The first paper: Squished microtubules
So.. here's the first paper summary. I'm not all that good at writing them, so this one's a bit of a mess, and probably hard to understand... (Um... I certainly don't expect anyone to read this... In fact... just thinking about it, I'll probably start another LJ for these paper things. Still; any comments welcome if you're brave enough to continue!)
The paper is:
Microtubules are elements of a cell's cytoskeleton; they're long string-like polymers made up from tubulin dimers. One characteristic behaviour of microtubules is "dynamic instability": microtubules go through phases of growth and retraction, randomly transitioning between the two. Microtubule dynamic instability appears to be "used" as a form of stochastic searching, with microtubules extending in random directions for a period of time, then collapsing unless stabilised by contact with some target structure. Studies of the timing distribution for growth and retraction phases have shown that they are typically "gamma-distributed", which just means that very long and very short extension or retraction times are uncommon. This is a nice thing for stochastic search, as it means that the searching behaviour of the microtubules can potentially be "tuned" so that if a target is typically found within a certain range of distances, time isn't wasted by long, fruitless extensions or lots of extensions which are too small.
Most mathematical models of microtubule dynamics have assumed that the average concentration of unpolymerised tubulin is constant. This is fair enough for large volumes, however, for small volumes, microtubule polymerisation and depolymerisation can exert large effects on the local tubulin concentration. That's the situation the authors consider in this paper, finding that: (1) for a single microtubule, as the size of the compartment decreases, the time distribution for both extension and retraction moves away from exponential, towards gamma and (2) for multiple microtubules, as the compartment size decreases, the extension time distribution remains exponential, while the retraction distribution again approaches a gamma-form.
The reason for (1) is that, when an extension phase begins, the concentration of tubulin is typically high, meaning that the probability of a switch is low, and vice-versa for a retraction phase.
(2) is slightly harder to explain: it comes about because the rate of extension is much slower than the rate of retraction, which means that at any one time, more MTs are likely to be extending than retracting. This means that a slight decrease in concentration can be compensated for in a number of different ways (i.e. different numbers of MTs could start to retract), and this tends to smear out the correlations needed to form a gamma distribution, while a slight increase in concentration can be compensated for only by a few changes in dynamics (there are less retracting MTs), and as a result, concentration correlations following a decrease tend to have a longer timescale.
The paper is:
Microtubules are elements of a cell's cytoskeleton; they're long string-like polymers made up from tubulin dimers. One characteristic behaviour of microtubules is "dynamic instability": microtubules go through phases of growth and retraction, randomly transitioning between the two. Microtubule dynamic instability appears to be "used" as a form of stochastic searching, with microtubules extending in random directions for a period of time, then collapsing unless stabilised by contact with some target structure. Studies of the timing distribution for growth and retraction phases have shown that they are typically "gamma-distributed", which just means that very long and very short extension or retraction times are uncommon. This is a nice thing for stochastic search, as it means that the searching behaviour of the microtubules can potentially be "tuned" so that if a target is typically found within a certain range of distances, time isn't wasted by long, fruitless extensions or lots of extensions which are too small.
Most mathematical models of microtubule dynamics have assumed that the average concentration of unpolymerised tubulin is constant. This is fair enough for large volumes, however, for small volumes, microtubule polymerisation and depolymerisation can exert large effects on the local tubulin concentration. That's the situation the authors consider in this paper, finding that: (1) for a single microtubule, as the size of the compartment decreases, the time distribution for both extension and retraction moves away from exponential, towards gamma and (2) for multiple microtubules, as the compartment size decreases, the extension time distribution remains exponential, while the retraction distribution again approaches a gamma-form.
The reason for (1) is that, when an extension phase begins, the concentration of tubulin is typically high, meaning that the probability of a switch is low, and vice-versa for a retraction phase.
(2) is slightly harder to explain: it comes about because the rate of extension is much slower than the rate of retraction, which means that at any one time, more MTs are likely to be extending than retracting. This means that a slight decrease in concentration can be compensated for in a number of different ways (i.e. different numbers of MTs could start to retract), and this tends to smear out the correlations needed to form a gamma distribution, while a slight increase in concentration can be compensated for only by a few changes in dynamics (there are less retracting MTs), and as a result, concentration correlations following a decrease tend to have a longer timescale.