Nikolaos K. Voulgarakis

Bubble Nucleation and Cooperativity in DNA Melting

The onset of intermediate states (denaturation bubbles) and their role during the melting transition of DNA are studied using the Peyrard-Bishop-Dauxois model by Monte Carlo simulations with no adjustable parameters. Comparison is made with previously published experimental results finding excellent agreement. Melting curves, critical DNA segment length for stability of bubbles, and the possibility of a two-state transition are studied.

Bridging fluctuating hydrodynamics and molecular dynamics simulations of fluids

A new multiscale coarse-graining (CG) methodology is developed to bridge molecular and hydrodynamic models of a fluid. The hydrodynamic representation considered in this work is based on the equations of fluctuating hydrodynamics (FH). The essence of this method is a mapping from the position and velocity vectors of a snapshot of a molecular dynamics (MD) simulation to the field variables on Eulerian cells of a hydrodynamic representation. By explicit consideration of the effective lengthscale d(mol) that characterizes the volume of a molecule, the computed density fluctuations from MD via our mapping procedure have volume dependence that corresponds to a grand canonical ensemble of a cold liquid even when a small cell length (5-10 A) is used in a hydrodynamic representation. For TIP3P water at 300 K and 1 atm, d(mol) is found to be 2.4 A, corresponding to the excluded radius of a water molecule as revealed by its center-of-mass radial distribution function. By matching the density fluctuations and autocorrelation functions of momentum fields computed from solving the FH equations with those computed from MD simulation, the sound velocity and shear and bulk viscosities of a CG hydrodynamic model can be determined directly from MD. Furthermore, a novel staggered discretization scheme is developed for solving the FH equations of an isothermal compressive fluid in a three dimensional space with a central difference method. This scheme demonstrates high accuracy in satisfying the fluctuation-dissipation theorem. Since the causative relationship between field variables and fluxes is captured, we demonstrate that the staggered discretization scheme also predicts correct physical behaviors in simulating transient fluid flows. The techniques presented in this work may also be employed to design multiscale strategies for modeling complex fluids and macromolecules in solution.

Pre-melting dynamics of DNA and its relation to specific functions

We discuss connections between the nonlinear dynamics of double-stranded DNA, experimental findings, and specific DNA functions. We begin by discussing how thermally induced localized openings (bubbles) of the DNA double strand are important for interpreting dynamic force spectroscopy data. Then we demonstrate a correlation between a sequence-dependent propensity for pre-melting bubble formation and transcription initiation and other regulatory effects in viral DNA. Finally, we discuss the possibility of a connection between DNA dynamics and the ability of repair proteins to recognize ultraviolet (UV) radiation damage sites.

Probing the mechanical unzipping of DNA.

A study of the micromechanical unzipping of DNA in the framework of the Peyrard-Bishop-Dauxois model is presented. We introduce a Monte Carlo technique that allows accurate determination of the dependence of the unzipping forces on unzipping speed and temperature. Our findings agree quantitatively with experimental results for homogeneous DNA, and for lamda-phage DNA we reproduce the recently obtained experimental force-temperature phase diagram. Finally, we argue that there may be fundamental differences between in vivo and in vitro DNA unzipping.

Dendrimers as synthetic gene vectors: Cell membrane attachment

We present molecular-level simulations of dendrimer/DNA complexes in the presence of a model cell membrane. We determine the required conditions for the complex to arrive intact at the membrane, and the lifetime of the complex as it resides attached to the membrane. Our simulations directly pertain to critical issues arising in emerging gene delivery therapeutic applications, where a molecular carrier is required to deliver DNA segments to the interior of living cells.

Fluctuating hydrodynamics for multiscale simulation of inhomogeneous fluids: Mapping all-atom molecular dynamics to capillary waves

We introduce a multiscale framework to simulate inhomogeneous fluids by coarse-graining an all-atom molecular dynamics (MD) trajectory onto sequential snapshots of hydrodynamic fields. We show that the field representation of an atomistic trajectory is quantitatively described by a dynamic field-theoretic model that couples hydrodynamic fluctuations with a Ginzburg-Landau free energy. For liquid-vapor interfaces of argon and water, the parameters of the field model can be adjusted to reproduce the bulk compressibility and surface tension calculated from the positions and forces of atoms in an MD simulation. These optimized parameters also enable the field model to reproduce the static and dynamic capillary wave spectra calculated from atomistic coordinates at the liquid-vapor interface. In addition, we show that a density-dependent gradient coefficient in the Ginzburg-Landau free energy enables bulk and interfacial fluctuations to be controlled separately. For water, this additional degree of freedom is necessary to capture both the bulk compressibility and surface tension emergent from the atomistic trajectory. The proposed multiscale framework illustrates that bottom-up coarse-graining and top-down phenomenology can be integrated with quantitative consistency to simulate the interfacial fluctuations in nanoscale transport processes.

Fluctuating hydrodynamics for multiscale modeling and simulation: energy and heat transfer in molecular fluids.

This work illustrates that fluctuating hydrodynamics (FHD) simulations can be used to capture the thermodynamic and hydrodynamic responses of molecular fluids at the nanoscale, including those associated with energy and heat transfer. Using all-atom molecular dynamics (MD) trajectories as the reference data, the atomistic coordinates of each snapshot are mapped onto mass, momentum, and energy density fields on Eulerian grids to generate a corresponding field trajectory. The molecular length-scale associated with finite molecule size is explicitly imposed during this coarse-graining by requiring that the variances of density fields scale inversely with the grid volume. From the fluctuations of field variables, the response functions and transport coefficients encoded in the all-atom MD trajectory are computed. By using the extracted fluid properties in FHD simulations, we show that the fluctuations and relaxation of hydrodynamic fields quantitatively match with those observed in the reference all-atom MD trajectory, hence establishing compatibility between the atomistic and field representations. We also show that inclusion of energy transfer in the FHD equations can more accurately capture the thermodynamic and hydrodynamic responses of molecular fluids. The results indicate that the proposed MD-to-FHD mapping with explicit consideration of finite molecule size provides a robust framework for coarse-graining the solution phase of complex molecular systems.

Modeling the nanoscale viscoelasticity of fluids by bridging non-Markovian fluctuating hydrodynamics and molecular dynamics simulations.

A multiscale computational method is developed to model the nanoscale viscoelasticity of fluids by bridging non-Markovian fluctuating hydrodynamics (FHD) and molecular dynamics (MD) simulations. To capture the elastic responses that emerge at small length scales, we attach an additional rheological model parallel to the macroscopic constitutive equation of a fluid. The widely used linear Maxwell model is employed as a working choice; other models can be used as well. For a fluid that is Newtonian in the macroscopic limit, this approach results in a parallel Newtonian-Maxwell model. For water, argon, and an ionic liquid, the power spectrum of momentum field autocorrelation functions of the parallel Newtonian-Maxwell model agrees very well with those calculated from all-atom MD simulations. To incorporate thermal fluctuations, we generalize the equations of FHD to work with non-Markovian rheological models and colored noise. The fluctuating stress tensor (white noise) is integrated in time in the same manner as its dissipative counterpart and numerical simulations indicate that this approach accurately preserves the set temperature in a FHD simulation. By mapping position and velocity vectors in the molecular representation onto field variables, we bridge the non-Markovian FHD with atomistic MD simulations. Through this mapping, we quantitatively determine the transport coefficients of the parallel Newtonian-Maxwell model for water and argon from all-atom MD simulations. For both fluids, a significant enhancement in elastic responses is observed as the wave number of hydrodynamic modes is reduced to a few nanometers. The mapping from particle to field representations and the perturbative strategy of developing constitutive equations provide a useful framework for modeling the nanoscale viscoelasticity of fluids.

Polaronic electron transfer in β-sheet protein models

We consider electron transfer (ET) along β-sheet forms of proteins. The secondary structure of the β-sheet proteins is modelled by a two-dimensional oscillator network whose constituents represent peptide units. Covalent and hydrogen bonds between the peptide units are represented by point-point interaction potentials. Intrapeptide vibrational degrees of freedom are taken into account by means of harmonic oscillators while the electronic motion is described within the framework of a tight-binding system. We construct polarons as stationary localized solution states utilizing a non-linear map approach. The polaron state represents a self-trapped electron in conjunction with its intrapeptide deformation field and the static deformation of the protein scaffolding. Furthermore, in the dynamical study we focus attention on the initiation of polaron motion, utilizing its pinning modes. We show that both the covalent and the hydrogen channel provide a path for coherent ET in β-sheet proteins. It is demonstrated that the interplay of the vibrations of the protein scaffolding and the electron dynamics promotes long-lived localized excitation patterns travelling coherently along the lattice of peptide units.

Allostery through protein-induced DNA bubbles

Allostery through DNA is increasingly recognized as an important modulator of DNA functions. Here, we show that the coalescence of protein-induced DNA bubbles can mediate allosteric interactions that drive protein aggregation. We propose that such allostery may regulate DNAs flexibility and the assembly of the transcription machinery. Mitochondrial transcription factor A (TFAM), a dual-function protein involved in mitochondrial DNA (mtDNA) packaging and transcription initiation, is an ideal candidate to test such a hypothesis owing to its ability to locally unwind the double helix. Numerical simulations demonstrate that the coalescence of TFAM-induced bubbles can explain experimentally observed TFAM oligomerization. The resulting melted DNA segment, approximately 10 base pairs long, around the joints of the oligomers act as flexible hinges, which explains the efficiency of TFAM in compacting DNA. Since mitochondrial polymerase (mitoRNAP) is involved in melting the transcription bubble, TFAM may use the same allosteric interaction to both recruit mitoRNAP and initiate transcription.