Dah-Yen Yang

Energetics of hydrogen bonds in peptides

Hydrogen bonds and their relative strengths in proteins are of importance for understanding protein structure and protein motions. The correct strength of such hydrogen bonds is experimentally known to vary greatly from ≈5–6 kcal/mol for the isolated bond to ≈0.5–1.5 kcal/mol for proteins in solution. To estimate these bond strengths, here we suggest a direct novel kinetic procedure. This analyzes the timing of the trajectories of a properly averaged dynamic ensemble. Here we study the observed rupture of these hydrogen bonds in a molecular dynamics calculation as an alternative to using thermodynamics. This calculation is performed for the isolated system and contrasted with results for water. We find that the activation energy for the rupture of the hydrogen bond in a β-sheet under isolated conditions is 4.76 kcal/mol, and the activation energy is 1.58 kcal/mol for the same β-sheet in water. These results are in excellent agreement with observations and suggest that such a direct calculation can be useful for the prediction of hydrogen bond strengths in various environments of interest.

The transition from nonadiabatic to solvent controlled adiabatic electron transfer: solvent dynamical effects in the inverted regime

We analyze the effect of dynamical solvent effects on the rate of a nonadiabatic electron transfer (ET) reaction. Starting from a Hamiltonian for a reaction coordinate for motion along the potential surfaces of donor and acceptor species, and a bath representing the solvent dynamical effects, we obtain a system of four coupled reduced equations of motion for the elements of the density matrix of the donor/acceptor system. In this derivation the dynamics along the reaction coordinate are reduced to a classical Fokker–Planck operator since we assume the temperature is high compared with bath frequencies. At temperatures where the nuclear motion describing the transition between the surfaces can be treated classically we show that the ET processes may be viewed as a consecutive reaction scheme with rate constant k=kNA kD/(kD+kNA), the steps are diffusion along the reaction coordinate with rate constant kD followed by crossing between the donor and acceptor surfaces at the point of intersection of the surface...

Monte Carlo simulation of the liquid–vapor interface of water using an ab initio potential

Monte Carlo calculations have been carried out to study the interfacial properties of liquid water, using the Matsuoka–Clementi–Yoshimine (MCY) potential for the water–water interaction. The surface tension calculated at 298 K is 23.7±3.4 dyn/cm, to be compared with the experimental value of 72 dyn/cm. The interfacial 10–90 thickness is 4.70 A, with the dipoles of the water molecules near the liquid phase pointing slightly towards the liquid phase and those near the gas phase pointing towards the gas phase. The interfacial water molecules are found to be more restricted in their rotation, as evidenced by the smaller root‐mean‐squared fluctuations of the dipole directions. The Volta potential difference across the interface arising from the permanent dipoles is estimated to be 0.024 V. A new and efficient method is proposed to calculated the surface excess energy. The excess energy calculated for the MCY water is 119 erg/cm2, to be compared with the experimental value of 120 erg/cm2. From the calculated su...

Molecular orbital calculations of electronic excited states in poly(p-phenylene vinylene)

Abstract The electronic structure of model oligomers (monomers, dimers, …, hexamers) of poly( p -phenylene vinylene) were studied using the intermediate neglect of differential overlap method with spectroscopic parametrization (INDO/S). The calculated first singlet-to-singlet transitions compare favorably with the experimental spectra. The results from the exciton theory are also presented. Our results show that the conjugation length is finite and the interactions between polymer chains play a very important role in optical properties. The theoretical results for the triplet-to-triplet transitions are in accord with the experimental values, supporting the experimentally ascribed triplet-to-triplet photoinduced absorption feature in oligomers.

Molecular dynamics of hydrogen bonds in protein-D2O: the solvent isotope effect.

We suggest that the H-bond in proteins not only mirrors the motion of hydrogen in its own atomistic setting but also finds its origin in the collective environment of the hydrogen bond in a global lattice of surrounding H2O molecules. This water lattice is being perturbed in its optimal entropic configuration by the motion of the H-bond. Furthermore, bonding interaction with the lattice drop the H-bond energy from some 5 kcal/mol for the pure protein in the absence of H2O, to some 1.6 kcal/mol in the presence of the H2O medium. This low value here is determined in a computer experiment involving MD calculations and is a value close to the generally accepted value for biological systems. In accordance with these computer experiments under ambient conditions, the H-bond energy is seriously depressed, hence confirming the subtle effect of the H2O medium directly interacting with the H-bond and permitting a strong fluxional behavior. Furthermore, water produces a very large change in the entropy of activation due to the hydrogen bond breakage, which affects the rate by as much as 2 orders of magnitude. We also observe that there is an entire ensemble of H-bond structures, rather than a single transition state, all of which contribute to this H-bond. Here the model is tested by changing to D2O as the surrounding medium resulting in a substantial solvent isotope effect. This demonstrates the important influence of the environment on the individual hydrogen bond.

Solvent dynamical effects on nonadiabatic electron transfer reactions at low temperature

The role of solvent dynamics on low temperature nonadiabatic electron transfer reactions is explored. The solvent degrees of freedom orthogonal to the nuclear motion reaction coordinate are represented by a frictional term. Thus, motion along the reaction coordinate is described by a damped quantum oscillator equation of motion. This equation of motion is used to construct the nonadiabatic electron transfer rate constant which describes long range electron transfer phenomena such as occurs in biological oxidation‐reduction reactions. The frictional dynamics are correctly described even for temperatures lower than the characteristic frequencies of the reaction coordinate and the friction. We exhibit the effects that friction can have on the electron transfer rate from room temperature down to 4 K, and qualitatively compare with typical biological electron transfer data, as interpreted using the conventional zero friction theory.

Determination of protein surface hydration shell free energy of water motion: theoretical study and molecular dynamics simulation.

Water on protein surface plays a crucial role in the mechanistic aspects of biological processes; principally, this is characterized into two kinds of water molecules, biological water and bulk water. As compared to pure water, many aspects of the dynamics and structure of the surrounding water near the protein surface are much less understood. Evidence shows that those properties of the surrounding water induced by the presence of the biological systems differ from those of bulk water and that water has low mobility in the hydration shell. An intriguing question remains as to how to make a quantitative estimate of the hydration shell free energy when there is interaction between the protein and the hydration water. To explore this problem, we perform molecular dynamics simulation of the water motion in the hydration shell with respect to bulk water. A fractional Brownian motion theory combined with numerical simulation and a molecular dynamics simulation was developed. This theory was used to directly establish the connection between the dynamics of the protein surface water motion and the interaction between water and protein; this offers the possibility of determining the hydration shell free energy. In this study, we focused on water motion at the protein surface that is within a 4.4 Å layer, which is referred to as the hydration shell. We demonstrate that it actually follows a fractional Brownian motion. In this regime, a developed fractional Fokker-Planck equation, which is used to describe the dynamics of protein surface water motion, permits us to solve the mean first passage time of water molecules through the hydration shell. We then estimate the protein surface hydration shell free energy (HSFE), which depends on the barrier height of the hydration shell. For myoglobin, its HSFE is about 1.73 kcal/mol, and the accompanying activation entropy is 1.40R, where R is the gas constant. Corresponding reduced water mobility is observed for water surrounding myoglobin. In accord with the analysis of the radial distribution function, it is revealed that the effect of temperature on the HSFE is weak. The results show that the protein surface is wrapped by a shell of low mobility water motion and this hydration shell is dynamic rather than static.

Gated escaping of ligand out of protein

We construct a new gating model and develop a new theory to study the escaping process of a ligand out of a spherical cavity with a puncture (or gate) on the surface. The gate undulation can be regulated by any time-dependent function and the motion of the ligand inside the spherical cavity is mapped into a two-dimensional entropy potential surface. Hence the driving force of our model is entropy only. For a static gate, the escaping process corresponds to climbing a two-dimensional entropy barrier. When the gate open angle is small, the escaping rate is proportional to the square of the opening angle. The prefactor of the escaping rate constant depends on the curvature of the entropy potential surface. For coherent gating, the survival time depends not only on the gate undulation frequency but also on how the initial state is defined. On the escaping from protein, our escaping rate shows it is qualitatively consistent with the experimental result of ligand recombination in myoglobin.

Kramers theory of chemical reactions in a slowly adjusting environment

When describing the reaction dynamics in a slowly relaxing environment, one has to include slow nonreactive modes of the environment in an explicit consideration along with the “chemical” mode intrinsically responsible for the chemical transformation. This is done within the framework of the Kramers approach to condensed phase chemical reaction dynamics. The problem is studied under the condition of high friction of the nonreactive mode (slow adjustment) while friction of the chemical mode covers the whole range from weak to high friction. It is found that the reaction dynamics and, hence, the kinetics depend strongly on the strength of the coupling of the reactive and the nonreactive modes. For strong mode coupling the rate constant monotonically decreases with the increase of the friction of the chemical mode. Such behavior is quite distinctive from one for fast adjustment of the environment when the rate constant demonstrates a turnover behavior. Turnover behavior takes place for moderate strength mode...

Hydrogen Bonds in Membrane Proteins

Hydrogen bonds are essential tie points inside protein structures. They undergo dynamic rupture and rebonding processes on the time scale of tens of picoseconds. Proteins can partially rearrange during such ruptures. In previous work, we performed molecular dynamics simulations of these fluctuating hydrogen bonds. This indicated long-range entropy and energy contributions extending far into the liquid environment. The results showed that the binding of a given hydrogen bond is much reduced as a result of these interactions in water, as is required for biological activity and in very good confirmation of known experimental results. The larger water environment directly interacts with the hydrogen bond essentially due to long-range molecular interactions. Such a substantial lowering of the energy of the hydrogen bond in water brings it into the range of activation by many biological processes ( Sheu et al. Chem. Phys. Lett. 2008 , 462 , 1 - 5 ). Thus, the water medium profoundly increases the rate. Furthermore, very large entropic changes are associated with the rupture of hydrogen bonds in water, whereas no such effects are seen for the isolated molecule. Interestingly, such an increase in rates in water is still accompanied by a large negative change in entropy in the extended solvent environment, and this reduces the rate by some 2 orders of magnitude. Recent molecular dynamics experiments in D(2)O substantiate this model and show a large solvent isotope effect. In this work, we used lipids as the environment for the hydrogen bond and discovered that the energy is also reduced from that found in the isolated molecule, but not as far as in water. On the other hand, we found that no entropy penalty exists for breaking the hydrogen bond in lipids, as seen for water. These two effects compensate, even though the energy is some 2 times larger. The entropic penalty is reduced such that the rate is higher than in water despite the higher energy. This is a significant result for understanding the reactivity and dynamics of proteins in lipids. It should be noted that these are very important solvent effects on entropies and free energies that are not usually reflected in statistical thermodynamic computations for reactants and products. The very long-range effect of the solvent makes substantial contributions to kinetic rate constants and is readily evaluated in this kinetic method. To ignore these long-range environmental effects on the entropy can lead to very spurious results when calculating rates of protein mobilities. Hence, the results not only agree very well with the known hydrogen-bond energies directly as a result of various environmental factors, but even correctly predict a phase transition in the lipid.