Suction effects in cratered surfaces.

It has been shown experimentally that cratered surfaces may have better adhesion properties than flat ones. However, the suction effect produced by the craters, which may be chiefly responsible for the improved adhesion, has not been properly modelled. This paper combines experimental, numerical simulation and analytical approaches towards developing a framework for quantifying the suction effect produced by isolated craters and cratered surfaces. The modelling approach emphasizes the essential role of large elastic deformation, while the airflow dynamics, microscopic mechanisms, like surface tension and air permeation, and rate-dependence are neglected. This approach is validated using experimental data for isolated hemi-spherical craters. The modelling approach is further applied to spherical cap (not necessarily hemi-spherical) craters with the objective of identifying optimal geometric and material properties, as well as the minimum preload necessary for attaining the maximum suction force. It is determined that stiff polymers with deep craters are capable of producing large suction forces. For soft materials, central to biomedical applications, large suction forces can be attained by reinforcing deep craters with thin stiff layers. Parametric optimization studies of reinforced craters reveal that some of them perform beyond common expectations. However, those high-performance reinforced craters are prone to surface instabilities, and therefore the practical use of such craters may be problematic.

Layered Elastomeric Fibrous Scaffolds: An In-Silico Study of the Achievable Range of Mechanical Behaviors.

Our goal herein is to understand the mechanisms underlying soft tissue and scaffold behaviors by developing a physically based micromechanical model as a means to connect the macroscopic behaviors to the underlying microstructural phenomena. Because of its well-documented capacity for generating elastomeric fibrous materials with a wide range of realizable architectures, the electrospun scaffold was used as the exemplar biomaterial. Fibrous network geometries based on a random walk algorithm were first generated to form the basis for subsequent micromechanical simulations. A basic understanding of randomly oriented fibrous network phenomena was then developed, and subsequently expanded on using networks with aligned fibers. Simulation results were then compared with experimental observations of electrospun scaffolds to evaluate the validity of the simulations. The effects of fiber alignment, tortuosity, and material properties on macroscopic mechanical behavior of the material have been presented both individually and in combination. We have seen that all three aspects of the scaffold network can have significant effects on the macroscopic behavior for different load cases. Overall, accurate representation of detailed fibrous network geometry permitted a greater understanding of the complex mechanisms underlying the macroscopic behavior unique to these biomaterials. Insights gained from such simulations can significantly aid the process of designing scaffold network geometries that result in engineered tissues that function as well as or better than the native tissues they are intended to replace.

Geometric characterization and simulation of planar layered elastomeric fibrous biomaterials.

Many important biomaterials are composed of multiple layers of networked fibers. While there is a growing interest in modeling and simulation of the mechanical response of these biomaterials, a theoretical foundation for such simulations has yet to be firmly established. Moreover, correctly identifying and matching key geometric features is a critically important first step for performing reliable mechanical simulations. The present work addresses these issues in two ways. First, using methods of geometric probability, we develop theoretical estimates for the mean linear and areal fiber intersection densities for 2-D fibrous networks. These densities are expressed in terms of the fiber density and the orientation distribution function, both of which are relatively easy-to-measure properties. Secondly, we develop a random walk algorithm for geometric simulation of 2-D fibrous networks which can accurately reproduce the prescribed fiber density and orientation distribution function. Furthermore, the linear and areal fiber intersection densities obtained with the algorithm are in agreement with the theoretical estimates. Both theoretical and computational results are compared with those obtained by post-processing of scanning electron microscope images of actual scaffolds. These comparisons reveal difficulties inherent to resolving fine details of multilayered fibrous networks. The methods provided herein can provide a rational means to define and generate key geometric features from experimentally measured or prescribed scaffold structural data.

Guided self-assembly of electrostatic binary monolayers via isothermal-isobaric control.

Self-assembly of a binary monolayer of charged particles is modeled using molecular dynamics and statistical mechanics. The equilibrium phase diagram for the system has three distinct phases: an ionic crystal; a geometrically ordered crystal with disordered charges; and a fluid. We show that self-assembly occurs near the phase transition between the ionic crystal and the fluid, and that the rate of ordering is sensitive to the applied pressure. By assuming an Arrhenius form for the rate of ordering, an optimality condition for the temperature and pressure is derived that maximizes the rate. Using the Clausius-Clapeyron equation, the optimal point on the phase boundary is expressed in terms of the thermodynamic changes in state variables across the boundary. The predicted optimal temperature and pressure conditions are in good agreement with numerical simulations and result in self-organization rates five times that of a simulation without applied pressure.

Rigorous coarse-graining for the dynamics of linear systems with applications to relaxation dynamics in proteins.

Reduced-dimensionality, coarse-grained models are commonly employed to describe the structure and dynamics of large molecular systems. In those models, the dynamics is often described by Langevin equations of motion with phenomenological parameters. This paper presents a rigorous coarse-graining method for the dynamics of linear systems. In this method, as usual, the conformational space of the original atomistic system is divided into master and slave degrees of freedom. Under the assumption that the characteristic timescales of the masters are slower than those of the slaves, the method results in Langevin-type equations of motion governed by an effective potential of mean force. In addition, coarse-graining introduces hydrodynamic-like coupling among the masters as well as non-trivial inertial effects. Application of our method to the long-timescale part of the relaxation spectra of proteins shows that such dynamic coupling is essential for reproducing their relaxation rates and modes.

Critical evaluation of simple network models of protein dynamics and their comparison with crystallographic B-factors.

In recent years, elastic network models (ENM) have been widely used to describe low-frequency collective motions in proteins. These models are often validated and calibrated by fitting mean-square atomic displacements estimated from x-ray crystallography (B-factors). We show that a proper calibration procedure must account for the rigid-body motion and constraints imposed by the crystalline environment on the protein. These fundamental aspects of protein dynamics in crystals are often ignored in currently used ENMs, leading to potentially erroneous network parameters. Here we develop an ENM that properly takes the rigid-body motion and crystalline constraints into account. Its application to the crystallographic B-factors reveals that they are dominated by rigid-body motion and thus are poorly suited for the calibration of models for internal protein dynamics. Furthermore, the translation libration screw (TLS) model that treats proteins as rigid bodies is considerably more successful in interpreting the experimental B-factors than ENMs. This conclusion is reached on the basis of a comparative study of various models of protein dynamics. To evaluate their performance, we used a data set of 330 protein structures that combined the sets previously used in the literature to test and validate different models. We further propose an extended TLS model that treats the bulk of the protein as a rigid body while allowing for flexibility of chain ends. This model outperforms other simple models of protein dynamics in interpreting the crystallographic B-factors.

Theoretical studies of the kinetics of mechanical unfolding of cross-linked polymer chains and their implications for single-molecule pulling experiments.

We have used kinetic Monte Carlo simulations to study the kinetics of unfolding of cross-linked polymer chains under mechanical loading. As the ends of a chain are pulled apart, the force transmitted by each cross-link increases until it ruptures. The stochastic cross-link rupture process is assumed to be governed by first order kinetics with a rate that depends exponentially on the transmitted force. We have performed random searches to identify optimal cross-link configurations whose unfolding requires a large applied force (measure of strength) and/or large dissipated energy (measure of toughness). We found that such optimal chains always involve cross-links arranged to form parallel strands. The location of those optimal strands generally depends on the loading rate. Optimal chains with a small number of cross-links were found to be almost as strong and tough as optimal chains with a large number of cross-links. Furthermore, optimality of chains with a small number of cross-links can be easily destroyed by adding cross-links at random. The present findings are relevant for the interpretation of single molecule force probe spectroscopy studies of the mechanical unfolding of "load-bearing" proteins, whose native topology often involves parallel strand arrangements similar to the optimal configurations identified in the study.

Configurational entropy and mechanical properties of cross-linked polymer chains: implications for protein and RNA folding.

We discuss the statistical mechanical properties of a single polymer chain that forms cross links among its monomers. Models of this type have served as prototypes in theories of RNA and protein folding. The chain is allowed to form pseudoknots and its monomers can each participate in multiple cross links. We demonstrate that the conformational free energy of such a chain can be estimated by using an algorithm that scales as a power of the number of cross links N(N1-N3, depending on the problem). Straightforward exact evaluation of the chain partition function via multidimensional integration scales exponentially with N and often is computationally prohibitive. Our approach can also be used to compute the "entropic force" generated by a cross-linked chain when it is stretched at its ends. Such forces can be directly measured by atomic force microscopy or by laser optical trap experiments performed on single RNA, DNA, and protein molecules.