GEOTROPIC CREEPING OF YOUNG RATS

The rate of upward creeping in negatively geotropic rats aged 13 to 14 days is a function of the gravitational stimulus. The rate of upward movement on the creeping plane, like the angle of orientation, is directly proportional to the logarithm of the gravity component. The variability in the speed of creeping decreases in proportion to the logarithm of the gravitational effect. When weights are attached to the animals'' tails the rate of upward creeping varies almost directly as the logarithm of the attached weight, and the speed of creeping is still proportional to the angle of upward orientation.     

ON THE GEOTROPIC ORIENTATION OF HELIX

The snail Helix nemoralis in negatively geotropic creeping orients upward upon an inclined surface until the angle of the path of progression (θ) is related to the tilt of the surface (α) as (Δ sin θ) (Δ sin α) = – const.; θ is very nearly a rectilinear function of log sin α. The precision of orientation (P.E._θ) declines in proportion to increasing sin α, P.E._θ/^θ in proportion to θ. These facts are comprehensible only in terms of the view that the limitation of orientation is controlled by the sensorial equivalence of impressed tensions in the anterior musculature.     

THE GEOTROPIC RESPONSE IN ASTERINA

Upon a surface inclined at angle α Asterina gibbosa orients upward during negatively geotropic creeping until the average angle (θ) of the path is such that Δ sin θ/Δ sin α = const. This is true also in positively geotropic movement. The direction of orientation may be temporarily reversed by mechanical disturbance. The variation of θ is greater at low slopes. Tests with directed impressed pulls, due to an attached cork float, show that the pull upon the tube feet is of primary consequence for the determination of θ. When the component of gravitational pull in the direction of movement reaches a fraction of the total pull which is proportional to the gravitational vector parallel to the surface, the laterally acting component is ineffective. On this basis, it follows that Δ sin θ/Δ sin α = const.     

GEOTROPIC ORIENTATION IN ARTHROPODS : III. THE FIDDLER CRAB UCA.

On an inclined surface the fiddler crab Uca pugnax, during sidewise progression, orients upward through an angle θ on the surface. The extent of negatively geotropic orientation (θ) is a rectilinear function of sin α, where α is the inclination of the surface to the horizontal. This equation differs from that describing the geotropic orientation of various other animals. The difference is traced to the fact that from an initial position with the transverse axis of the body horizontal the crab is required to turn upward to an extent such that the vertical line from its center of gravity pierces the inclined surface within the base of support provided by the legs. This leads to the equation sec θ/tan α = const., which is obeyed within the limits of precision of the measurements. This type of control of geotropic orientation represents an extension of the "muscle tension theory," and is in no sense in conflict with this view. The assumptions underlying the analytical expression connecting θ and α are verified by the asymmetry in the orientation of male fiddlers, which is shown to be due to the presence of the enlarged chela and which disappears when the claws are removed.     

ON THE EQUILIBRATION OF GEOTROPIC AND PHOTOTROPIC EXCITATIONS IN THE RAT

The intensity of light required to just counterbalance geotropic orientation of young rats, with eyelids unopened, is so related to the angle of inclination (α) of the creeping plane that the ratio log I/log sin α is constant. This relationship, and the statistical variability of I as measured at each value of α, may be deduced from the known phototropic and the geotropic conduct as studied separately, and affords proof that in the compounding of the two kinds of excitation the rat is behaving as a machine.     

GEOTROPIC ORIENTATION IN ARTHROPODS : I. MALACOSOMA LARV?.

The geotropic orientation of caterpillars of Malacosoma americana during progression upon a surface inclined at angle α to the horizontal is such that the path makes an average angle θ upward on the plane, of a magnitude proportional to log sin α. More precisely, the product (sin α) (sin θ) is constant. This is traced to the fluctuation of the pull of the head region upon the lateral musculature of the upper side during the side to side swinging implicated in progression.     

ORIENTATION IN COMPOUND FIELDS OF EXCITATION; PHOTIC ADAPTATION IN PHOTOTROPISM

During upward geotropic orientation upon a vertical plate the slug Agriolimax creeps vertically, in darkness. Horizontal light from one side produces orientation of dark-adapted slugs away from the vertical path, through an angle (β). The magnitude of this angle is a function of the light intensity and of time. The moderately rapid course of light adaptation is followed by measurements of β at fixed intervals. Simple assumptions as to the nature of the orienting forces lead to the conclusion that the logarithm of the tangent of β should decrease linearly with time, and that the rate of the decrease should vary directly with the logarithm of the light intensity. Both expectations are adequately realized. Certain implications of these results for behavior analysis are pointed out.     

GEOTROPISM AND MUSCLE TENSION IN HELIX

1. The snail Helix aspersa Müller, is negatively geotropic during the daytime, but positive or indifferent at night. 2. The precision of geotropic orientation is a function of the gravity component acting on the body. 3. The rate of geotropic locomotion is also determined by the gravity component (sine of the angle of inclination). 4. The rate of upward movement is increased 1.51 times at 45° inclination by loading the snail with one-half its weight. No such increase is seen in loaded snails creeping on a horizontal surface. 5. Moderate centrifugation results in orientation and locomotion towards the center of rotation. 6. A response analogous to the homostrophic reflex occurs when a backward pull to right or to left is exerted on the shell. Bilaterally equal tension applied to the shell causes locomotion along a path parallel and opposite to the direction of the pull. 7. All the observations go to show that the stimulus for geotropic orientation and locomotion is tension of the body muscles produced by the downward pull of gravity, and that the stimulus is received by the proprioreceptors of these muscles. Otolith apparatus and analogous organs, when present, may assist in the response, but they do not seem to be requisite in all cases. Since the precision of orientation and the rate of locomotion are functions of the gravity component acting on the body, the muscle tension theory of the geotropic reactions accords fully with Loeb''s tropism doctrine for animals.     

GEOTROPIC EXCITATION IN HELIX

Rotation of an inclined surface on which Helix is creeping straight upward, such that the axis of the animal is turned at a right angle to its previous position, but in the same plane, leads to negatively geotropic orientation after a measurable latent period or reaction time. The duration of the latent period is a function of the slope of the surface. The magnitude of the standard deviation of the mean latent period is directly proportional to the mean latent period itself, so that the relative variability of response is constant. The dependence of reaction time upon extent of displacement from symmetrical orientation in the gravitational field is found also by tilting the supporting surface, without rotation in the animal''s own plane. On slopes up to 55°, the relation between latent period and the sine of the slope is hyperbolic; above this inclination, the latent period sharply declines. This change in the curve is not affected by the attachment of moderate loads to the snail''s shell (up to 1/3 of its own mass), and is probably a consequence of loss of passive stable equilibrium when rotated. When added loads do not too greatly extend the snail''s anterior musculature, the latent period for the geotropic reaction is decreased, and, proportionately, its σ. These facts are discussed from the standpoint that geotropic excitation in these gasteropods is due to impressed muscle-tensions.     

GEOTROPIC ORIENTATION IN ARTHROPODS : II. TETRAOPES.

The creeping of the beetle Tetraopes tetraopthalmus during negatively geotropic orientation shows the angles of orientation (θ) on a surface inclined at α° to the horizontal to be proportional to sin α. The direction of orientation easily suffers temporary reversal to positive as result of handling. Mechanical stability during upward progression should be just possible when K ₁ cot α = K ₂ sin θ + K ₃ cos θ, the weight of the body being supported on the tripod formed by the legs on either side and by the posterior tip of the abdomen. Lack of this stability produces tensions on the legs through (1) the bilaterally distributed pull of the body mass on the legs, and (2) the torque on the legs due to the weight of the abdomen. The downward gravitational displacement of the tip of the abdomen causes K ₂ and K ₃ in the preceding formula to be functions of α. These relations have been tested in detail by shifting the location of the center of gravity, by attaching additional masses anteriorly and posteriorly, and by decreasing the total load through amputation of the abdomen; the latter operation changes the conditions for stability. Different formulæ are thus obtained (cf. earlier papers) for the orientation of animals in which the mechanics of progression and the method of support of the body weight on an inclined surface are not the same. This demonstrates in a direct way that the respective empirical equations cannot be regarded as accidents. The results are in essence the same as that already obtained with young mammals. The diversity of equations required for the physically unlike cases merely strengthens the conception of geotropic orientation as limited by the tensions applied to the musculature of the body (caterpillars, slugs) or of appendages (beetles, and certain other forms) when the body is supported upon an inclined surface, since equations respectively pertaining to the several instances, and satisfactorily describing the observations, are deduced on this basis.     

ANALYSIS OF THE GEOTROPIC ORIENTATION OF YOUNG RATS. VII

The intraperitoneal injection of standard young rats of race A with 2/5 cc. of adrenalin chloride 1:50,000 results in increased speed of geotropically oriented creeping upon an inclined surface. It was expected that the effect of such increased frequency of stepping must be analogous to that due to imposition of added loads carried by the rats during geotropic progression. This is verified. The curve connecting θ with log sin α is distorted, under adrenalin, so as to be comparable to that obtained with an added mass of approximately 2.5 gm. upon the young rat''s saddle; the threshold slope of surface for orientation is accordingly lowered, from α = 20° to α = 12.5°; at the new threshold slope of surface the mean orientation angle θ is the same as in the absence of adrenalin at the corresponding threshold slope of surface. The total variation of performance is significantly increased in the injected rats, and at given slope of surface the variation is slightly increased. The proportionate modifiable variation of response is quite unaffected by the distortion of the θ – α curve, and is the same as in standard young A rats untreated or carrying additional loads. It is pointed out that for the consideration of the problem as to whether a given experimental treatment, or a given natural situation, affects in any way the variation of performance of a living system, it is necessary to obtain indices of variability which involve the expression of variation of performance as a function of measured conditions governing the performance.     

ANALYSIS OF THE GEOTROPIC ORIENTATION OF YOUNG RATS. VIII

The upward geotropic orientation (angle θ) of adult rats (race A) has been measured as a function of slope of substratum. The relative variation of orientation angle is a declining rectilinear function of θ. The fraction of the total observable variation of performance (θ) which is controlled by the intensity of excitation (56 per cent) is identical with that found for young rats of the same strain, although the total variation is a little greater. Injection of adrenin distorts the θ vs. α graph in a manner quite concordant with the effect obtained in young rats. With the adults the absolute magnitudes of the variations of θ, at corresponding intensities of excitation, are not affected by the action of adrenin, and, as with the young, the proportion of modifiable variation of θ is not altered. The variability of performance, considered as a function of the performance, must therefore be regarded as an organic invariant. Certain consequences of this finding are referred to.     

ANALYSIS OF THE GEOTROPIC ORIENTATION OF YOUNG RATS. II

1. Equations describing the geotropic orientation of young rats as a function of the inclination of the surface on which creeping take place, under standardized conditions, are found to be of similar form but with different values of the contained constants, when several different, genetically stabilized lines or races are compared. The values of these constants are characteristic for the several races. 2. The biological "reality" of the differences between young rats of two races, as given mathematical form in terms of these parameters and coefficients, can be submitted to radical test by investigating their behavior in inheritance. A simple result favorable to the inquiry would be decisive; a complex, non-clear result would not however be definitely unfavorable to the view that "real" differences in behavior are in question. The actual result is of a kind demonstrating (a) the efficiency of the original formulations, and (b), at the same time, the definite inheritance of certain quantitative aspects of geotropic behavior. 3. On the assumption that orientation on a sloping surface is achieved when, within a threshold difference, the tension-excitations on the two sides of the body (legs) are the same, the angle of oriented progression (θ) can be taken as a direct measure of the total excitation. This is consistent with the equation, accurately obeyed by our initial races, Δ cos θ/Δ sin α = - const., where α is the slope of the surface. 4. The total excitation of tension-receptors must be regarded as involving, over a gross interval of time, (1) the total array of receptors with thresholds below a certain value, a function of the stretching force, and (2) the frequency of change of tension. The latter, largely determined (it is assumed) by the frequency of stepping, should be proportional to the speed of progression. This speed is directly proportional to log sin α. Hence Δθ/Δ log sin α. plotted against sin α, should give a picture of the distribution of effective thresholds among the available tension-receptors in terms of the exciting component of gravity. For the races investigated this distribution can be resolved in each case into three groups. 5. A "variability number" is employed which permits the demonstration that the variability of θ as measured is (1) definitely controlled by α, and is (2) a characteristic number for each of the pure races used. 6. By attaching a weight to rats of one race it is found that Δθ/Δα is modified in a manner concordant with the assumption that the three "groups of sense organs" are in fact discrete. 7. In race K these three groups (I, II, III) are large, in race A, small (i, ii, iii). F₁ rats of the cross between these two races show i, ii, III. 8. F₁ individuals back-crossed to A give in the progeny two sorts of individuals, in equal numbers: i, ii, III and i, ii, iii. 9. F₁ individuals back-crossed to K are expected to give in the progeny four types of individuals, I, II; i, II; I, ii; i, ii. In the numbers available these classes are reasonably clear, and occur with equal frequency. 10. It is pointed out that these considerations imply a mode of definition of a gene somewhat different from that commonly employed by tacit assumption; namely, a definition of the effect in inheritance as a function of some controlling, independent variable.     

THE PHOTOTROPIC EXCITATION OF LIMAX

The photic orientation of Limax creeping geotropically upon a vertical plate is such that the phototropic vector determining the angular deflection β from the vertical path is proportional to log I. This is proved by the fact that with horizontal illumination tan β is directly proportional to log I; with non-horizontal light rays from a small source the ratio See PDF for Equation is directly proportional to log I (where A = the angle between light rays and the path of orientation), the vector diagram of the field of excitation being in this case not a right-angled triangle.     

Angle of Inclination of Tank-Treading Red Cells: Dependence on Shear Rate and Suspending Medium

Red cells suspended in solutions much more viscous than blood plasma assume an almost steady-state orientation when sheared above a threshold value of shear rate. This orientation is a consequence of the motion of the membrane around the red cell called tank-treading. Observed along the undisturbed vorticity of the shear flow, tank-treading red cells appear as slender bodies. Their orientation can be quantified as an angle of inclination (θ) of the major axis with respect to the undisturbed flow direction. We measured θ using solution viscosities (η₀) and shear rates (γ˙) covering one and three orders of magnitude, respectively. At the lower values of η₀, θ was almost independent of γ˙. At the higher values of η₀, θ displayed a maximum at intermediate shear rates. The respective maximal values of θ increased by ∼10° from 10.7 to 104 mPas. After accounting for the absent membrane viscosity in models by using an increased cytoplasmic viscosity, their predictions of θ agree qualitatively with our data. Comparison of the observed variation of θ at constant γ˙ with model results suggests a change in the reference configuration of the shear stiffness of the membrane.     

The Transmembrane Helices of Beef Heart Cytochrome Oxidase

The locations of the transmembrane helices in the 12 subunits of beef heart cytochrome oxidase were predicted with a modified form of the von Heijne-Blomberg hydrophobicity scale. Based on ~20 residues per transmembrane helix, about 480 of the estimated 660 helical residues (36.8% of 1,793 total residues) are expected to be in transmembrane helices that have their axes tilted by a small angle α from the normal to the plane of the membrane. This angle is calculated to be ~30°, based on the observed overall tilt angle θ of 39° obtained from circular dichroism (CD) measurements on multilamellar films, or about 25°, based on the observed tilt angle θ of 36° obtained from the infrared linear dichroism of films. For 21 residues per transmembrane helix, the calculated values of α become 32° and 28°, respectively, depending upon the value of θ used. Thus, a transmembrane helical tilt angle of ~30° accounts for the predicted transmembrane stretches in cytochrome oxidase if 20-21 residues are sufficient to span the membrane. Additional helical residues in the lipid head region may deviate by a larger angle from the normal to the plane of the membrane in cytochrome oxidase.     

THE USE OF SHADOW-CASTING TECHNIQUE FOR MEASUREMENT OF THE WIDTH OF ELONGATED PARTICLES

A method is described for the estimation of the true width of fibrillar or rod-like structures from electron micrographs of metal-shadowed preparations. The method is based on variations in the image width as a function of the angle (β) between the long axis of the fibril and the direction of the shadow in the plane of the preparation. The image width when β = 0° practically represents the real width of the elongated particle but is often indistinguishable from the background. The fibril image width is conveniently measured at β values between 15° and 90°. The true width is obtained by plotting the image width versus sin β and extrapolating to β = 0°. Latex spheres are sprayed with the fibrils or rods to indicate the direction of shadow. Tobacco mosaic virus (TMV) was used as a model structure because of its known constant diameter of 150 A (5). The width (in the case of TMV equal to the diameter) found by the present method was 150 A ± 8 A.     

Electrodichroism of Purple Membrane: Ionic Strength Dependence

The dichroism of purple membrane suspension was measured in dc and ac electric fields. From these measurements three parameters can be obtained: the permanent dipole moment, μ, the electrical polarizability, α, and the retinal angle, δ, (relative to the membrane normal). The functional dependence of the dichroism on the electric field is analyzed. There is a small decrease (~2°) in retinal angle going from dark adapted to the light adapted form. No measurable difference in μ, α, and δ was found under the photocycle. The dichroism was measured in two different salt solutions (KCl and CaCl₂) in the range 0-10 mM. The retinal angle increases from 64° to 68° with increasing ionic strength going through a minimum. This is attributed to the changing (decreasing) inner electric field in the membrane. The polarizability, α, consists of two parts. One component is related to the polarization of the purple membrane and the second component to the ionic cloud. The second component decreases with ion concentration approximately as κ^-3 (κ is the Debye parameter) in agreement with a model calculation for the polarization of the ionic cloud. The origin of the slightly ionic strength dependent permanent dipole moment is not well understood.     

IOL Tilt and Decentration Estimation from 3 Dimensional Reconstruction of OCT Image

Purpose

To evaluate intraocular lens (IOL) tilt and decentration by anterior segment optical coherence tomography (AS-OCT) using 3-dimensional (3D) reconstruction method.

Design

Prospective observational case series.

Participants

Thirty-nine patients (39 eyes) were included.

Methods

The IOL positions of all eyes were examined by AS-OCT. Images were obtained in 4 axes (0–180 degrees, 45–225 degrees, 90–270 degrees, and 135–315 degrees) using the quadrant-scan model. The cross-sectional images were analyzed with MATLAB software.

Main Outcome Measures

The angle (θ) between the reference pupillary plane and the IOL plane, the distances between the center points of the pupil circle and the IOL on the x-axis (dx) and y-axis (dy) and the spatial distance (ds) were calculated after 3D-reconstruction.

Results

The mean angle (θ) between the pupillary plane and the IOL plane was 2.94±0.99 degrees. The mean IOL decentration of dx and dy was 0.32±0.26 mm and 0.40±0.27 mm, respectively. The ds of the IOL decentration was 0.56±0.31 mm. There was no significant correlation between the ocular residual astigmatism (ORA) and the tilted angle or the decentration distance. There was a significant correlation between the ORA and total astigmatism (r = 0.742, P<0.001). There was no significant correlation between the postoperative best corrected visual acuity (BCVA) and the ORA (r = 0.156; P = 0.344), total astigmatism (r = 0.012; P = 0.942), tilted angle (θ; r = 0.172; P = 0.295) or decentration distance (dx: r = 0.191, P = 0.244; dy: r = 0.253, P = 0.121; ds: r = 0.298, P = 0.065).

Conclusions

AS-OCT can be used as an alternative for the analysis of IOL tilt and decentration using 3D-reconstruction.     

PHOTOTROPIC CIRCUS MOVEMENTS OF LIMAX AS AFFECTED BY TEMPERATURE

1. The theory of animal phototropism requires for particular instances a knowledge of the action of light as exerted through each of two bilaterally located receptors functioning singly. The measurement of "circus movements" which this involves must be concerned with such aspects of the reaction as are demonstrably dependent upon the effect of light. 2. The negatively phototropic slug Limax maximus exhibits very definite and continuous circus movement under vertical illumination when one eye-tentacle has been removed. The amplitude of the circling movement, measured in degrees deflection per cm. of path as an index of maintained differential tonus, is intimately related to the concurrent velocity of creeping. Analysis of the orienting mechanism is facilitated by the fact that in gasteropods such as Limax the animal creeps by means of the pedal organ, but orients (turns) by a totally distinct set of muscles in the dorsal and lateral regions of the body wall. 3. The expression of the phototropic orienting tendency, with illumination constant, is greatly influenced by the temperature. Above a zone centering at 15°, the amplitude of turning (degrees per cm. of path) is determined by the temperature in accurate agreement with Arrhenius'' equation for chemical reaction velocity, with the critical increment µ = 16,820; and the rate of creeping is progressively less as the temperature rises, µ for its reciprocal being 10,900. Below 15°, the velocity of creeping becomes less the the lower the temperature, µ being again 16,800; while the amplitude of orientation is limited merely by the velocity of creeping, its reciprocal being directly proportional thereto. 4. Measurements of Limax circus movements in terms of turning deflection as function of light intensity must therefore be carried out at a temperature well above 15°. 5. The analysis provides a gross physical model of how an end-result may be influenced by temperature according to the effect of temperature upon each of several interconnected processes when the "temperature vs. effect" curves for these processes dynamically intersect. 6. It is pointed out that a certain type of unpredictability (quantative variability) in animal behavior under "normal" natural conditions probably results from dynamic equilibrium there obtaining between diverse mechanisms competing for effector control (in the present case, the creeping mechanism and that for turning, in the range 14–16°C.). It follows that the unraveling of the elements of conduct necessitates experimentation under diverse abnormal conditions favoring individual mechanism of response.