Testing a servoanalytic hypothesis for pupil oscillations.

allata are also a link in the humoral cycle initiating ovarian development in mosquitoes. JOSEPH R. WSEN Division of Medical Entomology, Johns Hopkins University School of Hygiene and Public Health, Baltimore, Maryland References and Notes ously recorded. When intensity increases, the pupil contracts. The resultant effect of light falling on the retina can be re- solved into two factors : ( i) an increase due to increase in applied intensity and (ii) a decrease due to contraction of the pupil. System gain is here defined as the ratio of (ii) to (i). An open-loop trans- fer function I. T. Hosoi, Jap. ]. Med. Sci. & Biol. 7, Ill (1954); P. A. Woke, Am. ]. H-yg. 25, 372 D. W. Twohy and L. R. Rozeboom, ibid. 65, A. N. Clements, ]. Exptl. Biol. 33, 211 (1956). This work was supported in part by a grant from the National Institute or Allergy and In· rectfous Diseases, U.S. Department of Health, Education, and Welfare. V. B. Wigglesworth, The Physiology of Insecl Metamorpl1osis (Cambridge Univ. Press, New York, 1954). T. S. Detinova, Zoo!. Zhur. 24, 291 (1945). J. D. Gillette, Nature 180, 656 (1957). 19 November 1957 Testing a Servoanalytic Hypothesis for Pupil Oscillations Oscillations are a common and im- portant instance of the malfunctioning of a servomechanjsm. Oscillations are also a common pathoJogical al;mormality in a wide variety of neurological diseases and are manifested in such 'clinical signs as tremor, ataxia, clonus, and nystagmus. This report indicates how a biological system has been analyzed by linear servo- analytic methods and experimentally jus- tifies this approach by quantitatively verifying a prediction. The pupil response to light-an exam- ple of neurological servosystem- has been studied by means of servoanalytic concepts and techniques (I). A sinu- soidally varying intensity of light was ap- plied, and the pupil area was continu- l - 9:o PlfAse; o.:G,s SHIFT-- Fig. 1. Nyquist diagram of pupil response. This is a vector plot of gain and phase shift. The scale of the modulus is shown, and a few frequencies are indicated. The curve is derived from fitted Jines from gain and phase frequency-response graphs, while the points are experimental. G(s) =0.!6e-O.lSs/(1 +O.ls)s was computed from data graphically dis- played in Fig. 1. This, the Nyquist dia- gram, is a vector plot of the relationship between gain and phase shift at various frequencies. For example, at 1.2 cy/sec, the gain is 0.12, with a phase lag of 180°. This gain means that the pupil compen- sates for 12 percent of the change in ap- plied light intensity. If the gain were to be increased to 1.0 or more, the system would become un- stable, and the pupil would oscillate at its natural frequency-that is, the fre- quency at which the phase lag is 180°. From the figure we see that this fre- quency is 1.2 cy/sec. Thus, from our servoanalysis of the normal, low-gain, stable pupil system, we are led to predict that a large increase in gain would pro- duce sustained oscillations and that the frequency of these oscillations would be 1.2 cy/sec (72 cy/min) . A test of the validity of the servoanalytic method would be the production of pupil oscil- lations in this manner and at the pre- dicted frequency. Observations which comprise such a test are already avail- able for evaluation. Clinical studies have been reported in which sustained oscillations of the pupil have been produced and in which the frequency of the oscillations has been measured. Stern (2) pointed out that a series of oscillations of the pupil could be induced by imaging a small point of light just on the margin of the pupil. This causes the iris to contract, and all the light is cut off in the early phase of con- traction. The iris therefore redilates, and full light intensity again enters the eye. The gain is thus increased to more than 1.0, and sustained oscillations result. Campbell and Whiteside (3) made a careful study of parameters affecting this induced pupil oscillation, using quanti- tative techniques on a group of normal subjects. A third report is that of Wybar ( 4), who studied a large number of nor- mal subjects and also patients with mul- tiple sclerosis (5) . In Table l the fre- quencies of the sustained oscillation ob- served are summarized. There is good agreement between the frequency of pupil oscillations observed in normal subjects and our prediction. Further experiments have been carried out by Stark and Baker ( 6) in which the transfer function of the pupil system has Table 1. Observed frequencies of pupil oscillations (references in parentheses) . Mean frequency (cy/min) Group studied 10 Normal subjects (2) 1 Normal subject (3) 37 Normal subjects (3) 34 Normal subjects (4) Patients with multiple sclerosis: 70 pupils ( 4) Predicted value (I) been altered by drugs. For example, when the 180°-phase cross-over frequency was changed from 1.5 to 0.9 cy/sec, the high- gain oscillation frequency shifted in a parallel fashion from 1.5 to 1.0 cy/sec The qualitative value of the servo- analytic approach is demonstrated by the clarification introduced through explana- tion of the natu re of these pupil oscil- lations. The quantitative nature of the method is illustrated by the accuracy of the prediction ( 7) . LA WREN CE STARK ToM N. CoRNSWEET Departments of Neurology and Psychology, Yale University, New Haven, Connecticut References a nd Notes l. L. Stark and P. Sherman, ]. Neurophysiol. 2. H. J. Stern, Brit. ]. Oplithalmo/. 28, 275 3. F. W. Campbell and T. C. D. Whiteside, ibid. 4. K . C. Wybar, Proc. Roy. Soc. Med. 45, 315 5. It is interest.ing to note that osci llation of the pupil in the multiple sclerosis group differs from that in the normal groups in mean fre- quency. This difference must be a result or a change in system parameters produced by the neurological lesions. 6. L. Stark and F. Baker, unpublished. 7. We gratefully acknowledge discussions with Peter Schultheiss, Philip Sherman, Fergus Campbell, and Gilbert Glaser. This work is being supported by the National Multiple Sclerosis Society, the National Science Foun- dation, the National Institute of Neurological Diseases and Blindness, and the George Knight Fund. 4 November 1957 Preparation of an Apoprotein from Ceruloplasmin by Reversible Dissociation of Copper The blue copper-protein of plasma, ceruloplasmin, with a molecular weight of 151,000, contains eight atoms of cop· per per molecule (I). The physiologic significance of this protein, while not clear, has usually been implicitly asso- ciated with its oxidase activity (2-5) . On the other hand, the possibility that reversible binding and release of copper by the protein may be the basis of its SCIENCE, VOL. 127