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1 Section of Plant Biology and 4 Department of Land, Air and Water Resources, University of California, Davis, California 95616-8627 USA; 2 S.E.P.F.-I.N.R.A. 86 600 Lusignan France; and 3 Department of Plant and Microbial Biology, University of California, Berkeley, California 94720-3102 USA
Received for publication February 25, 1999. Accepted for publication August 19, 1999.
ABSTRACT
The pleiotropic effects of the Rld1-O/+ mutation of Zea mays (Poaceae) on leaf phenotype include a suppression of normal transverse unrolling, a reversed top/bottom epidermal polarity, and an apparently straighter longitudinal shape. According to engineering shell theory, there might be mechanical coupling between transverse and longitudinal habit, i.e., the leaf rolling itself might produce the longitudinal straightening. We tested this possibility with quantitative curvature measurements and mechanical uncoupling experiments. The contributions of elastic bending under self weight, mechanical coupling, and rest state of leaf parts to the longitudinal and transverse habit were assessed in Rld1-O/+ mutants and a population of sibling +/+ segregants. Elastic bending and curvature coupling are shown to be relatively unimportant. The Rld1-O/+ mutation is shown to alter not only the unrolling process, but also the developmental longitudinal curving in the growing leaf, leading to a straighter midrib and a rolled lamina. The Rld1-O/+ mutant is thus a suitable model to study the relation between tissue polarity and differential curvature development in the maize leaf. Since on the abaxial side of the leaf, more abundant sclerenchyma is found in +/+ than in Rld1-O/+, a gradient in sclerification may contribute to the development of midrib curvature.
Key Words: biomechanics • curvature • development • grass • leaf rolling • leaf shape • Poaceae • Rld mutant • sclerenchyma • Zea mays
Leaf habit, or the spatial display of the leaf, affects light interception, leaf temperature, and water loss, three important ecophysiological factors for photosynthesis and growth (e.g., O'Toole and Cruz, 1979
; Ludlow and Bjorkman, 1984
). In maize the blade is a slender structure with bilateral symmetry. Therefore, the longitudinal curvature of the leaf blade and the angle of inclination of the blade joint (i.e., the junction between the blade and the sheath, also called leaf collar or ligular zone; Ledent, 1974
) provide the main specification of the habit of mature leaves. In growing leaves, and in mature leaves under water stress, a transverse rolling of the blade is observed. Thus the habit of the growing or stressed leaf requires an additional characterization of the transverse curvature. A number of studies have dealt with the anatomical, genetic, and ecophysiological aspects of the development of blade joint angles in grasses (e.g., Ledent, 1974
; Ariyanayagam, Moore, and Carangal, 1974
; Freeling and Walbot, 1994
; Drouet and Moulia, 1997
). Less attention has been devoted to the development of longitudinal and transverse curvature.
Because a leaf is subjected to gravity and to internal loading (related to turgor), unraveling the quantitative relations between the spatial display of the leaf and its anatomical and morphological development involves biomechanical analyses (Spatz, Speck, and Vogellehner, 1990
; Niklas, 1992
; Moulia, 1993, 1994
). Much of classical and recent literature on biomechanics of plant axes is based on engineering beam theory (e.g., Archer, 1988
; Silk, Wang, and Cleland, 1982
; Niklas, 1992
) In contrast, the mechanics of rolled leaves are better understood from the perspective of shell theory (Moulia, 1993, 1994
).
From a mechanical point of view, at a given time, the longitudinal curvature can be decomposed into the curvature resulting from bending under self weight and an intrinsic or built-in curvature that is displayed even in unloaded conditions. The built-in curvature has been called the "rest-state curvature" (Moulia, 1994
). Concerning the bending under self weight, Moulia demonstrated experimentally in maize leaves (using an in situ bending test) a mostly elastic behavior, with most of the bending stiffness being due to the midrib (Moulia, Fournier, and Guitard, 1994
). Subsequently the quantitative relationship between the midrib anatomy and the elastic bending stiffness was formalized through a composite beam model (Moulia and Fournier, 1997
). ("Bending stiffness" in this paper is used to denote the more formal "flexural rigidity" used in engineering theory, i.e., the mechanical resistance to bending under an applied bending moment). However, the elastic bending under leaf self-weight was found to account for only 30% of the observed total leaf curvature. The remaining 70% of curvature must be attributed to the rest-state curvature (Moulia, Fournier, and Guitard, 1994
). The physical and biological processes involved in the building of this curvature during leaf development and their relationship with leaf anatomy remain to be determined.
Transverse curvature is produced by leaf rolling and occurs in two different circumstances: (1) during the early stages of maize leaf development while basal expansion is still occurring and (2) for mature leaves under water stress. Under water stress, leaf rolling is a hydronastic mechanism that reduces light interception, transpiration, and leaf dehydration (O'Toole and Cruz, 1979
; Begg, 1980
). It results from a differential top-bottom elastic shrinkage in the leaf cross section (Moulia, 1994
). The role of the bulliform cells, large specialized adaxial epidermal cells that would act as motor cells causing leaf rolling by a larger decrease in size during turgor loss, has been argued (Esau, 1977
; Price, Young, and Tomos, 1997
), but their influence has been disputed (e.g., Burström, 1942
). A clear assessment of the involvement of anatomical traits in the building of transverse curvature is still lacking.
Leaf rolling during the early stages of maize leaf development (while expansion is still occurring) is not well understood. It has been shown that light-induced unrolling of the primary leaf of wheat is a growth process, regulated by phytochrome (Virgin, 1990
), but the developmental and mechanical aspects of the process are still unclear.
The mechanical analysis of the habit of rolled leaves is complicated by the possibility of a structural coupling between changes in longitudinal and transverse curvature within shells (Moulia, 1994
). When a change is made in one of the two curvatures (i.e., either in transverse curvature, such as in leaf rolling, or in the longitudinal curvature), an auto-stress field can be produced in the whole leaf, involving laminar tensions and transverse and longitudinal bending. As a consequence none of the parts of the leaves is in a rest (unstressed) state, even when the leaf as a whole is not subjected to external loads or to its self-weight (i.e., although the intact leaf is in a rest state). The coupling between changes in the two kinds of curvature and the existence of an auto-stress field have been demonstrated experimentally in maize leaves rolling under water stress and modeled using shell theory of mechanical engineering (Moulia, 1994
). An important implication of the model is that leaf rolling of water-stressed maize leaves conceals the rest-state curvature of the midrib. Concurrently, some of the transverse rolling is blocked. As a consequence, the rest states of longitudinal curvature of the midrib and transverse curvature of the lamina in rolled leaves cannot be assessed directly from the unloaded state of the whole leaf, but must be determined by uncoupling experiments based on lamina laceration (Moulia, 1993, 1994
).
From the perspective of curvature development studies, an interesting material is provided by the Rolled (Rld1-O/+) maize mutant. From qualitative morphological and anatomical observations, there are three main mutant phenotypic characteristics of the Rld1-O/+ leaf: a straighter longitudinal habit, a suppression of normal leaf unrolling causing a transversely rolled lamina, and a reversed top/bottom polarity between the leaf surfaces. The objective of this study was to unravel some of the biomechanical relations among these pleiotropic traits through a comparative study of the Rld1-O/+ mutants and of a population of sibling +/+ segregants (wild type). One hypothesis is that the straighter Rld1-O/+ leaf habit is not caused directly by the mutation in leaf surface polarity and is just a physical consequence of the suppression of the unrolling. It would predict that the mutant midrib, when isolated from the lamina, would have normal rest shape and would be straightened by the auto-stress coupling with transverse curvature of the lamina, as found in hydronastic rolling. A decreased bending stiffness in the mutant midrib would facilitate this mechanism. The related possibility that the Rld1-O/+ phenotype could result directly from a possible disrupted water transport in the mutant leaf, leading to loss of turgor, and thus to hydronastic rolling (suppressing the normal developmental unrolling) is also considered.
An alternative hypothesis is that the straighter habit is related to a lower rest-state longitudinal curvature in the mutant midrib. The straighter habit would thus be due to an alteration of the differential growth and differentiation in the mutant and probably related to the upside down polarity.
As a first step toward understanding the habit of the mutant leaf, we assessed quantitatively the contributions of elastic bending and rest-state longitudinal curvature of the intact leaf. Since leaf longitudinal curvature does not change much when the intact leaf is placed on its side, the elastic bending of the mutant leaf under self-weight is relatively unimportant. Next we analyzed the consequences of rolling on the longitudinal and transverse curvature (through structural coupling effects). It is demonstrated that the mutant midrib has a decreased bending stiffness, but shows also a much straighter longitudinal midrib rest shape when isolated from the lamina. The transverse curvature of the lamina seems to be mostly unaffected by coupling. Furthermore, since the transverse rest curvature is unchanged when leaf strips are immersed in distilled water, it does not result from impaired water status within the mutant leaf. Therefore, the straighter habit of the mutant leaf is due mainly to a lower rest-state longitudinal curvature of the midrib. This indicates a modification in the developmental curving of the midrib. Finally, the morphology and anatomy of the leaf were studied to gain insight into the mechanism of longitudinal curvature production during leaf development. The greater density of fibers on the abaxial side of the +/+ midrib suggests fiber shortening during development may be involved in the formation of the mature leaf habit.
MATERIALS AND METHODS
Plants and growth conditions
The maize stock used in this study was Rld1-O, originally described as Rld*1990 (Bird and Neuffer, 1985
). The semidominant mutant (Lane and Freeling, 1996
) was introgressed into a stock of inbred W23 for eight generations. All seeds used for this study were taken from a single ear segregating 1:1 for Rld1-O/+ mutant heterozygote and their +/+ wild type siblings. Maize seeds were germinated in moist vermiculite inside a Conviron growth chamber set for a 16-h photoperiod at a constant day/night temperature of 25°C. After germination and the emergence of the first visible leaf, seedlings were transferred singly or in pairs to (10-gallon) pots with a soil mixture composed of equal parts of sand, peat moss, and soil. Plants were regularly watered and fertilized twice a week with half-strength Hoagland's solution.
Morphological visual staging to determine observation timing
From a mechanical point of view, the situation of the blade changes with the angle at the blade joint (Ledent, 1976
), as the bending moment increases through increasing lever arm. We have thus chosen to focus our study on two particular morphological stages of the leaf. The first stage, denoted upright leaf stage, corresponds to the time where the blade is fully visible, but no blade joint angle has developed. The staging criterion is that leaf n is in its upright stage when its leaf collar becomes visible at the same height as the blade joint of the enclosing leaf (n - 1). This corresponds to the classical V plant staging system used in maize crop sciences (Ritchie, Hanway, and Benson, 1994
) and is denoted Vn, where n is the rank number of the upper leaf with visible blade joint, with coleoptile being given rank 0. Note, however, that the frequency of observation, several times a day, was much higher here than in crop studies, thus allowing more accurate determination of the V stage. The second morphological stage, called tilted leaf stage, corresponds to a blade joint angle close to the final display angle. In our sample, the tilted leaf stage was achieved in leaf n when leaf (n + 2) was in its upright stage and is therefore denoted Vn + 2.
Longitudinal shape recording
When a Rld1-O/+ or +/+ plant matured to the upright stage of the fifth oldest leaf (V5, ~15 d after germination for both Rld1-O/+ and +/+ plants), leaf 5 was photographed bending under self-weight. The plant was then rotated carefully so that leaf 5 was lying horizontally on a flat surface. In these conditions there is no more longitudinal bending under self-weight, and thus the "weightless" shape of the leaf could be recorded. A camera level was used to place the camera lens parallel to the plane in which the leaf midrib curved. (Previous studies [Sinoquet, Moulia, and Bonhomme, 1991
; Drouet and Moulia, 1997
] have demonstrated that most of the maize leaves have the major part of their midrib lying within a plane.) When a plant matured to the tilted stage, the longitudinal leaf habit of leaf 5 under self-weight was photographed again. Leaf 5 was then excised below the blade joint, and the longitudinal weightless shape, the "rest shape of the leaf," was photographed. Immediately afterwards, the lamina on both sides of the midrib of leaf 5 was removed with scissors. The longitudinal weightless shape of the isolated midrib, the "rest shape of the midrib," was then photographed. Excised leaves were handled gently to minimize mechanical damage and sprayed with water to minimize dehydration. A similar procedure was applied to leaves 6 and 7.
Transverse shape recording
Transverse rest shapes of the blades of leaf 6 at full turgor were recorded following the methods of Moulia (1994)
. Lamina strips, isolated from the rest of the lamina but attached to a 2.5-cm segment of midrib were excised and submerged in ice-cold water, to recover full turgor, before photography. With a camera mounted on an Olympus dissecting scope, photographs were taken of the rolled strips (to the right side of the midrib viewed from the leaf base). A stage micrometer was photographed with each image for scaling.
Image analysis
Photographs were digitized onto Kodak photo CDs. Sigma Scan, an image analysis software package (Jandel Scientific, San Rafael, California, USA), was used to determine x and y coordinates, identified by clicking points with the mouse along the curved midrib or lamina. Curvilinear abscissa, s (length), the distance from the base of the corn leaf blade, was estimated by taking the sum of the distances between adjacent points from the blade joint to the point of interest.
Quantification of curvature
In studies of tropisms, it is common to measure an "angle of curvature" that gives a global measure of the deviation of a plant axis from the vertical. However, in physiological studies it is more useful to use the definition of local curvature that can be evaluated at all locations along a curve (Silk and Erickson, 1978
). In calculus and differential geometry this local curvature has the units of reciprocal length and is defined by the rate of change of the angle 
of the tangent to the curve:
and equals the radius (here in millimeters) of the circle that fits the curve locally.
The program Courb2D (Moulia, Fournier, and Guitard, 1994
) was used to compute curvatures from the set of digitized points. The algorithm fits a curve to a defined vicinity of data points, calculates the curvature at each point, and then moves the vicinity to include the next data point. Positive longitudinal curvatures in this study characterize a shape with downward concavity. Data were averaged by first pooling all paired s and values from ten leaves. Then curvatures were averaged that corresponded to s values included in a 20-mm interval to estimate the longitudinal curvature at the midpoint of the interval. The process was repeated, moving the bounds of the interval by 10 mm each time. For example, an average of all curvatures corresponding to s values between 0 and 20 mm estimated curvature at s = 10 mm.
Blade segment weight and cross-sectional morphometrical and anatomical measurements
A series of plants was grown to the V7 stage. The blade of leaf 6 was cut into 5-cm segments. Each segment was weighed. Then the maximal height and width of the midrib cross section were measured with the compound microscope and stage micrometer. Next, transverse cuts of the midribs were made by hand, stained using toluidine blue, and viewed with a 10x ocular lens in a compound microscope. The number of cells within the sclerenchyma located on the abaxial side of the midrib, the hypodermal sclerenchyma on the adaxial side of the midrib, and the abaxial epidermal cells were counted for half the midrib.
Statistical analysis
Student t tests and factorial ANOVA analysis were performed on size and anatomical measurements (see text for the specification of each test).
To compare curvature profiles along the leaf between genotypes, the requirements of ANOVA are not a priori fulfilled. Longitudinal curvature is a local measurement characterizing a particular position in the midrib, but successive curvatures along the leaf are not necessarily independent (for example, leaf rolling changes the curvatures all along the leaf) and their variance is not constant. The statistical comparison of curvature profiles in these conditions would be a complicated problem in biometrics and is not readily available in advanced treatises on shape statistics (e.g., Small, 1996
). Here, we consider longitudinal shapes to be significantly different if there is a systematic difference of the same sign in the curvatures all along the leaf. As the leaves were characterized by their curvatures at ~50 points, the more repeated successive differences of the same sign, the lower the probability that this systematic trend could result from pure chance. This criterion, although not quantitative, should ensure reliable conclusions about the effects of genotype, developmental stage, and mechanical isolation.
RESULTS AND DISCUSSION
Phenotypic differences in general morphology and global leaf habit
The lengths of Rld1-O/+ and +/+ leaf blades are similar at comparable developmental stages. For example, the mature leaf length for leaf 6 is 595 ± 47 mm and 603 ± 50 mm for leaves of +/+ and Rld1-O/+, respectively [sample size = 10, (Pr > t) < 0.005]. In contrast, the leaf habits of the different phenotypes under self-weight were clearly different, although (as usual for curvature of plant axes), there was considerable variation in calculated curvature at any location. For instance, at the tilted leaf stage, longitudinal curvature at s = 50 cm was 3.66 ± 0.10 and 4.04 ± 0.64 mm-1 for Rld1-O/+ and +/+, respectively (Fig. 1). The global spatial pattern shows that longitudinal curvatures for all leaves were smaller in the Rld1-O/+ than in the +/+ (Fig. 1). For leaf 5 (Fig. 1), both phenotypes developed greater maximum curvature as they matured from the upright to the tilted stage (compare the open and closed symbols of Fig. 1a and b). Thus longitudinal curvature is time dependent even after the leaf has stopped expanding in the longitudinal direction. But at comparable developmental stages and locations in the leaf, the mutant had smaller curvature than the controls (compare Fig. 1a and b) with typical differences ranging from -13 to -70%. This proves quantitatively the subjective impression that the Rld1-O/+ leaf is straighter than the +/+ leaf.
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) and is due mainly to the increase in the bending stiffness of the leaf due to the change in transverse geometry related to rolling (Moulia, 1993
; King, Vincent, and Harris, 1996
). The effect of this "geometrical stiffening" is obviously higher where the bending stiffness of the midrib is low (i.e., where its cross section is smaller).
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that elastic bending under self-weight is relatively unimportant in producing leaf habit in maize and extends them to the Rld1-O/+ mutant. Although rolling has a clear geometrical stiffening effect inducing decreased bending under self-weight, most of the differences in longitudinal habit induced by the Rld1-O/+ mutation come from differences in the rest shape of the leaf, which is indeed highly modified by the mutation. The question is then to analyze the origin of these differences and the influence of curvature coupling.
Rest shapes of isolated leaf parts
For the rolling to be solely responsible for the straighter rest shape of the mutant leaf through curvature coupling, it is necessary that (1) the midrib rest shape is not straighter in the mutant than in controls; and (2) some part of the transverse curvature is blocked in situ. Paradoxically, a decreased relative bending stiffness in the mutant midrib could enhance the straightening of the intact leaf by promoting leaf rolling (3).
Figure 3 displays typical phenotypic effects on midrib cross-sectional area. The Rld1-O/+ midrib indeed appears thinner (but less tapered) than its +/+ counterpart. A two-way factorial analysis of variance supported the hypothesis that there are significant differences in average values of cross-sectional area at different locations (Pr > F = 0.0001) and for the different genotypes (Pr > F = 0.0001). However, there is no significant interaction between the genotype and position effects (Pr > F = 0.27), i.e., midrib tapers cannot be concluded to be statistically significant from this ANOVA. The mutant blade is not as heavy and has a slightly smaller material density (data not shown). Such differences should have dramatic effects on midrib bending stiffness, as the ratio of second moment of area to cross-sectional area varies as the square of midrib thickness (e.g., Niklas, 1992
). (The second moment of area is the geometric factor in the bending stiffness of a beam.) Thus criterion 3 is met for the structural importance of transverse rolling on longitudinal curvature. However, criterion 1 for similarity of rest-state curvatures in the midribs was not met. Figure 4 shows typical examples of longitudinal rest shapes of the leaf and of isolated midribs. Figure 5 depicts rest curvatures of leaves and midribs, for three different leaf ranks (leaves 5, 6, and 7) at the V7 plant stage. Note that at V7, leaf 5 was in its tilted stage, leaf 7 at its upright stage, and leaf 6 was intermediate. In leaf 5, the +/+ midrib shows virtually no changes in curvature upon mechanical isolation (except at the very tip). In the mutant there is a trend for the midrib to become slightly more curved when isolated, increasing near the tip. This trend following the changes in midrib bending stiffness along the leaf is consistent with the prediction of curvature coupling (Moulia, 1994
), indicating a (limited) straightening by auto-stresses in the Rld1-O/+ leaf. However, this trend is not repeated in leaves 6 and 7, where the effect of isolation, if significant, would be toward de-curving, both in the +/+ (leaves 6 and 7) and in the Rld1-O/+ (leaf 7). This would indicate that these midribs are slightly bent down within the leaf. There is thus a developmental change in the amount of curvature coupling either with leaf stage (increasing with time) or with leaf number (decreasing with leaf number). However, these effects are small. For longitudinal curvature the major difference between the Rld1-O/+ and +/+ comes from the rest shape of the isolated midrib. For example, in leaf 6, the +/+ and Rld1-O/+ blades had maximum longitudinal curvatures of .0035 mm-1 and .0025 mm-1, respectively, for the first 40 cm, and at s = 180 mm the +/+ leaf rest-state curvatures were 1.4 times greater than the Rld1-O/+. Stated in radii of curvature (inverse of curvature), the average radii of curvature at s = 180 mm were 417 and 294 mm for the Rld1-O/+ and +/+ leaves, respectively. Thus, the Rld1-O/+ midrib has a much lower rest-state curvature.
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. At ~20 cm from the blade joint, the maximum adaxial transverse curvature of the rolled lamina was 0.4 mm-1 at 6.5 mm from the center of the midrib. Toward the margin of the leaf there was a uniform curvature of 0.1 mm-1 (the distance from the center of the midrib to the edge of a leaf margin was ~15 mm). Compared with longitudinal curvatures, transverse curvatures are two orders of magnitude higher. The rest-state transverse curvatures for the Rld1-O/+ mutant leaf strips were thus very high under full turgor. The leaf rolling phenotype in the Rld1-O/+ mutant leaf is thus not a consequence of any loss of turgor.
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). This is consistent with the demonstration here that the Rld1-O/+ phenotype is not related to impaired water status.
Morphological and anatomical traits related to development of curvature
As the Rld1-O/+ mutation changes the development of the longitudinal rest curvature of the midrib, comparative analysis of morphology and anatomy in Rld1-O/+ and +/+ midribs is likely to give insights into the mechanisms involved in building rest-state curvature. Figure 7 depicts the longitudinal rest curvatures of the leaf at two developmental stages. Consistent with Fig. 1, there is a trend for rest curvature of the leaf to increase with developmental stage, especially at the base of the leaf. This trend is present in both genotypes, but is much clearer in the Rld1-O/+ genotype. The temporal increase in curvature is consistent with the hypothesis of an irreversible bending under self-weight through a passive creep or plastic behavior (Niklas, 1992
). It should be recalled that the V5 and V7 morphological plant stages have been chosen so that in stage V5 the leaf 5 is still mostly upright, whereas in stage V7 the ligule angle has fully developed. As the leaf blade tilts, the lever arm component of bending moment increases and causes greater loading in the midrib, which is the major load-bearing element at the base of the leaf (Moulia, 1994
; Okuyama et al., 1994
). This increased loading could cause some irreversible bending. Indeed, effects of leaf tilt on developmental changes in longitudinal curvature are greatest at distances close to the blade joint. Note that this is also reflected in the elastic bending under self-weight, which tends similarly to increase with time at the leaf base. (Compare Figs. 7 and 1 and note the increasing bending moment.) Apparently, the elastic equilibrium shape is made time dependent through developmental increase in loading due to self-weight. However, it is noteworthy that even at the upright stage, both the Rld1-O/+ and +/+ midrib have already acquired a large part of their "final" curvature. Indeed, when we observed dissected young leaves, which were enclosed within the sheaths of previous leaves and hence not submitted to any bending due to self-weight, we noted that they display a significant curvature in their mature part (Moulia and Silk, unpublished data). This demonstrates that building of rest curvature involves more than a passive creep under self-weight and that the Rld1-O/+ mutation affects this developmental process.
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; Fournier, Bailleres, and Chanson, 1994
; Okuyama et al., 1994
). Therefore, we looked for evidence that the +/+ leaves might have a greater density of fibers on their abaxial sides. Fiber shortening would lead to the downward curving as the fibers develop. To assess the statistical significance of the differences between abaxial and adaxial fiber densities in Rld1-O/+ and +/+ midribs and of the differences between genotypes in fiber densities, we did paired comparison hypothesis testing using the Student's t-test. At distances of 10 and 20 cm from the blade joint of leaf 6 (Fig. 8), the +/+ midrib cross section contained more fiber cells than the Rld1-O/+, although this difference was reduced when dividing by the total cross-sectional area (density of fiber cells per unit area), to account for the differences in cross-section scaling and a higher density (Pr > t = 0.06). On average, both Rld1-O/+ and +/+ midribs have greater fiber densities on the abaxial side compared to the adaxial side (Pr > t = 0.0001 and 0.001, respectively). However, the total number of abaxial fiber cells per unit area associated with lateral vascular bundles and between bundles was, on average, significantly greater for the +/+ cross section (Pr > t = 0.05). In contrast, the average number of abaxial epidermal cells and adaxial fiber cells per unit area was similar between Rld1-O/+ and +/+ (Pr > t = 0.205; see also Fig. 8)., Thus, on average, Rld1-O/+ and +/+ midribs have greater fiber densities on the abaxial side compared to the adaxial side; adaxial fiber densities are not different between Rld1-O/+ and +/+; and abaxial fiber densities are greater in +/+ than in Rld1-O/+. This supports the hypothesis that differential fiber development produces curvature. However, a rigorous test of this hypothesis would involve correlating the timing of the curving and fiber differentiation processes.
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), is an obvious alternative mechanism. Work is currently underway to assess the relative importance of growth rate gradients and fiber development in the production of the leaf habit. The present study has thus unravelled some of the relations among the pleiotropic phenotypic traits of the Rolled mutation. It demonstrates clearly that the Rld1-O/+ mutation affects both the transverse and the longitudinal curvatures of the leaf. Elastic bending and curvature coupling are shown to be relatively unimportant for the development of the Rld1-O/+ habit, and an intrinsic difference in the development of the rest-state curvature of the midrib is responsible for the straighter form of the Rld1-O/+ leaf. This brings into sharp focus the relationship between the anatomy of the midrib and its curvature. The comparative anatomical analyses of the mutant and wild type give some correlative support to the hypothesis that fiber shortening during cell wall differentiation might be the motor of the autotropic curvature. Work remains to test this last hypothesis more directly on the Rld-O/+ mutant.
FOOTNOTES
1 This work was supported by grant IBN-9604230 from the National Science Foundation to W.K.S. B.M. received support from Institut National de la Recherche Agronomique. J.O.H. received support from a U.C. Davis President's Undergraduate Fellowship. 
2 Current address: Section of Plant Biology, Cornell University, Ithaca, New York 14853 USA.
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