Analyzing growth in cell cultures. I. Calculating growth rates

Growth is the major parameter used to assess novel phenotypes derived from plant tissue cultures. Any quantitative analysis of growth must have an explicit rational basis. Frequently this criterion is not met. For example, the calculation (W2 − W1)/W1(W1 = initial weight; W2 = final weight) approximates neither linear nor exponential growth. Yet, it is a common method of analysis, as is the related calculation W2/W1. When absolute growth values provide insufficient information, meaningful relative growth rate equations can be utilized. Relative growth rates should be evaluated as ln (W2/W1)/(t2 − t1) for t = time, thereby yielding a constant growth rate for exponentially growing cell lines. Linear growth (root growth, for example) can be approximated by 2(W2 − W1)/((W1 + W2)(t2 − t1)). All methods of analysis we have encountered assume that relative growth at a given instant depends on total mass. The possibility exists that growth may actually be proportional to mass raised to some power less than one. For example, growth could be limited to a thin outer shell of a spherical callus. Then the relative growth rate would equal 3(W21/3 − W11/3)/(t2 − t1). Data can be seriously distorted when inappropriate calculations are used. Such distortions are exacerbated when comparisons are made. In all cases an adequate assessment of growth kinetics for each cell line and each treatment is essential.