A thin-layer model for viscoelastic, stress-relaxation testing of cells using atomic force microscopy: do cell properties reflect metastatic potential?

Atomic force microscopy has rapidly become a valuable tool for quantifying the biophysical properties of single cells. The interpretation of atomic force microscopy-based indentation tests, however, is highly dependent on the use of an appropriate theoretical model of the testing configuration. In this study, a novel, thin-layer viscoelastic model for stress relaxation was developed to quantify the mechanical properties of chondrosarcoma cells in different configurations to examine the hypothesis that viscoelastic properties reflect the metastatic potential and invasiveness of the cell using three well-characterized human chondrosarcoma cell lines (JJ012, FS090, 105KC) that show increasing chondrocytic differentiation and decreasing malignancy, respectively. Single-cell stress relaxation tests were conducted at 2 h and 2 days after plating to determine cell mechanical properties in either spherical or spread morphologies and analyzed using the new theoretical model. At both time points, JJ012 cells had the lowest moduli of the cell lines examined, whereas FS090 typically had the highest. At 2 days, all cells showed an increase in stiffness and a decrease in apparent viscosity compared to the 2-h time point. Fluorescent labeling showed that the F-actin structure in spread cells was significantly different between FS090 cells and JJ012/105KC cells. Taken together with results of previous studies, these findings indicate that cell transformation and tumorigenicity are associated with a decrease in cell modulus and apparent viscosity, suggesting that cell mechanical properties may provide insight into the metastatic potential and invasiveness of a cell.     

Allosteric transitions of the maltose transporter studied by an elastic network model

The maltose transporter from Escherichia coli is one of the ATP‐binding cassette (ABC) transporters that utilize the energy from ATP hydrolysis to translocate substrates across cellular membranes. Until 2011, three crystal structures have been determined for maltose transporter at different states in the process of transportation. Here, based on these crystal structures, the allosteric pathway from the resting state (inward‐facing) to the catalytic intermediate state (outward‐facing) is studied by applying an adaptive anisotropic network model. The results suggest that the allosteric transitions proceed in a coupled way. The closing of the nucleotide‐binding domains occurs first, and subsequently this conformational change is propagated to the transmembrane domains (TMD) via the EAA and EAS loops, and then to the maltose‐binding protein, which facilitates the translocation of the maltose. It is also found that there exist nonrigid‐body and asymmetric movements in the TMD. The cytoplasmic gate may only play the role of allosteric propagation during the transition from the pretranslocation to outward‐facing states. In addition, the results show that the movment of the helical subdomain towards the RecA‐like subdomain mainly occurs in the earlier stages of the transition. These results can provide some insights into the understanding of the mechanism of ABC transporters. © 2013 Wiley Periodicals, Inc. Biopolymers 101: 758–768, 2014.     

All‐atom and coarse‐grained simulations of the forced unfolding pathways of the SNARE complex

The SNARE complex, consisting of three proteins (VAMP2, syntaxin, and SNAP‐25), is thought to drive membrane fusion by assembling into a four‐helix bundle through a zippering process. In support of the above zippering model, a recent single‐molecule optical tweezers experiment by Gao et al. revealed a sequential unzipping of SNARE along VAMP2 in the order of the linker domain → the C‐terminal domain → the N‐terminal domain. To offer detailed structural insights to this unzipping process, we have performed all‐atom and coarse‐grained steered molecular dynamics (sMD) simulations of the forced unfolding pathways of SNARE using different models and force fields. Our findings are summarized as follows: First, the sMD simulations based on either an all‐atom force field (with an implicit solvent model) or a coarse‐grained Go model were unable to capture the forced unfolding pathway of SNARE as observed by Gao et al., which may be attributed to insufficient simulation time and inaccurate force fields. Second, the sMD simulations based on a reparameterized coarse‐grained model (i.e., modified elastic network model) were able to predict a sequential unzipping of SNARE in good agreement with the findings by Gao et al. The key to this success is to reparameterize the intrahelix and interhelix nonbonded force constants against the pair‐wise residue–residue distance fluctuations collected from all‐atom MD simulations of SNARE. Therefore, our finding supports the importance of accurately describing the inherent dynamics/flexibility of SNARE (in the absence of force), in order to correctly simulate its unfolding behaviors under force. This study has established a useful computational framework for future studies of the zippering function of SNARE and its perturbations by point mutations with amino‐acid level of details, and more generally the forced unfolding pathways of other helix bundle proteins. Proteins 2014; 82:1376–1386. © 2014 Wiley Periodicals, Inc.     

Coupled oscillations of a protein microtubule immersed in cytoplasm: an orthotropic elastic shell modeling

Revealing vibration characteristics of sub-cellular structural components such as membranes and microtubules has a principal role in obtaining a deeper understanding of their biological functions. Nevertheless, limitations and challenges in biological experiments at this scale necessitates the use of mathematical and computational models as an alternative solution. As one of the three major cytoskeletal filaments, microtubules are highly anisotropic structures built from tubulin heterodimers. They are hollow cylindrical shells with a ∼ 25 nm outer diameter and are tens of microns long. In this study, a mechanical model including the effects of the viscous cytosol and surrounding filaments is developed for predicting the coupled oscillations of a single microtubule immersed in cytoplasm. The first-order shear deformation shell theory for orthotropic materials is used to model the microtubule, whereas the motion of the cytosol is analyzed by considering the Stokes flow. The viscous cytosol and the microtubule are coupled through the continuity condition across the microtubule–cytosol interface. The stress and velocity fields in the cytosol induced by vibrating microtubule are analytically determined. Finally, the influences of the dynamic viscosity of the cytosol, filament network elasticity, microtubule shear modulus, and circumferential wave-number on longitudinal, radial, and torsional modes of microtubule vibration are elucidated.     

Large scale motions in a biosensor protein glucose oxidase: a combined approach by QENS, normal mode analysis, and molecular dynamics studies

The characteristics of the glucose oxidase were studied using a combination of experimental and theoretical techniques. Quasi elastic neutron scattering experiments were used to obtain the vibrational frequencies of the protein. These were compared to theoretical results obtained by normal mode analysis. Results indicate a good match between the experimental and theoretical values. Molecular dynamic simulation with covariant analysis was used to study the structure and dynamics of glucose oxidase. Various parameters like the radius of gyration, root mean square fluctuations, solvent accessibility were studied for evaluating the structural stability of the protein. The frequency of vibration calculated from the three methods is used to derive the large scale motions. Theses studies were used to predict the suitable lysine residues for linkage with carbon nanotubes.     

Predicting the order in which contacts are broken during single molecule protein stretching experiments

We combine two methods to enable the prediction of the order in which contacts are broken under external stretching forces in single molecule experiments. These two methods are Gō-like models and elastic network models. The Gō-like models have shown remarkable success in representing many aspects of protein behavior, including the reproduction of experimental data obtained from atomic force microscopy. The simple elastic network models are often used successfully to predict the fluctuations of residues around their mean positions, comparing favorably with the experimentally measured crystallographic B-factors. The behavior of biomolecules under external forces has been demonstrated to depend principally on their elastic properties and the overall shape of their structure. We have studied in detail the muscle protein titin and green fluorescent protein and tested for ten other proteins. First, we stretch the proteins computationally by performing stochastic dynamics simulations with the Gō-like model. We obtain the force-displacement curves and unfolding scenarios of possible mechanical unfolding. We then use the elastic network model to calculate temperature factors (B-factors) and compare the slowest modes of motion for the stretched proteins and compare them with the predicted order of breaking contacts between residues in the Gō-like model. Our results show that a simple Gaussian network model is able to predict contacts that break in the next time stage of stretching. Additionally, we have found that the contact disruption is strictly correlated with the highest force exerted by the backbone on these residues. Our prediction of bond-breaking agrees well with the unfolding scenario obtained with the Gō-like model. We anticipate that this method will be a useful new tool for interpreting stretching experiments.     

A QM/MM study of proton transport pathways in a [NiFe] hydrogenase

A theoretical QM/MM study of the [NiFe] hydrogenase from Desulfovibrio fructosovorans has been performed to investigate possible routes of proton transfer between the active site and the protein surface. We obtained the minimum energy paths, with a modified version of the nudged elastic band method, for a set of proposed pathways. The calculations were carried out for the crystallographic structure and for several structures of the protein obtained from a molecular dynamics simulation. The results show one of the studied pathways to be preferred for transport from the active site to the surface, but the preference is not so strong when transport occurs in the opposite direction.     

Conformational variability of the stationary phase survival protein E from Xylella fastidiosa revealed by X‐ray crystallography,small‐angle X‐ray scattering studies,and normal mode analysis

Xylella fastidiosa is a xylem‐limited bacterium that infects a wide variety of plants. Stationary phase survival protein E is classified as a nucleotidase, which is expressed when bacterial cells are in the stationary growth phase and subjected to environmental stresses. Here, we report four refined X‐ray structures of this protein from X. fastidiosa in four different crystal forms in the presence and/or absence of the substrate 3′‐AMP. In all chains, the conserved loop verified in family members assumes a closed conformation in either condition. Therefore, the enzymatic mechanism for the target protein might be different of its homologs. Two crystal forms exhibit two monomers whereas the other two show four monomers in the asymmetric unit. While the biological unit has been characterized as a tetramer, differences of their sizes and symmetry are remarkable. Four conformers identified by Small‐Angle X‐ray Scattering (SAXS) in a ligand‐free solution are related to the low frequency normal modes of the crystallographic structures associated with rigid body‐like protomer arrangements responsible for the longitudinal and symmetric adjustments between tetramers. When the substrate is present in solution, only two conformers are selected. The most prominent conformer for each case is associated to a normal mode able to elongate the protein by moving apart two dimers. To our knowledge, this work was the first investigation based on the normal modes that analyzed the quaternary structure variability for an enzyme of the SurE family followed by crystallography and SAXS validation. The combined results raise new directions to study allosteric features of XfSurE protein.