Convex polytopes and quantization of symplectic manifolds

Quantum mechanics associate to some symplectic manifolds M a quantum model Q(M), which is a Hilbert space. The space Q(M) is the quantum mechanical analogue of the classical phase space M. We discuss here relations between the volume of M and the dimension of the vector space Q(M). Analogues for convex polyhedra are considered.

Intrastriatal injection of an adenoviral vector expressing glial-cell-line-derived neurotrophic factor prevents dopaminergic neuron degeneration and behavioral impairment in a rat model of Parkinson disease

Glial-cell-line-derived neurotrophic factor (GDNF) is a potent neurotrophic factor for adult nigral dopamine neurons in vivo. GDNF has both protective and restorative effects on the nigro-striatal dopaminergic (DA) system in animal models of Parkinson disease. Appropriate administration of this factor is essential for the success of its clinical application. Since it cannot cross the blood–brain barrier, a gene transfer method may be appropriate for delivery of the trophic factor to DA cells. We have constructed a recombinant adenovirus (Ad) encoding GDNF and injected it into rat striatum to make use of its ability to infect neurons and to be retrogradely transported by DA neurons. Ad-GDNF was found to drive production of large amounts of GDNF, as quantified by ELISA. The GDNF produced after gene transfer was biologically active: it increased the survival and differentiation of DA neurons in vitro. To test the efficacy of the Ad-mediated GDNF gene transfer in vivo, we used a progressive lesion model of Parkinson disease. Rats received injections unilaterally into their striatum first of Ad and then 6 days later of 6-hydroxydopamine. We found that mesencephalic nigral dopamine neurons of animals treated with the Ad-GDNF were protected, whereas those of animals treated with the Ad-β-galactosidase were not. This protection was associated with a difference in motor function: amphetamine-induced turning was much lower in animals that received the Ad-GDNF than in the animals that received Ad-β-galactosidase. This finding may have implications for the development of a treatment for Parkinson disease based on the use of neurotrophic factors.

Hepatocyte gene therapy in a large animal: A neonatal bovine model of citrullinemia

The development of gene-replacement therapy for inborn errors of metabolism has been hindered by the limited number of suitable large-animal models of these diseases and by inadequate methods of assessing the efficacy of treatment. Such methods should provide sensitive detection of expression in vivo and should be unaffected by concurrent pharmacologic and dietary regimens. We present the results of studies in a neonatal bovine model of citrullinemia, an inborn error of urea-cycle metabolism characterized by deficiency of argininosuccinate synthetase and consequent life-threatening hyperammonemia. Measurements of the flux of nitrogen from orally administered 15NH4 to [15N]urea were used to determine urea-cycle activity in vivo. In control animals, these isotopic measurements proved to be unaffected by pharmacologic treatments. Systemic administration of a first-generation E1-deleted adenoviral vector expressing human argininosuccinate synthetase resulted in transduction of hepatocytes and partial correction of the enzyme defect. The isotopic method showed significant restoration of urea synthesis. Moreover, the calves showed clinical improvement and normalization of plasma glutamine levels after treatment. The results show the clinical efficacy of treating a large-animal model of an inborn error of hepatocyte metabolism in conjunction with a method for sensitively measuring correction in vivo. These studies will be applicable to human trials of the treatment of this disorder and other related urea-cycle disorders.

Herpes simplex virus vector-mediated expression of Bcl-2 prevents 6-hydroxydopamine-induced degeneration of neurons in the substantia nigra in vivo

6-Hydroxydopamine (6-OHDA) is widely used to selectively lesion dopaminergic neurons of the substantia nigra (SN) in the creation of animal models of Parkinson’s disease. In vitro, the death of PC-12 cells caused by exposure to 6-OHDA occurs with characteristics consistent with an apoptotic mechanism of cell death. To test the hypothesis that apoptotic pathways are involved in the death of dopaminergic neurons of the SN caused by 6-OHDA, we created a replication-defective genomic herpes simplex virus-based vector containing the coding sequence for the antiapoptotic peptide Bcl-2 under the transcriptional control of the simian cytomegalovirus immediate early promoter. Transfection of primary cortical neurons in culture with the Bcl-2-producing vector protected those cells from naturally occurring cell death over 3 weeks. Injection of the Bcl-2-expressing vector into SN of rats 1 week before injection of 6-OHDA into the ipsilateral striatum increased the survival of neurons in the SN, detected either by retrograde labeling of those cells with fluorogold or by tyrosine hydroxylase immunocytochemistry, by 50%. These results, demonstrating that death of nigral neurons induced by 6-OHDA lesioning may be blocked by the expression of Bcl-2, are consistent with the notion that cell death in this model system is at least in part apoptotic in nature and suggest that a Bcl-2-expressing vector may have therapeutic potential in the treatment of Parkinson’s disease.

Folding protein models with a simple hydrophobic energy function: The fundamental importance of monomer inside/outside segregation

The present study explores a “hydrophobic” energy function for folding simulations of the protein lattice model. The contribution of each monomer to conformational energy is the product of its “hydrophobicity” and the number of contacts it makes, i.e., E(h⃗, c⃗) = −Σi=1N cihi = −(h⃗.c⃗) is the negative scalar product between two vectors in N-dimensional cartesian space: h⃗ = (h1, … , hN), which represents monomer hydrophobicities and is sequence-dependent; and c⃗ = (c1, … , cN), which represents the number of contacts made by each monomer and is conformation-dependent. A simple theoretical analysis shows that restrictions are imposed concomitantly on both sequences and native structures if the stability criterion for protein-like behavior is to be satisfied. Given a conformation with vector c⃗, the best sequence is a vector h⃗ on the direction upon which the projection of c⃗ − c̄⃗ is maximal, where c̄⃗ is the diagonal vector with components equal to c̄, the average number of contacts per monomer in the unfolded state. Best native conformations are suggested to be not maximally compact, as assumed in many studies, but the ones with largest variance of contacts among its monomers, i.e., with monomers tending to occupy completely buried or completely exposed positions. This inside/outside segregation is reflected on an apolar/polar distribution on the corresponding sequence. Monte Carlo simulations in two dimensions corroborate this general scheme. Sequences targeted to conformations with large contact variances folded cooperatively with thermodynamics of a two-state transition. Sequences targeted to maximally compact conformations, which have lower contact variance, were either found to have degenerate ground state or to fold with much lower cooperativity.