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.

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.

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 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.

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 [...].

Bidirectional, unlike unidirectional transport, allows transporting axonal cargos against their concentration gradient.

Even though most axonal cargos are synthesized in the soma, the concentration of many of these cargos is larger at the presynaptic terminal than in the soma. This requires transport of these cargos from the soma to the presynaptic terminal or other active sites in the axon. Axons utilize both bidirectional (for example, slow axonal transport) and unidirectional (for example, fast anterograde axonal transport) modes of cargo transport. Bidirectional transport seems to be less efficient because it requires more time and takes more energy to deliver cargos. In this paper, we studied a family of models which differ by the modes of axonal cargo transport (such as anterograde and retrograde motor-driven transport and passive diffusion) as well as by the presence or absence of pausing states. The models are studied to investigate their ability to describe axonal transport against the cargo concentration gradient. We argue that bidirectional axonal transport is described by a higher-order mathematical model, which allows imposing cargo concentration not only at the axon hillock but also at the axon terminal. The unidirectional transport model allows only for the imposition of cargo concentration at the axon hillock. Due to the great lengths of the axons, anterograde transport mostly relies on molecular motors, such as kinesins, to deliver cargos synthesized in the soma to the terminal and other active sites in the axon. Retrograde transport can be also motor-driven, in which case cargos are transported by dynein motors. If cargo concentration at the axon tip is higher than at the axon hillock, retrograde transport can also occur by cargo diffusion. However, because many axonal cargos are large or they assemble in multiprotein complexes for axonal transport, the diffusivity of such cargos is very small. We investigated the case of a small cargo diffusivity using a perturbation technique and found that for this case the effect of diffusion is limited to a very thin diffusion boundary layer near the axon tip. If cargo diffusivity is decreased in the model, we show that without motor-driven retrograde transport the model is unable to describe a high cargo concentration at the axon tip. To the best of our knowledge, our paper presents the first explanation for the utilization of seemingly inefficient bidirectional transport in neurons.

Model of drug delivery to populations composed of two cell types.

The rate of drug delivery to cells and the subsequent rate of drug metabolism are dependent on the cell membrane permeability to the drug. In some cases, tissue may be composed of different types of cells that exhibit order of magnitude differences in their membrane permeabilities. This paper presents a brief review of the components of the tissue scale three-compartment pharmacokinetic model of drug delivery to single-cell-type populations. The existing model is extended to consider tissue composed of two different cell types. A case study is presented of infusion mediated delivery of doxorubicin to a tumor that is composed of a drug reactive cell type and of a drug resistive cell type. The membrane permeabilities of the two cell types differ by an order of magnitude. A parametric investigation of the population composition is conducted and it is shown that the drug metabolism of the low permeability cells are negatively influenced by the fraction of the tissue composed of the permeable drug reactive cells. This is because when the population is composed mostly of drug permeable cells, the extracellular space is rapidly depleted of the drug. This has two compounding effects: (i) locally there is simply less drug available to the neighboring drug resistant cells, and (ii) the depletion of the drug from the extracellular space near the vessel-tissue interface leaves less drug to be transported to both cell types farther away from the vessel.

Analysis of Mitochondrial Function, Structure, and Intracellular Organization In Situ in Cardiomyocytes and Skeletal Muscles.

Analysis of the function, structure, and intracellular organization of mitochondria is important for elucidating energy metabolism and intracellular energy transfer. In addition, basic and clinically oriented studies that investigate organ/tissue/cell dysfunction in various human diseases, including myopathies, cardiac/brain ischemia-reperfusion injuries, neurodegenerative diseases, cancer, and aging, require precise estimation of mitochondrial function. It should be noted that the main metabolic and functional characteristics of mitochondria obtained in situ (in permeabilized cells and tissue samples) and in vitro (in isolated organelles) are quite different, thereby compromising interpretations of experimental and clinical data. These differences are explained by the existence of the mitochondrial network, which possesses multiple interactions between the cytoplasm and other subcellular organelles. Metabolic and functional crosstalk between mitochondria and extra-mitochondrial cellular environments plays a crucial role in the regulation of mitochondrial metabolism and physiology. Therefore, it is important to analyze mitochondria in vivo or in situ without their isolation from the natural cellular environment. This review summarizes previous studies and discusses existing approaches and methods for the analysis of mitochondrial function, structure, and intracellular organization in situ.

Mitochondrial permeability transition in cardiac ischemia-reperfusion: whether cyclophilin D is a viable target for cardioprotection?

Growing number of studies provide strong evidence that the mitochondrial permeability transition pore (PTP), a non-selective channel in the inner mitochondrial membrane, is involved in the pathogenesis of cardiac ischemia-reperfusion and can be targeted to attenuate reperfusion-induced damage to the myocardium. The molecular identity of the PTP remains unknown and cyclophilin D is the only protein commonly accepted as a major regulator of the PTP opening. Therefore, cyclophilin D is an attractive target for pharmacological or genetic therapies to reduce ischemia-reperfusion injury in various animal models and humans. Most animal studies demonstrated cardioprotective effects of PTP inhibition; however, a recent large clinical trial conducted by international groups demonstrated that cyclosporine A, a cyclophilin D inhibitor, failed to protect the heart in patients with myocardial infarction. These studies, among others, raise the question of whether cyclophilin D, which plays an important physiological role in the regulation of cell metabolism and mitochondrial bioenergetics, is a viable target for cardioprotection. This review discusses previous studies to provide comprehensive information on the physiological role of cyclophilin D as well as PTP opening in the cell that can be taken into consideration for the development of new PTP inhibitors.

Synchronism in mitochondrial ROS flashes, membrane depolarization and calcium sparks in human carcinoma cells.

Mitochondria are major producers of reactive oxygen species (ROS) in many cells including cancer cells. However, complex interrelationships between mitochondrial ROS (mitoROS), mitochondrial membrane potential (ΔΨm) and Ca2+ are not completely understood. Using human carcinoma cells, we further highlight biphasic ROS dynamics: - gradual mitoROS increase followed by mitoROS flash. Also, we demonstrate heterogeneity in rates of mitoROS generation and flash initiation time. Comparing mitochondrial and near-extra-mitochondrial signals, we show that mechanisms of mitoROS flashes in single mitochondria, linked to mitochondrial permeability transition pore opening (ΔΨm collapse) and calcium sparks, may involve flash triggering by certain levels of external ROS released from the same mitochondria. In addition, mitochondria-mitochondria interactions can produce wave propagations of mitoROS flashes and ΔΨm collapses in cancer cells similar to phenomena of ROS-induced ROS release (RIRR). Our data suggest that in cancer cells RIRR, activation of mitoROS flashes and mitochondrial depolarization may involve participation of extramitochondrial-ROS produced either by individual mitochondria and/or by neighboring mitochondria. This could represent general mechanisms in ROS-ROS signaling with suggested role in both mitochondrial and cellular physiology and signaling.

The impact of cardiac ischemia/reperfusion on the mitochondria-cytoskeleton interactions.

Cardiac ischemia-reperfusion (IR) injury compromises mitochondrial oxidative phosphorylation (OxPhos) and compartmentalized intracellular energy transfer via the phosphocreatine/creatine kinase (CK) network. The restriction of ATP/ADP diffusion at the level of the mitochondrial outer membrane (MOM) is an essential element of compartmentalized energy transfer. In adult cardiomyocytes, the MOM permeability to ADP is regulated by the interaction of voltage-dependent anion channel with cytoskeletal proteins, particularly with ß tubulin II. The IR-injury alters the expression and the intracellular arrangement of cytoskeletal proteins. The objective of the present study was to investigate the impact of IR on the intracellular arrangement of ß tubulin II and its effect on the regulation of mitochondrial respiration. Perfused rat hearts were subjected to total ischemia (for 20min (I20) and 45min (I45)) or to ischemia followed by 30min of reperfusion (I20R and I45R groups). High resolution respirometry and fluorescent confocal microscopy were used to study respiration, ß tubulin II and mitochondrial arrangements in cardiac fibers. The results of these experiments evidence a heterogeneous response of mitochondria to IR-induced damage. Moreover, the intracellular rearrangement of ß tubulin II, which in the control group colocalized with mitochondria, was associated with increased apparent affinity of OxPhos for ADP, decreased regulation of respiration by creatine without altering mitochondrial CK activity and the ratio between octameric to dimeric isoenzymes. The results of this study allow us to highlight changes of mitochondrial interactions with cytoskeleton as one of the possible mechanisms underlying cardiac IR injury.

Plectin isoform P1b and P1d deficiencies differentially affect mitochondrial morphology and function in skeletal muscle.

Plectin, a versatile 500-kDa cytolinker protein, is essential for muscle fiber integrity and function. The most common disease caused by mutations in the human plectin gene, epidermolysis bullosa simplex with muscular dystrophy (EBS-MD), is characterized by severe skin blistering and progressive muscular dystrophy. Besides displaying pathological desmin-positive protein aggregates and degenerative changes in the myofibrillar apparatus, skeletal muscle specimens of EBS-MD patients and plectin-deficient mice are characterized by massive mitochondrial alterations. In this study, we demonstrate that structural and functional alterations of mitochondria are a primary aftermath of plectin deficiency in muscle, contributing to myofiber degeneration. We found that in skeletal muscle of conditional plectin knockout mice (MCK-Cre/cKO), mitochondrial content was reduced, and mitochondria were aggregated in sarcoplasmic and subsarcolemmal regions and were no longer associated with Z-disks. Additionally, decreased mitochondrial citrate synthase activity, respiratory function and altered adenosine diphosphate kinetics were characteristic of plectin-deficient muscles. To analyze a mechanistic link between plectin deficiency and mitochondrial alterations, we comparatively assessed mitochondrial morphology and function in whole muscle and teased muscle fibers of wild-type, MCK-Cre/cKO and plectin isoform-specific knockout mice that were lacking just one isoform (either P1b or P1d) while expressing all others. Monitoring morphological alterations of mitochondria, an isoform P1b-specific phenotype affecting the mitochondrial fusion-fission machinery and manifesting with upregulated mitochondrial fusion-associated protein mitofusin-2 could be identified. Our results show that the depletion of distinct plectin isoforms affects mitochondrial network organization and function in different ways.

H9c2 and HL-1 cells demonstrate distinct features of energy metabolism, mitochondrial function and sensitivity to hypoxia-reoxygenation.

Dysfunction of cardiac energy metabolism plays a critical role in many cardiac diseases, including heart failure, myocardial infarction and ischemia-reperfusion injury and organ transplantation. The characteristics of these diseases can be elucidated in vivo, though animal-free in vitro experiments, with primary adult or neonatal cardiomyocytes, the rat ventricular H9c2 cell line or the mouse atrial HL-1 cells, providing intriguing experimental alternatives. Currently, it is not clear how H9c2 and HL-1 cells mimic the responses of primary cardiomyocytes to hypoxia and oxidative stress. In the present study, we show that H9c2 cells are more similar to primary cardiomyocytes than HL-1 cells with regard to energy metabolism patterns, such as cellular ATP levels, bioenergetics, metabolism, function and morphology of mitochondria. In contrast to HL-1, H9c2 cells possess beta-tubulin II, a mitochondrial isoform of tubulin that plays an important role in mitochondrial function and regulation. We demonstrate that H9c2 cells are significantly more sensitive to hypoxia-reoxygenation injury in terms of loss of cell viability and mitochondrial respiration, whereas HL-1 cells were more resistant to hypoxia as evidenced by their relative stability. In comparison to HL-1 cells, H9c2 cells exhibit a higher phosphorylation (activation) state of AMP-activated protein kinase, but lower peroxisome proliferator-activated receptor gamma coactivator 1-alpha levels, suggesting that each cell type is characterized by distinct regulation of mitochondrial biogenesis. Our results provide evidence that H9c2 cardiomyoblasts are more energetically similar to primary cardiomyocytes than are atrial HL-1 cells. H9c2 cells can be successfully used as an in vitro model to simulate cardiac ischemia-reperfusion injury.

Role of mitochondria-cytoskeleton interactions in respiration regulation and mitochondrial organization in striated muscles.

The aim of this work was to study the regulation of respiration and energy fluxes in permeabilized oxidative and glycolytic skeletal muscle fibers, focusing also on the role of cytoskeletal protein tubulin ßII isotype in mitochondrial metabolism and organization. By analyzing accessibility of mitochondrial ADP, using respirometry and pyruvate kinase-phosphoenolpyruvate trapping system for ADP, we show that the apparent affinity of respiration for ADP can be directly linked to the permeability of the mitochondrial outer membrane (MOM). Previous studies have shown that MOM permeability in cardiomyocytes can be regulated by VDAC interaction with cytoskeletal protein, ßII tubulin. We found that in oxidative soleus skeletal muscle the high apparent Km for ADP is associated with low MOM permeability and high expression of non-polymerized ßII tubulin. Very low expression of non-polymerized form of ßII tubulin in glycolytic muscles is associated with high MOM permeability for adenine nucleotides (low apparent Km for ADP).

Crosstalk between AMPK activation and angiotensin II-induced hypertrophy in cardiomyocytes: the role of mitochondria.

AMP-kinase (AMPK) activation reduces cardiac hypertrophy, although underlying molecular mechanisms remain unclear. In this study, we elucidated the anti-hypertrophic action of metformin, specifically, the role of the AMPK/eNOS/p53 pathway. H9c2 rat cardiomyocytes were treated with angiotensin II (AngII) for 24 hrs in the presence or absence of metformin (AMPK agonist), losartan [AngII type 1 receptor (AT1R) blocker], Nω-nitro-L-arginine methyl ester (L-NAME, pan-NOS inhibitor), splitomicin (SIRT1 inhibitor) or pifithrin-α (p53 inhibitor). Results showed that treatment with metformin significantly attenuated AngII-induced cell hypertrophy and death. Metformin attenuated AngII-induced activation (cleavage) of caspase 3, Bcl-2 down-regulation and p53 up-regulation. It also reduced AngII-induced AT1R up-regulation by 30% (P < 0.05) and enhanced AMPK phosphorylation by 99% (P < 0.01) and P-eNOS levels by 3.3-fold (P < 0.01). Likewise, losartan reduced AT1R up-regulation and enhanced AMPK phosphorylation by 54% (P < 0.05). The AMPK inhibitor, compound C, prevented AT1R down-regulation, indicating that metformin mediated its effects via AMPK activation. Beneficial effects of metformin and losartan converged on mitochondria that demonstrated high membrane potential (Δψm ) and low permeability transition pore opening. Thus, this study demonstrates that the anti-hypertrophic effects of metformin are associated with AMPK-induced AT1R down-regulation and prevention of mitochondrial dysfunction through the SIRT1/eNOS/p53 pathway.

The role of tubulin in the mitochondrial metabolism and arrangement in muscle cells.

Tubulin, a well-known component of the microtubule in the cytoskeleton, has an important role in the transport and positioning of mitochondria in a cell type dependent manner. This review describes different functional interactions of tubulin with cellular protein complexes and its functional interaction with the mitochondrial outer membrane. Tubulin is present in oxidative as well as glycolytic type muscle cells, but the kinetics of the in vivo regulation of mitochondrial respiration in these muscle types is drastically different. The interaction between VDAC and tubulin is probably influenced by such factors as isoformic patterns of VDAC and tubulin, post-translational modifications of tubulin and phosphorylation of VDAC. Important factor of the selective permeability of VDAC is the mitochondrial creatine kinase pathway which is present in oxidative cells, but is inactive or missing in glycolytic muscle and cancer cells. As the tubulin-VDAC interaction reduces the permeability of the channel by adenine nucleotides, energy transfer can then take place effectively only through the mitochondrial creatine kinase/phosphocreatine pathway. Therefore, closure of VDAC by tubulin may be one of the reasons of apoptosis in cells without the creatine kinase pathway. An important question in tubulin regulated interactions is whether other proteins are interacting with tubulin. The functional interaction may be direct, through other proteins like plectins, or influenced by simultaneous interaction of other complexes with VDAC.

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.

Mysterious Ca(2+)-independent muscular contraction: déjà vu.

The permeabilized cells and muscle fibres technique allows one to study the functional properties of mitochondria without their isolation, thus preserving all of the contacts with cellular structures, mostly the cytoskeleton, to study the whole mitochondrial population in the cell in their natural surroundings and it is increasingly being used in both experimental and clinical studies. The functional parameters (affinity for ADP in regulation of respiration) of mitochondria in permeabilized myocytes or myocardial fibres are very different from those in isolated mitochondria in vitro. In the present study, we have analysed the data showing the dependence of this parameter upon the muscle contractile state. Most remarkable is the effect of recently described Ca(2+)-independent contraction of permeabilized muscle fibres induced by elevated temperatures (30-37°C). We show that very similar strong spontaneous Ca(2+)-independent contraction can be produced by proteolytic treatment of permeabilized muscle fibres that result in a disorganization of mitochondrial arrangement, leading to a significant increase in affinity for ADP. These data show that Ca(2+)-insensitive contraction may be related to the destruction of cytoskeleton structures by intracellular proteases. Therefore the use of their inhibitors is strongly advised at the permeabilization step with careful washing of fibres or cells afterwards. A possible physiologically relevant relationship between Ca(2+)-regulated ATP-dependent contraction and mitochondrial functional parameters is also discussed.