Difference between revisions of "Homework/2"
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#Holy and Leibler (1994) estimate that the time wasted by a microtubule that nucleates in the wrong direction (away from a kinetochore) is, on average, $R/(r\delta)$ where $R$ is the radius of the cell, $r$ is the rate at which monomers both attach and detach at the MT tip and $\delta$ is the size of a monomer. If a MT starts at the cell centre with a single monomer and turns around whenever it reaches the cell boundary, derive the estimate above using the theory for a diffusing particle discussed in class. | #Holy and Leibler (1994) estimate that the time wasted by a microtubule that nucleates in the wrong direction (away from a kinetochore) is, on average, $R/(r\delta)$ where $R$ is the radius of the cell, $r$ is the rate at which monomers both attach and detach at the MT tip and $\delta$ is the size of a monomer. If a MT starts at the cell centre with a single monomer and turns around whenever it reaches the cell boundary, derive the estimate above using the theory for a diffusing particle discussed in class. | ||
| − | #Using the formalism discussed in class (see [[Media:MTCenteringForce.pdf|slides]]), calculate the net force generated by a MT aster in which motors pull on all MTs along their entire length rather than just at the tip. Is the | + | #Using the formalism discussed in class (see [[Media:MTCenteringForce.pdf|slides]]), calculate the net force generated by a MT aster in which motors pull on all MTs along their entire length rather than just at the tip. Is the centre a stable steady state for the aster? |
| − | # | + | #When an elastic filament is embedded in a surrounding elastic medium, the equation for the deflection of the filament is $$By^{(iv)} + F y'' + \alpha y = 0$$ where $\alpha$ is proportional to the stiffness of the medium. Microtubules embedded within the actin network of a cell are thought to behave this way (Brangwynne et al. 2006). Show that, for a filament pinned (but not clamped) at both ends, with a force $F$ less than $2\sqrt{\alpha B}$, the only solution is $y(x)=0$. With the given boundary conditions, under what condition will the filament buckle at $F=2\sqrt{\alpha B}$? |
Revision as of 23:24, 27 October 2013
- Holy and Leibler (1994) estimate that the time wasted by a microtubule that nucleates in the wrong direction (away from a kinetochore) is, on average, $R/(r\delta)$ where $R$ is the radius of the cell, $r$ is the rate at which monomers both attach and detach at the MT tip and $\delta$ is the size of a monomer. If a MT starts at the cell centre with a single monomer and turns around whenever it reaches the cell boundary, derive the estimate above using the theory for a diffusing particle discussed in class.
- Using the formalism discussed in class (see slides), calculate the net force generated by a MT aster in which motors pull on all MTs along their entire length rather than just at the tip. Is the centre a stable steady state for the aster?
- When an elastic filament is embedded in a surrounding elastic medium, the equation for the deflection of the filament is $$By^{(iv)} + F y'' + \alpha y = 0$$ where $\alpha$ is proportional to the stiffness of the medium. Microtubules embedded within the actin network of a cell are thought to behave this way (Brangwynne et al. 2006). Show that, for a filament pinned (but not clamped) at both ends, with a force $F$ less than $2\sqrt{\alpha B}$, the only solution is $y(x)=0$. With the given boundary conditions, under what condition will the filament buckle at $F=2\sqrt{\alpha B}$?
