Log 1/C values

Compound 1 has group A at position Ri, group E at position R2, and group J at position R3. Thus the matrix defines the exact structure of each compound. The only variable numbers are the log 1/C values, which are experimentally determined and whose variability is the reason why so many compounds are required in excess of the theoretical number... 

Note that Cp is required to have a coefficient of 1. If one calculates the predicted "log 1/C - Cp" values and adds back Cp, the log 1/C values obtained are not the same as those calculated from eq 14 their correlation with observed log 1/C is 0.946. I liken the difference to correcting for the initial partitioning using Fujita s method, but correcting for all subsequent partitionings as well using log D. Fujita s treatment would be drastically different from an equation that is quadratic in log D. 

Pre-Qsar" Series Development. Potency (Log 1/c) values for the first nineteen pyranenamlnes to be synthesized and tested In the PCA assay, prior to the use of QSAR In this series, appear In part A of Table I. The majority of these derivatives were synthesized in response to a newly proposed (at that time) decision model, the Topllss operation scheme or "tree .Q). Based on the observation that physlcochemlcally-based substituent constants are an aspect of the Hansch approach which is easier for synthetically oriented chemists to assimilate than is regression analysis, Topllss proposed specific sequences of substituted derivatives to be synthesized, with the next choice at each sequential step being governed by whether the preceding compound displayed either Increased, decreased, or unaltered potency. Retrospective studies... 

Initial analysis of the data In Table lA was carried out graphically, by plotting log (1/C) values for the nineteen compounds against measures of their physicochemical differences, specifically measures of size (molar refractlvlty), affinity for polar solvents (ir), and Intramolecular electronic effect (o). 

For odorants in air this point is further illustrated by considering vapor pressure, iog P and HB values and equation no. 2 in Table II. Substitution of log P and HB values for acetone and acetophenone into equation no. 2 in Table II produces log (1/c) values which indicate that over 2,000 times more acetone (vapor pressure = 202 torr at 25°C) is needed to produce the same odor intensity of acetophenone (vapor pressure = 1.09 torr at 25°C) based on molar concentration, needed to produce odor intensity equivalent to 87 ppm n-butanol. Thus the more volatile odorant acetone is a weaker odorant in terms of intensity than the more hydrophobic odorant, acetophenone. 

The molecules examined in this case study are in Table 1 along with the original, sequential, reverse sequential, and random bioactivities. The purpose of the sequential and reverse sequential bioactivities is to demonstrate the power of incorrectly constructed scramble models. The sequential and reverse sequential bioactivities also demonstrate that a good R2 value can be found, yet the model is poor based on large chi and RMSE values. The molecules were purposely ordered from poor to good binders based on the log(l/c) values (2). 

The exact optimal value of log P, sometimes labeled log P°, can be determined by taking the first derivative of log 1/C with respect to log P (Equation 12.24). 

Despite the high r-value of Equation 12.25, its implied correlation between log 1 /C and log P is flawed. 

The antihemolytic activity of phenothiazines (log 1 /C) was also correlated with log K iAM (Tab. 3.2). Again, it was found that the corresponding equation with log Doct is of significantly lower statistical value ... 

Log 1/C = Ea + i (ai are the group contribution of the individual substituents X to the biological activity values and p, is the calculated biological activity of a reference compound, most often the unsubstituted analogue). 

List all equations of the type log 1/C = alog P + bE8 + c Order them first according to increasing values of a and then according to increasing values of b. List the system and type of perturbation for each equation. 

Equation 42 is included because it has a negative slope—i.e., this set of congeners was selected so that all members had a superoptimal lipophilic character. Evidence now indicates 22, 25-27) that the general relationship one should expect between log 1/C and log P is parabolic. The apex of the parabola has been termed log P0. Molecules having this value of log P have ideal lipophilic character for the system under consideration. Since all of the above equations are linear in log P (the addition of a term in (log P)2 does not improve the correlation), greater activity could have been obtained in each example by designing molecules with better log P values. In all examples except Equation 42 this means increasing the lipophilic character. Equation 42 calls for less lipophilic molecules. 

In Equation 1, C is the molar MIC in vitro value, and Eh represents the oxidation-reduction potentials of the drugs. The figures in parenthesis are the 95% confidence limits. Equation 1 is statistically significant. Of the variance in the in vitro log l/C values 42% can be explained by a linear regression with E. This supports the hypothesis that the 5-nitro-thiazoles affect an important enzymatic reduction process of the tricho-... 

Where possible, activity has been expressed as log 1/C (i.e., pC) where C is the molar concentration required to cause a standard response (such as EDr)0, MIC, or LDioo). In many instances the intercepts of these equations can be compared. Where activity is expressed in other units, such comparisons are not possible. In a few examples the relative value, PC, the molar phenol coefficient, has been used. In Tables Ila-d new data not previously correlated are assembled. 

From the chromatographic Rm values it was found [278-280] that the lipophilicity requirements are not the same when gram-positive and gram-negative microorganisms are tested Figure 8.12). There is a parabolic dependence of log (1/C) on the Rm values of cephalosporins for E. coli. Staph, aureus and T. pallidum. This is in agreement with the... 

Of course there are reasons other than binding by lipids or proteins which might cause a departure from linearity in the relationship of log 1/C and log P or it. Metabolic or elimination reactions not significant at low values of log P could, with increasing log P, become very important. 

A refinement is given by Equation 1.28, where a is the group contribution of the /th substituent, X is as in Equation 1.27, jj. is log 1/c for the unsubstituted compound. A coefficient with a positive value means that the substituent... 

These methods find the best estimate of the coefficients of an equation by minimizing the sum of the squares of the deviations (errors) between the observed and the fitted log (1/C), or log of relative biological potency in the case of QSAR. They generally assume that the errors are normally distributed. The validity of a statistical fit is usually evaluated by calculating the probability that the overall fit is significantly better than simply using the mean value and, if more than one descriptor is used, each descriptor contributes significantly to the quality of the fit. 

Indeed, all analogs can be described much better by using n instead (eq. 39) [15]. The log 1/C vs. CT relationship in eq. 38 only exists by fortune. It results from a close relationship between n and a, if the nitro analog is excluded (n = 13 tt us. a r = 0.91) all equations were recalculated by using the rttenzene. and Op values presented in Table 10. 

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