages of neurons. The effects of A{beta} monomer and oligomer half-lives--key indicators of proteolytic efficiency--on biological age are examined. Both constant and age-dependent (exponentially increasing) half-life scenarios are considered. The findings indicate that increasing the half-life of A{beta} monomers and oligomers with age accelerates biological aging. Reducing A{beta} monomer production is shown to slow biological aging, with a linear relationship established between these two quantities. Additionally, biological age is found to depend linearly on the half-deposition time of A{beta} oligomers into senile plaques. The model demonstrates that biological age is irreversible, providing a theoretical explanation for why plaque-clearing therapies cannot reverse established cognitive impairment. The model also demonstrates that biological age is path-dependent rather than state-dependent.

biophysics↗

bioRxiv2025

Modeling of ATP Transport in an Axon: Effects of Spontaneous Neuron Firing and Mitochondrial Transfer via Tunneling Nanotubes

While electrical activity in neurons has been extensively studied, the transport and distribution of adenosine triphosphate (ATP), the primary cellular energy carrier, remain less understood, particularly in relation to metabolic processes in axons. ATP is primarily generated in mitochondria and consumed at synapses, the primary sites of energy demand. Even in healthy axons, approximately half of synaptic boutons lack stationary mitochondria, raising questions about ATP transport between boutons with and without mitochondrial ATP production. This study addresses two key questions: the role of spontaneous neuronal firing in maintaining ATP levels during periods of low energy demand and the ability of a single bouton with a donated mitochondrion to supply ATP to neighboring boutons lacking mitochondria. Using computational simulations, the study examines ATP transport under various firing patterns and mitochondrial distributions, incorporating factors such as quiescent periods, duty cycles, and ATP diffusivity. Spontaneous neuronal firing stabilizes ATP levels during periods of low energy demand, preventing reactive oxygen species (ROS) release from mitochondria. Simulations reveal that in neurons damaged by neurodegeneration, a single bouton containing a donated mitochondrion can support ATP levels in multiple empty boutons. However, as the number of empty boutons increases, ATP concentration declines, potentially falling below the critical threshold required for synaptic transmission. Nomenclaturea0 kinetic constant characterizing the rate of ATP consumption in a bouton Ac cross-sectional area of the axon C ATP concentration per unit length of the axon C0 typical value of ATP concentration per unit length of the axon Cmin minimum ATP concentration required to sustain synaptic transmission duty duty cycle D ATP diffusivity in the cytosol f frequency at which neuron fires during the active phase iactive number of action potentials that occur during the active phase itotal total number of action potentials that propagate down the axon during the active phase plus the number of action potentials that were missed during the quiescent phase L distance between boutons m ATP production rate per unit length of a mitochondrion [Formula]ATP production rate per unit mass of tissue Nempty number of boutons in the CV that lack stationary mitochondria t time x position along the axon xm half-length of a mitochondrion Greek symbols{gamma} percentage of tissue volume occupied by mitochondria {delta}half the width of an axonal varicosity {varpi}mass of an individual mitochondrion {Lambda}homeostatic portion of energy expended on homeostatic maintenance of a bouton

biophysics↗

bioRxiv2024

Evaluating Combined Neurotoxicity of Amyloid Beta and Tau Oligomers in Alzheimer's Disease: A New Criterion

A criterion characterizing the combined neurotoxicity of amyloid beta and tau oligomers is suggested. A mathematical model for calculating the value of this criterion during senile plaque and neurofibrillary tangle (NFT) formation is proposed. Computations show that for physiologically relevant parameter values, the value of the criterion increases approximately linearly with time. Once neurofibrillary tangles begin forming in addition to senile plaques, there is an increase in the slope characterizing the rate at which the criterion increases. The critical value of the criterion at which a neuron dies is estimated. Unless the production rates of amyloid beta and tau monomers are very large, computations predict that for the accumulated toxicity to reach the critical value, the neural machinery responsible for the degradation of amyloid beta and tau monomers and aggregates must become dysfunctional. The value of the criterion after 20 years of the aggregation process is strongly influenced by the deposition rates of amyloid beta and tau oligomers into senile plaques and NFTs. This suggests that deposition of amyloid beta and tau oligomers into senile plaques and NFTs may reduce accumulated toxicity by sequestering more toxic oligomeric species into less toxic insoluble aggregates.

biophysics↗

bioRxiv2024

Criterion for assessing accumulated neurotoxicity of alpha-synuclein oligomers in Parkinson's disease

The paper introduces a parameter called "accumulated neurotoxicity" of -syn oligomers, which measures the cumulative damage these toxic species inflict on neurons over time, given the years it typically takes for such damage to manifest. A threshold value for accumulated neurotoxicity is estimated, beyond which neuron death is likely. Numerical results suggest that rapid deposition of -syn oligomers into fibrils minimizes toxicity, indicating that the formation of Lewy bodies might play a neuroprotective role. Strategies such as reducing -syn monomer production or enhancing degradation can decrease accumulated toxicity. In contrast, slower degradation (reflected by longer half-lives of monomers and free aggregates) increases toxicity, supporting the idea that impaired protein degradation may contribute to Parkinsons disease progression. The study also examines the sensitivity of accumulated toxicity to different model parameters.

biophysics↗

bioRxiv2024

A criterion characterizing accumulated toxicity of Aβ oligomers in Alzheimer's disease

The paper develops a criterion to quantify the accumulated neurotoxicity of A{beta} oligomers in Alzheimers disease (AD). Accumulated neurotoxicity is determined by integrating the concentration of A{beta} oligomers within the control volume over time. In the scenario of a low rate of free A{beta} oligomer deposition into senile plaques and dysfunctional degradation machinery, resulting in an infinitely long half-life of A{beta} monomers and aggregates, the obtained analytical solution reveals a quadratic relationship between accumulated neurotoxicity and time. This suggests that initially, neurotoxicity increases slowly but accelerates as time progresses. This could help to understand the prolonged delay in the onset of AD symptoms. Furthermore, as the model indicates that accumulated neurotoxicity increases with the duration of the aggregation process, it implies that if the protein degradation system is compromised, the onset of AD becomes unavoidable. Eventually, neuronal death is only a question of time. The only way to prevent this outcome is to ensure that the degradation machinery for A{beta} peptides and their aggregates remains functional. A threshold value of accumulated neurotoxicity is suggested. The developed theory suggests that if this value is exceeded, nearby neurons will die. The progression of accumulated neurotoxicity over time is analyzed. An S-shaped growth pattern as the half-deposition time of A{beta} aggregates into senile plaques increases is revealed. Additionally, the sensitivity of accumulated neurotoxicity to different parameter values is examined.

biophysics↗

bioRxiv2024

Simulating the growth of TAF15 inclusions in neuron soma

To the best of the authors knowledge, this paper presents the first attempt to develop a mathematical model of the formation and growth of inclusions containing misfolded TATA-box binding protein associated factor 15 (TAF15). It has recently been shown that TAF15 inclusions are involved in approximately 10% of cases of frontotemporal lobar degeneration (FTLD). FTLD is the second most common neurodegenerative disease after Alzheimers disease (AD). It is characterized by a progressive loss of personality, behavioral changes, and a decline in language skills due to the degeneration of the frontal and anterior temporal lobes. The model simulates TAF15 monomer production, nucleation and autocatalytic growth of free TAF15 aggregates, and their deposition into TAF15 inclusions. The accuracy of the numerical solution of the model equations is validated by comparing it with analytical solutions available for limiting cases. Physiologically relevant parameter values were used to predict TAF15 inclusion growth. It is shown that the growth of TAF15 inclusions is influenced by two opposing mechanisms: the rate at which free TAF15 aggregates are deposited into inclusions and the rate of autocatalytic production of free TAF15 aggregates from monomers. A low deposition rate slows inclusion growth, while a high deposition rate hinders the autocatalytic production of new aggregates, thus also slowing inclusion growth. Consequently, the rate of inclusion growth is maximized at an intermediate deposition rate of free TAF15 aggregates into TAF15 inclusions.

biophysics↗

bioRxiv2024

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

The formation of amyloid beta (A{beta}) deposits (senile plaques) is one of the hallmarks of Alzheimers disease (AD). This study investigates what processes are primarily responsible for their formation. A model is developed to simulate the diffusion of amyloid beta (A{beta}) monomers, the production of free A{beta} aggregates through nucleation and autocatalytic processes, and the deposition of these aggregates into senile plaques. The model suggests that efficient degradation of A{beta} monomers alone may suffice to prevent the growth of senile plaques, even without degrading A{beta} aggregates and existing plaques. This is because the degradation of A{beta} monomers interrupts the supply of reactants needed for plaque formation. The impact of A{beta} 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 A{beta} 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 A{beta} aggregates into senile plaques. If this rate is small, the plaque grows slowly. However, if the rate of deposition of A{beta} aggregates into senile plaques is very large, the free A{beta} aggregates are removed from the intracellular fluid by deposition into the plaques, leaving insufficient free A{beta} aggregates to catalyze the production of new aggregates. This suggests that under certain conditions, A{beta} plaques may offer neuroprotection and impede their own growth. Additionally, it indicates that there exists an optimal rate of deposition of free A{beta} aggregates into the plaques, at which the plaques attain their maximum size.

biophysics↗

bioRxiv2024

Effects of time-dependent ATP consumption caused by neuron firing on ATP concentrations in synaptic boutons containing and lacking a stationary mitochondrion

The precise mechanism behind the absence of a stationary mitochondrion in approximately half of presynaptic release sites in axons, and how these sites lacking a stationary mitochondrion receive ATP, 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.

biophysics↗

bioRxiv2024

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

This paper introduces a method to simulate the progression of senile plaques, focusing on scenarios where concentrations of amyloid beta (A{beta}) monomers and aggregates vary between neurons. Extracellular variations in these concentrations may arise due to limited diffusivity of A{beta} monomers and a high rate of A{beta} monomer production at lipid membranes, requiring a substantial concentration gradient for diffusion-driven transport of A{beta} monomers. The dimensionless formulation of the model is presented, identifying four key dimensionless parameters governing the solutions for A{beta} monomer and aggregate concentrations, as well as the radius of a growing A{beta} plaque within the control volume. These parameters include the dimensionless diffusivity of A{beta} monomers, the dimensionless rate of A{beta} monomer production, and the dimensionless half-lives of A{beta} monomers and aggregates. A dimensionless parameter is introduced to assess the validity of the lumped capacitance approximation. An approximate solution is derived for the scenario involving large diffusivity of A{beta} monomers and dysfunctional protein degradation machinery, resulting in infinitely long half-lives for A{beta} monomers and aggregates. In this scenario, the concentrations of A{beta} aggregates and the radius of the A{beta} plaque depend solely on a single dimensionless parameter that characterizes the rate of A{beta} monomer production. According to the approximate solution, the concentration of A{beta} aggregates is linearly dependent on the rate of monomer production, and the radius of an A{beta} 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 A{beta} 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.

biophysics↗

bioRxiv2023

Simulating growth of TDP-43 cytosolic inclusion bodies in neuron soma

This paper introduces a mathematical model for the growth of transactive response DNA binding protein of 43 kDa (TDP-43) inclusion bodies in neuron soma. The parameter representing the accumulated neurotoxicity caused by misfolded TDP-43 oligomers is also introduced. The models equations enable the numerical calculation of the concentrations of TDP-43 monomers, dimers, free oligomers, and oligomers deposited in inclusion bodies. By simulating the deposition of free oligomers into inclusion bodies, the model predicts the size of TDP-43 inclusion bodies. An approximate solution to the model equations is derived for the scenario where protein degradation machinery is dysfunctional, leading to infinite half-lives for TDP-43 dimers, monomers, and both free and deposited oligomers. This solution, valid at large times, predicts that the radius of the inclusion body increases proportionally to the cube root of time, whereas the accumulated neurotoxicity increases linearly with time. To the best of the authors knowledge, this study is the first to model the relationship between the size of TDP-43 inclusion bodies and time, and the first to introduce the concept of accumulated neurotoxicity caused by misfolded TDP-43 oligomers. Sensitivity analysis of the approximate solution indicates that the inclusion body radius and accumulated neurotoxicity become independent of the kinetic constants at large timescales. While the numerical solution of the full mathematical model continues to work with finite half-lives, the approximate solution becomes invalid for scenarios with physiologically relevant (finite) half-lives of TDP-43 dimers, monomers, and free misfolded oligomers. In contrast to the scenario with infinite half-lives, the numerical solution reveals that, for different values of the kinetic constants, the curves representing the inclusion body radius and accumulated neurotoxicity converge to distinct curves over time.

biophysics↗

bioRxiv2023

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 Parkinsons 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 (-syn) fibrils. The Finke-Watzky model is employed to simulate the aggregation of lipid fragments and -syn monomers. By analytically and numerically exploring the solutions of the governing equations, approximate solutions were derived, which are applicable for large 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 -syn monomers. The model suggests that large LBs relevant to PD can only develop when the machinery responsible for degrading lipid membrane fragments, -syn monomers, and their aggregates is dysfunctional.

biophysics↗

bioRxiv2023

Numerical and analytical simulation of the growth of amyloid-β plaques

Numerical and analytical solutions were employed to calculate the radius of an amyloid-{beta} (A{beta}) plaque over time. To the authors knowledge, this study presents the first model simulating the growth of A{beta} plaques. Findings indicate that the plaque can attain a diameter of 50 m after 20 years of growth, provided the A{beta} 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 A{beta} monomer half-life, an analytical solution was found. Assuming that A{beta} 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 A{beta} aggregates. This led to the "cube root hypothesis," positing that A{beta} 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 A{beta} plaque agglomeration, indicating that the kinetics of A{beta} plaque agglomeration is not a limiting factor for plaque growth. Instead, the plaque growth rate is limited by the rates of A{beta} monomer production and degradation.

biophysics↗