**Susan Dunford, University of Cincinnati, Cincinnati, OH, USA**

The speed of sugar molecules along the sieve elements of the phloem is known as the **mass transfer rate**. Measurements of mass transfer rates were among the earliest quantitative determinations made in phloem physiology. The early studies measured either gain in weight by developing fruits or storage organs (sinks) or loss of weight by mature leaves (sources) over a known time interval; the sink experiments are generally the more accurate.

For example, in 1926 Mason and Lewin determined weights of individual tubers of the greater yam (*Dioscorea alata*) over a growing season. The increase in dry weight was divided by the time interval to obtain an average mass transfer rate. This rate, divided by the average sieve element area per stem, yields a specific mass transfer rate of 5.7 g h^{–1} cm^{–2} of sieve elements. Several similar studies obtained mass transfer rates of 0.2 to 4.8 g h^{–1} cm^{–2} of phloem. If sieve elements are assumed to occupy approximately one-third of the phloem cross-sectional area (a reasonable estimate), these results yield specific mass transfer rates of 0.6 to 14.5 g h^{–1} cm^{–2} for sieve elements (Mason and Lewin, 1926).

A more recent technique for determining mass transfer rates by use of radioactive tracers gives rates in excellent agreement with the earlier measurements (Geiger and Swanson, 1965). In this method the plant is usually pruned to a single mature source leaf and a single immature sink leaf. Carbon dioxide labeled with ^{14}C is supplied to the source leaf in such a way that the rate of supply is equal to the rate of fixation. The rate of arrival of label in the sink tissue is monitored for the duration of the experiment. The supplied radioactive CO_{2} contains a predetermined amount of radioactivity per unit weight of carbon (specific activity). After a certain period of time, the sugars in transit from the source to the sink reach the same specific activity as the supplied CO_{2}. When this state, called *isotopic saturation,* has been reached, the mass transfer rate can be calculated from the rate of arrival of label in the sink tissue, as follows:

where Bq stands for becquerel, a unit of radioactivity, and s stands for seconds. (A becquerel or [Bq] is equivalent to 1 disintegration per second. Another unit of radioactivity that has been used quite often is the curie or [Ci], which is equivalent to 3.7 × 10^{10} disintegrations per second.) The rate determined in this way, corrected for the cross-sectional area of sieve elements in the transit pathway, provides an estimate of specific mass transfer. For sugar beet, which transports sucrose, the value obtained is equivalent to a rate of 4.8 g h^{–1} cm^{–2} of sieve elements, in excellent agreement with the values determined in earlier investigations.

**References**

Geiger DR, Swanson CA (1965) Evaluation of Selected Parameters in a Sugar Beet Translocation System. *Plant Physiol* 40: 942–947.

Mason TG, Lewin CJ (1926) On the rate of carbohydrate transport in the greater yam, *Dioscorea alata* Linn. *Sci. Proc. Roy. Dublin Soc* 18: 203–205.