Journal Club Theme of May 2013: Mechanics of biological and bio-inspired supramolecular assemblies

Supramolecular assemblies are dynamic structures composed of simple molecular building blocks that self-assemble into hierarchically organized complexes driven by reversible (weak) intermolecular interactions (e.g. hydrogen bonds). This bottom-up approach to materials synthesis is utilized in nature to create flaw tolerant, highly functional materials that exhibit extraordinary mechanical properties arising from parallel clusters of weak interactions such as hydrogen bonds that work collectively. Such geometric arrangements are observed in stable biomolecular assemblies such as spider’s silk and amyloid plaques (see for instance an earlier journal club entry on protein materials node/2653 ).

In this journal club, we highlight some of the recent advances in our understanding of supramolecular assemblies in biological, biomolecular and bio-inspired systems. The mechanical behavior of weak bonds lies at the heart of this discussion. Weak bonds are reversible, follow non-deterministic dynamics, and their lifetime depends on the magnitude, direction and rate of the applied load, with higher loads leading to stiffer responses. Force dependent single barrier kinetic models such as Bell’s model (G.I. Bell, Science, 1978) provide a convenient starting point on the discussion of the breaking mechanisms of weak reversible bonds. This simple model is usually used in conjunction with Monte Carlo (MC) techniques to study the collaborative response of bond clusters with specific bond network architecture. It has also been instrumental in interpreting single molecule atomic force microscopy experiments and molecular dynamics simulations on protein unfolding, as well as cell adhesion and motility experiments. We refer the reader to the work of Prof. Ben Freund, Prof. Huajian Gao and colleagues for the theoretical predictions of the optimum size of a molecular bond clusters under various boundary conditions. These studies illustrated that larger clusters are favored by bond reversibility while the nonuniform load distribution between the individual bonds favors small ones [1]. Additionally, it was found that the optimal size can arise from a transition between surface- and bulk-dominated interaction regimes at the nanoscale [2].

The counterintuitive mechanical behavior of supramolecular materials (high strength from weak interactions) often arises from size and confinement effects at different length scales or hierarchies (Buehler & Keten, Reviews of Modern Physics, 2010). Several examples can be found in the literature of materials that through size restrictions or geometrical constraints achieve optimum performance [3]. Keten et al. showed, using MD simulations that beta-sheet crystals, responsible for the high strength of spider silk, use geometric nanoconfinement to achieve optimum stiffness and toughness. By limiting their size, the failure mechanisms of the beta-sheet become restricted to the one that optimizes the mechanical response (stick-slip mechanism under uniform shear), emphasizing the importance of size and confinement effects in supramolecular systems [4]. More recently, designer peptides and organic polymers have been developed to leverage hydrogen bonds and other non-covalent interactions in new bio-inspired high performance functional materials that are capable of exceptional stimuli-responsiveness, self-healing, and mechanical properties. However, numerous challenges lie ahead in modeling the mechanical response of these novel materials systems. In particular, the dynamic character of supramolecular assemblies, arising from the stochastic nature of the non-covalent bonds under thermal fluctuations, poses an important challenge on the assessment of their mechanical response using classical engineering analysis tools. Meso-scale models based on statistical mechanics and coarse-grained approaches are critically needed to explain the interplay between assembly, structure and fracture. An additional consideration is that in self-assembling systems, coupling between these three factors are observed at all stages of the materials development continuum, including processing.

In our group, we are currently studying cyclic peptide nanotubes (CPNs), a type of supramolecular organic nanotubes that exhibit outstanding mechanical stiffness and transport properties that match those of biological transmembrane proteins, having an alluring potential as synthetic nanopores in membranes for applications such as carbon capture or low energy water desalination. Using Bell’s model and MC simulations on a dimer, we characterized the load dependence strength of a CPN and were able to predict the probability distribution of the failure location along the nanotube under bending deformation [5]. These findings are important for understanding the fragmentation and ultimate size-distribution of these self-assembling systems, which may involve secondary growth mechanisms arising from tube fracture similar to self-replicating systems in biology (e.g. amyloids).

Our more recent investigations have focused on understanding how attachment of polymers to the nanotube building blocks can be used to control the mechanical properties and stacking order in binary mixtures of functional peptides. The meso-scale mechanics of these polymer-peptide conjugates is enigmatic in many ways, involving competing effects such as enthalpic gain through hydrogen bonding versus entropy loss upon binding due to confinement, as well as kinetic effects characteristic of non-equilibrium self-assembly processes.  We are currently establishing a mechanics approach to quantify the forces arising from the nanoconfinement of entropic polymer springs and weak interactions. We anticipate that if successful, this approach can be exploited to direct the stacking order of mixed CPs within block-copolymer membranes to generate artificial ion channels with well-defined interior properties. More broadly, new theories and mechanics models that lead to a fundamental understanding of the physics of supramolecular materials will be crucial for discovering strong, tough and multifunctional systems inspired from biology.

Luis Ruiz (PhD student, Theoretical and Applied Mechanics, Northwestern University)

Computational Nanodynamics Laboratory (PI: Prof. Sinan Keten)

Suggested Reading:

 1.         Lin, Y. and L.B. Freund, Optimum size of a molecular bond cluster in adhesion.  Physical Review E, 2008. 78(2): p. 021909.

2.         Yao, H., P. Guduru, and H. Gao, Maximum strength for intermolecular adhesion of nanospheres at an optimal size . Journal of The Royal Society Interface, 2008. 5(28): p. 1363-1370.

3.         Gao, H., et al., Materials become insensitive to flaws at nanoscale: Lessons from nature . Proceedings of the National Academy of Sciences, 2003. 100(10): p. 5597-5600.

4.         Keten, S., et al., Nanoconfinement controls stiffness, strength and mechanical toughness of [beta]-sheet crystals in silk.  Nature materials, 2010. 9(4): p. 359-367.

5.         Ruiz, L., et al., Persistence length and stochastic fragmentation of supramolecular nanotubes under mechanical force . Nanotechnology, 2013. 24(19): p. 195103.