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.

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.

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.

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.

Self-organized optimal packing of kinesin-5-driven microtubule asters scales with cell size.

Radial microtubule (MT) arrays or asters determine cell geometry in animal cells. Multiple asters interacting with motors, such as those in syncytia, form intracellular patterns, but the mechanical principles behind this are not clear. Here, we report that oocytes of the marine ascidian Phallusia mammillata treated with the drug BI-D1870 spontaneously form cytoplasmic MT asters, or cytasters. These asters form steady state segregation patterns in a shell just under the membrane. Cytaster centers tessellate the oocyte cytoplasm, that is divide it into polygonal structures, dominated by hexagons, in a kinesin-5-dependent manner, while inter-aster MTs form 'mini-spindles'. A computational model of multiple asters interacting with kinesin-5 can reproduce both tessellation patterns and mini-spindles in a manner specific to the number of MTs per aster, MT lengths and kinesin-5 density. Simulations predict that the hexagonal tessellation patterns scale with increasing cell size, when the packing fraction of asters in cells is ∼1.6. This self-organized in vivo tessellation by cytasters is comparable to the 'circle packing problem', suggesting that there is an intrinsic mechanical pattern-forming module that is potentially relevant to understanding the role of collective mechanics of cytoskeletal elements in embryogenesis. This article has an associated First Person interview with the first author of the paper.

Collective dynein transport of the nucleus by pulling on astral microtubules during Saccharomyces cerevisiae mitosis.

Positioning the nucleus at the bud neck during Saccharomyces cerevisiae mitosis involves pulling forces of cytoplasmic dynein localized in the daughter cell. Although genetic analysis has revealed a complex network positioning the nucleus, quantification of the forces acting on the nucleus and the number of dyneins driving the process has remained difficult. To better understand the collective forces involved in nuclear positioning, we compare a model of dyneins-driven microtubule (MT) pulling, MT pushing, and cytoplasmic drag to experiments. During S. cerevisiae mitosis, MTs interacting with the cortex nucleated by the daughter spindle pole body (SPB) (SPB-D) are longer than the mother SPB (SPB-M), increasing further during spindle elongation in anaphase. Interphasic SPB mobility is effectively diffusive, while the mitotic mobility is directed. By optimizing a computational model of the mobility of the nucleus due to diffusion and MTs pushing at the cell membrane to experiment, we estimate the viscosity governing the drag force on nuclei during positioning. A force balance model of mitotic SPB mobility compared to experimental mobility suggests that even one or two dynein dimers are sufficient to move the nucleus in the bud neck. Using stochastic computer simulations of a budding cell, we find that punctate dynein localization can generate sufficient force to reel in the nucleus to the bud neck. Compared to uniform motor localization, puncta involve fewer motors suggesting a functional role for motor clustering. Stochastic simulations also suggest that a higher number of force generators than predicted by force balance may be required to ensure the robustness of spindle positioning.

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.

Polymerization kinetics of tubulin from mung seedlings modeled as a competition between nucleation and GTP-hydrolysis rates.

Microtubules (MTs) form physiologically important cytoskeletal structures that are assembled by tubulin polymerization in nucleation- and guanosine triphosphate (GTP)-dependent manner. GTP hydrolysis competes with the addition of monomers, to determine the GTP-cap size, and the onset of shrinkage, which alternates with growth. Multiple theoretical models of MT polymerization dynamics have been reconciled to the kinetics of animal brain tubulins, but more recently, rapid kinetics seen in Arabidopsis tubulin polymerization suggest the need to sample a wider diversity in tubulin polymerization kinetics and reconcile it to theory. Here, we isolated tubulin from seedlings of Vigna sp. (mung bean), compared polymerization kinetics to animal brain tubulin, and used a computational model to understand the differences. We find that activity-isolated mung tubulin polymerizes in a nucleation-dependent manner, based on turbidimetry, qualitatively similar to brain tubulin, but with a 10-fold smaller critical concentration. GTP-dependent polymerization kinetics also appear to be transient, indicative of high rates of GTP hydrolysis. Computational modeling of tubulin nucleation and vectorial GTP hydrolysis to examine the effects of high nucleation and GTP-hydrolysis rates predicts a dominance of the latter in determining MT lengths and numbers. Microscopy of mung tubulin filaments stabilized by GMPCPP or taxol results in few and short MTs, compared to the many long MTs arising from goat tubulin, qualitatively matching the model predictions. We find GTP-hydrolysis outcompetes nucleation rates in determining MT lengths and numbers.

Aster swarming by symmetry breaking of cortical dynein transport and coupling kinesins.

Microtubule (MT) radial arrays or asters establish the internal topology of a cell by interacting with organelles and molecular motors. We proceed to understand the general pattern forming potential of aster-motor systems using a computational model of multiple MT asters interacting with motors in cellular confinement. In this model dynein motors are attached to the cell cortex and plus-ended motors resembling kinesin-5 diffuse in the cell interior. The introduction of 'noise' in the form of MT length fluctuations spontaneously results in the emergence of coordinated, achiral vortex-like rotation of asters. The coherence and persistence of rotation require a threshold density of both cortical dyneins and coupling kinesins, while the onset is diffusion-limited with relation to the cortical dynein mobility. The coordinated rotational motion emerges due to the resolution of a 'tug-of-war' of multiple cortical dynein motors bound to MTs of the same aster by 'noise' in the form of MT dynamic instability. This transient symmetry breaking is amplified by local coupling by kinesin-5 complexes. The lack of widespread aster rotation across cell types suggests that biophysical mechanisms that suppress such intrinsic dynamics may have evolved. This model is analogous to more general models of locally coupled self-propelled particles (SPP) that spontaneously undergo collective transport in the presence of 'noise' that have been invoked to explain swarming in birds and fish. However, the aster-motor system is distinct from SPP models with regard to the particle density and 'noise' dependence, providing a set of experimentally testable predictions for a novel sub-cellular pattern forming system.

Modeling the tunability of the dual-feedback genetic oscillator.

Oscillatory gene circuits are ubiquitous to biology and are involved in fundamental processes of cell cycle, circadian rhythms, and developmental systems. The synthesis of small, non-natural oscillatory genetic circuits has been increasingly used to test the fundamental principles of genetic network dynamics. While the "repressilator" was used to first demonstrate the proof of principle, a more recently developed dual-feedback, fast, tunable genetic oscillator has demonstrated a greater degree of robustness and control over oscillatory behavior by combining positive- and negative-feedback loops. This oscillator, combining lacI (negative-) and araC (positive-) feedback loops, was, however, modeled using multiple layers of differential equations to capture the molecular complexity of regulation, in order to explain the experimentally measured oscillations. In the search for design principles of such minimal oscillatory circuits, we have developed a reduced model of this dual-feedback loop oscillator consisting of just six differential equations, two of which are delay differential equations. The delay term is optimized, as the only free parameter, to fit the experimental dynamics of the oscillator period and amplitude tunability by the two inducers isopropyl ß-D-1-thiogalactopyranoside (IPTG) and arabinose. We proceed to use our reduced and experimentally validated model to redesign the network by comparing the effect of asymmetry in gene expression at the level of (a) DNA copy numbers and the rates of (b) mRNA translation and (c) degradation, since experimental and theoretical work had predicted a need for an asymmetry in the copy numbers of activator (araC) and repressor (lacI) genes encoded on plasmids. We confirm that the minimal period of the oscillator is sensitive to DNA copy number asymmetry, and can demonstrate that while the asymmetry in the translation rate has an identical effect as the plasmid copy numbers, modulating the asymmetry in mRNA degradation can improve the tunability of the period and amplitude of the oscillator. Thus, our model predicts control at the level of translation can be used to redesign such networks, for improved tunability, while at the same time making the network robust to replication "noise" and the effects of the host cell cycle. Thus, our model predicts experimentally testable principles to redesign a potentially more robust oscillatory genetic network.

Collective effects of yeast cytoplasmic dynein based microtubule transport.

Teams of cortically anchored dyneins pulling at microtubules (MTs) are known to be essential for aster, spindle and nuclear positioning during cell division and fertilization. While the single-molecule basis of dynein processivity is now better understood, the effect of increasing numbers of motors on transport is not clear. Here, we examine the collective transport properties of a Saccharomyces cerevisiae cytoplasmic dynein fragment, widely used as a minimal model, by a combination of quantitative MT gliding assays and stochastic simulations. We find both MT lengths and motor densities qualitatively affect the degree of randomness of MT transport. However, the directionality and velocity of MTs increase above a threshold number of motors (N) interacting with a filament. To better understand this behavior, we simulate a gliding assay based on a model of uniformly distributed immobilized motors transporting semi-flexible MTs. Each dynein dimer is modeled as an effective stochastic stepper with asymmetric force dependent detachment dynamics, based on single-molecule experiments. Simulations predict increasing numbers of motors (N) result in a threshold dependent transition in directionality and transport velocity and a monotonic decrease in effective diffusivity. Thus both experiment and theory show qualitative agreement in the emergence of coordination in transport above a threshold number of motor heads. We hypothesize that the phase-transition like property of this dynein could play a role in vivo during yeast mitosis, when this dynein localizes to the cortex and pulls astral MTs of increasing length, resulting in correct positioning and orientation of the nucleus at the bud-neck.

Role of spatial inhomogenity in GPCR dimerisation predicted by receptor association-diffusion models.

G protein-coupled receptor (GPCR) association is an emerging paradigm with far reaching implications in the regulation of signalling pathways and therapeutic interventions. Recent super resolution microscopy studies have revealed that receptor dimer steady state exhibits sub-second dynamics. In particular the GPCRs, muscarinic acetylcholine receptor M1 (M1MR) and formyl peptide receptor (FPR), have been demonstrated to exhibit a fast association/dissociation kinetics, independent of ligand binding. In this work, we have developed a spatial kinetic Monte Carlo model to investigate receptor homo-dimerisation at a single receptor resolution. Experimentally measured association/dissociation kinetic parameters and diffusion coefficients were used as inputs to the model. To test the effect of membrane spatial heterogeneity on the simulated steady state, simulations were compared to experimental statistics of dimerisation. In the simplest case the receptors are assumed to be diffusing in a spatially homogeneous environment, while spatial heterogeneity is modelled to result from crowding, membrane micro-domains and cytoskeletal compartmentalisation or 'corrals'. We show that a simple association-diffusion model is sufficient to reproduce M1MR association statistics, but fails to reproduce FPR statistics despite comparable kinetic constants. A parameter sensitivity analysis is required to reproduce the association statistics of FPR. The model reveals the complex interplay between cytoskeletal components and their influence on receptor association kinetics within the features of the membrane landscape. These results constitute an important step towards understanding the factors modulating GPCR organisation.

Threshold effect of growth rate on population variability of Escherichia coli cell lengths.

A long-standing question in biology is the effect of growth on cell size. Here, we estimate the effect of Escherichia coli growth rate (r) on population cell size distributions by estimating the coefficient of variation of cell lengths (CVL) from image analysis of fixed cells in DIC microscopy. We find that the CVL is constant at growth rates less than one division per hour, whereas above this threshold, CVL increases with an increase in the growth rate. We hypothesize that stochastic inhibition of cell division owing to replication stalling by a RecA-dependent mechanism, combined with the growth rate threshold of multi-fork replication (according to Cooper and Helmstetter), could form the basis of such a threshold effect. We proceed to test our hypothesis by increasing the frequency of stochastic stalling of replication forks with hydroxyurea (HU) treatment and find that cell length variability increases only when the growth rate exceeds this threshold. The population effect is also reproduced in single-cell studies using agar-pad cultures and 'mother machine'-based experiments to achieve synchrony. To test the role of RecA, critical for the repair of stalled replication forks, we examine the CVL of E. coli ΔrecA cells. We find cell length variability in the mutant to be greater than wild-type, a phenotype that is rescued by plasmid-based RecA expression. Additionally, we find that RecA-GFP protein recruitment to nucleoids is more frequent at growth rates exceeding the growth rate threshold and is further enhanced on HU treatment. Thus, we find growth rates greater than a threshold result in increased E. coli cell lengths in the population, and this effect is, at least in part, mediated by RecA recruitment to the nucleoid and stochastic inhibition of division.

Automated Multi-Peak Tracking Kymography (AMTraK): A Tool to Quantify Sub-Cellular Dynamics with Sub-Pixel Accuracy.

Kymographs or space-time plots are widely used in cell biology to reduce the dimensions of a time-series in microscopy for both qualitative and quantitative insight into spatio-temporal dynamics. While multiple tools for image kymography have been described before, quantification remains largely manual. Here, we describe a novel software tool for automated multi-peak tracking kymography (AMTraK), which uses peak information and distance minimization to track and automatically quantify kymographs, integrated in a GUI. The program takes fluorescence time-series data as an input and tracks contours in the kymographs based on intensity and gradient peaks. By integrating a branch-point detection method, it can be used to identify merging and splitting events of tracks, important in separation and coalescence events. In tests with synthetic images, we demonstrate sub-pixel positional accuracy of the program. We test the program by quantifying sub-cellular dynamics in rod-shaped bacteria, microtubule (MT) transport and vesicle dynamics. A time-series of E. coli cell division with labeled nucleoid DNA is used to identify the time-point and rate at which the nucleoid segregates. The mean velocity of microtubule (MT) gliding motility due to a recombinant kinesin motor is estimated as 0.5 µm/s, in agreement with published values, and comparable to estimates using software for nanometer precision filament-tracking. We proceed to employ AMTraK to analyze previously published time-series microscopy data where kymographs had been manually quantified: clathrin polymerization kinetics during vesicle formation and anterograde and retrograde transport in axons. AMTraK analysis not only reproduces the reported parameters, it also provides an objective and automated method for reproducible analysis of kymographs from in vitro and in vivo fluorescence microscopy time-series of sub-cellular dynamics.

A Motor-Gradient and Clustering Model of the Centripetal Motility of MTOCs in Meiosis I of Mouse Oocytes.

Asters nucleated by Microtubule (MT) organizing centers (MTOCs) converge on chromosomes during spindle assembly in mouse oocytes undergoing meiosis I. Time-lapse imaging suggests that this centripetal motion is driven by a biased 'search-and-capture' mechanism. Here, we develop a model of a random walk in a drift field to test the nature of the bias and the spatio-temporal dynamics of the search process. The model is used to optimize the spatial field of drift in simulations, by comparison to experimental motility statistics. In a second step, this optimized gradient is used to determine the location of immobilized dynein motors and MT polymerization parameters, since these are hypothesized to generate the gradient of forces needed to move MTOCs. We compare these scenarios to self-organized mechanisms by which asters have been hypothesized to find the cell-center- MT pushing at the cell-boundary and clustering motor complexes. By minimizing the error between simulation outputs and experiments, we find a model of "pulling" by a gradient of dynein motors alone can drive the centripetal motility. Interestingly, models of passive MT based "pushing" at the cortex, clustering by cross-linking motors and MT-dynamic instability gradients alone, by themselves do not result in the observed motility. The model predicts the sensitivity of the results to motor density and stall force, but not MTs per aster. A hybrid model combining a chromatin-centered immobilized dynein gradient, diffusible minus-end directed clustering motors and pushing at the cell cortex, is required to comprehensively explain the available data. The model makes experimentally testable predictions of a spatial bias and self-organized mechanisms by which MT asters can find the center of a large cell.

What can simulations tell us about GPCRs: Integrating the scales.

The functional dynamics of G protein-coupled receptors (GPCRs) encompasses multiple spatiotemporal scales, ranging from femtoseconds to seconds and Ångströms to micrometers. Computational approaches, often in close collaboration with experimental methods, have been invaluable in unraveling GPCR structure and dynamics at these various hierarchical levels. The binding of natural and synthetic ligands to the wild-type and naturally occurring variant receptors have been analyzed by several computational methods. The activation of receptors from the inactive to the active state has been investigated by atomistic simulations and ongoing work on several receptors will help uncover general and receptor-specific mechanisms. The interaction of GPCRs with complex membranes that contain phospholipids and cholesterol have been probed by coarse-grain methods and shown to directly influence receptor association. In this chapter, we discuss computational approaches that have been successful in analyzing each scale of GPCR dynamics. An overview of these approaches will allow a more judicious choice of the appropriate method. We hope that an appreciation of the power of current computational approaches will encourage more critical collaborations. A comprehensive integration of the different approaches over the entire spatiotemporal scales promises to unravel new facets of GPCR function.

Thermodynamic and kinetic characterization of transmembrane helix association.

The transient dimerization of transmembrane proteins is an important event in several cellular processes and computational methods are being increasingly used to quantify their underlying energetics. Here, we probe the thermodynamics and kinetics of a simple transmembrane dimer to understand membrane protein association. A multi-step framework has been developed in which the dimerization profiles are calculated from coarse-grain molecular dynamics simulations, followed by meso-scale simulations using parameters calculated from the coarse-grain model. The calculated value of ΔGassoc is approx. -20 kJ mol(-1) and is consistent between three methods. Interestingly, the meso-scale stochastic model reveals low dimer percentages at physiologically-relevant concentrations, despite a favorable ΔGassoc. We identify generic driving forces arising from the protein backbone and lipid bilayer and complementary factors, such as protein density, that govern self-interactions in membranes. Our results provide an important contribution in understanding membrane protein organization and linking molecular, nano-scale computational studies to meso-scale experimental data.

Collective behavior of minus-ended motors in mitotic microtubule asters gliding toward DNA.

Microtubules (MTs) nucleated by centrosomes form star-shaped structures referred to as asters. Aster motility and dynamics is vital for genome stability, cell division, polarization and differentiation. Asters move either toward the cell center or away from it. Here, we focus on the centering mechanism in a membrane independent system of Xenopus cytoplasmic egg extracts. Using live microscopy and single particle tracking, we find that asters move toward chromatinized DNA structures. The velocity and directionality profiles suggest a random-walk with drift directed toward DNA. We have developed a theoretical model that can explain this movement as a result of a gradient of MT length dynamics and MT gliding on immobilized dynein motors. In simulations, the antagonistic action of the motor species on the radial array of MTs leads to a tug-of-war purely due to geometric considerations and aster motility resembles a directed random-walk. Additionally, our model predicts that aster velocities do not change greatly with varying initial distance from DNA. The movement of asymmetric asters becomes increasingly super-diffusive with increasing motor density, but for symmetric asters it becomes less super-diffusive. The transition of symmetric asters from superdiffusive to diffusive mobility is the result of number fluctuations in bound motors in the tug-of-war. Overall, our model is in good agreement with experimental data in Xenopus cytoplasmic extracts and predicts novel features of the collective effects of motor-MT interactions.

Spatial and temporal sensing limits of microtubule polarization in neuronal growth cones by intracellular gradients and forces.

Neuronal growth cones are the most sensitive among eukaryotic cells in responding to directional chemical cues. Although a dynamic microtubule cytoskeleton has been shown to be essential for growth-cone turning, the precise nature of coupling of the spatial cue with microtubule polarization is less understood. Here we present a computational model of microtubule polarization in a turning neuronal growth cone. We explore the limits of directional cues in modifying the spatial polarization of microtubules by testing the role of microtubule dynamics, gradients of regulators, and retrograde forces along filopodia. We analyze the steady state and transition behavior of microtubules on being presented with a directional stimulus. Our model makes novel, to our knowledge, predictions about the minimal angular spread of the chemical signal at the growth cone and the fastest polarization times. A regulatory reaction-diffusion network based on the cyclic phosphorylation-dephosphorylation of a regulator predicts that the receptor-signal magnitude can generate the maximal polarization of microtubules and not feedback loops or amplifications in the network. Using both the phenomenological and network models, we have demonstrated some of the physical limits within which the microtubule polarization system works in turning the neuron.

Population length variability and nucleoid numbers in Escherichia coli.

MOTIVATION: Cell sizes and shapes are a fundamental defining characteristic of all cellular life. In bacteria like Escherichia coli, the machinery that determines cell length is complex and interconnected, spanning extracellular cues, biosynthesis and cell division. Few tools exist to study cell lengths in a population. We have developed and tested three automated image analysis routines on growing E.coli cultures to simultaneously measure cell lengths and nucleoid numbers in populations of bacteria. We find population profiles changing with culture density-higher density of culture leads to fewer long cells. Additionally, lab strains mutant for recA show a correlation between the number of nucleoids and cell length. CONTACT: cathale@iiserpune.ac.in; chaitanya.athale@gmail.com. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.