Calculating the bound spectrum by path summation in action-angle variables

The density of states n(E) is calculated for a bound system whose classical motion is integrable, starting from an expression in terms of the trace of the time-dependent Green function. The novel feature is the use of action-angle variables. This has the advantages that the trace operation reduces to a trivial multiplication and the dependence of n(E) on all classical closed orbits with different topologies appears naturally. The method is contrasted with another, not applicable to integrable systems except in special cases, in which quantization arises from a single closed orbit which is assumed isolated and the trace taken by the method of stationary phase.

Platelet endothelial cell adhesion molecule 1 (PECAM-1) and its interactions with glycosaminoglycans: 2. Biochemical analyses

Platelet endothelial cell adhesion molecule 1 (PECAM-1) (CD31), a member of the immunoglobulin (Ig) superfamily of cell adhesion molecules with six Ig-like domains, has a range of functions, notably its contributions to leukocyte extravasation during inflammation and in maintaining vascular endothelial integrity. Although PECAM-1 is known to mediate cell adhesion by homophilic binding via domain 1, a number of PECAM-1 heterophilic ligands have been proposed. Here, the possibility that heparin and heparan sulfate (HS) are ligands for PECAM-1 was reinvestigated. The extracellular domain of PECAM-1 was expressed first as a fusion protein with the Fc region of human IgG1 fused to domain 6 and second with an N-terminal Flag tag on domain 1 (Flag-PECAM-1). Both proteins bound heparin immobilized on a biosensor chip in surface plasmon resonance (SPR) binding experiments. Binding was pH-sensitive but is easily measured at slightly acidic pH. A series of PECAM-1 domain deletions, prepared in both expression systems, were tested for heparin binding. This revealed that the main heparin-binding site required both domains 2 and 3. Flag-PECAM-1 and a Flag protein containing domains 1-3 bound HS on melanoma cell surfaces, but a Flag protein containing domains 1-2 did not. Heparin oligosaccharides inhibited Flag-PECAM-1 from binding immobilized heparin, with certain structures having greater inhibitory activity than others. Molecular modeling similarly identified the junction of domains 2 and 3 as the heparin-binding site and further revealed the importance of the iduronic acid conformation for binding. PECAM-1 does bind heparin/HS but by a site that is distinct from that required for homophilic binding.

Crystal state conformation of three model monomer units for the beta-bend ribbon structure

The molecular and crystal structures of three compounds, representing the repeating units of the -bend ribbon (an approximate 310-helix, with an intramolecular hydrogen-bonding donor every two residues), have been determined by x-ray diffraction. They are Boc-Aib-Hib-NHBzl, Z-Aib-Hib-NHBzl, and Z-L-Hyp-Aib-NHMe (Aib, -aminoisobutyric acid; Bzl, benzyl; Boc, t-butyloxycarbonyl; Hyp, hydroxyproline Hib, -hydroxyisobutyric acid; Z, benzyloxycarbonyl). The two former compounds are folded in a -bend conformation: type III (III) for Boc-Aib-Hib-NHBzl, while type II (II) for the Z analogue. Conversely, the structure of Z-L-Hyp-Aib-NHMe, although not far from a type II -bend, is partially open.

X-ray studies on crystalline complexes involving amino acids and peptides. XXIII. Variability in ionization state, conformation and molecular aggregation in the complexes of succinic acid with DL- and L-lysine

Crystalline complexes of succinic acid with DL- and L-lysine have been prepared and analysed by X-ray diffraction. DL-Lysine complex: C6HIsN202 + 1 2- 1 ~C4H404 .~C4H604, Mr -- 264"2, PI, a = 5"506 (4), =8.070(2), c=14.089(2) A,, a=92.02(1), /3= 100"69 (3), y = 95"85 (3) ~>, Z = 2, Dx = 1"44 g cm -3, R = 0.059 for 2546 observed reflections. Form I of the e-lysine complex: C6HIsN20-, ~ .C4H504, Mr = 264.2, P1, a = 5" 125 (2), b = 8"087 (1), c = 8"689 (1) A,, a = 112.06 (1), /3 = 99.08 (2), y = 93"77(2) °, Z--l, D,,,=1"34(3), Dx=l"34gcm 3 R = 0.033 for 1475 observed reflections. Form II of + I 2- the e-lysine complex: C6H15N202 .,iC4H404 .- 1 I ") 4C4H604.4(C4HsO4""H'"CaH404)" , Mr = 264"2, P1, a = 10.143 (4), b = 10.256 (2), c = 12"916 (3) A,, a = 105.00 (2),/3 = 99-09 (3), y = 92"78 (3)::, Z = 4, Dm= 1"37(4), D,.= 1.38gcm 3, R=0.067 for 2809 observed reflections. The succinic acid molecules in the structures exhibit a variety of ionization states. Two of the lysine conformations found in the complexes have been observed for the first time in crystals containing lysine. Form II of the L-lysine complex is highly pseudosymmetric. In all the complexes, unlike molecules aggregate into separate alternating layers. The basic element of aggregation in the lysine layer in the complexes is an S2-type head-to-tail sequence. This element combines in different ways in the three structures. The basic element of aggre gation in the succinic acid layer in the complexes is a hydrogen-bonded ribbon. The ribbons are interconnected indirectly through amino groups in the lysine layer.

Preservation of native conformation during aluminium-induced aggregation of tau protein

ALUMINIUM exposure has been shown to result in aggregation of microtubule-associated protein tau in vitro. In the light of recent observations that the native random structure of tau protein is maintained in its monomeric and dimeric states as well as in the paired helical filaments characteristic of Alzheimer's disease, it is likely that factors playing a causative role in neurofibrillary pathology would not drastically alter the native conformation of tau protein. We have studied the interaction of tau protein with aluminium using circular dichroism (CD) and 27(Al) NMR spectroscopy. The CD studies revealed a five-fold increase in the observed ellipticity of the tau-aluminium assembly. The increase in elipticity was not associated with a change in the general conformation of the protein and was most likely due to an aggregation of the tau protein induced by aluminium. Al-27 NMR spectroscopy confirmed the binding of aluminium to tau protein. Hyperphosphorylation of tau in Alzheimer's disease is known to be associated with defective microtubule assembly in this condition. Abnormally phosphorylated tau exists in a polymerized form in the paired helical filaments (PHF) which constitute the neurofibrillary tangles found in Alzheimer's disease. While it is hypothesized that its altered biophysical characteristics render abnormally phosphorylated tau resistant to proteolysis, causing the formation of stable deposits,the sequence of events resulting in the polymerization of tau are little understood, as are the additional factors or modifications required for tills process. Based on the results of our spectroscopic studies, a model for the sequence of events occurring in neurofibrillary pathology is proposed.

Pi-turns in proteins and peptides: Classification, conformation, occurrence, hydration and sequence.

The i + 5-->i hydrogen bonded turn conformation (pi-turn) with the fifth residue adopting alpha L conformation is frequently found at the C-terminus of helices in proteins and hence is speculated to be a "helix termination signal." An analysis of the occurrence of i + 5-->i hydrogen bonded turn conformation at any general position in proteins (not specifically at the helix C-terminus), using coordinates of 228 protein crystal structures determined by X-ray crystallography to better than 2.5 A resolution is reported in this paper. Of 486 detected pi-turn conformations, 367 have the (i + 4)th residue in alpha L conformation, generally occurring at the C-terminus of alpha-helices, consistent with previous observations. However, a significant number (111) of pi-turn conformations occur with (i + 4)th residue in alpha R conformation also, generally occurring in alpha-helices as distortions either at the terminii or at the middle, a novel finding. These two sets of pi-turn conformations are referred to by the names pi alpha L and pi alpha R-turns, respectively, depending upon whether the (i + 4)th residue adopts alpha L or alpha R conformations. Four pi-turns, named pi alpha L'-turns, were noticed to be mirror images of pi alpha L-turns, and four more pi-turns, which have the (i + 4)th residue in beta conformation and denoted as pi beta-turns, occur as a part of hairpin bend connecting twisted beta-strands. Consecutive pi-turns occur, but only with pi alpha R-turns. The preference for amino acid residues is different in pi alpha L and pi alpha R-turns. However, both show a preference for Pro after the C-termini. Hydrophilic residues are preferred at positions i + 1, i + 2, and i + 3 of pi alpha L-turns, whereas positions i and i + 5 prefer hydrophobic residues. Residue i + 4 in pi alpha L-turns is mainly Gly and less often Asn. Although pi alpha R-turns generally occur as distortions in helices, their amino acid preference is different from that of helices. Poor helix formers, such as His, Tyr, and Asn, also were found to be preferred for pi alpha R-turns, whereas good helix former Ala is not preferred. pi-Turns in peptides provide a picture of the pi-turn at atomic resolution. Only nine peptide-based pi-turns are reported so far, and all of them belong to pi alpha L-turn type with an achiral residue in position i + 4. The results are of importance for structure prediction, modeling, and de novo design of proteins.

Ligand dependent intra and inter subunit communication in human tryptophanyl tRNA synthetase as deduced from the dynamics of structure networks

Homodimeric protein tryptophanyl tRNA synthetase (TrpRS) has a Rossmann fold domain and belongs to the 1c subclass of aminoacyl tRNA synthetases. This enzyme performs the function of acylating the cognate tRNA. This process involves a number of molecules (2 protein subunits, 2 tRNAs and 2 activated Trps) and thus it is difficult to follow the complex steps in this process. Structures of human TrpRS complexed with certain ligands are available. Based on structural and biochemical data, mechanism of activation of Trp has been speculated. However, no structure has yet been solved in the presence of both the tRNA(Trp) and the activated Trp (TrpAMP). In this study, we have modeled the structure of human TrpRS bound to the activated ligand and the cognate tRNA. In addition, we have performed molecular dynamics (MD) simulations on these models as well as other complexes to capture the dynamical process of ligand induced conformational changes. We have analyzed both the local and global changes in the protein conformation from the protein structure network (PSN) of MD snapshots, by a method which was recently developed in our laboratory in the context of the functionally monomeric protein, methionyl tRNA synthetase. From these investigations, we obtain important information such as the ligand induced correlation between different residues of this protein, asymmetric binding of the ligands to the two subunits of the protein as seen in the crystal structure analysis, and the path of communication between the anticodon region and the aminoacylation site. Here we are able to elucidate the role of dimer interface at a level of detail, which has not been captured so far.

Mechanism of RNA Translocation by a Viral Packaging Motor

Molecular motors are proteins that convert chemical energy into mechanical work. The viral packaging ATPase P4 is a hexameric molecular motor that translocates RNA into preformed viral capsids. P4 belongs to the ubiquitous class of hexameric helicases. Although its structure is known, the mechanism of RNA translocation remains elusive. Here we present a detailed kinetic study of nucleotide binding, hydrolysis, and product release by P4. We propose a stochastic-sequential cooperative model to describe the coordination of ATP hydrolysis within the hexamer. In this model the apparent cooperativity is a result of hydrolysis stimulation by ATP and RNA binding to neighboring subunits rather than cooperative nucleotide binding. Simultaneous interaction of neighboring subunits with RNA makes the otherwise random hydrolysis sequential and processive. Further, we use hydrogen/deuterium exchange detected by high resolution mass spectrometry to visualize P4 conformational dynamics during the catalytic cycle. Concerted changes of exchange kinetics reveal a cooperative unit that dynamically links ATP binding sites and the central RNA binding channel. The cooperative unit is compatible with the structure-based model in which translocation is effected by conformational changes of a limited protein region. Deuterium labeling also discloses the transition state associated with RNA loading which proceeds via opening of the hexameric ring. Hydrogen/deuterium exchange is further used to delineate the interactions of the P4 hexamer with the viral procapsid. P4 associates with the procapsid via its C-terminal face. The interactions stabilize subunit interfaces within the hexamer. The conformation of the virus-bound hexamer is more stable than the hexamer in solution, which is prone to spontaneous ring openings. We propose that the stabilization within the viral capsid increases the packaging processivity and confers selectivity during RNA loading. Finally, we use single molecule techniques to characterize P4 translocation along RNA. While the P4 hexamer encloses RNA topologically within the central channel, it diffuses randomly along the RNA. In the presence of ATP, unidirectional net movement is discernible in addition to the stochastic motion. The diffusion is hindered by activation energy barriers that depend on the nucleotide binding state. The results suggest that P4 employs an electrostatic clutch instead of cycling through stable, discrete, RNA binding states during translocation. Conformational changes coupled to ATP hydrolysis modify the electrostatic potential inside the central channel, which in turn biases RNA motion in one direction. Implications of the P4 model for other hexameric molecular motors are discussed.

Soft gluon k(t)-resummation and the Froissart bound

We study soft gluon k(t)-resurnmation and the relevance of InfraRed (IR) gluons for the energy dependence of total hadronic cross-sections. In our model, consistency with the Froissart bound is directly related to the ansatz that the IR behaviour of the QCD coupling constant follows an inverse power law.

Nonspecifically bound proteins spin while diffusing along DNA

It is known that DNA-binding proteins can slide along the DNA helix while searching for specific binding sites, but their path of motion remains obscure. Do these proteins undergo simple one-dimensional (1D) translational diffusion, or do they rotate to maintain a specific orientation with respect to the DNA helix? We measured 1D diffusion constants as a function of protein size while maintaining the DNA-protein interface. Using bootstrap analysis of single-molecule diffusion data, we compared the results to theoretical predictions for pure translational motion and rotation-coupled sliding along the DNA. The data indicate that DNA-binding proteins undergo rotation-coupled sliding along the DNA helix and can be described by a model of diffusion along the DNA helix on a rugged free-energy landscape. A similar analysis including the 1D diffusion constants of eight proteins of varying size shows that rotation-coupled sliding is a general phenomenon. The average free-energy barrier for sliding along the DNA was 1.1 +/- 0.2 k(B)T. Such small barriers facilitate rapid search for binding sites.

A lower bound to the survival probability and an approximate first passage time distribution for Markovian and non-Markovian dynamics in phase space

We derive a very general expression of the survival probability and the first passage time distribution for a particle executing Brownian motion in full phase space with an absorbing boundary condition at a point in the position space, which is valid irrespective of the statistical nature of the dynamics. The expression, together with the Jensen's inequality, naturally leads to a lower bound to the actual survival probability and an approximate first passage time distribution. These are expressed in terms of the position-position, velocity-velocity, and position-velocity variances. Knowledge of these variances enables one to compute a lower bound to the survival probability and consequently the first passage distribution function. As examples, we compute these for a Gaussian Markovian process and, in the case of non-Markovian process, with an exponentially decaying friction kernel and also with a power law friction kernel. Our analysis shows that the survival probability decays exponentially at the long time irrespective of the nature of the dynamics with an exponent equal to the transition state rate constant.

A Search for Energy Minimized Sequences of Proteins

In this paper, we present numerical evidence that supports the notion of minimization in the sequence space of proteins for a target conformation. We use the conformations of the real proteins in the Protein Data Bank (PDB) and present computationally efficient methods to identify the sequences with minimum energy. We use edge-weighted connectivity graph for ranking the residue sites with reduced amino acid alphabet and then use continuous optimization to obtain the energy-minimizing sequences. Our methods enable the computation of a lower bound as well as a tight upper bound for the energy of a given conformation. We validate our results by using three different inter-residue energy matrices for five proteins from protein data bank (PDB), and by comparing our energy-minimizing sequences with 80 million diverse sequences that are generated based on different considerations in each case. When we submitted some of our chosen energy-minimizing sequences to Basic Local Alignment Search Tool (BLAST), we obtained some sequences from non-redundant protein sequence database that are similar to ours with an E-value of the order of 10(-7). In summary, we conclude that proteins show a trend towards minimizing energy in the sequence space but do not seem to adopt the global energy-minimizing sequence. The reason for this could be either that the existing energy matrices are not able to accurately represent the inter-residue interactions in the context of the protein environment or that Nature does not push the optimization in the sequence space, once it is able to perform the function.

Free and ATP-bound structures of Ap(4)A hydrolase from Aquifex aeolicus V5

Asymmetric diadenosine tetraphosphate (Ap(4)A) hydrolases degrade the metabolite Ap(4)A back into ATP and AMP. The three-dimensional crystal structure of Ap(4)A hydrolase (16 kDa) from Aquifex aeolicus has been determined in free and ATP-bound forms at 1.8 and 1.95 angstrom resolution, respectively. The overall three-dimensional crystal structure of the enzyme shows an alpha beta alpha-sandwich architecture with a characteristic loop adjacent to the catalytic site of the protein molecule. The ATP molecule is bound in the primary active site and the adenine moiety of the nucleotide binds in a ring-stacking arrangement equivalent to that observed in the X-ray structure of Ap(4)A hydrolase from Caenorhabditis elegans. Binding of ATP in the active site induces local conformational changes which may have important implications in the mechanism of substrate recognition in this class of enzymes. Furthermore, two invariant water molecules have been identified and their possible structural and/or functional roles are discussed. In addition, modelling of the substrate molecule at the primary active site of the enzyme suggests a possible path for entry and/or exit of the substrate and/or product molecule.

Antibodies specific for 1-methylguanosine as a probe of tRNA conformation

Antibodies specific for 1-methylguanosine (m1G) were produced by immunization of rabbits with a bovine serum albumin conjugate of m1G. Antibodies specificity was determined by measuring the inhibition of binding of 3H-m1G trialcohol by various nucleosides or related derivatives. The relative affinities of the unpurified antibodies for various nucleosides showed that m1G trialcohol had an 8-fold higher affinity than m1G; further, guanosine and 2'-O-methylguanosine had at least a 500-fold lower affinity than m1G. The antibodies were purified on m1G-AH-Sepharose column and subsequently immobilized to Sepharose. Immobilized m1G antibodies quantitatively and exclusively retained m1G-containing oligonucleotides derived from ribonuclease A digests of 32P-labeled phage T4 tRNAPro. On the other hand, intact 32P-labeled T4 tRNAPro or its precursor RNA(s) did not bind to the same column. These findings indicate that at least a portion of m1G adjacent to the 3' end of the anticodon in intact T4 tRNAPro is not accessible for antibody binding.

The 310 helical conformation of a pentapeptide containing a-aminoisobutyric acid (Aib): X-ray crystal structure of Tos-(Aib)5 OMe

The pentapeptide Tos-(Aib)5-OMe adopts a 310 helical conformation in the solid state, with three consecutive Type III B-turns stabilized by intramolecular hydrogen bonds.