Role of cross-linking proteins and angular diffusion in the formation of microtubule bundles

Za vrijeme mitoze, mikrotubuli tvore diobeno vreteno čija je biološka uloga razdvajanje genetskog materijala. U stanicama kvasca diobeno vreteno ima oblik ravnog štapa kojeg sačinjavaju mikrotubuli koji rastu iz dva pola, a povezani su vezivnim proteinima. Mikrotubuli su organizirani u svežnjeve koji mogu biti paralelni, ako oba mikrotubula rastu iz istog pola, ili antiparalelni ako mikrotubuli rastu iz različitih polova, a naš cilj je razumijevanje dinamike nastanka ovakve strukture. Model uključuje kutno gibanje mikrotubula oko polova diobenog vretena pokretano termalnim silama i elastičnim silama koje proizvode vezivni proteini koji se mogu vezati za mikrotubule, odvezivati natrag u nukleoplazmu, te kad su vezani se mogu gibati duž mikrotubula. Rješenja modela pokazuju da mikrotubuli nasumičnim gibanjem pretražuju prostor, a kad dođu u blizinu svog para povezuju ih vezivni proteini koji efektivno proizvode kratkodosežne interakcije između mikrotubula. Paralelni svežnjevi mogu nastati djelovanjem pasivnih vezivnih proteina ili motora koji se kreću prema plus kraju mikrotubula, a za nastajanje antiparalelnih mikrotubula su potrebni motori koji se kreću prema minus kraju mikrotubula. Model predviđa očekivano vrijeme nastajanja svežnjeva, koje se slaže s eksperimentalnim podacima. Također, u slučaju antiparalelnog vezanja, model predviđa da se mikrotubuli koji dođu u kontakt gibaju jedan duž drugog brzinom motora, što je također potvrđeno i u eksperimentima. Zaključujemo da su glavni čimbenici u procesu nastajanja svežnjeva mikrotubula nasumično gibanje mikrotubula oko polova koje ima omogućava da dođu u kontakt i kratkodosežne interakcije između njih uzrokovane vezivnim proteinima.During mitosis, microtubules form a spindle, which is responsible for the segregation of chromosomes. In yeast cells, the spindle has a rod-like structure and is made of microtubules emanating from two poles connected by cross-linking proteins. Microtubules self-organize into parallel or antiparallel bundles, depending on whether they grow from the same or two different poles and our goal here is understanding how such structures form. Our model includes thermally driven angular pivoting of microtubules around the poles and elastic forces between them mediated by crosslinking proteins, which can detach to and detach from microtubules, as well as move along them. The solutions of our model imply that the random motion of the microtubules allows them to find a their pair, while the short-range interactions caused by the cross-linking proteins align them into bundles. Parallel bundling can occur in the presence of either passive crosslinkers or plus-end directed motors, while the formation of antiparallel bundles requires minus-end directed motors. The model predicts the average bundling time, which is in agreement with our experimental measurements. Additionally, for the case of antiparallel bundle formation, the model predicts that the velocity of the microtubules gliding along each other is the same as the velocity at which the motors move along the microtubules, and this was also confirmed experimentally. In conclusion, the main contributors to the formation of microtubule bundles are angular diffusion of microtubules around the poles allowing them to come into contact and shortrange forces caused by cross-linking proteins that align them

Role of cross-linking proteins and angular diffusion in the formation of microtubule bundles

Za vrijeme mitoze, mikrotubuli tvore diobeno vreteno čija je biološka uloga razdvajanje genetskog materijala. U stanicama kvasca diobeno vreteno ima oblik ravnog štapa kojeg sačinjavaju mikrotubuli koji rastu iz dva pola, a povezani su vezivnim proteinima. Mikrotubuli su organizirani u svežnjeve koji mogu biti paralelni, ako oba mikrotubula rastu iz istog pola, ili antiparalelni ako mikrotubuli rastu iz različitih polova, a naš cilj je razumijevanje dinamike nastanka ovakve strukture. Model uključuje kutno gibanje mikrotubula oko polova diobenog vretena pokretano termalnim silama i elastičnim silama koje proizvode vezivni proteini koji se mogu vezati za mikrotubule, odvezivati natrag u nukleoplazmu, te kad su vezani se mogu gibati duž mikrotubula. Rješenja modela pokazuju da mikrotubuli nasumičnim gibanjem pretražuju prostor, a kad dođu u blizinu svog para povezuju ih vezivni proteini koji efektivno proizvode kratkodosežne interakcije između mikrotubula. Paralelni svežnjevi mogu nastati djelovanjem pasivnih vezivnih proteina ili motora koji se kreću prema plus kraju mikrotubula, a za nastajanje antiparalelnih mikrotubula su potrebni motori koji se kreću prema minus kraju mikrotubula. Model predviđa očekivano vrijeme nastajanja svežnjeva, koje se slaže s eksperimentalnim podacima. Također, u slučaju antiparalelnog vezanja, model predviđa da se mikrotubuli koji dođu u kontakt gibaju jedan duž drugog brzinom motora, što je također potvrđeno i u eksperimentima. Zaključujemo da su glavni čimbenici u procesu nastajanja svežnjeva mikrotubula nasumično gibanje mikrotubula oko polova koje ima omogućava da dođu u kontakt i kratkodosežne interakcije između njih uzrokovane vezivnim proteinima.During mitosis, microtubules form a spindle, which is responsible for the segregation of chromosomes. In yeast cells, the spindle has a rod-like structure and is made of microtubules emanating from two poles connected by cross-linking proteins. Microtubules self-organize into parallel or antiparallel bundles, depending on whether they grow from the same or two different poles and our goal here is understanding how such structures form. Our model includes thermally driven angular pivoting of microtubules around the poles and elastic forces between them mediated by crosslinking proteins, which can detach to and detach from microtubules, as well as move along them. The solutions of our model imply that the random motion of the microtubules allows them to find a their pair, while the short-range interactions caused by the cross-linking proteins align them into bundles. Parallel bundling can occur in the presence of either passive crosslinkers or plus-end directed motors, while the formation of antiparallel bundles requires minus-end directed motors. The model predicts the average bundling time, which is in agreement with our experimental measurements. Additionally, for the case of antiparallel bundle formation, the model predicts that the velocity of the microtubules gliding along each other is the same as the velocity at which the motors move along the microtubules, and this was also confirmed experimentally. In conclusion, the main contributors to the formation of microtubule bundles are angular diffusion of microtubules around the poles allowing them to come into contact and shortrange forces caused by cross-linking proteins that align them

Role of cross-linking proteins and angular diffusion in the formation of microtubule bundles

Za vrijeme mitoze, mikrotubuli tvore diobeno vreteno čija je biološka uloga razdvajanje genetskog materijala. U stanicama kvasca diobeno vreteno ima oblik ravnog štapa kojeg sačinjavaju mikrotubuli koji rastu iz dva pola, a povezani su vezivnim proteinima. Mikrotubuli su organizirani u svežnjeve koji mogu biti paralelni, ako oba mikrotubula rastu iz istog pola, ili antiparalelni ako mikrotubuli rastu iz različitih polova, a naš cilj je razumijevanje dinamike nastanka ovakve strukture. Model uključuje kutno gibanje mikrotubula oko polova diobenog vretena pokretano termalnim silama i elastičnim silama koje proizvode vezivni proteini koji se mogu vezati za mikrotubule, odvezivati natrag u nukleoplazmu, te kad su vezani se mogu gibati duž mikrotubula. Rješenja modela pokazuju da mikrotubuli nasumičnim gibanjem pretražuju prostor, a kad dođu u blizinu svog para povezuju ih vezivni proteini koji efektivno proizvode kratkodosežne interakcije između mikrotubula. Paralelni svežnjevi mogu nastati djelovanjem pasivnih vezivnih proteina ili motora koji se kreću prema plus kraju mikrotubula, a za nastajanje antiparalelnih mikrotubula su potrebni motori koji se kreću prema minus kraju mikrotubula. Model predviđa očekivano vrijeme nastajanja svežnjeva, koje se slaže s eksperimentalnim podacima. Također, u slučaju antiparalelnog vezanja, model predviđa da se mikrotubuli koji dođu u kontakt gibaju jedan duž drugog brzinom motora, što je također potvrđeno i u eksperimentima. Zaključujemo da su glavni čimbenici u procesu nastajanja svežnjeva mikrotubula nasumično gibanje mikrotubula oko polova koje ima omogućava da dođu u kontakt i kratkodosežne interakcije između njih uzrokovane vezivnim proteinima.During mitosis, microtubules form a spindle, which is responsible for the segregation of chromosomes. In yeast cells, the spindle has a rod-like structure and is made of microtubules emanating from two poles connected by cross-linking proteins. Microtubules self-organize into parallel or antiparallel bundles, depending on whether they grow from the same or two different poles and our goal here is understanding how such structures form. Our model includes thermally driven angular pivoting of microtubules around the poles and elastic forces between them mediated by crosslinking proteins, which can detach to and detach from microtubules, as well as move along them. The solutions of our model imply that the random motion of the microtubules allows them to find a their pair, while the short-range interactions caused by the cross-linking proteins align them into bundles. Parallel bundling can occur in the presence of either passive crosslinkers or plus-end directed motors, while the formation of antiparallel bundles requires minus-end directed motors. The model predicts the average bundling time, which is in agreement with our experimental measurements. Additionally, for the case of antiparallel bundle formation, the model predicts that the velocity of the microtubules gliding along each other is the same as the velocity at which the motors move along the microtubules, and this was also confirmed experimentally. In conclusion, the main contributors to the formation of microtubule bundles are angular diffusion of microtubules around the poles allowing them to come into contact and shortrange forces caused by cross-linking proteins that align them

Pivot-and-bond model explains microtubule bundle formation

During mitosis, microtubules form a spindle, which is responsible for proper segregation of the genetic material. A common structural element in a mitotic spindle is a parallel bundle, consisting of two or more microtubules growing from the same origin and held together by cross-linking proteins. An interesting question is what are the physical principles underlying the formation and stability of such microtubule bundles. Here we show, by introducing the pivot-and-bond model, that random angular movement of microtubules around the spindle pole and forces exerted by cross-linking proteins can explain the formation of microtubule bundles as observed in our experiments. The model predicts that stable parallel bundles can form in the presence of either passive crosslinkers or plus-end directed motors, but not minus-end directed motors. In the cases where bundles form, the time needed for their formation depends mainly on the concentration of cross-linking proteins and the angular diffusion of the microtubule. In conclusion, the angular motion drives the alignment of microtubules, which in turn allows the cross-linking proteins to connect the microtubules into a stable bundle

Pivoting of microtubules driven by minus-end-directed motors leads to spindle assembly

Background At the beginning of mitosis, the cell forms a spindle made of microtubules and associated proteins to segregate chromosomes. An important part of spindle architecture is a set of antiparallel microtubule bundles connecting the spindle poles. A key question is how microtubules extending at arbitrary angles form an antiparallel interpolar bundle. Results Here, we show in fission yeast that microtubules meet at an oblique angle and subsequently rotate into antiparallel alignment. Our live- cell imaging approach provides a direct observation of interpolar bundle formation. By combining experiments with theory, we show that microtubules from each pole search for those from the opposite pole by performing random angular movement. Upon contact, two microtubules slide sideways along each other in a directed manner towards the antiparallel configuration. We introduce the contour length of microtubules as a measure of activity of motors that drive microtubule sliding, which we used together with observation of Cut7/kinesin-5 motors and our theory to reveal the minus-end- directed motility of this motor in vivo. Conclusion Random rotational motion helps microtubules from the opposite poles to find each other and subsequent accumulation of motors allows them to generate forces that drive interpolar bundle formation