Septins

Yeast strains used in this study are listed in Table I; construction of strains LSY305 and LSY388 is described below. Standard methods of yeast genetics were used (Guthrie and Fink, 1991 ; Gietz et al., 1992 (link)). Except where noted, cells were grown at 23°C on YM-P rich liquid medium, YPD rich solid medium, or synthetic complete (SC) medium lacking appropriate nutrients as needed to maintain plasmids (Lillie and Pringle, 1980 (link); Guthrie and Fink, 1991 ). All media contained 2% glucose as carbon source. Cells to be examined for GFP fluorescence were grown in the dark to minimize photobleaching.
To synchronize cells as a population of unbudded, G1-phase cells, α factor (Sigma-Aldrich) was added to a final concentration of 30 ng/ml to an exponentially growing culture (∼10⁷ cells/ml), and incubation was continued for 90 min. For Northern blot analyses (see below), cells were collected by centrifugation at 650 g for 5 min at 23°C, resuspended at a similar density in fresh medium without α factor, and incubated further. At intervals, samples were collected by centrifugation at high speed in a table-top centrifuge for 2 min at 23°C, and the pellets were flash frozen in an ethanol/dry ice bath. To investigate the actin dependence of Bud9p localization, Lat A (Molecular Probes) was added to a final concentration of 100 μM from a 20-mM stock solution in DMSO. Lat A (or the same concentration of DMSO alone as a control) was added to the synchronized culture 70 min after the shift back to medium without α factor, and the cells were examined 20 min later. To investigate the septin dependence of Bud9p localization, the α factor–arrested cells were resuspended in fresh medium without α factor that had been prewarmed to 37°C, incubation was continued at 37°C, and cells were examined after 90 min.
To synchronize cells late in the cell cycle using the cdc15-2 temperature-sensitive mutation, a culture growing exponentially at 23°C was shifted to 37°C and incubated for 3 to 4 h, at which point ∼98% of the cells had large buds. To release cells from the arrest, they were collected by centrifugation at 650 g for 5 min and resuspended in fresh medium at 23°C.
Plasmids used in this study are listed in Table II and/or described in the Supplemental materials and methods (available at http://www.jcb.org/cgi/content/full/jcb.200107041/DC1). Escherichia coli strains DH12S and DH5α (Life Technologies) were used for plasmid maintenance by standard procedures (Sambrook et al., 1989 ). Standard methods of DNA manipulation were used (Sambrook et al., 1989 ; Ausubel et al., 1995 ). PCR was performed using Taq DNA polymerase (Promega). Other enzymes were purchased from New England Biolabs, and oligonucleotide primers (Integrated DNA Technologies) are listed in Table III (Supplemental materials and methods, available at http://www.jcb.org/cgi/content/full/jcb.200107041/DC1). DNA sequencing was performed by the UNC-Chapel Hill Automated DNA Sequencing Facility.

Indirect immunofluorescence assay (IFA), Western blotting, immunoprecipitation, mass spectrometry, protein microarray, and cell-based transfection assays were used to identify and confirm septin-5 as a target antigen (appendix e-1, links.lww.com/NXI/A55). Testing for previously characterized neural IgGs are also described (appendix e-1). Serum controls tested by IFA (470 total) were 317 healthy controls, 63 patients with cancer without neurologic disease, and 90 with other neurologic diseases (Creutzfeldt-Jakob disease [30], CNS systemic lupus erythematous [10], MS [20], and amyotrophic lateral sclerosis [30]). Sera tested by septin-5 IgG cell-based assay (CBA) were 30 healthy and 17 with ≥1 other paraneoplastic antibodies (anti-Hu, 13; collapsin response mediator protein [CRMP]-5-IgG, 7).

We have now developed the required pieces for modeling binding, unbinding, surface diffusion, end-on annealing, and fragmentation processes and their curvature dependence that ultimately determine the time-dependent adsorption and assembly of septin filaments on membranes. The equations describing these processes are summarized in Table 1. The kinetic equations describing the general assembly process are $$\begin{array}{cc}\hfill \frac{d{n}_1}{dt}& =J_{\text{on}}^{\text{direct}}+J_{\text{on}}^{\text{coop,1}}+J_{\text{anneal}}^1+J_{\text{frag}}^1+J_{\text{off}}^1,\end{array}$$ $$\begin{array}{cc}\hfill \frac{d{n}_i}{dt}& =J_{\text{on}}^{\text{coop,}i}+J_{\text{anneal}}^i+J_{\text{frag}}^i+J_{\text{off}}^i,i>1,\end{array}$$ where i denotes the number of oligomer units in the filament.
For filaments to polymerize, their ends must be within a critical distance of each other, which is accomplished through their subdiffusive motion. The parameters that appear in modeling these processes are listed in Table 2. The parameters labeled as “S” under the source column (except for n_i and l_ave, which are determined by specifying the other parameters) are determined through a least-square optimization that minimizes the difference between the predicted and measured time-dependent adsorption curves at different bulk concentrations and curvatures. In order to solve this inverse problem, we first need a method to solve the direct problem: given all the parameters in Table 2, predict the time-dependent adsorption.
The typical choice for solving the direct problem is to integrate the overdamped Langevin equation to compute the displacements of septin on the membrane using Eq. 4 in combination with Eq. 6 to describe the kinetic processes. The main challenge in using this method is that the timescale for reaching steady-state adsorption (minutes) is significantly larger than a single oligomer dwell time (≈0.1 s), during which the oligomers are undergoing subdiffusive displacements. As a result, an exceedingly large number of time steps are needed to reach steady state and resolve the subdiffusive dynamics of the septins, making this method computationally prohibitive.
As an alternative, we consider the two limits for the annealing process: 1) reaction-limited, where the annealing kinetics are controlled by the slower reaction rate when the septins meet and 2) diffusion-limited reaction, where the annealing kinetics are solely determined by the time it takes the septins to meet. We separately consider these two limits as approximations to the kinetics of annealing. Our results strongly suggest that septin assembly is reaction limited. The detailed analysis is provided in SI Appendix, section C. In the reaction-limited case, the annealing reaction of bound septin filaments of length i and j oligomers is simply given by dn_{i + j}/dt = k_annealn_in_j, where n_i denotes surface density of a filament of length i oligomers, and k_anneal is only a function of bead’s curvature and independent of bulk concentration, filaments’ lengths, and surface densities.
Table 1 shows the set of equations that describe the assembly process. These equations can now be numerically integrated to compute the density of septins of different lengths, n_i, as a function of time. As a result, we can compute the probability density distribution of septins of different lengths and, thus, the total surface density of bound septins (marked as adsorption here) vs. time for a given set of parameters. We can then search for a combination of parameters that gives the least error between the experiments and simulation results given a fitness function. We use the nonlinlsq function in Matlab for our optimization process.

Bl21 (DE3) E. coli cells were transformed using a duet construct expression system (AGB827 and AGB1281 or 1481 depending on desired purification) using ampicillin and chloramphenicol selection (Bridges et al., 2014 (link)). Selected transformants were then grown overnight in 25 ml of Luria broth (LB) with ampicillin and chloramphenicol selection at 37°C while shaking. 1/60 of LB liquid cultures were added to 1 liter of terrific broth with ampicillin and chloramphenicol selection and were grown to an O.D.600 nm between 0.6 and 0.8. Upon reaching the appropriate O.D.600 nm, 1 mM of isopropyl-B-D-1-thiogalactopyranoside was added to the cultures to begin induction. To achieve a stoichiometric septin complex of Ashbya septins, we use Cdc12 with a primary sequence derived from S. cerevisiae, while all other subunits were Ashbya-derived sequences. Induced cultures were grown for 18 h at 18°C while shaking before harvesting by centrifugation at 10,000 elative centrigual force for 15 min. Pellets were resuspended in lysis buffer (1 M KCl, 50 mM Hepes pH 7.4, 40 mM imidazole, 1 mM MgCl2, 10% glycerol, 0.1% Tween-20, 1 mg/ml lysozyme, and a 1× protease inhibitor tablet (Roche) at 4°C for 30 min to generate cell lysates. Cell lysates were then sonicated on ice for 10 s every 2 min. Lysates were clarified by spinning at 20,000 RPM for 30 min using an SS-34 rotor at 4°C. The supernatant was passed through a 0.44-um filter and then incubated with 2 ml of equilibrated cobalt resin at 4° for 1 h. The lysate-resin mixture was then added to a gravity flow column. Following the initial flow-through of unbound lysate, the resin was washed 4× (50 ml each wash) using wash buffer (1 M KCl, 50 mM Hepes pH 7.4, 40 mM imidazole, 5% glycerol). Bound protein was then eluted using elution buffer (500 mM imidazole, 300 mM KCl, 50 mM Hepes pH 7.4, 5% glycerol) and then dialyzed into septin storage buffer (300 mM KCl, 50 mM Hepes pH 7.4, 1 mM BME, and 5% glycerol) for 24 h using two steps. Protein purity was determined via SDS-PAGE and protein concentration was determined using a Bradford assay.

Persistence length measurements were calculated from raw TIRF microscopy images of septin filaments seeded onto planar-supported lipid bilayers using a previously published MATLAB GUI method (Graham et al., 2014 (link)).