PMC

Ai: The oscillators with voltage trajectories and and phase difference determine the membrane potential at the ends of a cable with electrotonic length . Aii: The interaction function gives the phase shift of oscillator A as a function of . This interaction function is shifted along the -axis by the parameters and , which capture the oscillator and cable properties, respectively. Aiii: The stable phase-locked solution is determined by and and is either at (e.g. for the solid curve) or at (e.g. for the dash-dotted curve). Aiv: The stable phase-locked solution as a function of . The value of uniquely determines where the in-phase (black solid line) or the anti-phase solution (red dotted line) is stable, given a fixed value of . B: as a function of the electrotonic distance between the oscillators, ms and ms (dotted line in panel D). For illustrative purposes we chose so that the stable in-phase and anti-phase solutions are given by the white and gray areas, respectively. C: as a function of the membrane resistance for cable diameter m, distance between the oscillators 1000 m, membrane capacitance F/cm, intracellular resistivity kcm and oscillator period ms. D: as a function of the oscillator frequency . The distance between the oscillators is (dotted line in B), ms.

The oscillations are generated by interactions between and (see ). A: Voltage trajectory (blue) and phase response function (black) of the oscillator. B: Corresponding bifurcation diagrams showing the stable (solid black lines) and unstable (dashed red lines) phase-locked solutions as a function of . The bifurcation diagram is shown for a passive cable (top), a cable with a regenerative current (middle), and a cable with a restorative current (bottom). The restorative current and regenerative current (described in ) are inserted in the cable with relative densities of and , respectively. Linearizing these currents around mV gives the parameters , and ms for the regenerative current, and , and ms for the restorative current. The membrane time constant of the connecting dendrite is ms. Cross marks in the bifurcation diagrams give the stable phase difference determined with numerical simulations using S cm, ms, and is mV, mV and mV, respectively for the three panels, so that the cable's resting potential is mV. Note that the numerical simulations use the original (i.e. not the linearized) active currents in the connecting cable.

The three panels A-B-C show triangular functions with different skewness with their peaks at where is a phase shift that results from the cable coupling. The oscillators are identical so that . A: Right-skewed with (solid black line) plotted from left to right for three values of together with the corresponding (dashed blue line). Below each graph is plotted (green lines) with the stable (black dots) and unstable (red dots) phase-locked solutions. The lower right panel shows the bifurcation diagram with the stable (solid black line) and unstable (dotted red line) phase-locked solutions. The right-skewed yields gradual transitions between the in-phase and anti-phase solutions. B: Symmetrical with yields abrupt transitions between in-phase and anti-phase solutions. C: Left-skewed with yields bistable regions where both the in-phase and the anti-phase solution are stable.

The oscillators (described in ) are coupled via a passive cable of electrotonic length , ms. A: Voltage trajectory (blue) and phase response function (black) of the Morris-Lecar type II oscillator, period ms. B: Shape of for (solid curve), (dashed curve) and (dash-dotted curve). The functions have been rescaled and aligned in order to show the different degrees of skewness. C: Bifurcation diagram showing the stable (solid black line) and unstable (dashed red line) phase-locked solutions as a function of . Cross marks give the stable phase difference determined with numerical simulations using S cm with ms, and mV. D: The middle two panels show simulations of the phase difference dynamics (red curves) for (top) and (bottom) with S cm. Space-time plots of the membrane potential along the dendritic cable cable are plotted for the first 200 ms (left) and for the final 200 ms (right) of the two simulations.

Bistable conduction in the cable equation of the HH model. (A and B) Stimulus-dependent fast (A) and slow (B) conduction in the same cable. The stimulus in (A) is 200 μA/cm² with a 0.5 ms duration while the stimulus in (B) is 5 μA/cm² with a 20 ms duration. The stimulus is applied to the first 0.225 cm of the cable. Insets show action potentials from the middle of the cable for the two cases. G_Na = 95 mS/cm² and G_Ca = 0 mS/cm². (C) Phase diagram showing conduction behaviors in the G_Na and G_Ca plane. Regions I and II are monostable fast conduction, region III is monostable slow conduction, region IV is conduction failure, and the gray region is bistable conduction. The phase diagram is obtained using the strong and weak stimulus protocols as in (A and B). (D) CV (c) versus G_Na for G_Ca = 3 mS/cm². Solid circles are stable conduction and open circles are unstable conduction (the saddle points). The saddle points are determined by a stimulus very close to the critical stimulus (see A for an example). The gray marks the bistable region. (E) Same as (D) but for G_Ca = 0. To see this figure in color, go online.

Oscillatory behaviors induced by a repolarization gradient. (a) The b_H-b_L phase plane showing excitation behaviors. γ=1. The typical behaviors of different regions are shown in (b)–(f). The black dashed curve separating the green and yellow region is the Hopf bifurcation line obtained via bifurcation analysis. Panels (b)–(f) are space-time plots of u(x,t) for different b_H values marked on the vertical line on panel (a). b_L = 1.5. The upper magenta traces are u(x,t) in the b_H region. (b) b_H = 20. Stable steady state. (c) b_H = 11. Regional oscillations without excitations. (d) b_H = 8. Oscillations leading to propagating excitations. The spontaneous excitations are marked by the red ”*”. (e) b_H = 7.0767. Transient excitations. (f) b_H = 6. Normal repolarization in the whole cable.

KEL1 and KEL2 function with BUD14 to regulate BNR1. A, deletions of KEL1 and/or KEL2 do not alter Bni1 or Bnr1 localization in cells. Strains with the genotypes indicated and expressing integrated Bnr1-RFP and Bni1–3×GFP were imaged. B, kel1Δ and kel2Δ, like bud14Δ, suppress the growth defects of bnr1ΔDAD. Strains were grown to log phase, serially diluted, spotted on YPD plates, and compared for growth at 25 and 37 °C. C, representative images of the same strains as in B at different stages of the cell cycle. Cells were grown to log phase, fixed, and stained with Alexa 488 phalloidin. D, quantification of bent cable phenotype (as in B). Data averaged from two experiments (scoring >100 cells per strain per experiment). Error bars represent S.D. E, example images from D. Yellow arrows indicate the presence of kinked cables in these strains.

Effects of I_Na kinetics on bistable conduction. (A) Conduction velocity c versus calculated from the analytical result . K and S mark the saddle-node bifurcation points, and F marks the point of conduction failure of the slow conduction. Solid lines are stable conduction and dashed line is unstable conduction. Gray marks the bistable conduction region. , mV, mV, , , mV. We used for . (B) Conduction behaviors versus and obtained from the analytical result . K, F, and S are the boundaries as marked on (A). The gray region is the bistable region. The red regions are monostable fast conduction, the blue region is monostable slow conduction, and the blank region is conduction failure. The parameters are the same as for (A). (C) Conduction behaviors versus and from the simulation of the cable equation using the HH model. The gray region is the bistable conduction region. G_Na = 100 mS/cm² and G_Ca = 0. (D) Conduction behaviors versus and from the simulation of the cable equation using the HH model. Other parameters are the same as for (C). The phase diagrams in (C and D) are obtained and colored the same way as for C. To see this figure in color, go online.

Defects in actin cable morphology and transport of secretory vesicles in kel1Δ and kel2Δ mutants. A, cells were grown to log phase, fixed, and stained with Alexa 488 phalloidin. Yellow arrows highlight some of the “bent” cables in mutant cells. B, quantification of cable phenotype. Cables exhibiting a change in direction of at least 75 degrees at the cell cortex were scored as bent. Data averaged from two experiments (scoring >100 cells per strain in each experiment). C, comparison of GFP-Sec4 secretory vesicle movements in wild type, kel1Δ, kel2Δ, and bud14Δ cells (> 200 vesicles per strain). Vesicle movements classified as “direct” were rapid anterograde movements toward the neck. Movements classified as “circuitous” were (i) stalled, (ii) retrograde (away from the bud), or (iii) highly angled off the mother-bud axis. D, representative images of wild type, bud14Δ, kel1Δ, and kel2Δ cells treated with LatA for 60 s, fixed, and stained with Alexa 488 phalloidin. E, graphs show the average from two experiments as in D, with >100 cells scored per strain per experiment. Error bars represent S.D.

Roles for Kel1, Kel2, and Bud14 in cytokinesis. A and B, differential interference contrast (DIC) imaging and quantification of chained phenotype in bni1Δ, kel1Δbni1Δ, kel2Δbni1Δ, and bud14Δbni1Δ cells. Data averaged from two experiments, scoring >200 cells per strain in each experiment. Error bars represent S.D. C, cell images of chitin defects. Strains were grown to log phase, fixed, and stained with Calcofluor white to visualize chitin. D, quantification of chitin defects. White bars are the percentage of cells with normal chitin rings, resembling those in wild type cells. Gray bars are the percentage of cells with abnormal chitin rings, which are much thicker than in wild type cells, e.g. yellow arrows in differential interference contrast images. E, ultrastructural analysis of septum defects. Cells were grown to log phase, fixed, thin sectioned, stained by the Thiery method, and visualized by electron microscopy. Representative images are shown for each strain.

Endocytosis is required for wound edge actin remodeling and wound closure. (A) Time-lapse live imaging of an embryo expressing Dynamin-GFP (Dyn-GFP, green) and mCherry-Moesin (magenta). At 2 min and 30 s, Dynamin-GFP and F-actin colocalize at puncta on the wound edge, at (yellow arrowheads) and also outside (blue arrowheads) former-TCJs. The Dynamin-GFP puncta at former-TCJs were relatively stable and stationary, whereas those at other sites were more transient and mobile. See also Video 4. (B) Time-lapse live imaging of mCherry-Moesin, expressed in control and shi² embryos (top and middle rows, respectively), and a shi² embryo expressing Dynamin-GFP (shi² + Dyn-GFP, bottom row). Representative actin puncta (arrowheads), cables (single arrows), and protrusions (double arrows) are indicated. (C) Quantitation of wound edge actin puncta, cable, protrusions, and wound closure (left to right, respectively) in control embryos, shi² embryos, and shi² embryos expressing Dynamin-GFP. Note that puncta were quantified only at 5 min because at later time points, they are obscured by the actin cable and protrusions (see also ). n = 12–21 embryos (actin puncta, cable, and protrusions) or 15–16 (wound closure). For the measurement of wound closure, wound area was normalized against the value at 5 min after wounding. The table at the top summarizes the results of statistical analyses of the data. (D) Time-lapse live imaging of a control or shi² mutant embryo expressing Clathrin light chain-GFP (CLC-GFP; green) and mCherry-Moesin (magenta). Merged images at the right show the wound edge around the arrowheads in the 10:00 images. Note the punctate accumulations of Clathrin-GFP at the wound edge in the control but not in shi² embryos (arrowheads). (E, top) A more detailed analysis of the formation of actin structures in control or shi² embryos in the early phase of wound closure. Here, F-actin was visualized using GFP-Moesin. The results confirm the actin remodeling defects observed for shi² embryos in the longer term analysis in B and C. n = 3–4 embryos. (bottom) Quantitation of actin puncta, cable, and protrusions in control or Rab5DN-expressing embryos. F-actin was visualized using GFP-Moesin. n = 6–8 embryos. Photographs at the right are representative images at 2 min and 30 s after wounding, of the embryos of indicated genotype. See also Videos 5 and 6. (F) Quantitation of wound closure control or Rab5DN-expressing embryos, performed as in C, rightmost graph. n = 10–11. Time points indicate time after wounding (minutes and seconds). Bars, 10 µm. All experiments involving shi² were performed at 30°C, the restrictive temperature of this mutant. Bars in column scatter plot (C, left) indicate means ± SEM of all plotted values. Line graphs in C, E, and F show means ± SEM of the data.

A) Junction of the AS2 helix and the first methylation helix (MH1) of the kinase control domain. Residue positions for AS2 are shaded as in Figures and . The N-terminal (MH1) and C-terminal (MH2) methylation helices form a 4-helix coiled-coil in the Tsr dimer () (see ), with packing interactions mediated by a-d heptad repeats (; ). Left: The heptad packing residues of MH1 are four residues out of phase with those of AS2. Right: Helical wheels of the Tsr subunits at the AS2/MH1 junction, showing the alignment of residues in the AS2 helices as they emerge from a stable x-da bundle. The x positions (not highlighted) are connected by a dashed line. The a and d positions of the MH1 helices are nearly 180° out-of-phase, which should destabilize the methylation helices and packing interactions.
B) A modulated dynamics model of HAMP signaling. The model proposes that the x-da HAMP bundle is important to both the kinase-activating and kinase-deactivating signaling states because it controls the range of inter-subunit motions of the kinase control domain in the Tsr dimer. However, the dynamic states of the x-da bundle and methylation helices are oppositionally coupled through an out-of-register helical phase relationship; see (A). An unstable x-da bundle allows inter-subunit interactions of the methylation helices. Conversely, a stable x-da bundle destabilizes the methylation helix bundle. The structural interactions between AS2 and MH1 helices are bi-directional. Changes in methylation state modulate stability of the methylation region, which in turn impacts stability of the HAMP bundle. Importantly, this model predicts that attractant stimuli suppress CheA activity by enhancing stability of the HAMP bundle, whereas repellent stimuli should destabilize the bundle. These stimulus-induced changes in HAMP stability could be triggered by small vertical displacements of the transmembrane segments (TM2) adjoining the AS1 helices. The TM2/AS1 connection could act like a control cable to adjust structural tension on the HAMP domain, altering its dynamic properties. See text for additional explanation.

(a) Block diagram of the imaging apparatus. 780 nm excitation light (red arrow) from a Ti:sapphire laser is routed to a Bio-Rad MRC600 scanbox, which raster scans the beam through the objective lens and across the sample. The sample consists of an aqueous suspension of GUVs (red circles) between two glass coverslips (dark blue) and sealed from the bath water by clear nail polish and Fomblin perfluorinated vacuum grease. The entire sample and part of the objective lens are contained within the sample bath and submerged in water as shown. Two heaters (orange) and two RTD thermometers (one for each heater) are connected to the CryCon model 32B temperature controller, which is remotely operated by an RS232 connection to a PC. The excitation light is separated from the fluorescence light (orange and green arrows, denoting two different fluorophores) by dichroic mirror 1, and the fluorescence emissions are then separated by color by dichroic mirror 2 before being collected by the PMTs. (b) Close-up of the sample bath. The components are labeled i–xi: (i) Pt100 RTD, (ii) copper sample holder, (iii) small (loop 2) cable immersion heater, (iv) Teflon cup (purple), (v) large (loop 1) bath water heater, (vi) Teflon rod for the sample holder, (vii) o-ring seal (black) between objective lens and Teflon cup, (viii) foam insulation (blue), (ix) objective lens (UPlan Apochromat 60×, Olympus), (x) thermal isolator for objective lens, and (xi) GUV (red circles) samples between two round coverslips (dark blue).

A) Transcript elongation. Panels (1–2) are modified from. The rDNA and rRNA segments are color-coded: red for 5’ETS and SSU rRNA/DNA, green for LSU rRNA/DNA.
Panel 1: EM of a spread of yeast rDNA during transcription. Note the horizontal rDNA axis and the lateral emergence of transcripts. A SSU terminal knob is circled in red, and a putative LSU knob is circled in green. ITS1 is indicated as (a). The removal of SSU knobs occurs at (b).
Panel 2: Once transcription reaches ITS1, SSU pre-knobs (pink) and knobs (red) appear. They persist until transcription has reached into LSU sequences.
Panel 3: Since cleavage at ITS1 is delayed well beyond the point at which the 3’ extremity of the SSU rRNA coding sequences has been reached, we propose that removal requires transfer to the outer layer. This could allow them to undergo further maturation and, likely, to be cleaved by Rcl1 or Utp24. Further elongation, processing, and formation of particulate intermediates would also occur along the outer layer. Final cleavage occurs at site B_o near the 3’ extremity.
B) Suggested sequential processing of rRNA. See the text for a detailed description of these T-Diagrams. In frames (2a) and (3), the interruption of the perimeter of the large red circles designates progressive release of AFs. AFs that are required for both subunits are not included. The solid circular symbols imply that the indicated AFs are associated with maturing subunits. When not associated, the symbols have a white center.
C) Vectorial 2-Phase Partitioning. Schematic of the relocation of SSU-F AFs and LSU-F AFs. The upper two rows pertain to SSU maturation and the lower two rows pertain to LSU maturation. We consider the localization of these AFs after cycloheximide treatment to be an indication of the phase in which they are most stable (S). By contrast, once they become associated with nascent transcripts, they localize to phases in which they are relatively unstable (U).
D) Energy Relations. During a single cycle, the present observations suggest that 5’-ETS AFs and SSU-F AFs begin in the outer layer and relocate to the inner layer as they load onto nascent rRNA. Phase transfer then allows them to return to the outer layer. This is energetically downhill. Reciprocally, the LSU-F AFs (green line) begin in the inner layer, but shift to the outer layer, perhaps in conjunction with transfer of SSU-Fs. At the end of the cycle, their downhill return to the inner layer resets the system for repeated use. The vertical arrows at the left designate the energy relations. Coupling of inner-to-outer flux of both SSU precursors and LSU-F AFs (states 2b/3) could make their reciprocal flux energetically neutral.
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