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We are dealing with a numerical method for solving the problem of minimizing a difference of two convex functions (a d.c. function) over a closed convex set in R". This algorithm combines a new prismatic branch and bound technique with polyhedral outer approximation in such a way that only linear programming problems have to be solved.

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The mechanism of the reaction catalyzed by yeast hexokinase has been investigated by means of spectrophotometric investigations. Two binding sites, one for the sugar and one for the nucleotide substrate, have been characterized.The interaction of sugar substrates with yeast hexokinase induces spectral perturbations of aromatic residues of the protein molecule. The specificity of the enzyme towards its sugar substrates is discussed.The interaction of ATP-Mg can only be visualized spectrophotometrically when the sugar substrate or inhibitor is already bound to the enzyme.Furthermore, spectrophotometric studies evidence the formation of a binary complex (sugar However, the true mechanism of the reaction and the way in which the ternary complex is formed is still a matter of controversy. properties suggest the formation of a catalytic transitory phosphoryl enzyme [ll]. To explain the glucose-6-phosphate exchange, a second hypothesis in which glucose-6-phosphate is supposed to be bound a t the ATP site and glucose at the sugar site has been postulated [13]. Finally, the binding of some pentoses like lyxose or xylose produces an induced fit of the protein which enhances the hydrolysis rate of ATP [la]. After a n initial activating effect of xylose, De La Fuente has observed that the enzyme is inactivated [15]. I n a recent paper, Colowick has shown that this inactivation is related to the phosphorylation of hexokinase [16]. From this result, he has postulated [ 171 that "catalysis involves an active phosphoryl enzyme derivative which in the presence of D-xylose undergoes rearrangement to form the inactive derivative. It is also possible that the phosphorylation of the protein occurs only as a side reaction".By studying the interaction of various substrates with yeast hexokinase by means of difference spectrophotometry we can provide some information on the mechanism of this reaction; herein, we report the data on the formation of binary and ternary complexes between hexokinase and various substrates and analogs. We have also characterized a binding site specific for nucleotide substrates and another one for sugar phosphorylated sugar.Eur. J. Bioohem. 44 (1974)

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The overall reaction catalyzed by the phosphotransferase arginine kinase was studied at normal and subzero temperatures. Ethylene glycol was used as the antifreeze and its effects on the K , values of substrates, k,,, and pH profiles were investigated in detail.a) The K , values for the substrate (2 mM for ATP and 0.6 mM for arginine) were little affected by the solvent composition or temperature of the reaction mixture.b) At concentration of ethylene glycol higher than 40% there was a sharp drop of enzyme activity. c) Ethylene glycol induces a large shift in the enzymic pK d) At -5 "C in 40% of solvent there was a break in the Arrhenius plot suggesting a change of the rate-limiting step.The relevance of these results to the reaction pathway of arginine kinase is discussed. In addition, controlled perturbations induced by cosolvent and temperature appear as useful tools for further kinetic investigations.The study of enzyme systems in hydro-organic solvent at subzero temperatures is a means of accumulating and trapping intermediates in the chemical processes which occur in enzyme-catalyzed reactionsThere is at present little information on the reaction pathways of the phosphagen kinases. This is in part due to their high turnover numbers and, in general, to their relatively poor substrate affinity constants.It seemed of interest to apply the methods of cryoenzyniology to this important group of enzymes. Such studies could provide a model not only for the reaction mechanisms of two substrate enzymes (hitherto not studied by cryoenzymology) but also for ATP cleavage reactions, such as that catalyzed by the myosin system.Our first choice was arginine kinase; this enzyme is relatively stable and the fact that it is a monomer facilitates the interpretation of the data.Arginine kinase catalyzes the following reaction : ADP-Mg+phosphoarginine+ H + $ATP-Mg+ar-ginine and most of our studies were determined in the reverse direction.In the present work we chose ethylene glycol as the antifreeze. Our initial efforts were directed towards establishing the effect of this solvent and of temperature and pH on the overall reaction. In this way we prepared the ground for more detailed studies on the transient intermediates in the reaction pathway of this enzyme.In addition these studies could provide information on such fundamental aspects of enzyme catalysis as the nature of enzyme-substrate interactions 141 and the identity of the charged groups responsible for the observed pH profiles 151.Our results indicate the possibilities as well as the limitations ofinvestigatingenzyme reactions in ethylene glycol/water mixtures at subzero temperatures. Thus, under suitable conditions, we have been able to induce and to analyse a significant shift in enzymic pK, which has provided us with information about the nature of the ionic group(s) at the active site of arginine kinase. Furthermore, our results show that there is a temperature-induced change of the ratelimiting step in the reaction pathway of this enzyme. MATERIALS AND METHODS Pro...