Contains reports on four research projects

Lettvin, Jerome Y.

Maturana, Humberto R.

McCulloch, Warren S.

Wall, P. D.

DSpace@MIT

Neurophysiology

Contains reports on two research projects.Bell Telephone Laboratories, IncorporatedNational Institutes of HealthTeagle Foundation, Incorporate

Pitts, Walter H.

XVI. NEUROPHYSIOLOGYW. S. McCulloch R. C. Gesteland W. H. PittsJ. R. Cronly-Dillon A. R. Johnson A. TaubE. M. Duchane J. Y. Lettvin P. D. WallH. R. MaturanaA. INFALLIBLE NETS OF FALLIBLE FORMAL NEURONSAt the time of the Quarterly Progress Report of April 15, 1958, I thought that nocircuit could preserve error-free action if it were composed of 3 neurons, eachreceiving only 2 inputs. To correct this, let me replace the jot in any Venn symbol (1)by 1 if the jot is always present, by 0 if it is always absent, and by p if it is presentwith a probability p due to a shift of the threshold 0 of the neuron that it represents.Thus 1 p represents a neuron that always fires when A alone occurs or both A andB occur, and fires with a probability p when B alone or neither A nor B occurs.For error-free operation, some spaces in the Venn symbols must have 0 or 1. I placeeach symbol inside the idiogram of its neuron and draw Fig. XVI-1, in which each ofthe neurons of the first rank receives signals from A and from B, and both play on theoutput neuron at the bottom.For nets of neurons of 2 inputs, that is, with 6 = 2, zero error can be achieved onlyfor tautology and contradiction with some p in every chi (X), that is, by keeping thefixed jots or blanks in such positions that, when added, they form tautology or contra-diction. But, since the complement of tautology is contradiction and the complement ofcontradiction is tautology, these lead only to themselves and to no significant functionsof their primitive propositions.This limitation disappears with 6 = 3. For instance, consider the net of Fig. XVI-2afor nondegenerate neurons, with 6 = 3, and their Venn symbols showing the successionof jots with decrease of 8 (Fig. XVI-2b). Let J = 2 mod 6, and let L be the numberof jots that may be added harmlessly to the Venn symbol that can stand fewest additionsof any Venn symbol in its rank; write the desired function of J or fewer jots as 1's inmore than half of the Vj, write a 1 in the corresponding space of V k , and write p inall of its other spaces for the intersections of more than half of its arguments(see Fig. XVI-3). There are 2 6 - 1 of these spaces, one of which contains the 1. There-S6-1) _fore the number of p's in V k , call it k' is 26 - 1. In Every Vj there remain 2 -empty spaces in which p's may be placed if they do not occur in the same space in morethan (6-1) of the V.. This permits them harmlessly in (2 - J) (6-1) 1] spaces2 ( 2of each V.. Now, for 6 odd, J is even, and it is 2 if 6 is prime. Harmless p's areJThis work was supported in part by Bell Telephone Laboratories, Incorporated;National Institutes of Health; and Teagle Foundation, Incorporated.189AIO A100A B5<9 7P0 po P 000Sp 4 <5<7(a)3 2 5v.S 4 7 6 4 7 68 8 8j= j=io j=10oo3V k  7 48Vr  0 00(b)Fig. XVI-1. Fig. XVI-2.190(XVI. NEUROPHYSIOLOGY)most numerous when J is smallest. Hence the maximum6 -1 1 -1 1S= (2 -  2)(5 1) (6- 1) = ( - 1) (6-1) 6-* 6Writing Y for 2 w max' e have* -6 6-1 1 1-6k 2 (2 - 1)= (1-2 )and* -6 - 6-1 1 1-) -)S= 2 6 - (2 - 1) (6-1) = - 1- ( - 68-1Hence,* * 1Lim k Limj6-oo 6-ooThe binomial coefficient for the central term when 6 is even has toted either to the Vj or to Vk , and its effectsA10diminish comparatively slowly,A1000Vj I p0VkI I0PIO P P00p0 lk=30010 0OOi 0Fig. XVI-3.191be allot-(XVI. NEUROPHYSIOLOGY)without affecting the limits.Functions of J or fewer O's can be constructed similarly; but any additional 1 or0 decreases . by 1, reaching a maximum loss of 2( 2 - J) in the V., thus effectivelyj Jhalving .. When not all J are used for l's or O's, this space can be occupied by p inJ ,only some of the Vj, and so I.j is not increased.For nets with two ranks of neurons (Vj and Vh), and one third-rank or output neuron(Vk), 4j and h increase to equal L4k for all neurons, and almost all may have one addi-tional p harmlessly, as in Fig. XVI-4, where 4 = 3 in V and in Vh=  and in Vk.j 100 h=10 kWe compute the number of nondegenerate infallible nets of two ranks thus: Foreach V. there are . !6- which meet the requirements, and for Vk there areJ 16-1 kk (4+k ' ! The number of nondegenerate nets isk ! j 6-1 , 6-16-1 26+2and, for large 6, it is nearly (2 !)2 , which is a large number but, divided by thenumber of all nets, is the negligible fraction(26-1 2(6 + 1 )(26!)6+ 1If nets with more jots than J were equally numerous, and they are not, this fractionwould not be multiplied by more than (22 - 4, which still leaves it negligible. Chanceis unlikely to produce such nets or to discover them among nets supposed to be equi-probable.No comparable measures of the number or fraction of diagrams that are degenerate,either because (a) they do not change the fraction computed with every step of 0 orbecause (b) they change the symbol by two or more jots per step in 0, can be similarlycomputed. What misled me before was that I had examined only output neuronal dia-grams in which 6 < 3 and in which there was no inhibition of afferents by afferents butonly a direct action on the recipient neuron, and that, among these, only degeneratediagrams give k.' Clearly, the degeneracy of the second kind is greatest when allafferents have equal signal strength; and the degeneracy of the first kind is greatestwhen the strength of the afferents goes up maximally between none and the least one,and so on. The first kind is therefore minimized by using the smallest whole numberspossible, and the second by having them as unequal as possible.Since, in Vk the spaces for 1 arguments must be filled before any spaces forfewer arguments are filled, inputs each equal to one would produce the desired resultwith no degeneracy of the first kind but with maximum degeneracy of the second kind.192Al0Vj p p p0Vh p p OpVkAI 001p p p p00IO p p pOOpOp P0AIop10 00pA Opp0PO0Vr 0 0 0Fig. XVI-4.193(XVI. NEUROPHYSIOLOGY)To minimize degeneracy of the second kind, we define the least as x + 1 and supposethat the values differ from each other by 1 step in 0. Then16+ (6+1) 62x + 2 (integers) > 6- x + (integers)1 1-(6+1)+1andF+ \+ 1 6+1 6+1 6-3S> (6+1) - + 1)] which is 6-2 2 2 2 2Hence the least term is 1 + 2 = 2 + 1, and the greatest is 2; butthis, which yields k,' is as far from equal strengths as possible. The allowable changein threshold is decreased only by a factor 62 .For example: if Vk has 7 inputs, each with a value of +13, its output is error-freefor 39 < 0 < 91, which is reduced by letting the inputs range from +10 to +16 to45 < 0 < 91. Thus the remaining usable range of 0, A G, exceeds , while k 2 )Note that if we are willing to forego the possibility of a jot appearing in the positionfor none in Vk, thus reducing k to -6 the value of A 0 is 66. 6 per cent for equalafferents and 56 per cent for afferents ranging from +10 to +16.Since the measured variation, Ae, of real neurons is ±5 per cent, we look next atthe permissible independent variation of the strength of afferent signals to Vk whenthese strengths were intended to be equal. Clearly, any selection of 1signals has amaximum sum less than the minimum sum for 5 signals. Let t be the intended strengthof a signal and At its variation. Then12( )6I (t + At) < (t - At)0 0HenceAt 6+ 1 1 4t 36- 1 3 36 - 1which always exceeds 1/3. For example, for 6 = 3, with the intended strength t equalto 2, we have 1 < (t ± At) < 3. To retain AG of ±5 per cent of its intended value reducesthese limits to 1. 05 < (t ± At) < 2. 85, or I At = 0. 425.t[When a variation of this size is experimentally produced in the afferent terminationin the spinal cord of the cat, it alters the circuit action. Even posttetanic potentiationand convulsive doses of strychnine alter the voltage of signals by less than 10 per cent.]If we hold AO to a minimum and the signals to their intended strength, we may194Vk4<8564624 4 22SIGNAL STRENGTHSAO= + 16.6%INTENDED VARIANTI2 74 -ISIGNAL STRENGTHSA8= + 6.25%00Vr 1 001OV,0Fig. XVI-5.195(XVI. NEUROPHYSIOLOGY)permit variation, As, in the connections, or synapsis, s, to obtain a similar limit.As 1 ( 4s 3 36 -But it is more reasonable to suppose that, on real neurons, the sum of the afferents,6 IAs 6 +1S(s ± As) = 6s; whence A - whose limit as 6 approaches oo is unity. For 6 = 3,1 s 6-1to the nearest integer, s ± As = 2 ± 3 (see Vk of Fig. XVI-5). Note that the range of 0of the permissible variant is from -1 to +7, and that 5 < 0 <6, or A0 = ±6. 25 per cent.From the preceding paragraphs it is clear that the number of p's that mayappear in any Venn symbol for a given change in 0 is fixed only for nondegeneratediagrams, and that, for degenerate diagrams, the fractional change in the jots isgenerally less than the fractional change in 0. Thus the actual reliability tends toexceed expectation as the specifications of strengths of signals or of coupling(i. e., synapsis) are randomly perturbed. But it would be a work of supererogationto inquire into this in general, for the nature of real or of artificial neurons andthe statistical specifications of their connections necessarily determine the weightto be allotted to each factor.If an educated guess as to real neurons and their nets is now permissible, it musttake the general form of a AO of ±5 per cent and a At of ±10 per cent, which leaves As,for 6 >3, less than ±100 per cent for synapsis for neurons of the second or higher rank.This presupposes that neurons of the first rank are relatively closely specified insynapsis in order to segregate possible errors. This is in harmony with muchthat is known of the auditory system, wherein pitch, loudness, and direction areinitially decoded and thence transmitted over separate channels or in dissimilarcodes. It begins to look as though the same were true of vision, of proprioception,and of the stages of afferents from the skin following detection and amplification.Thus by the time information from any source reaches our great central computerswe are in a region wherein crude specifications of statistical kinds should insureerror-free calculation despite gross perturbation of threshold, of excitation, and evenof local synapsis. This conclusion follows from two assumptions: first, that we aredealing with a parallel computer of more than two afferents per neuron; and second,that the functions which their neurons compute are sufficiently dissimilar to insure, atat least one level, incompatibility of error in the functions computed. All else may besafely left in large measure to chance.W. S. McCullochReferences1. J. Venn, On the diagrammatic and mechanical representation of propositions andreasonings, Phil. Mag. 10, 1-18 (July 1880).196(XVI. NEUROPHYSIOLOGY)B. PHYSIOLOGICAL EVIDENCE THAT CUT OPTIC NERVE FIBERS IN A FROGREGENERATE TO THEIR PROPER PLACES IN THE TECTUMSperry (1) pointed out that the results of his experiments on optic nerve regenera-tion in adult frogs were consistent with specific reconnection of the optic fibers. Heproposed that each individual neuron grew back to its original terminus in the tectum,for the behavior after visual recovery was as if the nerve had not been cut. In additionto the behavioral evidence, he produced scotomata in predicted quadrants by fairlylarge tectal lesions in frogs that had regrown their optic connections. The implicationsof his proposal are so odd that, while his elegant experiments were accepted, the inter-pretation was much disputed. Furthermore, the experiments with tectal lesions cannotbe considered conclusive, since, by destroying part of the tectum, the ability of theanimal to respond is also impaired. The purpose of this note is to give electrophysio-logical evidence for Sperry's hypothesis.We have developed a technique for recording single fibers in the frog's optic nerveand single terminal bushes in the tectum (2). In this work we have found that normallythe frog's tectum has the following organization. The fibers of each optic nerve crosscompletely in the optic chiasma and enter the opposite colliculus after dividing into twobundles. One is rostromedial; the other, caudolateral. They sweep over the surfaceand are distributed in several layers in the outer neuropil that forms the superficialhalf (250i) of the tectal cortex (Fig. XVI-6). Most tectal' cell bodies lie below thisneuropil and send their main dendrites through it up to the pial surface. The axons ofCBL STNMOB.. * e0.00 .00PS0 0 , LOBFig. XVI-6. Transverse section of the tectum of the frog at the level of theoculomotor nerves.CBL: cell-body layers PS: palisade stratumMOB: medial optic bundle LOB: lateral optic bundleSTN: superficial tectal neuropil HYP: hypophysis197(XVI. NEUROPHYSIOLOGY)the majority of these cells form a narrow stratum that lies immediately above the com-pact layers of the cell bodies. The optic fibers end in a systematic way both along thesurface and in the depths of the superficial neuropil, mapping the retina in a pattern thatis constant from animal to animal. There are three layers of these optic fiber terminalswhich we have thus far identified only physiologically. Each displays a continuous mapof the retina with respect to each of the three following operations on the image at thereceptors. The three maps are in registration with each other and show position on theretina according to the cartography of Gaze (3).In the uppermost layer lie the endings of two sorts of fibers which subdivide intotwo poorly defined strata. One stratum is composed of those elements each of whichis sensitive to moving or maintained contrast within its receptive field. The sharperthe contrast, the better is the response. These are equivalent to Hartline's (4) andBarlow's (5) "on" fibers. The other stratum is made up of terminals of units each ofwhich detects a moving or recently stopped boundary within its receptive field, pro-vided there is a net positive curvature of the edge of the darker phase. Such a fiberwill not respond, for example, to a straight-edge boundary moving across its receptivefield or to a preestablished edge within that field. Both of these strata represent theendings of the unmyelinated fibers of the optic nerve.The second layer is made up of terminal bushes from "on-off" fibers.The third layer is composed of endings from "off" fibers.The layers of endings are distinct in depth, rarely merging even at the transitionzones. In this conspicuous order, both along the surface and in the depths, the areaof the retina "seen" from any point in the superficial neuropil is at most 100 in radius.Most of the ganglion cells whose terminals appear at that point are crowded toward themiddle of that area.For the purpose of testing Sperry's hypothesis of the specific regrowth of the opticfibers after section of the optic nerve, we cut one optic nerve in several adult frogs(R. pipiens), ensuring the complete separation of the two stumps. At the end of twomonths the first signs of visual recovery were apparent, but full use of the eye did notoccur for another month. When the visual recovery seemed complete, we exposed thecolliculi and tested the initially deafferented one for mapping of the retina. We foundthat the map had been regenerated along the surface, although the ganglion cells fromwhose terminals we were recording at any point were now spread over an area abouttwo times as large as normal. The separation of operations in depth was also restored,and there was no sign of confusion between the operational layers.The specific regrowth of the terminals to their proper stations cannot be explainedby saying that an initial orderly array of fibers in the optic nerve crudely orders thefibers again at the time of regeneration. The fibers in the nerve simply are notin order ab initio. Any two contiguous fibers can come from as diverse points198(XVI. NEUROPHYSIOLOGY)on the retina as possible (2, 6).This finding strongly supports Sperry's hypothesis that optic nerve fibers grow backto their original destinations. They do so in an even more highly specific way than heproposed; the regrowth of the termini is also proper in depth.[After the preparation of this manuscript we noticed that R. M. Gaze, Universityof Edinburgh, has presented to the Physiological Society (J. Physiol. 146, 40P, 1959)similar findings in Xenopus laevis. He, however, has not studied the reconstitution ofthe distribution in depth of the optic fibers.]H. R. Maturana, J. Y. Lettvin,W. S. McCulloch, W. H. PittsReferences1. R. W. Sperry, Mechanisms of Neural Maturation, Handbook of ExperimentalPsychology, S. S. Stevens, ed. (John Wiley and Sons, Inc., New York, 1951), pp. 236-280.2. J. Y. Lettvin and H. R. Maturana, Frog Vision, Quarterly Progress ReportNo. 53, Research Laboratory of Electronics, M.I.T., Cambridge, Mass., April 15,1959, pp. 191-197.3. R. M. Gaze, Quart. J. Exptl. Physiol. 43, 209-214 (1958).4. H. K. Hartline, J. Gen. Physiol. 130, 690-699 (1940).5. H. B. Barlow, J. Physiol. 119, 69-87 (1953).6. H. R. Maturana, The Fine Structure of the Optic Nerve and Tectum of Anurans.An Electron Microscope Study, Ph.D. Thesis, Department of Biology, Harvard Univer-sity, Cambridge, Mass., 1958.199

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