Antenna mechanism of length control of actin cables

Actin cables are linear cytoskeletal structures that serve as tracks for myosin-based intracellular transport of vesicles and organelles in both yeast and mammalian cells. In a yeast cell undergoing budding, cables are in constant dynamic turnover yet some cables grow from the bud neck toward the back of the mother cell until their length roughly equals the diameter of the mother cell. This raises the question: how is the length of these cables controlled? Here we describe a novel molecular mechanism for cable length control inspired by recent experimental observations in cells. This antenna mechanism involves three key proteins: formins, which polymerize actin, Smy1 proteins, which bind formins and inhibit actin polymerization, and myosin motors, which deliver Smy1 to formins, leading to a length-dependent actin polymerization rate. We compute the probability distribution of cable lengths as a function of several experimentally tuneable parameters such as the formin-binding affinity of Smy1 and the concentration of myosin motors delivering Smy1. These results provide testable predictions of the antenna mechanism of actin-cable length control

Design Principles of Length Control of Cytoskeletal Structures

Cells contain elaborate and interconnected networks of protein polymers which make up the cytoskeleton. The cytoskeleton governs the internal positioning and movement of vesicles and organelles, and controls dynamic changes in cell polarity, shape and movement. Many of these processes require tight control of the size and shape of cytoskeletal structures, which is achieved despite rapid turnover of their molecular components. Here we review mechanisms by which cells control the size of filamentous cytoskeletal structures from the point of view of simple quantitative models that take into account stochastic dynamics of their assembly and disassembly. Significantly, these models make experimentally testable predictions that distinguish different mechanisms of length-control. While the primary focus of this review is on cytoskeletal structures, we believe that the broader principles and mechanisms discussed herein will apply to a range of other subcellular structures whose sizes are tightly controlled and are linked to their functions.Comment: 61 pages, 11 figure

Design Principles of Length Control of Cytoskeletal Structures

Cells contain elaborate and interconnected networks of protein polymers, which make up the cytoskeleton. The cytoskeleton governs the internal positioning and movement of vesicles and organelles and controls dynamic changes in cell polarity, shape, and movement. Many of these processes require tight control of the size and shape of cytoskeletal structures, which is achieved despite rapid turnover of their molecular components. Here we review mechanisms by which cells control the size of filamentous cytoskeletal structures, from the point of view of simple quantitative models that take into account stochastic dynamics of their assembly and disassembly. Significantly, these models make experimentally testable predictions that distinguish different mechanisms of length control. Although the primary focus of this review is on cytoskeletal structures, we believe that the broader principles and mechanisms discussed herein will apply to a range of other subcellular structures whose sizes are tightly controlled and are linked to their functions

The antenna model of actin-cable length control.

<p>(A) Smy1 proteins (red) are delivered to the formin (green) at the barbed end of the actin cable by myosin motors (yellow). Smy1 inhibits the polymerization activity of formins upon binding. The directed transport of Smy1 by myosin motors towards the formins leads to a length dependent average assembly rate <i>k</i>_<i>on</i>(<i>l</i>) = <i>wl</i>; the longer the cables, the larger the number of Smy1 proteins delivered, and consequently, smaller the average assembly rate. (B) A schematic showing all possible transitions between different chemical states in the antenna model. An uninhibited formin assembles cables at a constant rate <i>r</i>. Smy1+myosin complexes bind to formin at a rate <i>k</i>_<i>on</i>(<i>l</i>) = <i>wl</i> where, <i>l</i> is the length of the cable. Smy1 proteins detach from the formin with a rate <i>k</i>_<i>off</i>. Regardless of the state of the formin, i.e. whether it has Smy1 bound or not, the filament is disassembled by removal of subunits at a rate <i>d</i>.</p

The mean and variance of the cable length can be independently controlled within the antenna model.

<p>The same mean cable length (5 microns), is obtained either by a combination of a large Smy1-formin binding affinity and a small Smy1 concentration (parametrized by <i>k</i>_<i>off</i> and <i>w</i> respectively), or by a weak affinity and large concentration. The distribution in the weak affinity case (blue) is sharper than in the strong affinity case (red). Parameters used for the polymerization and depolymerisation rate were <i>r</i> = 370 s^-1, <i>d</i> = 45 s^-1, <i>k</i>_<i>off</i> = 0.5 s^-1(red) and 50 s^-1(blue); for chosen values of <i>k</i>_<i>off</i>, the rate <i>w</i> was calculated from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004160#pcbi.1004160.e005" target="_blank">Eq 1</a> for the mean length. Inset: Square of the coefficient of variation of the cable length distribution (measured by variance/mean²) decreases with <i>k</i>_<i>off</i> when the mean length is kept fixed by adjusting <i>w</i>. Parameters used for the simulations (in black line) were <i>r</i> = 370 s^-1, <i>d</i> = 45 s^-1, <i>w</i> = 0.004 s^-1 and <i>k</i>_<i>off</i> was varied from 0.5–20 s^-1 in steps of 0.125 s^-1.</p

Variance in the cable length distribution.

<p>(A) With decreasing Smy1 binding affinity (parametrized by the off rate <i>k</i>_<i>off</i>) the variance of the cable length distribution slightly increases. The black line was obtained by computing the variance of the cable length distribution by Gillespie simulations for <i>w</i> = 0.004 s^-1 and <i>k</i>_<i>off</i> values 0.5–5.5 s^-1 with a spacing of 0.0625 s^-1. The inset shows that the noise, as measured by the square of coefficient of variation, decreases. (B) With increasing concentration of Smy1 (parametrized by the rate <i>w</i>) the variance increases while the noise (as shown in the inset) decreases. The black line was obtained from simulations using <i>k</i>_<i>off</i> = 1 s^-1 and <i>w</i> = 0.0008–0.01 s^-1 with a spacing of 0.000125 s^-1. The parameters <i>r</i> = 370 s^-1 and <i>d</i> = 45 s^-1 are our best estimates for yeast cells (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004160#sec009" target="_blank">Methods</a>) also used in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004160#pcbi.1004160.g003" target="_blank">Fig 3</a>.</p

Steady state cable length distributions depend on Smy1 concentration and binding affinity to formins.

<p>(A) With decreasing Smy1 binding affinity (parametrized by the off rate <i>k</i>_<i>off</i>) to formins the mean length increases. The inset compares simulation results for the mean cable length and the analytic formula (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004160#pcbi.1004160.e005" target="_blank">Eq 1</a>), in black line. (B) With increasing Smy1 concentration (parametrized by the rate <i>w</i>) the average length of the cable decreases. Inset shows comparison of simulation results with analytic theory (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004160#pcbi.1004160.e005" target="_blank">Eq 1</a>), in black line. The parameter values used in both plots for the polymerization and depolymerization rate are: r = 370 s^-1 and d = 45 s^-1 (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004160#sec009" target="_blank">Methods</a>). Also in (A) we set <i>w</i> = 0.004 s^-1 while in (B) we used <i>k</i>_<i>off</i> = 1 s^-1, which are values estimated for these two parameters based on in vivo experiments. In both plots, the blue curves are for estimated parameters for yeast cells.</p