For the anabolic reaction (4) the initial system is lower in energy and higher in entropy than the fi-
nal system. In symbolic notation,
Eanab. 0 (6)and
Sanab. 0 (7)Thus, the anabolic reaction must extract energy from the catabolic reaction and the catabolic reac-
tion must increase the entropy of the surroundings more than the anabolic reaction decreases the en-
tropy of the system. The system is defined by reaction (2). These conditions can be expressed in equation
form as
Esystem 0 (8)and
Ssurr.Ssystem 0 (9)Note that Eq. (9) is simply a statement of the second law of thermodynamics [19]. The value of Ssurr.is
related to the heat (Q) exchanged between the system and surroundings and the absolute temperature (T)
by Eq. (10).
Ssurr.Q/T (10)Neglecting pressure-volume work, which is negligible for most terrestrial biological systems [20], allows
equatingQtoH, the enthalpy change, where the minus sign indicates that heat goes from the system
to the surroundings, and equating EtoG, the Gibbs free energy change. Substituting and rearranging
in Eqs. (8), (9), and (10) provides the result
GsystemHsystemTSsystem (11)whereGsystemis the total energy change for the energy-coupled anabolic and catabolic reactions and
must be less than zero for growth to occur.
Because the entropies of the products and reactants are nearly equal, the value of TSsystemfor re-
action (2) is small and can be either negative or positive. Thus, Gsystemis negative as required for a spon-
taneous growth process only because Hsystemis negative; i.e., metabolic heat must always be exother-
mic. This requires that growing organisms with aerobic metabolism must produce heat energy that is lost
to the surroundings. This metabolic heat, which is absolutely required for growth, is not “wasteful,” is
path (condition) dependent, and should not be confused with the “maintenance rate” that appears as an
energy compartment in the model used in the reviews [15–17].
V. CALORIMETRY
Respiration has usually been measured as the rate of oxygen uptake or carbon dioxide evolution. How-
ever, this is insufficient information [Eq. (11)] to predict growth and/or ability to handle stress from abi-
otic or biotic factors. In addition to gas exchange rate, the energy lost as heat must be measured. In some
instances, where there is little or no change in substrate carbon conversion efficiency (), it is possible to
predict plant growth from gas exchange measurements alone [Eq. (2)]. But if the efficiency of conversion
of photosynthate to biomass changes, gas exchange measurements by themselves will be of limited util-
ity. Measurements of both gas exchange and heat rates are necessary to determine both rate and efficiency
of growth.
Using modern calorimeters, it is possible to make rapid, isothermal measurements of metabolic heat
rate (q) and respiration rate (RCO2) at several temperatures for small samples (~100 mg fresh weight) of
plant tissues. Much can be learned from these two simple measurements.
Plant tissue (80–100 mg fresh weight) is placed in each of three ampules of the calorimeter (Hart Sci-
entific model 7707 or Calorimetry Sciences Corporation MCDSC model 4100). After 15–20 min of ther-
mal equilibration at the desired temperature, the metabolic heat rate (q) is measured for another 15–20
min. The ampules are removed from the calorimeter and a small vial filled with 40 L of 0.40 M NaOH
TIME, PLANT GROWTH, RESPIRATION, TEMPERATURE 3