Figure 5. Computational simulation of... | Rockefeller University Press

Figure 5.

$Figure 5. Computational simulation of the initial KT encounter with spindle MTs reveals redundancy and synergy between multiple facilitating factors. (A) Diagram outlines computer simulation that recapitulates the initial KT–MT interaction in budding yeast (Gandhi et al., 2011). Upon CEN replication, KTs disassemble and CENs move away from a pole (Kitamura et al., 2007). KTs are then reassembled on CENs (green dots; noncaptured KTs). They are subsequently captured by MTs that extend from a spindle pole. We simulate how efficiently KTs are captured by MTs, i.e., how rapidly the fraction of noncaptured KTs decreases. The effects of the following three factors are analyzed (right): (1) KT-derived MTs, (2) KT diffusion, and (3) MT pivoting. (B) Computer simulation recapitulates kinetics of KT capture by spindle MTs. Black and red dots show the observed fraction of noncaptured KTs along the time course in Stu1 wild-type and Stu1-depleted cells, respectively (see Figs. 3 and S3 A; time 0 is as in Fig. 3, A and C; error bars are as in Fig. 4 D). Black and red lines show the results of spatiotemporal simulations (100,000×) in wild-type cells (a larger and smaller KT capture radius interchange) and in the absence of KT-derived MTs (always a smaller capture radius). A standard error of the fraction of noncaptured KTs is <0.001 (see the Spatiotemporal simulation of KT–MT interaction section of Materials and methods). A half-life obtained from each simulation is shown in each condition (a standard error is <0.3 s). (C) Kinetics of KT capture by spindle MTs in the absence of KT diffusion or MT pivoting. The decline of noncaptured KTs is plotted in each condition (red line) based on the spatiotemporal simulations. The decline in wild type is also shown as a control (black line). Time 0 is as in B. Errors in fractions and half-lives are as in B. (D) Kinetics of KT capture by spindle MTs in the absence of two factors. The decline of noncaptured KTs is plotted when two factors are missing (red line) based on the spatiotemporal simulations. The decline in wild type is also shown as a control (black line). Time 0 is as in B. Errors in fractions and half-lives are as in B. (E) Redundancy and synergy in facilitating KT capture by spindle MTs between KT-derived MTs, KT diffusion, and MT pivoting. Graph shows the half-life of noncaptured KTs (see B, C, and D) in the absence of each factor (bars in green, blue, and orange) or two factors (bars in magenta) relative to the half-life in the wild-type condition. An “additive effect” is estimated by adding a half-life relative to that in wild-type in the absence of each factor; for example, the half-life with no KT diffusion (blue bar) and with no KT-derived MT (orange bar) is 7.6 s and 17.5 s, respectively, relative to that in wild type; thus, the additive effect is 7.6 + 17.5 = 25.1 s. An arrow indicates the difference between an additive effect and an observed half-life without two factors; for example, when KT diffusion and KT-derived MTs are missing, the observed half-life is 36.3 s (relative to that in wild type), which is 11.2 s (36.3 – 25.1 = 11.2) more than the corresponding additive effect. When this difference shows a positive value, it is defined as a synergistic effect. Errors in half-lives are as in B.$

Computational simulation of the initial KT encounter with spindle MTs reveals redundancy and synergy between multiple facilitating factors. (A) Diagram outlines computer simulation that recapitulates the initial KT–MT interaction in budding yeast (Gandhi et al., 2011). Upon CEN replication, KTs disassemble and CENs move away from a pole (Kitamura et al., 2007). KTs are then reassembled on CENs (green dots; noncaptured KTs). They are subsequently captured by MTs that extend from a spindle pole. We simulate how efficiently KTs are captured by MTs, i.e., how rapidly the fraction of noncaptured KTs decreases. The effects of the following three factors are analyzed (right): (1) KT-derived MTs, (2) KT diffusion, and (3) MT pivoting. (B) Computer simulation recapitulates kinetics of KT capture by spindle MTs. Black and red dots show the observed fraction of noncaptured KTs along the time course in Stu1 wild-type and Stu1-depleted cells, respectively (see Figs. 3 and S3 A; time 0 is as in Fig. 3, A and C; error bars are as in Fig. 4 D). Black and red lines show the results of spatiotemporal simulations (100,000×) in wild-type cells (a larger and smaller KT capture radius interchange) and in the absence of KT-derived MTs (always a smaller capture radius). A standard error of the fraction of noncaptured KTs is <0.001 (see the Spatiotemporal simulation of KT–MT interaction section of Materials and methods). A half-life obtained from each simulation is shown in each condition (a standard error is <0.3 s). (C) Kinetics of KT capture by spindle MTs in the absence of KT diffusion or MT pivoting. The decline of noncaptured KTs is plotted in each condition (red line) based on the spatiotemporal simulations. The decline in wild type is also shown as a control (black line). Time 0 is as in B. Errors in fractions and half-lives are as in B. (D) Kinetics of KT capture by spindle MTs in the absence of two factors. The decline of noncaptured KTs is plotted when two factors are missing (red line) based on the spatiotemporal simulations. The decline in wild type is also shown as a control (black line). Time 0 is as in B. Errors in fractions and half-lives are as in B. (E) Redundancy and synergy in facilitating KT capture by spindle MTs between KT-derived MTs, KT diffusion, and MT pivoting. Graph shows the half-life of noncaptured KTs (see B, C, and D) in the absence of each factor (bars in green, blue, and orange) or two factors (bars in magenta) relative to the half-life in the wild-type condition. An “additive effect” is estimated by adding a half-life relative to that in wild-type in the absence of each factor; for example, the half-life with no KT diffusion (blue bar) and with no KT-derived MT (orange bar) is 7.6 s and 17.5 s, respectively, relative to that in wild type; thus, the additive effect is 7.6 + 17.5 = 25.1 s. An arrow indicates the difference between an additive effect and an observed half-life without two factors; for example, when KT diffusion and KT-derived MTs are missing, the observed half-life is 36.3 s (relative to that in wild type), which is 11.2 s (36.3 – 25.1 = 11.2) more than the corresponding additive effect. When this difference shows a positive value, it is defined as a synergistic effect. Errors in half-lives are as in B.