Oxygen balance for small organisms: an analytical model

An analytical model is developed that describes oxygen transport and oxygen consumption for small biological structures without a circulatory system. Oxygen inside the organism is transported by diffusion alone. Oxygen transfer towards the organism is retarded by a thin static fluid film at the surface of the organism. The thickness of this film models the outward water conditions, which may range from completely stagnant water conditions to so-called well-stirred water conditions. Oxygen consumption is concentration-independent above a specified threshold concentration (regulator behaviour) and is proportional to the oxygen concentration below this threshold (conformer behaviour). The model takes into account shape and size of the organism and predicts the transition from (pure) regulator behaviour to (pure) conformer behaviour, as well as the mean oxygen consumption rate. Thereby the model facilitates a proper analysis of the physical constraints set on shape and size of organisms without an active internal oxygen transport mechanism. This analysis is carried out in some detail for six characteristic shapes (infinite sheet, cylinder and beam; finite cylinder, sphere and block). In a well-stirred external medium, a flattened shape appears to be the most favourable for oxygen supply, while a compact shape (cube) is more favourable if the external medium is nearly stagnant. The theoretical framework is applied to oxygen consumption data of eight teleost embryos. This reveals relative insensitivity to external flow conditions in some species (e.g., winter flounder, herring), while others appear to rely on external stirring for a proper oxygen supply (e.g., largemouth bass). Interestingly, largemouth bass is the only species in our analysis that exhibits ‘fin-fanning’.     

Looking into the water with a facet eye

The apparent velocity and apparent size of objects approaching an animal strongly depend on their size, their position within the visual field and on the path along which they move. It also makes a considerable difference whether both the animal and the objects are in air, or whether the animal looks from one medium into the other, as is the case in animals that live at the water surface. To systematically investigate this situation we calculated apparent velocity and size in the midsagittal plane of approaching objects of flat horizontal, rodlike vertical and spherical shape. We confine our investigation to object movements along straight horizontal and vertical paths and consider the situation for eyes with and without acute zones. The apparent velocity of an approaching object is low in the far field and increases rapidly close to the eye in both air and water. Along horizontal paths and close to the animal it is higher in water than in air. Along vertical paths and close to the animal it is higher in air than in water. Both relationships are exaggerated when there is an acute zone for vertical resolution along the animal's horizon. Boundary curves are calculated along which an approaching object is seen by a linearly increasing number of receptors. The change of apparent size is characterized by the density of these lines. Below the water surface the change of apparent size is similar to that of the apparent velocity. The apparent size of a horizontally elongated object approaching along a horizontal path increases steadily, that of a vertically elongated object along a vertical line initially increases, but can decrease again near the water surface. An acute zone substantially changes the shape and density of these contour lines. The biological consequences of these effects are discussed.     

Behavioral discrimination of water motions caused by moving objects.

We tested whether goldfish, Carassius auratus, discriminate hydrodynamic stimuli caused by moving objects. Blindfolded goldfish responded to a passing object with changes in inter-gill-movement intervals. To learn whether goldfish can discriminate water motions caused by different moving objects we habituated them to a certain object stimulus. If the stimulus was altered, e.g., by altering speed, direction of motion, or size or shape of the object, fish again showed a temporary suspension of breathing when the object passed by. If animals failed to respond to an altered stimulus, we paired this stimulus with a weak electric shock during training. Goldfish discriminated object motion direction. In addition, in two choice experiments goldfish discriminated water motions caused by objects which moved with different speeds (e.g., 5 cm s(-1) versus 6 cm s(-1)), or by objects which differed in size (e.g., 1 cm x 1 cm versus 1.4 cm x 1.4 cm cross section), or shape (e.g., a round versus a triangular object). If object size and/or shape was varied quasi-randomly such that the faster moving object not always caused the greatest water velocities, fish still discriminated object speed.     

Physical constraints on body size in teleost embryos

All members of the subphylum "Vertebrata" display the characteristics of the vertebrate body plan. These characteristics become apparent during the phylotypic period, in which all vertebrate embryos have a similar body shape and internal organization. Phylogenetic constraints probably limit the morphological variation during the phylotypic period. Physical laws, however, also limit growth and morphogenesis in embryos. We investigated to what extent oxygen availability-as a physical constraint-might limit morphological variation during embryonic development. This paper gives an analysis of time-dependent diffusion into spherical embryos without a circulatory system. Equilibrium appeared to settle in about 1.5 min in running water and in about 10min in stagnant water. Hence, steady-state conditions were assumed and expressions for maximum body size were obtained for spherical, cylindrical and sheet-like embryos in running water and spherical embyros in stagnant water. Predictions of the model based on literature data suggest that in running water-both for spherical, cylindrical and sheet-like embryos-diffusion alone suffices to cover the oxygen needs of a teleost embryo in its phylotypic period. The size of carp (Cyprinus carpio) and African catfish (Clarias gariepinus) embryos is very close to the predicted maximum. This suggests that in these species the development of a functional circulatory system is correlated with the onset of oxygen shortage. Oxygen availability is therefore a potentially important physical constraint on embryonic morphology, though in most species the circulatory system becomes functional well in advance of the onset of oxygen shortage and other demands than oxygen delivery (e.g. nutrient distribution, waste disposal, osmoregulation) might require the development of a circulatory system.     

Streamlining of plant patches in streams

1. Plants in shallow streams often grow in well‐defined monospecific patches experiencing a predictable unidirectional flow, though of temporally variable velocity. During maximum patch development in summer we studied: (i) the shape and streamlining of 59 patches of Callitriche cophocarpa, (ii) allometric relationships between canopy size and sediment area colonized by roots (root area) and (iii) fine‐scale flow gradients for a representative patch exposed to a range of velocities to evaluate relationships between patch shape and physical impact. 2. Canopy and root area viewed from above were elongated and streamlined in the flow direction, while uniform vegetative growth in all directions from a single colonizing shoot would have generated a circular form. Canopies were slightly wider in the upstream part than in the gradually tapering part downstream and the maximum height to length ratio averaged 0.25. The canopy and root area of the patches were more elongate and slender in sites with shallow water, where currents accelerate alongside patches and restrict lateral expansion, compared to deeper sites where currents can pass above the canopy. Similarly, the frontal area relative to planform area or root area was significantly lower in shallow water . Canopy shape and indices of streamlining did not change significantly with approach velocity (0.02–0.40 m s^?1), either because canopy shape is not sensitive to approach velocity or summer velocities were too low to induce such changes. 3. Sediment elevation within patches (avg. 4.1 cm) increased significantly with patch length, but did not differ between unstable sand or more stable coarse sediment for the same patch length. Shape of canopy and root area did not change significantly with sediment type. 4. Pressure drag on the canopy as a whole is probably reduced by its rounded front, restricted height and overall slender form with a low frontal area, while the downstream overhanging canopy increases drag compared to an ideal streamlined object. Across a 100‐fold range of root areas from 0.01 to 1 m², the frontal area of the canopy increased 29 times, planform area increased 38 times and volume increased 76 times, suggesting a trade‐off between physical impact of flow, light interception and anchoring strength. 5. The canopy was compressed at high approach velocities, with low current velocity within the canopy while steep velocity gradients developed across the exposed outer surfaces as the diverted flow accelerated. Because drag processes are additive, and exist at different spatial scales and Reynolds numbers on the surface and inside of plant canopies, direct measurements on entire canopies under controlled conditions are needed to test the functional importance of their shape, size and porosity to flow.     

Diffusivity in a marine macrophyte canopy: implications for submarine pollination and dispersal

The dispersion and capture of differently shaped particles within a Zostera marina L. (eelgrass; Zosteraceae) bed were examined to understand submarine pollination and other dispersals. During periods of moderate flow in the canopy, the capture rate of "spherical" (the shape of ancestral pollen) and "filamentous" (the shape of eelgrass pollen) particles was greater for particles released at the top of the canopy (3.07 and 4.53% × 10(-5) cm(-2) of collector; i.e., percentage of particles captured normalized to collector area) and greater for filamentous than for spherical particles (4.51% × 10(-5) cm(-2) vs. 2.01% × 10(-5) cm(-2)). Estimates of the horizontal P (Joseph-Sendner diffusion velocity) and the vertical diffusivity (Gaussian K) of filamentous particles were small (P ≈ 4 × 10(-4) m/s; K ≈ 10(-4) m(2)/s) compared to theoretical values that do not consider plant canopies. These findings support the concept that eelgrass canopies modify the fluid dynamics (i.e., reduced turbulent mixing) within their canopies. These results indicate that 1000-10?000 Z. marina pollen are required to pollinate a single flower. Similarly, it was estimated that under some conditions, the probability of particle impaction on eelgrass vegetation approaches certainty. These results provide insight into the evolution of filamentous pollen and submarine pollination, as well as dispersal and other mass transport phenomena within macrophyte canopies.     

Creating Objects and Object Categories for Studying Perception and Perceptual Learning

In order to quantitatively study object perception, be it perception by biological systems or by machines, one needs to create objects and object categories with precisely definable, preferably naturalistic, properties¹. Furthermore, for studies on perceptual learning, it is useful to create novel objects and object categories (or object classes) with such properties².Many innovative and useful methods currently exist for creating novel objects and object categories^3-6 (also see refs. 7,8). However, generally speaking, the existing methods have three broad types of shortcomings.First, shape variations are generally imposed by the experimenter^5,9,10, and may therefore be different from the variability in natural categories, and optimized for a particular recognition algorithm. It would be desirable to have the variations arise independently of the externally imposed constraints.Second, the existing methods have difficulty capturing the shape complexity of natural objects^11-13. If the goal is to study natural object perception, it is desirable for objects and object categories to be naturalistic, so as to avoid possible confounds and special cases.Third, it is generally hard to quantitatively measure the available information in the stimuli created by conventional methods. It would be desirable to create objects and object categories where the available information can be precisely measured and, where necessary, systematically manipulated (or ''tuned''). This allows one to formulate the underlying object recognition tasks in quantitative terms.Here we describe a set of algorithms, or methods, that meet all three of the above criteria. Virtual morphogenesis (VM) creates novel, naturalistic virtual 3-D objects called ''digital embryos'' by simulating the biological process of embryogenesis¹⁴. Virtual phylogenesis (VP) creates novel, naturalistic object categories by simulating the evolutionary process of natural selection^9,12,13. Objects and object categories created by these simulations can be further manipulated by various morphing methods to generate systematic variations of shape characteristics^15,16. The VP and morphing methods can also be applied, in principle, to novel virtual objects other than digital embryos, or to virtual versions of real-world objects^9,13. Virtual objects created in this fashion can be rendered as visual images using a conventional graphical toolkit, with desired manipulations of surface texture, illumination, size, viewpoint and background. The virtual objects can also be ''printed'' as haptic objects using a conventional 3-D prototyper.We also describe some implementations of these computational algorithms to help illustrate the potential utility of the algorithms. It is important to distinguish the algorithms from their implementations. The implementations are demonstrations offered solely as a ''proof of principle'' of the underlying algorithms. It is important to note that, in general, an implementation of a computational algorithm often has limitations that the algorithm itself does not have.Together, these methods represent a set of powerful and flexible tools for studying object recognition and perceptual learning by biological and computational systems alike. With appropriate extensions, these methods may also prove useful in the study of morphogenesis and phylogenesis.     

Effects of convective transport on chemical signal propagation in epithelia

We study effects of convective transport on a chemical front wave representing a signal propagation at a simple (single layer) epithelium by means of mathematical modeling. Plug flow and laminar flow regimes were considered. We observed a nonmonotonous dependence of the propagation velocity on the ligand receptor binding constant under influence of the convective transport. If the signal propagates downstream, the region of high velocities becomes much broader and spreads over several orders of magnitude of the binding constant. When the convective transport is oriented against the propagating signal, either velocity of the traveling front wave is slowed down or the traveling front wave can stop or reverse the direction of propagation. More importantly, chemical signal in epithelial systems influenced by the convective transport can propagate almost independently of the ligand-receptor binding constant in a broad range of this parameter. Furthermore, we found that the effects of the convective transport becomes more significant in systems where either the characteristic dimension of the extracellular space is larger/comparable with the spatial extent of the ligand diffusion trafficking or the ligand-receptor binding/ligand diffusion rate ratio is high.     

The spherical deformation model

Miller et al. (1994) describe a model for representing spatial objects with no obvious landmarks. Each object is represented by a global translation and a normal deformation of a sphere. The normal deformation is defined via the orthonormal spherical-harmonic basis. In this paper we analyse the spherical deformation model in detail and describe how it may be used to summarize the shape of star-shaped three-dimensional objects with few parameters. It is of interest to make statistical inference about the three-dimensional shape parameters from continuous observations of the surface and from a single central section of the object. We use maximum-likelihood-based inference for this purpose and demonstrate the suggested methods on real data.     

Environmental influences on the development of the cardiac system in fish and amphibians

In poikilothermic animals body temperature varies with environmental temperature, and this results in a change in metabolic activity (Q10 of enzymatic reactions typically is around 2-3). Temperature changes also modify gas transport in body fluids. While the diffusion coefficient increases with increasing temperatures, physical solubility and also hemoglobin oxygen affinity decrease. Therefore, an increase in temperature typically requires adjustments in cardiac activity because ventilatory and convectional transport of respiratory gases usually are tightly coupled in adults in order to meet the oxygen demand of body tissues. Hypoxic conditions also provoke adaptations in the central circulatory system, like the hypoxic bradycardia, which has been described for many adult lower vertebrates, combined with an increase in stroke volume and peripheral resistance. In embryos and larvae the situation is much more complicated, because nervous control of the heart is established only late during development, and because the site of gas exchange changes from mainly cutaneous gas exchange during early development to mainly pulmonary or branchial gas exchange in late stages. In addition, recent studies in amphibian and fish embryos and larvae reveal, that at least in very early stages convectional gas transport of the hemoglobin is not essential, which means that in these early stages ventilatory and convectional gas transport are not yet coupled. Accordingly, in early stages of fish and amphibians the central cardiac system often does not respond to hypoxia, although in some species behavioral adaptations indicate that oxygen sensors are functional. If a depression of cardiac activity is observed, it most likely is a direct effect of oxygen deficiency on the cardiac myocytes. Regulated cardiovascular responses to hypoxia appear only in late stages and are similar to those found in adult species.     

Water transport through carbon nanotubes with defects

Non-equilibrium molecular dynamics simulations are performed to investigate how changing the number of structural defects in the wall of a (7,7) single-walled carbon nanotube (CNT) affects water transport and internal fluid dynamics. Structural defects are modelled as vacancy sites (missing carbon atoms). We find that, while fluid flow rates exceed continuum expectations, increasing numbers of defects lead to significant reductions in fluid velocity and mass flow rate. The inclusion of such defects causes a reduction in the water density inside the nanotubes and disrupts the nearly frictionless water transport commonly attributed to CNTs.     

Morphological models of radiate accretive growth and the influence of hydrodynamics

In many marine sessile organisms (for example sponges and stony corals) the skeleton is formed by an accretive growth process, where layers of material are secreted on top of each other in a surface normal deposition process. In many of these organisms the growth process exhibits a strong morphological plasticity due to differences in exposure to water movement. In general, many of these organisms tend to form thin-branching growth forms under sheltered conditions, while the growth form gradually transforms into a more compact shape when the exposure of water movement increases. In this paper, we investigate this phenomenon by combining a three-dimensional simulation model of radiate accretive growth driven by the local availability of simulated food particles and a model, based on the lattice Boltzmann method, for simulating food particle distributions caused by a combination of flow and diffusion. In the simulations two different models of a suspension feeder with accretive growth were compared. In the first model, the deposition process is exclusively driven by the local availability of food particles, in the second model the deposition process was determined by the combination of local amount of contact to the environment and availability of food particles. In the simulations it was found that hydrodynamics has a strong impact on the overall morphologies which develop in the accretive growth process. In the model exclusively driven by the local availability of food particles, column-shaped objects emerged under diffusion conditions, while more spherical and lobed object were found for the flow-dominated case. In the simulations, the Péclet number was varied independently from the Reynolds number, which was kept at a relatively low constant value. In a range of increasing Péclet numbers, indicating an increasing influence of hydrodynamics, the simulated morphologies gradually transformed from thin-branching ones into more spherical and compact morphologies in the model where deposition was controlled by the local availability of food particles and the local amount of contact with the environment.     

Pore‐network modeling of biofilm evolution in porous media

The influence of bacterial biomass on hydraulic properties of porous media (bioclogging) has been explored as a viable means for optimizing subsurface bioremediation and microbial enhanced oil recovery. In this study, we present a pore network simulator for modeling biofilm evolution in porous media including hydrodynamics and nutrient transport based on coupling of advection transport with Fickian diffusion and a reaction term to account for nutrient consumption. Biofilm has non‐zero permeability permitting liquid flow and transport through the biofilm itself. To handle simultaneous mass transfer in both liquid and biofilm in a pore element, a dual‐diffusion mass transfer model is introduced. The influence of nutrient limitation on predicted results is explored. Nutrient concentration in the network is affected by diffusion coefficient for nutrient transfer across biofilm (compared to water/water diffusion coefficient) under advection dominated transport, represented by mass transport Péclet number >1. The model correctly predicts a dependence of rate of biomass accumulation on inlet concentration. Poor network connectivity shows a significantly large reduction of permeability, for a small biomass pore volume. Biotechnol. Bioeng. 2011;108: 2413–2423. © 2011 Wiley Periodicals, Inc.     

ISOLATION AND CHARACTERIZATION OF A PARTICULATE CELL-AGGREGATION FACTOR FROM SEA URCHIN EMBRYOS*

A particulate factor promoting an aggregation of dissociated embryonic cells was isolated from sea urchin embryos. It was isolated from the supernatant of dissociated embryos with artificial sea water devoid of divalent cations. The factor is a spherical particle in shape and consists of mucopolysaccharide-protein complex rich in acidic groups.     

The contractility of elongated microvilli in early sea urchin embryos

Summary Elongated microvilli attach the early sea urchin embryo to the fertilization envelope and support it in a concentric position within the perivitelline space. The contractility of the elongated microvilli was demonstrated in several ways. (1) During normal cleavage, these microvilli change their length to adapt to the change in shape and numbers of blastomeres. (2) When treated with calcium-free sea water, embryos become eccentrically located and the microvilli extend further than normal on one side; when returned to normal sea water, the embryos become centered again. (3) Several agents cause the fertilization envelope to become higher and thinner than normal and the elongated microvilli to extend correspondingly if treated within ten min after fertilization. In some cases, both elongated microvilli and fertilization envelope return to normal size when returned to normal sea water. (4) Fertilization in a papain solution causes the elongated microvilli and the fertilization envelope to contract to the surface of the embryo. (5) Refertilization after the papain-induced contraction can bring about the elongation of these microvilli and the elevation of the fertilization envelope a second time. It was also shown that elongated microvilli are extended immediately upon fertilization, at the same time as the short microvilli. The firm adherence of the tips of elongated microvilli to the fertilization envelope by means of extracellular matrix fibers is shown in a high voltage electron microscope stereoimage. This allows us to understand why it is that when the elongated microvilli extend or contract, the fertilization envelope also extends and contracts accordingly.     

Binocular information in the control of prehensile movements in multiple-object scenes

Recent evidence suggests that the visual control of prehension may be less dependent on binocular information than has previously been thought. Studies investigating this question, however, have generally only examined reaches to single objects presented in isolation, even though natural prehensile movements are typically directed at objects in cluttered scenes which contain many objects. The present study was designed, therefore, to assess the contribution of binocular information to the control of prehensile movements in multiple-object scenes. Subjects reached for and grasped objects presented either in isolation or in the presence of one, two or four additional 'flanking' objects, under binocular and monocular viewing conditions. So that the role of binocular information could be clearly determined, subjects made reaches both in the absence of a visible scene around the target objects (self-illuminated objects presented in the dark) and under normal ambient lighting conditions. Analysis of kinematic parameters indicated that the removal of binocular information did not significantly affect many of the major indices of the transport component, including peak wrist velocity. However, peak grip apertures increased and subjects spent more time in the final slow phase of movement, prior to grasping the object, during monocularly guided reaches. The dissociation between effects of binocular versus monocular viewing on transport and grasp parameters was observed irrespective of the presence of flanking objects. These results therefore further question the view that binocular vision is pre-eminent in the control of natural prehensile movements.     

Wind-induced ventilation of the burrow of the prairie-dog,Cynomys ludovicianus

Summary Where a fluid flows across a surface, such as wind over the earth, the velocity gradient created provides a potential source of work. This gradient might be employed by one burrowing animal to induce air-flow in its long, narrow burrow. The burrow of the black-tailed prairie-dog constitutes a respiratory dead-space of extraordinary magnitude in which diffusion appears inadequate for gas exchange. But the burrow is arranged in a manner appropriate for wind-induced ventilation, typically with two openings at opposite ends and with mounds surrounding these openings of two forms (Fig. 3), with one form on each end. When a breeze crosses the mounds, air enters the burrow through the lower mound and leaves through the higher. The same unidirectional flow is evident with scale models of real mounds on a model burrow in a wind tunnel; flow inside the burrow is nearly a linear function of flow across the mounds (Fig. 4). Wind-induced ventilation in the model burrow could also be induced with model mounds differing in shape but not height. Mounds with sharp rims were more effective exits for air than mounds with rounded tops; in nature such shape differences complement the differences in height. This study was supported by the Duke University Research Council, NIH Biomedical Sciences Support Grant K-01-GM-1222, and NIH Research Grant HL-02228. We thank Knut Schmidt-Nielsen, William Bretz, and Marvin Bernstein for useful advice, Carl Mills for the use of a flow meter, Vance Tucker for the use of the wind tunnel, and LeRoy Smith for assistance in the field.     

The effects of simple objects on the electric field of Apteronotus

How might electric fish determine, from patterns of transdermal voltage changes, the size, shape, location, and impedance of a nearby object? I have investigated this question by measuring and simulating electric images of spheres and ellipsoids near an Apteronotus leptorhynchus. Previous studies have shown that this fish's electric field magnitude, and perturbations of the field due to objects, are complicated nonliner functions of distance from the fish. These functions become much simpler when distance is measured from the axes of symmetry of the fish and the object, instead of their respective edges. My analysis suggests the following characteristics of high frequency electric sense and electric images. 1. The shape of electric images on the fish's body is relatively independent of a spherical object's radius, conductivity, and rostrocaudal location. 2. An image's relative width increases linearly with lateral distance, and might therefore unambiguously encode object distance. 3. Only objects with very large dielectric constants cause appreciable phase shifts, and the degree of shift depends strongly on water conductivity. 4. Several parameters, such as the range of electric sense, may depend on the rostrocaudal location of an object. Large objects may be detectable further from the head than the tail, and conversely, small objects may be detectable further from the tail than head. 5. Asymmetrical objects produce different electric images, correlated with their cross-sections, for different orientations and phases of the electric field. 6. The steep attenuation with distance of the field magnitude causes spatial distortions in electric images, somewhat analogous to the perspective distortion inherent in wide angle optical lenses.     

Morphological studies of different mitochondrial populations in monkey myocardial cells

Summary The ultrastructure of mitochondria in monkey myocardial cells was investigated by scanning electron microscopy, thin sections and freeze-fracturing. Mitochondria with well-developed cristae were distributed around the nucleus, between the myofibrils and beneath the sarcolemma. Those clustered near the the poles of the nucleus were generally spherical in shape. Interfibrillar mitochondia were arranged in longitudinal rows between the myofibrils, were elongated and usually about the same length as a sarcomere. Subsarcolemmal mitochondria varied in size and shape, being rod-like, spherical, polygonal or horseshoe-like. There were usually two profiles of subsarcolemmal mitochondria in each section of sarcomere, although sometimes one or three occurred, and they were typically oriented perpendicularly to the myofibrils. These morphological differences among mitochondria could reflect functional and/or mechanical properties in the various cellular locations.