Tianxiang Su

Structural Transition from Helices to Hemihelices

Helices are amongst the most common structures in nature and in some cases, such as tethered plant tendrils, a more complex but related shape, the hemihelix forms. In its simplest form it consists of two helices of opposite chirality joined by a perversion. A recent, simple experiment using elastomer strips reveals that hemihelices with multiple reversals of chirality can also occur, a richness not anticipated by existing analyses. Here, we show through analysis and experiments that the transition from a helical to a hemihelical shape, as well as the number of perversions, depends on the height to width ratio of the strips cross-section. Our findings provides the basis for the deterministic manufacture of a variety of complex three-dimensional shapes from flat strips.

Differential Contributions of Conformation Extension and Domain Unfolding to Properties of Fibronectin Nanotextiles

Fibronectin (FN) textiles are built as nanometer-thick fabrics. When uniaxially loaded, these fabrics exhibit a distinct threshold between elastic and plastic deformation with increasing stretch. Fabric mechanics are modeled using an eight-chain network and two-state model, revealing that elastic properties of FN depend on conformational extension of the protein and that plastic deformation depends on domain unfolding. Our results suggest how the molecular architecture of a molecule can be exploited for designer mechanical properties of a bulk material.

Mechanics of forced unfolding of proteins.

We describe and solve a two-state kinetic model for the forced unfolding of proteins. The protein oligomer is modeled as a heterogeneous, freely jointed chain with two possible values of Kuhn length and contour length representing its folded and unfolded configurations. We obtain analytical solutions for the force-extension response of the protein oligomer for different types of loading conditions. We fit the analytical solutions for constant-velocity pulling to the force-extension data for ubiquitin and fibrinogen and obtain model parameters, such as Kuhn lengths and kinetic coefficients, for both proteins. We then predict their response under a linearly increasing force and find that our solutions for ubiquitin are consistent with a different set of experiments. Our calculations suggest that the refolding rate of proteins at low forces is several orders larger than the unfolding rate, and neglecting it can lead to lower predictions for the unfolding force, especially at high stretching velocities. By accounting for the refolding of proteins we obtain a critical force below which equilibrium is biased in favor of the folded state. Our calculations also suggest new methods to determine the distance of the transition state from the energy wells representing the folded and unfolded states of a protein.

Semiflexible filament networks viewed as fluctuating beam-frames

We present a new method combining structural and statistical mechanics to study the entropic elasticity of semiflexible filament networks. We view a filament network as a frame structure and use structural mechanics to determine its static equilibrium configuration under applied loads in the first step. To account for thermal motion around this static equilibrium state, we then approximate the potential energy of the deformed frame structure up to the second order in kinematic variables and obtain a deformation-dependent stiffness matrix characterizing the flexibility of the network. Using statistical mechanics, we then evaluate the partition function, free energy and thermo-mechanical properties of the network in terms of the stiffness matrix. We show that penalty methods commonly used in finite elements to account for constraints, are applicable even when statistical and structural mechanics are combined in our method. We apply our framework to understand the expansion, shear, uniaxial tension and compression behavior of some simple filament networks. We are able to capture the stress-stiffening behavior due to filament reorientation and stretching out of thermal fluctuations, as well as the reversible stress-softening behavior due to filament buckling. Finally, we apply our method to square networks and show how their mechanical behavior is different from triangular networks with similar filament density and persistence length.

Extending the Reach of a Rod Injected Into a Cylinder Through Axial Rotation

We investigate continuous axial rotation as a mechanism for extending the reach of an elastic rod injected into a horizontal cylindrical constraint, prior to the onset of helical buckling. Our approach focuses on the development of precision desktop experiments to allow for a systematic investigation of three parameters that affect helical buckling: rod rotation speed, rod injection speed, and cylindrical constraint diameter. Within the parameter region explored, we found that the presence of axial rotation increases horizontal reach by as much as a factor of 5, when compared to the nonrotating case. In addition, we develop an experimentally validated theory that takes into account anisotropic friction and torsional effects. Our theoretical predictions are found to be in good agreement with experiments, and our results demonstrate the benefits of using axial rotation for extending reach of a rod injected into a constraining pipe. [DOI: 10.1115/1.4032500]

MECHANICS OF HETEROGENEOUS FLUCTUATING ELASTIC RODS

Biofilaments, such as actin and DNA, have for long been modeled as thermally fluctuating elastic rods with homogeneous material properties. Such models are adequate if the length scale of the filaments being studied is much larger than the scale of the heterogeneity. However, advanced single molecule experimental techniques have now made it possible to probe the properties of biomolecules at the scale of a few nanometers. The data emerging from these experiments ought to be greeted with appropriately detailed models. In this paper we study the mechanics of a thermally fluctuating elastic rod whose moduli are a function of position. Such a rod can be used as a model for DNA whose sequence specific properties are known or for a protein oligomer in an AFM where some of the monomers might be unfolded. The mechanics of these rods is understood by first evaluating a partition function through path integral techniques. We develop a computational technique to efficiently evaluate the partition function and use it to obtain the force-extension relation of a fluctuating rod with two different bending moduli as would be the case for a partially unfolded protein oligomer stretched in an AFM. The variance of the transverse fluctuations of the protein oligomer is also evaluated and are found to agree with the results of a Monte Carlo simulation.Copyright