A new method for examining the complexity and relationships of “timers” in developing systems☆

摘要

Simplemethodsaredevelopedforanalyzingtherate-limitingpathways,ora€?developmentaltimers,a€?forconsecutivestagesinadevelopingsystem.Twoconditionsarefirstdefinedforshortandlongtimingtoadevelopmentalstage.Shiftsarethenperformedattimeintervalsfromshorttolongandlongtoshortconditions.Thetotaltimetothestage(timeunderfirstconditionplustimeundersecondcondition)isscoredandplottedasafunctionofthetimeofshift,resultingintwoplots,oneforshiftsfromtheshorttolongcondition,andtheotherforshiftsfromthelongtoshortcondition.Eachplotisthenanalyzedforthenumberofcomponents,slopesofcomponents,absolutetimesoforiginsandterminiofcomponents,anddiscontinuitiesbetweencomponents.Thisinformationisthenused(1)todistinguishbetweensingle-andmultiple-componenttimers,(2)toassessthesensitivityofeachtimercomponenttothechangeintheenvironmentalconditionemployedinthemethod,includingreversibility,(3)totestfortheadditionofanewtimercomponentunderlongconditions,and(4)totestforanidentitychangeofatimercomponentbetweenshortandlongconditions.Theseinterpretationsinturnprovideaminimumestimateofthecomplexityoftherate-limitingpathwaytoadevelopmentalstage,temporallydefinemajortransitionpointsbetweentimercomponents,andprovidesomeinsightintothenatureoftimercomponents.Bycharacterizingtherate-limitingpathwayfromtheoriginofadevelopmentalprogramforeachconsecutivestageinthatprogram,distinctionscanalsobemadebetweensingle,parallel,sequential,andbranchingtimerrelationships.Fromtheseinterpretations,adetailedtemporala€?mapa€?oftherate-limitingprogramcanbegeneratedforanydevelopmentalsysteminwhichconsecutivestagescanbereproduciblymonitoredwithtime.