Here I introduce some examples of molecular structures related to disease therapy. One is oseltamivir which is also given the trade name Tamiflu. The important processes of influenza infection are to ENTER the host cell and to GO OUT from it, and some of the antiviral medicines target these processes. The enzyme neuraminidase clips off a sialic acid from the cell membrane to assist the replicated viruses to go out. Tamiflu is a molecule with a similar structure to it which also binds to neuraminidase, and inhibits the enzyme function (Figure 1). In the case of mutant enzyme (H274Y), Tamiflu binds to it weaker than the wild type, so Tamiflu has less effect than the mutant type. The replaced 274th residue tyrosine is bulkier than the original amino acid histidine and causes orientation change of the amino acid at the active site (Figure 2). Another example is involved in Ebolavirus causing epidemics in West Africa. Although the effective therapeutic medicine and vaccine have not been found yet, the molecular structure of the antibody complex with virus glycoprotein from a human survivor is already deposited to PDB (Figure 3). Now scientists are searching for some effective chemicals and methods using this information.
In contrast to Bohr's concept of a simple circular "orbit" with a fixed radius, a quantum chemical "orbital" is represented by the probability density of finding an electron. A three dimensional (3-D) representation of the probability density of a hydrogen 1s orbital in a glass block (Figure 1 (a)) was developed. It was compared with other models of the atomic orbital, such as several 3-D isosurface models (Figure 1 (b-d)), a 2-D probability density model (Figure 2 (a)), 2-D contour maps (Figure 2 (b, c)), and a pseudo 3-D contour map (Figure 2 (d)). Isosurface models shown in Figure 1 (b), (c), and (d) represent the boundary or contour surface where probability density χ1s2 has a constant value, chosen so that there is a certain probability − for example 90% − of finding the electron within the contour. These diagrams cannot show the entire region where an electron can be found. On the other hand, in the diagram of Figure 1 (a), an electron is found everywhere around the nucleus. The density of the dots sculptured in the glass block shows the probability density of finding an electron. The distribution of the probability density χ1s2 on the x-y plane is well described by the contour map in Figure 2 (b), or by the solid line in Figure 3 (the plot of χ1s2 versus distance from the nucleus r). In this Figure, the electron probability density is greatest at r = 0 (the nucleus) and falls off with increasing distance r. The 1s atomic orbital is spherically symmetric, so the probability of finding a 1s electron is the same at every point on a spherical shell having a constant radius r. The surface area of each spherical shell, 4πr2, increases very rapidly with increasing r(the dashed line in Figure 3). The product of the probability χ1s2 and the surface area of the spherical shell 4πr2 is illustrated in Figure 4 as the radial distribution function 4πr2χ1s2 . Where r is very small, the surface area 4πr2 is so small that the total probability of finding an electron on that surface is very low. It has a maximum at a particular distance of r = 1 au (atomic unit), namely, the Bohr radius, 52.92 p.m. In the classical Bohr model of hydrogen, an electron is found only at the radius of 52.92 p.m., whereas in the quantum chemical refined orbital model, an electron can potentially be found at any distance from the nucleus, but, depending on the square of the hydrogen 1s wavefunction, exists more frequently on the spherical shell at the Bohr radius. If we divide the hydrogen atom into very thin (thickness: dr) concentric shells, much like the layers of an onion, we can calculate the probability of finding an electron on each spherical shell. The delicacy of each shell, namely, the electron probability density is greatest at r = 0. In contrast, the volume of the spherical shell 4πr2dr at r = 0 is 0, and the total delicacy at the center of the atom is 0, but the volume increases rapidly with increasing r, the total delicacy of each shell has a maximum at the Bohr radius.
The fragment molecular orbital (FMO) method enables us to calculate electronic states of large molecules such as proteins. The FMO method has been employed by researchers in the drug discovery and related fields, because inter fragment interaction energy (IFIE), which can be obtained in the FMO calculation, is useful to understand interactions between proteins and their ligands, In the present study, we implemented pair interaction energy decomposition analysis (PIEDA) into the FMO calculation program ABINIT-MP and its GUI program BioStation Viewer. PIEDA is a method which divides the IFIE into four energy components: electrostatic (ES), exchange repulsion (EX), charge-transfer and mixing term (CT+mix), and dispersion (DI) energies. After the implementation, we applied the PIEDA to three protein-ligand systems in order to clarify which energy components play main roles in their binding interactions. The results show that the protein-ligand interactions in complexes of influenza protein neuraminidase-oseltamivir, EGFR tyrosine kinase-erlotinib, and estrogen receptor-ligand consist of clearly different energy components. This indicated that PIEDA is useful to understand details of ligand binding mechanisms.
A simple, universal equation of state (EOS) for hydrocarbons is proposed. This EOS allows estimation of the effective potential parameters ε and σ in the Lennard-Jones function as analytic functions of n, the number of electrons in the hydrocarbon molecule. Using these parameters, the thermodynamic properties of hydrocarbons may be calculated based on the EOS for a perfect liquid, as already proposed in the Lennard-Jones system. The thermodynamic properties estimated in this manner for various hydrocarbons have been found to be reasonably similar to experimentally obtained values.
A molecular dynamics program is developed by EXCEL for the Lennard-Jones system. How to use the program is shown. The conditions for the simulation like the temperature and the number density are given in the worksheet. The following quantities are calculated; thermodynamic properties, pair correlation function, running coordination number, mean square displacement, velocity autocorrelation function and self-diffusion coefficient. The program is available in the appendix.