Bio-molecules and proteins are building blocks of life as is known, and understanding

their dynamics and functions are necessary to better understand life and improve its

quality. While ergodicity and fluctuation dissipation theorem (FDT) are fundamental

and crucial concepts regarding study of dynamics of systems in equilibrium, biological

function is not possible in equilibrium.

In this work, dynamical and orientational structural crossovers in low-temperature

glycerol are investigated. A sudden and notable increase in the orientational Kirk-

wood factor and the dielectric constant is observed, which appears in the same range

of temperatures that dynamic crossover of translational and rotational dynamics oc-

cur.

Theory and electrochemistry of cytochrome c is also investigated. The seeming

discrepancy in reorganization energies of protein electron transfer produced by atom-

istic simulations and those reported by protein electrochemistry (which are smaller)

is resolved. It is proposed in this thesis that ergodicity breaking results in an effective

reorganization energy (0.57 eV) consistent with experiment.

Ergodicity breaking also affects the iron displacement in heme proteins. A model

for dynamical transition of atomic displacements in proteins is provided. Different

temperatures for rotational and translational crossovers of water molecules are re-

ported, which all are ergodicity breaking transitions depending on the corresponding

observation windows. The comparison with Mössbauer spectroscopy is presented.

Biological function at low temperatures and its termination is also investigated in

this research. Here, it is proposed that ergodicity breaking gives rise to the violation

of the FDT, and this violation is maintained in the entire range of physiological

temperatures for cytochrome c. Below the crossover temperature, the protein returns

to the FDT, which leads to a sudden jump in the activation barrier for electron

itransfer.

Finally the interaction of charges in dielectric materials is discussed. It is shown

that the potential of mean force between ions in polar liquids becomes oscillatory at

short distances.

How water behaves at interfaces is relevant to many scientific and technological applications; however, many subtle phenomena are unknown in aqueous solutions. In this work, interfacial structural transition in hydration shells of a polarizable solute at critical polarizabilities is discovered. The transition is manifested in maximum water response, the reorientation of the water dipoles at the interface, and an increase in the density of dangling OH bonds. This work also addresses the role of polarizability of the active site of proteins in biological catalytic reactions. For proteins, the hydration shell becomes very heterogeneous and involves a relatively large number of water molecules. The molecular dynamics simulations show that the polarizability, along with the atomic charge distribution, needs to be a part of the picture describing how enzymes work. Non Gaussian dynamics in time-resolved linear and nonlinear (correlation) 2D spectra are also analyzed.



Additionally, a theoretical formalism is presented to show that when preferential orientations of water dipoles exist at the interface, electrophoretic charges can be produced without free charge carriers, i.e., neutral solutes can move in a constant electric field due to the divergence of polarization at the interface. Furthermore, the concept of interface susceptibility is introduced. It involves the fluctuations of the surface charge density caused by thermal motion and its correlation over the characteristic correlation length with the fluctuations of the solvent charge density. Solvation free energy and interface dielectric constant are formulated accordingly. Unlike previous approaches, the solvation free energy scales quite well in a broad range of ion sizes, namely in the range of 2-14 A° . Interface dielectric constant is defined such that the boundary conditions in the Laplace equation describing a micro- or mesoscopic interface are satisfied. The effective dielectric constant of interfacial water is found to be significantly lower than its bulk value. Molecular dynamics simulation results show that the interface dielectric constant for a TIP3P water model changes from nine to four when the effective solute radius is increased from 5 A° to 18 A° . The small value of the interface dielectric constant of water has potentially dramatic consequences for hydration.

Molecular dynamics simulations were used to study properties of water at the interface with nanometer-size solutes. We simulated nonpolar attractive Kihara cavities given by a Lennard-Jones potential shifted by a core radius. The dipolar response of the hydration layer to a uniform electric field substantially exceeds that of the bulk. For strongly attractive solutes, the collective dynamics of the hydration layer become slow compared to bulk water, as the solute size is increased. The statistics of electric field fluctuations at the solute center are Gaussian and tend toward the dielectric continuum limit with increasing solute size. A dipolar probe placed at the center of the solute is sensitive neither to the polarity excess nor to the slowed dynamics of the hydration layer. A point dipole was introduced close to the solute-water interface to further study the statistics of electric field fluctuations generated by the water. For small dipole magnitudes, the free energy surface is single-welled, with approximately Gaussian statistics. When the dipole is increased, the free energy surface becomes double-welled, before landing in an excited state, characterized again by a single-welled surface. The intermediate region is fairly broad and is characterized by electrostatic fluctuations significantly in excess of the prediction of linear response. We simulated a solute having the geometry of C180 fullerene, with dipoles introduced on each carbon. For small dipole moments, the solvent response follows the results seen for a single dipole; but for larger dipole magnitudes, the fluctuations of the solute-solvent energy pass through a second maximum. The juxtaposition of the two transitions leads to an approximately cubic scaling of the chemical potential with the dipole strengh. Umbrella sampling techniques were used to generate free energy surfaces of the electric potential fluctuations at the heme iron in Cytochrome B562. The results were unfortunately inconclusive, as the ionic background was not effectively represented in the finite-size system.