What you can get from measuring gas exchange of leaves on green plants Leaf photosynthetic rate,

A L

Caveat: you get the net CO 2 fixation rate; other PS is nitrate reduction, e.g.

Net means that you see the CO 2 uptake after subtracting respiration (done in mitochondria) from gross CO 2 uptake (done, or at least started, in chloroplasts) This can lead to: Estimates of growth potential for the plant Finding diurnal patterns of photosynthesis - checking for incipient stress, for one Determining temperature responses - optima, and failure of genotypes to hit them Measuring responses to light level - finding accumulated damage or protective downregulation of photosynthetic electron transport (photoinhibition) Measuring responses to humidity - explaining seasonal and diurnal differences in PS rates, in part Relating PS capacity to treatment, esp. nutrition Leaf "dark" respiration rates (turn off the lights! There is a correction to this raw estimate; in the light, respiration was partly repressed)

Stomatal conductance,

g s

- getting a lot more info!

How

g s

figures in transpiration per unit leaf area, EL

E L = g bs (e i - e a )/P g bs

is the total conductance for water vapor moving across the leaf boundary layer (conductance

g b

) and through the leaf stomata (conductance

g s

)

g b

is the boundary-layer conductance of the leaf, set by the physics of air flow; it depends on leaf dimension along the airflow,

d

, and on windspeed,

u

, very closely as

constant*sqrt(u/d)

We use conductances; they are 1/resistances Resistances in series add, so conductances of two paths in series have this relation:

e i 1/g bs = 1/g b + 1/g s is the partial pressure of water vapo

r inside the leaf, set almost wholly by leaf temperature, as the saturated vapor pressure (leaves are very wet) e a is the partial pressure of water vapor in outside air Why is total air pressure, P, in this relation? It makes results almost independent of differences in temperature between air and leaf Note that g s then has the same units, called molar units, as does PS rate, A L

How can we measure g s ?

We can measure

E L

, by measuring the water vapor pumped out into the air passing over a leaf We can measure

g b

(with a wet filter paper instead of a leaf), or estimate it from leaf dimension and windspeed We can measure total air pressure We can measure

e a

various ways - in the LI-6400, directly, using infrared light absorption by water vapor (in the IRGA = infrared gas analyzer) The value of

e i

is determined by leaf temperature, with an effectively negligible correction from leaf water potential So, we can invert the equation and get

g s

How g s figures in photosynthesis: Transport relation:

A L = g bs '(C a -C i) /P

Similarly to the case for water vapor movement:

1/g bs ' = 1/g b ' + 1/g s '

Why all the primes (')? They denote values for CO 2 ; unprimed values are for water vapor

C a

is the partial pressure of CO 2 in the outside air;

C i

is the partial pressure of CO 2 in the air spaces inside the leaf

A focus on

C i

, too How is

C i

measured? We can't have little sensors inside leaves; we compute it from

C a

and

g bs

 we get

g s

from the transpiration rate per leaf area,

E L

What is the real significance of

C i

?

How is it determined by physiology? Enzyme kinetics:

A = V c,max (C i Γ)/(Ci+K CO )

- in high light; a brilliant simplification of complex multi-enzyme pathways by FvCB

Γ

is a compensation partial pressure - it depends on temperature (and on O 2 partial pressure, which only varies with elevation) Really, we should include liquid-phase conductance in cells,

g m

; replace

C i

with

C c

, the partial pressure at the chloroplast, vs. in air spaces

Set the two formulas equal:

g bs '(C a -C i) /P = V c,max (C i Γ)/(Ci+K CO )

 a quadratic in

C i We can solve for C i

, for given:

* leaf physiology (g s , V c,max

)

* environment (g b , C a , P

, leaf temperature 

Γ, K CO

)

* Well, these are intertwined: * g s

responds to environment, too

* leaf temperature depends on what the leaf is doing, too



There are more fundamental parameters of physiology

C i

is a measure of stress, and also of water-use efficiency All else equal, if

g s

drops (as to reduce water loss rate = transpiration), then

C i

drops If

C i

drops, so does PS rate,

A L

The relative drop in

A L

is less than the relative drop in g s - e.g., if

g s

drops 20%,

A L

might only drop 7% The drop is transpiration, however, is almost in proportion to that in

g s

The water-use efficiency goes up. The leaf gains here, and also in delaying potentially damaging total water loss

We can formulate water-use efficiency on several different scales of time (instantaneous to seasonal) and space (leaf to canopy to ecosystem). On the leaf scale, the instantaneous WUE is

WUE = A L /E L = g bs ' (C a - C i ) / P --------------- g bs (e i - e a ) / P

We usually considered CO 2 level in the air,

C a

, as constant. We often compare leaves operating at the same temperature and humidity, so that

e i

and

e a

are constant. The ratio of

g bs '

to

g bs

is very nearly constant

(g s '/g s = 0.62; g b //g b = 0.71

). So, we can write

WUE ≈ 0.62 ( C a / [e i - e a ] ) (1 - C i /C a )

The ratio

C i /C a

is an intrinsic measure of stress and of WUE. This ratio can be measured in gas exchange. For long-term studies, as in comparing cultivars or past and current climates, it is better measured by the ratio of stable isotopes, [ 13 C]/[ 12 C], in plant tissues (no details here)

More information: patterns of stomatal conductance - stomatal control *

g s

in any one condition is just a number; what does it tell us 'in the large'?

*

g s

responds to light level, temperature, humidity, CO 2 level, etc.

Are there regular patterns that capture it all?

Yes, and a good fit is typically the Ball-Berry relation, with only two parameters,

m

and

b

(slope and intercept) and these are often very similar among plants…and they change with water stress, primarily

g s ≈ m A h s / C s + b

g s ≈ m A h s / C s + b A

is the PS rate we've been talking about.

h s

is the relative humidity at the leaf surface, beneath the leaf boundary layer.

It equals

e s /e i

, where

e s

is the water vapor partial pressure at the surface.

We clearly can't measure this directly but it is expressed in transport equations:

E L = g s (e i - e s )/P = g b (e s - e a )/P

We can solve for

e s

and for

e s /e i

, using the known quantities

e i , e a , g s , g b

:

h s = e s /e i = (g s + g b e a /e i ) / (g s + g b ) C s

is the CO 2 mixing ratio (CO 2 partial pressure at the surface, divided by total air pressure). It can be computed from the PS rate and other known quantities, using transport relations:

C s = C a /P - A L /g b '

Yes, the PS rate itself appears in the equation. This represents a real physiological feedback that has been verified.

This has lots of implications for predicting the PS rate from physiological and environmental conditions - many nonlinear equations are linked, but the solution methods exist and are robust.

Alternative empirical equations for stomatal control exist; none are really better than this Ball-Berry equation, overall. Truly mechanistic equations are being developed, but are incomplete to date.

We can get even more detail by simultaneously measuring chlorophyll fluorescence.

This gives details on the photochemistry inside the leaf From the notes above, it's clear (I hope) that we can do gas-exchange measurements on: * Different leaves of a plant, to see their relative contributions to fluxes and to growth * Different plants, genotypes, species, to see their intrinsic differences in performance * Different environmental conditions - temperature, humidity, light level, even CO 2 level, to get more information. The LI-6400 allows control over all these environmental variables. It has a Peltier heater/cooler that can change leaf T up or down. It has desiccants that can reduce the humidity to a controlled level, and there is a separate humidity generator that can be used to set an almost arbitrarily higher or lower humidity. We can angle the leaf to or away from the sun to get various light levels, or we can use an electronically controlled light source that attaches to the LI-COR as an option (extra cost). We can plug in a CO 2 cartridge and let the LI-COR automatically control the CO 2 level at the leaf.

While we're on the subject of different environments, here are a few considerations and caveats: * A leaf in the LI-6400 chamber is almost always under conditions (light, temperature, humidity, windspeed) that differ from those when it was on the plant, undisturbed.

* Foremost, this means that its PS rate and esp. its transpiration rate have changed. While the PS rate can be close to its original rate, the transpiration rate is often changed notably; you should not estimate WUE for the ratio of

AL/E L

inside the chamber.

* Stomatal conductance can change slowly in adjusting to new conditions. With an open system such as the LI-6400, you can keep the leaf 'happy' in stable new conditions and wait for the new g s to stabilize, in response. Be aware that this can be a long time for woody plants, in particular - up to 15 min. Fortunately, you can watch the leaf performance in real time and see if it has stabilized.

More about responses of leaves to light levels (and to physiological limitations): * The expression used earlier is very good for high light - at so-called light saturation. Let's call this value

A sat

* At low light levels, the PS rate is linearly proportional to light level, measured as a quantum flux density,

I L

, in the photosynthetically active radiation (PAR) band, between 400 and 700 nm in wavelength (essentially the visible spectrum). Call this the light-limited rate,

A LL = Q 0 I L

Here,

Q 0

is called the initial quantum yield. It depends on temperature and O 2 level. In normal ranges of both, it is near 0.05 (as mol CO 2 fixed per mol of light intercepted).

* At any intermediate light level,

I L

, there is a transition between the two rates, well expressed using a "convexity" parameter,

θ

:

θA 2 - A(A LL +A sat ) + A LL A sat



A = [0.5/ θ][ A sat + A LL = 0 - sqrt( {A sat + A LL } 2 4 θ A sat A LL ) ] Fortunately, θ

is about 0.8 for many different plants.

There is one more potential internal limitation to PS rates - from maximal rates of triose phosphate utilization (shipping sugars out of the chloroplast). This can be fitted into a generalization of the above equation.

Finally, another topic in PS rates is the transient behavior. Sudden changes of light level can occur (a leaf find itself in a sunfleck); the steady-state biochemical models don't apply; they have been extended to cover this case, such as in the work by Bob Pearcy and his group.

Other transients occur in stomatal control. A leaf shocked by a sudden drop in humidity can go into stomatal oscillation, or even close up for extended times. You don't learn anything useful from causing these kinds of transients, so you should avoid them by not imposing sudden changes on the leaf, esp. changes in humidity.

How does gas exchange work?

Basically, you flow air over a leaf and find how much CO 2 was taken out and how much water vapor was added. You divide by the leaf area to report rates per area.

The leaf is clamped into a chamber that seals well. Air is actively pumped into and out of the chamber across the leaf.

(Image from the LI-COR manual, Using_the_LI-6400-v5.3.pdf) Actually, the LI-6400 uses a better system, with the IRGAs right in the sensor head, for faster response:

The input conditions need to be stable - total air flow rate, CO 2 content, humidity, light level.

Otherwise, the leaf develops transients that may not average out. Also, the system has lag times between air flowing in and flowing out; the instantaneous readings refer to a past time and are hard to interpret.

This means that you can't breathe near the input if you're not using the CO 2 control. Normal air has about 385 ppm CO 2 ; your breath is typically 20,000 ppm CO 2 …and you'll be trying to measure shifts in CO 2 that are commonly 10-20 ppm.

It also means you have to be careful about leaks into or out of the cuvette that you clamp onto the leaf. The leaf petiole has to be kept intact, so the seal has to be made around this relatively bulky item.

Measuring transpiration: (LI-COR manual) It's important to keep track of units and the meaning of each quantity.

Air flows in at a rate

u i

("i"=input). Gas-exchange systems measure this as a mass flow rate (as in your fuel-injected car), reported equivalently as moles per second (mol s -1 ).

The incoming air contains CO 2 , which constitutes a mole fraction

c i

. (Try not to confuse this with capital-C

C i ,

leaf-internal CO 2 level.) This is the commonly termed mixing ratio, such as 385 ppm (as 385 mol CO 2 per million mol air. Note that, as a mass fraction, it is larger, since CO 2 is heavier than the rest of the air).

Similarly, the incoming air contains water vapor at a mole fraction

w i

.

This is related to other standard measures of water content: Relative humidity = (partial pressure of water vapor)/(saturated vapor pressure) =

e a / e sat (T air ) e sat (T air )

is a nearly exponential function, close to

610.8 Pa * exp(0.065 T air )

So,

e a

= (relative humidity, as a fraction)*

e sat (T air )

At any partial pressure of water vapor, the moles of water,

n w

, per volume

V

of air follows the ideal gas law extremely closely:

n w / V = e a / (R T air,abs )

,

R

= universal gas constant = 8.314 J mol -1 K -1 and

T air,abs

is the absolute air temperature,

T air (ºC)

+273.2K

The mixing ratio is simply

e a / P

You don't have to do all these calculations yourself. The g-x system measures the water-vapor content spectroscopically and computes

w i

and all other measures.

So, the incoming air contains

u i w i

moles of water and

u i c i

moles of CO 2 .

The leaf has an area

s

and a transpiration rate

E

. It adds water vapor at a rate

E s

, in moles per second.

This adds to the incoming flow. The outgoing flow is

u o = u i + E s

, all in mol s -1 . (The loss of CO 2 to uptake by photosynthesis is too small, in comparison, to consider.) By mass balance:

u i w i + E s = u o w o = (u i + E s) w o

The system measures

ui, wi, and wo

. You measure the leaf area (we'll get to some details on this), so we can solve for

E

: A few notes: The LI-6400 reports flows in micromol s -1 , not mol s -1 . It reports mole fractions of water vapor, w i and w o , in parts per thousand (mmol water per mol air). The conversion factors are simple.

Computing stomatal conductance In my original notation,

E = g bs (e i - e a )/P

The LI-6400 reports mole fractions, which it calls

w L

("L" = leaf, meaning inside the leaf) and

w s

("s" = in the sample stream of air, as constrasted with the reference stream, the input).

The manual for the LI-6400 also uses the notation

g rw

instead of

g bs

. We have:

E = g rw (e i /P - e a /P) = g rw (w L - w s )

Actually, there's a small correction for mass flow of water vapor coming out of the leaf, affecting the flow:

E = g rw (w L - w s )/ (1 - 0.5*(w L + w s ) )

The LI-6400 thus computes total stomatal + boundary layer conductance as

The boundary layer is symmetrical on both sides of the leaf (typically), but stomata are commonly more abundant on one side of the leaf vs. the other. Consider first the case of equal stomatal conductance on both sides. We would have my simple formula on p. 2 here. Stomatal conductance for water vapor would be computed as

g s

 1 1

g rw

 1

g b

If stomatal conductance on one side is

K

times the value on the other, there is a correction or conversion factor, k f :

Here, the LI-6400 manual puts in an explicit extra subscript,

w

, so that

g sw

means the stomatal conductance for water. The usual convention is to drop this extra subscript; without qualifications,

g s

means conductance for water (not CO 2 ).

The factor

k f

is You can check that it gives the same answer if

K

= 2 or

K

= ½ (that is, it doesn't matter which side of the leaf you choose as the reference for the other side).

Computing the photosynthetic rate: The same kinds of mass balance calculations apply as for water vapor: Incoming air has a molar flow rate of CO 2 equal to

u i c i

.

The leaf removes CO 2 at a rate

s A

, with

A

as the PS rate per unit leaf area and

s

as the leaf area..

The outgoing air has a total molar flow rate

u o c o = (u i + E s) c o

. (Again, we can neglect the small change in flow rate from CO 2 uptake rate compared to the water added by transpiration, several hundred times larger.) We get:

A s = u i c i - (u i + E s) c o

Or:

A = u i (c i - c o )/s - E c o

Note how transpiration dilutes the CO 2 mole fraction, even in the absence of photosynthesis. The term in

E c o

is important.

The LI-COR reports

c i

and

c o

in ppm (micromol per mol), not mol per mol = mole fraction, and it reports

A

in practical units of micromol m -2 s -1 , not mol m -2 s -1 . The conversion factors are straightforward.

The LI-6400 also calculates internal CO 2 in the leaf,

C i

. See the calculations on p. 40 of the manual: Here,

g tc

is the total conductance for CO 2 (my original g bs ') and

C s

is my

C a /P

, the mole fraction of CO 2 in "outside" air (the air around the leaf in the chamber).

Setting up the physical system, configuring the software, and running the system These topics are extensive. They are described in the manual in full detail. One needs hands-on experience over a few hours to really learn this. LI-COR also makes available software that simulates the operation of the LI-6400.

There are a number of checks to go through. These assure that: * The IRGA sensors that measure water and CO 2 on the sample and reference sides are balanced, to that the differences recorded between the two side truly represent the action of leaves (A and E) and not systematic offsets.

* There are no leaks into or out of the cuvette.

* The subsystems to remove water vapor and CO 2 are working. To get accurate readings of the full spans of water vapor and CO 2 content, you are asked to switch in tubes containing magnesium perchlorate (desiccant, to remove water vapor) or soda lime (scrubber, to remove CO 2 ). If the system fails to read zero on either water vapor or CO 2 , then it is likely that the desiccant or the scrubber is exhausted and must be replaced.

* Electrical connections are good.

* All the sensors are working, such as leaf temperature (not all the checks are automatic; I found a broken leaf-T sensor once, suspecting it from data readings and verifying it by touching the thermocouple sensor with my finger to warm it up).

You need to verify that the sensors you have attached are the ones whose calibration data are stored in the system memory.

* Data are recorded properly.

You may also need to hook up a buffer volume of intake air (p. 49 of the manual). This can be an empty 2-liter soda bottle. It is useful because CO 2 content of air varies moderately (several ppm or more) over times as short as seconds, as air moves in cyclical eddies, down into the canopy (at high CO 2 ) and up (at lower CO 2 ). In the buffer volume, these changes are averaged out very well. The small changes that remain are slow to occur and average out well between the sample and reference sides of the system. Here's a cut from p. 209 of the manual):

Software to run the system is pre-installed. The only time you have to consider installing software is when you update it. Instructions are on pp. 68 ff. in the manual.

The console of the LI-6400 has alphanumeric keys, like any other keyboard. It also has special function keys (like all PC keyboards) and cursor control keys that are mixed in with some other special keys (page up, page down, home, and end). If you use a computer, these look familiar. You have to learn what the functions are, and, more so, what the various displays mean.

The displays begin with a simple welcome screen:

After the system warms up (quickly), you can choose the mode (configuration) that you will use. There is a factory default (using a standard leaf chamber or cuvette; using a thermocouple to measure leaf T…), and there may be special configurations that you set up and then saved. In the example here, one special configuration is for using the conifer needle chamber. Another uses computed energy balance on leaves when one can't assure good contact with the thermocouple).

You'll get to the main screen for the open mode: It is clearly packed with information. You'll get used to it. Be sure to watch for alerts, such as about blown fuses.

The welcome menu isn't used often, but it tells you about service dates, etc.

The configuration menu lets you set up any special items, such as a different leaf chamber. Se p. 81 in the manual.

The calibration menu is used every time you start. You have to zero the readings of the flowmeter, the IRGAs, and any auxiliary devices, such as a CO 2 control system. See p. 82 in the manual.

The utility menu (p. 84) lets you set up communication ports, export and import data, recalculate data, etc.

Finally, the new measurements menu lets you start taking new data (p. 85):

There are two other display modes that you can access,, including the very useful graphics mode that lets you see how leaf performance is stabilizing (or not!): Actual logging of data is controlled by you. Until you hit log, you're just monitoring readings that won't be saved. The logging steps (manual or automatic) are given on pp. 120 ff.

You can do many things to improve accuracy and control conditions while you examine the system performance. For example, you can change the fan speed or the air flow rate. These are not the same thing. Air flow is for net exchange of air, out of the chamber. Fan speed is for stirring the air within the chamber, to alter the leaf boundary-layer conductance. There is a lot more detail on pp. 99 ff.

You can change which measurements you are viewing and the order in which they are displayed. For example, you may be most interested in the CO 2 difference, to be sure that it is large enough to be measured accurately but small enough so that the leaf is operating near the free-air conditions. You can save the display groups (p. 91).

Finally, you'll have data that you can view, graph, export, and manipulate. See pp. 122 ff.

The options for further calculations and graphs are remarkable. You even write programs in LPL language to process data, including from multiple data files (e.g., you want to determine the Ball-Berry parameters by plotting

g s

against the index

A h s / C s

from runs under different conditions).

The manual has a section (pp. 161 ff.) on making good measurements - checking stability, leaks, etc. This includes how to do some advanced measurements, such as "

A-C i

" or

A(C i )

curves - measuring how photosynthetic rate varies as you manipulate

C i

, by changing the incoming air CO 2 content. There is also a good discussion on why these curves are informative about leaf physiology:

Another section describes how to measure light response curves, including giving the leaf time to stabilize at each new light level.

Other details include how the system can correct for remaining diffusive leaks into or out of the cuvette seals (pp. 203 ff.) The manual goes on for many more pages, covering everything you need to know. LI-COR is famous for its great support, in the manuals and on the phone. The length of the manual (1106 pp.) is an indication that gas exchange is a rich field, as well as one that needs care in setting up and taking measurements.