Mechanical Constraint Effect on DNA Persistence Length.

Persistence length is a significant criterion to characterize the semi-flexibility of DNA molecules. The mechanical constraints applied on DNA chains in new single-molecule experiments play a complex role in measuring DNA persistence length; however, there is a difficulty in quantitatively characterizing the mechanical constraint effects due to their complex interactions with electrostatic repulsions and thermal fluctuations. In this work, the classical buckling theory of Euler beam and Manning's statistical theories of electrostatic force and thermal fluctuation force are combined for an isolated DNA fragment to formulate a quantitative model, which interprets the relationship between DNA persistence length and critical buckling length. Moreover, this relationship is further applied to identify the mechanical constraints in different DNA experiments by fitting the effective length factors of buckled fragments. Then, the mechanical constraint effects on DNA persistence lengths are explored. A good agreement among the results by theoretical models, previous experiments, and present molecular dynamics simulations demonstrates that the new superposition relationship including three constraint-dependent terms can effectively characterize changes in DNA persistence lengths with environmental conditions, and the strong constraint-environment coupling term dominates the significant changes of persistence lengths; via fitting effective length factors, the weakest mechanical constraints on DNAs in bulk experiments and stronger constraints on DNAs in single-molecule experiments are identified, respectively. Moreover, the consideration of DNA buckling provides a new perspective to examine the bendability of short-length DNA.

Influence of Microscopic Interactions on the Flexible Mechanical Properties of Viral DNA.

During the packaging and ejection of viral DNA, its mechanical properties play an essential role in viral infection. Some of these mechanical properties originate from different microscopic interactions of the encapsulated DNA in the capsid. Based on an updated mesoscopic model of the interaction potential by Parsegian et al., an alternative continuum elastic model of the free energy of the confined DNA in the capsid is developed in this work. With this model, we not only quantitatively identify the respective contributions from hydration repulsion, electrostatic repulsion, entropy and elastic bending but also predict the ionic effect of viral DNA's mechanical properties during the packaging and ejection. The relevant predictions are quantitively or qualitatively consistent with the existing experimental results. Furthermore, the nonmonotonous or monotonous changes in the respective contributions of microscopic interactions to the ejection force and free energy at different ejection stages are revealed systematically. Among these, the nonmonotonicity in the entropic contribution implies a transition of viral DNA structure from order to disorder during the ejection.

The pH-dependent elastic properties of nanoscale DNA films and the resultant bending signals for microcantilever biosensors.

The diverse mechanical properties of nanoscale DNA films on solid substrates have a close correlation with complex detection signals of micro-/nano-devices. This paper is devoted to formulating several multiscale models to study the effect of pH-dependent ionic inhomogeneity on the graded elastic properties of nanoscale DNA films and the resultant bending deflections of microcantilever biosensors. First, a modified inverse Debye length is introduced to improve the classical Poisson-Boltzmann equation for the electrical potential of DNA films to consider the inhomogeneous effect of hydrogen ions. Second, the graded characteristics of the particle distribution are taken into consideration for an improvement in Parsegian's mesoscopic potential for both attraction-dominated and repulsion-dominated films. Third, by the improved interchain interaction potential and the thought experiment about the compression of a macroscopic continuum DNA bar, we investigate the diversity of the elastic properties of single-stranded DNA (ssDNA) films due to pH variations. The relevant theoretical predictions quantitatively or qualitatively agree well with the relevant DNA experiments on the electrical potential, film thickness, condensation force, elastic modulus, and microcantilever deflections. The competition between attraction and repulsion among the fixed charges and the free ions endows the DNA film with mechanical properties such as a remarkable size effect and a non-monotonic behavior, and a negative elastic modulus is first revealed in the attraction-dominated ssDNA film. There exists a transition between the pH-sensitive parameter interval and the pH-insensitive one for the bending signals of microcantilevers, which is predominated by the initial stress effect in the DNA film.

Theoretical Analysis for Bending of Single-Stranded DNA Adsorption on Microcantilever Sensors.

An energy-based model is presented to establish the bending deformation of microcantilever beams induced by single-stranded DNA (ssDNA) adsorption. The total free energy of the DNA-microcantilever sensor was obtained by considering the excluded-volume energy and the polymer stretching energy of DNA chains from mean-field theory, and the mechanical energy of three non-biological layers. The radius of curvature and deflection of the cantilever were determined through the minimum principle of energy. The efficiency of the present model was confirmed through comparison with experimental data. The effects of length, grafting density, salt concentration, thickness, and elastic modulus of substrate on tip deflections are also discussed in this paper. These factors can significantly affect the deflections of the biosensor. This work demonstrates that it is useful to develop a theoretical model for the label-free nanomechanical detection technique.

Effect of surface charge state on the surface stress of a microcantilever.

The surface charge state at a liquid-solid interface is important to the variations in the physical/chemical properties of adsorbate film such as surface stress and the ensuing tip deflection of the microcantilever. The well-known Stoney's equation, derived more than 100 years ago, conceals the film electrical properties with the replacement of substrate deformation induced by adsorptions of particles. This implicit expression provides a shortcut to circumvent the difficulty in identifying some film properties, however, it limits the capacity to ascertain the relation between surface stress variation and the surface charge state. In this paper, we present an analytical expression to quantify the cantilever deflection/surface stress and the film potential difference by combining the piezoelectric theory and Poisson-Boltzmann equation for electrolyte solution. This updated version indicates that the two linear correlations between surface stress and surface charge density or the bias voltage are not contradictory, but two aspects of one thing under different conditions. Based on Parsegian's mesoscopic interaction potential, a multiscale prediction for the piezoelectric coefficient of double-stranded DNA (dsDNA) film is done, and the results show that the distinctive size effect with variations in salt concentration and nucleotide number provides us with an opportunity to obtain a more sensitive potential-actuated microcantilever sensor by careful control of packing conditions.

A multi-scale model for the analysis of the inhomogeneity of elastic properties of DNA biofilm on microcantilevers.

In nanoscale diagnostic systems, inhomogeneity in near-surface systems and flexibility in biostructures greatly influence the mechanical/electrical/thermal properties of biosensors and resultant detection signals. This study focuses on inhomogeneity and flexibility of DNA biofilm and characterizes its local interactions and mechanical properties. First, a flexible cylinder model of DNA chain is employed to capture the local geometric deformation characteristics of DNA molecules on microcantilever. In order to describe the inhomogeneous properties of DNA biofilm at thickness direction, the Strey's empirical formula for mesoscopic DNA liquid crystal theory is improved with the assumption of a net charge distribution in film. The model parameters are obtained by curve fitting with experimental data. Second, the biaxial iso-strain compression of thought experiment and the energy conservation law are used to predict macroscopic effective tangent modulus of DNA biofilm in terms of nanoscopic properties of dsDNA, buffer salt concentration.

Mechanical properties of DNA biofilms adsorbed on microcantilevers in label-free biodetections.

Biomolecule adsorption is a fundamental process in the design of biosensors. Mechanical/electrical/thermal properties of biofilms have great influences on biodetection signals. The double-stranded DNA (dsDNA) biofilm adhered on microcantilever is treated as a bending beam with a macroscopic elastic modulus in the viewpoint of continuum mechanics. Accounting for hydration force, electrostatic repulsion and conformational entropy, moment-angle diagrams of dsDNA biofilm in pure bending state are depicted with the help of the energy conservation law and a mesoscopic liquid crystal theory presented by Strey et al. An analytical model is provided to predict macroscopic elastic modulus of dsDNA biofilm as a function of nanoscopic properties of dsDNA, packing density, buffer salt concentration and etc. The parameters for microcantilever-DNA system are obtained by curve fitting with Stachowiak's experimental data based on a modified Stoney's formula. Elastic modulus grows exponentially with the enhancement of packaging density, but diminishes with the increase of buffer salt concentration, and its order is about 1 approximately 10 MPa. Conformational entropy is one of predominant factors considered in near-surface system whether in high or low salt consternation.

Mechanical properties of double-stranded DNA biolayers immobilized on microcantilever under axial compression.

In label-free biodetections based on microcantilever technology, double-stranded DNA (dsDNA) structures form through the linkage between probe single-stranded DNA (ssDNA) molecules immobilized on solid substrates and target ssDNA molecules in solutions. Mechanical/electrical properties of these biolayers are important factors for nanomechanical deflections of microcantilevers. In this paper, the biolayer immobilized on microcantilever is treated as a bar with a macroscopic elastic modulus on the basis of continuum mechanics viewpoints. In consideration of hydration force, screened electrostatic repulsion and conformational fluctuation in biolayers, load-deformation curves of dsDNA biolayers under axial compression are depicted with the help of the energy conservation law and a mesoscopic free energy presented by Strey et al. (1997, 1999) [Strey, H.H., Parsegian, V.A., Podgornik, R., 1997. Equation of state for DNA liquid crystals: fluctuation enhanced electrostatic double layer repulsion. Physical Review Letters 78, 895-898; Strey, H.H., Parsegian, V.A., Podgornik, R., 1999. Equation of state for polymer liquid crystals: theory and experiment. Physical Review E 59, 999-1008] from a liquid crystal theory. And the analytical relation between macroscopic Young's modulus of biolayers and nanoscopic geometrical properties of dsDNA, packing density, buffer salt solution concentration, etc. is also formulated.