Curve fitting problem: torque - velocity relationship with polynomials and Boltzmann sigmoid functions.

PURPOSE: The aim of this study was to investigate the curve fitting and model selection problem of the torque-velocity relationship of elbow flexors and extensors in untrained females. The second goal was to determine the optimal models in different function classes and the best, among the optimal ones. Lastly, test the best models to predict the torque were tested. METHODS: Using the polynomials (second - fourth degree) and Boltzmann sigmoid functions, and a different presentation of data points (averages, a point cloud, etc.), we determined the optimal models by both error criteria: minimum residual sum of squares and minimum of the maximal absolute residue. To assess the best models, we applied Akaike and Bayesian information criteria, Hausdorff distance and the minimum of the smallest maximal absolute residue and the predictive torque-velocity relationships of the best models with torque values, calculated beyond the experimental velocity interval. RESULTS: The application of different error and model selection criteria showed that the best models in the majority of cases were polynomials of fourth degree, with some exceptions from second and third degree. The criteria values for the optimal Boltzmann sigmoids were very close to those of the best polynomial models. However, the predicted torque-velocity relationships had physiological behavior only in Boltzmann's sigmoid functions, and their parameters had a clear interpretation. CONCLUSION: The results obtained suggest that the Boltzmann sigmoid functions are suitable for modeling and predicting of the torque-velocity relationship of elbow flexors and extensors in untrained females, as compared to polynomials, and their curves are physiologically relevant.

Opioid profiles of Cys2-containing enkephalin analogues.

To elucidate the structural features determining delta-opioid receptor properties of enkephalin analogues containing Cys(O2NH2) in position 2, a series of Cys2-containing derivatives were synthesized and tested for their effectiveness in depressing electrically evoked contractions of the mouse vas deferens (predominantly enkephalin-selective delta-opioid receptors) and the guinea-pig ileum (mu- and kappa-opioid receptors). The peptidase resistance of the compounds was also tested. The ratio IC50 in the guinea-pig ileum/IC50 in the mouse vas deferens, indicating selectivity for delta-opioid receptors, was high for Cys(O2NH2)2-containing analogues and especially for [Cys(O2NH2)2, Leu5]enkephalin, which was about seven times more selective than delta-opioid receptor selective ligand cyclic [D-Pen2, D-Pen5]enkephalin (DPDPE). The dissociation constant (KA) and relative efficacy (e(rel)) of the compounds in the mouse-isolated vas deferens were determined using explicit formulae derived by fitting of the data points with two-parametric hyperbolic function. The obtained values for KA and e(rel) suggest that: (i) incorporation of Cys(O2NH2)2 in the molecule of [Leu5]enkephalin highly increases the efficacy and does not change significantly the affinity of the respective analogues to delta-opioid receptors; [Cys(O2NH2)2, Leu5]enkephalin has higher affinity than DPDPE, but is less resistant to enzyme degradation; the effect of this modification on the efficacy is decreased when methionine is in position 5; (ii) D-configuration of Cys(O2NH2)2-containing analogues increases their peptidase resistance, but reduces efficacy and affinity of the peptides towards delta-opioid receptors; (iii) the substitution of Cys(O2NH2) with Hcy(O2NH2) reduces the efficacy, affinity and potency of the respective analogues and maintains their sensitivity to endogenous peptidases; (iv) the substitution of the sulfonamide group with benzyl group in the molecule of Cys in position 2 decreases their efficacy and affinity toward delta-opioid receptors, but attaches resistance to enzyme degradation. The results obtained in this study allow: (i) to involve the receptor affinity and agonist efficacy as drug-design consideration for delta-opioid receptor properties of newly synthesized compounds and (ii) to characterize some of the structural features, which set the pattern for their opioid profiles.

Aminoderivatives of cycloalkanespirohydantoins: synthesis and biological activity.

3-Aminocycloalkanespiro-5-hydantoins were synthesized and their biological activity was studied. In contrast to hydantoins, these compounds failed to induce either anticonvulsive effects in the central nervous system or inhibitory effects on cholinergic contractions in the enteric nervous system. However, they exerted well pronounced, atropinsensitive, contractile effects on the guinea-pig ileum longitudinal muscle preparations. Structure-activity relationships established allow the assumption that: (i) the reduction of the ring size in the molecule of the spirohydantoins leads to an increase in the potency of the respective analogue to induce contractile effect; (ii) the introduction of -NH2 in position 3 increases the ability of all the compounds studied to exert contractions; (iii) the enlargement of the ring leads to: (1) an increase of the degree of desensitization of the preparations; and (2) a decrease (except 1a) of the potency of the analogues to exert contractile effects.