On the controllability of distributed systems

To “control” a system is to make it behave (hopefully) according to our “wishes,” in a way compatible with safety and ethics, at the least possible cost. The systems considered here are distributed—i.e., governed (modeled) by partial differential equations (PDEs) of evolution. Our “wish” is to drive the system in a given time, by an adequate choice of the controls, from a given initial state to a final given state, which is the target. If this can be achieved (respectively, if we can reach any “neighborhood” of the target) the system, with the controls at our disposal, is exactly (respectively, approximately) controllable. A very general (and fuzzy) idea is that the more a system is “unstable” (chaotic, turbulent) the “simplest,” or the “cheapest,” it is to achieve exact or approximate controllability. When the PDEs are the Navier–Stokes equations, it leads to conjectures, which are presented and explained. Recent results, reported in this expository paper, essentially prove the conjectures in two space dimensions. In three space dimensions, a large number of new questions arise, some new results support (without proving) the conjectures, such as generic controllability and cases of decrease of cost of control when the instability increases. Short comments are made on models arising in climatology, thermoelasticity, non-Newtonian fluids, and molecular chemistry. The Introduction of the paper and the first part of all sections are not technical. Many open questions are mentioned in the text.

Control of alternative pre-mRNA splicing by distributed pentameric repeats

Multiple copies of the hexamer TGCATG have been shown to regulate fibronectin pre-mRNA alternative splicing. GCATG repeats also are clustered near the regulated calcitonin-specific 3′ splice site in the rat calcitonin/CGRP gene. Specific mutagenesis of these repeats in calcitonin/CGRP pre-mRNA resulted in the loss of calcitonin-specific splicing, suggesting that the native repeats act to enhance alternative exon inclusion. Mutation of subsets of these elements implies that alternative splicing requires a minimum of two repeats, and that the combination of one intronic and one exonic repeat is necessary for optimal cell-specific splicing. However, multimerized intronic repeats inhibited calcitonin-specific splicing in both the wild-type context and in a transcript lacking endogenous repeats. These results suggest that both the number and distribution of repeats may be important features for the regulation of tissue-specific alternative splicing. Further, RNA containing a single repeat bound cell-specific protein complexes, but tissue-specific differences in protein binding were not detected by using multimerized repeats. Together, these data support a novel model for alternative splicing regulation that requires the cell-specific recognition of multiple, distributed sequence elements.

Repetitive-DNA elements are similarly distributed on Caenorhabditis elegans autosomes

The positions of ≈4,800 individual miniature inverted-repeat transposable element (MITE)-like repeats from four families were mapped on the Caenorhabditis elegans chromosomes. These families represent 1–2% of the total sequence of the organism. The four MITE families (Cele1, Cele2, Cele14, and Cele42) displayed distinct chromosomal distribution profiles. For example, the Cele14 MITEs were observed clustering near the ends of the autosomes. In contrast, the Cele2 MITEs displayed an even distribution through the central autosome domains, with no evidence for clustering at the ends. Both the number of elements and the distribution patterns of each family were conserved on all five C. elegans autosomes. The distribution profiles indicate chromosomal polarity and suggest that the current genetic and physical maps of chromosomes II, III, and X are inverted with respect to the other chromosomes. The degree of conservation of both the number and distribution of these elements on the five autosomes suggests a role in defining specific chromosomal domains.

Mutations in HYAL1, a member of a tandemly distributed multigene family encoding disparate hyaluronidase activities, cause a newly described lysosomal disorder, mucopolysaccharidosis IX

Hyaluronan (HA), a large glycosaminoglycan abundant in the extracellular matrix, is important in cell migration during embryonic development, cellular proliferation, and differentiation and has a structural role in connective tissues. The turnover of HA requires endoglycosidic breakdown by lysosomal hyaluronidase, and a congenital deficiency of hyaluronidase has been thought to be incompatible with life. However, a patient with a deficiency of serum hyaluronidase, now designated as mucopolysaccharidosis IX, was recently described. This patient had a surprisingly mild clinical phenotype, including notable periarticular soft tissue masses, mild short stature, an absence of neurological or visceral involvement, and histological and ultrastructural evidence of a lysosomal storage disease. To determine the molecular basis of mucopolysaccharidosis IX, we analyzed two candidate genes tandemly distributed on human chromosome 3p21.3 and encoding proteins with homology to a sperm protein with hyaluronidase activity. These genes, HYAL1 and HYAL2, encode two distinct lysosomal hyaluronidases with different substrate specificities. We identified two mutations in the HYAL1 alleles of the patient, a 1412G → A mutation that introduces a nonconservative amino acid substitution (Glu268Lys) in a putative active site residue and a complex intragenic rearrangement, 1361del37ins14, that results in a premature termination codon. We further show that these two hyaluronidase genes, as well as a third recently discovered adjacent hyaluronidase gene, HYAL3, have markedly different tissue expression patterns, consistent with differing roles in HA metabolism. These data provide an explanation for the unexpectedly mild phenotype in mucopolysaccharidosis IX and predict the existence of other hyaluronidase deficiency disorders.

How are close residues of protein structures distributed in primary sequence?

Structurally neighboring residues are categorized according to their separation in the primary sequence as proximal (1-4 positions apart) and otherwise distal, which in turn is divided into near (5-20 positions), far (21-50 positions), very far ( > 50 positions), and interchain (from different chains of the same structure). These categories describe the linear distance histogram (LDH) for three-dimensional neighboring residue types. Among the main results are the following: (i) nearest-neighbor hydrophobic residues tend to be increasingly distally separated in the linear sequence, thus most often connecting distinct secondary structure units. (ii) The LDHs of oppositely charged nearest-neighbors emphasize proximal positions with a subsidiary maximum for very far positions. (iii) Cysteine-cysteine structural interactions rarely involve proximal positions. (iv) The greatest numbers of interchain specific nearest-neighbors in protein structures are composed of oppositely charged residues. (v) The largest fraction of side-chain neighboring residues from beta-strands involves near positions, emphasizing associations between consecutive strands. (vi) Exposed residue pairs are predominantly located in proximal linear positions, while buried residue pairs principally correspond to far or very far distal positions. The results are principally invariant to protein sizes, amino acid usages, linear distance normalizations, and over- and underrepresentations among nearest-neighbor types. Interpretations and hypotheses concerning the LDHs, particularly those of hydrophobic and charged pairings, are discussed with respect to protein stability and functionality. The pronounced occurrence of oppositely charged interchain contacts is consistent with many observations on protein complexes where multichain stabilization is facilitated by electrostatic interactions.