Can Dissipative Properties of Single Molecules Be Extracted from a Force Spectroscopy Experiment?

Multi-Channel Signals in Dynamic Force-Clamp Mode of Microcantilever Sensors for Detecting Cellular Peripheral Brush

The development of numerous diseases, such as renal cyst, cancer, and viral infection, is closely associated with the pathological changes and defects in the cellular peripheral brush. Therefore, it is necessary to develop a potential new method to detect lesions of cellular peripheral brush. Here, a piecewise linear viscoelastic constitutive model of cell is established considering the joint contribution of the peripheral brush and intra-cellular structure. By combining the Laplace transformation and its inverse transformation, and the differential method in the temporal domain and differential quadrature method (DQM) in the spatial domain, the signal interpretation models for quasi-static and dynamic signals of microcantilever are solved. The influence mechanisms of the peripheral brush on the viscoelastic properties of cells and quasi-static/dynamic signals of microcantilever are clarified. The results not only reveal that the peripheral brush has significant effects on the complex modulus of the cell and multi-channel signals of the microcantilever, but also suggest that an alternative mapping method by collecting multi-channel signals including quasi-static and higher frequency signals with more brush indexes could be potentially used to identify cancerous cells.

Effects of Proline on Internal Friction in Simulated Folding Dynamics of Several Alanine-Based α-Helical Peptides

We have studied in silico the effect of proline, a model cosolvent, on local and global friction coefficients in (un)folding of several typical alanine-based α-helical peptides. Local friction is related to dwell times of a single, ensemble-averaged hydrogen bond (HB) within each peptide. Global friction is related to energy dissipated in a series of configurational changes of each peptide experienced by increasing the number of HBs during folding. Both of these approaches are important in relation to future atomic force microscopic-based measurements of internal friction via force-clamp single-molecule force spectroscopy. Molecular dynamics (MD) simulations for six peptides, namely, ALA5, ALA8, ALA15, ALA21, (AAQAA)3, and H2N-GN(AAQAA)2G-COONH2, have been conducted at 2 and 5 M proline solutions in water. Using previously obtained MD data for these peptides in pure water as well as upgraded theoretical models, we obtained variations of local and global internal friction coefficients as a function of solution viscosity. The results showed the substantial role of proline in stabilizing the folded state and slowing the overall folding dynamics. Consequently, larger friction coefficients were obtained at larger viscosities. The local and global internal friction, i.e., respective, friction coefficients approximated to zero viscosity, was also obtained. The evolution of friction coefficients with viscosity was weakly dependent on the number of concurrent folding pathways but was rather dominated by a stabilizing effect of proline on the folded states. Obtained values of local and global internal friction showed qualitatively similar results and a clear dependency on the structure of the studied peptide.

Analytical Approaches for Deriving Friction Coefficients for Selected α-Helical Peptides Based Entirely on Molecular Dynamics Simulations

In this paper we derive analytically from molecular dynamics (MD) simulations the friction coefficients related to conformational transitions within several model peptides with α-helical structures. We study a series of alanine peptides with various length from ALA₅ to ALA₂₁ as well as their two derivatives, the (AAQAA)₃ peptide and a 13-residue KR1 peptide that is a derivative of the (AAQAA)₂ peptide with the formula GN(AAQAA)₂G. We use two kinds of approaches to derive their friction coefficients. In the local approach, friction associated with fluctuations of single hydrogen bonds are studied. In the second approach, friction coefficients associated with a folding transitions within the studied peptides are obtained. In both cases, the respective friction coefficients differentiated very well the subtle structural changes between studied peptides and compared favorably to experimentally available data.

Quantitative Elasticity of Flexible Polymer Chains Using Interferometer-Based AFM

We estimate the elasticity of single polymer chains using atomic force microscope (AFM)-based oscillatory experiments. An accurate estimate of elasticity using AFM is limited by assumptions in describing the dynamics of an oscillating cantilever. Here, we use a home-built fiber-interferometry-based detection system that allows a simple and universal point-mass description of cantilever oscillations. By oscillating the cantilever base and detecting changes in cantilever oscillations with an interferometer, we extracted stiffness versus extension profiles for polymers. For polyethylene glycol (PEG) in a good solvent, stiffness-extension data showed significant deviation from conventional force-extension curves (FECs) measured in constant velocity pulling experiments. Furthermore, modeling stiffness data with an entropic worm-like chain (WLC) model yielded a persistence length of (0.5 ± 0.2 nm) compared to anomaly low value (0.12 nm ± 0.01) in conventional pulling experiments. This value also matched well with equilibrium measurements performed using magnetic tweezers. In contrast, polystyrene (PS) in a poor solvent, like water, showed no deviation between the two experiments. However, the stiffness profile for PS in good solvent (8M Urea) showed significant deviation from conventional force-extension curves. We obtained a persistence length of (0.8 ± 0.2 nm) compared to (0.22 nm ± 0.01) in pulling experiments. Our unambiguous measurements using interferometer yield physically acceptable values of persistence length. It validates the WLC model in good solvents but suggests caution for its use in poor solvents.

Validity of point-mass model in off-resonance dynamic atomic force microscopy

The quantitative measurement of viscoelasticity of nano-scale entities is an important goal of nanotechnology research and there is considerable progress with advent of dynamic atomic force microscopy. The hydrodynamics of cantilever, the force sensor in AFM measurements, plays a pivotal role in quantitative estimates of nano-scale viscoelasticity. The point-mass (PM) model, wherein the AFM cantilever is approximated as a point-mass with mass-less spring is widely used in dynamic AFM analysis and its validity, particularly in liquid environments, is debated. It is suggested that the cantilever must be treated as a continuous rectangular beam to obtain accurate estimates of nano-scale viscoelasticity of materials it is probing. Here, we derived equations, which relate stiffness and damping coefficient of the material under investigation to measured parameters, by approximating cantilever as a point-mass and also considering the full geometric details. These equations are derived for both tip-excited as well as base-excited cantilevers. We have performed off-resonance dynamic atomic force spectroscopy on a single protein molecule to investigate the validity of widely used PM model. We performed measurements with AFMs equipped with different cantilever excitation methods as well as detection schemes to measure cantilever response. The data was analyzed using both, continuous beam model and the PM model. We found that both models yield same results when the experiments are performed in truly off-resonance regime with small amplitudes and the cantilever stiffness is much higher than the interaction stiffness. Our findings suggest that a simple PM approximation based model is adequate to describe the dynamics, provided care is taken while performing experiments so that the approximations used in these models are valid.

The nano-scale viscoelasticity using atomic force microscopy in liquid environment

We measured viscoelasticity of two nanoscale systems, single protein molecules and molecular layers of water confined between solid walls. In order to quantify the viscoelastic response of these nanoscale systems in liquid environment, the measurements are performed using two types of atomic force microscopes (AFMs), which employ different detection schemes to measure the cantilever response. We used a deflection detection scheme, available in commercial AFMs, that measures cantilever bending and a fibre-interferometer based detection which measures cantilever displacement. The hydrodynamics of the cantilever is modelled using Euler-Bernoulli equation with appropriate boundary conditions which accommodate both detection schemes. In a direct contradiction with many reports in the literature, the dissipation coefficient of a single octomer of titin I27₈ is found to be immeasurably low. The upper bound on the dissipation coefficient is 5 × 10^-7 kg s^-1, which is much lower than the reported values. The entropic stiffness of single unfolded domains of protein measured using both methods is in the range of 10 mN m^-1. We show that in a conventional deflection detection measurement, the phase of the bending signal can be a primary source of artefacts in the dissipation estimates. It is recognized that the measurement of cantilever displacement, which has negligibly small phase lag due to hydrodynamics of the cantilever at low excitation frequencies, is better suited for ensuring artefact-free measurement of viscoelasticity compared to the measurement of the cantilever bending. Further, it was possible to measure dissipation in molecular layers of water confined between the tip and the substrate using fibre interferometer based AFM with similar experimental parameters. It confirms that the dissipation coefficient of a single I27₈ is below the detection limit of AFM. The results shed light on the discrepancy observed in the measured diffusional dynamics of protein collapse measured using Force spectroscopic techniques and single-molecule optical techniques.