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...

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.

In an NMR sample, precise measurement of the absolute absorption frequencies of nuclei is difficult. A standard internal reference compound is added, and the frequency difference between the reference signal and sample signals is measured.
The internal reference compound generally used in NMR spectroscopy is tetramethylsilane (TMS). TMS is preferred because it is chemically inert, soluble in NMR solvents, and easily removable. Also, the highly shielded methyl protons in TMS yield an intense...

A solvent is a substance, most often a liquid, that can dissolve other substances. Here, the substance being dissolved is called a solute. When a solvent and a solute combine, they form a solution - a homogenous mixture of both the solvent and the solute. Water is a universal biological solvent. Its polar structure allows it to dissolve many other polar compounds. The ability of water to dissolve is governed by a balance between water molecules binding to each other and binding to the solute.
A...

The free energy change associated with dissolving a solute in a liter of solvent is called the free energy of a solution, ΔGsolution. The overall ΔGsolution is expressed as the balance of ΔGinteraction against the always-favorable free-energy of mixing, ΔGmixing. Solution formation is favorable if  ΔGsolution is less than zero, whereas it is unfavorable if ΔGsolution is greater than zero. In short, for a solution to form and complete dissolution to take place,...

The process of surrounding a solute with solvent is called solvation. It involves evenly distributing the solute within the solvent. The rule of thumb for determining a solvent for a given compound is that like dissolves like. A good solvent has molecular characteristics similar to those of the compound to be dissolved. For example, polar solutions dissolve polar solutes, and apolar solvents dissolve apolar solutes. A polar solvent is a solvent that has a high dielectric constant (ϵ...