Mechanisms of Self-Organization of Cortical Microtubules in Plants Revealed by Computational Simulations

Microtubules confined to the two-dimensional cortex of elongating plant cells must form a parallel yet dispersed array transverse to the elongation axis for proper cell wall expansion. Some of these microtubules exhibit free minus-ends, leading to migration at the cortex by hybrid treadmilling. Collisions between microtubules can result in plus-end entrainment (“zippering”) or rapid depolymerization. Here, we present a computational model of cortical microtubule organization. We find that plus-end entrainment leads to self-organization of microtubules into parallel arrays, whereas catastrophe-inducing collisions do not. Catastrophe-inducing boundaries (e.g., upper and lower cross-walls) can tune the orientation of an ordered array to a direction transverse to elongation. We also find that changes in dynamic instability parameters, such as in mor1-1 mutants, can impede self-organization, in agreement with experimental data. Increased entrainment, as seen in clasp-1 mutants, conserves self-organization, but delays its onset and fails to demonstrate increased ordering. We find that branched nucleation at acute angles off existing microtubules results in distinctive sparse arrays and infer either that microtubule-independent or coparallel nucleation must dominate. Our simulations lead to several testable predictions, including the effects of reduced microtubule severing in katanin mutants.     

A Stochastic Multiscale Model That Explains the Segregation of Axonal Microtubules and Neurofilaments in Neurological Diseases

The organization of the axonal cytoskeleton is a key determinant of the normal function of an axon, which is a long thin projection of a neuron. Under normal conditions two axonal cytoskeletal polymers, microtubules and neurofilaments, align longitudinally in axons and are interspersed in axonal cross-sections. However, in many neurotoxic and neurodegenerative disorders, microtubules and neurofilaments segregate apart from each other, with microtubules and membranous organelles clustered centrally and neurofilaments displaced to the periphery. This striking segregation precedes the abnormal and excessive neurofilament accumulation in these diseases, which in turn leads to focal axonal swellings. While neurofilament accumulation suggests an impairment of neurofilament transport along axons, the underlying mechanism of their segregation from microtubules remains poorly understood for over 30 years. To address this question, we developed a stochastic multiscale model for the cross-sectional distribution of microtubules and neurofilaments in axons. The model describes microtubules, neurofilaments and organelles as interacting particles in a 2D cross-section, and is built upon molecular processes that occur on a time scale of seconds or shorter. It incorporates the longitudinal transport of neurofilaments and organelles through this domain by allowing stochastic arrival and departure of these cargoes, and integrates the dynamic interactions of these cargoes with microtubules mediated by molecular motors. Simulations of the model demonstrate that organelles can pull nearby microtubules together, and in the absence of neurofilament transport, this mechanism gradually segregates microtubules from neurofilaments on a time scale of hours, similar to that observed in toxic neuropathies. This suggests that the microtubule-neurofilament segregation can be a consequence of the selective impairment of neurofilament transport. The model generates the experimentally testable prediction that the rate and extent of segregation will be dependent on the sizes of the moving organelles as well as the density of their traffic.     

Interactions between the Translation Machinery and Microtubules

Microtubules are components of eukaryotic cytoskeleton that are involved in the transport of various components from the nucleus to the cell periphery and back. They also act as a platform for assembly of complex molecular ensembles. Ribonucleoprotein (RNP) complexes, such as ribosomes and mRNPs, are transported over significant distances (e.g. to neuronal processes) along microtubules. The association of RNPs with microtubules and their transport along these structures are essential for compartmentalization of protein biosynthesis in cells. Microtubules greatly facilitate assembly of stress RNP granules formed by accumulation of translation machinery components during cell stress response. Microtubules are necessary for the cytoplasm-to-nucleus transport of proteins, including ribosomal proteins. At the same time, ribosomal proteins and RNA-binding proteins can influence cell mobility and cytoplasm organization by regulating microtubule dynamics. The molecular mechanisms underlying the association between the translation machinery components and microtubules have not been studied systematically; the results of such studies are mostly fragmentary. In this review, we attempt to fill this gap by summarizing and discussing the data on protein and RNA components of the translation machinery that directly interact with microtubules or microtubule motor proteins.     

A Spatially Detailed Model of Isometric Contraction Based on Competitive Binding of Troponin I Explains Cooperative Interactions between Tropomyosin and Crossbridges

Biophysical models of cardiac tension development provide a succinct representation of our understanding of force generation in the heart. The link between protein kinetics and interactions that gives rise to high cooperativity is not yet fully explained from experiments or previous biophysical models. We propose a biophysical ODE-based representation of cross-bridge (XB), tropomyosin and troponin within a contractile regulatory unit (RU) to investigate the mechanisms behind cooperative activation, as well as the role of cooperativity in dynamic tension generation across different species. The model includes cooperative interactions between regulatory units (RU-RU), between crossbridges (XB-XB), as well more complex interactions between crossbridges and regulatory units (XB-RU interactions). For the steady-state force-calcium relationship, our framework predicts that: (1) XB-RU effects are key in shifting the half-activation value of the force-calcium relationship towards lower [Ca²⁺], but have only small effects on cooperativity. (2) XB-XB effects approximately double the duty ratio of myosin, but do not significantly affect cooperativity. (3) RU-RU effects derived from the long-range action of tropomyosin are a major factor in cooperative activation, with each additional unblocked RU increasing the rate of additional RU’s unblocking. (4) Myosin affinity for short (1–4 RU) unblocked stretches of actin of is very low, and the resulting suppression of force at low [Ca²⁺] is a major contributor in the biphasic force-calcium relationship. We also reproduce isometric tension development across mouse, rat and human at physiological temperature and pacing rate, and conclude that species differences require only changes in myosin affinity and troponin I/troponin C affinity. Furthermore, we show that the calcium dependence of the rate of tension redevelopment k_tr is explained by transient blocking of RU’s by a temporary decrease in XB-RU effects.     

Dense Neuron Clustering Explains Connectivity Statistics in Cortical Microcircuits

Local cortical circuits appear highly non-random, but the underlying connectivity rule remains elusive. Here, we analyze experimental data observed in layer 5 of rat neocortex and suggest a model for connectivity from which emerge essential observed non-random features of both wiring and weighting. These features include lognormal distributions of synaptic connection strength, anatomical clustering, and strong correlations between clustering and connection strength. Our model predicts that cortical microcircuits contain large groups of densely connected neurons which we call clusters. We show that such a cluster contains about one fifth of all excitatory neurons of a circuit which are very densely connected with stronger than average synapses. We demonstrate that such clustering plays an important role in the network dynamics, namely, it creates bistable neural spiking in small cortical circuits. Furthermore, introducing local clustering in large-scale networks leads to the emergence of various patterns of persistent local activity in an ongoing network activity. Thus, our results may bridge a gap between anatomical structure and persistent activity observed during working memory and other cognitive processes.     

Probing Interactions between CLIP-170, EB1, and Microtubules

Cytoplasmic linker protein 170 (CLIP-170) is a microtubule (MT) plus-end tracking protein (+ TIP) that dynamically localizes to the MT plus end and regulates MT dynamics. The mechanisms of these activities remain unclear because the CLIP-170-MT interaction is poorly understood, and even less is known about how CLIP-170 and other + TIPs act together as a network. CLIP-170 binds to the acidic C-terminal tail of α-tubulin. However, the observation that CLIP-170 has two CAP-Gly (cytoskeleton-associated protein glycine-rich) motifs and multiple serine-rich regions suggests that a single CLIP-170 molecule has multiple tubulin binding sites, and that these sites might bind to multiple parts of the tubulin dimer. Using a combination of chemical cross-linking and mass spectrometry, we find that CLIP-170 binds to both α-tubulin and β-tubulin, and that binding is not limited to the acidic C-terminal tails. We provide evidence that these additional binding sites include the H12 helices of both α-tubulin and β-tubulin and are significant for CLIP-170 activity. Previous work has shown that CLIP-170 binds to end-binding protein 1 (EB1) via the EB1 C-terminus, which mimics the acidic C-terminal tail of tubulin. We find that CLIP-170 can utilize its multiple tubulin binding sites to bind to EB1 and MT simultaneously. These observations help to explain how CLIP-170 can nucleate MTs and alter MT dynamics, and they contribute to understanding the significance and properties of the + TIP network.     

Stabilization of Cortical Microtubules in Maize Mesocotyl Cells by Gibberellin A3

Effects of GA₃ on the stability of cortical microtubules (MTs)were studied in mesocotyl cells of etiolated maize seedlings.Propyzamide, an MT-disrupting agent specific for plant tubulin,disrupted cortical MTs in cells in the upper regions of mesocotylsof GA₃-untreated seedlings and caused swelling of the cells.GA₃ prevented propyzamide from disrupting MTs and from causingsuch swelling. Chilling of mesocotyls at 4°C for 60 minbrought about the disruption of cortical MTs in cells in theupper regions of mesocotyls of GA₃-untreated seedlings, butnot in cells in corresponding regions of GA₃-treated seedlings,suggesting that treatment with GA₃ increased the stability ofcortical MTs in maize mesocotyl cells. Cortical MTs in protoplastsisolated from mesocotyls of GA₃-untreated seedlings failed towithstand chilling at 0°C for 90 min, while those in protoplastsisolated from mesocotyls of GA₃-treated seedlings withstoodchilling successfully. It appears that the cell wall is notinvolved in the stabilization of cortical MTs by GA₃ in maizemesocotyl cells. (Received July 6, 1993; Accepted November 29, 1993)     

A Three-Dimensional Computer Simulation Model Reveals the Mechanisms for Self-Organization of Plant Cortical Microtubules into Oblique Arrays

The noncentrosomal cortical microtubules (CMTs) of plant cells self-organize into a parallel three-dimensional (3D) array that is oriented transverse to the cell elongation axis in wild-type plants and is oblique in some of the mutants that show twisted growth. To study the mechanisms of CMT array organization, we developed a 3D computer simulation model based on experimentally observed properties of CMTs. Our computer model accurately mimics transverse array organization and other fundamental properties of CMTs observed in rapidly elongating wild-type cells as well as the defective CMT phenotypes observed in the Arabidopsis mor1-1 and fra2 mutants. We found that CMT interactions, boundary conditions, and the bundling cutoff angle impact the rate and extent of CMT organization, whereas branch-form CMT nucleation did not significantly impact the rate of CMT organization but was necessary to generate polarity during CMT organization. We also found that the dynamic instability parameters from twisted growth mutants were not sufficient to generate oblique CMT arrays. Instead, we found that parameters regulating branch-form CMT nucleation and boundary conditions at the end walls are important for forming oblique CMT arrays. Together, our computer model provides new mechanistic insights into how plant CMTs self-organize into specific 3D arrangements.     

One-Dimensional Brownian Motion of Charged Nanoparticles along Microtubules: A Model System for Weak Binding Interactions

Various proteins are known to exhibit one-dimensional Brownian motion along charged rodlike polymers, such as microtubules (MTs), actin, and DNA. The electrostatic interaction between the proteins and the rodlike polymers appears to be crucial for one-dimensional Brownian motion, although the underlying mechanism has not been fully clarified. We examined the interactions of positively-charged nanoparticles composed of polyacrylamide gels with MTs. These hydrophilic nanoparticles bound to MTs and displayed one-dimensional Brownian motion in a charge-dependent manner, which indicates that nonspecific electrostatic interaction is sufficient for one-dimensional Brownian motion. The diffusion coefficient decreased exponentially with an increasing particle charge (with the exponent being 0.10 k_BT per charge), whereas the duration of the interaction increased exponentially (exponent of 0.22 k_BT per charge). These results can be explained semiquantitatively if one assumes that a particle repeats a cycle of binding to and movement along an MT until it finally dissociates from the MT. During the movement, a particle is still electrostatically constrained in the potential valley surrounding the MT. This entire process can be described by a three-state model analogous to the Michaelis-Menten scheme, in which the two parameters of the equilibrium constant between binding and movement, and the rate of dissociation from the MT, are derived as a function of the particle charge density. This study highlights the possibility that the weak binding interactions between proteins and rodlike polymers, e.g., MTs, are mediated by a similar, nonspecific charge-dependent mechanism.     

Calcium-Sensitivity of Cortical Microtubules in the Green Alga Mougeotia

Membrane ghosts were prepared from protoplasts of the greenalga Mougeotia, and the Ca²⁺-sensitivity of microtubules onthe ghosts was examined. Microtubules on the protoplast ghosts were not depolymerizedby 3 min treatment with 1 mM Ca²⁺. As the treatment was prolonged,some depolymerization of microtubules became evident, but evenafter 10 min about 50% of the ghosts showed no depolymerization.Ca²⁺ introduced into intact protoplasts seemed to be ineffectivein depolymerizing microtubules; abundant microtubules were presenton membrane ghosts prepared from protoplasts which had beentreated with 2x10^–5M Ca²⁺-ionophore A23187 [GenBank] plus 1 mM Ca²⁺for 20 or 30 min. Neither 3 min treatment with 0.2% Triton X-100 nor with 1 mMCa²⁺ solution containing 5 min MgSO₄ and 100 mM KCl caused depolymerisationof microtubules on protoplast ghosts. However, when given successively,these treatments caused complete depolymerization of microtubules. These results suggest that Mougeotia microtubules are stableto Ca²⁺ and that the stability is conferred by a microtubule-associatedfactor which can easily be removed by Triton X-100 treatment. (Received July 19, 1985; Accepted October 25, 1985)     

Interaction between Cytokinesis-Related Callose and Cortical Microtubules in Dividing Cells of the Liverwort Riella helicophylla

Abstract: In juvenile walls of dividing cells of the liverwort Riella helicophylla the nitroso-derivative of photolysed Nifedipine (a calcium antagonist) stimulates the deposition of callose. This enhanced biosynthesis of β-1,3-glucan can only be observed in the cell plate, the juvenile cell walls and the walls of adjacent cells. An immunocytological analysis of this effect revealed that no cortical microtubules occurred at the sites of callose deposition. The cells of the control displayed a normal distribution of cortical microtubules at the plasma membrane as long as no callose was deposited along the corresponding walls. In a second set of experiments, inhibitors of microtubule polymerization and depolymerization (amiprophosmethyl and taxol, respectively) were used. At low concentrations, these substances also caused a significant stimulation of callose deposition in the plane of cell division. Based on these findings, we propose a regulatory model of callose and cellulose biosynthesis that depends on the binding of the cellulose/callose synthase complex to cortical microtubules that may be mediated by unknown binding protein(s).     

A Mechanochemical Model of Flagellar Activity

A theory is presented which quantitatively links the physical properties of a flagellum with parameters which characterize the chemical reactions responsible for deforming the flagellum. Realistic values for the wave parameters are predicted when order-of-magnitude values for the appropriate constants are used. The model may be useful in other fields where mechanochemical coupling occurs.     

Predicting the Growth Interactions between Plants in Mixed Species Stands using a Simple Mechanistic Model

The Conductance model is a simple mechanistic model used topredict the growth of species in monoculture or mixtures fromparameter values derived from plants grown in isolation. Incontrast to many mechanistic models that require extensive parameterization,the Conductance model is able to capture the growth of a broadrange of species using a few simplified assumptions regardingplant growth and easily derived species-specific parameter values.We examine the assumptions within the Conductance model thattotal leaf area per plant is proportional to total plant weight,and that an isolated plant has a projected crown zone area thatis proportional to the 2/3 power of its weight. Power ratherthan linear relations were found between weight and leaf areafor Brassica oleracea, Daucus carota, Matricaria inodora, Solanumnigrum,Stellaria media , Trifolium repens and Veronica persica.For all seven species, the value of the power was less thanunity. All species also exhibited a power relation between crownzone area and weight, with the slope of this relation beingless than 2/3 for B. oleracea, D. carota and S. media. Althoughmorphology type accounted for some of the variation in the parametervalues relating to light interception, there were considerabledifferences between species within upright or prostrate foliagespecies groups. The Conductance model was used to predict yieldsof B. oleracea, S. nigrum and V. persica grown in both monocultureand binary weed-crop mixtures over a range of temporal and spatialscales. After calibrating the model to non-competing plants,the model was used to predict growth of the weed and crop speciesin contrasting densities and stand types. In some crop-weedcombinations, predicted crop and weed weights were within 17%of observed values, with no systematic deviations. In others,systematic and large deviations occurred.Copyright 2001 Annalsof Botany Company Brassica oleracea L., Daucus carota L., Matricaria inodora L., Solanum nigrum L.,Stellaria media L., Trifolium repens L., Veronica persica L., competition, growth, leaf area, crown zone area, light, shoot morphology, canopy architecture     

Hormone-Virus Interactions in Plants

Symptoms of virus infection may be simplistically ascribed to a change in quantity of a particular plant hormone, and frequently virus-induced symptoms can be mimicked by application or removal of a plant hormone. In this review, we look critically at the information available concerning changes in the biosynthesis and metabolism of plant hormones following virus infection. In addition, we briefly review the effects of virus infection on endogenous jasmonates and salicylic acid. We also briefly assess the involvement of the classical plant hormones, jasmonic acid and salicylic acid in the induction of defense-related genes.     

Motor-Substrate Interactions in Mycoplasma Motility Explains Non-Arrhenius Temperature Dependence

Mycoplasmas exhibit a novel, substrate-dependent gliding motility that is driven by ∼400 “leg” proteins. The legs interact with the substrate and transmit the forces generated by an assembly of ATPase motors. The velocity of the cell increases linearly by nearly 10-fold over a narrow temperature range of 10-40°C. This corresponds to an Arrhenius factor that decreases from ∼45 k_BT at 10°C to ∼10 k_BT at 40°C. On the other hand, load-velocity curves at different temperatures extrapolate to nearly the same stall force, suggesting a temperature-insensitive force-generation mechanism near stall. In this article, we propose a leg-substrate interaction mechanism that explains the intriguing temperature sensitivity of this motility. The large Arrhenius factor at low temperature comes about from the addition of many smaller energy barriers arising from many substrate-binding sites at the distal end of the leg protein. The Arrhenius dependence attenuates at high temperature due to two factors: 1), the reduced effective multiplicity of energy barriers intrinsic to the multiple-site binding mechanism; and 2), the temperature-sensitive weakly facilitated leg release that curtails the power stroke. The model suggests an explanation for the similar steep, sub-Arrhenius temperature-velocity curves observed in many molecular motors, such as kinesin and myosin, wherein the temperature behavior is dominated not by the catalytic biochemistry, but by the motor-substrate interaction.     

Effect of Ions on the Orientation of Cortical Microtubules in Spirogyra Cells

Effects of ions on the orientation of cortical micro-lubules(MTs) in Spirogyra cells were studied. After depo-lymerizalionwith amiprophos-methyl (APM), MTs were allowed to reorganizein NaCI solutions of various concentrations. As the concentrationof NaCI increased, the frequency of cells that had oblique MTsincreased. When cells in NaCI solution were transferred intoartificial pond water (APW) and incubated for 6 h, all the MTschanged to become transverse to the longitudinal axis of thecell. KC1 and MgCl₂ also had effects on the orientation of MTs.However, NH₄Cl, CaCl₂;, CoCl₂, and Co(NO₃)₂ did not show anyeffect. These results suggest that Na⁺, K⁺, and Mg²⁺have effectson MT orientation and that NH⁺₄, Ca²⁺, Co²⁺, Cl^–, andNO^–₃ have little effect. When MTs were reorganized ineither NaCl or KCl solutions, all the oblique MTs were organizedinto an S-helix. In contrast, some of the oblique MTs were foundas a Z-helix in the cells incubated in MgCl₂ or mannitol solutions.These results suggest that effects of Na⁺ and K⁺ on the orientationof MTs are not the same as those of Mg²⁺ and mannitol. Theseresults provide the first evidence that ions are involved inthe orientation of MTs in algae. (Received January 27, 1998; Accepted August 10, 1998)