Temperature Coefficients for Biological Processes
Authors: Henry J. Glynn 
Published: March 2019

Abstract
The effects of low temperature on biological processes are normally described by a temperature coefficient which, at one time, was assumed to be constant over a limited temperature range. The coefficient has been employed in various forms of the Arrhenius relationship, the Streeter-Phelps equation or similar expressions to relate some metabolic activity to temperature.
Many investigators have demonstrated that temperature coefficients are in fact, not constant and vary widely; between various biological activities, with different processes, for diverse microbial populations and between laboratory results and field experience. Substrate concentration, cell yield and the type of microorganisms are among the factors which influence microbial activities and, therefore, affect temperature coefficients. Experimental work carried out with continuous laboratory models at the University of Toronto has indicated that:
1. The temperature coefficient for an unrestricted activity, like oxygen uptake for example, follows a saturation curve as a function of the substrate concentration.
2. In a food limiting situation such as occurs in a biological waste treatment plant, the quantity of cells from a unit amount of substrate, i.e. Cell Yield, is increased by lower temperature.
3. With decreasing temperature, the microbial population in a mixed culture shifts from predominantly mesophilic to psychrophilic bacteria which have temperature coefficients approximately half of those for mesophiles.
This paper examines how microbial activities in a waste treatment system interact to moderate the effect of low temperature on process efficiency. The microbial activities of most interest in treatment plants are growth rate, oxygen uptake and substrate utilization. With mixed cultures, the moderating effect of the shift to a predominantly psychrophilic population, which is much less sensitive to temperature changes, is another factor which must be taken into account.
Growth rate in a continuous system is a constant, set by the dilution rate in a flow-through process, or by the rate of return and solids concentration when recirculation is provided. This means that under constant flow conditions., growth rate is a restricted activity and not influenced by temperature. Oxygen uptake on the other hand is not fixed by the dilution rate. It can vary with temperature, provided that the proportion of the substrate which is oxidized for energy can also vary. Laboratory models have verified that Yield is not constant but becomes larger at lower temperature. With some variation in Yield, it is possible then for oxygen uptake to vary with substrate concentration as a saturation function. These interdependent mechanisms of growth and oxygen uptake are the major means for substrate utilization. The influence of temperature on substrate removal, therefore, depends upon its effect on growth and uptake. For a system where growth rate is constant and oxygen uptake follows the Monod equation, then only uptake is temperature dependent. Since uptake accounts for about one-third of the substrate utilized then the effect of temperature on organic removal as compared to its effects on oxygen uptake, should be proportionately reduced.
The paper illustrates diagramatically how growth and oxygen uptake rate vary with substrate concentration and temperature and how psychrophiles contribute to a lower temperature coefficient for process efficiency. The diagrams help to explain why the influence of temperature on substrate utilization can be so much less than its effect on individual activities. The final part of the paper demonstrates how the basic equations relating activity, substrate concentration and temperature, together with the associated change in the psychrophilic population can be used to determine temperature coefficients from laboratory studies.