Stochastic computer model of the cell microtubule dynamics

To study the effect of various factors on the microtubule system, one of the main cytoskeletal elements in the cell, which organizes the intracellular transport of different organelles and is necessary for mitosis and meiosis, a computer model of this system is created. Using a stochastic approach, the model describes the microtubule assembly/disassembly as a set of chemical reactions with certain rate constants. Microtubules are visualized in the computer program field, which makes the model vivid. The program imitates the dynamics and structure of the microtubule system with high reliability. The parameters calculated by the model correlate with the corresponding parameters of microtubules in living cells. This approach to modeling microtubules and similar systems continues to be developed so that the models would better describe living systems and the effect of a still broader range of factors could be studied.     

Free and centrosome-attached microtubules: quantitative analysis and the modeling of two-component system

In the internal cytoplasm of interphase cells the density of microtubules is the highest in the centrosome area and decreases to the cell periphery. As a rule, the quantity of fluorescent microtubules cannot be counted up in the internal cytoplasm, but it is possible to estimate microtubules quantity using measuring of their optical density. In living 3T3 and CHO cells the microtubules optical density decreased according to different mathematical dependences that apparently reflected the differences of their microtubule system organization. To determine appropriateness that circumscribe the reduction of microtubules optical density from the centrosome region to the direction of cell margin, we modeled cell contours with the certain ratio and interposition of centrosome-attached and free microtubules in vector schedules CorelDraw program. The decrease of optical density was analyzed in MetaMorph program as it was described earlier (Smurova et al., 2002). It was shown that fluorescent microtubules optical density decreased exponentially (y = ae(-bx)) if the system joined only microtubules growing from the centrosome up to the cell margin. The curve became smoother in the case of not all radial centrosome-attached microtubules reached the margin, and adding of free microtubules into the system led to the sharp fall in optical density in the centrosome area and to its gradual decrease at the cell periphery. The increase in free microtubules quantity changed the character of the curve describing the reduction of optical density microtubule system which included free and centrosome-attached microtubules in proportions of 5 : 1 was described by the equation of linear regression (f= k . x + b). Thus, the mathematical dependence describing the microtubules distribution from the centrosome to the cell periphery, depends on the ratio of microtubules and their relative positioning in the cell volume. The data obtained using model systems have coincided with the results of experiments. The graphs which described the increase in microtubules optical density during microtubule repolymerization after nocodazole treatment, corresponded to the graphs for model cells. Thus, the method we used allows to analyze the microtubule system in the cases when the direct observation of individual microtubules is difficult.     

A mechanics model of microtubule buckling in living cells

As the most rigid cytoskeletal filaments, microtubules bear compressive forces in living cells, balancing the tensile forces within the cytoskeleton to maintain the cell shape. It is often observed that, in living cells, microtubules under compression severely buckle into short wavelengths. By contrast, when compressed, isolated microtubules in vitro buckle into single long-wavelength arcs. The critical buckling force of the microtubules in vitro is two orders of magnitude lower than that of the microtubules in living cells. To explain this discrepancy, we describe a mechanics model of microtubule buckling in living cells. The model investigates the effect of the surrounding filament network and the cytosol on the microtubule buckling. The results show that, while the buckling wavelength is set by the interplay between the microtubules and the elastic surrounding filament network, the buckling growth rate is set by the viscous cytosol. By considering the nonlinear deformation of the buckled microtubule, the buckling amplitude can be determined at the kinetically constrained equilibrium. The model quantitatively correlates the microtubule bending rigidity, the surrounding filament network elasticity, and the cytosol viscosity with the buckling wavelength, the buckling growth rate, and the buckling amplitude of the microtubules. Such results shed light on designing a unified experimental protocol to measure various critical mechanical properties of subcellular structures in living cells.     

Evaluation of various methods of measurement of the microtubule length in the cytoplasm of cultured cells

It is generally assumed that microtubules in tissue culture cells extend from the centrosome to cell periphery, and the length of individual microtubules averages several dozens of microns. However, direct electron-microscopic measurements have cast some doubt on this assumption. In this study, the average length of microtubules in cultured Vero cells was estimated using a combined approach. The length of free cytoplasmic and centrosomal microtubules was determined by means of electron microscopy in serial sections; concurrently, the length of free microtubules in the lamella was measured in preparations stained with tubulin antibodies (an indirect immunofluorescent method), by tracing saltatory particle movements along the microtubules in living cells. According to the data of immunofluorescent microscopy, microtubule length in the lamella averaged 4.57 +/- 3.69 microns. However, since two or more microtubules can overlap, their length may be slightly overestimated by this method. On the other hand, saltatory movements are easy to monitor and measure fairly accurately, but their range may be shorter than the actual microtubule length because of a limited processiveness of motors (kinesin and dynein). On average, the trajectories of saltatory movements in living cells were 3.85 +/- 0.72 microns long. At the electron-microscopic level, microtubule length was analyzed using pseudo-three-dimensional reconstructions of the microtubule systems around the centrosome and in the lamella. The length of free microtubules in the lamella reached 18 microns, averaging 3.33 +/- 2.43 microns; the average length of centrosomal microtubules was 1.49 +/- 0.82 microns. Good correspondence between the data on microtubule length and arrangement obtained by different methods allows the conclusion that most of free microtubules in Vero cells actually have a length of 2-5 microns; i.e., they are much shorter than the cell radius (about 25 microns). Microtubules extending from the centrosome are shorter still and do not reach the cell periphery. Thus, most microtubules in the lamella of Vero cells are free and their ordered arrangement is not associated with their attachment to the centrosome.     

Exploring the Contribution of Collective Motions to the Dynamics of Forced-Unfolding in Tubulin

Decomposition of the intrinsic dynamics of proteins into collective motions among distant regions of the protein structure provides a physically appealing approach that couples the dynamics of the system with its functional role. The cellular functions of microtubules (an essential component of the cytoskeleton in all eukaryotic cells) depend on their dynamic instability, which is altered by various factors among which applied forces are central. To shed light on the coupling between forces and the dynamic instability of microtubules, we focus on the investigation of the response of the microtubule subunits (tubulin) to applied forces. We address this point by adapting an approach designed to survey correlations for the equilibrium dynamics of proteins to the case of correlations for proteins forced-dynamics. The resulting collective motions in tubulin have a number of functional implications, such as the identification of long-range couplings with a role in blocking the dynamic instability of microtubules. A fundamental implication of our study for the life of a cell is that, to increase the likelihood of unraveling of large cytoskeletal filaments under physiological forces, molecular motors must use a combination of pulling and torsion rather than just pulling.     

Type-I IFN signaling is required for the induction of antigen-specific CD8(+) T cell responses by adenovirus vector vaccine in the gut-mucosa

Microtubules in living cells are very important component for various cellular functions as well as to maintain the cell shape. Mechanical properties of microtubules play a vital role in their functions and structure. To understand the mechanical properties of microtubules in living cells, we developed an orthotropic-Pasternak model and investigated the vibrational behavior when microtubules are embedded in surrounding elastic medium. We considered microtubules as orthotropic elastic shell and its surrounding elastic matrix as Pasternak foundation. We found that due to mechanical coupling of microtubules with elastic medium, the flexural vibration is increased with the stiffening of elastic medium. We noticed that foundation modulus (H) and shear modulus (G) have more effect on radial vibrational mode as compared to longitudinal vibrational mode and torsional vibrational mode.     

Levels of organization of living systems: Cooperons

All creatures living on Earth are traditionally discussed in the context of structuralmorphological approach, in frame of which there are considered various systems (for instance, organisms and ecosystems) that have different sizes and organization and use different resources for their existence. These characteristics are sometimes added by some particular functional and ecological characteristics, but usually with respect to the structural ones. We believe that such traditional approach, although illustrating, but distracts from the circumstance that any living systems is to be considered an integrated structural-functional complex, the maintenance of existence of this system being impossible without the processes occurring constantly in it and aimed at preserving this complex. This leads us to the concept of cooperons—the self-preserved dynamic structures existing only as a result of various specifically organized cooperative processes (their intensities can vary depending on circumstances). From our point of view, all living systems are cooperons of different hierarchy levels. Some other systems, specifically the symbiotic ones, also are cooperons. In frame of this concept, it is possible to discuss functioning of living systems of different types of organization in a new context closer to physiologists, both for the case of “norm” and for the situation when the cooperative interrelations of parts of the system are impaired (for instance, in systemic diseases).     

Subcellular metabolic organization in the context of dynamic energy budget and biochemical systems theories

The dynamic modelling of metabolic networks aims to describe the temporal evolution of metabolite concentrations in cells. This area has attracted increasing attention in recent years owing to the availability of high-throughput data and the general development of systems biology as a promising approach to study living organisms. Biochemical Systems Theory (BST) provides an accurate formalism to describe biological dynamic phenomena. However, knowledge about the molecular organization level, used in these models, is not enough to explain phenomena such as the driving forces of these metabolic networks. Dynamic Energy Budget (DEB) theory captures the quantitative aspects of the organization of metabolism at the organism level in a way that is non-species-specific. This imposes constraints on the sub-organismal organization that are not present in the bottom-up approach of systems biology. We use in vivo data of lactic acid bacteria under various conditions to compare some aspects of BST and DEB approaches. Due to the large number of parameters to be estimated in the BST model, we applied powerful parameter identification techniques. Both models fitted equally well, but the BST model employs more parameters. The DEB model uses similarities of processes under growth and no-growth conditions and under aerobic and anaerobic conditions, which reduce the number of parameters. This paper discusses some future directions for the integration of knowledge from these two rich and promising areas, working top-down and bottom-up simultaneously. This middle-out approach is expected to bring new ideas and insights to both areas in terms of describing how living organisms operate.     

Free and centrosome-attached microtubules: Quantitative analysis and modeling of two-component system

In cultivated in vitro interphase animal cells, microtubules form a network whose density is highest in the central cell area, in the region of centrosome, and decreases towards the cell periphery. Since identification of individual microtubules in the central cell area is significantly difficult and more often is impossible, there are several approaches to studying microtubules in the internal cell cytoplasm. These approaches are based on a decrease of microtubule density—both real, due to their partial depolymerization (by the action of cold temperatures or cytostatics), or apparent, due to a decrease of cell thickness (by photobleaching of preexisting microtubules and analysis of newly formed ones). In the present work, we propose a method based on the determination of optical density which allows evaluation of the state of the cytoplasmic microtubule system as a whole. The method consists of a comparison of the dependences describing changes of the microtubule optical density from the cell center to the periphery in controls and in experiments. Analysis of living cells by the proposed method has shown that the character of curves describing the decrease of optical density from the cell center to its periphery is different for various cell types; the dependence can be described both as an exponential regression (the CHO cell line) and as a linear regression (the NIH-3T3 and REF cell lines). Our previous studies have allowed the suggestion that the character of the dependence is determined by the ratio of free and centrosome-attached microtubules and by the position of their ends in the cell cytoplasm. To test this hypothesis, we considered model systems with all microtubules assumed to be in a straight orientation and divergent radially from the centrosome, but with different arrangements of plus-and minus-ends. In the model system, in which all the microtubule minus-ends are attached to the centrosome while the plus-ends are at different distances from it, the microtubule density is described by the exponential (f(x) = ae ^?bx ). Introduction of free microtubules into the system leads to a change of the character of this dependence, and the system in which the concentration of free microtubules with minus ends located at different distances from the cytoplasm is 5 times higher than that of the centrosome-attached microtubules is described by the linear regression equation (f(x) = k ^* x + b), which corresponds to the experimentally obtained dependences for 3T3 and REF cells. Thus, we believe that even in cells with a radial microtubule system, free microtubules may constitute the majority.     

Role of microtubules in tip growth of fungi

Polarized cell growth is observed ubiquitously in all living organisms. Tip growth of filamentous fungi serves as a typical model for polar growth. It is well known that the actin cytoskeleton plays a central role in cellular growth. In contrast, the role of microtubules in polar growth of fungal tip cells has not been critically addressed. Our recent study, using a green fluorescent protein (GFP)-labeled tubulin-expressing strain of the filamentous fungus Aspergillus nidulans and treatment with an anti-microtubule reagent, revealed that microtubules are essential for rapid hyphal growth. Our results indicated that microtubule organization contributes to continuous tip growth throughout the cell cycle, which in turn enables the maintenance of an appropriate mass of cytoplasm for the multinucleate system. In filamentous fungi, the microtubule is an essential component of the tip growth machinery that enables continuous and rapid growth. Recent research developments are starting to elucidate the components of the tip growth machinery and their functions in many organisms. This recent knowledge, in turn, is starting to enhance the importance of fungal systems as simple model systems to understand the polar growth of cells.     

Dielectric measurement of individual microtubules using the electroorientation method

Little is known about the electrostatic/dynamic properties of microtubules, which are considered to underlie their electrostatic interactions with various proteins such as motor proteins, microtubule-associated proteins, and microtubules themselves (lateral association of microtubules). To measure the dielectric properties of microtubules, we developed an experiment system in which the electroorientation of microtubules was observed under a dark-field microscope. Upon application of an alternating electric field (0.5-1.9 x 10(5) V/m, 10 kHz-3 MHz), the microtubules were oriented parallel to the field line in a few seconds because of the dipole moment induced along their long axes. The process of this orientation was analyzed based on a dielectric ellipsoid model, and the conductivity and dielectric constant of each microtubule were calculated. The analyses revealed that the microtubules were highly conductive, which is consistent with the counterion polarization model-counterions bound to highly negatively charged microtubules can move along the long axis, and this mobility might be the origin of the high conductivity. Our experiment system provides a useful tool to quantitatively evaluate the polyelectrolyte nature of microtubules, thus paving the way for future studies aiming to understand the physicochemical mechanism underlying the electrostatic interactions of microtubules with various proteins.     

Soft- and hard-modeling approaches for the determination of stability constants of metal-peptide systems by voltammetry

The Zn(2+)-glutathione system is studied as a model for metal-peptide systems where some critical factors must be considered when using voltammetric techniques for the determination of stability constants. These factors are the presence of side reactions (in this case, both the protonation of glutathione and the hydrolysis of Zn(2+)), the association-dissociation rates of the complexes compared with the time scales of the measurements (which makes the complexes electrochemically labile or inert), and the electron transfer kinetics on the electrode surface (which makes the metal ion reduction reversible or irreversible). For the study of these factors, three data treatment approaches have been applied: (i) the electrochemical hard-modeling approach (modelization of both chemical equilibrium and electrochemical processes), (ii) a chemical hard-modeling approach (modelization of chemical equilibria only, based on the least-squares curve-fitting program SQUAD), and (iii) a previously developed model-free soft-modeling approach based on multivariate curve resolution with a constrained alternating least-squares optimization. By analyzing differential pulse polarographic data obtained under different experimental conditions, the influence of the mentioned factors on every approach is discussed and, if possible, the corresponding stability constants are computed. The results of this study showed the potential usefulness of voltammetry in combination with hard- and soft-modeling data analysis for the study of peptide complexation equilibria of metal ions such as Zn which have neither relevant spectroscopic properties nor proper isotopes for NMR measurements.     

Physico-chemical study of the heterogeneous population of opioid receptors

A physico-chemical analysis of the heterogenous population of opioid receptors was carried out. A new difference approach to the analysis of heterogenous receptor systems was developed. This procedure permits to estimate even in high stringency conditions of parameters of three or more types of receptors from the binding isotherms or competitive replacement curves as well as to determine the total receptor concentration in the system. A DELTA computer program based on this difference approach has been developed. The experimental results obtained through the use of the difference technique led to a kinetic model of interaction between morphine and D-Ala2, D-Leu5-enkephalin with rat brain receptors. This model based on the interaction of each ligand with three types of specific binding sites can be used for the determination of kinetic and thermodynamic parameters.     

Chromosome elasticity and mitotic polar ejection force measured in living Drosophila embryos by four-dimensional microscopy-based motion analysis

BACKGROUND: Mitosis involves the interaction of many different components, including chromatin, microtubules, and motor proteins. Dissecting the mechanics of mitosis requires methods of studying not just each component in isolation, but also the entire ensemble of components in its full complexity in genetically tractable model organisms. RESULTS: We have developed a mathematical framework for analyzing motion in four-dimensional microscopy data sets that allows us to measure elasticity, viscosity, and forces by tracking the conformational movements of mitotic chromosomes. We have used this approach to measure, for the first time, the basic biophysical parameters of mitosis in wild-type Drosophila melanogaster embryos. We found that Drosophila embryo chromosomes are significantly less rigid than the much larger chromosomes of vertebrates. Anaphase kinetochore force and nucleoplasmic viscosity were comparable with previous estimates in other species. Motion analysis also allowed us to measure the magnitude of the polar ejection force exerted on chromosome arms during metaphase by individual microtubules. We find the magnitude of this force to be approximately 1 pN, a number consistent with force generation either by collision of growing microtubules with chromosomes or by single kinesin motors. CONCLUSIONS: Motion analysis allows noninvasive mechanical measurements to be made in complex systems. This approach should allow the functional effects of Drosophila mitotic mutants on chromosome condensation, kinetochore forces, and the polar ejection force to be determined.     

Switching of membrane organelles between cytoskeletal transport systems is determined by regulation of the microtubule-based transport

Intracellular transport of membrane organelles occurs along microtubules (MTs) and actin filaments (AFs). Although transport along each type of the cytoskeletal tracks is well characterized, the switching between the two types of transport is poorly understood because it cannot be observed directly in living cells. To gain insight into the regulation of the switching of membrane organelles between the two major transport systems, we developed a novel approach that combines live cell imaging with computational modeling. Using this approach, we measured the parameters that determine how fast membrane organelles switch back and forth between MTs and AFs (the switching rate constants) and compared these parameters during different signaling states. We show that regulation involves a major change in a single parameter: the transferring rate from AFs onto MTs. This result suggests that MT transport is the defining factor whose regulation determines the choice of the cytoskeletal tracks during the transport of membrane organelles.     

Multiple-color fluorescence imaging of chromosomes and microtubules in living cells

Microscopic observation of fluorescently-stained intracellular molecules within a living cell provides a straightforward approach to understanding their temporal and spatial relationships. However, exposure to the excitation light used to visualize these fluorescently-stained molecules can be toxic to the cells. Here we describe several important considerations in microscope instrumentation and experimental conditions for avoiding the toxicity associated with observing living fluorescently-stained cells. Using a computer-controlled fluorescence microscope system designed for live observation, we recorded time-lapse, multi-color images of chromosomes and microtubules in living human and fission yeast cells. In HeLa cells, a human cell line, microtubules were stained with rhodamine-conjugated tubulin, and chromosomes were stained with a DNA-specific fluorescent dye, Hoechst33342, or with rhodamine-conjugated histone. In fission yeast cells, microtubules were stained with alpha-tubulin fused with the jellyfish green fluorescent protein (GFP), and chromosomes were stained with Hoechst33342.     

Mining protein sequences for motifs.

We use methods from Data Mining and Knowledge Discovery to design an algorithm for detecting motifs in protein sequences. The algorithm assumes that a motif is constituted by the presence of a "good" combination of residues in appropriate locations of the motif. The algorithm attempts to compile such good combinations into a "pattern dictionary" by processing an aligned training set of protein sequences. The dictionary is subsequently used to detect motifs in new protein sequences. Statistical significance of the detection results are ensured by statistically determining the various parameters of the algorithm. Based on this approach, we have implemented a program called GYM. The Helix-Turn-Helix motif was used as a model system on which to test our program. The program was also extended to detect Homeodomain motifs. The detection results for the two motifs compare favorably with existing programs. In addition, the GYM program provides a lot of useful information about a given protein sequence.     

A spatial model of cellular molecular trafficking including active transport along microtubules

We consider models of Ran-driven nuclear transport of molecules such as proteins in living cells. The mathematical model presented is the first to take into account for the active transport of molecules along the cytoplasmic microtubules. All parameters entering the models are thoroughly discussed. The model is tested by numerical simulations based on discontinuous Galerkin finite element methods. The numerical experiments are compared to the behavior observed experimentally.     

The coordination of protein motors and the kinetic behavior of microtubule--a computational study

Utilizing the mechanical energy converted from chemical energy through hydrolysis of ATP, motor proteins drive cytoskeleton filaments to move in various biological systems. Recent technological advance has shown the potential of the motor proteins for powering future nano-bio-mechanical systems. In order to effectively use motor proteins as a biological motor, the interaction between the protein motors and bio-filaments needs to be well clarified, since such interaction is largely influenced by many factors, such as the coordination among the motors, their dynamic behavior, physical properties of microtubules, and the viscosity of solution involved, etc. In this study, a two-dimensional model was proposed to simulate the motion of a microtubule driven by protein motors based on a dissipative particle dynamics (DPD) method with attempt to correlate the microtubule's kinetic behavior to the coordination among protein motors.