Animals and fungi assemble a contractile ring of actin filaments and the motor protein myosin to separate into individual daughter cells during cytokinesis. We used fluorescence microscopy of live fission yeast cells to observe that membrane-bound nodes containing myosin were broadly distributed around the cell equator and assembled into a contractile ring through stochastic motions, after a meshwork of dynamic actin filaments appeared. Analysis of node motions and numerical simulations supported a mechanism whereby transient connections are established when myosins in one node capture and exert force on actin filaments growing from other nodes.

Cells promote polarized growth by activation of Rho-family protein Cdc42 at the cell membrane. We combined experiments and modeling to study bipolar growth initiation in fission yeast. Concentrations of a fluorescent marker for active Cdc42, Cdc42 protein, Cdc42-activator Scd1, and scaffold protein Scd2, exhibited anti-correlated fluctuations and oscillations with a five-minute average period at polarized cell tips. These dynamics indicate competition for active Cdc42, or its regulators, and the presence of positive and delayed negative feedbacks. Cdc42 oscillations and spatial distribution were sensitive to the amounts of Cdc42-activator Gef1 and to the activity of Cdc42-dependent kinase Pak1, a negative regulator. Feedbacks regulating Cdc42 oscillations and spatial self-organization appear to provide a flexible mechanism for fission yeast cells to explore polarization states and control their morphology.

We used fluorescence microscopy to determine how polymerization of Mg-ADP-actin depends on the concentration of phosphate. From the dependence of the elongation rate on the actin concentration and direct observations of depolymerizing filaments, we measured the polymerization rate constants of ADP-actin and ADP-Pi-actin. Saturating phosphate reduces the critical concentration for polymerization of Mg-ADP-actin from 1.8 to 0.06 M almost entirely by reducing the dissociation rate constants at both ends. Saturating phosphate increases the barbed end association rate constant of Mg-ADP-actin 15%, but this value is still threefold less than that of ATP-actin. Thus, ATP hydrolysis without phosphate dissociation must change the conformation of polymerized actin. Analysis of depolymerization experiments in the presence of phosphate suggests that phosphate dissociation near the terminal subunits is much faster than in the interior. Remarkably, 10 times more phosphate is required to slow the depolymerization of the pointed end than the barbed end, suggesting a weak affinity of phosphate near the pointed end. Our observations of single actin filaments provide clues about the origins of the difference in the critical concentration at the two ends of actin filaments in the presence of ATP.filaments ͉ rate constant ͉ treadmilling A full understanding of actin dynamics in cells will require a complete set of kinetic and equilibrium constants for the polymerization and depolymerization reactions for the three different nucleotide states of actin monomers and polymers, which can bind ATP, ADP-P i (ADP with inorganic phosphate [P i ] bound noncovalently in the ␥-phosphate position), or ADP. Each of these species can bind and dissociate at both the fast growing barbed end and the slow growing pointed end of a filament. Monomeric actin hydrolyzes ATP very slowly (1), but polymerization changes the conformation of the subunits so that they hydrolyze ATP irreversibly (2) at 0.3 s Ϫ1 (3), assuming hydrolysis is random. The ␥-phosphate dissociates slowly from the ADP-P i intermediate with a half time of Ϸ350 s (4). The reaction is reversible, but the affinity of polymerized ADP-actin for inorganic phosphate is low, with a K d in the millimolar range (5). Electron microscopy (6, 7) and limited proteolysis (8) indicate that P i dissociation is coupled to a conformation change in the actin filament.As a result of ATP hydrolysis, single actin filaments at steady state add fresh ATP-subunits at the barbed end balanced by dissociation of ADP-actin at the pointed end in a process known as treadmilling (9-12). Treadmilling in a medium containing ATP depends on hydrolysis of ATP bound to polymerized subunits and P i dissociation coupled to differences in the rate constants for subunit association and dissociation at the two ends (9, 13). The critical concentrations of ATP-actin and ADP-P i -actin are similar (14, 15), but some of the kinetic parameters required to model the steady state behavior of actin (16) were unknown, such as the associati...

Formin FH2 domains associate processively with actin-filament barbed ends and modify their rate of growth. We modeled how the elongation rate depends on the concentrations of profilin and actin for four different formins. We assume that (1) FH2 domains are in rapid equilibrium among conformations that block or allow actin addition and that (2) profilin-actin is transferred rapidly to the barbed end from multiple profilin binding sites in formin FH1 domains. In agreement with previous experiments discussed below, we find an optimal profilin concentration with a maximal elongation rate that can exceed the rate of actin alone. High profilin concentrations suppress elongation, largely because free profilin displaces profilin-actin from FH1. The model supports a common polymerization mechanism for the four formin FH1FH2 constructs with differences attributed to varying parameter values. The mechanism does not require ATP hydrolysis by polymerized actin, but we cannot exclude that formins accelerate hydrolysis.

ATP cap ͉ length diffusivity ͉ modeling ͉ critical concentration

The small Rho-family GTPase Cdc42 is critical for cell polarization and polarizes spontaneously in absence of upstream spatial cues. Spontaneous polarization is thought to require dynamic Cdc42 recycling through Guanine nucleotide Dissociation Inhibitor (GDI)-mediated membrane extraction and vesicle trafficking. Here, we describe a functional fluorescent Cdc42 allele in fission yeast, which demonstrates Cdc42 dynamics and polarization independent of these pathways. Furthermore, an engineered Cdc42 allele targeted to the membrane independently of these recycling pathways by an amphipathic helix is viable and polarizes spontaneously to multiple sites in fission and budding yeasts. We show that Cdc42 is highly mobile at the membrane and accumulates at sites of activity, where it displays slower mobility. By contrast, a near-immobile transmembrane domain-containing Cdc42 allele supports viability and polarized activity, but does not accumulate at sites of activity. We propose that Cdc42 activation, enhanced by positive feedback, leads to its local accumulation by capture of fast-diffusing inactive molecules.

Many animal cells initiate crawling by protruding lamellipodia, consisting of a dense network of actin filaments, at their leading edge. We imaged XTC cells that exhibit flat lamellipodia on poly-L-lysine-coated coverslips. Using active contours, we tracked the leading edge and measured the total amount of F-actin by summing the pixel intensities within a 5-μm band. We observed protrusion and retraction with period 130-200 s and local wavelike features. Positive (negative) velocities correlated with minimum (maximum) integrated actin concentration. Approximately constant retrograde flow indicated that protrusions and retractions were driven by fluctuations of the actin polymerization rate. We present a model of these actin dynamics as an excitable system in which a diffusive, autocatalytic activator causes actin polymerization; F-actin accumulation in turn inhibits further activator accumulation. Simulations of the model reproduced the pattern of actin polymerization seen in experiments. To explore the model's assumption of an autocatalytic activation mechanism, we imaged cells expressing markers for both F-actin and the p21 subunit of the Arp2/3 complex. We found that integrated Arp2/3-complex concentrations spike several seconds before spikes of F-actin concentration. This suggests that the Arp2/3 complex participates in an activation mechanism that includes additional diffuse components. Response of cells to stimulation by fetal calf serum could be reproduced by the model, further supporting the proposed dynamical picture.

We use open active contours to quantify cytoskeletal structures imaged by fluorescence microscopy in two and three dimensions. We developed an interactive software tool for segmentation, tracking, and visualization of individual fibers. Open active contours are parametric curves that deform to minimize the sum of an external energy derived from the image and an internal bending and stretching energy. The external energy generates (i) forces that attract the contour toward the central bright line of a filament in the image, and (ii) forces that stretch the active contour toward the ends of bright ridges. Images of simulated semiflexible polymers with known bending and torsional rigidity are analyzed to validate the method. We apply our methods to quantify the conformations and dynamics of actin in two examples: actin filaments imaged by TIRF microscopy in vitro, and actin cables in fission yeast imaged by spinning disk confocal microscopy.