Author Affliations
University of California, Los Angeles; Brown University
Overview
The surface area of mesophyll cells per leaf area (A_{mes}/A) is a measure of the area available for CO_{2} uptake within the leaf. This trait may be used as a relative index or proxy for comparing species’ light saturated photosynthetic rate. This protocol and spreadsheet tool enable the estimation of A_{mes}/A from leaf cell and tissue dimensions measured from transverse cross-sections.
Background
The A_{mes}/A (also known as S_{m}/S) is one of the determinants of the diffusion conductance of CO_{2} from the stomata to the site of photosynthesis (g_{m}), which in addition to stomatal conductance (g_{s}), determines the rate of CO_{2} assimilation for a given ambient CO_{2} availability and biochemical assimilation rate. The g_{m} is determined by multiple anatomical factors, including the tortuosity of the airspaces, the cell surface area exposed to airspace, the proportion of that surface area in contact with chloroplasts, and the permeability of cell wall, cell membrane and chloroplast membrane to CO_{2} (Nobel, 2009; Terashima et al., 2011; Tomás et al., 2013).The A_{mes}/A has been estimated for many species, and is frequently correlated with leaf transpiration rate and net photosynthetic rate within and across species, as expected if it accounts for a major limitation in the pathway, and/or if there is relatively low variation in the other determinants of photosynthesis and/or if these other determinants themselves correlate with A_{mes}/A across species (Turrell, 1933; Turrell, 1944; Nobel et al., 1975; Nobel, 1976; Nobel, 1977; Longstreth and Nobel, 1980; Patton and Jones, 1989; Evans et al., 1994; Syvertsen et al., 1995; Nobel, 2009; Chatelet et al., in review.)
Classically, the A_{mes}/A has been estimated using the total length of cell wall exposed to airspace in transverse and paradermal cross-sections and applying correction factors (Turrell, 1944; Morris and Thain, 1983; Thain, 1983; Patton and Jones, 1989; Evans et al., 1994; Syvertsen et al., 1995; Tosens et al., 2012; Tomás et al., 2013). Alternatively, the A_{mes}/A has been estimated from cell dimensions with assumptions of their geometry, using both transverse and paradermal cross-sections of the leaf (Nobel et al., 1975; Nobel, 1976; Nobel, 1977). Basing the estimation of A_{mes}/A on cell geometry has the advantage of showing how cell size, numbers and tissue types contribute to the A_{mes}/A . Our protocol estimates A_{mes}/A from cell dimensions and requires only transverse cross-sections. Future work should compare the estimates determined from these different methods for their similarity and accuracy, and in the meantime each is considered feasible for comparing species.
We estimate A_{mes}/A by modeling mesophyll cells as standard geometric objects. We model spongy mesophyll cells as spheres, and typical palisade cells (“I-cells”) as capsules (Nobel et al., 1975; Nobel, 1976; Longstreth and Nobel, 1980). We model arm-palisade cells (“H-cells”) as a short cylinder with arms projecting from the top and bottom, with the arms modeled as narrow cylinders with hemispheric caps (Fig. 1). The transverse cross-sections must be thin enough to allow resolution of individual cell sizes and airspaces within the mesophyll; thus sections of ca. 1 μm are recommended, which typically require embedding in resin and microtoming. From the digital images of transverse cross-sections, using ImageJ or other image analysis software, replicate measurements should be made for each variable in random locations. We suggest making three measurements of each variable in each cross-section, as close as possible to the center of each of the left, middle and right thirds of the cross-section. Measurements should be made on cells that appear to be sectioned through their centers. All measurements should be made for cross-sections of at least 3 leaves per species/treatment.
Units, terms, definitions
See Figure 1 (attached).
Cells should be measured that appear to be sectioned approximately through their centers.
P_{sc – }Cell perimeters for spongy mesophyll cells.
D_{pic} – Cell diameters for palisade mesophyll I-cells.
H_{pic} – Height for palisade mesophyll I-cells.
ASF_{st }and ASF_{pt} respectively – Airspace fraction in spongy and palisade mesophyll tissue. This can be measured, or estimated to the nearest 5% by a trained observer.
T_{st }and T_{pt} respectively – Thickness of spongy and palisade mesophyll tissue layers.
Note: If “arm palisade” (aka “H-cell palisade”) is present, then measurements should be made of the diameter and height of the central horizontal cylinder, number of projecting arms, and their diameters and heights.
Procedure
For formulae, please see attached Spreadsheet tool below.
Estimating the surface area of mesophyll components per leaf area
In our approach, the A_{mes}/A is calculated for individual tissue layers. These can be summed for leaves with multiple distinctive mesophyll layers. The general strategy is based on an estimation of the cell surface area of each type of mesophyll tissue in the entire leaf, by multiplying the surface area of a cell by the number of cells per leaf in that mesophyll tissue, where the number of cells is estimated as the total volume of that mesophyll tissue (unmeasured; see below) minus the airspace divided by the volume of a mesophyll cell. The A_{mes}/A for that tissue layer can be determined by dividing the equation by leaf area (unmeasured), which replaces tissue volume by the tissue thickness. Thus, for each tissue
- A_{mes}= SA_{c}x(V_{t} x(1-ASF_{t}))/V_{c}
Where ASF_{s} is the intercellular airspace fraction in the given tissue, V_{t} the volume of the given tissue in the whole leaf (unmeasured), SA_{c} is the surface area and V_{c} is the volume of the average cell in that tissue. Because V_{t} is equal to the leaf area (unmeasured) x the tissue thickness (T_{t}), dividing both sides of the equation by leaf area gives the surface area of cells in that tissue per leaf area ( A_{mes}/A ):
- A_{mes}/A = SA_{c}x(T_{t} x(1-ASF_{t}))/V_{c}
For spongy mesophyll, cells can be modeled as spheres. The mesophyll surface area of spongy mesophyll (A_{mes,s}/A) can be estimated from eqn 2, determining the surface area and volume of a spongy mesophyll cell (SA_{sc} and V_{sc}) using formulae in Table 1, based on the measurements taken of the perimeter of a spongy mesophyll cell (P_{sc}), the airspace fraction of spongy mesophyll tissue (ASF_{st}) and the thickness of spongy mesophyll tissue (T_{st}).
For palisade I-cells, cells can be modeled as capsules. The mesophyll surface area of palisade mesophyll (A_{mes,p}/A) can be estimated from eqn 2, determining the surface area and volume of a palisade mesophyll I-cell (SA_{pic} and V_{pic} ) using formulae in Table 1, based on the measurements taken of the height and diameter of a palisade mesophyll I-cell (H_{pic} and D_{pic}), the airspace fraction of palisade mesophyll tissue (ASF_{pt}) and the thickness of palisade mesophyll tissue (T_{pt}).
When the palisade mesophyll is constructed of H-cells, cells can be modeled as a short central cylinder with arms projecting from the top and bottom, with the arms modeled as narrow cylinders with hemispheric caps. The mesophyll surface area of palisade mesophyll (A_{mes,p}/A) can be estimated from eqn 2, determining the surface area and volume of a palisade mesophyll H-cell (SA_{phc} and V_{phc}) using formulae in Table 1, based on the diameters and heights of the central cylinders and projecting arms, the airspace fraction of palisade mesophyll tissue (ASFpt) and the thickness of palisade mesophyll tissue (T_{pt}).
Given that replicate measurements were made for dimensional measurements for cells within the cross-section, eqn 2 should be applied using the average values for each term determined from a given leaf based on averaging the SA_{c} and V_{c} for the replicate cells within the cross-section in each leaf.
Table 1: Formulae for cell surface area (SA_{c}) and cell volume (V_{c}) for spongy mesophyll cells, modeling these as spheres, for palisade mesophyll I-cells, modeling these as capsules; and palisade mesophyll H-cells, modeling these as a short central cylinder with arms projecting from the top and bottom, with the arms modeled as narrow cylinders with hemispheric caps. Geometric formula from http://mathworld.wolfram.com/, and see Appendix for derivations of formulae for palisade mesophyll H-cells.
Mesophyll cell type | ||
---|---|---|
Cell surface area (SA_{c}) | Cell volume (V_{c}) | |
Spongy mesophyll cell | SA_{sc}=4ℼx(P_{sc}/2ℼ)^{2} | V_{sc}=^{4}/_{3}ℼx(P_{sc}/2ℼ)^{3} |
Palisade mesophyll I-cell | SA_{pic}=2ℼx(D_{pic}/2)xH_{pic} | V_{pic}=ℼx(D_{pic}/2)^{2}x(^{4}/_{3}x(D_{pic}/2)+H_{pic}–D_{pic}) |
Palisade mesophyll H-cell |
SA_{phc}=2ℼ(D_{phc,c}/2)x((D_{phc,c}/2) +H_{phc,c}) + ^{j}_{i=1}(2ℼ(D_{phc,arm,i}/2)xH_{phc,arm,i}) +3ℼ(D_{phc,arm,i}/2)^{2}-2ℼ(D_{phc,arm,i}/2)^{2} |
V_{phc}=ℼ(D_{phc,c}/2)^{2}xH_{phc,c} + ^{j}_{i=1}(ℼ(D_{phc,arm,i}/2)^{2}xH_{phc,arm,i} +^{2}/_{3}ℼ(D_{phc,arm,i}/2)^{3})) |
where P_{sc} is the spongy mesophyll cell perimeter,
D_{pic} and H_{pic} are the diameter and the height of the palisade mesophyll I-cell,
and D_{phc,c} and H_{phc,c} are the diameter and height of the central cylinder of the palisade mesophyll H-cell, and D_{phc,arm,i} and H_{phc,arm,i} are the diameter and height of the arm i projecting from the central cylinder of the palisade mesophyll H-cell, and j is the total number of arms in the palisade mesophyll H-cell.
Assumptions and potential corrections
For the estimation of a functional A_{mes}/A based on cell surface area, we assume that virtually all the cell wall of mesophyll cells is in contact with airspace, even when it appears to contact other cells in the cross-section (Nobel, 2009).
We assume that cells can be chosen for measurements that are sectioned approximately through their centers.
The modeling of cells as geometric objects described by their mean dimensions assumes approximate regularity and normal variation of form. Further, the modeling of spongy cells as spheres neglected their projections and assumes these to contribute relatively little to the surface area or volume of the cells (Nobel, 1976).
These formulae would be improved by also subtracting from the tissue volume and tissue thickness (eqns 1 and 2) the space taken up by non-mesophyll tissues, including veins and bundle sheath and/or water storage cells.
Estimating the total surface area of mesophyll per leaf area
- A_{mes} A=A_{mes,s }/A+A_{mes,p}/A
Other resources
Notes and troubleshooting tips
Appendix: derivation of palisade mesophyll H-cell surface area and volume (SA_{phc} and V_{phc}, respectively)
The surface area of a palisade mesophyll H-cell (SA_{phc}) can be estimated as the sum of the surface area of the central cylinder with the surface areas of each projecting arm (modeled as cylinders with one hemispheric cap) minus twice the contact area of the arms and central cylinder.
SA_{phc}=(2ℼ(D_{phc,c}/2)xH_{phc,c}+2ℼ(D_{phc,c}/2)^{2})+ ^{j}_{i=1}(2ℼ(D_{phc,arm,i}/2)xH_{phc,arm,i}
+3ℼ(D_{phc,arm,i}/2)^{2})- ^{j}_{i}(2ℼ(D_{phc,arm,i}/2)^{2})
(A1)
The volume of a palisade mesophyll H-cell (SA_{phc}) can be estimated as the sum of the volume of the central cylinder and the volumes of the projecting arms (modeled as cylinders with one hemispheric cap).The volume of a palisade mesophyll H-cell (SA_{phc}) can be estimated as the sum of the volume of the central cylinder and the volumes of the projecting arms (modeled as cylinders with one hemispheric cap).
V_{phc}=ℼ(D_{phc,c}/2)^{2}xH_{phc,c}+ ^{j}_{i=1}(ℼ(D_{phc,arm,i}/2)^{2}xH_{phc,arm,i}+^{1}/_{2}(^{4}/_{3}ℼ(D_{phc,arm,i}/2)^{3}))
(A2)
Links to resources and suppliers
Literature references
Evans JR, von Caemmerer S, Setchell BA, Hudson GS (1994) The relationship between CO_{2} transfer conductance and leaf anatomy in transgenic tobacco with a reduced content of Rubisco. Australian Journal of Plant Physiology 21: 475-495
Longstreth DJ, Nobel PS (1980) Nutrient influences on leaf photosynthesis: effects of nitrogen, phosphorus, and potassium for Gossypium hirsutum L. Plant Physiology 65: 541-543
Morris P, Thain JF (1983) Improved methods for the measurement of total cell surface area in leaf mesophyll tissue. Journal of Experimental Botany 34: 95-98
Nobel PS (1976) Photosynthetic rates of sun versus shade leaves of Hyptis emoryi Torr. Plant Physiology 58: 218-223
Nobel PS (1977) Internal leaf area and cellular CO_{2} resistance: photosynthetic implications of variations with growth conditions and plant species. Physiologia Plantarum 40: 137-144
Nobel PS (2009) Physicochemical and Environmental Plant Physiology, 5th edition. Academic Press, San Diego
Nobel PS, Zaragoza LJ, Smith WK (1975) Relation between mesophyll surface area, photosynthetic rate, and illumination level during development for leaves of Plectranthus parviflorus Henckel. Plant Physiology 55: 1067-1070
Patton L, Jones MB (1989) Some relationships between leaf anatomy and photosynthetic characteristics of willows. New Phytologist 111: 657-661
Syvertsen JP, Lloyd J, McConchie C, Kriedemann PE, Farquhar GD (1995) On the relationship between leaf anatomy and CO_{2} diffusion through the mesophyll of hypostomatous leaves. Plant Cell and Environment 18: 149-157
Terashima I, Hanba YT, Tholen D, Niinemets U (2011) Leaf functional anatomy in relation to photosynthesis. Plant Physiology 155: 108-116
Thain JF (1983) Curvature correction factors in the measurement of cell surface areas in plant tissues. Journal of Experimental Botany 34: 87-94
Tomás M, Flexas J, Copolovici L, Galmés J, Hallik L, Medrano H, Ribas-Carbó M, Tosens T, Vislap V, Niinemets Ü (2013) Importance of leaf anatomy in determining mesophyll diffusion conductance to CO_{2} across species: quantitative limitations and scaling up by models. Journal of Experimental Botany in press
Tosens T, Niinemets U, Westoby M, Wright IJ (2012) Anatomical basis of variation in mesophyll resistance in eastern Australian sclerophylls: news of a long and winding path. Journal of Experimental Botany 63: 5105-5119
Turrell FM (1933) The internal exposed surface of foliage leaves. Science 78: 536-537
Turrell FM (1944) Correlation between internal surface and transpiration rate in mesomorphic and xeromorphic leaves grown under artificial light. Botanical Gazette 105: 413-425
Health, safety & hazardous waste disposal considerations
For health and safety advice for embedding leaves refer to the Embedding leaves in Araldite protocol.
For health and safety advice for microtomy refer to the Vibrating microtome sectioning of fresh or fixed tissues protocol.