Prof. Rony Granek
Theoretical studies of the behavior of polymer molecules and assemblies which impact biological systems.

Prof. Granek is involved in theoretical studies of the behaviour of polymer molecules and assemblies which impact biological systems.

1. Active transport along microtubule networks (with M. Elbaum , WIS)
Many important processes in eukaryotic cells depend on the molecular exchange between its two major compartments, the cytoplasm and the nucleus. Delivery of lipids and proteins in the cytoplasm after their synthesis is largely dependent on active mechanisms provided by the cytoskeleton and its associated motor proteins. Transported cargo interacts with one or more types of motor proteins, which in turn carry it toward its target. Due to their typical radial distribution and polarization in the cell, microtubules are the more obvious choice for “tracks” for the transport. The group of M. Elbaum has developed an experimental system that would allow detecting the transport of Nuclear Localization Signal (NLS) proteins along microtubules. Our research is focused on the general theoretical problem of active transport along microtubule networks having different topologies, and, in particular, the transport of NLS with an attempt to explain the experimental results. It appears the transport is sensitive to the topology of the microtubule array. The results of the initial stage of the research appear promising.
We have studied the dynamics of polystyrene beads driven through a cytoskeletal network by microtubule-associated motor proteins in an in vitro system. The motion exhibits an enhanced diffusion with a MSD scaling as t3/2 that extended to much longer times than observed in living cells. Moreover, we were able to study the effect of motor-specific chemical inhibition and to discern a sub-diffusive behavior at the shortest time regime, due to intermittent adhesion of the motor proteins to the microtubules. At longer times the continuing drive of the more weakly affected motor proteins takes over, and the MSD crosses over to the same t3/2 scaling seen in the absence of inhibitors.
These results provide support for the assertion that the t3/2 enhanced diffusion is not an intermediate crossover between a ballistic motion at short times (<x2> ~ t2) and a normal diffusion at long times (<x2> ~ t), but rather an intrinsic behavior caused by the interplay between the driven motion along microtubules and the time-dependent drag imposed by the surrounding microtubule network.

2. Dynamics of semiflexible polymers at large extensions (with M. Feingold, BGU):
Semiflexible polymers, such as DNA, f-actin, and microtubules, are common examples of biomaterials. We have started a joint theoretical and experimental study of the dynamic response of individual semiflexible chains that are strongly stretched and of networks at large stresses. Regarding single chains, experiments have been already performed on the relaxation dynamics of a single DNA molecule that is initially strongly stretched. A comprehensive theoretical interpretation of the results has been offered, and this project is now extended in several directions, in particular, the response to an oscillatory force at large extensions.
We have studied the relaxation dynamics of a semiflexible chain by introducing a time-dependent tension (PRL 2004, 92, art # 098101). The chain has one of its ends attached to a large bead, and the other end is fixed. We focus on the initial relaxation of the chain that is initially strongly stretched. Using a tension that is self-consistently determined, we obtain the evolution of the end-to-end distance with no free parameters. Our results are in good agreement with single molecule experiments on double stranded DNA.

3. Response to force of a bilayer membrane surrounded by viscoelastic networks, as a possible model for Lamellipodia dynamics
The dynamics and response to forces of a bilayer membrane that is surrounded by viscoelastic networks is studied. The motivation to these studies stems from lamellipodia dynamics in animal cells. The bilayer membrane of the cell is surrounded by the extracellular matrix from outside and by the cystoskeleton from inside. Froces generated by polymerizing actin filaments push the membrane outward and create a podium. These podia take part in the locomotion of cells on surfaces. The theory is based on previous work in the absence of surrounding networks.