Molecular equivalence numbers

Johnson, M.A. and Xu, Y.-j. Using molecular equivalence numbers to visually explore structural features that distinguish chemical libraries. 

Fig. 1. Empiric observation that more than approx 20 compounds from any scaffold need to be tested in order to be sure that an active will be found. (A) This shows the results from a whole cell assay in which the compounds have been classified using the Level 1 Ring System of the Structural Browsing Index (SBI) also known as molecular equivalence numbers or meqnums, which is the most-detailed level. The most-populated SBI containing only inactives is labeled 1, it contains 16 compounds. The most populated SBI containing actives is labeled 2. (B) Looking at only the compounds present in the most-populated SBI (2 above) and arranging the compounds in this SBI randomly, the smallest set of compounds in which an active (indicated by +) can be found is approx 30 compounds.

Fig. 4. Comparision of molecular equivalence numbers or structural browsing indices (SBI) containing active molecules from four different sublibraries. This figure shows how, even though the libraries described in Fig. 3 occupy similar chemistry spaces, they still undersample certain areas so that some active classes are only found when screening one particular sublibrary and not the others. This figure takes the active compounds represented in Fig. 3B using structural Browsing Indices and shows which library the actives came from. This serves to emphasize how active compounds with particular structural features may be identified in only one of the three sublibraries, e.g., compounds containing the SBI 7704 are only found in the CAC sublibrary.

Molecular equivalence numbers are derived by breaking the molecule into separate components e.g. rings and acyclic groups), and sequentially blurring detailed distinctions within each e.g. precise atom and bond types, or ring sizes) to form equivalence classes . A unique naming function (essentially a canonicalisation process) is then used to generate alphanumeric identifiers for these classes. 

A typical electrospray spectrum of a high-molecular-weight material, i.e. that of horse heart myoglobin, is shown in Figure 4.11. Each of the ions observed arises from attachment of a different number of protons, and an equivalent number of charges, to the intact molecule. 

In first-order reactions, the rate expression depends upon the concentration of only one species, whereas second-order reactions show dependence upon two species, which may be the same or different. The molecularity, or number of reactant molecules involved in the rate-determining step, is usually equivalent to the kinetic reaction order, though there can be exceptions. For instance, a bimolecular reaction can appear to be first order if there is no apparent dependence on the concentration of one of the... 

Throughout this discussion, we have been considering pure substances, i.e. substances composed of a single material, whether element or compound. A compound may be molecular or ionic, or both. A compound is a single chemical substance. To anticipate slightly, sodium chloride is an ionic compound that contains two atomic species, Na" and d . If a sample of sodium chloride is formally manipulated to remove some Cl ions and replace them by Br ions in equivalent number, the resultant material is a mixture. The same is true of a sample containing neutral species such as P4, Sg and CsHg. 

Based on maximum mean channel number for a bead evaluated for highest ligand concentration and calibrated to molecular equivalent soluble fluorescence via Bang Labs calibration beads. 

One further step toward calibration has been taken with the use of a calibration curve made with sets of beads with known numbers of fluorochromes on their surface. Such calibrated beads are available with known numbers of PE molecules. Similar, but less direct, beads are available with fluorochrome molecules that have been calibrated in units equivalent to the intensity of fluorochrome molecules in solution ( MESF units = molecular equivalents of soluble fluorochrome ). With these beads, a curve can be obtained (Fig. 6.6), giving each channel on the ADC a calibration in number of fluorochrome molecules (for PE) or MESF values (for fluorescein). In this way, the background fluorescence of a control sample can be expressed as an equivalent number of fluorochrome (or MESF) molecules and can be subtracted from the number of fluorochrome molecules of a stained sample. The fluorescence of the stained sample can then be expressed as, for example, PE molecules over and above the background level. 

The need for computer simulations introduces some constraints in the description of solvent-solvent interactions. A simulation performed with due care requires millions of moves in the Monte Carlo method or an equivalent number of time steps of elementary trajectories in Molecular Dynamics, and each move or step requires a new calculation of the solvent-solvent interactions. Considerations of computer time are necessary, because methodological efforts on the calculation of solvation energies are motivated by the need to have reliable information on this property for a very large number of molecules of different sizes, and the application of methods cannot be limited to a few benchmark examples. There are essentially two different strategies. 

These resins are most often characterized by their epoxy equivalent weight (EEW), molecular weight (number of repeating units ri), and viscosity. Table 4.2 shows the relationship between EEW and viscosity. These DGEBA epoxy resins can be used alone or in blends with other DGEBA resins, other epoxy resins, or even other types of polymeric resins. Very often commercial epoxy resin products are actually blends of resins having a broad molecular weight distribution. 

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