Mechanics of locomotion of dogs (Canis familiaris) and sheep (Ovis aries)

Records have been made of the forces exerted on the ground by dogs and a sheep, in walking, trotting, cantering and slow galloping. Film has been taken simultaneously. The difference between walking and trotting was much less marked for the sheep than for the dogs.
Step length and stride length increase as speed increases. They are expressed as functions of the Froude number.
The vertical component of the force exerted by a foot on the ground shows two main maxima in walking, except in the case of the fore feet of sheep. In this case and in other gaits there is only one main maximum. The vertical movements of the fore and hind quarters which occurred in examples of each gait have been calculated from the force records.
The force exerted by a foot on the ground changes direction in the course of a step so as to remain more or less in line with a point fixed relative to the animal, but dorsal to its back.
The force records show impact disturbances in the first 003 sec of contact of each foot with the ground.
The point of application of the force on the sole of a foot tends to move posteriorly as the force increases.
The results are discussed in relation to a theoretical account of the mechanics of locomotion on legs.     

Limb kinematics during locomotion in the two-toed sloth (Choloepus didactylus,Xenarthra) and its implications for the evolution of the sloth locomotor apparatus

In order to gain insight into the function of the extant sloth locomotion and its evolution, we conducted a detailed videoradiographic analysis of two-toed sloth locomotion (Xenarthra: Choloepus didactylus). Both unrestrained as well as steady-state locomotion was analyzed. Spatio-temporal gait parameters, data on interlimb coordination, and limb kinematics are reported. Two-toed sloths displayed great variability in spatio-temporal gait parameters over the observed range of speeds. They increase speed by decreasing the durations of contact and swing phases, as well as by increasing step length. Gait utilization also varies with no strict gait sequence or interlimb timing evident in slow movements, but a tendency to employ diagonal sequence, diagonal couplet gaits in fast movements. In contrast, limb kinematics were highly conserved with respect to ‘normal’ pronograde locomotion. Limb element and joint angles at touch down and lift off, element and joint excursions, and contribution to body progression of individual elements are similar to those reported for non-cursorial mammals of small to medium size. Hands and feet are specialized to maintain firm connection to supports, and do not contribute to step length or progression. In so doing, the tarsometatarsus lost its role as an individual propulsive element during the evolution of suspensory locomotion. Conservative kinematic behavior of the remaining limb elements does not preclude that muscle recruitment and neuromuscular control for limb pro- and retraction are also conserved. The observed kinematic patterns of two-toed sloths improve our understanding of the convergent evolution of quadrupedal suspensory posture and locomotion in the two extant sloth lineages.     

BigDog-inspired studies in the locomotion of goats and dogs

Collision-based expenditure of mechanical energy and the compliance and geometry of the leg are fundamental, interrelated considerations in the mechanical design of legged runners. This article provides a basic context and rationale for experiments designed to inform each of these key areas in Boston Dynamic's BigDog robot. Although these principles have been investigated throughout the past few decades within different academic disciplines, BigDog required that they be considered together and in concert with an impressive set of control algorithms that are not discussed here. Although collision reduction is an important strategy for reducing mechanical cost of transport in the slowest and fastest quadrupedal gaits, walking and galloping, BigDog employed an intermediate-speed trotting gait without collision reduction. Trotting, instead, uses a spring-loaded inverted pendulum mechanism with potential for storage and return of elastic strain energy in appropriately compliant structures. Rather than tuning BigDog's built-in leg springs according to a spring-mass model-based virtual leg-spring constant , a much stiffer distal leg spring together with actuation of the adjacent joint provided good trotting dynamics and avoided functional limitations that might have been imposed by too much compliance in real-world terrain. Adjusting the directional compliance of the legs by adopting a knee-forward, elbow-back geometry led to more robust trotting dynamics by reducing perturbations about the pitch axis of the robot's center of mass (CoM). BigDog is the most successful large-scale, all-terrain trotting machine built to date and it continues to stimulate our understanding of legged locomotion in comparative biomechanics as well as in robotics.     

Elastic extension of leg tendons in the locomotion of horses (Equus caballus)

Several of the distal leg muscles of horses have such extremely short muscle fibres that their changes of length in locomotion must be due almost entirely to elastic extension of their tendons. Films of a horse have been analysed to determine these extensions, using data obtained by experiments on dissected legs. The tendons investigated experience peak strains of 3–6% in walking, 3–7% in trotting and 4–9% in galloping. These strains occur while the foot is on the ground.     

Mechanisms of stick insect locomotion in a gap-crossing paradigm

Locomotion of stick insects climbing over gaps of more than twice their step length has proved to be a useful paradigm to investigate how locomotor behaviour is adapted to external conditions. In this study, swing amplitudes and extreme positions of single steps from gap-crossing sequences have been analysed and compared to corresponding parameters of undisturbed walking. We show that adaptations of the basic mechanisms concern movements of single legs as well as the coordination between the legs. Slowing down of stance velocity, searching movements of legs in protraction and the generation of short steps are crucial prerequisites in the gap-crossing task. The rules of leg coordination described for stick insect walking seem to be modified, and load on the supporting legs is assumed to have a major effect on coordination especially in slow walking. Stepping into the gap with a front leg and antennal contact with the far edge of the gap provide information, as both events influence the following leg movements, whereas antennal non-contact seems not to contain information. Integration of these results into the model of the walking controller can improve our understanding of insect locomotion in highly irregular environments.Abbreviations AEP anterior extreme position - fAEP fictive anterior extreme position - PEP posterior extreme position - TOT treading-on-tarsus     

The functions of the lumbar spine during stepping in the cat

To examine the functional roles played by the lumbar spine during overground stepping, seven adult cats were run in electromyographic (EMG) experiments. Recordings were made bilaterally from mm. iliocostalis, longissimus dorsi and multifidus at a single vertebral level (L₃) and from m. rectus abdominis. Stepping movements were monitored synchronously either by videotape or by high speed cinematography. During alternate use of the hindlimbs (walking and trotting), both epaxial and abdominal muscles were active bilaterally and biphasically. During in-phase use of the hindlimbs (galloping and half-bounding), single bursts of activity were observed. Phasic bursts of activity in rectus abdominus were reciprocal to those of epaxial muscles. Second bursts of activity in either group were noted infrequently. Recordings from the same back muscle at several vertebral levels indicated little difference from these patterns. Movements of the lumbar spine during galloping and half-bounding steps, both angular and linear, are easily correlated with muscle activity patterns. Movements of the lumbar spine during walking and trotting show no particular pattern. Only small angular and linear movements are found. It is concluded that the lumbar spine contributes substantially to step length and limb speed during galloping and half-bounding steps and the epaxial and abdominal musculature may also act as elastic bodies. During walking and trotting steps, the epaxial muscles are proposed to act to stabilize the pelvic girdle to provide a firm base for limb muscles which arise on the pelvis and are synchronously active.     

Insects Use Two Distinct Classes of Steps during Unrestrained Locomotion

Background

Adaptive, context-dependent control of locomotion requires modulation of centrally generated rhythmic motor patterns through peripheral control loops and postural reflexes. Thus assuming that the modulation of rhythmic motor patterns accounts for much of the behavioural variability observed in legged locomotion, investigating behavioural variability is a key to the understanding of context-dependent control mechanisms in locomotion. To date, the variability of unrestrained locomotion is poorly understood, and virtually nothing is known about the features that characterise the natural statistics of legged locomotion. In this study, we quantify the natural variability of hexapedal walking and climbing in insects, drawing from a database of several thousand steps recorded over two hours of walking time.

Results

We show that the range of step length used by unrestrained climbing stick insects is large, showing that step length can be changed substantially for adaptive locomotion. Step length distributions were always bimodal, irrespective of leg type and walking condition, suggesting the presence of two distinct classes of steps: short and long steps. Probability density of step length was well-described by a gamma distribution for short steps, and a logistic distribution for long steps. Major coefficients of these distributions remained largely unaffected by walking conditions. Short and long steps differed concerning their spatial occurrence on the walking substrate, their timing within the step sequence, and their prevalent swing direction. Finally, ablation of structures that serve to improve foothold increased the ratio of short to long steps, indicating a corrective function of short steps.

Conclusions

Statistical and functional differences suggest that short and long steps are physiologically distinct classes of leg movements that likely reflect distinct control mechanisms at work.     

Abdominal muscle function in ventilation and locomotion in new world opossums and basal eutherians: Breathing and running with and without epipubic bones

All tetrapods have the same four basic abdominal hypaxial muscle layers that wrap around the abdomen between the pelvis, ribcage, and spine. However, the marsupials and our immediate mammalian ancestors have epipubic bones extending anteriorly into the ventral hypaxial layers with two additional muscles connecting them to the ventral midline and femur. Studies of two marsupials have shown that all of the abdominal hypaxials play a part bilaterally in resting ventilation and during locomotion there is an asymmetrical pattern of activity as the hypaxial muscles form a cross‐couplet linkage that uses the epipubic bone as a lever to provide long‐axis support of the body between diagonal limb couplets during each step. The cross‐couplet epipubic lever system defines the earliest mammals and is lost in placental mammals. To expand our understanding of the evolution of mammalian abdominal muscle function and loco‐ventilatory integration we tested the generality of the cross‐couplet system in marsupials and conducted the first formal studies of hypaxial abdominal motor patterns in generalized placental mammals focusing on a representative rodent and insectivore. These new data reveal 1) that continuous abdominal muscle tonus during resting ventilation and a 1:1 breath to step cycle during locomotion appear to be the basal condition for mammals, 2) that the loss of epipubic bones in eutherians is associated with a shift from the cross‐couplet dominated motor pattern of marsupials to a shoulder‐to‐pelvis system with unilateral activation of abdominal muscles during locomotion and 3) that hypaxial function in generalized eutherians is more similar to marsupials than cursorial mammals. J. Morphol. 2009. © 2009 Wiley‐Liss, Inc.     

A Bio-Inspired Hopping Kangaroo Robot with an Active Tail

Inspired by kangaroo＇s locomotion, we report on developing a kangaroo-style hopping robot. Unlike bipeds, quadrupeds, or hexapods which altemate the legs for forward locomotion, the kangaroo uses both legs synchronously and generates the forward locomotion by continuous hopping behavior, and the tail actively balances the unwanted angular momentum generated by the leg motion. In this work, we generate the Center of Mass （CoM） locomotion of the robot based on the reduced-order Rolling Spring Loaded Inverted Pendulum （R-SLIP） model, for matching the dynamic behavior of the empirical robot legs. In order to compensate the possible body pitch variation, the robot is equipped with an active tail for pitch variation compensation, emulating the balance mechanism of a kangaroo. The robot is empirically built, and various design issues and strategies are addressed. Finally, the experimental evaluation is executed to validate the performance of the kangaroo-style robot with hopping locomotion.     

The intercalating beta-hairpin of T7 RNA polymerase plays a role in promoter DNA melting and in stabilizing the melted DNA for efficient RNA synthesis

Phage T7 RNA polymerase contains within its single polypeptide all the elements for specific recognition and melting of its promoter DNA. Crystallographic studies indicate that a beta-hairpin (230-245) with an intercalating valine residue plays a role in promoter opening. We mutated V237 to several amino acids, deleted five amino acid residues at the tip of the hairpin, and mutated E242 and D240 at the base of the hairpin to define the roles of the tip and base of the hairpin in DNA strand separation. The affinity of the hairpin mutants for the promoter DNA was not significantly affected. Stopped-flow kinetic studies showed that the bimolecular rate of DNA binding and the observed rate of pre-initiation open complex formation that corresponds to the sum of DNA opening and closing steps were within 20 to 40 % of the wild-type polymerase. Yet, most mutants showed a smaller amount of the pre-initiation open complex at equilibrium, indicating that the individual rates of promoter opening and closing steps were altered in the mutants. The base mutants, E242A and D240A, showed both a lower rate of promoter opening and a higher rate of promoter closing, suggesting their role in stabilization of the open complex. The V237D and the deletion mutant showed mainly a lower rate of promoter opening, suggesting that the tip of the hairpin may nucleate DNA opening. The defect in pre-initiation open complex formation affected downstream steps such as the rate of the first phosphodiester bond formation step, but did not affect significantly the apparent K(d) of initiating GTPs. We propose that D240 and E242 anchor the hairpin to the DNA and position the tip of the hairpin to allow V237 to intercalate and distort the DNA during open complex formation. The interactions of E242 and D240 with the upstream junction of the melted dsDNA promoter also align the template strand within the active site for efficient RNA synthesis.     

Fast locomotion in caterpillars

The maximum forward crawling speeds of caterpillars are limited by the hydraulic design of the body and the peristaltic mode of operation of the segmental muscles. High speed locomotory manoeuvers can be achieved by reversing the direction of the normal peristaltic wave (from posterior-anterior to anterior-posterior) although the penalty is a dramatically reduced duty factor of the legs and potential instability. This study describes the suite of reverse gaits available to caterpillars, from reverse walking (the kinematic inverse of normal forward walking), through to reverse galloping (in which all the legs save the claspers are wrenched free of the ground with each step) to recoil-and-roll, a unique form of locomotion in which the insect free-wheels backwards at high-speed. These reverse forms of locomotion are produced primarily in response to threat, involve bilateral activation of the intersegmental muscles and are relatively simple in terms of neural control. The ecological roles of high-speed locomotion are considered in the light of potential predators and the normal habitat and terrain.     

Bird terrestrial locomotion as revealed by 3D kinematics

Most birds use at least two modes of locomotion: flying and walking (terrestrial locomotion). Whereas the wings and tail are used for flying, the legs are mainly used for walking. The role of other body segments remains, however, poorly understood. In this study, we examine the kinematics of the head, the trunk, and the legs during terrestrial locomotion in the quail (Coturnix coturnix). Despite the trunk representing about 70% of the total body mass, its function in locomotion has received little scientific interest to date. This prompted us to focus on its role in terrestrial locomotion. We used high-speed video fluoroscopic recordings of quails walking at voluntary speeds on a trackway. Dorso-ventral and lateral views of the motion of the skeletal elements were recorded successively and reconstructed in three dimensions using a novel method based on the temporal synchronisation of both views. An analysis of the trajectories of the body parts and their coordination showed that the trunk plays an important role during walking. Moreover, two sub-systems participate in the gait kinematics: (i) the integrated 3D motion of the trunk and thighs allows for the adjustment of the path of the centre of mass; (ii) the motion of distal limbs transforms the alternating forward motion of the feet into a continuous forward motion at the knee and thus assures propulsion. Finally, head bobbing appears qualitatively synchronised to the movements of the trunk. An important role for the thigh muscles in generating the 3D motion of the trunk is suggested by an analysis of the pelvic anatomy.     

Abdominal muscle and epipubic bone function during locomotion in Australian possums: Insights to basal mammalian conditions and eutherian‐like tendencies in Trichosurus

Mammals have four hypaxial muscle layers that wrap around the abdomen between the pelvis, ribcage, and spine. However, the marsupials have epipubic bones extending anteriorly into the ventral hypaxial layers with two additional muscles extending to the ventral midline and femur. Comparisons of South American marsupials to basal eutherians have shown that all of the abdominal hypaxials are active bilaterally in resting ventilation. However, during locomotion marsupials employ an asymmetrical pattern of activity as the hypaxial muscles form a crosscouplet linkage that uses the epipubic bone as a lever to provide long‐axis support of the body between diagonal limb couplets during each step. In basal eutherians, this system shifts off the femur and epipubic bones (which are lost) resulting in a shoulder to pelvis linkage associated with shifts in both the positions and activity patterns of the pectineus and rectus abdominis muscles during locomotion. In this study, we present data on hypaxial function in two species (Pseudocheirus peregrinus and Trichosurus vulpecula) representing the two major radiations of possums in Australia: the Pseudocheiridae (within the Petauroidea) and the Phalangeridae. Patterns of gait, motor activity, and morphology in these two Australian species were compared with previous work to examine the generality of 1) the crosscouplet lever system as the basal condition for the Marsupialia and 2) several traits hypothesized to be common to all mammals (hypaxial tonus during resting ventilation, ventilation to step synchrony during locomotion, and bilateral transversus abdominis activity during locomotor expiration). Our results validate the presence of the crosscouplet pattern and basic epipubic bone lever system in Australian possums and confirm the generality of basal mammalian patterns. However, several novelties discovered in Trichosurus, reveal that it exhibits an evolutionary transition to intermediate eutherian‐like morphological and motor patterns paralleling many other unique features of this species. J. Morphol., 2010. © 2009 Wiley‐Liss, Inc.     

Analysis of the gait generation principle by a simulated quadruped model with a CPG incorporating vestibular modulation

This study aims to understand the principles of gait generation in a quadrupedal model. It is difficult to determine the essence of gait generation simply by observation of the movement of complicated animals composed of brains, nerves, muscles, etc. Therefore, we build a planar quadruped model with simplified nervous system and mechanisms, in order to observe its gaits under simulation. The model is equipped with a mathematical central pattern generator (CPG), consisting of four coupled neural oscillators, basically producing a trot pattern. The model also contains sensory feedback to the CPG, measuring the body tilt (vestibular modulation). This spontaneously gives rise to an unprogrammed lateral walk at low speeds, a transverse gallop while running, in addition to trotting at a medium speed. This is because the body oscillation exhibits a double peak per leg frequency at low speeds, no peak (little oscillation) at medium speeds, and a single peak while running. The body oscillation autonomously adjusts the phase differences between the neural oscillators via the feedback. We assume that the oscillations of the four legs produced by the CPG and the body oscillation varying according to the current speed are synchronized along with the varied phase differences to keep balance during locomotion through postural adaptation via the vestibular modulation, resulting in each gait. We succeeded in determining a single simple principle that accounts for gait transition from walking to trotting to galloping, even without brain control, complicated leg mechanisms, or a flexible trunk.     

Tripedal knuckle-walking: a proposal for the evolution of human locomotion and handedness.

A comparative morphological analysis of human and non-human hominoids was conducted in an attempt to determine the mode of locomotion of the protohominid. Although the generalized hominoid anatomy permits variation of locomotion: brachiation, knuckle-walking, etc., minor variations in structure determine which behavior is favored. Arboreal arm swinging requires a flexible forelimb while terrestrial fist or knuckle-walking demands more rigidity of the hand and wrist. It is demonstrated that the large human thumb accompanied by the strong adduction of the thenar, hypothenar, and palmar interosseous muscles offer powerful rigidity to the hand, while fusion of the os centrale with the scaphoid during gestation permits the formation of an arch of carpals which imbue the wrist with the stability necessary for weight bearing. Fascialization of the contrahentes and dorsiepitrochlearis muscles in the human as well as depilation of the middle phalanges; the webbing (syndactyly) of the palm; the direction of the fibers of the interosseous membrane of the forearm; the shape of the puerile annular ligament, and the direction of the human glenoid fossa strongly suggest that the ancestor of man used a knuckle-walking form of locomotion prior to becoming bipedal. A model is presented that suggests that bipedalism was attained through an intermediate stage of tripedalism. The model is based on the fact that man's anatomy is much more asymmetric than that of the great apes. A presumption is made that due to the absence of trees for climbing in the transition from forest to open plain, the protohominid needed to carry tools (stones) at all times for protection. Stones could be carried for long distances on the posterior iliac crest since the weight would be shifted posteriorly over the legs. Pick up, medial rotation and adduction of the stone would employ a two-muscle chain of biceps brachii and latissimus dorsi. On the iliac crest, the stone is posterior to the coronal plane of the glenohumeral joint, and with the contraction of this two-muscle chain, the shoulder on one side is moved posteriorly effecting a semi-erect posture. It is proposed that tripedalism of the protohominid may be an explanation for the handedness unique to hominids.     

Stick insects walking on a wheel: Perturbations induced by obstruction of leg protraction

Summary Stick insects (Carausius morosus) walking on a wheel were perturbed by restricting the forward protraction of individual legs. A barrier placed before a single middle or rear leg prevented that leg from reaching its normal protraction endpoint but allowed it unimpeded retraction. Upon striking the barrier, the protracting leg attempted to get past it and thereby prolonged protraction. This prolongation increased with the extent to which the obstruction infringed upon the leg's normal step range. Barriers placed near the midpoint of this range elicited large perturbations: the blocked leg often continued its protraction throughout many step cycles of the other legs (Fig. 1 E, F). For the most part walking was irregular and smooth forward progression was disrupted. Nevertheless, the infrequent steps by the affected leg usually were coordinated with those of the adjacent ipsilateral legs.More rostral barrier positions elicited smaller perturbations: the blocked leg usually made one step in each step cycle of the other legs (Fig. 1 B, C, D, G). Measurements for these regular step sequences showed quantitatively that protraction duration increased in proportion to the severity of the infringement on normal leg movement (Figs. 3, 4). The fraction of the step period occupied by protraction increased from ca. 10% for normal walking to ca. 50% for caudal barrier positions. This proportionality is interpreted to show the importance of spatial components of the walking program.When one leg was obstructed, its extended protraction influenced the stepping of the three adjacent legs as follows. First, the ipsilateral rostral leg showed the largest change: its protraction onset was regularly delayed for the duration of the extended protraction (Figs. 4, 7, 8), demonstrating a strong, centrally mediated inhibition. The presence of a further delay of up to 100 to 140 ms suggests that peripheral input from the protracting leg may be important for releasing this inhibition. Second, steps by an adjacent caudal leg were not measurably affected. However, the method may not have sufficed to reveal such effects because during regular walking middle leg protractions rarely lasted long enough to conflict with subsequent steps by the ipsilateral rear leg. Third, contralateral effects differed between middle and rear leg obstructions. If the obstructed leg was a middle leg, its extended protraction had little effect upon stepping by the contralateral middle leg: the latter leg frequently protracted while the blocked leg continued its protraction and there was no consistent change in the phase relation of these two legs (Table 1). In contrast, if the obstructed leg was a rear leg, protractions by the contralateral rear leg tended to be delayed (Table 1).     

Mechanism of gating of T-type calcium channels

We have analyzed the gating kinetics of T-type Ca channels in 3T3 fibroblasts. Our results show that channel closing, inactivation, and recovery from inactivation each include a voltage-independent step which becomes rate limiting at extreme potentials. The data require a cyclic model with a minimum of two closed, one open, and two inactivated states. Such a model can produce good fits to our data even if the transitions between closed states are the only voltage-dependent steps in the activating pathway leading from closed to inactivated states. Our analysis suggests that the channel inactivation step, as well as the direct opening and closing transitions, are not intrinsically voltage sensitive. Single-channel recordings are consistent with this scheme. As expected, each channel produces a single burst per opening and then inactivates. Comparison of the kinetics of T-type Ca current in fibroblasts and neuronal cells reveals significant differences which suggest that different subtypes of T-type Ca channels are expressed differentially in a tissue specific manner.     

Coordination of legs during straight walking and turning in Drosophila melanogaster

Leg coordination of Drosophila melanogaster was studied using frame-by-frame film analysis. 1. For fastest walking alternating tripod coordination is observed which slightly deviates towards tetrapody as a function of step period. During acceleration or deceleration legs may transiently recover in diagonal pairs. 2. Mean step length increases with step frequency. 3. Mean recovery stroke duration increases with step period and plateaus beyond a period of about 110 ms. Middle legs recover significantly faster than others. 4. Ipsilateral footprints are transversally separated. 5. Walking is usually initiated in tripod coordination (frequently in combination with a turn), otherwise in an accelerating sequence which rapidly shifts towards tripod pattern. Flies can stop abruptly or decelerate over about one metachronal wave. 6. Short interruptions in walking are observed. Legs interrupted during swing phase stay lifted and finish recovery thereafter. 7. Slight changes in walking direction are obtained by altering step lengths only. Tight turns are composed of two or three phases with backward, zero and forward translatory components. In fast turning tripod coordination is maintained. Otherwise body sides can decouple widely. In all turns numbers of contralateral metachronal waves were equal. Results are compared to those for other walking insects and their relevance in screens for locomotor mutants is discussed.     

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.     

A STRUCTURAL AND FUNCTIONAL STUDY OF THE COORDINATED REACTIONS OF INDIVIDUAL COMMELINA COMMUNIS L. STOMATA (COMMELINACEAE)

Opening and closure movements of individual stomata were analyzed by light microscopy, scanning electron microscopy, and time-lapse photomicrography. Turgor-pressure-induced changes in pore shape of Commelina communis L. stomata were observed in vivo and in fixed material. The ventral wall of the guard cells undergoes three-dimensional alterations during opening and closing. Stomatal aperture increases with increase in light intensity and with decrease in CO₂ concentration as previously described, while reactions to relative humidity and anaerobiosis are somewhat divergent from common experience. Low humidity induces opening rather than closure of stomata in well watered greenhouse plants, and lack of oxygen induces consecutive opening and closure movements. Individual stomata characteristically open by three distinct steps: (1) rapid opening; (2) immobility or slow closure; (3) relatively rapid opening. Since the timing of the second step varies for individual stomata, it is obscured by methods that integrate the responses of several stomata. The movements of individual stomata are well synchronized, but active communication between stomata in different areas can not be confirmed.