Cross-linkers at growing microtubule ends generate forces that drive actin transport.

SignificanceComplex cellular processes such as cell migration require coordinated remodeling of both the actin and the microtubule cytoskeleton. The two networks for instance exert forces on each other via active motor proteins. Here we show that, surprisingly, coupling via passive cross-linkers can also result in force generation. We specifically study the transport of actin filaments by growing microtubule ends. We show by cell-free reconstitution experiments, computer simulations, and theoretical modeling that this transport is driven by the affinity of the cross-linker for the chemically distinct microtubule tip region. Our work predicts that growing microtubules could potentially rapidly relocate newly nucleated actin filaments to the leading edge of the cell and thus boost migration.

Diffusible Cross-linkers Cause Superexponential Friction Forces.

The friction between cytoskeletal filaments is of central importance for the formation of cellular structures such as the mitotic spindle and the cytokinetic ring. This friction is caused by passive cross-linkers, yet the underlying mechanism and the dependence on cross-linker density are poorly understood. Here, we use theory and computer simulations to study the friction between two filaments that are cross-linked by passive proteins, which can hop between discrete binding sites while physically excluding each other. The simulations reveal that filaments move via rare discrete jumps, which are associated with free-energy barrier crossings. We identify the reaction coordinate that governs the relative microtubule movement and derive an exact analytical expression for the free-energy barrier and the friction coefficient. Our analysis not only elucidates the molecular mechanism underlying cross-linker-induced filament friction, but also predicts that the friction coefficient scales superexponentially with the density of cross-linkers.

Frustrated binding of biopolymer crosslinkers.

Transiently crosslinked actin filament networks allow cells to combine elastic rigidity with the ability to deform viscoelastically. Theoretical models of semiflexible polymer networks predict that the crosslinker unbinding rate governs the timescale beyond which viscoelastic flow occurs. However a direct comparison between network and crosslinker dynamics is lacking. Here we measure the network's stress relaxation timescale using rheology and the lifetime of bound crosslinkers using fluorescence recovery after photobleaching (FRAP). Intriguingly, we observe that the crosslinker unbinding rate measured by FRAP is more than an order of magnitude slower than the rate measured by rheology. We rationalize this difference with a three-state model where crosslinkers are bound to either 0, 1 or 2 filaments, which allows us to extract crosslinker transition rates that are otherwise difficult to access. We find that the unbinding rate of singly bound crosslinkers is nearly two orders of magnitude slower than for doubly bound ones. We attribute the increased unbinding rate of doubly bound crosslinkers to the high stiffness of biopolymers, which frustrates crosslinker binding.

Energetic constraints on filament-mediated cell polarization.

Cell polarization underlies many cellular processes, such as differentiation, migration, and budding. Many living cells, such as budding yeast and fission yeast, use cytoskeletal structures to actively transport proteins to one location on the membrane and create a high-density spot of membrane-bound proteins. Yet, the thermodynamic constraints on filament-based cell polarization remain unknown. We show by mathematical modeling that cell polarization requires detailed balance to be broken, and we quantify the free-energy cost of maintaining a polarized state of the cell. Our study reveals that detailed balance cannot only be broken via the active transport of proteins along filaments but also via a chemical modification cycle, allowing detailed balance to be broken by the shuttling of proteins between the filament, membrane, and cytosol. Our model thus shows that cell polarization can be established via two distinct driving mechanisms, one based on active transport and one based on nonequilibrium binding. Furthermore, the model predicts that the driven binding process dissipates orders of magnitude less free energy than the transport-based process to create the same membrane spot. Active transport along filaments may be sufficient to create a polarized distribution of membrane-bound proteins, but an additional chemical modification cycle of the proteins themselves is more efficient and less sensitive to the physical exclusion of proteins on the transporting filaments, providing insight in the design principles of the Pom1/Tea1/Tea4 system in fission yeast and the Cdc42 system in budding yeast.

Quantifying fluctuations in reversible enzymatic cycles and clocks.

Biochemical reactions are fundamentally noisy at a molecular scale. This limits the precision of reaction networks, but it also allows fluctuation measurements that may reveal the structure and dynamics of the underlying biochemical network. Here, we study nonequilibrium reaction cycles, such as the mechanochemical cycle of molecular motors, the phosphorylation cycle of circadian clock proteins, or the transition state cycle of enzymes. Fluctuations in such cycles may be measured using either of two classical definitions of the randomness parameter, which we show to be equivalent in general microscopically reversible cycles. We define a stochastic period for reversible cycles and present analytical solutions for its moments. Furthermore, we associate the two forms of the randomness parameter with the thermodynamic uncertainty relation, which sets limits on the timing precision of the cycle in terms of thermodynamic quantities. Our results should prove useful also for the study of temporal fluctuations in more general networks.