BIOCHIMIE, 1979, 61, 263-273. Dynamics of macromolecular populations: a of the quantitative changes of RNA in the the last larval instar. mathematical model silkgland during Alain PAVIa. Laboratoire de Biom~trie, Universit~ Claude Bernard Lyon I, 43, Boulevard du 11 Novembre 1918, 69621 Villenrbanne, France. (and Greco : ¢ Analyse des syst~mes ~, C.N.R.S.). R~sum~. Le medble de Volterra-Kostitzin est utilis6 pour l'analyse de l'6volution quantitative des RNA dans la glande s~ricigbne de Bombyx mort au cours du dernier ~ge larvaire. On propose d'associer & ce meddle un m6camisme global traduisant notamment la synth~se el la d~jza- dation de ces macromol6cules. Les m6thodes num~riques et statistiques d'utilisation du too- dale sont expos6es en appendice. Les variations des quantit6s de RNA total (essentiellement ribosomiques) ont 6t6 compa- r6es aprbs traitement (hormone juv6nile) et entre diff6rentes souches. On note l'importance du terme de d6qradation, qui explique & hi seul la plupart des diff6rences enreqistr6es, a]ors que la synthbse reste relativement stable. Ces observations peuvent mener ~ une inter- pr6tation mol6culaire de l'effet d'une s61ection portant sur l'auqraentation de la production de sole : plut6t qu'auqmenter la productivit6 de la machinerie cellulaire, la d$qradation aurait 6t6 limit6e. Summary. The quantitative changes of RNA in the silk- gland of Bombyx mori have been studied during the last larval instar by using a mathematical model (Volterra-Kostitzin model). This model can be associated with a global mechanism includ- ing synthesis and deqradative processes. The numerical and statistical methods used for mo- del analysis are described in an appendix. Thus we have compared the accumulation of total RNA (essentially ribosomal) after a treat- ment (juvenile hormone) and between several strains. The importance of the deqradative fac- tor is denoted to explain the observed diffe- rences, whereas the synthesis rates remain relatively stable. The last observation may lead us to an inter- pretation of the molecular effect of a selection to increase silk production: rather than an increase of the productivity of cellular machi- nery, the degradative process has been limited. Key words: Mathematical model, Biochemistry, Biometry, Silkworm, RNA. Introduction. Very often, when mathematical modelling of dynamics of macromolecules is needed, approa- ches derived from Biochemical kinetics are attempted. However frequently the lack of data and the formal expression of the model itself (often nonlinear and .complex with many unk- nown parameters) make them difficult to use. Furthermore many hypothesis have to be assumed on involved mechanisms, this last characteristic is in fact their principal property : they are con- sidered as models of knonvledge in the precise sense. Thus we have thought that an other point of view is possible, even desirable, it consists to chose a class of dynamical models in the field of dynamics of populations. Such an approach is based on the assumption that macromolecules can be looked like individuals of populations, in the ecological sense [1]. If we consider on the one