Browsing by Subject "Diffusion coefficient"

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A computational model for the diffusion coefficients of DNA with applications
(2010-05) Li, Jun, 1977-; Gonzalez, Oscar, 1968-; Demkowicz, Leszek F.; Makarov, Dmitrii E.; Rodin, Gregory J.; van de Geijn, Robert A.
The sequence-dependent curvature and flexibility of DNA is critical for many biochemically important processes. However, few experimental methods are available for directly probing these properties at the base-pair level. One promising way to predict these properties as a function of sequence is to model DNA with a set of base-pair parameters that describe the local stacking of the different possible base-pair step combinations. In this dissertation research, we develop and study a computational model for predicting the diffusion coefficients of short, relatively rigid DNA fragments from the sequence and the base-pair parameters. We focus on diffusion coefficients because various experimental methods have been developed to measure them. Moreover, these coefficients can also be computed numerically from the Stokes equations based on the three-dimensional shape of the macromolecule. By comparing the predicted diffusion coefficients with experimental measurements, we can potentially obtain refined estimates of various base-pair parameters for DNA. Our proposed model consists of three sub-models. First, we consider the geometric model of DNA, which is sequence-dependent and controlled by a set of base-pair parameters. We introduce a set of new base-pair parameters, which are convenient for computation and lead to a precise geometric interpretation. Initial estimates for these parameters are adapted from crystallographic data. With these parameters, we can translate a DNA sequence into a curved tube of uniform radius with hemispherical end caps, which approximates the effective hydrated surface of the molecule. Second, we consider the solvent model, which captures the hydrodynamic properties of DNA based on its geometric shape. We show that the Stokes equations are the leading-order, time-averaged equations in the particle body frame assuming that the Reynolds number is small. We propose an efficient boundary element method with a priori error estimates for the solution of the exterior Stokes equations. Lastly, we consider the diffusion model, which relates our computed results from the solvent model to relevant measurements from various experimental methods. We study the diffusive dynamics of rigid particles of arbitrary shape which often involves arbitrary cross- and self-coupling between translational and rotational degrees of freedom. We use scaling and perturbation analysis to characterize the dynamics at time scales relevant to different classic experimental methods and identify the corresponding diffusion coefficients. In the end, we give rigorous proofs for the convergence of our numerical scheme and show numerical evidence to support the validity of our proposed models by making comparisons with experimental data.
From confinement to clustering : decoding the structural and diffusive signatures of microscopic frustration
(2016-12) Bollinger, Jonathan Allen; Truskett, Thomas Michael, 1973-; Bonnecaze, Roger T.; Ganesan, Venkat; Lynd, Nathaniel A.; Makarov, Dmitrii E.
There are diverse technological contexts where fluids and suspensions are perturbed by applied fields like interfaces or intrinsically governed by complex interparticle potentials. When these interactions act over lengthscales comparable to the fluid particle size and become strong enough to frustrate particle packing or rearrangements, they drive systems to exhibit microscopically inhomogeneous (i.e., position-dependent) structural and relaxation responses. We use computer simulations and statistical-mechanical tools to find connections between such frustrating interactions and inhomogeneous fluid responses, which can profoundly impact macroscopic material properties and processing requirements. We first consider how to measure and predict the position-dependent and average diffusion coefficients of particles along inhomogeneous free-energy landscapes (i.e., potentials of mean force). Characterizing diffusion in such inhomogeneous fluids is crucial for modeling, e.g., the transit of colloids across microfluidic devices and of solutes through biological membranes. We validate a practical technique based on the Fokker-Planck diffusion formalism that measures diffusivities based solely on particle trajectory data. We focus on hard-sphere fluids confined to thin channels or subjected to external fields that impose density fluctuations at various wavelengths. We find, for example, that hydrodynamic predictions of tracer diffusion in confinement are surprisingly robust given non-continuum solvents. We also demonstrate that correlations between fluid static structure and diffusivity can qualitatively depend on the lengthscale of density fluctuations or the onset of supercooling. We next examine fluids governed by competing short-range attractions and long-range repulsions that drive formation of equilibrium cluster phases, which comprise monodisperse aggregates of monomers. The formation of such morphologies greatly impacts, e.g., the manufacturing of therapeutic protein solutions. We first address a major challenge in probing the real-space structure of such suspensions: detecting and characterizing cluster phases based on the static structure factor accessible via scattering experiments. Using computer simulations and liquid-state theory, we validate rules for interpreting low-wavenumber features in the structure factor in terms of cluster emergence, size, spatial distribution, etc. We then validate a thermodynamic model that predicts cluster size based on the strengths of monomer interactions, adapting classical nucleation theory to incorporate new empirical scalings for the surface energies of small stable droplets.