Modeling Elasto-Mechanical Phenomena Involved in the Motor-Driven Assembly of Nanomaterials

As the ability to manipulate materials and components at the nanoscale continues to grow, it will become increasingly critical to understand the dynamic interactions that occur among multiple components. For example, the dynamic interactions among proteins (i.e., nanoscale molecular machines) lead to complex, emergent behaviors such as photosynthesis, self-repair, and cell division. Recently, the research group at Sandia National Labs and The Center for Integrated Nanotechnologies (CINT), headed by George Bachand, has developed a molecular transport system capable of transporting and manipulating a wide range of nanoscale components. This system is based on the kinesin motor molecule and cytoskeletal filament microtubules (MTs), in which the kinesin are mounted to a substrate in an inverted fashion, and capable of binding and transporting the MTs across a surface as a molecular shuttle. In the presence of ATP, the kinesins are capable of generating ∼40 pN·nm of work, and transporting MTs along the substrate at velocities of ∼1 micro-m/sec. The MTs may also serve as a transport platform for various inorganic and biological nanoparticles. During transport, the cargo is transferred, via elastic collisions, from one MT to another or to where two MT carry a single cargo. Bending of the MT and various other elasto-dynamic phenomena such as particle ejection, MT sticking, etc are observed via fluorescence microscopy. The interaction observed by the Bachand team is not unlike the interaction of macroscale devices. The kinesin provide motivation to the MT via a hand-over-hand ratchet like motion driven by ATP hydrolysis. As the kinesin motor domains come into contact with and bind the MT, it is not inconceivable to think of this action from the framework of instantly applied constraints in a manner similar to the macroscopic action of devices coming into and out of constrained interaction. The hypothesis of our work is that the elasto-dynamic phenomenon observed can be modeled with the tools of multiple body dynamics modeling. The modeling perspective is based on the lead author’s hybrid parameter multiple body dynamics modeling methodology. This technique is a variational approach based on the projection methods of Gibbs-Appell. The constrained interaction through contact and impact are modeled with the idea of instantly applied non-holonomic constraints, where the interactions on the boundaries and in the domain of elastic continua are modeled via projections of the d’Alembert force deficit along conjugate directions generated via so called pseudo-generalized-speeds. In this paper we present motivation for our approach, the underlying modeling theory, and current results of our efforts at understanding the kinesin/MT shuttle system interaction.