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We consider diffusion processes with a spatially varying diffusivity giving rise to anomalous diffusion. Such heterogeneous diffusion processes are analysed for the cases of exponential, power-law, and logarithmic dependencies of the diffusion coefficient on the particle position. Combining analytical approaches with stochastic simulations, we show that the functional form of the space-dependent diffusion coefficient and the initial conditions of the diffusing particles are vital for their statistical and ergodic properties. In all three cases a weak ergodicity breaking between the time and ensemble averaged mean squared displacements is observed. We also demonstrate a population splitting of the time averaged traces into fast and slow diffusers for the case of exponential variation of the diffusivity as well as a particle trapping in the case of the logarithmic diffusivity. Our analysis is complemented by the quantitative study of the space coverage, the diffusive spreading of the probability density, as well as the survival probability.
Label-free electrical detection of consecutive deoxyribonucleic acid (DNA) hybridization/denaturation by means of an array of individually addressable field-effect-based nanoplate silicon-on-insulator (SOI) capacitors modified with gold nanoparticles (Au-NP) is investigated. The proposed device detects charge changes on Au-NP/DNA hybrids induced by the hybridization or denaturation event. DNA hybridization was performed in a high ionic-strength solution to provide a high hybridization efficiency. On the other hand, to reduce the screening of the DNA charge by counter ions and to achieve a high sensitivity, the sensor signal induced by the hybridization and denaturation events was measured in a low ionic-strength solution. High sensor signals of about 120, 90, and 80 mV were registered after the DNA hybridization, denaturation, and re-hybridization events, respectively. Fluorescence microscopy has been applied as reference method to verify the DNA immobilization, hybridization, and denaturation processes. An electrostatic charge-plane model for potential changes at the gate surface of a nanoplate field-effect sensor induced by the DNA hybridization has been developed taking into account both the Debye length and the distance of the DNA charge from the gate surface.
We analyze theoretically the influence of low-dielectric boundaries on the adsorption of flexible polyelectrolytes onto planar and spherical oppositely charged surfaces in electrolyte solutions. We rationalize to what extent polymer chains are depleted from adsorbing interfaces by repulsive image forces. We employ the WKB (Wentzel-Kramers-Brillouin) quantum mechanical method for the Green function of the Edwards equation to determine the adsorption equilibrium. Scaling relations are determined for the critical adsorption strength required to initiate polymer adsorption onto these low-dielectric supports. Image-force repulsion shifts the equilibrium toward the desorbed state, demanding larger surface charge densities and polyelectrolyte linear charge densities for the adsorption to take place. The effect is particularly pronounced for a planar interface in a low-salt regime, where a dramatic change in the scaling behavior for the adsorption-desorption transition is predicted. For the adsorbed state, polymers with higher charge densities are displaced further from the interface by image-charge repulsions. We discuss relevant experimental evidence and argue about possible biological applications of the results.
We explore the properties of adsorption of flexible polyelectrolyte chains in confined spaces between the oppositely charged surfaces in three basic geometries. A method of approximate uniformly valid solutions for the Green function equation for the eigenfunctions of polymer density distributions is developed to rationalize the critical adsorption conditions. The same approach was implemented in our recent study for the inverse problem of polyelectrolyte adsorption onto a planar surface, and on the outer surface of rod-like and spherical obstacles. For the three adsorption geometries investigated, the theory yields simple scaling relations for the minimal surface charge density that triggers the chain adsorption, as a function of the Debye screening length and surface curvature. The encapsulation of polyelectrolytes is governed by interplay of the electrostatic attraction energy toward the adsorbing surface and entropic repulsion of the chain squeezed into a thin slit or small cavities. Under the conditions of surface-mediated confinement, substantially larger polymer linear charge densities are required to adsorb a polyelectrolyte inside a charged spherical cavity, relative to a cylindrical pore and to a planar slit (at the same interfacial surface charge density). Possible biological implications are discussed briefly in the end.
Chromatin domains formed in vivo are characterized by different types of 3D organization of interconnected nucleosomes and architectural proteins. Here, we quantitatively test a hypothesis that the similarities in the structure of chromatin fibers (which we call "structural homology") can affect their mutual electrostatic and protein-mediated bridging interactions. For example, highly repetitive DNA sequences in heterochromatic regions can position nucleosomes so that preferred inter-nucleosomal distances are preserved on the surfaces of neighboring fibers. On the contrary, the segments of chromatin fiber formed on unrelated DNA sequences have different geometrical parameters and lack structural complementarity pivotal for stable association and cohesion. Furthermore, specific functional elements such as insulator regions, transcription start and termination sites, and replication origins are characterized by strong nucleosome ordering that might induce structure-driven iterations of chromatin fibers. We propose that shape-specific protein-bridging interactions facilitate long-range pairing of chromatin fragments, while for closely-juxtaposed fibers electrostatic forces can in addition yield fine-tuned structure-specific recognition and pairing. These pairing effects can account for some features observed for mitotic and inter-phase chromatins.
We consider diffusion processes with a spatially varying diffusivity giving rise to anomalous diffusion. Such heterogeneous diffusion processes are analysed for the cases of exponential, power-law, and logarithmic dependencies of the diffusion coefficient on the particle position. Combining analytical approaches with stochastic simulations, we show that the functional form of the space-dependent diffusion coefficient and the initial conditions of the diffusing particles are vital for their statistical and ergodic properties. In all three cases a weak ergodicity breaking between the time and ensemble averaged mean squared displacements is observed. We also demonstrate a population splitting of the time averaged traces into fast and slow diffusers for the case of exponential variation of the diffusivity as well as a particle trapping in the case of the logarithmic diffusivity. Our analysis is complemented by the quantitative study of the space coverage, the diffusive spreading of the probability density, as well as the survival probability.
We consider diffusion processes with a spatially varying diffusivity giving rise to anomalous diffusion. Such heterogeneous diffusion processes are analysed for the cases of exponential, power-law, and logarithmic dependencies of the diffusion coefficient on the particle position. Combining analytical approaches with stochastic simulations, we show that the functional form of the space-dependent diffusion coefficient and the initial conditions of the diffusing particles are vital for their statistical and ergodic properties. In all three cases a weak ergodicity breaking between the time and ensemble averaged mean squared displacements is observed. We also demonstrate a population splitting of the time averaged traces into fast and slow diffusers for the case of exponential variation of the diffusivity as well as a particle trapping in the case of the logarithmic diffusivity. Our analysis is complemented by the quantitative study of the space coverage, the diffusive spreading of the probability density, as well as the survival probability.
We model theoretically the electrostatic effects taking place upon DNA hybridization in dense DNA arrays immobilized on a layer of Au nano-particles deposited on the surface of a field-effect-based DNA capacitive biosensor. We consider the influence of separation of a charged analyte from the sensor surface and the salinity of electrolyte solution, in the framework of both linear and nonlinear Poisson-Boltzmann theories. The latter predicts a substantially weaker sensor signals due to electrostatic saturation effects that is the main conclusion of this paper. We analyze how different physical parameters of dense DNA brushes affect the magnitude of hybridization signals. The list includes the fraction of DNA charge neutralization, the length and spatial conformations of adsorbed DNA molecules, as well as the discreteness of DNA charges. We also examine the effect of Donnan ionic equilibrium in DNA lattices on the sensor response. The validity of theoretical models is contrasted against recent experimental observations on detection of DNA hybridization via its intrinsic electric charge. The sensitivity of such biochemical sensing devices, their detection limit, and DNA hybridization efficiency are briefly discussed in the end.
The semiconductor field-effect platform represents a powerful tool for detecting the adsorption and binding of charged macromolecules with direct electrical readout. In this work, a capacitive electrolyte-insulator-semiconductor (EIS) field-effect sensor consisting of an Al-p-Si-SiO2 structure has been applied for real-time in situ electrical monitoring of the layer-by-layer formation of polyelectrolyte (PE) multilayers (PEM). The PEMs were deposited directly onto the SiO2 surface without any precursor layer or drying procedures. Anionic poly(sodium 4-styrene sulfonate) and cationic weak polyelectrolyte poly(allylamine hydrochloride) have been chosen as a model system. The effect of the ionic strength of the solution, polyelectrolyte concentration, number and polarity of the PE layers on the characteristics of the PEM-modified EIS sensors have been studied by means of capacitance-voltage and constant-capacitance methods. In addition, the thickness, surface morphology, roughness and wettabilityof the PE mono- and multilayers have been characterised by ellipsometry, atomic force microscopy and water contact-angle methods, respectively. To explain potential oscillations on the gate surface and signal behaviour of the capacitive field-effect EIS sensor modified with a PEM, a simplified electrostatic model that takes into account the reduced electrostatic screening of PE charges by mobile ions within the PEM has been proposed and discussed.
We demonstrate the non-ergodicity of a simple Markovian stochastic process with space-dependent diffusion coefficient D(x). For power-law forms D(x) similar or equal to vertical bar x vertical bar(alpha), this process yields anomalous diffusion of the form < x(2)(t)> similar or equal to t(2/(2-alpha)). Interestingly, in both the sub- and superdiffusive regimes we observe weak ergodicity breaking: the scaling of the time-averaged mean-squared displacement <(delta(2)(Delta))over bar> remains linear in the lag time Delta and thus differs from the corresponding ensemble average < x(2)(t)>. We analyse the non-ergodic behaviour of this process in terms of the time-averaged mean- squared displacement (delta(2)) over bar and its random features, i.e. the statistical distribution of (delta(2)) over bar and the ergodicity breaking parameters. The heterogeneous diffusion model represents an alternative approach to non- ergodic, anomalous diffusion that might be particularly relevant for diffusion in heterogeneous media.