Mathematics for Biologists
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Mathematics for Biologists
Part Biology
Morphometric - Stereologic Analyses
based on
C3 and C4 Plants in a Carbon-rich World
Protocol
Jan. 26th 1998
Headed by: Prof. Dr. Alexandra Sänger
Handed in by:
Pierre Madl (Mat-#: 9521584)
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Morphologic-stereologic investigation of plants in a CO2 rich world
1. Introduction:
As people in industrialized countries burn more fossil fuels than ever before, and cut and burn down more forests,
atmospheric CO2 levels will continue to rise over the next decades. Those increases may stimulate the efficiency
of some plants (more CO2 fixed), although this is not the unmitigated blessing it may at first seem.
Before deepening this argument, I would like to consider the anatomical and physiological principles of
photosynthesis first.
1.1. Leaf Tissues:
A leaf epidermis has a waxy coating, the cuticle. In fact, the leaf is so well sealed that it needs tiny openings
called stomata, surrounded by guard cells, to admit CO2 for photosynthesis and to release water-vapor and O2.
The stomata are most numerous on the underside of leafs, and the opening and closing are based on the plants
conflicting needs to conserve water and taking CO2. Sandwiched between the upper and lower epidermal layers is
the leafs mesophyll layer, made out of two types of parenchyma (see scan on page 3):
• Pallisade parenchyma, the main photosynthetic tissue, lies just beneath the upper epidermis. It usually consists
of one or more rows of vertically oriented, column-shaped cells, each enclosing dozens of chloroplasts.
• A layer of rounded cells, the spongy parenchyma, lies between the pallisade parenchyma and the lower
epidermis. The loosely packed spongy parenchyma cells provide a huge surface area that absorbs CO2 from
the air which entered the stomata. CO2 entering the stomata can move rapidly to the spongy parenchyma to the
pallisade-parenchyma above, where most of the photosynthesis takes place. The vascular tissue within the
spongy parenchyma is an elaborate pluming system which distributes the products of photosynthesis out to
target tissues (root and shoot) and brings in water and minerals (from the root).
1.2 Photosynthesis:
Is the metabolic process by which plants
Photosynthetic reaction taking place in mesophyll cells of
and many microorganisms trap solar
leaves:
energy, converting it to chemical energy, to
6CO2 + 12NADPH + 12H+ + 18ATP
be stored it in the bonds of organic nutrient
↓
molecules such as sugar phosphates and
1glucose + 12NADP+ + 18ADP + 18Pi + 6H2O
other carbohydrates.
Pigments found within chloroplasts capture
energy from light by virtue of a distinct photochemical reaction:
• Phase one (light-dependent reaction), traps light energy via a light harvesting complex and converts it to ATP
and NADPH, energized electron carrier;
• a second phase (light-independent reaction), transfers this chemical energy to CO2, originating from the air
and in the process, synthesizing sugars and other high energy carbohydrates.
1.3 Chloroplasts: (Gk. chloros, light + plastid, closed compartment); see scan on page 3;
The photosynthetic pigments in a green leaf of a plant are concentrated in layers of cell and carry out
photosynthesis. This cells contain chloroplasts, green organelles in which both the energy-trapping and carbonfixing reaction of photosynthesis take place. Chloroplasts have an outer and an inner membrane that lie side-byside. Together they enclose a space filled with a watery solution, the stroma. A third membrane system lies within
the inner membrane and forms a complicated network of stacked disk-like sacs, the thylakoids, interconnected by
flat-like channels. Each stack of thylakoids is called a granum, and each individual thylakoid-disk has an internal
compartment, the thylakoid-space. Chlorophyll and other color pigments are embedded in the thylakoidmembrane and make this membrane the only part of the entire plant that is truly green.
The energy trapped in reaction of photosynthesis takes place in the thylakoid-membrane and thylakoid space. This
reactions provide the chloroplast solar cell activity. The carbon fixing reaction, which begin in the stroma and
continue in the cytoplast, collectively produce sugar-phosphate molecules.
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1.4 Calvin Cycle (C-fixing reaction):
In C-fixation, CO2 from the air becomes attached to a biological molecule, which makes carbon available for
carbohydrate synthesis. The acceptor of CO2 is a C5 molecule called ribulose biphosphate (RuBP). When a single
carbon of CO2 is joined to this C5 molecule, the result is an unstable C6 molecule that immediately breaks down to
two C3 molecules. This process is mediated by an enzyme nicknamed rubisco (for ribulose biphosphate
carboxylase). The net result of C-fixation, the first step in the calvin cycle, is the linkage of inorganic CO2 to a
biological molecule within the plant cell. The fixed C is the molecular starting point from which the plant will
build proteins, DNA, and cellulose.
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1.5 The water-oxygen dilemma:
When the weather is hot and dry, stomata on leaf surfaces of plants close to prevent excess water loss. This
closure, however, shuts out CO2 and shuts in O2, leading to its build up and a simultaneous decline of CO2 in
leaves. Consequently, O2 competes with CO2 for the rubisco enzyme (see 1.4 calvin cycle). When levels of O2 rise
inside the leaf, the rubisco enzyme carries out reactions that result in the loss of fixed carbon rather than the gain
of carbon; this process is termed photorespiration. Up to 50% of CO2 fixed in some plants (C3 plants) may be
again reoxidized to CO2, lowering the CO2-fixing efficiency.
1.6 Plant Adaptations:
Some plants, such as corn and crabgrass, have evolved a solution to this seeming defect in rubisco. CO2 is
supplied to cells that specialize in the C-fixing reactions by a special CO2-pumping cycle by the action of the
PEP-carboxylase enzyme. This biochemical cycle increases CO2 concentrations inside the photosynthesizing cells
in the mesophyll of leaves and thus decreases wasteful photorespiration. The plants can then grow with partially
closed stomata even when the weather is hot and dry.
There are two different types of CO2 pumping cycles in different groups of plants. Corn, crabgrass, sugarcane,
and many other tropical plants are called C4 plants because the first stable compound after C-fixation via PEP has
four carbons. To avoid photorespiration (common in C3 plants making them efficient C-fixing plants), initial Cfixation done via PEP occurs in chloroplasts, whereas actual C-fixation (calvin cycle) takes place elsewhere
(bundle sheath); consequently this intermediate (malate) needs to be relocated (C4 plants experience a spatial
separated C-fixation), lowering itself the efficiency of C4 plants.
Succulents such as ice plant, jade plant and other plants with water stored in thick leaves, as well as some cacti,
have a slightly different CO2 pumping cycle and are called crassulacean acid metabolism (CAM) plants.
In CAM plants, the CO2 pump fixes C at night, when temperatures are lower, humidity is higher, and the dangers
of desiccation is reduced. During the daytime, when the sun comes up and the risk of drying out rises, the stored
CO2 can be delivered to the calvin cycle without a need for the stomata to open (CAM plants experience a
temporal separated C-fixation).
CO2 assimilation with the resulting accumulation
of organic mater in relation to light exposure:
CAM plants (Tidestromia sp.) are found to be far
more efficient in C-fixation than C4 plants
(Atriplxs sp.) or C3 plants (Alocasia sp.).
On the other hand, accumulation of fixed organic
matter is greatest in C3 plants, and lowest in CAM
plants.
Since C3 plants lack PEP-prefixation, these plants
can directly fuel solar energy into the C-fixing
reaction.
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2. Working Hypothesis:
Based on my current knowledge, I would assume the following developments:
• As levels of CO2 rise in the atmosphere, the C-fixing reactions of photosynthesis should lower the carbon-loss
reactions of photorespiration in C3 plants.
• In a CO2 rich environment, the photosynthetic efficiency of many plants should increase rather than decrease.
• Since CO2, as one of the limiting resources of plants will be more abundant in a CO2 rich world, plants should
therefore increase their photosynthetic activities by boosting the number of chloroplasts contained within each
leaf.
Because of the CO2 pumping cycle, in C4 and CAM plants (which can withstand hot, dry, and sunny conditions),
those plants should have a significant advantage over the more common C3 plants.
On the other hand, C4 and CAM plants have to provide extra energy (molecules of ATP) to keep this ”turbo
charging PEP-cycle” running, hence, biomass production per acre should be lower in C4- than in C3 plants where
this extra energy is directly fueled into the C-fixing calvin cycle, i.e.: C3 plants should grow faster than their C4
and CAM competitors, creating an ecological imbalance. Following this assumption, important conclusions could
be drawn, such as that essential C4 crops like corn and sugarcane may suffer stiffer competition from ”C3 weeds”
worsening the already stressed situation for an ever increasing world-nutritional demand. To consolidate that
hypothesis, small scale experiments under elevated CO2-levels should be undertaken with representatives of all
three plant.
Based on these theories, morphologic-stereological methods are chosen for this protocol, to predict the distinct
rate of photochemical activity by way of chloroplasts present in a leaf of both sun-loving (C3, CAM) as well as
shade (C3) plants.
Consequently I would summarize the consequences of increased CO2 -levels as follows:
• General increase in rate of growth with a more prosperous and abundant leaf development.
• An upset balance of C3, C4, CAM plants by stiffer competition amongst species,
• going along with a fluctuating number of chloroplasts within plant cells, as well as an
• elevated concentration of grana contained within.
Remarks regarding stereological techniques:
All stereological measurements are in principle obtained as relative measurements, i.e.: a ratio of at least two joint
measurements, one relating to the components (phase), the other to the structure as a whole (reference system).
To obtain a more or less reliable result, the thickness of microtomial cuts should be significantly smaller than the
average thickness of the objects under investigation.
2.1. Components of the Structure (model):
Each parameters is obtained as the ratio of two measurements, one estimating the size of the objects under
investigation, the other the size of the space in which they are contained, which we may call the reference space.
Structure
Objects
Reference: Leaf represents the reference unit.
vs
Phase: The number of mesophyll / parenchyma cells contained within a
Mesophyll / p.p.
compartment
Mesophyll / p. p.
Reference: Mesophyll / pallisade parenchyma cell as the reference unit housing
vs
the objects of interests (chloroplasts).
Chloroplast Phase: The number of chloroplasts contained within a compartment.
Chloroplasts
Reference: Photosynthetic pigment is found within the stacks of thylakoids;
vs
within chloroplasts.
Granum Phase: Light dependent reaction occurs on the membrane of the thylakoids (part
of a granum) facing the stroma.
Leaf
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2.2. Evaluation of Parameters:
The fundamental quantitative descriptor of the make-up if the structure is density of the various components
within the structure (the quantity per unit volume).
Structure
Quantitative Property
Volume density: Irregularly shaped mesophyll / parenchyma cells require the
vs
determination of volume density (volume of the phase in the unit volume of
Mesophyll / p.p.
the structure).
Mesophyll / p. p.
Volume density: Irregularly shaped chloroplast in the matrix requires the
vs
determination of volume density (volume of the phase in the unit volume of
Chloroplast
the structure).
Chloroplasts
Surface density: Only thylakoid membrane contains photosynthetic pigments,
vs
hence the larger the area the more photosynthetic active is the organism; the
Granum
surface area of the phase contained in the unit volume of the structure.
Leaf
2.3. Measuring Methods:
Since 2-dimensional cuts obtained by a series of microtomial cuts do not reveal the actual 3-dimensional
structure, indirect census techniques like point-, intersection-, or number-counting are used to rebuild the original
spatial structure.
Structure
Census Technique
Point Count: The previously (under 2.2) determined procedure (volume density)
vs
requires the use of the point count. It is the fastest and by far the easiest way
Mesophyll / p.p.
to estimate the volume of photosynthetic active cells.
Point Count: The previously (under 2.2) determined procedure (volume density)
Mesophyll / p.p.
requires the use of the point count. It is the fastest and by far the easiest way
vs
to estimate the volume of chloroplasts.
Chloroplast
Chloroplasts
Intersection Count: The previously (under 2.2) determined procedure (surface
vs
density) requires the use the intersection count. Uncertainties whether lines
Granum
intersect a membrane or not can be overcome by taking the upper and the
right hand edge of the lines to represent the actual test line.
Leaf
2.4. Testgrid:
Measurements determining the relative density requires the use of a test-chart to be superimposed to every
sampled tissue (2D-section); the spatial distances between testlines should not exceed dimensions of objects under
investigation; i.e.:
• Mesophyll /parenchyma cells: spatial distance between testlines should be the size of an average cell;
• Chloroplast: spatial distance between testlines should be the size of average chloroplast;
• Granum: spatial distance between testlines should be the size of average thylakoid length.
Structure
Testsystem
Double quadratic TS: Since chloroplasts do not seem to have a specialized
vs
orientation within the compartment contained, a coherent test system is
Mesophyll / p.p.
sufficient for this purpose. Double quadratic, to make sure that sliced
samples with low content of chloroplasts do not falsify reading.
Mesophyll / p.p.
Double quadratic TS: Since chloroplasts do not seem to have a specialized
vs
orientation within the compartment contained, a coherent test system is
Chloroplast
sufficient for this purpose. Double quadratic, to make sure that sliced
samples with low content of chloroplasts do not falsify reading.
Chloroplasts
Isotropic curvilinear TS: To overcome difficulties of anisotropism (preferred
vs
orientation of membranes or boundaries) a semi-circular testsystem, based on
Granum
a square lattice, is best suited.
Leaf
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A typical plant cell
containing differently
shaped chloroplasts, a
vacuole, and some
amyloplasts; the
nucleus of the plant
cell is not visible in
this scan.
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Chloroplast with the
contained organelles
Anatomical differences
between C3 species (top)
and C4 species (bottom)
References:
• Stereological Methods Vol. 1, Ewald. R. Weibel, Academic Press London 1979 - UK
• Plant Physiology 4th ed., Frank B. Salisbury, Cleon W. Ross, Wadsworth Publishing Belmont 1992 - USA
• The Nature of Life. 3rd ed., Postlethwait J.H., Hopson J.L, McGraw Hill, New York 1995 - USA
• Biology of Plants 5th ed., Worth Publishers, New York 1992, - USA
• Molecular Cell Biology 3rd ed., H. Lodish, et al., W. H. Freeman, New York 1995 - USA
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