KnotResolver: tracking self-intersecting filaments in microscopy using directed graphs.

MOTIVATION: Quantification of microscopy time series of in vitro reconstituted motor-driven microtubule transport in "gliding assays" is typically performed using computational object tracking tools. However, these are limited to non-intersecting and rod-like filaments. RESULTS: Here, we describe a novel computational image-analysis pipeline, KnotResolver, to track image time series of highly curved self-intersecting looped filaments (knots) by resolving cross-overs. The code integrates filament segmentation and cross-over or "knot" identification based on directed graph representation, where nodes represent cross-overs and edges represent the path connecting them. The graphs are mapped back to contours and the distance to a reference minimized. The accuracy of contour detection is sub-pixel with a robustness to noise. We demonstrate the utility of KnotResolver by automatically quantifying "flagella-like" curvature dynamics and wave-like oscillations of clamped microtubules in a "gliding assay." AVAILABILITY AND IMPLEMENTATION: The MATLAB-based source code is released as OpenSource and is available at https://github.com/CyCelsLab/MTKnotResolver.

Wave-like oscillations of clamped microtubules driven by collective dynein transport.

Microtubules (MTs) are observed to move and buckle driven by ATP-dependent molecular motors in both mitotic and interphasic eukaryotic cells as well as in specialized structures such as flagella and cilia with a stereotypical geometry. In previous work, clamped MTs driven by a few kinesin motors were seen to buckle and occasionally flap in what was referred to as flagella-like motion. Theoretical models of active-filament dynamics and a following force have predicted that, with sufficient force and binding-unbinding, such clamped filaments should spontaneously undergo periodic buckling oscillations. However, a systematic experimental test of the theory and reconciliation to a model was lacking. Here, we have engineered a minimal system of MTs clamped at their plus ends and transported by a sheet of dynein motors that demonstrate the emergence of spontaneous traveling-wave oscillations along single filaments. The frequencies of tip oscillations are in the millihertz range and are statistically indistinguishable in the onset and recovery phases. We develop a 2D computational model of clamped MTs binding and unbinding stochastically to motors in a "gliding-assay" geometry. The simulated MTs oscillate with a frequency comparable to experiment. The model predicts the effect of MT length and motor density on qualitative transitions between distinct phases of flapping, regular oscillations, and looping. We develop an effective "order parameter" based on the relative deflection along the filament and orthogonal to it. The transitions predicted in simulations are validated by experimental data. These results demonstrate a role for geometry, MT buckling, and collective molecular motor activity in the emergence of oscillatory dynamics.

Quantification of cell shape, intracellular flows and transport based on DIC object detection and tracking.

Computational image analysis combined with label-free imaging has helped maintain its relevance for cell biology, despite the rapid technical improvements in fluorescence microscopy with the molecular specificity of tags. Here, we discuss some computational tools developed in our lab and their application to quantify cell shape, intracellular organelle movement and bead transport in vitro, using differential interference contrast (DIC) microscopy data as inputs. The focus of these methods is image filtering to enhance image gradients, and combining them with segmentation and single particle tracking (SPT). We demonstrate the application of these methods to Escherichia coli cell length estimation and tracking of densely packed lipid granules in Caenorhabditis elegans one-celled embryos, diffusing beads in solutions of different viscosities and kinesin-driven transport on microtubules. These approaches demonstrate how improvements to low-level image analysis methods can help obtain insights through quantitative cellular and subcellular microscopy.

Allometry ofEscherichia colisurface area with volume: effect of size variability, filamentation and division dynamics.

The cell surface area (SA) increase with volume (V) is determined by growth and regulation of size and shape. Most studies of the rod-shaped model bacteriumEscherichia colihave focussed on the phenomenology or molecular mechanisms governing such scaling. Here, we proceed to examine the role of population statistics and cell division dynamics in such scaling by a combination of microscopy, image analysis and statistical simulations. We find that while the SA of cells sampled from mid-log cultures scales with V by a scaling exponent 2/3, i.e. the geometric law SA ∼V2/3, filamentous cells have higher exponent values. We modulate the growth rate to change the proportion of filamentous cells, and find SA-V scales with an exponent>2/3, exceeding that predicted by the geometric scaling law. However, since increasing growth rates alter the mean and spread of population cell size distributions, we use statistical modeling to disambiguate between the effect of the mean size and variability. Simulating (i) increasing mean cell length with a constant standard deviation (s.d.), (ii) a constant mean length with increasing s.d. and (iii) varying both simultaneously, results in scaling exponents that exceed the 2/3 geometric law, when population variability is included, with the s.d. having a stronger effect. In order to overcome possible effects of statistical sampling of unsynchronized cell populations, we 'virtually synchronized' time-series of cells by using the frames between birth and division identified by the image-analysis pipeline and divided them into four equally spaced phases-B, C1, C2 and D. Phase-specific scaling exponents estimated from these time series and the cell length variability were both found to decrease with the successive stages of birth (B), C1, C2 and division (D). These results point to a need to consider population statistics and a role for cell growth and division when estimating SA-V scaling of bacterial cells.

Quantifying Intracellular Particle Flows by DIC Object Tracking.

Label-free imaging techniques such as differential interference contrast (DIC) allow the observation of cells and large subcellular structures in their native, unperturbed states with minimal exposure to light. The development of robust computational image-analysis routines is vital to quantitative label-free imaging. The reliability of quantitative analysis of time-series microscopy data based on single-particle tracking relies on accurately detecting objects as distinct from the background, i.e., segmentation. Typical approaches to segmenting DIC images either involve converting images to those resembling phase contrast, mimicking the optics of DIC object formation, or using the morphological properties of objects. Here, we describe MATLAB based, single-particle tracking tool with a GUI for mobility analysis of objects from in vitro and in vivo DIC time-series microscopy. The tool integrates contrast enhancement with multiple modified Gaussian filters, automated threshold detection for segmentation and minimal distance-based two-dimensional single-particle tracking. We compare the relative performance of multiple filters and demonstrate the utility of the tool for DIC object tracking (DICOT). We quantify subcellular dynamics of a time series of Caenorhabditis elegans embryos in the one-celled stage by detecting birefringent yolk granules in the cytoplasm with high precision. The resulting two-dimensional map of oscillatory dynamics of granules quantifies the cytoplasmic flows driven by anaphasic spindle oscillations. The frequency of oscillations across the anterior-posterior (A-P) and transverse axes of the embryo correspond well with the reported frequency of spindle oscillations. We validate the quantitative accuracy of our method by tracking the in vitro diffusive mobility of micron-sized beads in glycerol solutions. Estimates of the diffusion coefficients of the granules are used to measure the viscosity of a dilution series of glycerol. Thus, our computational method is likely to be useful for both intracellular mobility and in vitro microrheology.

Evolutionary divergence of anaphase spindle mechanics in nematode embryos constrained by antagonistic pulling and viscous forces.

Cellular functions such as cell division are remarkably conserved across phyla. However, the evolutionary principles of cellular organization that drive them are less well explored. Thus, an essential question remains: to what extent do cellular parameters evolve without altering the basic functions they sustain? Here we have observed six different nematode species for which the mitotic spindle is positioned asymmetrically during the first embryonic division. Whereas the C. elegans spindle undergoes oscillations during its displacement, the spindle elongates without oscillations in other species. We asked which evolutionary changes in biophysical parameters could explain differences in spindle motion while maintaining a constant output. Using laser microsurgery of the spindle, we revealed that all species are subjected to cortical pulling forces of varying magnitudes. Using a viscoelastic model to fit the recoil trajectories and with an independent measurement of cytoplasmic viscosity, we extracted the values of cytoplasmic drag, cortical pulling forces, and spindle elasticity for all species. We found large variations in cytoplasmic viscosity, whereas cortical pulling forces and elasticity were often more constrained. In agreement with previous simulations, we found that increased viscosity correlates with decreased oscillation speeds across species. However, the absence of oscillations in some species despite low viscosity can only be explained by smaller pulling forces. Consequently, we find that spindle mobility across the species analyzed here is characterized by a tradeoff between cytoplasmic viscosity and pulling forces normalized by the size of the embryo. Our work provides a framework for understanding mechanical constraints on evolutionary diversification of spindle mobility.