David J. Odde

Traction Dynamics of Filopodia on Compliant Substrates

Cells sense the environments mechanical stiffness to control their own shape, migration, and fate. To better understand stiffness sensing, we constructed a stochastic model of the “motor-clutch” force transmission system, where molecular clutches link F-actin to the substrate and mechanically resist myosin-driven F-actin retrograde flow. The model predicts two distinct regimes: (i) “frictional slippage,” with fast retrograde flow and low traction forces on stiff substrates and (ii) oscillatory “load-and-fail” dynamics, with slower retrograde flow and higher traction forces on soft substrates. We experimentally confirmed these model predictions in embryonic chick forebrain neurons by measuring the nanoscale dynamics of single–growth-cone filopodia. Furthermore, we experimentally observed a model-predicted switch in F-actin dynamics around an elastic modulus of 1 kilopascal. Thus, a motor-clutch system inherently senses and responds to the mechanical stiffness of the local environment.

Potential for Control of Signaling Pathways via Cell Size and Shape

BACKGROUND In order for signals generated at the plasma membrane to reach intracellular targets, activated messengers, such as G proteins and phosphoproteins, must diffuse through the cytoplasm. If the deactivators of these messengers, GTPase activating proteins (GAPs) and phosphatases, respectively, are sufficiently active in the cytoplasm, then the signal could in principle decay before reaching the target and a stable spatial gradient in phosphostate would be generated. Recent experiments document the existence of such gradients in living cells and suggest a role for them in mitotic spindle morphogenesis and cell migration. However, how such systems behave theoretically when embedded in a cell of varying size or shape has not been considered. RESULTS Here we use a simple mathematical model to explore the theoretical consequences of a plasma membrane bound activator (i.e., guanine nucleotide exchange factor, GEF, or kinase) and a cytoplasmic deactivator (i.e., GAP or phosphatase), and we find that as a model cell grows, the substrate becomes progressively dephosphorylated as a result of decreased proximity to the activator. Conversely, as a cell spreads and flattens, the substrate becomes globally phosphorylated because of increased proximity of the substrate to the activator. Similarly, in the leading edge of polarized cells and in protrusions such as lamellipodia or filopodia, the substrate is highly phosphorylated. As a specific test of the model, we found that the experimentally observed preferential activation of the G protein Cdc42 in the periphery of fibroblasts that was recently reported is consistent with model predictions. CONCLUSIONS We conclude that cell-signaling pathways can theoretically be turned on and off, both locally and globally, in response to alterations in cell size and shape.

Estimates of lateral and longitudinal bond energies within the microtubule lattice

We developed a stochastic model of microtubule (MT) assembly dynamics that estimates tubulin–tubulin bond energies, mechanical energy stored in the lattice dimers, and the size of the tubulin-GTP cap at MT tips. First, a simple assembly/disassembly state model was used to screen possible combinations of lateral bond energy (ΔGLat) and longitudinal bond energy (ΔGLong) plus the free energy of immobilizing a dimer in the MT lattice (ΔGS) for rates of MT growth and shortening measured experimentally. This analysis predicts ΔGLat in the range of −3.2 to −5.7 kBT and ΔGLong plus ΔGS in the range of −6.8 to −9.4 kBT. Based on these estimates, the energy of conformational stress for a single tubulin-GDP dimer in the lattice is 2.1–2.5 kBT. Second, we studied how tubulin-GTP cap size fluctuates with different hydrolysis rules and show that a mechanism of directly coupling subunit addition to hydrolysis fails to support MT growth, whereas a finite hydrolysis rate allows growth. By adding rules to mimic the mechanical constraints present at the MT tip, the model generates tubulin-GTP caps similar in size to experimental estimates. Finally, by combining assembly/disassembly and cap dynamics, we generate MT dynamic instability with rates and transition frequencies similar to those measured experimentally. Our model serves as a platform to examine GTP-cap dynamics and allows predictions of how MT-associated proteins and other effectors alter the energetics of MT assembly.

Stable Kinetochore-Microtubule Attachment Constrains Centromere Positioning in Metaphase

With a single microtubule attachment, budding-yeast kinetochores provide an excellent system for understanding the coordinated linkage to dynamic microtubule plus ends for chromosome oscillation and positioning. Fluorescent tagging of kinetochore proteins indicates that, on average, all centromeres are clustered, distinctly separated from their sisters, and positioned equidistant from their respective spindle poles during metaphase. However, individual fluorescent chromosome markers near the centromere transiently reassociate with their sisters and oscillate from one spindle half to the other. To reconcile the apparent disparity between the average centromere position and individual centromere proximal markers, we utilized fluorescence recovery after photobleaching to measure stability of the histone-H3 variant Cse4p/CENP-A. Newly synthesized Cse4p replaces old protein during DNA replication. Once assembled, Cse4-GFP is a physically stable component of centromeres during mitosis. This allowed us to follow centromere dynamics within each spindle half. Kinetochores remain stably attached to dynamic microtubules and exhibit a low incidence of switching orientation or position between the spindle halves. Switching of sister chromatid attachment may be contemporaneous with Cse4p exchange and early kinetochore assembly during S phase; this would promote mixing of chromosome attachment to each spindle pole. Once biorientation is attained, centromeres rarely make excursions beyond their proximal half spindle.

MICROTUBULE ASSEMBLY DYNAMICS AT THE NANOSCALE

BACKGROUND The labile nature of microtubules is critical for establishing cellular morphology and motility, yet the molecular basis of assembly remains unclear. Here we use optical tweezers to track microtubule polymerization against microfabricated barriers, permitting unprecedented spatial resolution. RESULTS We find that microtubules exhibit extensive nanometer-scale variability in growth rate and often undergo shortening excursions, in some cases exceeding five tubulin layers, during periods of overall net growth. This result indicates that the guanosine triphosphate (GTP) cap does not exist as a single layer as previously proposed. We also find that length increments (over 100 ms time intervals, n = 16,762) are small, 0.81 +/- 6.60 nm (mean +/- standard deviation), and very rarely exceed 16 nm (about two dimer lengths), indicating that assembly occurs almost exclusively via single-subunit addition rather than via oligomers as was recently suggested. Finally, the assembly rate depends only weakly on load, with the average growth rate decreasing only 2-fold as the force increases 7-fold from 0.4 pN to 2.8 pN. CONCLUSIONS The data are consistent with a mechanochemical model in which a spatially extended GTP cap allows substantial shortening on the nanoscale, while still preventing complete catastrophe in most cases.

Chromosome Congression by Kinesin-5 Motor-Mediated Disassembly of Longer Kinetochore Microtubules

During mitosis, sister chromatids congress to the spindle equator and are subsequently segregated via attachment to dynamic kinetochore microtubule (kMT) plus ends. A major question is how kMT plus-end assembly is spatially regulated to achieve chromosome congression. Here we find in budding yeast that the widely conserved kinesin-5 sliding motor proteins, Cin8p and Kip1p, mediate chromosome congression by suppressing kMT plus-end assembly of longer kMTs. Of the two, Cin8p is the major effector and its activity requires a functional motor domain. In contrast, the depolymerizing kinesin-8 motor Kip3p plays a minor role in spatial regulation of yeast kMT assembly. Our analysis identified a model where kinesin-5 motors bind to kMTs, move to kMT plus ends, and upon arrival at a growing plus end promote net kMT plus-end disassembly. In conclusion, we find that length-dependent control of net kMT assembly by kinesin-5 motors yields a simple and stable self-organizing mechanism for chromosome congression.

Rapid Microtubule Self-Assembly Kinetics

Melissa K. Gardner,1,2,3 Blake D. Charlebois,4 Imre M. Jánosi,5 Jonathon Howard,2 Alan J. Hunt,4,* and David J. Odde1,* 1Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN 55455, USA 2Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany 3Department of Genetics, Cell Biology, and Development, University of Minnesota, Minneapolis, MN 55455, USA 4Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI 48109, USA 5Department of Physics of Complex Systems, Loránd Eötvös University, Budapest, Hungary *Correspondence: ajhunt@umich.edu (A.J.H.), oddex002@umn.edu (D.J.O.) DOI 10.1016/j.cell.2011.06.053Microtubule assembly is vital for many fundamental cellular processes. Current models for microtubule assembly kinetics assume that the subunit dissociation rate from a microtubule tip is independent of free subunit concentration. Total-Internal-Reflection-Fluorescence (TIRF) microscopy experiments and data from a laser tweezers assay that measures in vitro microtubule assembly with nanometer resolution, provides evidence that the subunit dissociation rate from a microtubule tip increases as the free subunit concentration increases. These data are consistent with a two-dimensional model for microtubule assembly, and are explained by a shift in microtubule tip structure from a relatively blunt shape at low free concentrations to relatively tapered at high free concentrations. We find that because both the association and the dissociation rates increase at higher free subunit concentrations, the kinetics of microtubule assembly are an order-of-magnitude higher than currently estimated in the literature.

Mechanisms of Microtubule-Based Kinetochore Positioning in the Yeast Metaphase Spindle

It has been hypothesized that spatial gradients in kMT dynamic instability facilitate mitotic spindle formation and chromosome movement. To test this hypothesis requires the analysis of kMT dynamics, which have not been resolved at the single kMT level in living cells. The budding yeast spindle offers an attractive system in which to study kMT dynamics because, in contrast to animal cells, there is only one kMT per kinetochore. To visualize metaphase kMT plus-end dynamics in yeast, a strain containing a green fluorescent protein fusion to the kinetochore protein, Cse4, was imaged by fluorescence microscopy. Although individual kinetochores were not resolvable, we found that models of kMT dynamics could be evaluated by simulating the stochastic kMT dynamics and then simulating the fluorescence imaging of kMT plus-end-associated kinetochores. Statistical comparison of model-predicted images to experimentally observed images demonstrated that a pure dynamic instability model for kMT dynamics in the yeast metaphase spindle was unacceptable. However, when a temporally stable spatial gradient in the catastrophe or rescue frequency was added to the model, there was reasonable agreement between the model and the experiment. These results provide the first evidence of temporally stable spatial gradients of kMT catastrophe and/or rescue frequency in living cells.

Kinetics of microtubule catastrophe assessed by probabilistic analysis

Microtubules are cytoskeletal filaments whose self-assembly occurs by abrupt switching between states of roughly constant growth and shrinkage, a process known as dynamic instability. Understanding the mechanism of dynamic instability offers potential for controlling microtubule-dependent cellular processes such as nerve growth and mitosis. The growth to shrinkage transitions (catastrophes) and the reverse transitions (rescues) that characterize microtubule dynamic instability have been assumed to be random events with first-order kinetics. By direct observation of individual microtubules in vitro and probabilistic analysis of their distribution of growth times, we found that while the slower growing and biologically inactive (minus) ends obeyed first-order catastrophe kinetics, the faster growing and biologically active (plus) ends did not. The non-first-order kinetics at plus ends imply that growing microtubule plus ends have an effective frequency of catastrophe that depends on how long the microtubules have been growing. This frequency is low initially but then rises asymptotically to a limiting value. Our results also suggest that an additional parameter, beyond the four parameters typically used to describe dynamic instability, is needed to account for the observed behavior and that changing this parameter can significantly affect the distribution of microtubule lengths at steady state.

Micropatterning of living cells by laser-guided direct writing: application to fabrication of hepatic–endothelial sinusoid-like structures

Here, we describe a simple protocol for the design and construction of a laser-guided direct writing (LGDW) system able to micropattern the self-assembly of liver sinusoid-like structures with micrometer resolution in vitro. To the best of our knowledge, LGDW is the only technique able to pattern cells “on the fly” with micrometer precision on arbitrary matrices, including soft gels such as Matrigel. By micropatterning endothelial cells on Matrigel, one can control the self-assembly of vascular structures and associated liver tissue. LGDW is therefore uniquely suited for studying the role of tissue architecture and mechanical properties at the single-cell resolution, and for studying the effects of heterotypic cell–cell interactions underlying processes such as liver morphogenesis, differentiation and angiogenesis. The total time required to carry out this protocol is typically 7 h.