Method for predicting properties of a chemical compound

This invention relates to method for predicting properties of a chemical compound, wherein, on the basis of all available information about the chemical structure and observed activities, an optimal range of the chemical structure of a desired property is described with a control chart or the Mahalanobis' generalized distance, thereby the properties of the chemical compound is able to be predicted by analyzing only the chemical structure.

BACKGROUND OF THE INVENTION 
This invention relates to method for predicting properties of a chemical 
compound from its structure, by which it is possible to design a new 
chemical structure having a desired property. 
Today, the industrial need to find an effective molecular design technique 
is growing rapidly. The probability of success in the conventional 
screening process to discover a useful compound is extremely low. Even the 
task of selecting the best compound in a given homologous group requires 
an astronomical number of trials. .alpha.-Naphthoic acid, for example, has 
seven replaceable positions as shown below. 
##STR1## 
The number of possible compounds by replacing these positions with 20 
commonly used substituents amounts to 20.sup.7 (=1.28.times.10.sup.9). 
Considering the fact that the number of compounds registered each year to 
the chemical abstracts is in the order of 10.sup.5, the time and money for 
this task is at the impossible level. In reality, experiences, intuition, 
ease of synthesis and various kinds of mechanistic knowledge allow some 
selections rather than random approach, but the predictability of the 
activity from the chemical structure is generally very poor. 
Any practical property of compounds, sometimes more aptly called activity, 
is multivariate in nature. This recognition led many people to apply 
multivariate analysis techniques for the problems of the 
structure-activity analysis, but at present no universal technique is 
known. 
To classify the prior art of this field, it is customary to follow Cramer's 
example (R. D. Cramer, et al., Chemical Society Reviews 3, 273 (1974)): 
(1) lead-generation techniques and (2) lead-optimization techniques. The 
former group of techniques attempt to predict a new lead compound from 
known results. At present, there is no industrially dependable prior art 
in this field. The latter prior art aims only at predicting the best 
compound in the homologs after a lead was discovered. Although some 
successful cases have been reported, they naturally lack the universal 
applicability. (Y. C. Young, Journal of Medicinal Chemistry, 24, 230 
(1981)). 
The common feature of the prior arts is that they are method-oriented 
rather than problem-oriented. The models developed elsewhere to explain 
certain phenomena have been rather mechanically applied to more complex 
systems. The following comment by one of the experts in this field 
describes the state of this art (R. Cramer, Chemical Technology, 744 
(1980)); "Let's not emulate the drunk who searched for his key under 
lamppost, where he could see, rather than the dark corner, where he lost 
it!" 
This invention contains two new elements: (1) Use of control chart to 
define the target, and (2) Use of the principle of equilibrium as a 
powerful means to find the cause-effect relationship. Unlike many other 
prior arts, this process is not designed to "explain" the given phenomena, 
but it relies on a well-established engineering art of 
problem-solving--construction and use of control chart. (W. A. Shewhart, 
"Economic Control of Quality of Manufacturing Products", Chap. XX, P. 301, 
D. van Nostrand Co., Inc., New York 1931). Such an engineering art is 
based on the assumption that a desirable outcome is the consequence of 
selecting optimum causes. It tacitly implies that an engineer has to 
search for causes when the cause-effect relations are not readily 
apparent. In applying the control chart technique to the molecular design, 
it will not be complete unless a technique of the cause-finding is 
established. Now, in the following section I will described this part of 
art in detail. A practical property or activity of a compound is measured 
with a particular scale suitable to the object. Such a practical measure, 
such as LD.sub.50 and ED.sub.50, is usually broken down to several 
elementary properties in an attempt to define the cause-effect 
relationships. These elementary properties, such as acidity, 
lipophilicity, electronegativity and so on, are less complex, are 
well-defined and has a universal meaning. 
Because these elementary properties themselves are not generally 
predictable from the chemical structures, such an approach has an 
intrinsic limitation as a universal technique of molecular design. To 
eliminate this limitation, some people have been attempting to correlate a 
practical property directly to structural parameters (B. R. Kowalski & C. 
F. Bender, Journal of the American Chemical Society, 94, 5632 (1972); A. 
J. Stuper and P. C. Jurs, ibid., 97, 182 (1974)). Although such an 
approach has an advantage in offering the direct structure-activity 
relationships, the choice of structural parameters are rather arbitrary 
and, because of this, this approach has not met with a significant 
success. For such an approach to be successful, the arbitrariness of the 
choice of parameters must be minimized by the introduction of some new 
principles. I have done this by "the principle of balance". 
Any practically useful compound should have a certain balance of elementary 
properties. Because the practical working environments of a compound are 
generally complex, the compound of high activity is expected to satisfy 
more than one requirements. According to this principle, the activity will 
decrease if the desirable balance of elementary properties is displaced. 
This principle has been proven in practical world in a variety of ways. 
The art of control chart, as mentioned earlier, seeks the optimum ranges 
of causes to get a desired effect, and it worked well. In a biological 
field, the invariance of partition coefficients of highly active 
compounds, in spite of the variety of structures, has been well 
recognized. (C. Hansch, Chemical Technology, 120 (1977)). 
Because an elementary property of a compound is, in turn, related to a 
certain structural features, a highly active compound should, then, 
possess a certain equilibrium of structural features. The control chart 
technique is best to express such a structural equilibrium with a certain 
allowance. Although the concept of control chart is a product of 
engineering wisdom, the idea can be safely applied to the biological 
problem. Homeostasis, a principle of equilibrium, should control the 
requirements of biologically active compounds. As long as the cause-effect 
relationships are expressed by the control chart, this process has no 
limitation in its applicability. 
A thorough examination of structural parameters and the correlation 
coefficients among them is the essential preparatory step to construct a 
reliable control chart. Once the chart is constructed, the structures to 
be designed should fall within the control limit of the chart, just as the 
reaction temperatures and pressures should be kept within the optimal 
ranges to obtain a desired product. 
The control limit can be shown either on paper or in terms of the 
Mahalanobis' generalized distance from the center of the desirable zone. 
The former method is advantageous when a particular compound outside of 
the limit is to be modified to obtain a higher activity, because the 
deviation from the target area is visibly grasped, but it has a natural 
limitation of dimension. The Mahalanobis' generalized distance is a 
convenient scale in sorting out hopeful candidates even in the case of 
multivariate control chart. 
In practice, this process involves the following steps: 
(1) A set of compounds of known structures and activities are grouped by 
the activity levels. Each compound is, then, converted to a series of 
numerals in a predetermined format. Each of the numerals describes an 
aspect of the structure called structural parameters. These values are fed 
into a computer for the processing described below. This coding process is 
not particularly new, except the choice of the parameters. 
(2) Using the data set prepared above, the correlation coefficients of all 
combinations of two parameters are calculated and are compared among 
different activity groups. There are, nearly always, such combinations of 
parameters that give very high correlation coefficients for the most 
active group, whereas those for other groups are significantly lower. This 
monopoly of high correlation by the most active group indicates that this 
is one of the required structural equilibria for the highest activity. 
When the structural parameters x.sub.i and x.sub.j are the case, an 
estimated equilibrium constant a.sub.ij is expressed by a.sub.ij =(x.sub.j 
-b.sub.ij)/x.sub.i, wherein b.sub.ij is a correction factor. This 
equilibrium equation is derived from the regression line x.sub.j =a.sub.ij 
x.sub.i +b.sub.ij which is obtained for the group of compounds with the 
desired property. The value (x.sub.j -b.sub.ij)/x.sub.i of the most active 
group is nearly constant around the value a.sub.ij, while the values of 
other groups vary widely. 
The value a.sub.ij is the estimated equilibrium constant of two structural 
parameters x.sub.i and x.sub.j, which reflects a certain equilibrium of 
elementary properties for the highest activity. This simple process gives 
a new light to the problem and, in fact, creates a new structural 
parameter. This process has not been tried. 
(3) By using all parameters prepared in (1) and (2), the control charts are 
produced. This is nothing but plotting data either on paper or in the 
n-dimensional space by the aid of computer and determine from the plots 
the structural outer limit of the most active group. The discrimination 
power is the only criterion to compare among several control charts. 
Thus, the construction and selection of the control charts are complete. 
But this process is repeated when a new addition of data becomes available 
or when better structural parameters are suggested.

DETAILED DESCRIPTION OF THE EXAMPLES 
Preferred examples of this invention will now be described with reference 
to the accompanying drawings. 
EXAMPLE 1 
Method for Predicting Acute Toxicity of Chemical Substances From Their 
Structural Formula 
Conventionally, the degree of toxicity of a compound has been known only 
after actual dose. LD.sub.50 data for small animals (intravenous dose) 
contained in the Merck Index (9th edition) were thoroughly taken to use as 
a learning set, which amounts to more than 300 compounds. The control 
chart from these data is shown in FIG. 1. The predictability of this chart 
was tested with 82 other compounds. The scores of prediction are 
summarized in Table I. 
In FIG. 1, the following definitions are employed: 
LD.sub.50 /M: 
Toxicity scale used for this study. Unit of ordinary LD.sub.50 values are 
mg/kg, where mg is the quantity of substance dosed for 50% lethality and 
kg is the weight of the test animal. 
To standardize this value on the millimore base, the LD.sub.50 values is 
divided by the molecular weight. In FIG. 1, the quantity is further 
multiplied by 100 to avoid unfamiliarly small digits. 
C--COOH--COHN: 
The structural parameter along X-axis. This is an approximate measure ot 
lipophilicity, which is produced by subtracting the numbers of carboxylic 
acids and amides from the total number of carbon atoms. 
hCh: 
The structural parameter along Y-axis. This value is the sum of the numbers 
of such groups that has two-hereto-atoms on both sides of carbon atoms. 
They include COOH, CONH, COOR, 
##STR2## 
and so forth. This parameter would be related to the hydrophilicity of 
molecule. The hCh value is 1 for carboxylic group and 3 for urea group. 
TABLE 1 
______________________________________ 
Scores of Predictability of Toxicity 
No. of Compounds 
Control 
LD.sub.50 /M 
found in the limit 
limit observed (Total No.) Note 
______________________________________ 
1000 .gtoreq.1000 
3/3 100% predicted 
.gtoreq.300 
1/2 50% discriminated 
.gtoreq.30 
8/29 72.5% discriminated 
.gtoreq.0 
8/48 83.3% discriminated 
300 .gtoreq.300 
5/5 100% predicted 
.gtoreq.30 
12/27 55.6% discriminated 
.gtoreq.0 
9/48 81.2% discriminated 
______________________________________ 
The following two cases are shown to illustrate the way to use FIG. 1. 
__________________________________________________________________________ 
Compound I 
##STR3## CCOOHCONH = 8 hCh = 3 observed LD.sub.50 (mg/kg) = 14700 
MW = 642 LD.sub.50 /M = 2290 Mahalanobis' distance = 
0.814 C.sub.11 N.sub.2 O.sub.4 H.sub.8 I.sub.3 Na 
Compound II 
##STR4## 
CCOOHCOHN = 31 
hCh = 3 
LD.sub.50 (observed) = 26.6 mg/kg 
MW = 677 
LD.sub.50 /M = 32.768 
Mahalanobis' distance = 32.768 
C.sub.31 N.sub.2 O.sub.10 H.sub.44.2HCl 
__________________________________________________________________________ 
Compound I is located within the control limit 1000. Since Mahalanobis' 
generalized distance of the control limit 1000 is calculated to be 7.6702. 
This number alone can tell that it is found within the limit. In the 
similar way, Compound II is located in the high toxicity region. In order 
to design a less toxic homolog, this chart clearly show the direction of 
modification. 
EXAMPLE 2 
Method for Predicting Good-Taste Compounds From Other Taste-Active 
Compounds 
Structure-taste relationships are still poorly known. A general control 
chart to define the structural requirements of taste-active compounds are 
shown in FIG. 2A. The sources of the data are those published in the last 
10 years on the low-molecular weight tastants. The total number of 
compounds used for this analysis is 831. 
Areas T.sub.1 and T.sub.2 are those of umami (good taste rather than sweet 
taste) compounds where all 37 known compounds are included without 
exception. The areas Sweet-100, -1, and -0 are those of respective 
sweetness levels (sweetness of sucrose=1). Sweet-100 consists of 98 
compounds whose sweetness are more than 100. Sweet-1 group has 102 
compounds with sweetness less than 100 but at least 1, including sucrose 
itself. Sweet-0 (157 compounds) are those reported to have sweetness less 
than 1. The trilateral chart is borrowed from the usual way to describe 
the three-component-system and, here, expresses the proportion of three 
structural parameters (A+1.989), B+1.16, and D, which are defined as 
follows: 
A: The number of active protons (Example: COOH, OH, aromatic NH, active CH 
etc.) 
B: The number of branches 
##STR5## 
D: The number of electron-donors (Example: hetero-atoms, halogen atoms, 
armatic c-ring, isolated C.dbd.C etc.) 
The denominators appeared in D/1.1 or (A+1.989)/1.2 has no particular 
meaning except bringing area T.sub.1 to the center of the chart. In this 
trilateral chart, the sum of three components is adjusted to become 1. 
Within T.sub.1 and T.sub.2, only two bitter-tasting compounds are found 
out of 437 compounds (discrimination power is 99.5%). While many known 
sweeteners are known to show bitter taste at the same time, sucrose (1), 
cyclamic acid (2) and aspartame (3) are known to be lacking bitter taste. 
These three ideal sweeteners are found very near to one of good taste 
zones, whereas saccharine (4), which is known to have a slight bitterness, 
is located a little apart from good taste zones. 
To construct FIG. 2A, the principle of balance was applied. In Table 2, a 
part of the list of correlation coefficients is reproduced. 
Here, high correlations are shown for umami compounds and highly sweet 
compounds, while the coefficients gradually decrease toward bitter group. 
The coefficient of A and D for umami group is rather low, but a close 
examination of data revealed that it consists of two clusters entirely 
apart, and the coefficients for each group turned out to be 0.995 and 
0.900. These two clusters correspond to T.sub.1 and T.sub.2. 
TABLE 2 
______________________________________ 
Examples of comparison of correlation coefficients 
Parameter combinations 
B and D A and D C and D 
______________________________________ 
Umami group 
0.981 0.679 0.932 
(0.995)* 
(0.900) 
Sweet-100 0.896 0.933 0.834 
Sweet-1 0.915 0.870 0.663 
Sweet-0 0.945 0.854 0.838 
Bitter 0.805 0.800 0.678 
______________________________________ 
*See the text. 
Now that the umami compounds are taken as those of most favorably-balanced 
structures, the equilibrium constants of two structural parameters are 
determined by obtaining the regression lines for the group. When two 
structural equilibria are simultaneously required. (A and D, and B and D) 
with one parameter in common, one can reach such an expression of 
equilibrium as FIG. 2A to visibly show the balancing point of three 
parameters. 
EXAMPLE 3 
Method for Predicting the Structure of Sweet Tasting Dipeptides 
FIG. 2A is the control chart covering all kinds of taste-active compounds. 
It is a general map, but naturally too crude for lead-optimization. 
In this example, only dipeptides are dealt with. Although aspartame and 
some similar dipeptides are known to show strong sweetness, many of 
similar dipeptides are bitter. To discriminate sweet dipeptides (sweetness 
more than 100) from bitter ones, FIG. 3 was prepared. 
In FIG. 3, the structural limit for sweetness is circled. 
##EQU1## 
C: The number of carbon atoms A and D were already defined elesewhere. 
This 3-parameter-balance may be expressed with a trilateral chart, but X-Y 
coordinate is more general and easy to handle. 
When aspartame (I) is modified to free acid (II), to glutamyl derivative 
(V, VI) or to other similar structures (III, IV), bitter taste is 
observed. On the other hand, VII, VIII are sweet peptides. They are 
well-discriminated with FIG. 3, therefore, it can be used for 
lead-optimization research. 
______________________________________ 
(I) 
##STR6## 
When the taste of sucrose is 1 (one), that of 
this compound is about 150 times sweeter than 
the former. 
(II) 
##STR7## 
Bitter taste 
(III) 
##STR8## 
Bitter taste 
(IV) 
##STR9## 
Bitter taste 
(V) 
##STR10## 
Bitter taste 
(VI) 
##STR11## 
Bitter taste 
(VII) 
##STR12## 
The sweet taste of this compound is about 
120 times sweeter than sucrose. 
(VIII) 
##STR13## 
The sweet taste of this compound is about 200 
times sweeter than sucrose. 
______________________________________