Grigori Sigalov

Analytical electrostatics for biomolecules: Beyond the generalized Born approximation

The modeling and simulation of macromolecules in solution often benefits from fast analytical approximations for the electrostatic interactions. In our previous work [G. Sigalov et al., J. Chem. Phys. 122, 094511 (2005)], we proposed a method based on an approximate analytical solution of the linearized Poisson-Boltzmann equation for a sphere. In the current work, we extend the method to biomolecules of arbitrary shape and provide computationally efficient algorithms for estimation of the parameters of the model. This approach, which we tentatively call ALPB here, is tested against the standard numerical Poisson-Boltzmann (NPB) treatment on a set of 579 representative proteins, nucleic acids, and small peptides. The tests are performed across a wide range of solvent/solute dielectrics and at biologically relevant salt concentrations. Over the range of the solvent and solute parameters tested, the systematic deviation (from the NPB reference) of solvation energies computed by ALPB is 0.5-3.5 kcal/mol, which is 5-50 times smaller than that of the conventional generalized Born approximation widely used in this context. At the same time, ALPB is equally computationally efficient. The new model is incorporated into the AMBER molecular modeling package and tested on small proteins.

Incorporating variable dielectric environments into the generalized Born model.

A generalized Born (GB) model is proposed that approximates the electrostatic part of macromolecular solvation free energy over the entire range of the solvent and solute dielectric constants. The model contains no fitting parameters, and is derived by matching a general form of the GB Green function with the exact Greens function of the Poisson equation for a random charge distribution inside a perfect sphere. The sphere is assumed to be filled uniformly with dielectric medium epsilon(in), and is surrounded by infinite solvent of constant dielectric epsilon(out). This model is as computationally efficient as the conventional GB model based on the widely used functional form due to Still et al. [J. Am. Chem. Soc. 112, 6127 (1990)], but captures the essential physics of the dielectric response for all values of epsilon(in) and epsilon(out). This model is tested against the exact solution on a perfect sphere, and against the numerical Poisson-Boltzmann (PB) treatment on a set of macromolecules representing various structural classes. It shows reasonable agreement with both the exact and the numerical solutions of the PB equation (where available) considered as reference, and is more accurate than the conventional GB model over the entire range of dielectric values.

Dynamics of an Eccentric Rotational Nonlinear Energy Sink

The paper introduces a novel type of nonlinear energy sink, designed as a simple rotating eccentric mass, which can rotate with any frequency and; therefore, inertially couple and resonate with any mode of the primary system. We report on theoretical and experimental investigations of targeted energy transfer in this system.

Analyzing the forces binding a restriction endonuclease to DNA using a synthetic nanopore

Restriction endonucleases are used prevalently in recombinant DNA technology because they bind so stably to a specific target sequence and, in the presence of cofactors, cleave double-helical DNA specifically at a target sequence at a high rate. Using synthetic nanopores along with molecular dynamics (MD), we have analyzed with atomic resolution how a prototypical restriction endonuclease, EcoRI, binds to the DNA target sequence—GAATTC—in the absence of a Mg2+ ion cofactor. We have previously shown that there is a voltage threshold for permeation of DNA bound to restriction enzymes through a nanopore that is associated with a nanonewton force required to rupture the complex. By introducing mutations in the DNA, we now show that this threshold depends on the recognition sequence and scales linearly with the dissociation energy, independent of the pore geometry. To predict the effect of mutation in a base pair on the free energy of dissociation, MD is used to qualitatively rank the stability of bonds in the EcoRI–DNA complex. We find that the second base in the target sequence exhibits the strongest binding to the protein, followed by the third and first bases, with even the flanking sequence affecting the binding, corroborating our experiments.

Dynamics of a linear oscillator coupled to a bistable light attachment: Numerical study

The conservative and dissipative dynamics of a 2DOF, system composed of a grounded linear oscillator coupled to a lightweight mass by means of both strongly nonlinear and linear negative stiffnesses is investigated. Numerical studies are presented aiming to assess the influence of this combined coupling on the transient dynamics. In particular, these studies are focused on passive nonlinear targeted energy transfer from the impulsively excited linear oscillator to the nonlinear bistable lightweight attachment. It is shown that the main feature of the proposed configuration is the ability of assuring broadband efficient energy transfer over a broad range of input energy. Due to the bistability of the attachment, such favorable behavior is triggered by different nonlinear dynamic mechanisms depending on the energy level. For high energy levels, strongly modulated oscillations occur, and the dynamics is governed by fundamental (1:1) and superharmonic (1:3) resonances; for low energy levels, chaotic cross-well oscillations of the nonlinear attachment as well as subharmonic resonances lead to strong energy exchanges between the two oscillators. The results reported in this work indicate that properly designed attachments of this type can be efficient absorbers and dissipators of impulsively induced vibration energy.

Nonstationary energy localization vs conventional stationary localization in weakly coupled nonlinear oscillators

In this paper we study the effect of nonstationary energy localization in a nonlinear conservative resonant system of two weakly coupled oscillators. This effect is alternative to the well-known stationary energy localization associated with the existence of localized normal modes and resulting from a local topological transformation of the phase portraits of the system. In this work we show that nonstationary energy localization results from a global transformation of the phase portrait. A key to solving the problem is the introduction of the concept of limiting phase trajectories (LPTs) corresponding to maximum possible energy exchange between the oscillators. We present two scenarios of nonstationary energy localization under the condition of 1:1 resonance. It is demonstrated that the conditions of nonstationary localization determine the conditions of efficient targeted energy transfer in a generating dynamical system. A possible extension to multi-particle systems is briefly discussed.

Designing a New Type of Energy Trap: A Classical Analog of Quantum Landau-Zener Tunneling

We present a novel type of energy trap providing targeted energy transfer (TET) in a system of weakly coupled pendulums. Our approach is based on the analogy, presented in [1, 2], between the behavior of two weakly coupled classical parametric pendulums and nonadiabatic Landau-Zener tunneling (LZT) in a two-state quantum system. The two systems, however dissimilar, turn out to be described by the same asymptotic equations. Well-known properties of LZT allow us to predict the possibility of efficient irreversible transfer of vibration energy from one subsystem to another in mechanical systems. The TET takes place when the eigenfrequency of a subsystem changes in time so that the coupled subsystems pass through internal resonance. The existence of such a phenomenon is not restricted to coupled pendulums but is inherent to a wide class of both linear and nonlinear parametric oscillatory systems. This opens up the possibility of designing new types of energy traps and absorbers for the dynamic protection of various mechanical systems. Experimental data obtained in this work corroborate theoretical predictions.Copyright