Shape, Function and Granularity
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This document discusses shape from multiple perspectives including biology, chemistry, philosophy, and computer science. It explores how shape relates to function across natural and artificial systems, and how the shapes of parts relate to wholes. Some key topics covered include the flexible and rigid shapes of biological molecules like ATP and cyclohexane/benzene, the perplexing ontology of holes, holes behaving like binding sites in proteins, and how the definition of a hole depends on the level of granularity. The document aims to further understanding of shape across domains and how machines can be taught to reason about shapes.
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Shape, Function and Granularity
- 1. SHAPEThe final frontier? Janna Hastings1 Oliver Kutz2, MehulBhatt2, Stefano Borgo3 1 European Bioinformatics Institute, University of Geneva 2 University of Bremen, Germany 3 Laboratory for Applied Ontology, ISTC-CNR Image credit: Jonathan J. Dickau
- 2. SHAPE is outline or form closely related to function across different domains It is a property of the whole object that may disappear in its parts
- 3. What is shape? How does shape relate to function in natural and artificial systems? What is the relationship of the shapes of wholes to that of their parts? How do humans and computers perceive shape? How do humans and computers reason about shapes? What are the puzzles of shape, and how do we teach machines to solve them?
- 4. Parts and wholes, shapes and holesin living beings Janna Hastings, EBI, UK; Geneva, CH Colin Batchelor, RSC, UK Stefan Schulz, MUG, Graz, Austria
- 5. Is the human hand bucket-shaped?
- 6. Biological reality is dynamic and multifaceted
- 7. Ontology background CONTINUANT colour weight Independent Dependent inheres ability – and desire – to catch mice participates digestion sleeping time OCCURRENT Image credit (cat): Panther
- 8. Biological molecules have shapes,some are flexible ATP? RIGID FLEXIBLE WHAT IS THE SHAPE OF CYCLOHEXANE? BENZENE?
- 9. The perplexing ontology of holes(Typology according to Casati &Varzi) TUNNEL HOLLOW located in a wall part of the cheese CAVITY contained in the egg HOLE = nothing? HOLE = absence? HOLE = hole lining? HOLE = SHAPE? SHAPE OF HOLE = shape of ideal filler “inverse” to SHAPE OF HOST
- 10. Binding sites in proteins behave like holes Glycogen phosphorylase caffeine another ligand(jointly inhibitory)
- 11. The minimal lining for a hole in a protein must be subatomic Casati and Varzi: hole liningsdefined in terms of the surface of the host object -- the minimal part of the host object that is in contact with the external world -- the outermost part of the object … that we can “see and touch” Hole lining = thinnest outer layer of atoms? Hole lining = area whereelectron density of atomsis sufficiently low
- 12. Holes are granularity-dependent CAVITY MANY TUNNELS
- 13. Cavity of stomach: Organ cavity which is bound by the internal surface of the wall of stomach
- 14. Anatomical cavities serve a protective function CHANGE GRANULARITY SELECTIVEFILTERING
- 15. Conclusions Flexibility is a shape-related disposition – the disposition of an entity to change shape (without breaking) Explicitly taking granularity into account requires redefinition of the notion of hole lining as the disposition to resist intrusion by other objects (at the same level of granularity)
- 17. For more information: http://cindy.informatik.uni-bremen.de/cosy/events/shapes/
Hinweis der Redaktion
- The shapes of biological entitiesare intricately linked to their functions, and providing descriptions of shapesallows for predictions about their behaviour in various contexts, through theirinteractions with one another. In particular, during these interactions, objectsinterlock and fit together in a fashion similar to a three-dimensional jigsaw puzzle,with overall shape and the presence of holes of various sorts enabling diverseactivities. Traditional ontological analyses of part-whole relationships and of shapes andholes have largely been focused on the macro level at which human perceptionoperates { the level of buckets and lakes, tunnels and trains. In these cases, thereis a clear distinction between solid material objects and hollow spaces, and thecharacterization and delineation of shapes can appear rather straightforward.By contrast, accurate description of living systems requires accounting for theperspectives from multiple different granularity levels from the macroscopic rightdown to the molecular, to which we have limited perceptual access. Moreover, thedynamic nature of such systems means that the shapes of the entities involvedare subject to constant change in a way that the shapes of tunnels and bucketstypically are not.
- Carbon chemistry allows infinitely varied molecular backbones with specificsites of reactivity leading to diverse functionality. Water provides the substrate in which weak interactions betweenbiological molecules can unite to create stable but flexible three-dimensionalarrangements of these constituents into larger and larger composites. All of thisprovides the vehicle for the complex and localised processes that sustain lifeto take place.Living organisms are composed of an extremely wide diversityof parts, which are organised at increasing levels of granularity to form acomplex whole.
- Continuants exist through time; occurrents unfold over time. C -> participates -> O. c -> dependent vs. independentFollowing [8], we distinguish between continuants, which are entities that existthrough time, such as atoms, cells, and organisms, and occurrents, entitiesthat unfold over time, such as chemical reactions, digestions and births. Continuantsparticipate in occurrents, and through so doing, they may be changed.Continuants can be further distinguished between those that are independent andthose which are dependent, that is, they cannot exist without a bearer in whichthey inhere, just as colour cannot exist without something that it is the colourof. Dependent continuants can be further subdivided into qualities (categorialproperties) and realizable properties such as roles and functions [2]. Dispositionsare a special kind of realizable that inhere in their bearers by virtue of what willhappen if the bearer comes into the right circumstances [2]. One example of adisposition is the disposition of the stomach to participate in the digestion offood, another is the disposition of carbon atoms to form chemical bonds witheach other.We will consider shapes to be paradigmatic qualities, dependent on spatiallyextended objects. All of the biological objects illustrated in Figure 1 extend inthree-dimensional space and have shapes. But unlike the conventional objectsreferred to in typical analyses of shapes, biological objects in living systems are,by and large, in constant motion and interaction within their environments.Their shapes are capable of changing in response to the circumstances of theirenvironments. On one view, all this amounts to is that they simply adopt severaldierent shapes over time, the way several dierent shapes appear in a turningkaleidoscope. This is not incorrect, but it makes it dicult to express the rela-tionships between the dierent shapes which biological objects can adopt, northe constraints on such shapes (i.e. shapes which they cannot adopt).
- Molecules have shapes!Flexibility is not the same ontological kind as shape, since it relates differently to time
- Shapes are closely related to holes, another class of dependent entities. Holesexist in material objects precisely when those objects are shaped in a certainway. Holes themselves have shapes which are shared by their ideal fillers. Theshapes of the material objects in which holes are located are further related tothe shapes of the holes themselves in a negative, or figure-ground relationship[4]. There are different types of holes [5]: (superficial) hollows, (closed) cavitiesand (penetrating) tunnels. The philosophical interest in holes is driven by theapparent tension between their appearance in common sense ontology as bonade objects figuring in various relationships and functional roles in the worldbeing described (a hole in my boot is why my sock became wet from the snow),and their apparent emptiness or status as nothings (the hole is, by definition,precisely where the boot is not) [5]. Different theses have been defended, insome of which holes have been denied existence as entities altogether, and inothers they have been equated with the linings (minimal surfaces) or shapesof their hosts [5]. Following [5], we allow holes the ontological status of entitiesin their own rights, located at the surface of material objects (their hosts).Some consequences of this view are that holes are dependent on their hosts,in the sense that there is no hole without some host, but holes are not partof their hosts, although they may be contained in them (as is the case forcavities). This contrasts with the standard biological view of anatomical cavitiesas holes which are part of their anatomical hosts, for example, the cavities ofthe heart (ventricles, atriums) are considered to be part of the heart [7]. Butthis distinction can be seen as partly a matter of convention. An uncontroversialspatial relationship between host and hole might refer to location and externalconnection.
- The definition in terms of part of the host object precludes its interpretation as a boundary at a lower dimensionalityElectron density only tends towards zero, it never reaches it
- Helium balloons (rubber) allow helium out slowly. But the metal foil ones leak much more slowly.
- If it breaks, it has really become two objects rather than being one object changing shape.