Shape anisotropy of a single random-walk polymer

Random walks have been used to describe a wide variety of systems ranging from cell colonies to polymers. Sixty-five years ago, Kuhn [Kuhn, W. (1934) Kolloid-Z. 68, 2–11] made the prediction, backed later by computer simulations, that the overall shape of a random-walk polymer is aspherical, yet no experimental work has directly tested Kuhn's general idea and subsequent computer simulations. By using fluorescence microscopy, we monitored the conformation of individual, long, random-walk polymers (fluorescently labeled DNA molecules) at equilibrium. We found that a polymer most frequently adopts highly extended, nonfractal structures with a strongly anisotropic shape. The ensemble-average ratio of the lengths of the long and short axes of the best-fit ellipse of the polymer was much larger than unity.

Broken symmetry and critical transport properties of random metals

Recent experimental data on the conductivity σ+(T), T → 0, on the metallic side of the metal–insulator transition in ideally random (neutron transmutation-doped) 70Ge:Ga have shown that σ+(0) ∝ (N − Nc)μ with μ = ½, confirming earlier ultra-low-temperature results for Si:P. This value is inconsistent with theoretical predictions based on diffusive classical scaling models, but it can be understood by a quantum-directed percolative filamentary amplitude model in which electronic basis states exist which have a well-defined momentum parallel but not normal to the applied electric field. The model, which is based on a new kind of broken symmetry, also explains the anomalous sign reversal of the derivative of the temperature dependence in the critical regime.

Critical transport properties of random metals in large magnetic fields

The threshold behavior of the transport properties of a random metal in the critical region near a metal–insulator transition is strongly affected by the measuring electromagnetic fields. In spite of the randomness, the electrical conductivity exhibits striking phase-coherent effects due to broken symmetry, which greatly sharpen the transition compared with the predictions of effective medium theories, as previously explained for electrical conductivities. Here broken symmetry explains the sign reversal of the T → 0 magnetoconductance of the metal–insulator transition in Si(B,P), also previously not understood by effective medium theories. Finally, the symmetry-breaking features of quantum percolation theory explain the unexpectedly very small electrical conductivity temperature exponent α = 0.22(2) recently observed in Ni(S,Se)2 alloys at the antiferromagnetic metal–insulator transition below T = 0.8 K.

Random locomotion and chemotaxis of human blood polymorphonuclear leukocytes (PMN) in the presence of EDTA: PMN in close quarters require neither leukocyte integrins nor external divalent cations

Divalent cations are thought essential for motile function of leukocytes in general, and for the function of critical adhesion molecules in particular. In the current study, under direct microscopic observation with concomitant time-lapse video recording, we examined the effects of 10 mM EDTA on locomotion of human blood polymorphonuclear leukocytes (PMN). In very thin slide preparations, EDTA did not impair either random locomotion or chemotaxis; motile behavior appeared to benefit from the close approximation of slide and coverslip (“chimneying”). In preparations twice as thick, PMN in EDTA first exhibited active deformability with little or no displacement, then rounded up and became motionless. However, on creation of a chemotactic gradient, the same cells were able to orient and make their way to the target, often, however, losing momentarily their purchase on the substrate. In either of these preparations without EDTA, specific antibodies to β2 integrins did not prevent random locomotion or chemotaxis, even when we added antibodies to β1 and αvβ3 integrins and to integrin-associated protein, and none of these antibodies added anything to the effects of EDTA. In the more turbulent environment of even more media, effects of anti-β2 integrins became evident: PMN still could locomote but adhered to substrate largely by their uropods and by uropod-associated filaments. We relate these findings to the reported independence from integrins of PMN in certain experimental and disease states. Moreover, we suggest that PMN locomotion in close quarters is not only integrin-independent, but independent of external divalent cations as well.

Torsional directed walks, entropic elasticity, and DNA twist stiffness

DNA and other biopolymers differ from classical polymers because of their torsional stiffness. This property changes the statistical character of their conformations under tension from a classical random walk to a problem we call the “torsional directed walk.” Motivated by a recent experiment on single lambda-DNA molecules [Strick, T. R., Allemand, J.-F., Bensimon, D., Bensimon, A. & Croquette, V. (1996) Science 271, 1835–1837], we formulate the torsional directed walk problem and solve it analytically in the appropriate force regime. Our technique affords a direct physical determination of the microscopic twist stiffness C and twist-stretch coupling D relevant for DNA functionality. The theory quantitatively fits existing experimental data for relative extension as a function of overtwist over a wide range of applied force; fitting to the experimental data yields the numerical values C = 120 nm and D = 50 nm. Future experiments will refine these values. We also predict that the phenomenon of reduction of effective twist stiffness by bend fluctuations should be testable in future single-molecule experiments, and we give its analytic form.

Identification of fission yeast nuclear markers using random polypeptide fusions with green fluorescent protein

We describe a method for identifying genes encoding proteins with stereospecific intracellular localizations in the fission yeast Schizosaccharomyces pombe. Yeast are transformed with a gene library in which S. pombe genomic sequences are fused to the gene encoding the Aequorea victoria green fluorescent protein (GFP), and intracellular localizations are subsequently identified by rapid fluorescence screening in vivo. In a model application of these methods to the fission yeast nucleus, we have identified several novel genes whose products are found in specific nuclear regions, including chromatin, the nucleolus, and the mitotic spindle, and sequence similarities between some of these genes and previously identified genes encoding nuclear proteins have validated the approach. These methods will be useful in identifying additional components of the S. pombe nucleus, and further extensions of this approach should also be applicable to a more comprehensive identification of the elements of intracellular architecture in fission yeast.

Random allocation or allocation at random? Patients’ perspectives of participation in a randomised controlled trial

Objectives To explore trial participants’ understandings of randomisation.

Identification of two short internal ribosome entry sites selected from libraries of random oligonucleotides

Sequences that control translation of mRNA may play critical roles in regulating protein levels. One such element is the internal ribosome entry site (IRES). We previously showed that a 9-nt segment in the 5′ leader sequence of the mRNA encoding Gtx homeodomain protein could function as an IRES. To identify other short sequences with similar properties, we designed a selection procedure that uses a retroviral vector to express dicistronic mRNAs encoding enhanced green and cyan fluorescent proteins as the first and second cistrons, respectively. Expression of the second cistron was dependent upon the intercistronic sequences and was indicative of IRES activity. B104 cells were infected with two retroviral libraries that contained random sequences of 9 or 18 nt in the intercistronic region. Cells expressing both cistrons were sorted, and sequences recovered from selected cells were reassayed for IRES activity in a dual luciferase dicistronic mRNA. Two novel IRESes were identified by this procedure, and both contained segments with complementarity to 18S rRNA. When multiple copies of either segment were linked together, IRES activities were dramatically enhanced. Moreover, these synthetic IRESes were differentially active in various cell types. These properties are similar to those of the previously identified 9-nt IRES module from Gtx mRNA. These results provide further evidence that short nucleotide sequences can function as IRESes and support the idea that some cellular IRESes may be composed of shorter functional modules. The ability to identify IRES modules with specific expression properties may be useful in the design of vectors for biotechnology and gene therapy.

An essential amino acid residue in the protein translocation channel revealed by targeted random mutagenesis of SecY

The SecY/Sec61α family of membrane proteins are the central subunits of the putative protein translocation channel. We introduced random mutations into a segment of Escherichia coli SecY within its cytoplasmic domain 5, which was shown previously to be important for the SecA-dependent translocation activity. Mutations were classified into those retaining function and those gaining a dominant-interfering ability caused by a loss of function. These analyses showed that Arg-357, Pro-358, Gly-359, and Thr-362 are functionally important; Arg-357, conserved in almost all organisms, was identified as an indispensable residue.

Advances in random matrix theory, zeta functions, and sphere packing

Over four hundred years ago, Sir Walter Raleigh asked his mathematical assistant to find formulas for the number of cannonballs in regularly stacked piles. These investigations aroused the curiosity of the astronomer Johannes Kepler and led to a problem that has gone centuries without a solution: why is the familiar cannonball stack the most efficient arrangement possible? Here we discuss the solution that Hales found in 1998. Almost every part of the 282-page proof relies on long computer verifications. Random matrix theory was developed by physicists to describe the spectra of complex nuclei. In particular, the statistical fluctuations of the eigenvalues (“the energy levels”) follow certain universal laws based on symmetry types. We describe these and then discuss the remarkable appearance of these laws for zeros of the Riemann zeta function (which is the generating function for prime numbers and is the last special function from the last century that is not understood today.) Explaining this phenomenon is a central problem. These topics are distinct, so we present them separately with their own introductory remarks.

Random circular permutation of genes and expressed polypeptide chains: application of the method to the catalytic chains of aspartate transcarbamoylase.

Recent studies on proteins whose N and C termini are in close proximity have demonstrated that folding of polypeptide chains and assembly of oligomers can be accomplished with circularly permuted chains. As yet no methodical study has been conducted to determine how extensively new termini can be introduced and where such termini cannot be tolerated. We have devised a procedure to generate random circular permutations of the catalytic chains of Escherichia coli aspartate transcarbamoylase (ATCase; EC 2.1.3.2) and to select clones that produce active or stable holoenzyme containing permuted chains. A tandem gene construct was made, based on the desired linkage between amino acid residues in the C- and N-terminal regions of the polypeptide chain, and this DNA was treated with a suitable restriction enzyme to yield a fragment containing the rearranged coding sequence for the chain. Circularization achieved with DNA ligase, followed by linearization at random with DNase I, and incorporation of the linearized, repaired, blunt-ended, rearranged genes into a suitable plasmid permitted the expression of randomly permuted polypeptide chains. The plasmid with appropriate stop codons also contained pyrI, the gene encoding the regulatory chain of ATCase. Colonies expressing detectable amounts of ATCase-like molecules containing permuted catalytic chains were identified by an immunoblot technique or by their ability to grow in the absence of pyrimidines in the growth medium. Sequencing of positive clones revealed a variety of novel circular permutations. Some had N and C termini within helices of the wild-type enzyme as well as deletions and insertions. Permutations were concentrated in the C-terminal domain and only few were detected in the N-terminal domain. The technique, which is adaptable generally to proteins whose N and C termini are near each other, can be of value in relating in vivo folding of nascent, growing polypeptide chains to in vitro renaturation of complete chains and determining the role of protein sequence in folding kinetics.

Random phage mimotopes recognized by monoclonal antibodies against the pyruvate dehydrogenase complex-E2 (PDC-E2).

Dihydrolipoamide acetyltransferase, the E2 component of the pyruvate dehydrogenase complex (PDC-E2), is the autoantigen most commonly recognized by autoantibodies in primary biliary cirrhosis (PBC). We identified a peptide mimotope(s) of PDC-E2 by screening a phage-epitope library expressing random dodecapeptides in the pIII coat protein of fd phage using C355.1, a murine monoclonal antibody (mAb) that recognizes a conformation-dependent epitope in the inner lipoyl domain of PDC-E2 and uniquely stains the apical region of bile duct epithelium (BDE) only in patients with PBC. Eight different sequences were identified in 36 phage clones. WMSYPDRTLRTS was present in 29 clones; WESYPFRVGTSL, APKTYVSVSGMV, LTYVSLQGRQGH, LDYVPLKHRHRH, AALWGVKVRHVS, KVLNRIMAGVRH and GNVALVSSRVNA were singly represented. Three common amino acid motifs (W-SYP, TYVS, and VRH) were shared among all peptide sequences. Competitive inhibition of the immunohistochemical staining of PBC BDE was performed by incubating the peptides WMSYPDRTLRTS, WESYPDRTLRTS, APKTYVSVSGMV, and AALWGVKVRHVS with either C355.1 or a second PDC-E2-specific mAb, C150.1. Both mAbs were originally generated to PDC-E2 but map to distinct regions of PDC-E2. Two of the peptides, although selected by reaction with C355.1, strongly inhibited the staining of BDE by C150.1, whereas the peptide APKTYVSVSGMV consistently inhibited the staining of C355.1 on biliary duct epithelium more strongly than the typical mitochondrial staining of hepatocytes. Rabbit sera raised against the peptide WMSYPDRTLRTS stained BDE of livers and isolated bile duct epithelial cells of PBC patients more intensively than controls. The rabbit sera stained all size ducts in normals, but only small/medium-sized ductules in PBC livers. These studies provide evidence that the antigen present in BDE is a molecular mimic of PDC-E2, and not PDC-E2 itself.

Random mutagenesis of Thermus aquaticus DNA polymerase I: concordance of immutable sites in vivo with the crystal structure.

Expression of Thermus aquaticus (Taq) DNA polymerase I (pol I) in Escherichia, coli complements the growth defect caused by a temperature-sensitive mutation in the host pol I. We replaced the nucleotide sequence encoding amino acids 659-671 of the O-helix of Taq DNA pol I, corresponding to the substrate binding site, with an oligonucleotide containing random nucleotides. Functional Taq pol I mutants were selected based on colony formation at the nonpermissive temperature. By using a library with 9% random substitutions at each of 39 positions, we identified 61 active Taq pol I mutants, each of which contained from one to four amino acid substitutions. Some amino acids, such as alanine-661 and threonine-664, were tolerant of several or even many diverse replacements. In contrast, no replacements or only conservative replacements were identified at arginine-659, lysine-663, and tyrosine-671. By using a library with totally random nucleotides at five different codons (arginine-659, arginine-660, lysine-663, phenylalanine-667, and glycine-668), we confirmed that arginine-659 and lysine-663 were immutable, and observed that only tyrosine substituted for phenylalanine-667. The two immutable residues and the two residues that tolerate only highly conservative replacements lie on the side of O-helix facing the incoming deoxynucleoside triphosphate, as determined by x-ray analysis. Thus, we offer a new approach to assess concordance of the active conformation of an enzyme, as interpreted from the crystal structure, with the active conformation inferred from in vivo function.