GEOTROPISM OF AGRIOLIMAX

On an inclined glass plate the slug Agriolimax orients and creeps upward or downward. The angle of orientation on the plane (θ) is proportional to the logarithm of the component of gravity in the creeping plane. The coefficient of variability of the measured values of (θ) decreases linearly as the logarithm at the gravity component in the creeping plane increases. The cosine of the angle of orientation decreases almost directly in proportion to the sine of the angle of inclination of the creeping plane to the horizontal, as previously found for young rats (Crozier and Pincus). But a more satisfactory formulation for the present case shows that the sine of the angle of orientation (θ) decreases in direct proportion to the increase of the reciprocal of the sine of the angle of inclination of the creeping plane. This formulation is derived from the theory that the geotropic orientation is limited by the threshold difference between the pull of the body mass on the mutually inclined longitudinal muscles at the anterior end of the slug.     

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 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.     

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.     

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.     

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.     

ON REVERSAL OF GEOTROPISM IN ASTERINA

A certain level of strychninization induces in Asterina reversal of geotropism from the normally geonegative movement to a persistent downward creeping. The effect of an attached float producing upward pull is to induce upward creeping, under these conditions, whereas normally it leads to downward movement. This reversal cannot be regarded as due to a mere intensification of the sensory effect of tension. It must be understood as representing a true reversal of inhibition. The temporary reversal of geotropism following mechanical disturbances (in the absence of strychnine) is interpreted in the same way.     

THE LOCOMOTION OF LIMAX : I. TEMPERATURE COEFFICIENT OF PEDAL ACTIVITY.

Pedal progression of the slug Limax maximus was studied to obtain relations between wave velocity on the sole of the foot, wave frequency, the advance due to a single wave, and the velocity of vertically upward creeping. Each of the first three quantities is directly proportional to the simultaneous velocity of progression. Under comparable conditions, that is when work is done at a constant rate, the frequency of pedal waves is influenced by the temperature according to the equation of Arrhenius, with µ = 10,700 (Q ₁₀ for 11° to 21° = 2.1). The velocity of a single wave must have very nearly the same "temperature characteristic," which is found also in another case of nerve net transmission (in Renilla).     

ON STEREOTROPISM IN TENEBRIO LARV?

Larvæ of Tenebrio while creeping show homostrophic responses, and stereotropic orientation to lateral contacts. Homostrophic orientation is inhibited by stereotropism. Both depend upon the anterior portion of the central nervous system. Stereotropic orientation due to unilateral contact, particularly at the anterior end, persists briefly after the cessation of the contact. Equal posterior bilateral contact of the body obliterates stereotropic bending. Unequal posterior bilateral contacts lead to orientation through an angle roughly proportional to the differences in contact areas. Functional symmetry in such responses is not disturbed by asymmetrical distribution of the body "hairs." The stereotropic orientation undergoes reversal of direction, central in origin, when the stimulation is sufficiently intense. Stereotropic response, leading to maintained lateral contact with a surface or to bending when the end of such a surface has been passed, is inhibited by a definite intensity of light. These findings (1) round out the demonstration that stereotropism is truly of a tropistic character, and (2) make possible the understanding of conduct in a case involving the participation of contact stimulation, phototropism, temperature, and homostrophy.     

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.     

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.     

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.     

Inertial shear force and the impact on facilities for the International Space Station

Inertial shear force is a surface force that is generated in centrifuges especially with attached samples on flat surfaces and plays a significant role in gravitational and space research. The magnitude of this force is proportional to the radius of the centrifuge and surface area of the sample compartment. In gravitational research we want to study the impact of weight onto a system. However, the force of inertial shear is perpendicular to the gravity vector, hence, results may be obscured or even misinterpreted by this artifact.     

Running on a slope: A collision-based analysis to assess the optimal slope

When running, energy is lost during stance to redirect the center of mass of the body (COM) from downwards to upwards. The present study uses a collision-based approach to analyze how these energy losses change with slope and speed. Therefore, we evaluate separately the average collision angle, i.e. the angle of deviation from perpendicular relationship between the force and velocity vectors, during the absorptive and generative part of stance. Our results show that on the level, the collision angle of the absorptive phase is smaller than the collision angle of the generative phase, suggesting that the collision is generative to overcome energy losses by soft tissues. When running uphill, the collision becomes more and more generative as slope increases because the average upward vertical velocity of the COM becomes greater than on the level. When running downhill at a constant speed, the collision angle decreases during the generative phase and increases during the absorptive phase because the average downward vertical velocity of the COM becomes greater. As a result, the difference between the collision angles of the generative and absorptive phases observed on the level disappears on a shallow negative slope of ∼−6°, where the collision becomes 'pseudo-elastic' and collisional energy losses are minimized. At this 'optimal' slope, the metabolic energy consumption is minimal. On steeper negative slopes, the collision angle during the absorptive phase becomes greater than during the generative phase and the collision is absorptive. At all slopes, the collision becomes more generative when speed increases.     

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.     

Gravity sensing in oat coleoptiles: scatter in growth orientation under different g-conditions

Dark-grown oat seedlings depart from the expected vertical orientation, suggesting that the coleoptile is less responsive to the lateral component of a gravitational stimulus than would be expected. This phenomenon was studied by investigating the gravitropic curvatures of oat (Avena sativa L. cv. Seger) coleoptiles at 10g and over a range of longitudinally applied centripetal accelerations up to 19·4g. In most experiments, the plants were grown and observed at a particular g-level throughout the experiment. Time-lapse video recordings permitted studies of the scatter, measured as the variability of the plants' angle from the vertical (or root mean square value, RMS). The coleoptiles' heights at the end of the experiments were not significantly altered under the centrifugation. Scatter increased with plant age and decreased with increasing g. It decreased in an almost linear fashion as a function of the logarithm of the g-acceleration. In a series of experiments, the g-level was changed from 10g to a higher test g-acceleration. The scatter was then reduced within half an hour after the g-transition. It is pointed out that the experiments confirm that the scatter is g-related but that it was not predicted quantitatively by present theories of the oat coleoptile's gravitropic response kinematics.     

A three-dimensional model of the upper tracheobronchial tree

A new model of the upper tracheobronchial tree is proposed to account for the three-dimensional nature of the airway system. In addition to the tube length, the tube diameter, and the branching angle, the model includes information on the orientation angle of each tube relative to its parent tube. The orientation angle, defined as the angle between two successive bifurcations, is useful for calculating the gravitational inclination of each tube. The information on orientation angle is further used to construct a binary coding system for identifying individual tubes in the airway tree. The proposed model is asymmetrical, but the same principles can be readily used to construct a symmetrical one.     

Strategic Escape Direction: Orientation,Turning, and Escape Trajectories of Zebra‐Tailed Lizards (Callisaurus draconoides)

A prey's body orientation relative to a predator's approach path may affect risk of fleeing straight ahead. Consequently, prey often turn before fleeing. Relationships among orientation, turn, and escape angles and between these angles and predation risk have not been studied in terrestrial vertebrates and have rarely been studied in the field. Escape angles are expected to lead away from predators and be highly variable to avoid being predictable by predators. Using approach speed as a risk factor, we studied these issues in the zebra‐tailed lizard, Callisaurus draconoides. Lizards fled away from human simulated predators, but most did not flee straight away. Escape angles were variable, as expected under the unpredictability hypothesis, and had modes at nearly straight away (i.e., 0°) and nearly perpendicular to the predator's approach path (90°). The straight away mode suggests maximal distancing from the predator; the other mode suggests maintaining ability to monitor the predator or possibly an influence of habitat features such as obstacles and refuges that differ among directions. Turn angles were larger when orientation was more toward the predator, and escape angles were closer to straight away when turn angles were larger. Turning serves to reach a favorable fleeing direction. When orientation angle was more toward the predator, escape angle was unaffected, suggesting that turn angle compensates completely for increased risk of orientation toward the predator. When approached more rapidly, lizards fled more nearly straight away, as expected under greater predation risk. Turn angles were unrelated to approach speed.     

The simplest walking model: stability, complexity, and scaling.

We demonstrate that an irreducibly simple, uncontrolled, two-dimensional, two-link model, vaguely resembling human legs, can walk down a shallow slope, powered only by gravity. This model is the simplest special case of the passive-dynamic models pioneered by McGeer (1990a). It has two rigid massless legs hinged at the hip, a point-mass at the hip, and infinitesimal point-masses at the feet. The feet have plastic (no-slip, no-bounce) collisions with the slope surface, except during forward swinging, when geometric interference (foot scuffing) is ignored. After nondimensionalizing the governing equations, the model has only one free parameter, the ramp slope gamma. This model shows stable walking modes similar to more elaborate models, but allows some use of analytic methods to study its dynamics. The analytic calculations find initial conditions and stability estimates for period-one gait limit cycles. The model exhibits two period-one gait cycles, one of which is stable when 0 < gamma < 0.015 rad. With increasing gamma, stable cycles of higher periods appear, and the walking-like motions apparently become chaotic through a sequence of period doublings. Scaling laws for the model predict that walking speed is proportional to stance angle, stance angle is proportional to gamma 1/3, and that the gravitational power used is proportional to v4 where v is the velocity along the slope.     

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.