Further Evidence for the Relative Immobility of Water in Sieve Tubes of Willow

Gradients of tritiated water, ³⁵S-sulphate and ³²P-phosphate, were established in isolated segments of willow stems. Sieve tube exudate was collected as honeydew from the high activity end of the segment. After girdling the stem a few centimetres from the site of sieve tube puncture, the specific activity of ³⁵S and ³²P in the honeydew rose, whilst the specific activity of tritium remained constant. These findings indicate that prior to girdling, unlabelled sulphates and phosphates were contributing to the honeydew, whilst there had been no detectable contribution by unlabelled water from the low activity end of the segment. The data support the conclusions drawn from previous experiments by Peel et al. (1969), that water is relatively immobile in sieve tubes of willow when compared to solutes.     

Evidence for a Flow of Water into Sieve Tubes Associated with Phloem Loading

Evidence that there is a lateral water flow associated withthe loading of sieve tubes is presented. The change in phloemtransport dynamics, measured using ¹¹C, induced by leaf anoxiais shown to be consistent with a reduction in lateral waterflow brought about by a decline in sucrose loading. The temporalprofiles of tracer activity are used to derive a simple holisticmodel of the phloem pathway which is able to account for theobserved dynamics.     

Studies on the Movement of Solutes between the Sieve Tubes and Surrounding Tissues3: I. INTERFERENCE BETWEEN SOLUTES AND RATE OF TRANSLOCATION MEASUREMENTS

Certain aspects of the secretion of solutes into, and removalfrom, the sieve tubes of isolated stem segments and rooted cuttingsof Salix viminalis have been studied. Sieve-tube sap was obtainedeither as honeydew from whole individuals or via the severedstylets of the aphid Tuberolachnus salignus (Gmelin). It was shown that interference occurred between the chemicallyunrelated solutes, sucrose and the cations potassium and rubidium.On raising the potassium concentration in the sieve-tube sapby passing a solution of this ion through the xylem, the sucroseconcentration declined. When the sucrose concentration fellover a period of days due to respiratory loss of carbohydratesfrom an isolated stem segment, a concomitant rise in eitherthe potassium or rubidium level in the sap occurred. When a solution of sodium was passed through the xylem, theconcentration of this ion in the sieve-tube sap rose, whilstthat of potassium fell at first, but later rose higher thanits initial value, indicating that both antagonism and synergycan occur between these ions. On introducing both these cationsinto the xylem simultaneously, more sodium than potassium wastaken up by the segment, though the increase in the sodium concentrationin the sieve-tube sap was less than that of the potassium. Perfusingthe xylem with a calcium solution had no effect upon the concentrationof potassium in the sieve tube. It has been shown that the rate of translocation of a solutealong the sieve tube, as measured by the two colony technique,depends upon the rate of removal of this solute from the sievetube. The amount of such lateral loss from the sieve tube isrelated to the potential gradient for a solute between the sievetube and surrounding cells.     

Investigation of Bidirectional Movement of Tracers in Sieve Tubes of Salix Viminalis L.

Sieve-tube sap was collected as honeydew from the aphid Tuberolachnussalignus (Gmelin) feeding on a young shoot or a mature stemof willow (Salix viminalis L.). Two radioactive tracers (either³H-glucose and ¹⁴C-sucrose, or ¹⁴CO₂, Na₂ ¹⁴CO₃, and ³²P-orthophosphate)were applied to leaves or to bark abrasions at each end of thestem. In some experiments the tracers were applied after thestart of honeydew production, whilst in others the tracers wereapplied before the aphids were sited. In most cases aphids feeding between the tracer applicationpoints produced doubly-labelled honeydew during a 24–48-hperiod from tracer application. In some instances the firstdrops of honeydew contained one tracer, followed several hourslater by the other tracer, whilst some aphids produced doubly-labelledhoneydew from the first drop. Singly-labelled or inactive honeydewwas found in only a few cases. It was demonstrated that when ³H-glucose and ¹⁴C-sucrose wereapplied at opposite ends of a stem that the tracers moved inopposite directions in the form of sucrose. The data suggest that a simultaneous bidirectional movementof two tracers may occur in the same sieve tube. However, thepossibility that the doubly-labelled honeydew could be producedby lateral movement from one sieve tube carrying one tracerto an adjacent punctured sieve tube carrying the other tracercannot be discounted.     

The Contributory Length of Sieve Tubes in Isolated Segments of Willow, and the Effect on it of Low Temperatures

Using isolated stem segments in which a gradient of ³²P-phosphateactivity had been established, it has been demonstrated thatthe magnitude of the contributory length is much greater thanthe 16 cm previously measured by Weatherley et al. (1959). On cooling a portion of a stem segment between an aphid colonyand the high-activity end of a segment, a pattern of specificactivity changes were observed in collected honeydew which showthat the effect of cooling was to increase the magnitude ofthe contributory length. It is considered that this increaseprovides cogent evidence in favour of the concept that movementof solutes across the lateral wall of the sieve tube is directlyor indirectly dependent upon metabolic energy, whilst the longitudinalmovement down the sieve tube is not so dependent.     

Fine Structure of Sieve Tubes Prepared Mainly for Observation in the Electron Microscope by a Cryogenic Method

Using a cryogenic method of fixation, electron microscopic evidencewas obtained of structures in the sieve element lumina and sieveplate pores of Cucurbita pepo which can be interpreted as constituentsof the transcellular strands repeatedly seen in the light microscope.In longitudinal sections these appeared as more or less hollowtubes with clearly defined filamentous walls which showed someorganized substructure. Transverse and oblique sections revealedcircular or elliptical profiles of boundaries surrounding largelyempty central areas. Owing to the still inadequate preservationof specimens, the centres of the strands contained only sparsecytoplasmic material with an occasional indication of fibrilsin parallel arrangement. Improvement of fixation techniques,with rapid freezing as the preferential method, is seen as themain task in any effort to preserve the in vivo state of thesestructures.     

Growth and Nodulation Responses of Rhizobium meliloti to Water Stress Induced by Permeating and Nonpermeating Solutes

Isolates of Rhizobium meliloti, representing antigenically distinct indigenous serogroups 31 and 17, were grown in yeast extract-mannitol broth (YEM) containing NaCl or polyethylene glycol (PEG) to provide external water potentials ranging from −0.15 to −1.5 MPa. Several differences were found between representatives of the two groups in their abilities to adapt to water stress induced by the nonpermeating solute PEG. At potentials below −0.5 MPa, strain 31 had a lower specific growth rate than strain 17 and an irregular cell morphology. In contrast, neither growth nor cell morphology of either strain was affected significantly over the same range of water potentials created by a permeating solute, NaCl. Despite the superior growth of strain 17 at the low water potentials imposed by PEG, upshock of water-stressed cells (−1.0 MPa; PEG) into normal YEM (−0.15 MPa) resulted in a faster recovery of growth by strain 31 than by strain 17. Different responses of the two strains to a water potential increase were also revealed in nodulation studies. Strain 31 required significantly fewer days to nodulate alfalfa than strain 17 did when the strains were transferred from YEM with PEG at −1.0 MPa onto the roots of alfalfa seedlings in plant growth medium (−0.1 MPa). The addition of supplemental calcium (0.1 mM) to growth medium with PEG (−1.0 MPa) reduced the differences between strains in their responses to water stress. The severe growth restriction and morphological abnormalities shown by strain 31 were corrected, and the prolonged recovery time shown by water-stressed cells (−1.0 MPa; PEG) of strain 17 upon transfer to normal YEM was shortened. The latter strain also nodulated earlier and more rapidly after growth in PEG medium at −1.0 MPa in the presence of supplemental calcium ions. These results indicate that the efficacy of osmoregulation can vary among strains of the same species and that the mechanism of osmoregulation may differ depending on the nature of the water stress.     

The Supply of Water and Solutes by Phloem and Xylem to Growing Fruits of Yucca flaccida Haw

Analyses of successively collected fractions of phloem exudate of Yucca flaccida, and of Yucca fruits picked at various stages of growth, together with experiments on transpiration from fruits, have led to the following conclusions:

• 1 During fruit growth potassium, sodium, magnesium, phosphorus compounds, and nitrogenous substances are delivered to the fruit by both the xylem and the phloem. These solutes move also easily in radial direction between the xylem and phloem part of the vascular bundles. Actually they can be regarded as constituents of one stream of nutrients.
• 2 The overall efficiency of conversion of vascular-fluid dry matter into mature-fruit dry matter is approximately 61 %.
• 3 During its whole period of growth the fruit transpires an amount of water vapour of at least 6 times its own mature fresh weight.
• 4 Estimates could be made for the relative contributions of xylem and phloem in the delivery of fruit constituents. 18% of the water imported by the fruit during its growth had a phloem, 82 % a xylem origin; 89% is transpired, 11 % retained as a fruit constituent. At least 94 % of the dry matter, 69% of the potassium, 56% of the magnesium, 26% of the phosphorus, and 7% of the calcium of the average fruit have been delivered by the phloem. The translocation of nitrogenous substances occurs probably partly in a more indirect way with temporary storage in inflorescence parenchyma.

     

Willow growth in response to nutrients and moisture on a clay landfill cap soil. II: Water use

Water use by willow (Salix viminalis L.) was studied in lysimeters containing clay landfill cap and sandy loam soils under different watering and amendment regimes. With plentiful water and amendments, seasonal ET increased annually and was highest in the sandy loam, increasing from 360 l plant(-1) in the establishment year to almost 1200 l plant(-1) in the third year. Seasonal ET was highly correlated with leaf area duration. Amendment of Oxford clay resulted in increases in plant leaf area, dry matter production and seasonal ET. Water stress reduced seasonal ET by 10-14% in the second year and 25-41% in the third. Water use efficiency was low for the un-amended clay treatment (1.4 g kg(-1)) but was similar in the amended clay (5.0 g kg(-1)) and sandy loam (4.9 g kg(-1)). This highlights the interdependence of water use and biomass production in willow.     

Biology and Structure of Phytomonas staheli sp. n., a Trypanosomatid Located in Sieve Tubes of Coconut and Oil Palms

SYNOPSIS. Phytomonas staheli sp. n. is described from the oil palm ( Elaeis guineensis ) and the coconut palm ( Cocos nucifera ) of Surinam, South America. The phytomonad is the probable cause of Hartrot in the coconut palm and Marchitez sopresiva in oil palms. Parasites are confined to the sieve tubes in palms. Some success was obtained at cultivation of the organism from Elaeis.     

Comparison of Cadmium Effect on Willow and Poplar in Response to Different Cultivation Conditions

Salix alba L. and Populus×euroamericana cv. Robusta cuttings were grown in 10 μM Cd(NO₃)₂ (direct treatment) or in Knop solution and afterwards in Cd(NO₃)₂ (indirect treatment). Cd impact on rooting of directly treated plants and its impact on normally formed roots and shoots of indirectly treated plants were studied. The cumulative length, number and biomass of willow roots, pigment and starch contents, leaf net photosynthetic rate and dry mass/leaf area ratio of willow leaves were positively influenced by indirect treatment. However, indirectly treated poplars were more sensitive to Cd than directly treated ones. Indirect treatment lowered root Cd uptake in willow, Cd accumulation in cuttings of both species and Cd accumulation in poplar shoots. Cd-caused structural changes were similar in both species and in both treatments. Root apices, rhizodermis and cortex were the most seriously damaged root parts. In directly treated willow, the structure of central cylinder (0.5 – 1 cm from apex) remained unchanged in contrast to indirectly treated plants. Formation of cambium close to the apex indicated shortening of root elongation zone of indirectly treated plants. Directly Cd-treated poplar roots exhibited unusual defence activity of root apical meristem and accumulation of darkly stained material around central cylinder. This revised version was published online in July 2006 with corrections to the Cover Date.     

Movement of Abscisic Acid into the Apoplast in Response to Water Stress in Xanthium strumarium L

The effect of water stress on the redistribution of abcisic acid (ABA) in mature leaves of Xanthium strumarium L. was investigated using a pressure dehydration technique. In both turgid and stressed leaves, the ABA in the xylem exudate, the `apoplastic' ABA, increased before `bulk leaf' stress-induced ABA accumulation began. In the initially turgid leaves, the ABA level remained constant in both the apoplast and the leaf as a whole until wilting symptoms appeared. Following turgor loss, sufficient quantities of ABA moved into the apoplast to stimulate stomatal closure. Thus, the initial increase of apoplastic ABA may be relevant to the rapid stomatal closure seen in stressed leaves before their bulk leaf ABA levels rise.

Following recovery from water stress, elevated levels of ABA remained in the apoplast after the bulk leaf contents had returned to their prestress values. This apoplastic ABA may retard stomatal reopening during the initial recovery period.

     

Response of Organ Structure and Physiology to Autotetraploidization in Early Development of Energy Willow Salix viminalis

The biomass productivity of the energy willow Salix viminalis as a short-rotation woody crop depends on organ structure and functions that are under the control of genome size. Colchicine treatment of axillary buds resulted in a set of autotetraploid S. viminalis var. Energo genotypes (polyploid Energo [PP-E]; 2n = 4x = 76) with variation in the green pixel-based shoot surface area. In cases where increased shoot biomass was observed, it was primarily derived from larger leaf size and wider stem diameter. Autotetraploidy slowed primary growth and increased shoot diameter (a parameter of secondary growth). The duplicated genome size enlarged bark and wood layers in twigs sampled in the field. The PP-E plants developed wider leaves with thicker midrib and enlarged palisade parenchyma cells. Autotetraploid leaves contained significantly increased amounts of active gibberellins, cytokinins, salicylic acid, and jasmonate compared with diploid individuals. Greater net photosynthetic CO₂ uptake was detected in leaves of PP-E plants with increased chlorophyll and carotenoid contents. Improved photosynthetic functions in tetraploids were also shown by more efficient electron transport rates of photosystems I and II. Autotetraploidization increased the biomass of the root system of PP-E plants relative to diploids. Sections of tetraploid roots showed thickening with enlarged cortex cells. Elevated amounts of indole acetic acid, active cytokinins, active gibberellin, and salicylic acid were detected in the root tips of these plants. The presented variation in traits of tetraploid willow genotypes provides a basis to use autopolyploidization as a chromosome engineering technique to alter the organ development of energy plants in order to improve biomass productivity.Energy security and climate change as global problems urge increased efforts to use plants as renewable energy sources both for power generation and transportation fuel production. Selected wood species, such as willows (Salix spp.), can be cultivated as short-rotation coppice for the rapid accumulation of biomass and reduction of CO₂ emission. Coppicing reinvigorates shoot growth, resulting in a special woody plant life cycle that differs from natural tree development, which takes decades. In this cultivation system, small stem cuttings are planted at high densities (15,000–25,000 ha⁻¹). In the soil, these dormant wood cuttings first produce roots and shoots that emerge from reactivated buds. During the first year, the growing shoots mature to woody stems. In the winter, these stems are cut back, and in the following spring, the cut stumps develop multiple shoots. The short-rotation coppice plantations are characterized by a very short, 2- to 3-year rotation, and the most productive varieties can produce up to 15 tons of oven-dried wood per hectare per year (Cunniff and Cerasuolo, 2011). The high-density willow plantations can also be efficiently used for heavy metal or organic phytoremediation, as reviewed by Marmiroli et al. (2011).The biomass productivity of shrub willows is largely dependent on coppicing capability, early vigorous growth, shoot growth rate and final stem height, root system size, photosynthetic efficiency, formation and composition of woody stems, water and nutrient use, as well as abiotic and biotic stress tolerance. Genetic improvement of all these traits can be based on broad natural genetic resources represented by more than 400 species in the genus Salix. More than 200 species have hybrid origins, and ploidy levels vary from diploid up to dodecaploid (Suda and Argus, 1968; Newsholme, 1992). In addition to molecular marker-assisted clone selection, intraspecific and interspecific crosses have been shown to further extend genetic variability in breeding programs for biomass yield (Karp et al., 2011).During natural diversification and artificial crossings of Salix spp., the willow genomes frequently undergo polyploidization, resulting in triploid or tetraploid allopolyploids. In triploid hybrids, both heterosis and ploidy can contribute to the improved biomass yield (Serapiglia et al., 2014). While the alloploid triploids have attracted considerable attention in willow improvement, the potentials of autotetraploid willow genotypes have not been exploited so far. As shown for other short-rotation wood species (poplar [Populus spp.], black locust [Robinia pseudoacacia], Paulownia spp., and birch [Betula spp.]), doubling the chromosome set by colchicine treatment can cause significant changes in organ morphology or growth parameters (Tang et al., 2010; Cai and Kang, 2011; Harbard et al., 2012; Mu et al., 2012; Wang et al., 2013a, 2013b). In several polyploidization protocols, the in vitro cultured tissues are exposed to different doses of colchicine or other inhibitors of mitotic microtubule function, and plantlets are differentiated from polyploid somatic cells (Tang et al., 2010; Cai and Kang, 2011). Alternatively, seeds or apical meristems of germinating seedlings can be treated with a colchicine solution (Harbard et al., 2012). Allotetraploids of poplar were produced by zygotic chromosome doubling that was induced by colchicine and high-temperature treatment (Wang et al., 2013a).Since tetraploid willow plants with 2n = 4x = 76 chromosomes are expected to represent novel genetic variability, especially for organ development and physiological parameters, a polyploidization project was initiated that was based on a highly productive diploid energy willow (S. viminalis var. Energo). Colchicine treatment of reactivated axillary buds of the in vitro-grown energy willow plantlets resulted in autotetraploid shoots and, subsequently, plants. For comparison of diploid and tetraploid variants of willow plants, digital imaging of green organs and roots was used for phenotyping. Among the tetraploid lines, genotypes were identified with improved biomass production, better photosynthetic parameters, and altered organ structure and hormone composition. The new tetraploid willow variants produced can serve as a unique experimental material to uncover key factors in biomass production in this short-rotation energy plant. In the future, these plants can also serve as crossing partners of diploid lines for the production of novel triploid energy willow genotypes.     

Response of the Succulent Leaves of Peperomia magnoliaefolia to Dehydration: Water Relations and Solute Movement in Chlorenchyma and Hydrenchyma

Relative water content, solute concentrations, and osmolality were determined in the water storage tissue (hydrenchyma) and the assimilatory tissue (chlorenchyma) of the succulent leaves of Peperomia magnoliaefolia (Jac) (Piperaceae) during slow desiccation. Relative water loss was significantly greater for the hydrenchyma than for the chlorenchyma. When whole leaves had lost 50% of their initial water content, the concomitant decrease of the relative water content of the hydrenchyma was 75 to 85%, but of the chlorenchyma only 15 to 25%. In spite of this differential water loss, the osmolality in both tissues increased to the same extent, indicating solute flow from the hydrenchyma to the chlorenchyma during desiccation. Solute translocation appeared to be unspecific, probably reflecting symplastic mass flow from one tissue to the other. The observed volume preservation of the chlorenchyma stabilized photosynthesis of Peperomia magnoliaefolia (Jac) leaves, which was less inhibited by a given decrease of the relative water content of the whole leaves than in nonsucculent leaves.     

Intracellular Solutes,Photosynthesis and Respiration of the Green Alga Blidingia minima in Response to Salinity Stress

The effects of different salinities ranging from 7–68‰ on the internal inorganic and organic solute concentrations, and on the photosynthesis and respiration have been investigated in the green alga Bladingia minima (Näg. ex Kütz.) Kylin. The levels of the main osmotic solutes K⁺, sucrose and proline increased with increasing salinities and vice versa, while Na⁺, Mg²⁺, Cl^? and PO^3–₄ played a minor role in the osmotic acclimation. In contrast to related Enteromorpha species, B. minima exhibited high NO^?₃ concentrations, which decreased under hypo- and hypersaline conditions. B. minima differs also from Enteromorpha by accumulating the tertiary sulphonium compound DMSP in osmotically significant amounts under gentle hypersaline conditions. B. minima revealed typical characteristics of a “sun-plant” having a high light compensation point together with a saturation of photosynthesis at high photon flux densities. The alga showed a broad photosynthetic stability under osmotic stress; only with extreme hypersaline conditions was photosynthesis partly inhibited. The rate of respiration remained constant in hypersaline media, and was stimulated under hyposaline conditions.     

Transport of Water and Solutes across Maize Roots Modified by Puncturing the Endodermis (Further Evidence for the Composite Transport Model of the Root)

The effects of puncturing the endodermis of young maize roots (Zea mays L.) on their transport properties were measured using the root pressure probe. Small holes with a diameter of 18 to 60 [mu]m were created 70 to 90 mm from the tips of the roots by pushing fine glass tubes radially into them. Such wounds injured about 10-2 to 10-3% of the total surface area of the endodermis, which, in these hydroponically grown roots, had developed a Casparian band but no suberin lamellae. The small injury to the endodermis caused the original root pressure, which varied from 0.08 to 0.19 MPa, to decrease rapidly (half-time = 10-100 s) and substantially to a new steady-state value between 0.02 and 0.07 MPa. The radial hydraulic conductivity (Lpr) of control (uninjured) roots determined using hydrostatic pressure gradients as driving forces was larger by a factor of 10 than that determined using osmotic gradients (averages: Lpr [hydrostatic] = 2.7 x 10-7 m s-1 MPa-1; Lpr [osmotic] = 2.2 x 10-8 m s-1 MPa-1; osmotic solute: NaCl). Puncturing the endodermis did not result in measurable increases in hydraulic conductivities measured by either method. Thus, the endodermis was not rate-limiting root Lpr: apparently the hydraulic resistance of roots was more evenly distributed over the entire root tissue. However, puncturing the endodermis did substantially change the reflection ([sigma]sr) and permeability (Psr) coefficients of roots for NaCl, indicating that the endodermis represented a considerable barrier to the flow of nutrient ions. Values of [sigma]sr decreased from 0.64 to 0.41 (average) and Psr increased by a factor of 2.6, i.e. from 3.8 x 10-9 to 10.1 x 10.-9 m s-1(average). The roots recovered from puncturing after a time and regained root pressure. Measurable increases in root pressure became apparent as soon as 0.5 to 1 h after puncturing, and original or higher root pressures were attained 1.5 to 20 h after injury. However, after recovery roots often did not maintain a stable root pressure, and no further osmotic experiments could be performed with them. The Casparian band of the endodermis is discontinuous at the root tip, where the endodermis has not yet matured, and at sites of developing lateral roots. Measurements of the cross-sectional area of the apoplasmic bypass at the root tip yielded an area of 0.031% of the total surface area of the endodermis. An additional 0.049% was associated with lateral root primordia. These areas are larger than the artificial bypasses created by wounding in this study and may provide pathways for a "natural bypass flow" of water and solutes across the intact root. If there were such a pathway, either in these areas or across the Casparian band itself, roots would have to be treated as a system composed of two parallel pathways (a cell-to-cell and an apoplasmic path). It is demonstrated that this "composite transport model of the root" allows integration of several transport properties of roots that are otherwise difficult to understand, namely (a) the differences between osmotic and hydrostatic water flow, (b) the dependence of root hydraulic resistance on the driving force or water flow across the root, and (c) low reflection coefficients of roots.     

Movement of Cicindela hirticollis Say Larvae in Response to Moisture and Flooding

The larvae of the tiger beetle, Cicindela hirticollis Say, inhabit sandy shoreline areas that flood periodically. This species has declined over much of its range and at least one subspecies is near extinction, possibly as a result of human alteration of waterways. In addition to physiological tolerance for anoxia, the larvae have physical and behavioral adaptations to avoid drowning. We hypothesized that C. hirticollis larvae would exhibit behavioral responses to soil moisture change and flooding because, unlike most other tiger beetles, they frequently relocate their burrows. Our laboratory studies demonstrated that larvae select surface soil moisture levels of 7–50% saturation in which to dig new burrows. Within 96 h of immersion, most larvae abandon burrows and larvae do not form new burrows in darkness. Larvae may relocate when flooded, suggesting a previously undocumented mechanism for dispersal; however, dams often eliminate suitable habitat areas downstream, suggesting that this behavior may be detrimental in riverine populations. Because larvae move during daylight hours, they also are likely to suffer mortality from trampling due to human recreational activity.     

Scaling of myocardial mass to flow and morphometry of coronary arteries.

There is no doubt that scaling relations exist between myocardial mass and morphometry of coronary vasculature. The purpose of this study is to quantify several morphological (diameter, length, and volume) and functional (flow) parameters of the coronary arterial tree in relation to myocardial mass. Eight normal porcine hearts of 117-244 g (mean of 177.5 +/- 32.7) were used in this study. Various coronary subtrees of the left anterior descending, right coronary, and left circumflex arteries were perfused at pressure of 100 mmHg with different colors of a polymer (Microfil) to obtain rubber casts of arterial trees corresponding to different regions of myocardial mass. Volume, diameter, and cumulative length of coronary arteries were reconstructed from casts to analyze their relationship to the perfused myocardial mass. Volumetric flow was measured in relationship with perfused myocardial mass. Our results show that arterial volume is linearly related to regional myocardial mass, whereas the sum of coronary arterial branch lengths, vessel diameters, and volumetric flow show an approximately 3/4, 3/8, and 3/4 power-law relationship, respectively, in relation to myocardial mass. These scaling laws suggest fundamental design principles underlying the structure-function relationship of the coronary arterial tree that may facilitate diagnosis and management of diffuse coronary artery disease.