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Kinesin-1 is a nanoscale molecular motor that walks towards the fast-growing (plus) ends of microtubules, hauling molecular cargo to specific reaction sites in cells. Kinesin-driven transport is central to the self-organization of eukaryotic cells and shows great promise as a tool for nano-engineering1. Recent work hints that kinesin may also play a role in modulating the stability of its microtubule track, both in vitro2,3 and in vivo4, but the results are conflicting5–7 and the mechanisms are unclear. Here, we report a new dimension to the kinesin–microtubule interaction, whereby strong-binding state (adenosine triphosphate (ATP)-bound and apo) kinesin-1 motor domains inhibit the shrinkage of guanosine diphosphate (GDP) microtubules by up to two orders of magnitude and expand their lattice spacing by ~1.6%. Our data reveal an unexpected mechanism by which the mechanochemical cycles of kinesin and tubulin interlock, and so allow motile kinesins to influence the structure, stability and mechanics of their microtubule track.

Mitosis is a complex self-organising process that achieves high fidelity separation of duplicated chromosomes into two daughter cells through capture and alignment of chromosomes to the spindle mid-plane. Chromosome movements are driven by kinetochores (KTs), multi-protein machines that attach chromosomes to microtubules (MTs), and through those attachments both control and generate directional forces. Using lattice light sheet microscopy imaging and automated near-complete tracking of kinetochores at fine spatio-temporal resolution, we produce a detailed atlas of kinetochore metaphase-anaphase dynamics in untransformed human cells (RPE1). Such data allows dynamic models to be reverse engineered and biological hypotheses to be addressed. We determined the support from this dataset for 17 models of metaphase dynamics using Bayesian inference, demonstrating (1) substantial sister asymmetry that generates transverse organisation of the metaphase plate (MPP), (2) substantial spatial organisation of KT dynamic properties within the MPP, and (3) significant time dependence of the K-fiber mechanical parameters whereby K-fiber forces tune over the last 5 mins of metaphase towards a set point, referred to as the anaphase ready state. These spatio-temporal trends are robust to perturbation of the spindle assembly pathway (nocodazole washout treatment), suggesting that the underlying processes generating kinetochore heterogeneity are intrinsic to mitosis and possibly play a role in ensuring high-fidelity segregation.

A new payoff function is proposed for cancer treatment optimisation, the tumour elimination payoff (TEP), that incorporates the increase in lifespan if tumour elimination is achieved. The TEP is discounted by drug toxicity and by potential risks, such as metastasis and mutation. An approximation is used for the probability of tumour elimination, e−αN(T) $e^{-\\alpha N(T)}$ , giving a terminal payoff with an exponential dependence on the final tumour size N(T) $N(T)$ . The optimal solutions for this payoff for simple tumour growth models, (logistic and Gompertz growth), are determined. Using Pontryagin's maximum principle it is proved that bang–bang optimal solutions exist with a single switch; specifically delayed treatment and treat‐and‐stop solutions at maximum tolerated dose (MTD) exist. There is also a singular arc with constant tumour size. Solutions either have a high probability, respectively, low probability of tumour elimination; these correspond to a post‐treatment high probability of cure, and a high probability of relapse, respectively. Optimising over the time horizon T $T$results in solutions that are either MTD throughout or no treatment, that is, treatment is either beneficial or detrimental. For the logistic growth model, the treatment benefit phase diagram is derived with respect to the patient's expected increase in lifespan and tumour size. Optimal therapies are derived that maximise the tumour elimination payoff (TEP), a payoff motivated from branching processes that balances the expected lifespan under therapy against drug toxicity. The TEP provides a post‐treatment outcome probability for cure and relapse.

We develop a Bayesian analysis framework to detect heterogeneity in the diffusive behaviour of single particle trajectories on cells, implementing model selection to classify trajectories as either consistent with Brownian motion or with a two-state (diffusion coefficient) switching model. The incorporation of localisation accuracy is essential, as otherwise false detection of switching within a trajectory was observed and diffusion coefficient estimates were inflated. Since our analysis is on a single trajectory basis, we are able to examine heterogeneity between trajectories in a quantitative manner. Applying our method to the lymphocyte function-associated antigen 1 (LFA-1) receptor tagged with latex beads (4 s trajectories at 1000 frames s(-1)), both intra- and inter-trajectory heterogeneity were detected; 12-26% of trajectories display clear switching between diffusive states dependent on condition, whilst the inter-trajectory variability is highly structured with the diffusion coefficients being related by D1 = 0.68D0 - 1.5 × 10(4) nm2 s(-1), suggestive that on these time scales we are detecting switching due to a single process. Further, the inter-trajectory variability of the diffusion coefficient estimates (1.6 × 10(2) - 2.6 × 10(5) nm2 s(-1)) is very much larger than the measurement uncertainty within trajectories, suggesting that LFA-1 aggregation and cytoskeletal interactions are significantly affecting mobility, whilst the timescales of these processes are distinctly different giving rise to inter- and intra-trajectory variability. There is also an 'immobile' state (defined as D < 3.0 × 103 nm2 s-1) that is rarely involved in switching, immobility occurring with the highest frequency (47%) under T cell activation (phorbol-12-myristate-13-acetate (PMA) treatment) with enhanced cytoskeletal attachment (calpain inhibition). Such 'immobile' states frequently display slow linear drift, potentially reflecting binding to a dynamic actin cortex. Our methods allow significantly more information to be extracted from individual trajectories (ultimately limited by time resolution and time-series length), and allow statistical comparisons between trajectories thereby quantifying inter-trajectory heterogeneity. Such methods will be highly informative for the construction and fitting of molecule mobility models within membranes incorporating aggregation, binding to the cytoskeleton, or traversing membrane microdomains.

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.

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. Microtubules are built from GDP-tubulin lattices with small GTP caps at their plus-ends. Here, the authors reveal that microtubules that attach to kinetochores in mitosis contain, in addition to the GTP-cap and the GDP-lattices, a dynamic micron-sized mixed-nucleotide zone.

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.

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.

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.

Chromosome segregation is a mechanical process that requires assembly of the mitotic spindle – a dynamic microtubule-based force-generating machine. Connections to this spindle are mediated by sister kinetochore pairs, that form dynamic end-on attachments to microtubules emanating from opposite spindle poles. This bi-orientation generates forces that have been reported to stretch the kinetochore itself, which has been suggested to stabilise attachment and silence the spindle checkpoint. We reveal using three dimensional tracking that the outer kinetochore domain can swivel around the inner kinetochore/centromere, which results in large reductions in intra-kinetochore distance (delta) when viewed in lower dimensions. We show that swivel provides a mechanical flexibility that enables kinetochores at the periphery of the spindle to engage microtubules. Swivel reduces as cells approach anaphase, suggesting an organisational change linked to checkpoint satisfaction and/or obligatory changes in kinetochore mechanochemistry may occur before dissolution of sister chromatid cohesion.