In silico analytico‐mathematical interpretation of biopolymeric assemblies: Quantification of energy surfaces and molecular attributes via atomistic simulations

Abstract Static‐lattice atomistic simulations, in vacuum and solvent phase, have been recently employed to quantify the “in vitro—in vivo—in silico” performance‐correlation profile of various drug delivery systems and biomaterial scaffolds. The reactional profile of biopolymers was elucidated by exploring the spatial disposition of the molecular components with respect to the formulation conditions and the final release medium. This manuscript provides a brief overview of recently completed and published studies related to molecular tectonics of: (a) the nanoformation and solvation properties of the surfactant‐emulsified polymeric systems; (b) the formation and chemistry of polyelectrolyte complexes; (c) the effect of a plasticizer and/or drug on the physicomechanical properties of biomedical archetypes; (d) the molecular modeling templates to predict stimuli‐ and environmentally esponsive systems; and (e) the polymer‐mucopeptide complexes and intermacromolecular networks. Furthermore, this report provides a detailed account of the role of molecular mechanics energy relationships toward the interpretation and understanding of the mechanisms that control the formation, fabrication, selection, design, performance, complexation, interaction, stereospecificity, and preference of various biopolymeric systems for biomedical applications.


| INTRODUCTION
The elucidation of mechanism(s) inherent to the performance of biopolymer-based complex assemblies presents a significant challenge to pharmaceutical and biomedical scientists around the world with most of the studies only providing "qualitative estimation" based on "theoretical experience" and "quantitative experimental results." The use of phrases such as "probably," "may be," "perhaps," "theoretically," "might be," "supposed to," and so on are frequently used to describe

| Molecular mechanics-assisted model building and energy refinements
The MMER model for the energy factor in various molecular complexes can be written as: where V P is related to total steric energy for an optimized structure, V b corresponds to bond stretching contributions (reference values were assigned to all of a structure's bond lengths), V θ denotes the bond angle contributions (reference values were assigned to all of a structure's bond angles), V ϕ represents the torsional contribution arising from deviations from optimum dihedral angles, V ij incorporates van der Waals interactions due to nonbonded interatomic distances, V hb symbolizes hydrogen-bond energy function, and V el stands for electrostatic energy.
In addition, the total potential energy deviation, ΔE Total , was calculated as the difference between the total potential energy of the complex system (A/B) and the sum of the potential energies of isolated individual molecules (A, B), as follows:   and -NH 2 ) present in the polymer matrix. This further confirmed that insulin released from PLA-PEG 575 matrix will be slowest as low molecular weight PEGDA will have more NH 2 functional end groups than the higher molecular weight ones. 8

| MOLECULAR INTERACTIONS INHERENT TO POLYELECTROLYTE COMPLEXES
Polyelectrolyte complexes, as the name suggests, are complex molecular architectures composed of oppositely charged molecules. As the charged functional groups are "consumed" in the process, the inherent solubility and functionality of the individual molecules are reduced and hence an insoluble but hydrated and swellable matrix is formed. 9 In product. [10][11][12] The formation of NaCMC-Eudragit E100 I.E. was accompanied by dense H-bonding and van der Waals interactions. This was further confirmed by lower refractivity, reduced surface-to-volume ratio, and high-density of 0.442 amu/Å 3 . In addition, the molecular dynamics simulation supported the energy stabilization and it was concluded that "the potential energy decreased with an increase in the kinetic energy, obeying the well-known behavior of high underdamping harmonic oscillator." 12 Bawa forces. This further confirmed the in vitro controlled release of a highly soluble drug (diphenhydramine) due to matrix curing and formation of a "deforming-type" matrix. 13 Recently, Bijukumar and coworkers modeled a multimolecular alginate:chitosan:hyaluronic acid

| ENVIRONMENTALLY AND INHERENTLY RESPONSIVE DRUG DELIVERY SYSTEMS
Stimuli and environmentally responsive drug delivery systems form an important aspect of current drug delivery strategies given the "delivered only when needed" characteristic of these specialized platforms.
These systems can be easily, but nonconclusively, classified as thermo-, pH-, electro-, light-, ion-, oxidation-, and enzyme responsive. 24 The authors have thus far provided interesting evidence of matrix responsiveness via MMER for three different stimuli as well as the behavior of drug delivery system in response to the biological clock as described below: 1. Enzyme responsive drug delivery: Bawa and coworkers described  Table 1 for the steps). 26 Table 2). Mucoadhesion is a very important aspect of oral drug delivery (in particular peptide delivery) when the drug release and absorption are targeted for the small intestine. Given the close proximity to the intestinal membrane, the mucoadhesive devices are developed to provide a high concentration gradient at the site of absorption thereby enhancing absorption as well as protection from the enzymatic degradation of the bioactives. 37 Although there are abundant studies and data describing the "probable" muco-interacting functionalities within a biopolymer or biopolymeric matrices; the confirmatory visualizations of these interactions are lacking. For the studies below, the authors employed a glycoprotein sequence homologous to mucous extracellular matrix. The mucopeptide so developed was energetically and geometrically minimized to give a globular protein structure mimicking the native mucous network. 38

| CONCLUSION
The above discussion and cited literature proved that not-so-complex and time-efficient molecular mechanics simulations can provide an in depth account of the bonding and nonbonding interactions occurring within a biomedical device or system fabricated using biopolymers. The static-lattice atomistic simulations and MMER also confirmed that there is a direct relationship between the in silico findings and the in vitro and/or in vivo results and hence atomistic simulations can be employed for the construction of an "in vitro-in vivo-ex vivo-in cyto-in silico" performance-correlation profile within biomedical material assemblies.

ACKNOWLEDGMENT
This work was supported by the National Research Foundation (NRF) of South Africa.

CONFLICT OF INTERESTS
The authors declare that they have no conflicts of interest with the contents of this article.