A Stochastic Compartmental Model for Fast Axonal Transport

Subcellular Localization of Disease-Associated Prion Protein in the Human Brain

In this exposition, a three compartment model has established to analyze the purchasing behavior of buyer. Population for a specific product marketing is classified into non-adopter group N(t), thinker group I(t) and adopter group A(t). The relation within adopter and the non-adopter group is word of mouth. For enhance the impact of word of mouth, media is the another dominating factor for impressing the non-adopter population, who has to become an adopter. In this model, there are two types of buyers instant buyers and thinker buyers. Instant purchasing is an unplanned decision to purchase a brand-new product, done just before purchase. These types of non-adopters become instant adopters. Thinker buyer is not immediate-adopter, and it will take the time for the buying of a brand-new product. Boundedness, Positivity and Basic influence numbers(BINs) of the model is studied. Stability analysis is carried out for all the possible equilibrium points. Hopf bifurcation analysis has also been determined at the adopter-free state and interior equilibrium. Sensitivity analysis for the basic reproduction number and variables about the parameters of the model has been examined for the internal steady state. Finally, numerically experimentations have been carried out to support our analytical findings with a different set of parameters. https://doi.org/10.28919/jmcs/3496

Understanding the mechanisms underlying the self-assembly and organization of functional neuronal networks is a crucial problem confronting both experimental and theoretical neuroscience alike. Early in development, functional neuronal networks self-assemble with astonishing rapidity. It is, therefore, imperative to investigate and understand how far simple basic mechanisms can allow primary functioning neuronal circuits to develop. To address this ‘structure-function’ issue, we model anatomy and electrophysiology of young hatchling Xenopus tadpole’s spinal cord [1-3]. Our bottom-up approach to modeling of neuronal connectivity is based on developmental process of axon growth – we develop a gradient-based mathematical model for axon growth. It is known that in the developing vertebrate spinal cord, neurons arise from progenitor cells in the neural tube and thereafter the axons grow under influence of chemical morphogenes released from the dorsal roof plate (‘BMP’), ventral floor plate (‘shh’) and hindbrain regions (‘Wnt’). Distribution of these guidance molecules along the spinal cord set up a gradient field which steer the axons in appropriate locations and thus ensure formation of proper connections. We grow axons of spinal neurons and generate synaptic connections similar to biological developmental process based on the data from Professor Alan Roberts Lab at University of Bristol [4]. Using the gradient-based model we were able to grow axons for all seven types of spinal neurons which are believed to be involved in swimming and struggling behavior of tadpole. These spinal neurons include sensory neurons which are responsible for receiving stimulus from environment; interneurons which process the sensory information and pass it onto the motor which translate these signals into appropriate locomotive activities. We successfully modeled both morphologically different types of spinal neurons– firstly commissural neurons grow axons ventrally on the same side of the spinal cord at first and turn longitudinally on the other (contralateral) side of the spinal cord, whereas non-commissural neurons grow their axons on the same (ipsilateral) side of spinal cord. The model incorporates experimental data for somata distribution in the spinal cord, the outgrowth angles, axon lengths, etc. The computer modeling of the axon growth of spinal neurons has enabled both us and our Biology partners to construct and test various hypotheses particularly the roles of the different guidance cues in the axon growth. We also implemented an optimization technique to determine the model parameters for a particular type of neuron based on minimizing a cost function which comprises of the difference between the axon trajectory distribution of the model axons and the corresponding experimental data and also difference between the tortuisities of the model and experimental axons. The complete reconstruction of the spinal cord includes about 2000 neurons. In the reconstruction, both the neurons and the dendrites are randomly distributed along the spinal cord on the ‘left’ and ‘right’ side of the body according to the experimental measurements. Thus, the reconstruction of the connectivity is biologically realistic. To model spiking activity we use Hodgkin-Huxley type conductance model. Parameters of the model are chosen according to the available neurophysiological measurements. Activity dynamics of neural network comprising both the reconstruction model and conductance based spiking neurons demonstrates swimming patterns, i.e., anti-phase oscillations on opposite sides of the body and metachronal wave in longitudinal direction in a wide range of model parameters.

The general formulation of the classical kinetic theory, which is needed to predict transport properties of gases in situations where the hydrodynamic equations are valid, is reviewed. A rigid convex model of tetrahedral symmetry is used to predict the Senftleben-Beenakker effect of a static magnetic field on the thermal conductivity and viscosity of pure CH/sub 4/, CD/sub 4/ and CF/sub 4/. The parameters of the model are optimized and are found to assume physically reasonable values. The calculations agree with experiment to a degree comparable to that of similar work on diatomic molecules. A generalized scattering cross section, ..gamma.., is defined which can be evaluated exactly for the limiting cases of a spherical soft potential and rigid ovaloids. For a general soft nonspherical interaction of the Kihara type, a suitable approximation for the momentum dependence is made with the following attributes: ..gamma.. reduces to the form for soft sphere and rigid ovaloid in the limits and the resulting matrix elements of the collision operator can be written in terms of the familiar ..cap omega..* integrals. This formulation is used to investigate thermal diffusion in binary isotopic mixtures of CO. Calculations are made in an 80/sup 0/K to 300/sup 0/K range which includes the inversion temperatures for all mixtures studied. Thermal conductivity and diffusion coefficients of CO are also calculated. The parameters of the model can be adjusted to account for the major features of the experimental data. The physical significance of the parameters is discussed. (auth)

Multitask learning and nonlinear optimal control of the COVID-19 outbreak: A geometric programming approach

General Properties of Axoplasmic Transport.- General Properties of Axoplasmic Transport.- Section 1. The Physiological Role of Axoplasmic Transport.- Axoplasmic Transport and Synaptic Transmission.- Effect of Physiological Activity in Goldfish Optic Axons on Axonal Transport of Protein and Nucleosides.- Fate of Axonally Transported Proteins in the Nerve Terminal.- Transneuronal Transport: A Way for the Neuron to Communicate with Its Environment.- Axonal Transport, Neurosecretory Vesicles, and the Endocrine Neuron.- Section 2. The Role of Axoplasmic Transport in Growth and Regeneration.- Axonal Transport in the Sprouting Neuron: Transfer of Newly Synthesized Membrane Components to the Cell Surface.- The Role of Axonal Transport in the Growth of the Olfactory Nerve Axons.- Changes in Fast-Transported Protein in Regenerating Axons: Essential or Incidental?.- Recovery of Axonal Transport of Acetylcholinesterase in Regenerating Sciatic Nerve Precedes Muscle Reinnervation.- The Role of Axoplasmic Transport in the Restoration of Synaptic Transmission and in the Process of Sprouting During Nerve Regeneration.- Section 3. Experimental Neuropathies and Axoplasmic Transport.- Disruption of Axoplasmic Transport by Neurotoxic Agents. The 2,5-Hexanedione Model.- Axoplasmic Transport in the Experimental Neuropathy Induced by Acrylamide.- Axonal Transport in ?,?'-Iminodipropionitrile Neuropathy.- Disulfiram-Induced Impairment of Horseradish Peroxidase Retrograde Transport in Rat Sciatic Nerve.- Section 4. Neuronal Pathology and Axoplasmic Transport.- Axonal Transport in Human Nerve Disease and in the Experimental Neuropathy Induced by p-Bromophenylacetylurea.- Disturbances of Axoplasmic Transport in Alzheimer's Disease.- Axonal Transport of Acetylcholinesterase Molecular Forms in Sciatic Nerve of Genetically Diabetic Mice.- Effects of Graded Compression on Axonal Transport in Peripheral Nerves.- Role of Axonal Transport in the Pathophysiology of Retinal and Optic Nerve Disease.- Implications of Axoplasmic Transport for the Spread of Virus Infections in the Nervous System.- Section 5. Axoplasmic Transport as a Tool in Neurophysiology and Neuroanatomy.- Retrograde Migration of Transmitter-Related Molecules.- Intra-Axonal Transport of Horseradish Peroxidase (HRP) and Its Use in Neuroanatomy.- Axonal Transport of Fluorescent Compounds in the Brain and Spinal Cord of Cat and Rat.

The theoretical model of the hole mobility in poly[2-methoxy-5-(2′-ethylhexyloxy)-p-phenylene vinylene] doped with a photochromic polar additive is proposed. Our model involves description of the on-chain charge carrier states, charge carrier thermalization, and inter-chain hopping. While the on-chain states are calculated by means of quantum mechanical methods, the semi-classical Marcus approach is used for the description of inter-chain hopping. The dependence of the mobility on several parameters of the model is studied. The results predict the possibility to construct an efficient optoelectronic switch based on a polymer doped with a photochromic polar additive.

The Parker-Klingeman bedload transport model is an engineering tool, based on dimensional analysis, for gravel transport in streams. Its use for bedload prediction is shown for small mountain streams in Oregon. The fitting of the two parameters of the model is described. Bedload size distribution for any discharge and for the average annual load can be predicted.

The effects of acrylamide on fast axonal transport have been measured primarily using the indirect methods of isotope or enzyme accumulation. We report the first direct evaluation of the effects of subchronic acrylamide dosing (150, 300, or 500 mg/kg total dose, i.e., 50 mg/kg, 2x/wk, for 1.5, 3, 5 wk, respectively) on the fast axonal transport motility machinery itself using video-enhanced differential interference contrast optics with digital image processing and computer analysis. Four principle observations were made: (1) Rapid anterograde transport was not affected at any dosage level within 1 wk after cessation of dosing. (2) A high cumulative dosage (500 mg/kg total) of acrylamide or bisacrylamide produced approximately 7-18% decrease in the rate of retrograde transport in both myelinated and unmyelinated axons. (3) Lower dosages of acrylamide (150 or 300 mg/kg total) produced an increase in retrograde transport rates in myelinated axons only. (4) During the "recovery" phase for the 500 mg/kg acrylamide animals (i.e., 3 or 5 wk after the last dosage of acrylamide) the rate of anterograde transport in the myelinated axons was decreased at 3 wk but not at 5 wk, and the rate of retrograde transport in the myelinated axons returned to control levels while the retrograde transport in the unmyelinated axons continued at abnormally slow speeds. The application of this new technique to evaluate the neurotoxic effects of acrylamide provides evidence of dynamic changes in the axonal transport motility machinery itself and differential effects on myelinated versus unmyelinated fibers.

ObjectivePerson-to-person transmission can occur during outbreaks of verotoxigenic Escherichia coli (VTEC), however the impact of this transmission route is not well understood. This study aimed to examine the role of person-to-person transmission during a VTEC outbreak, and how targeting this route may reduce outbreak size. A deterministic compartmental model describing a VTEC outbreak was constructed and fit to data from a 2008 outbreak in Ontario, Canada. Using the best-fit model, simulations were run to calculate the: reduction in transmission rate after implementing interventions, proportion of cases infected through both transmission routes, and number of cases prevented by interventions. Latin hypercube sensitivity analysis was conducted to examine the sensitivity of the outbreak size to the model parameters.ResultsBased on the best-fit model, ~ 14.25% of the cases likely arose due to person-to-person transmission. Interventions reduced this transmission rate by ~ 73%, causing a reduction in outbreak size of ~ 17% (47 cases). Sensitivity analysis showed that the model was highly sensitive to changes in all parameters of the model. The model demonstrates that person-to-person could be an important transmission route during VTEC outbreaks. Targeting this route of transmission through hand hygiene and work exclusions could reduce the final outbreak size.

Optimal dynamic empirical therapy in a health care facility: A Monte-Carlo look-ahead method

Chapter 9 Fast axonal transport: recent developments

Cargo transport by molecular motors along microtubules is essential for the function of eukaryotic cells, in particular neurons in which axonal transport defects constitute the early pathological features of neurodegenerative diseases. Mainly studied in motor and sensory neurons, axonal transport is still difficult to characterize in neurons of the brain in absence of appropriate in vivo tools. Here, we measured fast axonal transport by tracing the second harmonic generation (SHG) signal of potassium titanyl phosphate (KTP) nanocrystals (nanoKTP) endocytosed by brain neurons of zebrafish (Zf) larvae. Thanks to the optical translucency of Zf larvae and to the perfect photostability of nanoKTP SHG, we achieved a high scanning speed of 20 frames (of ≈90 μm × 60 μm size) per second in Zf brain. We focused our study on endolysosomal vesicle transport in axons of known polarization, separately analyzing kinesin and dynein motor-driven displacements. To validate our assay, we used either loss-of-function mutations of dynein or kinesin 1 or the dynein inhibitor dynapyrazole and quantified several transport parameters. We successfully demonstrated that dynapyrazole reduces the nanoKTP mobile fraction and retrograde run length consistently, while the retrograde run length increased in kinesin 1 mutants. Taking advantage of nanoKTP SHG directional emission, we also quantified fluctuations of vesicle orientation. Thus, by combining endocytosis of nanocrystals having a nonlinear response, fast two-photon microscopy, and high-throughput analysis, we are able to finely monitor fast axonal transport in vivo in the brain of a vertebrate and reveal subtle axonal transport alterations. The high spatiotemporal resolution achieved in our model may be relevant to precisely investigate axonal transport impairment associated with disease models.

The optic nerve, as a part of the central nervous system (CNS), has been used to study axonal transport for decades. The present study has concentrated on the axonal transport of synaptic vesicle proteins in the optic nerve, using the "stop-flow/nerve crush" method. After blocking fast axonal transport, distinct accumulations of synaptic vesicle proteins developed during the first hour after crush-operation and marked increases were observed up to 8 h postoperative. Semiquantitative analysis, using cytofluorimetric scanning (CFS) of immunoincubated sections, revealed that the ratio between distal accumulations (organelles in retrograde transport) and proximal accumulations (organelles in anterograde transport) was much higher (up to 80-90%) for the transmembrane proteins than that for surface adsorbed proteins (only 10-20%). The pattern of axonal transport in the optic nerve was comparable to that in the sciatic nerve. However, clathrin and Rab3a immunoreactivities were accumulated in much lower amounts than that in the sciatic nerve. Most synaptic vesicle proteins were colocalized in the axons proximal to the crush. A differential distribution of synaptobrevin I and II, however, was observed in the optic nerve axons; synaptobrevin I was present in large-sized axons, while synaptobrevin II immunoreactivity was present in most axons, including the large ones. The two isoforms were, thus, partially colocalized. The results demonstrate that (1) cytofluorimetric scanning techniques could be successfully used to study axonal transport not only in peripheral nerves, but also in the CNS; (2) synaptic vesicles are transported with fast axonal transport in this nerve; and (3) some differences were noted compared with the sciatic nerve, especially for Rab3a and clathrin.

Effects of single and repeated doses of acrylamide on fast and slow axonal transport of radio labeled proteins following the injection of L-[4,5-3H] leucine have been studied in the optic system of male Sprague-Dawley rats. A single dose of acrylamide (100 mg/kg) had no effect, but higher concentrations (200-300 mg/kg) altered the distribution of fast axonally transported materials in optic nerves and optic tracts. Repeated doses of acrylamide (30 mg/kg/day, 5 days per week for 4 weeks) produced degeneration of tibial nerves but spared optic nerves and optic tracts. Fast axonal transport rate in optic axons was reduced by 50% (reduced to 4 mm/h from 8 mm/h) in acrylamide treated animals. Acrylamide also slowed the velocity of slow axonal transport of labeled proteins in optic axons to 1.0 mm per day from 1.3 mm per day. Since acrylamide impaired the rate of both fast and slow axonal transport in the absence of overt morphological damage, it can be concluded that deficit in axonal transport is an important factor in the pathogenesis of axonal degeneration in acrylamide neuropathy.