Oscillations in Biochemical Reaction Networks Arising from Pairs of Subnetworks

Biochemical reaction models show a variety of dynamical behaviors, such as stable steady states, multistability, and oscillations. Biochemical reaction networks with generalized mass action kinetics are represented as directed bipartite graphs with nodes for species and reactions. The bipartite graph of a biochemical reaction network usually contains at least one cycle, i.e., a sequence of nodes and directed edges which starts and ends at the same species node. Cycles can be positive or negative, and it has been shown that oscillations can arise as a result of either a positive cycle or a negative cycle. In earlier work it was shown that oscillations associated with a positive cycle can arise from subnetworks with an odd number of positive cycles. In this article we formulate a similar graph-theoretic condition, which generalizes the negative cycle condition for oscillations. This new graph-theoretic condition for oscillations involves pairs of subnetworks with an even number of positive cycles. An example of a calcium reaction network with generalized mass action kinetics is discussed in detail.     

Genomic organization of mouse gene zfp162.

We report the cloning and characterization of the alternatively spliced mouse gene zfp162, formerly termed mzfm, the homolog of the human ZFM1 gene encoding the splicing factor SF1 and a putative signal transduction and activation of RNA (STAR) protein. The zfp162 gene is about 14 kb long and consists of 14 exons and 13 introns. Comparison of zfp162 with the genomic sequences of ZFM1/SF1 revealed that the exon-intron structure and exon sequences are well conserved between the genes, whereas the introns differ in length and sequence composition. Using fluorescent in situ hybridization, the zfp162 gene was assigned to chromosome 19, region B. Screening of a genomic library integrated in lambda DASH II resulted in the identification of the 5'-flanking region of zfp162. Sequence analysis of this region showed that zfp162 is a TATA-less gene containing an initiator control element and two CCAAT boxes. The promoter exhibits the following motifs: AP-2, CRE, Ets, GRE, HNF5, MRE, SP-1, TRE, TCF1, and PU.1. The core promoter, from position -331 to -157, contains the motifs CRE, SP-1, MRE, and AP-2, as determined in transfected CHO-K1 cells and IC-21 cells by reporter gene assay using a secreted form of human placental alkaline phosphatase. The occurrence of PU.1/GRE supports the view that the zfp162 gene encodes a protein involved not only in nuclear RNA metabolism, as the human ZFM1/SF1, but also in as yet unknown macrophage-inherent functions.