Co-operativity and brain organization

80

TINS -April 1981

effect of occlusion on dyslexics' reading 2. The occlusion was usually aimed to shift dominance from one eye to the other, when preferred hand and eye were on opposite sides of the body. However, since the preferred eye is a highly unreliable indicator of ocular dominance; and since it is probable that unfixed, not crossed, dominance is the major problem from which visual dyslexics suffer, it is not surprising that these attempts were not very successful• The help with reading that occlusion gives to visual dyslexics lends further support to the hypothesis with which this article has been concerned, namely that

many dyslexic children fail to develop stable ocular dominance, and are not able to control their eye movements with sufficient precision, or to make the accurate associations between retinal and oculomotor signals relating to macular vision essential for correctly locating and sequencing letters and words when reading.

Reading list

I Benton. A. L. (1978) Dyslexia, Oxford University Press 2 Benton, C, D. and McCann, J. W. (1959) J. Padiatr. Ophthalmol. 6, 221)-227 3 Corbatlis, K. and Beale, I. L. (1976) Thepsychol- John Stein and S. Fowler are at the University l.aboraogy ofle~ and right, Laurence Erlbaum Assoc. tory o f Physiology, Oxford.

Co-operativity and brain organization Christoph yon der Malsburg and David Willshaw T h e c o n c e p t o f co-operativity, w h i c h is well k n o w n to the p h y s i c a l scientist, is n o w b e i n g a p p l i e d to p r o b l e m s in n e u r o b i o l o g y . To illustrate this the a u t h o r s d e s c r i b e their r e c e n t w o r k o n the d e v e l o p m e n t o f o r d e r e d n e r v e c o n n e c t i o n s b e t w e e n e y e a n d brain. Coo p e r a t i v i t y m a y well f i n d g e n e r a l applicability to the n e u r o s c i e n c e s .

In 1943 McCulloch and Pitts proved that any conceivable logical input--output function could be implemented by appropriately interconnecting simple model nerve cells (see Ref. 1). This result and the success of the new electronic computer inspired a great wave of enthusiasm, since it implied that the brain could ultimately be

tectum

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Fig. 1. The influence exerted on synapse (black square) by the others (in a one-dimensional retina and tectum). The presence o f other synapses within the shaded region increases its growth rate. Synapses within each horizontal hand, made by one retinal fibre or a small retinal region, compete with each other; likewise synapses within each vertical band, which are those contracting a given tectal cell or region. Interactions are optimally concatenated if synapses are arranged in a diagonal, i.e. in a retinotopic arrangement. The twodimensional case is analogotz~, but would need a fi~urdimensional dLsplay. ~ [ Nc~icr/North Holland Biomedical Prcs~ ] 4 N I

4 Dunlop, P. (1972) Aust. Orthoptic J. 12, 16-20 5 Noble, J.(1968) BrainRes. 10, 126-15l 60ber, M. (1980) Boswell's Clap and other essays, Universityof South 1111noisPress 7 Orlon, S. T. (1937)Reading, writing and speech problems in children Chapman and Hall, London 8 Pavlidis.G. T. (1978) Dyslexia Rev. I, 22 9 Porac, C. and Coren. S. (1976) P~ychol. Bull. 83, 880-897 10 Pona, I. B. (1593) De refractione J. (arlinus, Naples 11 Rourke, B. P. (1978) in Dyslexia (Benton, ed.), Oxford UniversityPress 12 Shatz. C. and Levay, S. (1979) Science 204, 328-350

understood as a complex network of logical switching devices. Although this approach has been fruitful in inspiring and shaping whole lines of research, the computer analogy has to date not brought about any significant breakthrough in brain theory. One striking difference between computer and brain is that the computer must carry out its instructions in sequence whereas much of the analysis in the brain appears to be undertaken by multiple systems operating in parallel. No efficient and universal selfprogramming scheme has yet been proposed for the conventional computer; it relies heavily on intimate communication between the machine and h u m a n programmer. The sequence of events in a computer is an extremely sensitive function of the structure both of the machine and of • the programme; if one connection is cut or one part of the programme changed the effect is usually a complete breakdown of useful action. There is, therefore, no natural and universal strategy of continuous improvements which could lead to a functional computer or programme. Only with the help of the programmer is it possible to create functional structures; the computer is in no way a self-contained entity. Conversely, the nervous system has evolved by stepwise improvement. Every

intermediate structure has had to be functional. The nervous system is re-created for each individual by the ontogenetic process of self-organization; it is self-programming, since it can learn; and its action is robust against all kinds of disturbance. The nervous system most likely contains, even in its basic mode of action, the principles necessary to guarantee these features, which in the computer could at best be the result of very special and complicated programmes.

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retina Fig. 2. The results of a computer simulation of the development of a projection between a one-dimensional retina and tectum, using the model outlined in Table IA. (A) Retinal markers. Four molecule types, with inhomogeneous but continuous distribution, the result of synthesis in isolated source locations, diffusion and decay• (13) Early distribution o f synapses. Each square represents the 'weight' of a synapse. The contacts made by each retinal fibre are represented by a row o f the matrix. Orientation information is imposed by suppression of synapses between retinal extremes and the 'wrong' end~ of the tectum. Smaller squares are synapses created by .sprouting from larger, initial. synapses. Filled squares correspond to growing .synapses. Note that gro wth starts at the ends of retina and rectum. ( C) Intermediate configuration. ( D ) Final configuration. (E) Tectal distribution o f markers in the final configuration. It is a dL~torted copy of the retinal markers. Details of the simulation are described in Ref 13. Here, a ten times smaller diffusion constant was used for the tectal marker~.

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The starting point for a new approach to brain theory is the observation that the non-biological world is full of complicated patterns which arise by self-organization. Basic examples, including crystal lattices and magnetic domains, have been intensively studied and are fairly well understood in physical terms• Central to the relevant theories is the notion of 'cooperativity'. Recently the analogy has been exploited in a n u m b e r of papers which discuss neurobiological p h e n o m e n a as cooperative ~. We will try to illustrate this approach by the discussion of an example which has been well studied both theoretically and experimentally 4.

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retinotopy

problem

In the course of vertebrate ontogenesis, the ganglion cells of the retina send axons through the eye stalk to the brain, where they establish connections with cells of central structures, such as the optic tectum. In the adult animal the retino-tectal connections are arranged 'retinotopically', i.e. the fibres from neighbouring retinal cells project on to neighbouring points in the tectum. Experimental manipulations performed on animals of various species have shown that there is enormous plasticity in the system'. For instance, if the eye is rotated prior to the establishment of the projection, the course of fibres is altered so that they still project to the appropriate regions of the tectum. In other experiments where the retina or the tectum is reduced surgically, the regenerating fibre projection is expanded or compressed to form an ordered projection extending across the whole of the rectum. From these experiments two simple rules can be abstracted to describe the final outcome of the process of fibre growth from retina to tectum: (i) match the perimeter of the retinal piece of tissue on to that of the tectal piece of tissue in a predetermined orientation (which in normal cases is genetically programmed); (ii) fill the interior of this frame with a continuous projection (that is, neighbouring retinal cells project to neighbouring tectal cells). The situation is complicated by the facts that new boundaries can be created in retina or tectum and that one piece of tissue may take part in more than one projection. These facts are exploited in the 'compound-eye' experiments*, in which pieces of different eyes are joined in one eye socket, and in 'graft manipulation' experiments 4, in which either a square graft is cut out of the tectum and rotated in its plane or two grafts are interchanged.

~2 A l t h o u g h t h e r e is little direct i n f o r m a tion available o n the n a t u r e o f the cellular m e c h a n i s m s involved in the f o r m a t i o n of p r o j e c t i o n s , the i n f o r m a t i o n we h a v e conc e r n i n g retino-tectal p r o j e c t i o n s , a c c u m u htted t h r o u g h e x p e r i m e n t s s u c h as those o u t l i n e d a b o v e , severely restricts the n u m b e r of possibilities.

A method for the establishment of ordered connections We n o w d e s c r i b e a g e n e r a l m e c h a n i s m for the f o r m a t i o n of t o p o g r a p h i c p r o j e c tions. S o m e o f the finer details will h a v e to be d e t e r m i n e d by f u t u r e e x p e r i m e n t s a n d these m a y also d e p e n d o n the p a r t i c u l a r species o r e v e n o n the special situation at hand. T h e m o d e l p r o p o s e d o p e r a t e s at t w o levels: a local o n e a n d a g l o b a l o n e . T h e local m e c h a n i s m is o f m o r e g e n e r a l interest a n d will be d e s c r i b e d first, it deals with the ability of fibres to f o r m a c o n t i n u o u s p r o j e c t i o n ( o r pieces o f a c o n t i n u o u s p r o j e c lion), i n d e p e n d e n t l y o f position, scale a n d orientation of that projectiom

A. Local mechanism. S u p p o s e fibres f r o m the retina h a v e a l r e a d y g r o w n to the tectum and have established synapses there (in a h a p h a z a r d f a s h i o n ) . T h e d e v e l o p m e n t of the r e t i n o - t e c t a l p r o j e c t i o n is t h e n d e t e r m i n e d by the f o l l o w i n g rules w h i c h g o v e r n the d e v e l o p m e n t o f the individual s y n a p s e s , e a c h o f w h i c h has a 'weight" ( w h i c h m a y s t a n d h~r size, o r f u n c t i o n a l effectiveness): ( i ) A retinal fibre c a n f o r m n e w s y n a p s e s in the t e c t u m in the n e i g h b o u r h o o d o f its existing s y n a p s e s . S y n a p s e s are b r o k e n if t h e y h a v e fallen b e l o w a l o w e r t h r e s h o l d w e i g h t o r are u n s u c c e s s f u l a c c o r d i n g to s o m e o t h e r c r i t e r i o n . (2) A s y n a p s e is a l l o w e d to g r o w in p r o p o r t i o n to the total w e i g h t o f the s y n a p s e s n e a r b y w h i c h a r e f r o m fibres o f similar retinal origin to its o w n fibre. T h e ability o f fibres to r e c o g n i z e e a c h o t h e r ' s retinal origin r e q u i r e s a n a p p r o p r i a t e c o d e o n the retinal fibres, f o r w h i c h t w o possibilities are d e s c r i b e d in T a b l e I. (3) T h e total g r o w t h o f the s y n a p s e s m a d e by o n e retinal cell ( o r small retinal r e g i o n ) is limited. C o n s e q u e n t l y the g r o w t h o f s o m e s y n a p s e s m u s t be c o m p e n s a t e d by the d e c r e a s e in w e i g h t o f less successful o n e s . A similar g r o w t h limitation operates on those synapses which contact the s a m e tectal cell ( o r small tectal r e g i o n ) . T h e effects o f t h e s e s y n a p t i c i n t e r a c t i o n s c a n be s h o w n m o s t easily in a simple m o d e l with a o n e - d i m e n s i o n a l c h a i n o f cells for b o t h r e t i n a a n d t e c t u m (Fig. 1). T h e

FINS -April 1981 ['ABI [~ I Iwo detailed mod¢ln tor the problem
B. Model from Reference 12

Retinal ct~dc (?ells and fibres carry a set of different molecule types (markers). Concentrations of molecules ~ary continuously from cell to cell ,aithin the retina. The retinal markers therefore encode distance~ ~ ithin the retina.

Retinal code Spontaneous spike activity of retinal cell, lhc probability of two cells firing together decreases with the distance between them,

Mechanism Different molecule types are synthesized at different source loci within the retina. Molecules diffuse within the retina and decay to ftmn stationary distributions,

Mechanism Short range excitatory connections and long range inhibitory connections.

Communication between s~napses Marker substances are carried by axonal transport to the lecture and are transported between tectal cells or diffuse freely within the tectal medium.

C o m m u n i c a t i o n between synapses Through tectal cells, which are excited by retino-tectal synapses and which exchange excitation and inhibition in a fashion similar to the retinal cells.

Properties of code (a) The distribution of the source loci (and consequently the marker distributions) are presumably genetically controlled Two retinae may carry identical marker sets (so that prolcctions from two retinae to one target structure can constructively interact). (b) After severance of the optic nerve a "memory' of the previous projection is preserved on the tectum.

Properties of code After severance of the optic nerve no record of the previous projection survives on the tectum.

Growth limitations (a) Convergent: a tectal neighbourhood is made less favourable for a given retinal fibre by the introduction of other markers from othe r fibres from more distant parts of the retina ('interference'). (b) Divergent: The total weights of the synapses made by each retinal fibre is kept constant ('sum rule').

Growth limitations (a) Convergent: total weight of the synapses converging on each tectal cell is kept constant. (b) Divergent: due to long range inhibition within the tectum the synapses from one small retinal region cannot impress their (synchronized) activity on more than one distinct tectal region simultaneously.

Orientation imposed by . . Nucleation from tectal boundary. Mechanism of establishment of initial conditions unspecified,

Orientation imposed b y . . . Nucleation from central zone. Mechanism of establishment of initial conditions unspecified.

A third, later modcP, to date only formulated in outline, is very similar to (B). The distinguishing features of this model are that fibres corn municate by contact, and orientation is imposed on the system with the help of a second set of tectal markers, which match those in the retina but are kept separate from them. 'Orientation information' is therefbre continuously available and amounts to precise position information. Information regarding an earlier projection is retained in the form of debris of retinal fibre terminals on the tectal surface.

s y n a p s e s are d i s p l a y e d as a matrix w h o s e r o w s c o r r e s p o n d to retinal cells o r fibres a n d the c o l u m n s c o r r e s p o n d to tectal cells. Fibres f r o m d i f f e r e n t small retinal reg i o n s will c o - o p e r a t e m a x i m a l l y with e a c h o t h e r if all t h e i r s y n a p s e s a r e c o n c e n t r a t e d in o n e o f the t w o d i a g o n a l s o f the m a t r i x , i.e. in a r e t i n o t o p i c p r o j e c t i o n , T h e s y s t e m t h e r e f o r e , h a s the t e n d e n c y to d e v e l o p f r o m m o s t initial states into a series o f r e t i n o t o p i c p a r t - p r o j e c t i o n s , L i n i n g u p the p a r t - p r o j e c t i o n s in a c o n s i s t e n t f a s h i o n is o n e o f the f u n c t i o n s o f the g l o b a l m e c h a n ism. (In the case o f a t w o - d i m e n s i o n a l r e t i n a a n d t e e t u m , t h e r e are, o f c o u r s e , m o r e t h a n t w o possible o r i e n t a t i o n s . ) B. Global mechanism. T h e g e n e r a l b o u n d a r y c o n d i t i o n s are: (1) t h a t retinal fibres m u s t be g u i d e d to the tectal s u r f a c e in the first p l a c e a n d m u s t be r e s t r a i n e d to within the c o r r e c t b o u n d a r i e s ; a n d (2) t h a t the o r i e n t a t i o n o f the p r o j e c t i o n within

t h o s e b o u n d a r i e s m u s t be specified. T h i s c a n be d o n e b y a p o s i t i o n i n g m e c h a n i s m w h i c h a c t s o n e a c h fibre s e p a r a t e l y . M a n y o r i e n t a t i o n m e c h a n i s m s c a n be i m a g i n e d . It is possible t h a t d i f f e r e n t m e c h a n i s m s act in d i f f e r e n t species, o r u n d e r d i f f e r e n t c o n ditions ( d e v e l o p m e n t o r r e g e n e r a t i o n ) in the s a m e species. T h e o r i e n t a t i o n m e c h a n ism m i g h t a c t o n l y initially. O n l y e x t r e m e l y w e a k i n f l u e n c e s a r e n e e d e d to g u i d e the local i n t e r a c t i o n s to f o r m a p r o j e c t i o n in the d e s i r e d o r i e n t a t i o n . E v e n if the o r i e n t a tion m e c h a n i s m w e r e very precise, it c o u l d n e v e r s u p p l a n t the local m e c h a n i s m o f f i b r e - f i b r e i n t e r a c t i o n s as it is t o o rigid. If the p r o c e s s o f o r g a n i z a t i o n starts o u t in o n e r e s t r i c t e d r e g i o n o n the t e c t u m , t h e n the o r i e n t a t i o n d e c i d e d u p o n in the first piece o f p r o j e c t i o n i m p o s e s itself o n the rest o f the d e v e l o p i n g m a p . In a n a l o g y to crystallization s t a r t i n g f r o m a seed, this s e q u e n c e o f e v e n t s m a y be c a l l e d n u c l e a -

83

T I N S - A p r i l 1981

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even though each element can choose among a n u m b e r of states. However, spatial continuity is not the central concept for co-operative systems. For instance, in animals with binocular vision there are projections from the two eyes which overlap in one central structure. In the mammalian cortex, for example, fibres from the two eyes segregate in layer IV to produce domains in the form of patches or stripes. Yet although the striking feature of ocularity domains is geometrical discontinuity, a co-operative theory for their ontogenesis can still be formulated 1°'tl. A n o t h e r example is the representation of orientation in the visual cortex. Here general retinotopic continuity is upset at the level of neighbouring cells in order to accommodate a continuous representation of orientation. A co-operative theory for the ontogeny of this structure has again been presented 9, showing that simple geometric continuity can be transcended.

Illi

tion. Graft manipulation experiments suggest that at the time of regeneration tectal cells accept contacts from only certain retinal cells. This could be the result of a 'memory' of the previous projection 7, or could be an expression of precise orientation information. The results of computer simulations of one of the models described in Table I are shown in Fig. 2.

Further examples of co-operation in the brain The aim of this discussion on the problem of retinotopy was to provide a concrete neurobiological example of a co-operative system. There have been other applications of the co-operative idea to the nervous system 2, both to problems of ontogeny and of function. Julesz has proposed a cooperative model which accounts for the stereoscopic interpretation of binocular images in the visual system6, i.e. the way in which particular visual features seen by one eye are identified with their counterpart in the other eye. The model was expressed by Julesz in terms of a physical analogy involving springs and magnets. A related problem is that of visual flow where points in a visual image seen at consecutive m o m e n t s in time must be related to one another ~. A c o m m o n feature of these applications is the problem of establishing point-topoint connections between two (twodimensional) patterned structures (retina and rectum, left-eye and right-eye image, two consecutive images, etc.). What makes these examples prototypes of co-operative systems is that in each case 19cal interactions give rise to overall spatial continuity

Co-operative organization

Co-operativity in this context is therefore the ability of a system of elements to form such globally ordered states. In computer terminology, the programme resides in the structure of the local interactions; the result of the computation being the globally ordered state, which is arrived at by a parallel computation, and which is resistant to small alterations. The programming of a co-operative system can be carried out in two ways. One corresponds to genetic programming: the a priori build-in of the local interactions. The other acts in the reverse direction: if, by some external means, a global state is projected onto the system, local interactions can adapt so as to be consistent with that global state. We started out with a criticism of the computer as a model for the brain. The features that it lacks were found to be parallel action of a multiplicity of elements, inherent stability of action, and selfprogrammability. These are the basic features of co-operative systems. However, the great asset of the computer, its universality, is not inherent to co-operative systems. It remains to be determined how much of this desirable property can be obtained with the help of properly designed co-operative systems.

Applications of co-operative effects which completely leave the context of geometry are known in the field of artifical intelligence under the name of 'relaxation method '5. The gist of this idea is that there is a large set of physical entities, 'elements' (analogous to neurons or synapses). These elements have inner variables (e.g. excitn- Reading list 1 Arbib, M. A. (1964) Brain, Machines and tory states of neurons), which vary continuMathematics, McGraw-Hill,New York ously in time. The constellation of 'states' 2 Arbib, M. A. (1981) in Self-organizing Systems, (the values assigned to each of the variables The Emergence of Order (Yates, F.E., ed.), possessed by an element), can be interPlenum Press, New York and London preted as the representation of some situa3 Fraser, S. E. and Hunt, R. K. (1980) Annu. Rev. Neurosci. 3, 319-352; Fraser, S. E. (1980) Dev. tion, e.g. a perceived scene. The elements Biol. 79,453--464 interact by exchanging signals. Each ele4 Gaze, R. M. (1978) in Specificity of Erabryologi. ment has a 'neighbourhood' which consists cal Interactions (Garrod, D.. ed.). Chapman and of that set of other elements with which it Hall, London can communicate. (Here, neighbourhood 5 Hinton, G. E. (1977) Relaxation andits Role in Vision, Ph.D. thesis, Cognitive Studies Program, has to do with connectivity, not necessarily Universityof Edinburgh with physical proximity.) The state of an 6 Julesz, B. (1971) Foundation of Cyclopean Perelement makes sense only in the context of ception, Universityof ChicagoPress a certain constellation of states in its neigh7 Schmidt. J.T. (1978) J. Comp. Neurol. 177, 279-299 bourhood. This mismatch between the 8 Ullman,S. (1979) Interpretation of Visual Motion, element's state and those in its neighbourMIT Press.Cambridge. Mass.,U.S.A. hood leads to changes in its state so as to 9 von der Malsburg, C. (1973) Kybernetik, 14. reduce the mismatch. These in turn entail 85-100 changes of state in the neighbourhood. The 10 yon der Malsburg,C. (1979) BioL Cybernetics, 32. 49-62 system eventually comes to rest, but only when a globally ordered state has been 11 yon der Malsburg,C. and Willshaw,D. J. (1977) Proc. Natl. Acad. Sci. U.S.A. 74, 5176-5178 installed in which the inner state of each 12 Willshaw,D. J. and yon der Malsburg,C, (1976) element and the constellation of states in its Proc. R. Soc. London, Ser. B, 194,431~,45 neighbourhood are consistent with each 13 Willshaw,D. J. and yon der Malsburg,C. (1979) other in terms of their interactions. There Philos. Trans. R. Soc. London, Ser, B, 287, 203-243 can be a rich multiplicity of globally ordered states satisfying this local consis- Christoph yon der Malsburg is a Staff ,Member of the tency condition. In the retinotopy problem Max Planck Institut fi~r Biophysikali~che Chemie, GOtthese are the ordered projections with dif- tingen, F.R.G., and David Will,haw is a Staff Member of the National Institute for Medical Research, Mill ferent position, scale and orientation. Hill, London, U.K.