Generalized flows, intrinsic stochasticity, and turbulent transport

The study of passive scalar transport in a turbulent velocity field leads naturally to the notion of generalized flows, which are families of probability distributions on the space of solutions to the associated ordinary differential equations which no longer satisfy the uniqueness theorem for ordinary differential equations. Two most natural regularizations of this problem, namely the regularization via adding small molecular diffusion and the regularization via smoothing out the velocity field, are considered. White-in-time random velocity fields are used as an example to examine the variety of phenomena that take place when the velocity field is not spatially regular. Three different regimes, characterized by their degrees of compressibility, are isolated in the parameter space. In the regime of intermediate compressibility, the two different regularizations give rise to two different scaling behaviors for the structure functions of the passive scalar. Physically, this means that the scaling depends on Prandtl number. In the other two regimes, the two different regularizations give rise to the same generalized flows even though the sense of convergence can be very different. The “one force, one solution” principle is established for the scalar field in the weakly compressible regime, and for the difference of the scalar in the strongly compressible regime, which is the regime of inverse cascade. Existence and uniqueness of an invariant measure are also proved in these regimes when the transport equation is suitably forced. Finally incomplete self similarity in the sense of Barenblatt and Chorin is established.

LXRα functions as a cAMP-responsive transcriptional regulator of gene expression

LXRα is a member of a nuclear receptor superfamily that regulates transcription. LXRα forms a heterodimer with RXRα, another member of this family, to regulate the expression of cholesterol 7α-hydroxylase by means of binding to the DR4-type cis-element. Here, we describe a function for LXRα as a cAMP-responsive regulator of renin and c-myc gene transcriptions by the interaction with a specific cis-acting DNA element, CNRE (an overlapping cAMP response element and a negative response element). Our previous studies showed that renin gene expression is regulated by cAMP, at least partly, through the CNRE sequence in its 5′-flanking region. This sequence is also found in c-myc and several other genes. Based on our cloning results using the yeast one-hybrid system, we discovered that the mouse homologue of human LXRα binds to the CNRE and demonstrated that it binds as a monomer. To define the function of LXRα on gene expression, we transfected the renin-producing renal As4.1 cells with LXRα expression plasmid. Overexpression of LXRα in As4.1 cells confers cAMP inducibility to reporter constructs containing the renin CNRE. After stable transfection of LXRα, As4.1 cells show a cAMP-inducible up-regulation of renin mRNA expression. In parallel experiments, we demonstrated that LXRα can also bind to the homologous CNRE in the c-myc promoter. cAMP promotes transcription through c-myc/CNRE:LXRα interaction in LXRα transiently transfected cells and increases c-myc mRNA expression in stably transfected cells. Identification of LXRα as a cAMP-responsive nuclear modulator of renin and c-myc expression not only has cardiovascular significance but may have generalized implication in the regulation of gene transcription.

Shared functions in vivo of a glycosyl-phosphatidylinositol-linked aspartyl protease, Mkc7, and the proprotein processing protease Kex2 in yeast.

The MKC7 gene was isolated as a multicopy suppressor of the cold-sensitive growth phenotype of a yeast kex2 mutant, which lacks the protease that cleaves pro-alpha-factor and other secretory proproteins at pairs of basic residues in a late Golgi compartment in yeast. MKC7 encodes an aspartyl protease most closely related to product of the YAP3 gene, a previously isolated multicopy suppressor of the pro-alpha-factor processing defect of a kex2 null. Multicopy MKC7 suppressed the alpha-specific mating defect of a kex2 null as well as multicopy YAP3 did, but multicopy YAP3 was a relatively weak suppressor of kex2 cold sensitivity. Overexpression of MKC7 resulted in production of a membrane-associated proteolytic activity that cleaved an internally quenched fluorogenic peptide substrate on the carboxyl side of a Lys-Arg site. Treatment with phosphatidylinositol-specific phospholipase C shifted Mkc7 activity from the detergent to the aqueous phase in a Triton X-114 phase separation, indicating that membrane attachment of Mkc7 is mediated by a glycosyl-phosphatidylinositol anchor. Although disruption of MKC7 or YAP3 alone resulted in no observable phenotype, mkc7 yap3 double disruptants exhibited impaired growth at 37 degrees C. Disruption of MKC7 and YAP3 in a kex2 null mutant resulted in profound temperature sensitivity and more generalized cold sensitivity. The synergism of mkc7, yap3, and kex2 null mutations argues that Mkc7 and Yap3 are authentic processing enzymes whose functions overlap those of Kex2 in vivo.