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How To Braid Nanoropes

October 15, 2005
Max Planck scientists identify essential control parameters for the assembly of filament bundles.

Three snapshots of a bundle formed by twenty filaments as observed in computer simulations: (a) Loose bundle for a crosslinker concentration that is only slightly above the threshold value; (b) and (c) show two different conformations of the same bundle corresponding to a segregated conformation with three sub-bundles and a compact conformation with roughly cylindrical shape, respectively.
Credit: Image : Max Planck Institute of Colloids and Interfaces

Biomimetic systems that are composed of rigid polymers orfilaments and crosslinking molecules can be used to assemble filamentnetworks and bundles. The bundles represent `nanoropes' and exhibitmaterial properties that are primarily determined by the number ofplaited filaments. Scientists at the Max Planck Institute of Colloidsand Interfaces in Potsdam, Germany have now shown that this assembly offilaments into bundles is prevented by the thermal motion of thefilaments, unless the crosslinker concentration exceeds a certainthreshold value. The latter value depends on the number of filaments,but remains finite in the limit of a large filament number. As thecrosslinker concentration is lowered, the bundles may segregate intosmall sub-bundles, or undergo abrupt unbinding transitions. (PhysicalReview Letters 95, 038102, July, 2005).

Biological cells aremechanically stable because they contain actin filaments andmicrotubules that form networks and bundles. These filamentarchitectures are determined and controlled by crosslinking proteins,which have two sticky ends that bind to different filaments. In orderto understand the underlying forces and to optimise the mechanicalproperties of these architectures, one must study biomimetic modelsystems that are solely composed of filaments and crosslinkingproteins. One important example is the assembly of several filamentsinto thick bundles or ‘nanoropes’ that are more rigid, and sustain alarger external load, than single filaments.

The assembly offilaments by molecular crosslinkers is disturbed by the thermal motionof the filaments. Scientists at the Max Planck Institute of Colloidsand Interfaces have now shown that this thermal motion preventsfilament assembly unless the crosslinker concentration exceeds acertain threshold value. The latter value depends on the filamentrigidity, on the binding energy of the crosslinkers, and on thetemperature. Furthermore, the threshold value decreases as the number Nof filaments within the bundle is increased, but remains finite in thelimit of large N.

Snapshots of filament bundles as observed incomputer simulations are displayed in Fig. 1. The snapshot in Figure1(a) shows a loose bundle for a crosslinker concentration only slightlyabove the threshold value. The simulations also reveal that thesebundles do not always reach their equilibrium shape, but oftensegregate into sub-bundles containing typically five filaments as shownin Figure 1(b). This bundle morphology differs strongly from the fullyequilibrated bundle shape as shown in Figure 1(c) for the same system.Which of the two morphologies is attained depends on the initialarrangement of the filaments and on the kinetics of the assemblyprocess.

Biomimetic systems, consisting of solutions of actinfilaments and crosslinking proteins, have also been studiedexperimentally by several research groups. The available experimentaldata is consistent with the new theory based on the interplay ofmolecular crosslinkers and thermal motion. In particular, there is someexperimental evidence for the threshold concentration of crosslinkersand the sudden onset of filament bundle formation above thisconcentration, but systematic experimental studies remain to be donethat explore the dependence on the filament number N.

Apart fromrepresenting important structural elements, filament bundles can alsoprovide strong pushing forces. These pushing forces arise from thedirected growth of the filaments by the addition of molecular buildingblocks. One important problem is to understand the dependence of thesepushing forces on the number of filaments within the bundle.

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