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ISTANFORD ARTIFICIAL INTELLIGENCE PROJECTMEMO A IM-141COMPUTER SCIENCE DEPARTMENTREPORT NO. CS-203
THE HEURISTIC DENDRAL PROGRAMFOR EXPLAINING EMPIRICAL DATA
BY
BRUCE G. BUCHANANJOSHUA LEDERBERG
CO-PRINCIPAL INVESTIGATORS: E. FEIGENBAUM & J. LEDERBERG
I FEBRUARY 1971
COMPUTER SCIENCE DEPARTMENTSTANFORD UNIVERSITY
Il
FEBRUARY 1971STANFORD ARTIFICIAL INTELLIGENCE PROJECTMEMO AIM- Ik1
COMPUTER SCIENCE DEPARTMENT REPORTNO. CS2O3
THE HEURISTIC DENDRAL PROGRAMFOR EXPLAINING EMPIRICAL DATA*l
by
Bruce G. BuchananJoshua Lederberg
Co-Principal investigators: E. Feigenbaum & J. Lederberg
ABSTRACT: The Heuristic DENDRAL program uses an information processingmodel of scientific reasoning to explain experimental data inorganic chemistry. This report summarizes the organizationand results of the program for computer scientists. The pro-gram is divided into three main parts : planning, structuregeneration, and evaluation.
The planning phase infers constraints on the search spacefrom the empirical data input to the system. The structuregeneration phase searches a tree whose termini are models ofchemical molecules using pruning heuristics of various kinds.The evaluation phase tests the candidate structures againstthe original data. Results of the program's analyses of sometest data are discussed.
#This research was supported by the Advanced Research Projects Agency(SD-I83). Much of the work reported here was performed by Mrs. GeorgiaSutherland and Mr. Allan Delfino. The assistance of Dr. Alan Duffieldand Professor Carl Djerassi is also gratefully acknowledged.
Reproduced in the USA. Available from the Clearinghouse for FederalScientific and Technical Information, Springfield, Virginia 22151.Price: Full size copy $3.00; microfiche copy $ .65.
1
I
IThe Heuristic DENDRAL Program
for Explaining Empirical Data
IThe Heuristic DENDRAL program applies an information processing model of
scientific reasoning to a specific problem in organic chemistry. It reasons
its way from experimental chemical data to explanatory hypotheses about the
molecular structure of compounds. For now, the program ignores other kinds
of scientific reasoning such as theory formation: its task is to explain
data within an established theory. This report describes the Heuristic DENDRAL
program for IFIP members who might have hoped for a succinct description in
our artificial intelligence reports (for example, [7], [B], [9]) and who would
like to avoid the chemical details found in our publications for chemists [2] ,[33, [k], [53, [63.
i
This paper is divided into three main parts: (i) a brief description of
the task area, mass spectroscopy; (il) a discussion of the artificial intelli-
gence aspects of the program; and (ill) a summary of results.
iI
I. THE TASK AREA
Organic chemists are primarily concerned with either the analysis or
synthesis of compounds, that is, with either identifying or manufacturing
chemical molecules. Mass spectrometry is a branch of analytic chemistry in
which the substance to be identified is vaporized and bombarded with electrons
in a mass spectrometer in order to obtain data on the resulting fragmentations.
lI
II
2
III The data are arranged in a mass spectrum, which shows the masses of fragments
produced in the instrument plotted against their relative abundance. Thus the
task of the chemist is to use his knowledge of the behavior of molecules in a
mass spectrometer to identify the structure of compounds.IThe information processing nature of the problem is one important reason
for selecting the analysis of mass spectra as the task area. Chemists them-
selves use non-mathematical models of organic molecules and of the mass spec-
trometer to analyze mass spectra. They also use many complex judgmental rules.
Another reason for selecting a branch of organic chemistry as the program's
task area is that a notational algorithm for representing and generating chemical
molecules invented by Lederberg [I] is particularly well-suited for computer use.
This algorithm, named DENDRAL, is described in section 11-B of this paper.
IIII
11. PROGRAM ORGANIZATION
Heuristic DENDRAL is organized as a heuristic search program which searches
the space of organic molecular structures for the molecule which best explains
the experimental data. The input to the program is the mass spectrum, empirically
determined by inserting a sample of a compound into the mass spectrometer. Out
of the implicit space of all possible molecular structures the program selects
the structures which best explain the data -- often a single structure. Because
of the size of the space, it is necessary to reduce the search through the
judicious use of heuristics. And, because several structures may be plausible
explanations, it is necessary to provide a means for evaluating alternatives.
iIIIi In test cases, where we know the structure of the sample compound, the
program usually produces the correct structure in its answer set. Its pruning
3
l
I
and evaluation heuristics are good enough that this is a small set, as can be
seen in the accompanying tables. The working chemist, of course, does not
ordinarilyknow the structure of his sample.IThe heart of Heuristic DENDRAL, as of any heuristic search program, is the
generator of the search tree. The tree, in this case, is the tree of successive
attachments of chemical atoms into larger and larger graph structures . The
generator is the DENDRAL algorithm. At the first node of the tree is the
initial set of unstructured atoms; deeper levels of the tree correspond to
partial structures with more atoms in the structure and fewer unattached atoms.
At the ends of all the branches are complete molecular structures with every
atom in the initial set allocated to some place in the structure. The DENDRAL
algorithm makes all possible attachments of atoms irredundantly at every level,
and it provides the capabilities for heuristic pruning of the tree. Constraints
on the generator take two forms: search reduction based on plans inferred from
the mass spectral data and search reduction based on considerations of chemical
stability.
I A. Planning : Search Reduction Based on the Mass Spectral Data
Among the large numbers of molecular structures at the termini of the
search tree, planning can describe constraints on the space which are severe
enough to limit the number of termini to a few dozen or even just one or two
structures. The search reduction power of the plan depends upon the amount
of chemical theory embodied in the underlying planning heuristics .Ili
1. Constructing Plans from the Data
A plan is a set of constraints for the generator which limits the output
structures to those which are most relevant to the data. The data may be the
lIII
mass spectrum or other experimental data on the sample, for example, a nuclear
magnetic resonance (NMR) spectrum.
From mass spectral data it is often possible to infer that particular
partial structures, or "superatoms" must be contained in each of the candidate
structures. And it is often possible to determine the positions of the super-
atoms within the context of the remaining unstructured atoms. Currently, the
program infers the presence of only one superatom at a time, so the form of
this part of a plan is
HiR2 | Rn
R3 —— y X :
The F in the center of this scheme is the superatom, which has been
identified,
(it is called a "functional group" by chemists, thus the "F".) The R's are
the weights of the appendant radicals, which surround F . Having this information
constrains the search to molecules which conform to the particulars of this
scheme.
Plans are constructed by the planning program by means of a complex set
of judgmental rules like those used by chemists. Sets of peaks in the mass
spectral data often characterize the functional group in the molecule, and thus
identify F in the plan. The context of those peaks in the data, then, place
the functional group in the molecule relative to the other atoms, and thus
identify the R's in the plan. For example, the functional group "ketone"
(C=o) can be identified by the existence of a pair of peaks in the spectrum at
mass points R]_+2B and R2+2B whose sum is the molecular weight plus 28 mass
units . (A few additional constraints insure that accidental peaks in the data
k
5
i
Iwill not indicate the ketone group. For example, at least one of the peaks
must be a prominent peak in the spectrum.) The existence of such a pair of
peaks identifies F as a carbon atom doubly bonded to an oxygen atom.. The
specific values of R-j_ and R2 , say k3 and 71, can then identify the masses
of the two radicals appendant from the ketone group. Thus the final plan
becomes :
I
iii
0
(10) - c - (71)
Other types of data may be employed by the planning program if they are
available. For the analysis of amines, for example, data from nuclear magnetic
resonance experiments greatly augment the power of the planning program. The
tables of results for amines, ethers, alcohols, thioethers and thiols show
the dramatic reduction possible when NMR data are used. In these cases the
NMR data were used to infer the numbers of methyl (CH^) radicals present in
the test samples and were used to help infer the structures of the superatoms.
It will be possible to incorporate judgmental rules to be used with still other
kinds of experimental data, as the need arises.
iThe planning program works best with data from unringed molecules containing
a single functional group. The reason for this is that the mass spectrometry
theory for these molecules is simpler and less ambiguous than for more complex
molecules. The next section digresses somewhat from the present discussion to
explain how we have been able to automate the generation of the planning
heuristics on the basis of the known theory.
i
I
1
6
i
II
2. Generating Planning Heuristics from the Theory
Some of the most powerful planning heuristics used by chemists (and by
the program) were noticed to be relatively straightforward consequences of the
theory of mass spectrometry. For the set of molecules containing a single
functional group, the planning heuristics can be generated from a few well-
known rules of mass spectrometry. We have written a program, external to the
Heuristic DENDRAL system, for generating these planning rules.
This external program is in two conceptually distinct parts: a superatom
generator and a planning rule generator. The superatom generator is a specialized
version of the DENDRAL structure generator mentioned previously. Its task is
to construct candidate superatoms for inclusion in the plan. The planning rule
generator uses the theory of mass spectrometry to construct a set of heuristics
for inferring the presence of each superatom in the mass spectral data. The
whole process of constructing plans, then, can be thought of as a problem solving
activity where the input is the mass spectrum together with a set of non-carbon
atoms that may be in functional groups, and the output is a plan or set of
alternative plans for generating candidate structures which explain the data.
I3 . Summary
Regardless of the source of the candidate superatoms and their planning
heuristics, whether from a chemist or from a program, the Heuristic DENDRAL
system uses them to construct plans. It tests each candidate functional group
(superatom) against the original data by applying the planning heuristics. If
the functional group satisfies the criteria, it is put into a plan together
with other inferred constraints. The search reduction effect of planning is
shown in Tables 2-5.
I
I
7
i
I
A severe limitation on this problem solver is that it depends upon knowing
that only one superatom containing non-carbon atoms is present in the structure
of the sample (ignoring hydrogens) and consequently that only one functional
group is present. The theory which the rule generator can use does not always
apply when several functional groups are present, nor has much theory been
developed to tell the program what does happen. Although chemists consider
more complex cases and the generator of superatoms can easily be extended to
handle them, the mass spectrometry theory, and consequently the planning rule
generator, cannot be so easily extended.I
B. Structure Generation
The DENDRAL algorithm provides a representation of objects in the search
space — chemical molecules — and describes the procedure for generating them.
Both the representation and the procedure have proved amenable to computer use,
with very few changes. The algorithm uses no other chemical knowledge than the
valence, or number of allowable links, for each type of chemical atom. Carbon,
for example, has a valence of four, oxygen two, and so forth. Within these mild
constraints the algorithm is capable of generating all topologically possible
non-ringed graph structures from a given collection of chemical atoms. The
actual canons of procedure will not be discussed here. The important point to
note is that the algorithm's output of topologically possible molecular struc-
tures can contain a very great number of structures which are implausible from
the standpoint of chemical stability. Search reduction heuristics on the list
known as BADLIST prune the tree as unstable chemical structures begin to emerge.
This reduction can be seen from Table 1. In the other cases BADLIST has no
effect unless a chemist wishes to change it so as to prune some structuresI
8
I
which are now allowed.
1. The Search Space
The search space itself is organized as an AND/ OR tree which is searched
depth-first. The first level of the tree, after the specification of the
initial collection of atoms, is the set of all possible molecule centers, or
centroids. 'Because any one of these centroids may lead to the solution of the
program, this level is a set of OR nodes. Also, for this reason, the OR nodes
are ordered by the program so that the most likely centroid appears first in
the set. The. next level of the tree, just beyond the node specifying a possible
centroid, specifies the possible ways the remaining atoms in the composition
can be partitioned to the unfilled links of the centroid. A central carbon
atom with three unfilled links, for example, must be completed by having three
radicals, made from the remaining composition, attached to the links. Thus,
beyond that node the program will grow several sets of AND nodes, each set
defining a possible partition of the remaining atoms into three clusters. The
scheme of the tree generation for these two levels is shown in the diagram below.
collection of atoms
d o . . ,^oo centroids with k. links
. . . o^o^ ... 6^ xo-l -o2 "" ; ~-ok . . . partitions of remainingatoms into k clustersof atoms
For each AND set of subproblems, all of which must be successfully completed
if the program is to grow the tree beyond any of the nodes, the program attempts
the most difficult subproblem first. That is, it orders the clusters of atoms
9
I
in the AND nodes so that the cluster of atoms which is least likely to produce
stable radicals is chosen first. If, in fact, no radicals can be built from
the node then all subproblems in the AND set are discarded.
After the first two levels of tree generation, the program is recursive.
Each cluster of unstructured atoms is taken up as a fresh problem: the program
lists all possible centroids and then partitions the remaining atoms into the
appropriate numbers of clusters. And again, at every level until there are no
more unstructured atoms. At this point, the program has completed its generation
of the space.
2. Heuristics Used to Guide Search
Besides selecting likely branches at OR nodes and unlikely branches at AND
nodes, the program reduces its total effort by saving the results of previously-
solved subproblems in a "dictionary". A subproblem of constructing radicals
from a cluster of six carbon atoms, for example, may appear several times over
the whole search space. By saving the result of the first solution of this sub-
problem the program is able to save much work. All that it needs to do is fetch
from the dictionary the list of radicals which have been built from six carbons
and attach them, one at a time, to the partially built molecular structure.
Planning information is passed from the Planner to the Structure Generator
on a list known as GOODLIST. As the name implies, GOODLIST is a list of super-
atoms (and associated partitioning information) which should be included in the
output of the generator. The generator uses this information in two ways.
First, the starting set of atoms is reduced by the composition of the superatoms
on GOODLIST and the superatom names are added to the set. Second, planning infor
mation is used in constructing partitions of the initial composition. Starting
10
I
from the superatom as centroid, the program explores only that part of the tree
in which the primary partitions of the remaining atoms are compatible with the
radical weights specified in the plan. Consider again the planning example
considered in part (A) , where the plan was
cOtf ) - C - (7.1)
This means that generation proceeds by first removing a carbon and an oxygen
atom from the initial set of atoms and then constructing only the partitions
of the remaining atoms which are compatible with weights k-3 and 71? that is,
partitions of C^H-? and CgE^Although rarely used, the ability to accept a chemist's intuitions or
biases is a powerful search reduction tool. BADLIST itself reflects one
scientist's intuitions about the subgraphs responsible for unstable structures.
But beyond that, it is easy for an individual to guide the search by adding
(or deleting) constraints to BADLIST and GOODLIST. A chemist can supress all
occurrences of a superatom from the generator's output by adding that superatom
to BADLIST. Conversely, he can force the occurrence of a superatom in every
output structure by adding that superatom to GOODLIST.
The Structure Generator is the central part of the total Heuristic DENDRAL
program. It was mentioned earlier that the planning program can often specify
such a detailed plan that only a single structure fits the plan. In spite of
this power it is necessary to retain the capabilities of a general heuristic
search program to deal with cases outside the scope of the Planner's power.
The output of the Structure Generator is a list of molecular structures. They
are all plausible candidates for explaining the given mass spectrum because
11
they are all chemically stable and they all fit the constraints of the plan
inferred from the experimental data.
C. Evaluation
The purpose of the last phase of the Heuristic DENDRAL program is to cull
the least promising of the plausible candidate structures and rank the remaining
ones. For both of these jobs the program obtains a predicted mass spectrum from
its internal model of the mass spectrometer. The significant peaks in the pre-
dicted mass spectrum are then matched against the original spectrum. A candidatestructure is rejected if its predicted spectrum is inconsistent with the original
data, and the remaining candidates are ranked by how well they explain the
original data
The prediction program, known as the Predictor, consists of two main parts:
a theory of mass spectrometry plus a large number of routines for describing
mass spectrometric processes and manipulating molecular structures in accordance
with those processes. It is not necessary to describe the details of either of
these parts, but the separation of theory from the rest of the program is of
some interest .By separating the theory of mass spectrometry in the Predictor from the
routines which reference it, the theory is much easier to change -- either by
hand or by a program. The theory is a set of data which the program sortsthrough to determine the actions to perform and the parameter settings associated
with those actions. The theory embodied in this data structure is organized as
situation-action rules (or productions). The program checks for the truth of
each situation in the current context and, if true, executes the associated
set of actions. For example, the Predictor checks for the occurrence of the
12
I
ketone functional group by looking for the subgraph C=o in the graph structure
of the molecular structure. If the subgraph is present the program executes
routines for performing cleavages and rearrangement processes characteristic
of ketones.IThe input to this last phase of the program is a set of molecular structures;
the intermediate result is a set of predicted mass spectra, and the final output
is a ranked list of structures which are consistent with the original data.
Consistency, in this case, means that every significant feature of the predicted
spectrum for the candidate structure actually appears in the original data. Thus
the predictive test can only disconfirm candidates. Scoring the candidates on
the basis of how many peaks in the original data they can explain is meant to
estimate degrees of confirmation. The score for a candidate is the sum of the
significance weightings assigned to its predicted mass spectrum by the program.
Thus a candidate which explains peaks thought to be very significant will rank
higher than one which explains as many (or possibly more) peaks of less
significance.
111. RESULTS
Although results of the program's analyses of selected mass spectra have
been published, in chemistry journals (see [2] - [6]) they have not been ade-
quately summarized for computer scientists. The accompanying tables show the
sizes of the problem spaces for different classes of problems and the search
reduction achieved by the program.
i
The ammo acids shown in Table 1 were analyzed without planning, but with
references to the data during structure generation by a simple theory called
13
Ithe "zero-order" theory. Ammo acids are characterized by the presence of both
a nitrogen and a carboxylic acid group (-C=o) in the molecule. They happenXOH
to lend themselves to this simple kind of analysis because they tend to fragment
in almost every possible way in a mass spectrometer, just as the zero-order
theory predicts. This is not true of other classes of compounds. BADLIST is
able to constrain the size of the search space dramatically, as noted by the
difference between the columns entitled "Number of Possible Structures" and
"Number of Plausible Structures", because more than one non-carbon atom is
present in ammo acids. This desirable reduction is lost in the other cases,
as indicated in the footnote to the third column of Tables 2-5.
l
II
For the ketones, shown in Table 2, planning was necessary to achieve the
search reduction noted between the columns entitled "Number of Plausible
Structures" and "Number of Structures Generated". Applying a few well-known
rules of mass spectrometry was almost solely responsible for this reduction.
Other rules about the mass spectrometric behavior of ketones allowed the evalu-
ation program to exclude some of the candidates generated and successfully rank
the remaining ones. As noted before, ketones are characterized by the presence
of the chemical substructure C~O .
ili
I Tables 3~5 show the results of the program's analysis of unringed compounds
containing the substructures
■N- (amines)
I 0- (ethers)OH (alcohols)
SH (thiols)S- (thioethers)
14
IFor all of this work the planning program contained a much larger body of
theoretical knowledge than in the ketone case. Its theory about the mass
spectrometry of these classes of compounds, in fact, was as complete as .thetheory in the Predictor. And it included nuclear magnetic resonance (NMR)
theory which the Predictor does not. Thus, the plans which it was able to
construct were so detailed that the evaluation phase could make no further
improvements. In other words, there was no theory left to use for evaluation
which had not already been used in planning.
III
II
IV. CONCLUSION
The Heuristic DENDRAL program successfully explains experimental data for
many test problems in analytic organic chemistry. On a limited class of mole-
cules it performs at about the same level as a post-doctoral chemist. However,
the class of problems which can be solved is still very small relative to those
a practicing chemist may see. Much of our future work will be devoted to
extending the power of the program to cover, for example, compounds with several
functional groups and compounds containing an arbitrary number of rings . We
anticipate much work, also, on extending the program to cover more varied kinds
of scientific reasoning.
IIII
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BIBLIOGRAPHY
1. J. Lederberg and E.A. Feigenbaum, "Mechanization of Inductive Inferencein Organic Chemistry". In Formal Representation of Human Judgment .(B. Kleinmuntz- cd.), John Wiley & Sons, Inc., 1968. (Also StanfordArtificial Intelligence Project Memo No. 5k.)
2. J. Lederberg, G.L. Sutherland, B.G. Buchanan, E.A. Feigenbaum, A.V. Robertson,A.M. Duffield, and C. Djerassi, "Applications of Artificial Intelligence forChemical Inference I. The Number of Possible Organic Compounds: AcyclicStructures Containing C, H, 0 and N" . Journal of the .American ChemicalSociety, 91, 2973-2976 (1969).
3. A.M. Duffield, A.V. Robertson, C. Djerassi, B.G. Buchanan, G.L. Sutherland,E.A. Feigenbaum, and J. Lederberg, "Applications of Artificial Intelligencefor Chemical Inference 11. Interpretation of Low Resolution Mass Spectraof Ketones". Journal of the American Chemical Society, 91, 2977-2981 (1969) .
k. G. Schroll, A.M. Duffield, C. Djerassi, B.G. Buchanan, G.L. Sutherland,E.A. Feigenbaum, and J. Lederberg, "Application of Artificial Intelligencefor Chemical Inference 111. Aliphatic Ethers Diagnosed by Their LowResolution Mass Spectra and NMR Data". Journal of the American ChemicalSociety, 91, JkkO-'jkk 1? (1969).
5. A. Buchs, A.M. Duffield, G. Schroll, C. Djerassi, A.B. Delfino, B.G. Buchanan,G.L. Sutherland, E.A. Feigenbaum, and J. Lederberg, "Applications of ArtificialIntelligence for Chemical Inference IV. Saturated .Amines Diagnosed by TheirLow Resolution Mass Spectra and Nuclear Magnetic Resonance SpectraI. Journalof the American Chemical Society, Q2, 683l)(l970).
6. A. Buchs, A.B. Delfino, A.M. Duffield, C. Djerassi, B.G. Buchanan, E.A.Feigenbaum, and J. Lederberg, "Applications of Artificial Intelligence forChemical Inference VI. Approach to a General Method of Interpreting LowResolution Mass Spectra with a Computer"* Chemica Acta Helvetica, 53, 1394(1970)
7. B.G. Buchanan, G.L. Sutherland, and E.A. Feigenbaum, "Heuristic DENDRAL: AProgram for Generating Explanatory Hypotheses in Organic Chemistry". InMachine Intelligence k (B. Meltzer and D. Michie, eds . ) Edinburgh UniversityPress (1969). (Also Stanford Artificial Intelligence Project Memo No. 62.)
8. B.G. Buchanan,
G.L,
Sutherland, and E.A. Feigenbaum, "Toward an Understandingof Information Processes of Scientific Inference in the Context of OrganicChemistry". In Machine Intelligence 5, (B. Meltzer and D. Michie, eds.)Edinburgh University Press (1969). (Also Stanford Artificial IntelligenceProject Memo No. 99 ")
9. E.A. Feigenbaum, B.G. Buchanan, and J. Lederberg, "On Generality and ProblemSolving: A Case Study Using the DENDRAL Program". In Machine Intelligence 6(B. Meltzer and D. Michie, eds.) Edinburgh University Press (in press). (AlsoStanford Artificial Intelligence Project Memo No. 131.)