Kinematic Design of Functional Nanoscale Mechanisms From Molecular Primitives

Abstract

Natural nanomechanisms such as capillaries, neurotransmitters, and ion channels play a vital role in the living systems. But the design principles developed by nature through evolution are not well understood and, hence, not applicable to engineered nanomachines. Thus, the design of nanoscale mechanisms with prescribed functions remains a challenge. Here, we present a systematic approach based on established kinematics techniques to designing, analyzing, and controlling manufacturable nanomachines with prescribed mobility and function built from a finite but extendable number of available "molecular primitives." Our framework allows the systematic exploration of the design space of irreducibly simple nanomachines, built with prescribed motion specification by combining available nanocomponents into systems having constrained, and consequently controllable motions. We show that the proposed framework has allowed us to discover and verify a molecule in the form of a seven link, seven revolute (7R) close loop spatial linkage with mobility (degree of freedom) of one. Furthermore, our experiments exhibit the type and range of motion predicted by our simulations. Enhancing such a structure into functional nanomechanisms by exploiting and controlling their motions individually or as part of an ensemble could galvanize development of the multitude of engineering, scientific, medical, and consumer applications that can benefit from engineered nanomachines.

Chetaev Instability Framework for Kinetostatic Compliance-Based Protein Unfolding

“…Accordingly, if the protein molecule is under the effect of the forces generated by an optical tweezer as in (9), then the unfolding dynamics are given by (13), where the unfolding control torque vector u unfold (θ θ θ) is given by ( 11) and (12). Since the trap stiffness is modulated such that κ(θ θ θ * ) = 0 (see Remark 3.1), the conformation θ θ θ * is an equilibrium of (15). To analyze a folded conformation instability under the effect of optical tweezers, we are interested in deriving numerical conditions guaranteeing that PUCP objectives are met for the unfolding dynamics in (15).…”

“…Since the trap stiffness is modulated such that κ(θ θ θ * ) = 0 (see Remark 3.1), the conformation θ θ θ * is an equilibrium of (15). To analyze a folded conformation instability under the effect of optical tweezers, we are interested in deriving numerical conditions guaranteeing that PUCP objectives are met for the unfolding dynamics in (15). It is natural to expect that these conditions should depend on the direction of the applied force in (9).…”

“…for the unfolding dynamics in (15). At any conformation θ θ θ, the vector r NC (θ θ θ) ∈ R 3 in ( 16) connects the nitrogen atom in the N-terminus to the carbon atom in the C-terminus.…”

“…Proposition 4.4: Consider the optical tweezer-based unfolding dynamics in (15). The folded conformation θ θ θ * is an unstable equilibrium for (15) if…”

“…To address the high computational burden of physicsbased approaches, the framework of kinetostatic compli-ance method (KCM), which is based on modeling protein molecules as mechanisms with a large number of rigid nanolinkages that fold under the nonlinear effect of electrostatic and van der Waals interatomic forces, has been developed in the literature [8]- [12]. The KCM framework has been successful in investigating the effect of hydrogen bond formation on protein kinematic mobility [13] and synthesizing molecular nano-linkages [14], [15]. Furthermore, as demonstrated by [16], this framework lends itself to a nonlinear control theoretic interpretation, where entropy-loss constraints can be encoded in KCM-based folding via proper quadratic optimization-based nonlinear control techniques.…”