Dynamical properties of Discrete Reaction Networks

Reaction networks are commonly used to model the dynamics of populations subject to transformations that follow an imposed stoichiometry. This paper focuses on the efficient characterisation of dynamical properties of Discrete Reaction Networks (DRNs). DRNs can be seen as modeling the underlying discrete nondeterministic transitions of stochastic models of reaction networks. In that sense, a proof of non-reachability in a given DRN has immediate implications for any concrete stochastic model based on that DRN, independent of the choice of kinetic laws and constants. Moreover, if we assume that stochastic kinetic rates are given by the mass-action law (or any other kinetic law that gives non-vanishing probability to each reaction if the required number of interacting substrates is present), then reachability properties are equivalent in the two settings. The analysis of two types of global dynamical properties of DRNs is addressed: irreducibility, i.e., the ability to reach any discrete state from any other state; and recurrence, i.e., the ability to return to any initial state. Our results consider both the verification of such properties when species are present in a large copy number, and in the general case. The necessary and sufficient conditions obtained involve algebraic conditions on the network reactions which in most cases can be verified using linear programming. Finally, the relationship of DRN irreducibility and recurrence with dynamical properties of stochastic and continuous models of reaction networks is discussed.     

Product-Form Stationary Distributions for Deficiency Zero Chemical Reaction Networks

We consider stochastically modeled chemical reaction systems with mass-action kinetics and prove that a product-form stationary distribution exists for each closed, irreducible subset of the state space if an analogous deterministically modeled system with mass-action kinetics admits a complex balanced equilibrium. Feinberg’s deficiency zero theorem then implies that such a distribution exists so long as the corresponding chemical network is weakly reversible and has a deficiency of zero. The main parameter of the stationary distribution for the stochastically modeled system is a complex balanced equilibrium value for the corresponding deterministically modeled system. We also generalize our main result to some non-mass-action kinetics.     

Microsatellite evolution in congeneric mammals: domestic and bighorn sheep

We compared genotypes at eight (AC)n microsatellite loci in domestic sheep (Ovis aries) and wild Rocky Mountain bighorn sheep (O. canadensis). The domestic sheep had greater genetic variation, higher allele-size variances, and larger allele sizes than the wild sheep. Accumulating evidence from higher taxonomic comparisons shows that these parameters are biased if microsatellite loci are selected in one taxon and used in another. Our results demonstrate similar biases between congeneric species. We compared standard measures of genetic variation, differentiation, and distance within and between species (H, D, FST) to newer measures based on allele-size variance (SW, SB, RST). The size-based distances better detected species-level divergence, but standard measures better distinguished allopatric populations. Empirical calibration of these measures at the subspecies level is needed to establish their useful ranges.      

Bone markers during a 6-month space flight: effects of vitamin K supplementation

Rapid bone loss is a serious health problem for astronauts during long lasting missions in space. We have recorded the changes of biochemical markers for bone metabolism in one of the astronauts during the 6-month space flight of the EUROMIR-95 mission. Immediately after launch both bone resorption markers and urinary calcium excretion increased about two fold, whereas bone formation markers remained unchanged. After 12 1/2 weeks the astronaut received vitamin K1 (10 mg/day for 6 weeks). Vitamin K is known to be involved in the formation of gamma-carboxyglutamate (Gla) in proteins, such as the calcium-binding bone Gla-proteins osteocalcin and matrix Gla-protein. Concomitant with the start of vitamin K treatment, the calcium-binding capacity of osteocalcin increased, and so did the urinary excretion of free Gla. This is suggestive for a subclinical vitamin K-deficiency in the astronaut before vitamin K-supplementation. During periods of high vitamin K status markers for bone formation (osteocalcin and bone alkaline phosphatase) had increased as compared to the first part of the flight. The mean increases were 14 and 23%, respectively. Our data suggest that increased intake of vitamin K may contribute to counteracting microgravity-induced loss of bone mass during long lasting space missions, but need confirmation in more astronauts.     

Nucleotide sequence of the Acinetobacter calcoaceticus trpGDC gene cluster

A plasmid library of Acinetobacter calcoaceticus HindIII fragments was constructed, and clones that complemented an Escherichia coli pabA mutant were selected. Plasmids containing a 3.9-kb fragment of A. calcoaceticus DNA that also complemented E. coli trpD and trpC-(trpF+) mutants were obtained. We infer that complementation of E. coli pabA mutants was the result of the expression of the amphibolic anthranilate- synthase/p-aminobenzoate-synthase glutamine-amidotransferase gene and that the plasmid insert carried the entire trpGDC gene cluster. In E. coli minicells, the plasmid insert directed the synthesis of polypeptides of 44,000, 33,000, and 20,000 daltons, molecular masses that are consistent with the reported molecular masses of phosphoribosylanthranilate transferase, indoleglycerol-phosphate synthase, and anthranilate-synthase component II, respectively. A 3,105- bp nucleotide sequence was determined. Comparison of the A. calcoaceticus trpGDC sequences with other known trp gene sequences has allowed insight into (1) the evolution of the amphibolic trpG gene, (2) varied strategies for coordinate expression of trp genes, and (3) mechanisms of gene fusions in the trp operon.      

Distributions of two recently inserted long interspersed elements of the L1 repetitive family at the Alb and beta h3 loci in wild mice populations

The presence of the L1 sequences, L1Md4 next to the pseudogene beta h3 and I12 found in the twelfth intron of the albumin gene, in certain strains of laboratory mice but not of others has led to the suggestion that these sequences were recent insertions into the Mus mus domesticus genome. To be sure that they are really recent insertions and not relics of an ancestral chromosome, we investigated the presence or absence of these sequences in populations of wild mice belonging to the semispecies M. m. domesticus and M. m. musculus as well as in other species of the genus Mus and in related murids. The sequence I12 in the albumin gene was found in 34% of the chromosomes of the wild mice belonging to M. m. domesticus and to a lesser extent (6%) in M. m. musculus. Of 114 M. m. domesticus chromosomes, L1Md4 was found in only nine, seven of which came from the same locality. Its presence was associated with the haplotype Hbbp, which is relatively rare in European populations of M. musculus. Since there was no evidence for the presence of these two L1 sequences in more distantly related species, we conclude that they are recent insertions in the M. musculus genome.      

Protein and m-RNA expression of farnesyl-transferases,RhoA and RhoB in rat liver hepatocytes: action of perillyl alcohol and vitamin A <Emphasis Type="BoldItalic">in vivo</Emphasis>.

Summary We analysed the action, in rats in vivo, of the protein isoprenylation inhibitor perillyl alcohol (POH) and that of vitamin A, alone or in association, on m-RNA and protein expression of farnesyltransferases (FTases α and β subunits) and their protein substrates RhoA and RhoB, in isolated hepatocytes. Combined administration of POH and vitamin A induced a sharp decrease in FTase α protein after 96 h, suggesting an involvement not only of farnesyltransferases but also of geranylgeranyltransferases, which share the FTase α protein. FTase β protein did not decrease. POH plus vitamin A, in contrast with POH or vitamin A alone, induced a decrease in RhoB protein, probably because of different cleavages. No modification was observed in RhoA protein. Vitamin A alone increased RhoB m-RNA and protein expression. As one of the functions of RhoB is cell polarisation, these data support our previous hypothesis of a polarised transport of vitamin A from hepatocytes to hepatic stellate cells. As the behaviours of m-RNAs and proteins in this study were often different, cytoplasmic metabolic pathways must be considered for the parameters studied. The behaviour of Rho B, which is thought to have an antioncogene function, is discussed in view of its isoprenylated forms in the membranes. These preliminary findings stress the need, when studying the association of two isoprenoids in cancer therapy, to consider normal as well as tumour-bearing animals.     

A model of intracellular transport of particles in an axon

In this paper we develop a model of intracellular transport of cell organelles and vesicles along the axon of a nerve cell. These particles are moving alternately by processive motion along a microtubule with the aid of motor proteins, and by diffusion. The model involves a degenerate system of diffusion equations. We prove a maximum principle and establish existence and behavior of a unique solution. Numerical results show how the transportation of mass depends on the relevant parameters of the model.     

A dynamical system model of neurofilament transport in axons

We develop a dynamical system model for the transport of neurofilaments in axons, inspired by Brown's "stop-and-go" model for slow axonal transport. We use fast/slow time-scale arguments to lower the number of relevant parameters in our model. Then, we use experimental data of Wang and Brown to estimate all but one parameter. We show that we can choose this last remaining parameter such that the results of our model agree with pulse-labeling experiments from three different nerve cell types, and also agree with stochastic simulation results.