Density estimation and random variate generation using multilayer networks

In this paper we consider two important topics: density estimation and random variate generation. We present a framework that is easily implemented using the familiar multilayer neural network. First, we develop two new methods for density estimation, a stochastic method and a related deterministic method. Both methods are based on approximating the distribution function, the density being obtained by differentiation. In the second part of the paper, we develop new random number generation methods. Our methods do not suffer from some of the restrictions of existing methods in that they can be used to generate numbers from any density provided that certain smoothness conditions are satisfied. One of our methods is based on an observed inverse relationship between the density estimation process and random number generation. We present two variants of this method, a stochastic, and a deterministic version. We propose a second method that is based on a novel control formulation of the problem, where a "controller network" is trained to shape a given density into the desired density. We justify the use of all the methods that we propose by providing theoretical convergence results. In particular, we prove that the L(infinity) convergence to the true density for both the density estimation and random variate generation techniques occurs at a rate O((log log N/N)((1-epsilon)/2)) where N is the number of data points and epsilon can be made arbitrarily small for sufficiently smooth target densities. This bound is very close to the optimally achievable convergence rate under similar smoothness conditions. Also, for comparison, the (2) root mean square (rms) convergence rate of a positive kernel density estimator is O(N(-2/5)) when the optimal kernel width is used. We present numerical simulations to illustrate the performance of the proposed density estimation and random variate generation methods. In addition, we present an extended introduction and bibliography that serves as an overview and reference for the practitioner.

Prevention of primary islet isograft nonfunction in mice with pravastatin

BACKGROUND

Nonspecific inflammatory damage in the early stages of transplantation is the major cause of primary islet graft nonfunction. Using murine isografts, we attempted to prevent this islet graft damage by treating recipients with pravastatin (Pravacol), a 3-hydroxy-3-methylglutaryl-coenzyme A reductase inhibitor. Nicotinamide was also tested to determine the synergistic effect of both agents.

METHODS

Unpurified newborn BALB/c islets, ranging in number from 1800 to 2500, were transplanted into the left renal subcapsular space of a syngeneic adult mouse made diabetic with streptozotocin. Recipient mice were divided into the following four groups, based on treatment protocols: treatment with 40 mg/kg pravastatin (group 1), 500 mg/kg nicotinamide (group 2), 40 mg/kg pravastatin and 500 mg/kg nicotinamide (group 3), and vehicle alone (group 4). Pravastatin and nicotinamide were administered orally every day for 14 days, starting on the day of transplantation (day 0). Nonfasting blood glucose levels, urine glucose levels, and the intravenous glucose tolerance test were used to monitor the diabetic state. The reversal of diabetes was defined by normoglycemia and negative urine glucose maintained for more than 7 days.

RESULTS

After islet transplantation, levels of blood and urine glucose were significantly lower in groups 1 and 3, compared with those in group 4. K-values of an intravenous glucose tolerance test performed on day 14 were significantly higher in groups 1 and 3 than those of group 4. Reversal of diabetes had occurred in 63% of mice in group 1 and 67% in group 3, levels that were higher than those in group 2 (17%) and group 4 (0%) (P<0.02, groups 1 and 3 vs. group 4). Histological examination of grafts, biopsied on day 21, revealed well preserved islets with little sign of inflammation in groups 1 and 3, whereas grafts in groups 2 and 4 contained broken, smaller islets surrounded by severe fibrosis and mononuclear cell infiltration.

CONCLUSION

Our results in mice have shown the effectiveness of pravastatin for protecting islets from nonspecific inflammatory damage. Nicotinamide did not show a synergistic effect with pravastatin at the dosage used in this study. These results indicate that pravastatin may be a useful agent for clinical islet transplantation.

Nitric oxide regulates insulin secretion in the isolated perfused human pancreas via a cholinergic mechanism

BACKGROUND

The purpose of this study was to determine whether nitric oxide regulates insulin secretion in the isolated perfused human pancreas.

METHODS

Single-pass perfusion was performed in four pancreata with a modified Krebs medium. Sequential 10-minute infusions (separated by 10-minute basal periods) of (1) 25 nmol/L acetylcholine, (2) 2.5 mumol/L acetylcholine, and (3) 16.7 mmol/L glucose were initially infused. Then 0.1 mumol/L of NG-monomethyl-L-arginine (NMMA) was infused during a period of 10 minutes, and steps (1) through (3) were repeated. The change in insulin secretion from basal levels during each stimulation was calculated and compared with that seen after NMMA infusion.

RESULTS

Infusion of 25 nmol/L and 2.5 mumol/L acetylcholine resulted in a significant stimulation of insulin secretion before NMMA infusion (p < 0.05) and after NMMA infusion for acetylcholine at 25 nmol/L (p < 0.05). There was a significant decrease in acetylcholine-induced insulin secretion after NMMA infusion for acetylcholine at 25 nmol/L and 2.5 mumol/L compared with before NMMA infusion (p < 0.05). Infusion of 16.7 mmol/L glucose significantly stimulated insulin secretion before and after NMMA infusion, but there was no significant difference seen with insulin secretion before and after NMMA infusion. Insulin secretion was significantly inhibited during NMMA infusion (p < 0.05).

CONCLUSIONS

These data show that infusion of the nitric oxide synthase inhibitor NMMA suppressed cholinergic-stimulated insulin secretion but did not affect glucose-stimulated insulin secretion. We conclude that nitric oxide regulates insulin secretion in the isolated perfused human pancreas.

Clinical islet transplantation experience of the University of California Islet Transplant Consortium

BACKGROUND

The University of California Islet Transplant Consortium was formed to evaluate the feasibility of performing clinical islet transplantation at different transplant centers by using a single centralized islet isolation laboratory.

METHODS

From July 1992 through February 1995 seven adult islet transplantations were performed, six allografts and one autograft. Once procured, human pancreata were brought to the UCLA-VA Islet Core Laboratory for islet isolation and purification, which were then transported to different centers for transplantation. Patients 1 through 3 received their transplants in Los Angeles, patient 4 received her islet transplant in Torrance, and patients 5 through 7 received their transplants in San Francisco.

RESULTS

Although none of these patients achieved insulin independence, four of seven had functioning grafts longer than 6 months as indicated by circulating C-peptide level greater than 0.7 ng/ml. Furthermore, improved glucose control as shown by a decreased insulin requirement was seen in 57% (four of seven patients) of these patients. The ability to isolate islets at a single laboratory and transport them long distances to different centers was shown in patients 4 through 7.

CONCLUSIONS

Islet transplantation can be performed with improvements in blood glucose control, and islets can be isolated at a centralized location and successfully transported to different centers for transplantation.

Somatostatin inhibits B-cell secretion via a subtype-2 somatostatin receptor in the isolated perfused human pancreas

Recently five somatostatin receptor subtypes (SSTR) have been cloned, allowing the development of highly specific selective agonists for these SSTR. The present study was undertaken to determine which SSTR is responsible for the inhibitory effect of somatostatin on islet hormone secretion. Single-pass perfusion of four agonists was performed in pancreata obtained from four cadaveric organ donors using a modified Krebs-media with 3.9 mM glucose. Sequential 10-min specific receptor agonist infusions (5 ng/ml) of DC32-87 (SSTR2), DC25-12 (SSTR3), DC32-97 (SSTR3), or DC32-92 (SSTR5) were performed in random order separated by 10-min basal periods. Infusion of SSTR2 agonist into the isolated perfused human pancreas resulted in a significant inhibition of insulin and C-peptide secretion (insulin = -1468 +/- 480 pM, P < 0.05, and C-peptide = -2328 +/- 437 pM, P < 0.05) but not islet amyloid polypeptide or somatostatin. These results suggest that the inhibitory effect of somatostatin on B-cell secretion is mediated through the subtype-2 receptor within the human islet.

A nuclear magnetic resonance study of the interactions of the antimalarials chloroquine, quinacrine, quinine and mefloquine with dipalmitoylphosphatidylcholine bilayers

The interaction of four cationic amphiphilic antimalarials (chloroquine, quinacrine, mefloquine and quinine) with model dipalmitoylphosphatidylcholine (DPPC) bilayer membranes was studied using 2H- and 31P-nuclear magnetic resonance (NMR). The results showed no significant perturbation of lipid bilayer structure by the presence of chloroquine up to a molar ratio of 1:2 of drug to lipid. Addition of quinacrine to DPPC at the same molar ratio resulted in a 2.5 degrees C decrease in the gel to liquid crystalline phase transition temperature (Tc) of the lipids, with only a small perturbation of the order parameters of the lipid side chains. 31P-NMR spectra of quinacrine-DPPC mixtures indicated a quinacrine-induced change of head group conformation of DPPC above the Tc. These findings are consistent with quinacrine interacting only with the surface of DPPC bilayers. In contrast, both mefloquine and quinine exhibited stronger interactions with DPPC, decreasing the Tc of the lipids by 10 degrees C and 9 degrees C, respectively, and causing significant disordering of the lipid side chains. The basic bilayer structure of DPPC was, however, maintained, even at the highest molar ratio 1:2 of drug to lipid. Such behavior is consistent with penetration of both mefloquine and quinine into the interior of the bilayers. This ability of mefloquine and quinine, but not chloroquine and quinacrine, to intercalate into lipid bilayers correlates with their lower pKa values, which ensures that at physiological pH significant amounts of mefloquine or quinine remain in their uncharged lipophilic form.