Modeling oscillatory Microtubule--Polymerization

Polymerization of microtubules is ubiquitous in biological cells and under certain conditions it becomes oscillatory in time. Here simple reaction models are analyzed that capture such oscillations as well as the length distribution of microtubules. We assume reaction conditions that are stationary over many oscillation periods, and it is a Hopf bifurcation that leads to a persistent oscillatory microtubule polymerization in these models. Analytical expressions are derived for the threshold of the bifurcation and the oscillation frequency in terms of reaction rates as well as typical trends of their parameter dependence are presented. Both, a catastrophe rate that depends on the density of {\it guanosine triphosphate} (GTP) liganded tubulin dimers and a delay reaction, such as the depolymerization of shrinking microtubules or the decay of oligomers, support oscillations. For a tubulin dimer concentration below the threshold oscillatory microtubule polymerization occurs transiently on the route to a stationary state, as shown by numerical solutions of the model equations. Close to threshold a so--called amplitude equation is derived and it is shown that the bifurcation to microtubule oscillations is supercritical.Comment: 21 pages and 12 figure

Analysis of in vivo turnover of tau in a mouse model of tauopathy

BACKGROUND: Intracellular accumulation of tau as neurofibrillary tangles (NFTs) is the hallmark of Alzheimer’s disease (AD) as well as in other tauopathies. Tau is present not only in the cytoplasm but also in the extracellular space such as cerebrospinal fluid (CSF) and brain interstitial fluid (ISF). Although clearance is one critical parameter leading to such intracellular/extracellular tau accumulation, in vivo turnover of tau has not been well characterized. The current study has attempted to precisely determine in vivo turnover rates of tau utilizing tet-off regulatable mice. In particular, we assessed intracellular tau and extracellular tau, soluble tau, insoluble tau and phosphorylated tau at certain sites utilizing a combination of in vivo microdialysis, biochemical analysis and specific ELISAs recognizing each species. To examine the effect of a tauopathy-associated mutation on tau clearance, half-lives of various tau species were compared between the mice with a FTDP-17 mutation that induces β-sheet formation, ΔK280 mutation (pro-aggregant mice) and control mice with additional β-sheet breaking mutations (anti-aggregant mice). RESULTS: Here we report that tau is metabolized at much slower turnover rates in vivo than in cell culture. We found that insoluble tau in pro-aggregant mice had a significantly slower half-life (t(1/2) = ~34.2 days) than soluble tau (t(1/2) = ~9.7 days). In contrast, soluble tau phosphorylated in the proline rich region was cleared faster than total soluble tau. When comparing pro-aggregant mice to anti-agregant mice, turnover rates of soluble tau species were not significantly different. CONCLUSIONS: The current study provides a comprehensive description of in vivo turnover of various tau species present in mice that express human tau. The turnover rate of soluble tau was not significantly altered between pro-aggregant mice and anti-aggregant mice. This suggests that altered conformation by ΔK280 does not have a major impact on clearance pathways for soluble tau. In contrast, different tau species displayed different half-lives. Turnover was significantly delayed for insoluble tau whereas it was accelerated for soluble tau phosphorylated in the proline rich region. These differences in susceptibilities to clearance suggest that aggregation and phosphorylation influences tau clearance which may be important in tau pathogenesis

Tau blocks traffic of organelles, neurofilaments, and APP vesicles in neurons and enhances oxidative stress

We studied the effect of microtubule-associated tau protein on trafficking of vesicles and organelles in primary cortical neurons, retinal ganglion cells, and neuroblastoma cells. Tau inhibits kinesin-dependent transport of peroxisomes, neurofilaments, and Golgi-derived vesicles into neurites. Loss of peroxisomes makes cells vulnerable to oxidative stress and leads to degeneration. In particular, tau inhibits transport of amyloid precursor protein (APP) into axons and dendrites, causing its accumulation in the cell body. APP tagged with yellow fluorescent protein and transfected by adenovirus associates with vesicles moving rapidly forward in the axon (∼80%) and slowly back (∼20%). Both movements are strongly inhibited by cotransfection with fluorescently tagged tau (cyan fluorescent protein–tau) as seen by two-color confocal microscopy. The data suggests a linkage between tau and APP trafficking, which may be significant in Alzheimer's disease

Inhibition of Tau aggregation with BSc3094 reduces Tau and decreases cognitive deficits in rTg4510 mice.

Background One of the major hallmarks of Alzheimer's disease (AD)is the aberrant modification and aggregation of the microtubule-associated protein Tau . The extent of Tau pathology correlates with cognitive decline, strongly implicating Tau in the pathogenesis of the disease. Because the inhibition of Tau aggregation may be a promising therapeutic target, we tested the efficacy of BSc3094, an inhibitor of Tau aggregation, in reducing Tau pathology and ameliorating the disease symptoms in transgenic mice. Methods Mice expressing human Tau with the P301L mutation (line rTg4510) were infused with BSc3094 into the lateral ventricle using Alzet osmotic pumps connected to a cannula that was placed on the skull of the mice, thus bypassing the blood-brain barrier (BBB) . The drug treatment lasted for 2 months, and the effect of BSc3094 on cognition and on reversing hallmarks of Tau pathology was assessed. Results BSc3094 significantly reduced the levels of Tau phosphorylation and sarkosyl-insoluble Tau. In addition, the drug improved cognition in different behavioral tasks and reduced anxiety-like behavior in the transgenic mice used in the study. Conclusions Our in vivo investigations demonstrated that BSc3094 is capable of partially reducing the pathological hallmarks typically observed in Tau transgenic mice, highlighting BSc3094 as a promising compound for a future therapeutic approach for AD

Ectopic A-lattice seams destabilize microtubules

Natural microtubules typically include one A-lattice seam within an otherwise helically symmetric B-lattice tube. It is currently unclear how A-lattice seams influence microtubule dynamic instability. Here we find that including extra A-lattice seams in GMPCPP microtubules, structural analogues of the GTP caps of dynamic microtubules, destabilizes them, enhancing their median shrinkage rate by >20-fold. Dynamic microtubules nucleated by seeds containing extra A-lattice seams have growth rates similar to microtubules nucleated by B-lattice seeds, yet have increased catastrophe frequencies at both ends. Furthermore, binding B-lattice GDP microtubules to a rigor kinesin surface stabilizes them against shrinkage, whereas microtubules with extra A-lattice seams are stabilized only slightly. Our data suggest that introducing extra A-lattice seams into dynamic microtubules destabilizes them by destabilizing their GTP caps. On this basis, we propose that the single A-lattice seam of natural B-lattice MTs may act as a trigger point, and potentially a regulation point, for catastrophe

Nanomechanics of microtubules

We have determined the mechanical anisotropy of a single microtubule by simultaneously measuring the Young's and the shear moduli in vitro. This was achieved by elastically deforming the microtubule deposited on a substrate tailored by electron-beam lithography with a tip of an atomic force microscope. The shear modulus is 2 orders of magnitude lower than the Young's, giving rise to a length-dependent flexural rigidity of microtubules. The temperature dependence of the microtubule's bending stiffness in the (5-40) degreesC range shows a strong variation upon cooling coming from the increasing interaction between the protofilaments

Transport by molecular motors in the presence of static defects

The transport by molecular motors along cytoskeletal filaments is studied theoretically in the presence of static defects. The movements of single motors are described as biased random walks along the filament as well as binding to and unbinding from the filament. Three basic types of defects are distinguished, which differ from normal filament sites only in one of the motors' transition probabilities. Both stepping defects with a reduced probability for forward steps and unbinding defects with an increased probability for motor unbinding strongly reduce the velocities and the run lengths of the motors with increasing defect density. For transport by single motors, binding defects with a reduced probability for motor binding have a relatively small effect on the transport properties. For cargo transport by motors teams, binding defects also change the effective unbinding rate of the cargo particles and are expected to have a stronger effect.Comment: 20 pages, latex, 7 figures, 1 tabl

Force and Motion Generation of Molecular Motors: A Generic Description

We review the properties of biological motor proteins which move along linear filaments that are polar and periodic. The physics of the operation of such motors can be described by simple stochastic models which are coupled to a chemical reaction. We analyze the essential features of force and motion generation and discuss the general properties of single motors in the framework of two-state models. Systems which contain large numbers of motors such as muscles and flagella motivate the study of many interacting motors within the framework of simple models. In this case, collective effects can lead to new types of behaviors such as dynamic instabilities of the steady states and oscillatory motion.Comment: 29 pages, 9 figure

Energy Transduction of Isothermal Ratchets: Generic Aspects and Specific Examples Close to and Far from Equilibrium

We study the energetics of isothermal ratchets which are driven by a chemical reaction between two states and operate in contact with a single heat bath of constant temperature. We discuss generic aspects of energy transduction such as Onsager relations in the linear response regime as well as the efficiency and dissipation close to and far from equilibrium. In the linear response regime where the system operates reversibly the efficiency is in general nonzero. Studying the properties for specific examples of energy landscapes and transitions, we observe in the linear response regime that the efficiency can have a maximum as a function of temperature. Far from equilibrium in the fully irreversible regime, we find a maximum of the efficiency with values larger than in the linear regime for an optimal choice of the chemical driving force. We show that corresponding efficiencies can be of the order of 50%. A simple analytic argument allows us to estimate the efficiency in this irreversible regime for small external forces.Comment: 16 pages, 10 figure