Kinetochore tracking in 3D from lattice light-sheet imaging data with KiT.

MOTIVATION: Lattice light-sheet microscopy (LLSM) is revolutionizing cell biology since it enables fast, high-resolution extended imaging in three dimensions combined with a drastic reduction in photo-toxicity and bleaching. However, analysis of such datasets still remains a major challenge. RESULTS: Automated tracking of kinetochores, the protein complex facilitating and controlling microtubule attachment of the chromosomes within the mitotic spindle, provides quantitative assessment of chromosome dynamics in mitosis. Here, we extend existing open-source kinetochore tracking software (KiT) to track (and pair) kinetochores throughout prometaphase to anaphase in LLSM data. One of the key improvements is a regularization term in the objective function to enforce biological information about the number of kinetochores in a human mitotic cell, as well as improved diagnostic tools. This software provides quantitative insights into how kinetochores robustly ensure congression and segregation of chromosomes during mitosis. AVAILABILITY AND IMPLEMENTATION: KiT is free, open-source software implemented in MATLAB and can be downloaded as a package from https://github.com/cmcb-warwick/KiT. The source repository is available at https://bitbucket.org/jarmond/kit (tag v2.4.0) and under continuing development. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Bayesian inference of multi-point macromolecular architecture mixtures at nanometre resolution.

Gaussian spot fitting methods have significantly extended the spatial range where fluorescent microscopy can be used, with recent techniques approaching nanometre (nm) resolutions. However, small inter-fluorophore distances are systematically over-estimated for typical molecular scales. This bias can be corrected computationally, but current algorithms are limited to correcting distances between pairs of fluorophores. Here we present a flexible Bayesian computational approach that infers the distances and angles between multiple fluorophores and has several advantages over these previous methods. Specifically it improves confidence intervals for small lengths, estimates measurement errors of each fluorophore individually and infers the correlations between polygon lengths. The latter is essential for determining the full multi-fluorophore 3D architecture. We further developed the algorithm to infer the mixture composition of a heterogeneous population of multiple polygon states. We use our algorithm to analyse the 3D architecture of the human kinetochore, a macro-molecular complex that is essential for high fidelity chromosome segregation during cell division. Using triple fluorophore image data we unravel the mixture of kinetochore states during human mitosis, inferring the conformation of microtubule attached and unattached kinetochores and their proportions across mitosis. We demonstrate that the attachment conformation correlates with intersister tension and sister alignment to the metaphase plate.

Bayesian inference of origin firing time distributions, origin interference and licencing probabilities from Next Generation Sequencing data.

DNA replication is a stochastic process with replication forks emanating from multiple replication origins. The origins must be licenced in G1, and the replisome activated at licenced origins in order to generate bi-directional replication forks in S-phase. Differential firing times lead to origin interference, where a replication fork from an origin can replicate through and inactivate neighbouring origins (origin obscuring). We developed a Bayesian algorithm to characterize origin firing statistics from Okazaki fragment (OF) sequencing data. Our algorithm infers the distributions of firing times and the licencing probabilities for three consecutive origins. We demonstrate that our algorithm can distinguish partial origin licencing and origin obscuring in OF sequencing data from Saccharomyces cerevisiae and human cell types. We used our method to analyse the decreased origin efficiency under loss of Rat1 activity in S. cerevisiae, demonstrating that both reduced licencing and increased obscuring contribute. Moreover, we show that robust analysis is possible using only local data (across three neighbouring origins), and analysis of the whole chromosome is not required. Our algorithm utilizes an approximate likelihood and a reversible jump sampling technique, a methodology that can be extended to analysis of other mechanistic processes measurable through Next Generation Sequencing data.

Changes in Gene Expression in Space and Time Orchestrate Environmentally Mediated Shaping of Root Architecture.

Shaping of root architecture is a quintessential developmental response that involves the concerted action of many different cell types, is highly dynamic, and underpins root plasticity. To determine to what extent the environmental regulation of lateral root development is a product of cell-type preferential activities, we tracked transcriptomic responses to two different treatments that both change root development in Arabidopsis thaliana at an unprecedented level of temporal detail. We found that individual transcripts are expressed with a very high degree of temporal and spatial specificity, yet biological processes are commonly regulated, in a mechanism we term response nonredundancy. Using causative gene network inference to compare the genes regulated in different cell types and during responses to nitrogen and a biotic interaction, we found that common transcriptional modules often regulate the same gene families but control different individual members of these families, specific to response and cell type. This reinforces that the activity of a gene cannot be defined simply as molecular function; rather, it is a consequence of spatial location, expression timing, and environmental responsiveness.

Computational modelling predicts substantial carbon assimilation gains for C3 plants with a single-celled C4 biochemical pump.

Achieving global food security for the estimated 9 billion people by 2050 is a major scientific challenge. Crop productivity is fundamentally restricted by the rate of fixation of atmospheric carbon. The dedicated enzyme, RubisCO, has a low turnover and poor specificity for CO2. This limitation of C3 photosynthesis (the basic carbon-assimilation pathway present in all plants) is alleviated in some lineages by use of carbon-concentrating-mechanisms, such as the C4 cycle-a biochemical pump that concentrates CO2 near RubisCO increasing assimilation efficacy. Most crops use only C3 photosynthesis, so one promising research strategy to boost their productivity focuses on introducing a C4 cycle. The simplest proposal is to use the cycle to concentrate CO2 inside individual chloroplasts. The photosynthetic efficiency would then depend on the leakage of CO2 out of a chloroplast. We examine this proposal with a 3D spatial model of carbon and oxygen diffusion and C4 photosynthetic biochemistry inside a typical C3-plant mesophyll cell geometry. We find that the cost-efficiency of C4 photosynthesis depends on the gas permeability of the chloroplast envelope, the C4 pathway having higher quantum efficiency than C3 for permeabilities below 300 µm/s. However, at higher permeabilities the C4 pathway still provides a substantial boost to carbon assimilation with only a moderate decrease in efficiency. The gains would be capped by the ability of chloroplasts to harvest light, but even under realistic light regimes a 100% boost to carbon assimilation is possible. This could be achieved in conjunction with lower investment in chloroplasts if their cell surface coverage is also reduced. Incorporation of this C4 cycle into C3 crops could thus promote higher growth rates and better drought resistance in dry, high-sunlight climates.

A Hidden Markov Model for Detecting Confinement in Single-Particle Tracking Trajectories.

State-of-the-art single-particle tracking (SPT) techniques can generate long trajectories with high temporal and spatial resolution. This offers the possibility of mechanistically interpreting particle movements and behavior in membranes. To this end, a number of statistical techniques have been developed that partition SPT trajectories into states with distinct diffusion signatures, allowing a statistical analysis of diffusion state dynamics and switching behavior. Here, we develop a confinement model, within a hidden Markov framework, that switches between phases of free diffusion and confinement in a harmonic potential well. By using a Markov chain Monte Carlo algorithm to fit this model, automated partitioning of individual SPT trajectories into these two phases is achieved, which allows us to analyze confinement events. We demonstrate the utility of this algorithm on a previously published interferometric scattering microscopy data set, in which gold-nanoparticle-tagged ganglioside GM1 lipids were tracked in model membranes. We performed a comprehensive analysis of confinement events, demonstrating that there is heterogeneity in the lifetime, shape, and size of events, with confinement size and shape being highly conserved within trajectories. Our observations suggest that heterogeneity in confinement events is caused by both individual nanoparticle characteristics and the binding-site environment. The individual nanoparticle heterogeneity ultimately limits the ability of interferometric scattering microscopy to resolve molecule dynamics to the order of the tag size; homogeneous tags could potentially allow the resolution to be taken below this limit by deconvolution methods. In a wider context, the presented harmonic potential well confinement model has the potential to detect and characterize a wide variety of biological phenomena, such as hop diffusion, receptor clustering, and lipid rafts.

Probing microtubule polymerisation state at single kinetochores during metaphase chromosome motion.

Kinetochores regulate the dynamics of attached microtubule bundles (kinetochore-fibres, K-fibres) to generate the forces necessary for chromosome movements in mitosis. Current models suggest that poleward-moving kinetochores are attached to depolymerising K-fibres and anti-poleward-moving kinetochores to polymerising K-fibres. How the dynamics of individual microtubules within the K-fibre relate to poleward and anti-poleward movements is poorly understood. To investigate this, we developed a live-cell imaging assay combined with computational image analysis that allows eGFP-tagged EB3 (also known as MAPRE3) to be quantified at thousands of individual metaphase kinetochores as they undergo poleward and anti-poleward motion. Surprisingly, we found that K-fibres are incoherent, containing both polymerising and depolymerising microtubules ­ with a small polymerisation bias for anti-poleward-moving kinetochores. K-fibres also display bursts of EB3 intensity, predominantly on anti-poleward-moving kinetochores, equivalent to more coherent polymerisation, and this was associated with more regular oscillations. The frequency of bursts and the polymerisation bias decreased upon loss of kinesin-13, whereas loss of kinesin-8 elevated polymerisation bias. Thus, kinetochores actively set the balance of microtubule polymerisation dynamics in the K-fibre while remaining largely robust to fluctuations in microtubule polymerisation.

KiT: a MATLAB package for kinetochore tracking.

UNLABELLED: During mitosis, chromosomes are attached to the mitotic spindle via large protein complexes called kinetochores. The motion of kinetochores throughout mitosis is intricate and automated quantitative tracking of their motion has already revealed many surprising facets of their behaviour. Here, we present 'KiT' (Kinetochore Tracking)-an easy-to-use, open-source software package for tracking kinetochores from live-cell fluorescent movies. KiT supports 2D, 3D and multi-colour movies, quantification of fluorescence, integrated deconvolution, parallel execution and multiple algorithms for particle localization. AVAILABILITY AND IMPLEMENTATION: KiT is free, open-source software implemented in MATLAB and runs on all MATLAB supported platforms. KiT can be downloaded as a package from http://www.mechanochemistry.org/mcainsh/software.php The source repository is available at https://bitbucket.org/jarmond/kit and under continuing development. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online. CONTACT: jonathan.armond@warwick.ac.uk.

Size matters for single-cell C4 photosynthesis in Bienertia.

Bienertia cycloptera belongs to a diverse set of plants, recently discovered to perform C4 photosynthesis within individual mesophyll cells. How these plants accomplish high photosynthetic efficiency without adopting Kranz anatomy remains unanswered. By modelling the processes of diffusion, capture, and release of carbon dioxide and oxygen inside a typical Bienertia mesophyll cell geometry, we show that a spatial separation as low as 10 µm between the primary and the secondary carboxylases, can, on its own, provide enough diffusive resistance to sustain a viable C4 pathway at 20 °C, with a CO2 leakage <35%. This critical separation corresponds to a cell diameter of 50 µm, consistent with the observed range where Bienertia's mesophyll cells start to develop their characteristic mature anatomy. Our results are robust to significant alterations in model assumptions and environmental conditions, their applicability extending even to aquatic plants.

Sub-cellular location of FtsH proteases in the cyanobacterium Synechocystis sp. PCC 6803 suggests localised PSII repair zones in the thylakoid membranes.

In cyanobacteria and chloroplasts, exposure to HL damages the photosynthetic apparatus, especially the D1 subunit of Photosystem II. To avoid chronic photoinhibition, a PSII repair cycle operates to replace damaged PSII subunits with newly synthesised versions. To determine the sub-cellular location of this process, we examined the localisation of FtsH metalloproteases, some of which are directly involved in degrading damaged D1. We generated transformants of the cyanobacterium Synechocystis sp. PCC6803 expressing GFP-tagged versions of its four FtsH proteases. The ftsH2-gfp strain was functional for PSII repair under our conditions. Confocal microscopy shows that FtsH1 is mainly in the cytoplasmic membrane, while the remaining FtsH proteins are in patches either in the thylakoid or at the interface between the thylakoid and cytoplasmic membranes. HL exposure which increases the activity of the Photosystem II repair cycle led to no detectable changes in FtsH distribution, with the FtsH2 protease involved in D1 degradation retaining its patchy distribution in the thylakoid membrane. We discuss the possibility that the FtsH2-GFP patches represent Photosystem II 'repair zones' within the thylakoid membranes, and the possible advantages of such functionally specialised membrane zones. Anti-GFP affinity pull-downs provide the first indication of the composition of the putative repair zones.

Regulation of Gene Expression in Shewanella oneidensis MR-1 during Electron Acceptor Limitation and Bacterial Nanowire Formation.

UNLABELLED: In limiting oxygen as an electron acceptor, the dissimilatory metal-reducing bacterium Shewanella oneidensis MR-1 rapidly forms nanowires, extensions of its outer membrane containing the cytochromes MtrC and OmcA needed for extracellular electron transfer. RNA sequencing (RNA-Seq) analysis was employed to determine differential gene expression over time from triplicate chemostat cultures that were limited for oxygen. We identified 465 genes with decreased expression and 677 genes with increased expression. The coordinated increased expression of heme biosynthesis, cytochrome maturation, and transport pathways indicates that S. oneidensis MR-1 increases cytochrome production, including the transcription of genes encoding MtrA, MtrC, and OmcA, and transports these decaheme cytochromes across the cytoplasmic membrane during electron acceptor limitation and nanowire formation. In contrast, the expression of the mtrA and mtrC homologs mtrF and mtrD either remains unaffected or decreases under these conditions. The ompW gene, encoding a small outer membrane porin, has 40-fold higher expression during oxygen limitation, and it is proposed that OmpW plays a role in cation transport to maintain electrical neutrality during electron transfer. The genes encoding the anaerobic respiration regulator cyclic AMP receptor protein (CRP) and the extracytoplasmic function sigma factor RpoE are among the transcription factor genes with increased expression. RpoE might function by signaling the initial response to oxygen limitation. Our results show that RpoE activates transcription from promoters upstream of mtrC and omcA The transcriptome and mutant analyses of S. oneidensis MR-1 nanowire production are consistent with independent regulatory mechanisms for extending the outer membrane into tubular structures and for ensuring the electron transfer function of the nanowires. IMPORTANCE: Shewanella oneidensis MR-1 has the capacity to transfer electrons to its external surface using extensions of the outer membrane called bacterial nanowires. These bacterial nanowires link the cell's respiratory chain to external surfaces, including oxidized metals important in bioremediation, and explain why S. oneidensis can be utilized as a component of microbial fuel cells, a form of renewable energy. In this work, we use differential gene expression analysis to focus on which genes function to produce the nanowires and promote extracellular electron transfer during oxygen limitation. Among the genes that are expressed at high levels are those encoding cytochrome proteins necessary for electron transfer. Shewanella coordinates the increased expression of regulators, metabolic pathways, and transport pathways to ensure that cytochromes efficiently transfer electrons along the nanowires.

Inferring the Forces Controlling Metaphase Kinetochore Oscillations by Reverse Engineering System Dynamics.

Kinetochores are multi-protein complexes that mediate the physical coupling of sister chromatids to spindle microtubule bundles (called kinetochore (K)-fibres) from respective poles. These kinetochore-attached K-fibres generate pushing and pulling forces, which combine with polar ejection forces (PEF) and elastic inter-sister chromatin to govern chromosome movements. Classic experiments in meiotic cells using calibrated micro-needles measured an approximate stall force for a chromosome, but methods that allow the systematic determination of forces acting on a kinetochore in living cells are lacking. Here we report the development of mathematical models that can be fitted (reverse engineered) to high-resolution kinetochore tracking data, thereby estimating the model parameters and allowing us to indirectly compute the (relative) force components (K-fibre, spring force and PEF) acting on individual sister kinetochores in vivo. We applied our methodology to thousands of human kinetochore pair trajectories and report distinct signatures in temporal force profiles during directional switches. We found the K-fibre force to be the dominant force throughout oscillations, and the centromeric spring the smallest although it has the strongest directional switching signature. There is also structure throughout the metaphase plate, with a steeper PEF potential well towards the periphery and a concomitant reduction in plate thickness and oscillation amplitude. This data driven reverse engineering approach is sufficiently flexible to allow fitting of more complex mechanistic models; mathematical models of kinetochore dynamics can therefore be thoroughly tested on experimental data for the first time. Future work will now be able to map out how individual proteins contribute to kinetochore-based force generation and sensing.

Localisation and interactions of the Vipp1 protein in cyanobacteria.

The Vipp1 protein is essential in cyanobacteria and chloroplasts for the maintenance of photosynthetic function and thylakoid membrane architecture. To investigate its mode of action we generated strains of the cyanobacteria Synechocystis sp. PCC6803 and Synechococcus sp. PCC7942 in which Vipp1 was tagged with green fluorescent protein at the C-terminus and expressed from the native chromosomal locus. There was little perturbation of function. Live-cell fluorescence imaging shows dramatic relocalisation of Vipp1 under high light. Under low light, Vipp1 is predominantly dispersed in the cytoplasm with occasional concentrations at the outer periphery of the thylakoid membranes. High light induces Vipp1 coalescence into localised puncta within minutes, with net relocation of Vipp1 to the vicinity of the cytoplasmic membrane and the thylakoid membranes. Pull-downs and mass spectrometry identify an extensive collection of proteins that are directly or indirectly associated with Vipp1 only after high-light exposure. These include not only photosynthetic and stress-related proteins but also RNA-processing, translation and protein assembly factors. This suggests that the Vipp1 puncta could be involved in protein assembly. One possibility is that Vipp1 is involved in the formation of stress-induced localised protein assembly centres, enabling enhanced protein synthesis and delivery to membranes under stress conditions.

Correcting for link loss in causal network inference caused by regulator interference.

MOTIVATION: There are a number of algorithms to infer causal regulatory networks from time series (gene expression) data. Here we analyse the phenomena of regulator interference, where regulators with similar dynamics mutually suppress both the probability of regulating a target and the associated link strength; for instance, interference between two identical strong regulators reduces link probabilities by ∼50%. RESULTS: We construct a robust method to define an interference-corrected causal network based on an analysis of the conditional link probabilities that recovers links lost through interference. On a large real network (Streptomyces coelicolor, phosphate depletion), we demonstrate that significant interference can occur between regulators with a correlation as low as 0.865, losing an estimated 34% of links by interference. However, levels of interference cannot be predicted from the correlation between regulators alone and are data specific. Validating against known networks, we show that high numbers of functional links are lost by regulator interference. Performance against other methods on DREAM4 data is excellent. AVAILABILITY AND IMPLEMENTATION: The method is implemented in R and is publicly available as the NIACS package at http://www2.warwick.ac.uk/fac/sci/systemsbiology/research/software.

Metabolic switches and adaptations deduced from the proteomes of Streptomyces coelicolor wild type and phoP mutant grown in batch culture.

Bacteria in the genus Streptomyces are soil-dwelling oligotrophs and important producers of secondary metabolites. Previously, we showed that global messenger RNA expression was subject to a series of metabolic and regulatory switches during the lifetime of a fermentor batch culture of Streptomyces coelicolor M145. Here we analyze the proteome from eight time points from the same fermentor culture and, because phosphate availability is an important regulator of secondary metabolite production, compare this to the proteome of a similar time course from an S. coelicolor mutant, INB201 (ΔphoP), defective in the control of phosphate utilization. The proteomes provide a detailed view of enzymes involved in central carbon and nitrogen metabolism. Trends in protein expression over the time courses were deduced from a protein abundance index, which also revealed the importance of stress pathway proteins in both cultures. As expected, the ΔphoP mutant was deficient in expression of PhoP-dependent genes, and several putatively compensatory metabolic and regulatory pathways for phosphate scavenging were detected. Notably there is a succession of switches that coordinately induce the production of enzymes for five different secondary metabolite biosynthesis pathways over the course of the batch cultures.

Extracting regulator activity profiles by integration of de novo motifs and expression data: characterizing key regulators of nutrient depletion responses in Streptomyces coelicolor.

Determining transcriptional regulator activities is a major focus of systems biology, providing key insight into regulatory mechanisms and co-regulators. For organisms such as Escherichia coli, transcriptional regulator binding site data can be integrated with expression data to infer transcriptional regulator activities. However, for most organisms there is only sparse data on their transcriptional regulators, while their associated binding motifs are largely unknown. Here, we address the challenge of inferring activities of unknown regulators by generating de novo (binding) motifs and integrating with expression data. We identify a number of key regulators active in the metabolic switch, including PhoP with its associated directed repeat PHO box, candidate motifs for two SARPs, a CRP family regulator, an iron response regulator and that for LexA. Experimental validation for some of our predictions was obtained using gel-shift assays. Our analysis is applicable to any organism for which there is a reasonable amount of complementary expression data and for which motifs (either over represented or evolutionary conserved) can be identified in the genome.

Inferring the time-invariant topology of a nonlinear sparse gene regulatory network using fully Bayesian spline autoregression.

We propose a semiparametric Bayesian model, based on penalized splines, for the recovery of the time-invariant topology of a causal interaction network from longitudinal data. Our motivation is inference of gene regulatory networks from low-resolution microarray time series, where existence of nonlinear interactions is well known. Parenthood relations are mapped by augmenting the model with kinship indicators and providing these with either an overall or gene-wise hierarchical structure. Appropriate specification of the prior is crucial to control the flexibility of the splines, especially under circumstances of scarce data; thus, we provide an informative, proper prior. Substantive improvement in network inference over a linear model is demonstrated using synthetic data drawn from ordinary differential equation models and gene expression from an experimental data set of the Arabidopsis thaliana circadian rhythm.

Boltzmann energy-based image analysis demonstrates that extracellular domain size differences explain protein segregation at immune synapses.

Immune synapses formed by T and NK cells both show segregation of the integrin ICAM1 from other proteins such as CD2 (T cell) or KIR (NK cell). However, the mechanism by which these proteins segregate remains unclear; one key hypothesis is a redistribution based on protein size. Simulations of this mechanism qualitatively reproduce observed segregation patterns, but only in certain parameter regimes. Verifying that these parameter constraints in fact hold has not been possible to date, this requiring a quantitative coupling of theory to experimental data. Here, we address this challenge, developing a new methodology for analysing and quantifying image data and its integration with biophysical models. Specifically we fit a binding kinetics model to 2 colour fluorescence data for cytoskeleton independent synapses (2 and 3D) and test whether the observed inverse correlation between fluorophores conforms to size dependent exclusion, and further, whether patterned states are predicted when model parameters are estimated on individual synapses. All synapses analysed satisfy these conditions demonstrating that the mechanisms of protein redistribution have identifiable signatures in their spatial patterns. We conclude that energy processes implicit in protein size based segregation can drive the patternation observed in individual synapses, at least for the specific examples tested, such that no additional processes need to be invoked. This implies that biophysical processes within the membrane interface have a crucial impact on cell:cell communication and cell signalling, governing protein interactions and protein aggregation.

Transcriptomic studies of phosphate control of primary and secondary metabolism in Streptomyces coelicolor.

Phosphate controls the biosynthesis of many classes of secondary metabolites that belong to different biosynthetic groups, indicating that phosphate control is a general mechanism governing secondary metabolism. We refer in this article to the molecular mechanisms of regulation, mediated by the two-component system PhoR-PhoP, of the primary metabolism and the biosynthesis of antibiotics. The two-component PhoR-PhoP system is conserved in all Streptomyces and related actinobacteria sequenced so far, and involves a third component PhoU that modulates the signal transduction cascade. The PhoP DNA-binding sequence is well characterized in Streptomyces coelicolor. It comprises at least two direct repeat units of 11 nt, the first seven of which are highly conserved. Other less conserved direct repeats located adjacent to the core ones can also be bound by PhoP through cooperative protein-protein interactions. The phoR-phoP operon is self-activated and requires phosphorylated PhoP to mediate the full response. About 50 up-regulated PhoP-dependent genes have been identified by comparative transcriptomic studies between the parental S. coelicolor M145 and the ΔphoP mutant strains. The PhoP regulation of several of these genes has been studied in detail using EMSA and DNase I footprinting studies as well as in vivo expression studies with reporter genes and RT-PCR transcriptomic analyses.

Evidence for a HURP/EB free mixed-nucleotide zone in kinetochore-microtubules.

Current models infer that the microtubule-based mitotic spindle is built from GDP-tubulin with small GTP caps at microtubule plus-ends, including those that attach to kinetochores, forming the kinetochore-fibres. Here we reveal that kinetochore-fibres additionally contain a dynamic mixed-nucleotide zone that reaches several microns in length. This zone becomes visible in cells expressing fluorescently labelled end-binding proteins, a known marker for GTP-tubulin, and endogenously-labelled HURP - a protein which we show to preferentially bind the GDP microtubule lattice in vitro and in vivo. We find that in mitotic cells HURP accumulates on the kinetochore-proximal region of depolymerising kinetochore-fibres, whilst avoiding recruitment to nascent polymerising K-fibres, giving rise to a growing "HURP-gap". The absence of end-binding proteins in the HURP-gaps leads us to postulate that they reflect a mixed-nucleotide zone. We generate a minimal quantitative model based on the preferential binding of HURP to GDP-tubulin to show that such a mixed-nucleotide zone is sufficient to recapitulate the observed in vivo dynamics of HURP-gaps.