A critical assessment of the information processing capabilities of neuronal microtubules using coherent excitations

Evidence for signaling, communication, and conductivity in microtubules (MTs) has been shown through both direct and indirect means, and theoretical models predict their potential use in both classical and quantum information processing in neurons. The notion of quantum information processing within neurons has been implicated in the phenomena of consciousness, although controversies have arisen in regards to adverse physiological temperature effects on these capabilities. To investigate the possibility of quantum processes in relation to information processing in MTs, a biophysical MT model is used based on the electrostatic interior of the tubulin protein. The interior is taken to constitute a double-well potential structure within which a mobile electron is considered capable of occupying at least two distinct quantum states. These excitonic states together with MT lattice vibrations determine the state space of individual tubulin dimers within the MT lattice. Tubulin dimers are taken as quantum well structures containing an electron that can exist in either its ground state or first excited state. Following previous models involving the mechanisms of exciton energy propagation, we estimate the strength of exciton and phonon interactions and their effect on the formation and dynamics of coherent exciton domains within MTs. Also, estimates of energy and timescales for excitons, phonons, their interactions, and thermal effects are presented. Our conclusions cast doubt on the possibility of sufficiently long-lived coherent exciton/phonon structures existing at physiological temperatures in the absence of thermal isolation mechanisms. These results are discussed in comparison with previous models based on quantum effects in non-polar hydrophobic regions, which have yet to be disproved.     

Conduction pathways in microtubules, biological quantum computation, and consciousness.

Technological computation is entering the quantum realm, focusing attention on biomolecular information processing systems such as proteins, as presaged by the work of Michael Conrad. Protein conformational dynamics and pharmacological evidence suggest that protein conformational states-fundamental information units ('bits') in biological systems-are governed by quantum events, and are thus perhaps akin to quantum bits ('qubits') as utilized in quantum computation. 'Real time' dynamic activities within cells are regulated by the cell cytoskeleton, particularly microtubules (MTs) which are cylindrical lattice polymers of the protein tubulin. Recent evidence shows signaling, communication and conductivity in MTs, and theoretical models have predicted both classical and quantum information processing in MTs. In this paper we show conduction pathways for electron mobility and possible quantum tunneling and superconductivity among aromatic amino acids in tubulins. The pathways within tubulin match helical patterns in the microtubule lattice structure, which lend themselves to topological quantum effects resistant to decoherence. The Penrose-Hameroff 'Orch OR' model of consciousness is reviewed as an example of the possible utility of quantum computation in MTs.     

A biopolymer transistor: electrical amplification by microtubules

Microtubules (MTs) are important cytoskeletal structures engaged in a number of specific cellular activities, including vesicular traffic, cell cyto-architecture and motility, cell division, and information processing within neuronal processes. MTs have also been implicated in higher neuronal functions, including memory and the emergence of "consciousness". How MTs handle and process electrical information, however, is heretofore unknown. Here we show new electrodynamic properties of MTs. Isolated, taxol-stabilized MTs behave as biomolecular transistors capable of amplifying electrical information. Electrical amplification by MTs can lead to the enhancement of dynamic information, and processivity in neurons can be conceptualized as an "ionic-based" transistor, which may affect, among other known functions, neuronal computational capabilities.     

A nonlinear model of ionic wave propagation along microtubules

Microtubules (MTs) are important cytoskeletal polymers engaged in a number of specific cellular activities including the traffic of organelles using motor proteins, cellular architecture and motility, cell division and a possible participation in information processing within neuronal functioning. How MTs operate and process electrical information is still largely unknown. In this paper we investigate the conditions enabling MTs to act as electrical transmission lines for ion flows along their lengths. We introduce a model in which each tubulin dimer is viewed as an electric element with a capacitive, inductive and resistive characteristics arising due to polyelectrolyte nature of MTs. Based on Kirchhoff’s laws taken in the continuum limit, a nonlinear partial differential equation is derived and analyzed. We demonstrate that it can be used to describe the electrostatic potential coupled to the propagating localized ionic waves. An erratum to this article can be found at     

Microtubular Protofilament Analysis Based on Molecular Level Tubulin Interaction

Nonlinear microstructure of the microtubules (MTs) plays an important role in their mechanical properties. Despite the extensive efforts into the development of continuum models for microtubules, a mesoscale finite element model that can link the molecular level information to the overall performance of microtubules is still missing. The aim of this study is to develop a molecular dynamics model (MDM), finite element model (FEM) and structural mechanics beam model (SMBM) for tubulins of protofilament (PF). In MDM, the backbone atoms of α-tubulin were fixed while the backbone atoms of β-tubulin were attached to a molecular dynamics (MD) atom through a virtual spring. In FEM, both α and β tubulins are modeled as spherical shells and adjacent tubulins are connected by linear springs. The spherical shells were framed as beams in SMBM. Corresponding parameters such as the elasticity of tubulin-tubulin interaction (TTI) and the stiffness of springs and beam are derived from MD simulation. Marginal differences in the force-deflection curve among the FEM, the MDM and SMBM indicate the good accuracy in describing the mechanical properties of microtubules. Simulation results show that the protofilament behaves non-linearly under tension and torsion but linearly under bending. Deformation pattern of a PF from the SMBM frame bending can be well captured by the classical Euler-Bernouli beam theory and the flexural rigidity derived from FEM is in good agreement with SMBM. These findings lend compelling credence in our developed models of PF to deepen our understanding of the underlying mechanism of statics and dynamics of MTs. In perspective our approach provides a tool for the analysis of MTs mechanical behavior under different conditions.     

Analysis of microtubule arms and bridges in mitotic and interphase amebae of Dictyostelium discoideum

We have analyzed transparencies of electron micrographs from ultrathin longitudinal sections through mitotic spindles of undifferentiated amebae of Dictyostelium discoideum for the presence of arms on microtubules (MTs) and bridges between them. We used the technique of microdensitometer scanning and computer-based model matching by cross-correlation and autocorrelation. We also determined that spindle MTs are composed of 13 protofilaments. Although regularly arranged lateral appendages are not a universal feature of MTs in these cells, both cross-correlation and autocorrelation analysis revealed that bridges between a kinetochore MT and its neighbor, and between MTs in the zone of overlap of the central spindle were significantly arranged on a 12-dimer superlattice. In addition, the autocorrelation analysis indicated a slight match with the 12-dimer model for neighboring non-kinetochore MTs. Although electron micrographs revealed putative arms on cytoplasmic and astral MTs, as well as bridges between central spindle MTs outside the zone of overlap, their arrangement did not match any of the models tested. Bridges between non-kinetochore MTs in the half-spindles possibly serve to reinforce the spindle scaffold. Bridges between kinetochore MTs and their neighbors may contribute to the mechanical stability of kinetochore fibers or they may be involved in poleward movements of the chromosomes. In the zone of overlap of the central spindle, the occurrence of frequent and regularly spaced bridges is consistent with models predicting that a sliding mechanism operates between MTs of opposite polarity in this region of the spindle to produce its elongation.     

Density and distribution of α-bungarotoxin-binding sites in postsynaptic structures of regenerated rat skeletal muscle

The polarity of kinetochore microtubules (MTs) has been studied in lysed PtK1 cells by polymerizing hook-shaped sheets of neurotubulin onto walls of preexisting cellular MTs in a fashion that reveals their structural polarity. Three different approaches are presented here: (a) we have screened the polarity of all MTs in a given spindle cross section taken from the region between the kinetochores and the poles, (b) we have determined the polarity of kinetochore MTs are more stable to cold-treated spindles; this approach takes advantage of the fact that kinetochore MTs are more stable to cold treatment than other spindle MTs; and (c) we have tracked bundles of kinetochore MTs from the vicinity of the pole to the outer layer of the kinetochore in cold- treated cells. In an anaphase cell, 90-95% of all MTs in an area between the kinetochores and the poles are of uniform polarity with their plus ends (i.e., fast growing ends) distal to the pole. In cold- treated cells, all bundles of kinetochore MTs show the same polarity; the plus ends of the MTs are located at the kinetochores. We therefore conclude that kinetochore MTs in both metaphase and anaphase cells have the same polarity as the aster MTs in each half-spindle. These results can be interpreted in two ways: (a) virtually all MTs are initiated at the spindle poles and some of the are "captured" by matured kinetochores using an as yet unknown mechanism to bind the plus ends of existing MTs; (b) the growth of kinetochore MTs is initiated at the kinetochore in such a way that the fast growing MT end is proximal to the kinetochore. Our data are inconsistent with previous kinetochore MT polarity determinations based on growth rate measurements in vitro. These studies used drug-treated cells from which chromosomes were isolated to serve as seeds for initiation of neurotubule polymerization. It is possible that under these conditions kinetochores will initiate MTs with a polarity opposite to the one described here.     

Compartment volume influences microtubule dynamic instability: a model study

Microtubules (MTs) are cytoskeletal polymers that exhibit dynamic instability, the random alternation between growth and shrinkage. MT dynamic instability plays an essential role in cell development, division, and motility. To investigate dynamic instability, simulation models have been widely used. However, conditions under which the concentration of free tubulin fluctuates as a result of growing or shrinking MTs have not been studied before. Such conditions can arise, for example, in small compartments, such as neuronal growth cones. Here we investigate by means of computational modeling how concentration fluctuations caused by growing and shrinking MTs affect dynamic instability. We show that these fluctuations shorten MT growth and shrinkage times and change their distributions from exponential to non-exponential, gamma-like. Gamma-like distributions of MT growth and shrinkage times, which allow optimal stochastic searching by MTs, have been observed in various cell types and are believed to require structural changes in the MT during growth or shrinkage. Our results, however, show that these distributions can already arise as a result of fluctuations in the concentration of free tubulin due to growing and shrinking MTs. Such fluctuations are possible not only in small compartments but also when tubulin diffusion is slow or when many MTs (de)polymerize synchronously. Volume and all other factors that influence these fluctuations can affect MT dynamic instability and, consequently, the processes that depend on it, such as neuronal growth cone behavior and cell motility in general.     

Filopodia and actin arcs guide the assembly and transport of two populations of microtubules with unique dynamic parameters in neuronal growth cones

We have used multimode fluorescent speckle microscopy (FSM) and correlative differential interference contrast imaging to investigate the actin-microtubule (MT) interactions and polymer dynamics known to play a fundamental role in growth cone guidance. We report that MTs explore the peripheral domain (P-domain), exhibiting classical properties of dynamic instability. MT extension occurs preferentially along filopodia, which function as MT polymerization guides. Filopodial bundles undergo retrograde flow and also transport MTs. Thus, distal MT position is determined by the rate of plus-end MT assembly minus the rate of retrograde F-actin flow. Short MT displacements independent of flow are sometimes observed. MTs loop, buckle, and break as they are transported into the T-zone by retrograde flow. MT breakage results in exposure of new plus ends which can regrow, and minus ends which rapidly undergo catastrophes, resulting in efficient MT turnover. We also report a previously undetected presence of F-actin arc structures, which exhibit persistent retrograde movement across the T-zone into the central domain (C-domain) at approximately 1/4 the rate of P-domain flow. Actin arcs interact with MTs and transport them into the C-domain. Interestingly, although the MTs associated with arcs are less dynamic than P-domain MTs, they elongate efficiently as a result of markedly lower catastrophe frequencies.     

Re-formation of microtubules in Closterium ehrenbergii Meneghini after cold-induced depolymerization

Immunofluorescence microscopy was used to examine the re-formation of microtubules (MT), after cold-induced depolymerization, in Closterium ehrenbergii. The C. ehrenbergii cells undergo cell division followed by semicell expansion in the dark period of daily light-dark cycles. Five types of MTs, namely the MT ring, hair-like MTs around the nuclei, spindle MTs, radially arranged MTs and transverse wall MTs, appeared and disappeared sequentially during and following cell division. The wall MTs were distributed transversely only in the expanding new semicells. When cells were chilled in ice water, wall MTs in expanding cells were fragmented, and then disappeared as did the other types of MTs, within 5 min. When cells were warmed at 20°C after 2 h chilling, wall MTs and the other types of MTs re-formed. At the early stage of wall-MT re-formation in expanding cells, small, star-like MTs were formed, and then randomly oriented MTs developed in both the expanding new and the old semicells. The MT ring was also re-formed at the boundary between the new and old semicells. There were no obvious MT-organizing centers in the random arrangement. As time passed, the randomly oriented wall MTs in the old semicells disappeared and those in the expanding new semicells gradually assumed a transverse orientation. These results indicate that wall MTs can be rearranged transversely after they have been re-formed and that nucleation of wall MTs is separable from the mechanism for ordering them.Abbreviations MT(s) microtubule(s) - MTOC(s) microtubule-organizing center(s)     

Red and green algal origin of diatom membrane transporters: insights into environmental adaptation and cell evolution

Membrane transporters (MTs) facilitate the movement of molecules between cellular compartments. The evolutionary history of these key components of eukaryote genomes remains unclear. Many photosynthetic microbial eukaryotes (e.g., diatoms, haptophytes, and dinoflagellates) appear to have undergone serial endosymbiosis and thereby recruited foreign genes through endosymbiotic/horizontal gene transfer (E/HGT). Here we used the diatoms Thalassiosira pseudonana and Phaeodactylum tricornutum as models to examine the evolutionary origin of MTs in this important group of marine primary producers. Using phylogenomics, we used 1,014 diatom MTs as query against a broadly sampled protein sequence database that includes novel genome data from the mesophilic red algae Porphyridium cruentum and Calliarthron tuberculosum, and the stramenopile Ectocarpus siliculosus. Our conservative approach resulted in 879 maximum likelihood trees of which 399 genes show a non-lineal history between diatoms and other eukaryotes and prokaryotes (at the bootstrap value ≥70%). Of the eukaryote-derived MTs, 172 (ca. 25% of 697 examined phylogenies) have members of both red/green algae as sister groups, with 103 putatively arising from green algae, 19 from red algae, and 50 have an unresolved affiliation to red and/or green algae. We used topology tests to analyze the most convincing cases of non-lineal gene history in which red and/or green algae were nested within stramenopiles. This analysis showed that ca. 6% of all trees (our most conservative estimate) support an algal origin of MTs in stramenopiles with the majority derived from green algae. Our findings demonstrate the complex evolutionary history of photosynthetic eukaryotes and indicate a reticulate origin of MT genes in diatoms. We postulate that the algal-derived MTs acquired via E/HGT provided diatoms and other related microbial eukaryotes the ability to persist under conditions of fluctuating ocean chemistry, likely contributing to their great success in marine environments.     

Structural evidence for cooperative microtubule stabilization by Taxol and the endogenous dynamics regulator MAP4

Microtubules (MTs) composed of αβ-tubulin heterodimers are highly dynamic polymers, whose stability can be regulated by numerous endogenous and exogenous factors. Both the antimitotic drug Taxol and microtubule-associated proteins (MAPs) stabilize this dynamicity by binding to and altering the conformation of MTs. In the current study, amide hydrogen/deuterium exchange coupled with mass spectrometry (HDX-MS) was used to examine the structural and dynamic properties of the MT complex with the microtubule binding domain of MAP4 (MTB-MAP4) in the presence and absence of Taxol. The changes in the HDX levels indicate that MTB-MAP4 may bind to both the outside and the luminal surfaces of the MTs and that Taxol reduces both of these interactions. The MTB-MAP4 binding induces conformational rearrangements of α- and β-tubulin that promote an overall stabilization of MTs. Paradoxically, despite Taxol's negative effects on MAP4 interactions with the MTs, its binding to the MTB-MAP4-MT complex further reduces the overall deuterium incorporation, suggesting that a more stable complex is formed in the presence of the drug.     

Enhanced stability of microtubules enriched in detyrosinated tubulin is not a direct function of detyrosination level

Interphase cultured monkey kidney (TC-7) cells contain distinct subsets of cellular microtubules (MTs) enriched in posttranslationally detyrosinated (Glu) or tyrosinated (Tyr) alpha tubulin (Gundersen, G. G., M. H. Kalnoski, and J. C. Bulinski. 1984. Cell. 38:779-789). To determine the relative stability of these subsets of MTs, we subjected TC-7 cells to treatments that slowly depolymerized MTs. We found Glu MTs to be more resistant than Tyr MTs to depolymerization by nocodazole in living cells, and to depolymerization by dilution in detergent-permeabilized cell models. However, in cold-treated cells, Glu and Tyr MTs did not differ significantly in their stability. Digestion of permeabilized cell models with pancreatic carboxypeptidase A, to generate Glu MTs from endogenous Tyr MTs, did not significantly alter the resistance of the endogenous Tyr MTs toward dilution-induced depolymerization. Furthermore, in human fibroblasts that contained no distinct Glu MTs, we observed a population of nocodazole-resistant MTs. These data suggest that Glu MTs possess enhanced stability against end-mediated depolymerization, yet detyrosination alone appears to be insufficient to confer this enhanced stability.     

Establishment of a stable, acetylated microtubule bundle during neuronal commitment

Two posttranslational modifications of alpha-tubulin, acetylation and detyrosination, are associated with stable microtubule (MT) populations, including those of neuronal processes. We have used a pluripotent embryonal carcinoma cell line, P19, to investigate changes in MT isotype and stability found in MT arrays during neurogenesis. This cell line has an advantage in that both commitment- and differentiation-related events can be observed. Uncommitted P19 cells have minimal arrays of acetylated and detyrosinated MTs. Following neuronal induction with retinoic acid (RA), indirect immunofluorescence microscopy shows that the first MT modifications occur during commitment and before any morphological change is observed. RA-induced cells initially polymerize a temporarily enlarged population of MTs. Included in this population is a new array of acetylated MTs arranged in a bundle of parallel MTs. This bundle is colchicine-stable, although no MT-associated proteins (MAPs) are detectable using a battery of anti-MAP antibodies. Observation of MT arrays with patterns that are intermediate between the early bundles and short neurites suggests that the acetylated MT bundle subsequently extends to form a neurite. MAP 2 is first detected at about the time of neurite extension. However, at this early stage of differentiation, MAP 2 is not yet limited to dendritic processes. This report provides the first evidence that the stable MTs of mature neurons may be initiated during neuronal commitment.     

Axonal transport of mitochondria along microtubules and F-actin in living vertebrate neurons

A large body of evidence indicates that microtubules (MTs) conduct organelle transport in axons, but recent studies on extruded squid axoplasm have suggested that actin microfilaments (MFs) may also play a role in this process. To investigate the separate contributions to transport of each class of cytoskeletal element in intact vertebrate axons, we have monitored mitochondrial movements in chick sympathetic neurons experimentally manipulated to eliminate MTs, MFs, or both. First, we grew neurons in the continuous presence of: (a) cytochalasin E to create neurites which had never contained MFs; or (b) nocodazole or vinblastine to produce neurites which had never contained MTs. Mitochondria moved bidirectionally at normal velocities along the length of neurites which contained MTs and lacked MFs, but did not even enter neurites grown without MTs but containing MFs. In a second approach, we treated established neuronal cultures with cytoskeletal drugs to disrupt either MTs or MFs in axons already containing mitochondria. In cytochalasin-treated cells, which retained MTs but lacked MFs, average mitochondrial velocity increased in both directions, but net directional transport decreased. In vinblastine- treated cells, which lacked MTs but retained essentially normal levels of MFs, mitochondria continued to move bidirectionally but the average mitochondrial velocity and excursion length were reduced for both directions of movement, and the mitochondria spent threefold as much time moving in the retrograde as in the anterograde direction, resulting in net retrograde transport. Treatment of established cultures with both drugs produced neurites lacking MTs and MFs but still rich in neurofilaments; these showed a striking absence of any mitochondrial motility. These data indicate that axonal organelle transport can occur along both MTs and MFs in vivo, but with different velocities and net transport properties.     

Application of logistic regression to case-control association studies involving two causative loci

Models in which two susceptibility loci jointly influence the risk of developing disease can be explored using logistic regression analysis. Comparison of likelihoods of models incorporating different sets of disease model parameters allows inferences to be drawn regarding the nature of the joint effect of the loci. We have simulated case-control samples generated assuming different two-locus models and then analysed them using logistic regression. We show that this method is practicable and that, for the models we have used, it can be expected to allow useful inferences to be drawn from sample sizes consisting of hundreds of subjects. Interactions between loci can be explored, but interactive effects do not exactly correspond with classical definitions of epistasis. We have particularly examined the issue of the extent to which it is helpful to utilise information from a previously identified locus when investigating a second, unknown locus. We show that for some models conditional analysis can have substantially greater power while for others unconditional analysis can be more powerful. Hence we conclude that in general both conditional and unconditional analyses should be performed when searching for additional loci.     

Microtubule Assembly from Single Flared Protofilaments—Forget the Cozy Corner?

A paradigm shift for models of MT assembly is suggested by a recent cryo-electron microscopy study of microtubules (MTs). Previous assembly models have been based on the two-dimensional lattice of the MT wall, where incoming subunits can add with longitudinal and lateral bonds. The new study of McIntosh et al. concludes that the growing ends of MTs separate into flared single protofilaments. This means that incoming subunits must add onto the end of single protofilaments, forming only a longitudinal bond. How can growth of single-stranded protofilaments exhibit cooperative assembly with a critical concentration? An answer is suggested by FtsZ, the bacterial tubulin homolog, which assembles into single-stranded protofilaments. Cooperative assembly of FtsZ is thought to be based on conformational changes that switch the longitudinal bond from low to high affinity when the subunit is incorporated in a protofilament. This novel mechanism may also apply to tubulin assembly and could be the primary mechanism for assembly onto single flared protofilaments.     

Mechanical Properties of a Complete Microtubule Revealed through Molecular Dynamics Simulation

Microtubules (MTs) are the largest type of cellular filament, essential in processes ranging from mitosis and meiosis to flagellar motility. Many of the processes depend critically on the mechanical properties of the MT, but the elastic moduli, notably the Young's modulus, are not directly revealed in experiment, which instead measures either flexural rigidity or response to radial deformation. Molecular dynamics (MD) is a method that allows the mechanical properties of single biomolecules to be investigated through computation. Typically, MD requires an atomic resolution structure of the molecule, which is unavailable for many systems, including MTs. By combining structural information from cryo-electron microscopy and electron crystallography, we have constructed an all-atom model of a complete MT and used MD to determine its mechanical properties. The simulations revealed nonlinear axial stress-strain behavior featuring a pronounced softening under extension, a possible plastic deformation transition under radial compression, and a distinct asymmetry in response to the two senses of twist. This work demonstrates the possibility of combining different levels of structural information to produce all-atom models suitable for quantitative MD simulations, which extends the range of systems amenable to the MD method and should enable exciting advances in our microscopic knowledge of biology.     

The structure of the cold-stable kinetochore fiber in metaphase PtK1 cells

When metaphase PtK₁ cells are cooled to 6–8 ° C for 4–6 h the free, polar, and astral spindle microtubules (MTs) disassemble while the MTs of each kinetochore fiber cluster together and persist as bundles of cold-stable MTs. These cold-stable kinetochore fibers are similar to untreated kinetochore fibers in both their length (i.e., 5–6 m) and in the number of kinetochore-associated MTs (i.e., 20–45) of which they are comprised. Quantitative information concerning the lengths of MTs within these fibers was obtained by tracking individual MTs between serial transverse sections. Approximately 1/2 of the kinetochore MTs in each fiber were found to run uninterrupted into the polar region of the spindle. It can be inferred from this and other data that a substantial number of MTs run uninterrupted between the kinetochore and the polar region in untreated metaphase PtK₁ cells.     

Mechanism for Anaphase B: Evaluation of “Slide-and-Cluster” versus “Slide-and-Flux-or-Elongate” Models

Elongation of the mitotic spindle during anaphase B contributes to chromosome segregation in many cells. Here, we quantitatively test the ability of two models for spindle length control to describe the dynamics of anaphase B spindle elongation using experimental data from Drosophila embryos. In the slide-and-flux-or-elongate (SAFE) model, kinesin-5 motors persistently slide apart antiparallel interpolar microtubules (ipMTs). During pre-anaphase B, this outward sliding of ipMTs is balanced by depolymerization of their minus ends at the poles, producing poleward flux, while the spindle maintains a constant length. Following cyclin B degradation, ipMT depolymerization ceases so the sliding ipMTs can push the poles apart. The competing slide-and-cluster (SAC) model proposes that MTs nucleated at the equator are slid outward by the cooperative actions of the bipolar kinesin-5 and a minus-end-directed motor, which then pulls the sliding MTs inward and clusters them at the poles. In assessing both models, we assume that kinesin-5 preferentially cross-links and slides apart antiparallel MTs while the MT plus ends exhibit dynamic instability. However, in the SAC model, minus-end-directed motors bind the minus ends of MTs as cargo and transport them poleward along adjacent, parallel MT tracks, whereas in the SAFE model, all MT minus ends that reach the pole are depolymerized by kinesin-13. Remarkably, the results show that within a narrow range of MT dynamic instability parameters, both models can reproduce the steady-state length and dynamics of pre-anaphase B spindles and the rate of anaphase B spindle elongation. However, only the SAFE model reproduces the change in MT dynamics observed experimentally at anaphase B onset. Thus, although both models explain many features of anaphase B in this system, our quantitative evaluation of experimental data regarding several different aspects of spindle dynamics suggests that the SAFE model provides a better fit.