DEVELOPMENTAL BIOLOGY 95, 73-91 (1983) There are a number of questions which remain un- A New Method for Examining the Complexity and Relationships of “Timers” in Developing Systems DAVID R. SOLL' Department of Zoology, University of Iowa, Iowa City, Iowu 52242 Received February 16, 1982; accepted in revised form August 27, 1982 Simple methods are developed for analyzing the rate-limiting pathways, or “developmental timers,” for consecutive stages in a developing system. Two conditions are first defined for short and long timing to a developmental stage. Shifts are then performed at time intervals from short to long and long to short conditions. The total time to the stage (time under first condition plus time under second condition) is scored and plotted as a function of the time of shift, resulting in two plots, one for shifts from the short to long condition, and the other for shifts from the long to short condition. Elach plot is then analyzed for the number of components, slopes of components, absolute times of origins and termini of components, and discontinuities between components. This information is then used (1) to distinguish betwe,en single- and multiple-component timers, (2) to assess the sensitivity of each timer component to the change in the environmental condition employed in the method, including reversibility, (3) to test for the addition of a new timer component under long conditions, and (4) to test for an identity change of a timer component between short and long co:nditions. These interpretations in turn provide a minimum estimate of the complexity of the rate- limiting pathway to a developmental stage, temporally define major transition points between timer components, and provide some insight into the nature of timer components. By characterizing the rate-limiting pathway from the origin of a developmenta. program for each consecutive stage in that program, distinctions can also be made between single, parallel, sequential, and branching timer relationships. From these interpretations, a detailed temporal “map” of the rate-limiting program can be generated for any developmental system in which consecutive stages can be reproducibly monitored with time. INTRODUCTION answered concerning the regulation of timing in most developing systems. These include the number, com- plexity, identity, and relationships of those essential pathways which are rate limiting and thus serve as developmental “timers.” There are several possible rea- sons for this lack of information. First, it has been as- sumed that because the stages of a developing system are in sequence, the rate-limiting pathways for consec- utive stages are also in sequence, an assumption which has recently been questioned in at least one system (Sol1 and Waddell, 1975; Soll, 1979). Second, it has been tac- itly assumed that all essential processes for the genesis of a particular developmental stage are rate limiting, an unlikely possibility for developmental changes in- volving large numbers of gene functions. Finally, few methods have been available for first distinguishing and then analyzing those essential processes which are also rate limiting for consecutive stages in a developing system. In a recent report, a formal set of methods were de- veloped for investigating the relationships of develop- * To whom all correspondence should be addressed: Department of Zoology, University of Iowa, Iowa City, Iowa 52242. mental timers (Soll, 1979). These methods depended upon the differential sensitivities of timers to small changes in a single environmental parameter. By timing the stages of a developing system at different temper- atures within a small range, and by measuring the in- tervals between two stages after a shift from low to high and from high to low temperature at the time the first stage is formed, distinctions could be made be- tween single, sequential, and parallel timer models. When these methods were applied to a model developing system, morphogenesis in the cellular slime mold Dic- tyostelium discoideum, unexpected results were ob- tained. A number of independent timers were distin- guished for consecutive developmental stages, and sev- eral of these timers appeared to function in parallel. However, as pointed out in this report, the original methods used to interpret timer relationships were based upon the underlying assumption that timers were not complex (i.e., were not themselves composed of multiple, consecutive processes) and therefore were uni- formly affected along their entire lengths by the en- vironmental change employed. Thus, interpretations of timer relationships employing this method were ten- tative. In the present report, we present a simple and direct method for testing this assumption. By very sim- ple shift experiments, minimum timer complexity can 73 0012-1606/83/0100’73-19$03.00/O Copyright 0 1933 by Academic Press, Inc. All rights of reproduction in any form reserved.