Solution of the pulse width modulation problem using orthogonal polynomials and Korteweg-de Vries equations

The mathematical underpinning of the pulse width modulation (PWM) technique lies in the attempt to represent “accurately” harmonic waveforms using only square forms of a fixed height. The accuracy can be measured using many norms, but the quality of the approximation of the analog signal (a harmonic form) by a digital one (simple pulses of a fixed high voltage level) requires the elimination of high order harmonics in the error term. The most important practical problem is in “accurate” reproduction of sine-wave using the same number of pulses as the number of high harmonics eliminated. We describe in this paper a complete solution of the PWM problem using Padé approximations, orthogonal polynomials, and solitons. The main result of the paper is the characterization of discrete pulses answering the general PWM problem in terms of the manifold of all rational solutions to Korteweg-de Vries equations.

Modification of the substrate specificity of an acyl-acyl carrier protein thioesterase by protein engineering.

The plant acyl-acyl carrier protein (ACP) thioesterases (TEs) are of biochemical interest because of their roles in fatty acid synthesis and their utilities in the bioengineering of plant seed oils. When the FatB1 cDNA encoding a 12:0-ACP TE (Uc FatB1) from California bay, Umbellularia californica (Uc) was expressed in Escherichia coli and in developing oilseeds of the plants Arabidopsis thaliana and Brassica napus, large amounts of laurate (12:0) and small amounts of myristate (14:0) were accumulated. We have isolated a TE cDNA from camphor (Cinnamomum camphorum) (Cc) seeds that shares 92% amino acid identity with Uc FatB1. This TE, Cc FatB1, mainly hydrolyzes 14:0-ACP as shown by E. coli expression. We have investigated the roles of the N- and C-terminal regions in determining substrate specificity by constructing two chimeric enzymes, in which the N-terminal portion of one protein is fused to the C-terminal portion of the other. Our results show that the C-terminal two-thirds of the protein is critical for the specificity. By site-directed mutagenesis, we have replaced several amino acids in Uc FatB1 by using the Cc FatB1 sequence as a guide. A double mutant, which changes Met-197 to an Arg and Arg-199 to a His (M197R/R199H), turns Uc FatB1 into a 12:0/14:0 TE with equal preference for both substrates. Another mutation, T231K, by itself does not effect the specificity. However, when it is combined with the double mutant to generate a triple mutant (M197R/R199H/T231K), Uc FatB1 is converted to a 14:0-ACP TE. Expression of the double-mutant cDNA in E. coli K27, a strain deficient in fatty acid degradation, results in accumulation of similar amounts of 12:0 and 14:0. Meanwhile the E. coli expressing the triple-mutant cDNA produces predominantly 14:0 with very small amounts of 12:0. Kinetic studies indicate that both wild-type Uc FatB1 and the triple mutant have similar values of Km,app with respect to 14:0-ACP. Inhibitory studies also show that 12:0-ACP is a good competitive inhibitor with respect to 14:0-ACP in both the wild type and the triple mutant. These results imply that both 12:0- and 14:0-ACP can bind to the two proteins equally well, but in the case of the triple mutant, the hydrolysis of 12:0-ACP is severely impaired. The ability to modify TE specificity should allow the production of additional "designer oils" in genetically engineered plants.

High Resolution Detection of Mechanical Forces Exerted by Locomoting Fibroblasts on the Substrate

We have developed a new approach to detect mechanical forces exerted by locomoting fibroblasts on the substrate. Cells were cultured on elastic, collagen-coated polyacrylamide sheets embedded with 0.2-μm fluorescent beads. Forces exerted by the cell cause deformation of the substrate and displacement of the beads. By recording the position of beads during cell locomotion and after cell removal, we discovered that most forces were radially distributed, switching direction in the anterior region. Deformations near the leading edge were strong, transient, and variable in magnitude, consistent with active local contractions, whereas those in the posterior region were weaker, more stable, and more uniform, consistent with passive resistance. Treatment of cells with cytochalasin D or myosin II inhibitors caused relaxation of the forces, suggesting that they are generated primarily via actin–myosin II interactions; treatment with nocodazole caused no immediate effect on forces. Immunofluorescence indicated that the frontal region of strong deformation contained many vinculin plaques but no apparent concentration of actin or myosin II filaments. Strong mechanical forces in the anterior region, generated by locally activated myosin II and transmitted through vinculin-rich structures, likely play a major role in cell locomotion and in mechanical signaling with the surrounding environment.

On the reaction mechanism of l-lactate oxidase: Quantitative structure-activity analysis of the reaction with para-substituted l-mandelates

The rate constants for reduction of the flavoenzyme, l-lactate oxidase, and a mutant (in which alanine 95 is replaced by glycine), by a series of para-substituted mandelates, in both the 2-1H- and 2-2H- forms, have been measured by rapid reaction spectrophotometry. In all cases, significant isotope effects (1H/2H = 3–7) on the rate constants of flavin reduction were found, indicating that flavin reduction is a direct measure of α-C-H bond breakage. The rate constants show only a small influence of the electronic characteristics of the substituents, but show a good correlation when combined with some substituent volume parameters. A surprisingly good correlation is found with the molecular mass of the substrate. The results are compatible with any mechanism in which there is little development of charge in the transition state. This could be a transfer of hydride to the flavin N(5) position or a synchronous mechanism in which the α-C-H is formally abstracted as a H+ while the resulting charge is simultaneously neutralized by another event.

The influence of the flow of the reacting gas on the conditions for a thermal explosion

The classical problem of thermal explosion is modified so that the chemically active gas is not at rest but is flowing in a long cylindrical pipe. Up to a certain section the heat-conducting walls of the pipe are held at low temperature so that the reaction rate is small and there is no heat release; at that section the ambient temperature is increased and an exothermic reaction begins. The question is whether a slow reaction regime will be established or a thermal explosion will occur. The mathematical formulation of the problem is presented. It is shown that when the pipe radius is larger than a critical value, the solution of the new problem exists only up to a certain distance along the axis. The critical radius is determined by conditions in a problem with a uniform axial temperature. The loss of existence is interpreted as a thermal explosion; the critical distance is the safe reactor’s length. Both laminar and developed turbulent flow regimes are considered. In a computational experiment the loss of the existence appears as a divergence of a numerical procedure; numerical calculations reveal asymptotic scaling laws with simple powers for the critical distance.

Investigation of the mechanisms of DNA binding of the human G/T glycosylase using designed inhibitors

Deamination of 5-methylcytosine residues in DNA gives rise to the G/T mismatched base pair. In humans this lesion is repaired by a mismatch-specific thymine DNA glycosylase (TDG or G/T glycosylase), which catalyzes specific excision of the thymine base through N-glycosidic bond hydrolysis. Unlike other DNA glycosylases, TDG recognizes an aberrant pairing of two normal bases rather than a damaged base per se. An important structural issue is thus to understand how the enzyme specifically targets the T (or U) residue of the mismatched base pair. Our approach toward the study of substrate recognition and processing by catalytic DNA binding proteins has been to modify the substrate so as to preserve recognition of the base but to prevent its excision. Here we report that replacement of 2′-hydrogen atoms with fluorine in the substrate 2′-deoxyguridine (dU) residue abrogates glycosidic bond cleavage, thereby leading to the formation of a tight, specific glycosylase–DNA complex. Biochemical characterization of these complexes reveals that the enzyme protects an ≈20-bp stretch of the substrate from DNase I cleavage, and directly contacts a G residue on the 3′ side of the mismatched U derivative. These studies provide a mechanistic rationale for the preferential repair of deaminated CpG sites and pave the way for future high-resolution studies of TDG bound to DNA.

Degradation of a Short-lived Glycoprotein from the Lumen of the Endoplasmic Reticulum: The Role of N-linked Glycans and the Unfolded Protein Response

We are studying endoplasmic reticulum–associated degradation (ERAD) with the use of a truncated variant of the type I ER transmembrane glycoprotein ribophorin I (RI). The mutant protein, RI332, containing only the N-terminal 332 amino acids of the luminal domain of RI, has been shown to interact with calnexin and to be a substrate for the ubiquitin-proteasome pathway. When RI332 was expressed in HeLa cells, it was degraded with biphasic kinetics; an initial, slow phase of ∼45 min was followed by a second phase of threefold accelerated degradation. On the other hand, the kinetics of degradation of a form of RI332 in which the single used N-glycosylation consensus site had been removed (RI332-Thr) was monophasic and rapid, implying a role of the N-linked glycan in the first proteolytic phase. RI332 degradation was enhanced when the binding of glycoproteins to calnexin was prevented. Moreover, the truncated glycoprotein interacted with calnexin preferentially during the first proteolytic phase, which strongly suggests that binding of RI332 to the lectin-like protein may result in the slow, initial phase of degradation. Additionally, mannose trimming appears to be required for efficient proteolysis of RI332. After treatment of cells with the inhibitor of N-glycosylation, tunicamycin, destruction of the truncated RI variants was severely inhibited; likewise, in cells preincubated with the calcium ionophore A23187, both RI332 and RI332-Thr were stabilized, despite the presence or absence of the N-linked glycan. On the other hand, both drugs are known to trigger the unfolded protein response (UPR), resulting in the induction of BiP and other ER-resident proteins. Indeed, only in drug-treated cells could an interaction between BiP and RI332 and RI332-Thr be detected. Induction of BiP was also evident after overexpression of murine Ire1, an ER transmembrane kinase known to play a central role in the UPR pathway; at the same time, stabilization of RI332 was observed. Together, these results suggest that binding of the substrate proteins to UPR-induced chaperones affects their half lives.

Interaction of the Hsp70 molecular chaperone, DnaK, with its cochaperone DnaJ

Chaperones of the Hsp70 family bind to unfolded or partially folded polypeptides to facilitate many cellular processes. ATP hydrolysis and substrate binding, the two key molecular activities of this chaperone, are modulated by the cochaperone DnaJ. By using both genetic and biochemical approaches, we provide evidence that DnaJ binds to at least two sites on the Escherichia coli Hsp70 family member DnaK: under the ATPase domain in a cleft between its two subdomains and at or near the pocket of substrate binding. The lower cleft of the ATPase domain is defined as a binding pocket for the J-domain because (i) a DnaK mutation located in this cleft (R167H) is an allele-specific suppressor of the binding defect of the DnaJ mutation, D35N and (ii) alanine substitution of two residues close to R167 in the crystal structure, N170A and T173A, significantly decrease DnaJ binding. A second binding determinant is likely to be in the substrate-binding domain because some DnaK mutations in the vicinity of the substrate-binding pocket are defective in either the affinity (G400D, G539D) or rate (D526N) of both peptide and DnaJ binding to DnaK. Binding of DnaJ may propagate conformational changes to the nearby ATPase catalytic center and substrate-binding sites as well as facilitate communication between these two domains to alter the molecular properties of Hsp70.

Arg-302 facilitates deprotonation of Glu-325 in the transport mechanism of the lactose permease from Escherichia coli

A mechanistic model for lactose/H+ symport via the lactose permease of Escherichia coli proposed recently indicates that the permease must be protonated to bind ligand with high affinity. Moreover, in the ground state, the symported H+ is shared between His-322 (helix X) and Glu-269 (helix VIII), whereas Glu-325 (helix X) is charge-paired with Arg-302 (helix IX). Substrate binding at the outer surface induces a conformational change that leads to transfer of the H+ to Glu-325 and reorientation of the binding site to the inner surface. After release of the substrate, Glu-325 is deprotonated on the inside because of rejuxtapositioning with Arg-302. To test the role of Arg-302 in the mechanism, the catalytic properties of mutants Arg-302→Ala and Arg-302→Ser were studied. Both mutants are severely defective in active lactose transport, as well as in efflux or influx down a concentration gradient, translocation modes that involve net H+ movement. In marked contrast, the mutants catalyze equilibrium exchange of lactose and bind ligand with high affinity. These characteristics are remarkably analogous to those of permease mutants with neutral replacements for Glu-325, a residue that plays a direct role in H+ translocation. These observations lend strong support for the argument that Arg-302 interacts with Glu-325 to facilitate deprotonation of the carboxylic acid during turnover.

Mutagenesis of the Glucose-1-Phosphate-Binding Site of Potato Tuber ADP-Glucose Pyrophosphorylase1

Lysine (Lys)-195 in the homotetrameric ADP-glucose pyrophosphorylase (ADPGlc PPase) from Escherichia coli was shown previously to be involved in the binding of the substrate glucose-1-phosphate (Glc-1-P). This residue is highly conserved in the ADPGlc PPase family. Site-directed mutagenesis was used to investigate the function of this conserved Lys residue in the large and small subunits of the heterotetrameric potato (Solanum tuberosum) tuber enzyme. The apparent affinity for Glc-1-P of the wild-type enzyme decreased 135- to 550-fold by changing Lys-198 of the small subunit to arginine, alanine, or glutamic acid, suggesting that both the charge and the size of this residue influence Glc-1-P binding. These mutations had little effect on the kinetic constants for the other substrates (ATP and Mg2+ or ADP-Glc and inorganic phosphate), activator (3-phosphoglycerate), inhibitor (inorganic phosphate), or on the thermal stability. Mutagenesis of the corresponding Lys (Lys-213) in the large subunit had no effect on the apparent affinity for Glc-1-P by substitution with arginine, alanine, or glutamic acid. A double mutant, SK198RLK213R, was also obtained that had a 100-fold reduction of the apparent affinity for Glc-1-P. The data indicate that Lys-198 in the small subunit is directly involved in the binding of Glc-1-P, whereas they appear to exclude a direct role of Lys-213 in the large subunit in the interaction with this substrate.

Higher plants contain homologs of the bacterial celA genes encoding the catalytic subunit of cellulose synthase.

In spite of much effort, no one has succeeded in isolating and characterizing the enzyme(s) responsible for synthesis of cellulose, the major cell wall polymer of plants. We have characterized two cotton (Gossypium hirsutum) cDNA clones and identified one rice (Oryza sativa) cDNA that are homologs of the bacterial celA genes that encode the catalytic subunit of cellulose synthase. Three regions in the deduced amino acid sequences of the plant celA gene products are conserved with respect to the proteins encoded by bacterial celA genes. Within these conserved regions, there are four highly conserved subdomains previously suggested to be critical for catalysis and/or binding of the substrate UDP-glucose (UDP-Glc). An overexpressed DNA segment of the cotton celA1 gene encodes a polypeptide fragment that spans these domains and binds UDP-Glc, while a similar fragment having one of these domains deleted does not. The plant celA genes show little homology at the N- and C-terminal regions and also contain two internal insertions of sequence, one conserved and one hypervariable, that are not found in the bacterial gene sequences. Cotton celA1 and celA2 genes are expressed at high levels during active secondary wall cellulose synthesis in developing cotton fibers. Genomic Southern blot analyses in cotton demonstrate that celA forms a small gene family.

NMR determination of the major solution conformation of a peptoid pentamer with chiral side chains

Polymers of N-substituted glycines (“peptoids”) containing chiral centers at the α position of their side chains can form stable structures in solution. We studied a prototypical peptoid, consisting of five para-substituted (S)-N-(1-phenylethyl)glycine residues, by NMR spectroscopy. Multiple configurational isomers were observed, but because of extensive signal overlap, only the major isomer containing all cis-amide bonds was examined in detail. The NMR data for this molecule, in conjunction with previous CD spectroscopic results, indicate that the major species in methanol is a right-handed helix with cis-amide bonds. The periodicity of the helix is three residues per turn, with a pitch of ≈6 Å. This conformation is similar to that anticipated by computational studies of a chiral peptoid octamer. The helical repeat orients the amide bond chromophores in a manner consistent with the intensity of the CD signal exhibited by this molecule. Many other chiral polypeptoids have similar CD spectra, suggesting that a whole family of peptoids containing chiral side chains is capable of adopting this secondary structure motif. Taken together, our experimental and theoretical studies of the structural properties of chiral peptoids lay the groundwork for the rational design of more complex polypeptoid molecules, with a variety of applications, ranging from nanostructures to nonviral gene delivery systems.

The solution structure of the Zα domain of the human RNA editing enzyme ADAR1 reveals a prepositioned binding surface for Z-DNA

Double-stranded RNA deaminase I (ADAR1) contains the Z-DNA binding domain Zα. Here we report the solution structure of free Zα and map the interaction surface with Z-DNA, confirming roles previously assigned to residues by mutagenesis. Comparison with the crystal structure of the (Zα)2/Z-DNA complex shows that most Z-DNA contacting residues in free Zα are prepositioned to bind Z-DNA, thus minimizing the entropic cost of binding. Comparison with homologous (α+β)helix–turn–helix/B-DNA complexes suggests that binding of Zα to B-DNA is disfavored by steric hindrance, but does not eliminate the possibility that related domains may bind to both B- and Z-DNA.

Solution structure of a 142-residue recombinant prion protein corresponding to the infectious fragment of the scrapie isoform

The scrapie prion protein (PrPSc) is the major, and possibly the only, component of the infectious prion; it is generated from the cellular isoform (PrPC) by a conformational change. N-terminal truncation of PrPSc by limited proteolysis produces a protein of ≈142 residues designated PrP 27–30, which retains infectivity. A recombinant protein (rPrP) corresponding to Syrian hamster PrP 27–30 was expressed in Escherichia coli and purified. After refolding rPrP into an α-helical form resembling PrPC, the structure was solved by multidimensional heteronuclear NMR, revealing many structural features of rPrP that were not found in two shorter PrP fragments studied previously. Extensive side-chain interactions for residues 113–125 characterize a hydrophobic cluster, which packs against an irregular β-sheet, whereas residues 90–112 exhibit little defined structure. Although identifiable secondary structure is largely lacking in the N terminus of rPrP, paradoxically this N terminus increases the amount of secondary structure in the remainder of rPrP. The surface of a long helix (residues 200–227) and a structured loop (residues 165–171) form a discontinuous epitope for binding of a protein that facilitates PrPSc formation. Polymorphic residues within this epitope seem to modulate susceptibility of sheep and humans to prion disease. Conformational heterogeneity of rPrP at the N terminus may be key to the transformation of PrPC into PrPSc, whereas the discontinuous epitope near the C terminus controls this transition.

The solution structure of the N-terminal domain of α2-macroglobulin receptor-associated protein

The three-dimensional structure of the N-terminal domain (residues 18–112) of α2-macroglobulin receptor-associated protein (RAP) has been determined by NMR spectroscopy. The structure consists of three helices composed of residues 23–34, 39–65, and 73–88. The three helices are arranged in an up-down-up antiparallel topology. The C-terminal 20 residues were shown not to be in a well defined conformation. A structural model for the binding of RAP to the family of low-density lipoprotein receptors is proposed. It defines a role in binding for both the unordered C terminus and the structural scaffold of the core structure. Pathogenic epitopes for the rat disease Heymann nephritis, an experimental model of human membranous glomerulonephritis, have been identified in RAP and in the large endocytic receptor gp330/megalin. Here we provide the three-dimensional structure of the pathogenic epitope in RAP. The amino acid residues known to form the epitope are in a helix–loop–helix conformation, and from the structure it is possible to rationalize the published results obtained from studies of fragments of the N-terminal domain.