=Paper=
{{Paper
|id=None
|storemode=property
|title=Shape Perception in Chemistry
|pdfUrl=https://ceur-ws.org/Vol-1007/paper6.pdf
|volume=Vol-1007
|dblpUrl=https://dblp.org/rec/conf/shapes/HastingsBO13
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==Shape Perception in Chemistry==
https://ceur-ws.org/Vol-1007/paper6.pdf
Shape Perception in Chemistry
Janna HASTINGS a,b,c,1 , Colin BATCHELOR d and Mitsuhiro OKADA e
a Cheminformatics and Metabolism, European Bioinformatics Institute, Hinxton, UK
b Swiss Centre for Affective Sciences, University of Geneva, Switzerland
c Evolutionary Bioinformatics, Swiss Institute of Bioinformatics, Switzerland
d Royal Society of Chemistry, Cambridge, UK
e Department of Philosophy, Keio University, Tokyo, Japan
Abstract. Organic chemists make extensive use of a diagrammatic language for
designing, exchanging and analysing the features of chemicals. In this language,
chemicals are represented on a flat (2D) plane following standard stylistic conven-
tions. In the search for novel drugs and therapeutic agents, vast quantities of chem-
ical data are generated and subjected to virtual screening procedures that harness
algorithmic features and complex statistical models. However, in silico approaches
do not yet compare to the abilities of experienced chemists in detecting more subtle
features relevant for evaluating how likely a molecule is to be suitable to a given
purpose. Our hypothesis is that one reason for this discrepancy is that human per-
ceptual capabilities, particularly that of ‘gestalt’ shape perception, make additional
information available to our reasoning processes that are not available to in silico
processes. This contribution investigates this hypothesis.
Algorithmic and logic-based approaches to representation and automated rea-
soning with chemical structures are able to efficiently compute certain features,
such as detecting presence of specific functional groups. To investigate the specific
differences between human and machine capabilities, we focus here on those tasks
and chemicals for which humans reliably outperform computers: the detection of
the overall shape and parts with specific diagrammatic features, in molecules that
are large and composed of relatively homogeneous part types with many cycles. We
conduct a study in which we vary the diagrammatic representation from the canon-
ical diagrammatic standard of the chemicals, and evaluate speed of human determi-
nation of chemical class. We find that human performance varies with the quality
of the pictorial representation, rather than the size of the molecule. This can be con-
trasted with the fact that machine performance varies with the size of the molecule,
and is of course impervious to the quality of diagrammatic representation.
This result has implications for the design of hybrid algorithms that take features
of the overall diagrammatic aspects of the molecule as input into the feature de-
tection and automated reasoning over chemical structure. It also has the potential
to inform the design of interactive systems at the interface between human experts
and machines.
Keywords. ontology, shape perception, cognition, spatial reasoning, logical
reasoning, molecular graph
1 Corresponding Author, e-mail: hastings@ebi.ac.uk
83
Introduction
“A mind that has the ability to choose how it will represent a particular problem it needs to
solve, choosing from a repertoire of representational capacities that include more analogical
and more symbolic notations is more flexible, hence more ‘intelligent’ ” [32]
Organic chemists make extensive use of chemical diagrams for designing, exchang-
ing and analysing the features of chemicals. In this language, chemicals are represented
on a flat (2D) plane following standard stylistic conventions [12]. The use of diagram-
matic languages to concisely convey information for humans to process is an essential
component of many sciences. In biology, pathway diagrams convey information about
biological processes [14]. A good visualization of scientific information facilitates rapid
understanding and can thereby lead to novel insights not otherwise possible [19]. One
such example is Category Theory in mathematics, in which the use of diagrams is essen-
tial for representing mathematical properties and proofs [30].
In the search for novel drugs and therapeutic agents, large quantities of chemical data
are generated. Interacting with these data and sifting a relevant subset (for a given prob-
lem) from the sizeable background is an ongoing challenge. Tools such as the molecule
cloud can give an overview of a chemical dataset by showing common scaffolds sized
for how often they appear in the dataset [9]. Many features of chemical entities have
relevance on whether a given molecule is suited to a given purpose. Algorithmic and
logic-based approaches are able to efficiently compute certain of these features, such as
the presence of specific atoms or functional groups, overall mass and charge [18]2 . Al-
gorithmic approaches can also gauge the overall shape of a molecule (at least in terms
of delineating the outline of the three-dimensional space it fills) and calculate the math-
ematical similarity of that shape to that of other molecules or the reciprocity to poten-
tial binding sites [40,2,20]. Yet, many problems in chemical informatics remain diffi-
cult to efficiently automate over large molecular collections (e.g. finding maximal shared
components between a set of molecular graphs [31], detecting all the cycles in a given
molecule [3]).
In what follows, we focus on a class of problems that are known to be challenging
for algorithmic solutions (in terms of efficiency), and yet are apparently straightforward
for human chemists: detecting the overall shape and class of a presented molecule, in
molecules that are large and composed of relatively homogeneous parts interconnected
in cycles (such as the class of fullerene molecules [23]). As discussed in [18], determi-
nation of overall shape and chemical class for these classes of molecules is particularly
challenging since the dense interconnection of the atoms in multiple fused cycles and
the homogeneity of the atom environments. We hypothesise that a contributing factor in
this performance discrepancy is that the use of a visual language in chemistry enables
humans to directly harness the ‘gestalt’ or shape-detecting features of their visual per-
ceptual machinery, seeing the whole molecule at once through the diagrammatic depic-
tion, and therefore not needing to do the same sorts of computations that our algorithms
need to do. If this line of thinking is correct, we should observe that the ability of hu-
mans to perform these tasks is affected by perturbances in the diagrammatic depiction
more than in the size of the molecule. We conducted a study in which we time experi-
2 As discussed in [18], we ignore statistical ‘black box’ approaches since they do not allow for explanations
of their deductions and are not provably correct.
84
enced chemists performing a classification task on molecular diagrams with varied (a)
diagrammatic faithfulness, and (b) size of the chemicals. We then evaluated the speed
and accuracy of the chemists’ performance given these variances.
The remainder of this document is organised as follows. In the next section, we give
our experimental design in the context of some background information about chemical
diagrams and the class of chemical problems that we will use as a case study. Thereafter,
we present our results and discussion. With only three participants and only 30 diagrams
included in our experiment, our results can be considered a pilot study rather than a
conclusive investigation. However, we consider these preliminary findings suggestive of
future research directions, and we go on to further speculate about the implications for
the use of artificial intelligence in chemistry applications.
1. Methods
1.1. The diagrammatic language of chemistry
Molecular entities are commonly represented visually as connected graphs, in which
the vertices represent atoms (or groups) and the edges chemical bonds [39]. Chemin-
formatics software use the underlying graph as chemical data structure that serves as
input to algorithmic calculations of features of the chemicals. Logic-based approaches
also use a graph-based underlying representation as input to automated reasoning pro-
cesses [26]. For human consumption, however, the underlying graph is projected onto a
two-dimensional plane for visual interpretation. This diagrammatic depiction is a core
offering of almost all chemical databases, and professional chemists develop an aptitude
at discerning molecular features via such representations. Some examples of chemical
diagrams are illustrated in Figure 1.
Figure 1. Some examples of chemical diagrams.
Chemical diagrams serve an invaluable purpose for chemists: they enable rapid eval-
uation of the overall chemistry of a given molecule, detection of errors or problems in
the chemical structure being represented (e.g. infeasibility or chemical instability), and
assessment of the properties or classifications that are relevant for the given molecule.
Chemical diagrams, like maps, represent spatial information. We have earlier re-
ferred to such spatial representations such as street maps, chemical diagrams, and en-
gineering design models as structural diagrams [12], and they were called analogical
representations in [36]. Here, we will focus not on the structural associations that we
85
highlighted before, but on the features of the overall shape and layout of chemicals that
are available in chemical diagrams.
Molecular flexibility is also very important for molecular shape [13], as one 2D de-
piction can, through flexibility, yield many different 3D conformers that have vastly dif-
ferent properties in vitro. Such flexibility is not explicitly represented in 2D illustrations
of molecules, but can be inferred from such representations given appropriate chemical
knowledge.
1.2. Chemical shape perception task
For our experiment, we have deliberately chosen classes of molecule that are known to
be challenging to represent with logic-based automated reasoning approaches. Earlier,
we have conducted an evaluation of the capabilities of algorithmic and logic-based ap-
proaches to reasoning tasks with molecular structures in [18]. The classes we selected
for use in this task are:
1. Macrocyclic molecules, including calixarenes;
2. Polycyclic cages, including several differently sized fullerenes;
3. Shape-characterised molecules such as the catenanes and molecular knots;
4. Molecules that were not members of the above three classes as ‘controls’.
Macrocyclic molecules are molecules that form a large cyclic structure composed of
linkages of smaller functional groups. Polycyclic cages are molecules that are composed
entirely of cycles that are fused together in such a way as to form an overall cage-like
structure, which is a feature that has interesting applications in medicinal chemistry and
in materials science as the structure can serve to protect or capture a smaller molecule
on the inside, or be engineered to lengthy tubes that are very strong. Examples are the
fullerenes, cucurbiturils (named for their similarity to pumpkins), nanotubes, and small
regular compounds such as cubane. Such nanomaterials have recently shown promise in
the challenge of capturing highly volatile nerve agents and thereby preventing damage
in vivo [22]. Molecules with specific shapes are of interest in the development of molec-
ular machines, including the presence of stationary and movable parts, and the ability to
respond with controlled movements to the external environment. Molecules that are me-
chanically interlocked—such as bistable rotaxanes and catenanes are some of the most
intriguing systems in this area because of their capacity to respond to stimuli with con-
trolled mechanical movements of one part of the molecule (e.g. one interlocked ring
component) with respect to the other stationary part [10]. Similarly, molecules which
display unusual energetic properties by virtue of their overall shape, such as molecular
Möbius strips and trefoil knots, are an active research area for many novel applications,
and in many cases mimic the extraordinary properties of biomolecular machinery such
as active sites within protein complexes [34,42].
We selected five individual molecule types for the first two classes (macrocyclic
molecules and cages). For the shape-characterised molecules, we were not able to find
as many representatives in public chemical databases (our main source was the ChEBI
database [15]), therefore we selected only four examples. Eight molecules that were not
members of any of the three target classes but which were highly similar to one of the
selected molecules (based on cheminformatics similarity scoring using Tanimoto over
the molecular fingerprint, as implemented in OrChem [33]). Molecules were selected
ranging from small to large, as measured in terms of counts of non-hydrogen atoms.
86
A randomly selected subset of eight of those 22 molecules was then subjected to
diagrammatic distortion. Different distortion mechanisms were used. Firstly, the original
molecule was computationally assigned a 3D conformation, which was then projected
back onto a 2D diagram (a common outcome of computational processing of chemicals
originally drawn by human chemists). Secondly, computational procedures for ‘clean’
2D diagram generation were used. Finally, some of the diagrams were subjected to image
processing to obscure the standard chemical representation either through blurring or
shape-based transformation. The total number of diagrams was thus 30. The full set of
molecules is shown in Figure 2.
Figure 2. The molecule diagrams used in the experiment, including those showing distortions.
These diagrams were then displayed to the three experienced chemist participants in
a random sequence3 . For each diagram, the chemist was asked to determine the chemi-
cal class of the molecule, presented with the three classes, a fourth option ‘none of the
above,’ and a final option ‘unable to tell from this diagram.’ Participants were timed as
they completed the task, and their accuracy and agreement were calculated. Figure 3
shows a screenshot of the interface we developed in order to complete the perceptual
task.
3 There were three participants, each of whom had an academic background in chemistry and interacted with
chemical data on a daily basis. The participants were explained the purpose of the experiment and each gave
their informed consent. All data were stored anonymously and securely.
87
Figure 3. The chemical perception task interface, showing the chemical diagram and class selection options.
2. Results
2.1. The effect of image distortion on performance
Image distortion had a significant effect on the accuracy of the chemical raters in choos-
ing the correct classification for the classes. Figure 4 (a)4 shows a boxplot of the classi-
fication task accuracy for the standard images as compared to the distorted images. The
time taken (Figure 4 (b)) shows less of an effect than the accuracy, with the means not
significantly different but the variance much larger in the case of the distorted images.
Ordinarily, chemists would look for additional information in case they encounter
a partially obscured image and needed to determine the chemical class. Therefore, we
do not restrict here our measure of accuracy to the percentage of correct classifications.
Agreement between chemists in a classification task is an alternative measure of accu-
racy, which is especially useful in case the correct classification is not known in advance,
but can supplement the known accuracy score used above with a clue as to the difficulty
of the task. It might, for example, have been the case that the chemists had all agreed on
incorrect classifications for the distorted images, leading to low accuracy but high agree-
ment. However, agreement also differed strongly between the non-distorted and the dis-
torted set of images, with the distorted images having a much lower agreement as mea-
sured by Cohen’s Kappa statistic for multiple raters [6]. For the non-distorted pictures,
the kappa was 0.88. For the distorted pictures, the kappa was 0.46%.
2.1.1. The effect of size on performance
The scatter plot in Figure 5 (a) shows that size did not have a large impact on the time
taken to perform the task. The red correlation line shows a weak positive correlation
4 For space considerations, we do not present the full raw data result table here. However, this is available on
request.
88
Figure 4. The display shows boxplots of (a) accuracy and (b) time taken (in ms), comparing the results for
good vs. obscured visual layouts of the chemicals
Figure 5. Scatter plot of average (a) time to complete task (ms), and (b) accuracy, against size of the molecule.
between size and time taken to complete the task. However, this correlation is largely
influenced by one data point, which itself depends on just one data point. The blue line
shows the much weaker correlation that results from excluding the single outlier from
the analysis.
Figure 5 (b) shows that accuracy was slightly anti-correlated with the size of the
molecule, but this effect is not significant, with the p-value of the correlation only 0.24,
and the 95% confidence interval for the correlation coefficient was from -0.54 to 0.15.
These results can be compared to algorithmic approaches and logic-based ap-
proaches for the relevant sort of feature detection that would be required to automati-
cally compute the same task, i.e. automatic classification into the correct class based on
chemical structures. Unfortunately, there is not yet any available generic system that is
89
able to perform the classifications tasks that were used in this experiment with which we
may have compared the performance to our human experts. Indeed, as discussed in [18]
our research has the long-term objective of enabling the development of just such a sys-
tem, however, at this preliminary stage we do not have an available benchmark but must
instead look to the performance profiles of algorithms that are known to be relevant.
2.2. Algorithmic cheminformatics approaches
The relevant algorithms that would be required to detect the classes specified include
the detection of subgraph isomorphism and finding the smallest set of rings [18,43].
These algorithms are known to scale supralinearly in the number of atoms. For example,
subgraph isomorphism in the general case is known to be NP-complete [7], although
optimisations exist for various sub-classes of molecules, such as those that are planar [8].
For the particularly shape-defined classes, shape similarity algorithms on molecular
structures exist that use ray-tracing of the projected surfaces of molecules to estimate the
overall shape of the molecule and use that as a descriptor e.g. in virtual screening [2].
These methods depend on 3D conformer though, and for flexible molecules many con-
formers may result from the same 2D diagrammatic depiction, dramatically decreasing
the performance of the algorithm.
Furthermore, a separate algorithm implementing a check on the rules of class mem-
bership would need to be hand-written for each of the three class types used in this task
(macrocyclic, cage, shape-defined). This hampers the extensibility and flexibility of a
system that needs to classify molecules in the general case [18,25]. On the other hand,
logic-based systems address these objectives of being generic, extensible and flexible.
2.3. Logic-based approaches
The popular Web Ontology Language, OWL [11], is highly efficient in representing tree-
like structures, but is unable to correctly represent cyclic structures [16]. A first-order
logic programming based formalism has been proposed specifically for the case of rep-
resenting chemical structures [26,25]. These description graph logic programs (DGLP)
are able to represent objects whose parts are interconnected in arbitrary ways, includ-
ing cyclic structures. The decidability of logic programs do not rely on the tree-model
property that underlies the description logics behind OWL. However, representation of
classes with more advanced overall topological features such as polycyclic cages is be-
yond the expressivity of DGLP as it requires quantification over all atoms in a molecule
rather than specific atoms, parts or properties within the molecule.
Perhaps motivated by similar concerns on the limits of the logic-based approaches
underlying languages such as OWL, Maojo et al. propose a ‘morphospatial’ approach to
ontology with application in the nanomaterials domain [27]. Shape features are explicitly
encoded in their ontology alongside other features such as composition. However, this
approach merely pushes the problem onto those computational methods that are needed
to derive the shape features automatically from some representation of the input chem-
ical structure and thereby assign appropriate ontological categories to nanomolecular
structures.
An approach for the representation of the overall structure or topology of highly
symmetrical polycyclic molecules is described in [17,23]. There, the authors propose us-
90
ing a combination of monadic second-order logic and ordinary OWL, with a heteroge-
neous logical connection framework used to bridge between the two formalisms. This
approach has not yet been implemented in practice, but shows promise for logical rea-
soning over features involving regularity in the overall structure of molecules. However,
arbitrary entailment in monadic second-order logic is known to be computationally ex-
pensive5 .
Spatial logics and spatial axiomatizations have been advanced in which it is possible
to perform computational deductive reasoning [5,41]. However, it is not immediately
straightforward to represent the problem of determining from an arbitrary chemical graph
whether it is a member of the class of fullerenes (for example) as a spatial reasoning
problem. We will develop this research question further in future work.
3. Discussion and Conclusions
While this study is small and exploratory in nature only, our results provide tentative
support for a role for perception in human performance in the presented classification
decision task, in that observed performance appeared to decrease with the quality of the
diagrammatic representation rather than the size of the molecule. On the other hand, it is
known that the best algorithmic and logical approaches to solving these particular tasks
scale dramatically in the size of the molecule, rendering their habitual application to large
numbers of molecules in a database problematic.
Larkin and Simon [24] attribute observed efficiencies of diagrammatic reasoning
relative to non-diagrammatic reasoning to efficiencies in searching and inference in the
reprentation space compared to that of a non-diagrammatic representation space, e.g. ax-
ioms. This may indeed be the root explanation, but it doesn’t give guidance on how best
to expose the representational efficiency that humans have (the ability to perceive the
overall shape and connectivity in molecular diagrams) to computational processes. Tra-
ditional logical reasoning relies on linguistic or symbolic representation of the properties
of objects together with the rules for deriving inferences on those properties. By contrast,
diagrammatic representation can explicitly encode the relevant properties of objects and
their background constraints such that the needed inferences can be directly drawn from
the spatial constraints evident in the illustration [32], known as the “free ride” property.
Systems have been developed that enable the representation of logical axioms dia-
grammatically and the formalisation of accompanying reasoning systems to the extent
that diagrammatic and traditional syllogistic reasoning can be combined in order to serve
as an aid for human capability [29,28]. Such logical diagrammatic representations do not
correspond directly to portions of reality, as the diagrammatic representations of chem-
icals correspond to classes of chemicals, but the correspondence is still analogical, i.e.
by analogy. For example, Euler diagrams represent axioms such as All A are B as a
smaller circle A entirely enclosed in a larger circle B [35]. This is analogous to spatial
inclusion, as (for example) a smaller fullerene molecule can be fully enclosed in a larger
fullerene molecule [23], and we could make corresponding statements such as All atoms
in molecule A are INSPAT IALLY molecule B.
5 Automated theorem provers such as LEO-II (http://www.ags.uni-sb.de/˜leo/) are able to approximate some
aspects of entailment checking.
91
Where perception is used as an aid to reasoning, care must be taken in the choice of
the visual representation. For example, when visual diagrams are used as an aid to human
logical reasoning, it has been found that Euler diagrams are more effective than Venn dia-
grams [28]. Irrelevant and distracting visual detail acts as a hindrance to reasoning rather
than as an aid [21]. In the chemistry domain, for the class of classification problems we
are interested in, this may be particularly important. Exposing the specifically visual in-
formation of a chemical diagram to computational processes would introduce additional
constraints on the representation of the chemicals that currently only obtain in case the
representation is intended for human consumption. Visual inference can sometimes be
much more expensive than normal inference in the corresonding axiomatization, espe-
cially when the visual information is incomplete or, as we have tested, perturbed [1].
Adherence to standards for clear and unambiguous diagrammatic representation such as
those put forward in [4] would go some way to address this concern in the chemistry
domain.
In chemical similarity searching and bioactivity predictive modelling, quantitative
shape-based 3D descriptors have met with mixed results stemming, on the one hand,
from their greater computational cost than their 2D counterparts, and on the other hand,
from the additional ‘noise’ that they can introduce in flexible molecules due to the vari-
ety of conformations [40]. One direction for our future research will be to evaluate the
performance of these shape-based descriptors in assigning shape classes to molecules,
such as ‘spherical’ and ‘cubic’. We are not aware of any existing work that applies this
type of descriptor to the problem of structure-based chemical classification.
Our result emphasises the need for hybrid reasoning systems in chemistry that are
able to combine features derived diagrammatically from visual representations of the
molecule with the now-standard logic-based and algorithmic reasoning over the graph-
based structure. Such hybrid systems have been advanced in other domains. For exam-
ple, the Vivid system offers some diagrammatic reasoning capability alongside logical
reasoning capability [1]. However, this system depends on algorithmic processes that
“observe” pre-defined features in the diagrams included in the system capability. In the
case of the chemical diagrams that form our case study here, some features are features
of the whole diagram for which computational “observation” algorithms do not (to the
best of our knowledge) yet exist. Research in machine vision may yield some methods
that can be harnessed in pursuit of this objective [38].
Sloman [37] speculates that the ability to integratively process different types of rep-
resentation with correspondingly different reasoning tasks might be a distinctive feature
of intelligence in general; it is certainly a feature of human intelligence.
Acknowledgements
JH thanks the Swiss Center for Affective Sciences, and the European Commission via
EU-OPENSCREEN, for funding.
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