Physical models representing molecular architectures of chemical compounds play essential roles in understanding chemistry. The use of molecular models makes it easier to visualize the structures and shapes of atoms and molecules.

An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum numbers:  n, l, ml, and...

The molecular orbital theory describes the distribution of electrons in molecules in a manner similar to the distribution of electrons in atomic orbitals. The region of space in which a valence electron in a molecule is likely to be found is called a molecular orbital. Mathematically, the linear combination of atomic orbitals (LCAO) generates molecular orbitals. Combinations of in-phase atomic orbital wave functions result in regions with a high probability of electron density, while...

Adrenergic agonists' structure-activity relationship (SAR) determines their selectivity and efficacy. These agonists comprise a phenylethylamine moiety with an aromatic ring and an ethylamine side chain.
Aromatic ring substitutions: Substituting the aromatic ring with –OH groups at positions 3 and 4 yields catecholamines (e.g., epinephrine), which have a high affinity for adrenoceptors. Hydrogen bonding between –OH groups and receptors enhances adrenergic activity.
Separation of the aromatic...

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...

Pharmacodynamic (PD) responses describe the interaction between a drug and its biological target, culminating in a physiological effect. These responses can be classified into different types: continuous variables, such as blood glucose levels; categorical outcomes, like survival rates; and time-to-event metrics, such as disease progression. Understanding and modeling PD responses are critical for optimizing drug efficacy and safety.PD models describe the relationship between drug concentration...