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.

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.

Kinetochore life histories reveal an Aurora-B-dependent error correction mechanism in anaphase.

Chromosome mis-segregation during mitosis leads to aneuploidy, which is a hallmark of cancer and linked to cancer genome evolution. Errors can manifest as "lagging chromosomes" in anaphase, although their mechanistic origins and likelihood of correction are incompletely understood. Here, we combine lattice light-sheet microscopy, endogenous protein labeling, and computational analysis to define the life history of >104 kinetochores. By defining the "laziness" of kinetochores in anaphase, we reveal that chromosomes are at a considerable risk of mis-segregation. We show that the majority of lazy kinetochores are corrected rapidly in anaphase by Aurora B; if uncorrected, they result in a higher rate of micronuclei formation. Quantitative analyses of the kinetochore life histories reveal a dynamic signature of metaphase kinetochore oscillations that forecasts their anaphase fate. We propose that in diploid human cells chromosome segregation is fundamentally error prone, with an additional layer of anaphase error correction required for stable karyotype propagation.

Subcellular Euclidean distance measurements with multicolor fluorescence localization imaging in cultured cells.

This protocol measures the 3D Euclidean distance (Δ3D) between two/three fluorescently labeled kinetochore components in fixed samples using Kinetochore Delta software (KiDv1.0.1, MATLAB based). Overestimation of mean Δ3D is corrected through a Bayesian algorithm, with ΔEC distances reflecting the ensemble average positions of fluorophores within a kinetochore population. This package also enables kinetochore categorization, which can be used to sub-sample kinetochores and measure ΔEC. Together, this allows the dynamic architecture of human kinetochores to be investigated (tested in hTERT-RPE1 cells). For complete details on the use and execution of this protocol, please refer to Roscioli et al. (2020).

An automatic adaptive method to combine summary statistics in approximate Bayesian computation.

To infer the parameters of mechanistic models with intractable likelihoods, techniques such as approximate Bayesian computation (ABC) are increasingly being adopted. One of the main disadvantages of ABC in practical situations, however, is that parameter inference must generally rely on summary statistics of the data. This is particularly the case for problems involving high-dimensional data, such as biological imaging experiments. However, some summary statistics contain more information about parameters of interest than others, and it is not always clear how to weight their contributions within the ABC framework. We address this problem by developing an automatic, adaptive algorithm that chooses weights for each summary statistic. Our algorithm aims to maximize the distance between the prior and the approximate posterior by automatically adapting the weights within the ABC distance function. Computationally, we use a nearest neighbour estimator of the distance between distributions. We justify the algorithm theoretically based on properties of the nearest neighbour distance estimator. To demonstrate the effectiveness of our algorithm, we apply it to a variety of test problems, including several stochastic models of biochemical reaction networks, and a spatial model of diffusion, and compare our results with existing algorithms.

Testing Models of mRNA Localization Reveals Robustness Regulated by Reducing Transport between Cells.

Robust control of gene expression in both space and time is of central importance in the regulation of cellular processes and for multicellular development. However, the mechanisms by which robustness is achieved are generally not identified or well understood. For example, messenger RNA (mRNA) localization by molecular motor-driven transport is crucial for cell polarization in numerous contexts, but the regulatory mechanisms that enable this process to take place in the face of noise or significant perturbations are not fully understood. Here, we use a combined experimental-theoretical approach to characterize the robustness of gurken/transforming growth factor-α mRNA localization in Drosophila egg chambers, where the oocyte and 15 surrounding nurse cells are connected in a stereotypic network via intracellular bridges known as ring canals. We construct a mathematical model that encodes simplified descriptions of the range of steps involved in mRNA localization, including production and transport between and within cells until the final destination in the oocyte. Using Bayesian inference, we calibrate this model using quantitative single molecule fluorescence in situ hybridization data. By analyzing both the steady state and dynamic behaviors of the model, we provide estimates for the rates of different steps of the localization process as well as the extent of directional bias in transport through the ring canals. The model predicts that mRNA synthesis and transport must be tightly balanced to maintain robustness, a prediction that we tested experimentally using an overexpression mutant. Surprisingly, the overexpression mutant fails to display the anticipated degree of overaccumulation of mRNA in the oocyte predicted by the model. Through careful model-based analysis of quantitative data from the overexpression mutant, we show evidence of saturation of the transport of mRNA through ring canals. We conclude that this saturation engenders robustness of the localization process in the face of significant variation in the levels of mRNA synthesis.

The impact of temporal sampling resolution on parameter inference for biological transport models.

Imaging data has become an essential tool to explore key biological questions at various scales, for example the motile behaviour of bacteria or the transport of mRNA, and it has the potential to transform our understanding of important transport mechanisms. Often these imaging studies require us to compare biological species or mutants, and to do this we need to quantitatively characterise their behaviour. Mathematical models offer a quantitative description of a system that enables us to perform this comparison, but to relate mechanistic mathematical models to imaging data, we need to estimate their parameters. In this work we study how collecting data at different temporal resolutions impacts our ability to infer parameters of biological transport models by performing exact inference for simple velocity jump process models in a Bayesian framework. The question of how best to choose the frequency with which data is collected is prominent in a host of studies because the majority of imaging technologies place constraints on the frequency with which images can be taken, and the discrete nature of observations can introduce errors into parameter estimates. In this work, we mitigate such errors by formulating the velocity jump process model within a hidden states framework. This allows us to obtain estimates of the reorientation rate and noise amplitude for noisy observations of a simple velocity jump process. We demonstrate the sensitivity of these estimates to temporal variations in the sampling resolution and extent of measurement noise. We use our methodology to provide experimental guidelines for researchers aiming to characterise motile behaviour that can be described by a velocity jump process. In particular, we consider how experimental constraints resulting in a trade-off between temporal sampling resolution and observation noise may affect parameter estimates. Finally, we demonstrate the robustness of our methodology to model misspecification, and then apply our inference framework to a dataset that was generated with the aim of understanding the localization of RNA-protein complexes.

A hybrid algorithm for coupling partial differential equation and compartment-based dynamics.

Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing particle numbers. An alternative description of many of these systems can be derived in the diffusive limit as a deterministic, continuum system of partial differential equations (PDEs). Although the numerical solution of such PDEs is, in general, much more efficient than the full stochastic simulation, the deterministic continuum description is generally not valid when copy numbers are low and stochastic effects dominate. Therefore, to take advantage of the benefits of both of these types of models, each of which may be appropriate in different parts of a spatial domain, we have developed an algorithm that can be used to couple these two types of model together. This hybrid coupling algorithm uses an overlap region between the two modelling regimes. By coupling fluxes at one end of the interface and using a concentration-matching condition at the other end, we ensure that mass is appropriately transferred between PDE- and compartment-based regimes. Our methodology gives notable reductions in simulation time in comparison with using a fully stochastic model, while maintaining the important stochastic features of the system and providing detail in appropriate areas of the domain. We test our hybrid methodology robustly by applying it to several biologically motivated problems including diffusion and morphogen gradient formation. Our analysis shows that the resulting error is small, unbiased and does not grow over time.