Several optimality principles reasonable for the evolution of enzyme reaction chains are formulated, considering the kinetic parameters of the enzymes to be variables. The solutions of these parametric programming problems are studied for the case of linear kinetics and turn out to be not unique in every case. The investigations are confined to stationary states. The net flux through the chain is considered a fixed parameter. The optimality criteria concern the osmotic pressure caused by the intermediates, various relaxation times, largest time scale, and controllability. They all yield distinct time hierarchies. The influence of a constraint concerning the sum of intermediate concentrations is studied. Various combinations of the single criteria are treated as multiobjective programming problems.

Biological Evolution↗

PubMed1987

Mathematical modeling of the effects of the signal recognition particle on translation and translocation of proteins across the endoplasmic reticulum membrane.

The kinetics of the signal recognition particle(SRP)-mediated process of protein translocation across the endoplasmic reticulum membrane was studied by mathematical modeling and complementary experiments. The following results were obtained. (1) A model according to which SRP directs the ribosome, rather than the mRNA, to the membrane is supported by experiments designed to discriminate between the two alternatives. (2) This model describes both steady-state and synchronized translation experiments and makes a number of predictions. (3) The interaction between a nascent protein and SRP may be described by two parameters: (i) a binding constant which can be attributed to the structure of the signal peptide, and (ii) the size of the "SRP-window", i.e. the distance between the first and the last site on the polypeptide chain that can interact with SRP. For preprolactin a binding constant of 1 to 2.5 nmol-1l was estimated. Modeling of the synchronized synthesis of ovalbumin indicates that it has a much weaker binding constant than preprolactin (approximately 0.25 nmol-1l) although we cannot exclude the possibility that the SRP-window may be also smaller. (4) A better understanding of the molecular effects of SRP on translation and translocation through the rough endoplasmic reticulum membrane has been achieved. Inhibition of the steady-state rate of translation by SRP requires a stoichiometric interaction of SRP with ribosomes carrying nascent polypeptide chains and will occur only when ribosomes are piled up back to the initiation site. Translocation, on the other hand, requires only the catalytic action of SRP and is determined by the local concentration of protein-synthesizing ribosomes accumulated at the site(s) of SRP interaction. As a consequence, translational inhibition by SRP may sometimes fail to occur, depending either on the type of protein or on experimental conditions, such as a high mRNA concentration, even if translocation can be demonstrated. (5) A rough extrapolation to the conditions in vivo indicates that all synthesized polypeptide chains destined for translocation across or integration into the endoplasmic reticulum membrane are indeed quantitatively translocated and that no translational inhibition occurs.

Endoplasmic Reticulum↗

PubMed1987