Study of the Chemical Space of Selected Bacteriostatic Sulfonamides from an Information Theory Point of View

Abstract

The relative structural location of a selected group of 27 sulfonamide-like molecules in a chemical space defined by three information theory quantities (Shannon entropy, Fisher information, and disequilibrium) is discussed. This group is composed of 15 active bacteriostatic molecules, 11 theoretically designed ones, and para-aminobenzoic acid. This endeavor allows molecules that share common chemical properties through the molecular backbone, but with significant differences in the identity of the chemical substituents, which might result in bacteriostatic activity, to be structurally classified and characterized. This is performed by quantifying the structural changes on the electron density distribution due to different functional groups and number of electrons. The macroscopic molecular features are described by means of the entropy-like notions of spatial electronic delocalization, order, and uniformity. Hence, an information theory three-dimensional space (IT-3D) emerges that allows molecules with common properties to be gathered. This space witnesses the biological activity of the sulfonamides. Some structural aspects and information theory properties can be associated, as a result of the IT-3D chemical space, with the bacteriostatic activity of these molecules. Most interesting is that the active bacteriostatic molecules are more similar to para-aminobenzoic acid than to the theoretically designed analogues.

Crámer-Rao complexity of the two-dimensional confined hydrogen

“…In addition we illustrate here the analytical computation of the other dispersion and Fisher information measures which we are interesting in. This is possible because the general expressions ( 7), ( 9), (11) and (12) strongly simplifies for such states as it is illustrated for convenience in the following.…”

“…These measures quantify a single facet of the density ρ( r) of local (Fisher) or global (variance, Shannon) character, such as the concentration around the mean value (variance), the gradient content (Fisher information) and the total extent (Shannon entropy) of the density. They have been shown to be very useful in numerous scientific areas, particularly to identify and characterize many atomic, molecular and chemical phenomena such as e.g., correlation properties, level avoided crossings of atoms in external electromagnetic fields, and transition states and other stationary points in chemical reactions [8][9][10][11][12]. The composite information-theoretic measures have been recently shown to be most appropriate to describe the intrinsic complexity of the quantum systems and to distinguish among their rich three-dimensional geometries, mainly because they jointly grasp different facets of their internal disorder.…”

Information-Theoretic Features of Many Fermion Systems: An Exploration Based on Exactly Solvable Models

“…The study of finite many-fermion systems has been enriched in recent years with the incorporation of new mathematical tools inspired in information theory. In particular, information measures and information-based complexity measures have been successfully applied to elucidate various aspects of the physics of atoms, molecules, and atomic nuclei [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Unfortunately, finite many-fermion systems rarely admit exact analytical treatment, and most studies must rest heavily on the numerical solution of the equations describing the system.…”

Crámer‐Raocomplexity of the confined two‐dimensional hydrogen

“…as correlation properties, level avoided crossings of atoms in external electromagnetic fields, and transition states and other stationary points in chemical reactions. [8][9][10][11][12] The composite information-theoretic measures have been recently shown to be the most appropriate to describe the intrinsic complexity of the quantum systems and to distinguish among their rich three-dimensional geometries, mainly because they jointly grasp different facets of their internal disorder. This is basically because (a) they are dimensionless; (b) they are invariant under replication (LMC), translation, and scaling transformations;…”

“…They have been shown to be very useful in numerous scientific areas, particularly in identifying and characterizing many atomic, molecular, and chemical phenomena, such as correlation properties, level avoided crossings of atoms in external electromagnetic fields, and transition states and other stationary points in chemical reactions. [ 8–12 ]…”