Semi-Classical Mechanics in Phase Space: A Study of Wigner's Function

We explore the semi-classical structure of the Wigner functions ($\Psi $(q, p)) representing bound energy eigenstates $|\psi \rangle $ for systems with f degrees of freedom. If the classical motion is integrable, the classical limit of $\Psi $ is a delta function on the f-dimensional torus to which classical trajectories corresponding to ($|\psi \rangle $) are confined in the 2f-dimensional phase space. In the semi-classical limit of ($\Psi $ ($\hslash $) small but not zero) the delta function softens to a peak of order ($\hslash ^{-\frac{2}{3}f}$) and the torus develops fringes of a characteristic 'Airy' form. Away from the torus, $\Psi $ can have semi-classical singularities that are not delta functions; these are discussed (in full detail when f = 1) using Thom's theory of catastrophes. Brief consideration is given to problems raised when ($\Psi $) is calculated in a representation based on operators derived from angle coordinates and their conjugate momenta. When the classical motion is non-integrable, the phase space is not filled with tori and existing semi-classical methods fail. We conjecture that (a) For a given value of non-integrability parameter ($\epsilon $), the system passes through three semi-classical regimes as ($\hslash $) diminishes. (b) For states ($|\psi \rangle $) associated with regions in phase space filled with irregular trajectories, ($\Psi $) will be a random function confined near that region of the 'energy shell' explored by these trajectories (this region has more than f dimensions). (c) For ($\epsilon \neq $0, $\hslash $) blurs the infinitely fine classical path structure, in contrast to the integrable case ($\epsilon $ = 0, where $\hslash $ )imposes oscillatory quantum detail on a smooth classical path structure.

Mechanisms for alphavirus nonstructural polyprotein processing

Replication and transcription of the RNA genome of alphaviruses relies on a set of virus-encoded nonstructural proteins. They are synthesized as a long polyprotein precursor, P1234, which is cleaved at three processing sites to yield nonstructural proteins nsP1, nsP2, nsP3 and nsP4. All the four proteins function as constitutive components of the membrane-associated viral replicase. Proteolytic processing of P1234 polyprotein is precisely orchestrated and coordinates the replicase assembly and maturation. The specificity of the replicase is also controlled by proteolytic cleavages. The early replicase is composed of P123 polyprotein intermediate and nsP4. It copies the positive sense RNA genome to complementary minus-strand. Production of new plus-strands requires complete processing of the replicase. The papain-like protease residing in nsP2 is responsible for all three cleavages in P1234. This study addressed the mechanisms of proteolytic processing of the replicase polyprotein in two alphaviruses Semliki Forest virus (SFV) and Sindbis virus (SIN) representing different branches of the genus. The survey highlighted the functional relation of the alphavirus nsP2 protease to the papain-like enzymes. A new structural motif the Cys-His catalytic dyad accompanied with an aromatic residue following the catalytic His was described for nsP2 and a subset of other thiol proteases. Such an architecture of the catalytic center was named the glycine specificity motif since it was implicated in recognition of a specific Gly residue in the substrate. In particular, the presence of the motif in nsP2 makes the appearance of this amino acid at the second position upstream of the scissile bond a necessary condition for the cleavage. On top of that, there were four distinct mechanisms identified, which provide affinity for the protease and specifically direct the enzyme to different sites in the P1234 polyprotein. Three factors RNA, the central domain of nsP3 and the N-terminus of nsP2 were demonstrated to be external modulators of the nsP2 protease. Here I suggest that the basal nsP2 protease specificity is inherited from the ancestral papain-like enzyme and employs the recognition of the upstream amino acid signature in the immediate vicinity of the scissile bond. This mechanism is responsible for the efficient processing of the SFV nsP3/nsP4 junction. I propose that the same mechanism is involved in the cleavage of the nsP1/nsP2 junction of both viruses as well. However, in this case it rather serves to position the substrate, whereas the efficiency of the processing is ensured by the capability of nsP2 to cut its own N-terminus in cis. Both types of cleavages are demonstrated here to be inhibited by RNA, which is interpreted as impairing the basal papain-like recognition of the substrate. In contrast, processing of the SIN nsP3/nsP4 junction was found to be activated by RNA and additionally potentiated by the presence of the central region of nsP3 in the protease. The processing of the nsP2/nsP3 junction in both viruses occurred via another mechanism, requiring the exactly processed N-terminus of nsP2 in the protease and insensitive to RNA addition. Therefore, the three processing events in the replicase polyprotein maturation are performed via three distinct mechanisms in each of two studied alphaviruses. Distinct sets of conditions required for each cleavage ensure sequential maturation of P1234 polyprotein: nsP4 is released first, then the nsP1/nsP2 site is cut in cis, and liberation of the nsP2 N-terminus activates the cleavage of the nsP2/nsP3 junction at last. The first processing event occurs differently in SFV and SIN, whereas the subsequent cleavages are found to be similar in the two viruses and therefore, their mechanisms are suggested to be conserved in the genus. The RNA modulation of the alphavirus nonstructural protease activity, discovered here, implies bidirectional functional interplay between the alphavirus RNA metabolism and protease regulation. The nsP2 protease emerges as a signal transmitting moiety, which senses the replication stage and responds with proteolytic cleavages. A detailed hypothetical model of the alphavirus replicase core was inferred from the data obtained in the study. Similar principles in replicase organization and protease functioning are expected to be employed by other RNA viruses.

Note on stereo-diagrams of molecules

The paper elucidates a simple way ooJ'dcriving the coordinates for &awing sfereo-&gram of molecules. This method is an alternative, but not a substitute, to the 'ORTEP (suggested by C. K. Johnsori) which, is extensively used in the literature. Illustrations are given using a progrunz which was written based on the method mentioned here. The program is also given in an appendix for practical help.

Metal-Nucleotide Interactions: Crystal Structures of Alkali (Li+, Na+, K+) and Alkaline Earth (Ca2+, Mg2+) Metal Complexes of Adenosine 2'-Monophosphate

Crystal structures of lithium, sodium, potassium, calcium and magnesium salts of adenosine 2'-monophosphate (2'-AMP) have been obtained at atomic resolution by X-ray crystallographic methods. 2'-AMP.Li belongs to the monoclinic space group P21 with a = 7.472(3)Å, b = 26.853(6) Å, c = 9.184(1)Å, b = 113.36(1)Å and Z= 4. 2'-AMP.Na and 2'-AMP.K crystallize in the trigonal space groups P31 and P3121 with a = 8.762(1)Å, c = 34.630(5)Å, Z= 6 and a = 8.931(4), Åc = 34.852(9)Å and Z= 6 respectively while 2'-AMP.Ca and 2'-AMP.Mg belong to space groups P6522 and P21 with cell parameters a = 9.487(2), c = 74.622(13), Z = 12 and a = 4.973(1), b = 10.023(2), c = 16.506(2), beta = 91.1(0) and Z = 2 respectively. All the structures were solved by direct methods and refined by full matrix least-squares to final R factors of 0.033, 0.028, 0.075, 0.069 and 0.030 for 2'-AMP.Li, 2'-AMP.Na, 2'- AMP.K, 2'-AMP.Ca and 2'-AMP.Mg, respectively. The neutral adenine bases in all the structures are in syn conformation stabilized by the O5'-N3 intramolecular hydrogen bond as in free acid and ammonium complex reported earlier. In striking contrast, the adenine base is in the anti geometry (cCN = -156.4(2)°) in 2'-AMP.Mg. Ribose moieties adopt C2'-endo puckering in 2'-AMP.Li and 2'-AMP.Ca, C2'-endo-C3'-exo twist puckering in 2'-AMP.Na and 2'-AMP.K and a C3'-endo-C2'-exo twist puckering in 2'-AMP.Mg structure. The conformation about the exocyclic C4'-C5' bond is the commonly observed gauche-gauche (g+) in all the structures except the gauche- trans (g-) conformation observed in 2'-AMP.Mg structure. Lithium ions coordinate with water, ribose and phosphate oxygens at distances 1.88 to 1.99Å. Na+ ions and K+ ions interact with phosphate and ribose oxygens directly and with N7 indirectly through a water oxygen. A distinct feature of 2'-AMP.Na and 2'-AMP.K structures is the involvement of ribose O4' in metal coordination. The calcium ion situated on a two-fold axis coordinates directly with three oxygens OW1, OW2 and O2 and their symmetry mates at distances 2.18 to 2.42Å forming an octahedron. A classic example of an exception to the existence of the O5'-N3 intramolecular hydorgen bond is the 2'-AMP.Mg strucure. Magnesium ion forms an octahedral coordination with three water and three phosphate oxygens at distances ranging from 2.02 to 2.11Å. A noteworthy feature of its coordination is the indirect link with N3 through OW3 oxygen resulting in macrochelation between the base and the phosphate group. Greater affnity of metal clays towards 5' compared to 2' and 3' nucleotides (J. Lawless, E. Edelson, and L. Manring, Am. Chem. Soc. Northwest Region Meeting, Seattle. 1978) due to macrochelation infered from solution studies (S. S. Massoud, H. Sigel, Eur. J. Biochem. 179, 451-458 (1989)) and interligand hydrogen bonding induced by metals postulated from metal-nucleotide structures in solid state (V. Swaminathan and M. Sundaralingam, CRC. Crit. Rev. Biochem. 6, 245-336 (1979)) are borne out by our structures also. The stacking patterns of adenine bases of both 2'-AMP.Na and 2'-AMP.K structures resemble the 2'-AMP.NH4 structure reported in the previous article. 2'-AMP.Li, 2'-AMP.Ca and 2'-AMP.Mg structures display base-ribose O4' stacking. An overview of interaction of monovalent and divalent cations with 2' and 5'-nucleotides has been presented.

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.

NUPARM and NUCGEN: software for analysis and generation of sequence dependent nucleic acid structures

Software packages NUPARM and NUCGEN, are described, which can be used to understand sequence directed structural variations in nucleic acids, by analysis and generation of non-uniform structures. A set of local inter basepair parameters (viz. tilt, roll, twist, shift, slide and rise) have been defined, which use geometry and coordinates of two successive basepairs only and can be used to generate polymeric structures with varying geometries for each of the 16 possible dinucleotide steps. Intra basepair parameters, propeller, buckle, opening and the C6...C8 distance can also be varied, if required, while the sugar phosphate backbone atoms are fixed in some standard conformation ill each of the nucleotides. NUPARM can be used to analyse both DNA and RNA structures, with single as well as double stranded helices. The NUCGEN software generates double helical models with the backbone fixed in B-form DNA, but with appropriate modifications in the input data, it can also generate A-form DNA ar rd RNA duplex structures.

Mycobacterium tuberculosis FtsZ requires at least one arginine residue at the C-terminal end for polymerization in vitro

We examined whether C-terminal residues of soluble recombinant FtsZ of Mycobacterium tuberculosis (MtFtsZ) have any role in MtFtsZ polymerization in vitro. MtFtsZ-delta C1, which lacks C-terminal extreme Arg residue (underlined in the C-terminal extreme stretch of 13 residues, DDDDVDVPPFMRR), but retaining the penultimate Arg residue (DDDDVDVPPFMR), polymerizes like full-length MtFtsZ in vitro. However, MtFtsZ-delta C2 that lacks both the Arg residues at the C-terminus (DDDDVDVPPFM), neither polymerizes at pH 6.5 nor forms even single- or double-stranded filaments at pH 7.7 in the presence of 10 mM CaCl2. Neither replacement of the penultimate Arg residue, in the C-terminal Arg deletion mutant DDDDVDVPPFMR, with Lys or His or Ala or Asp (DDDDVDVPPFMK/H/A/D) enabled polymerization. Although MtFtsZ-delta C2 showed secondary and tertiary structural changes, which might have affected polymerization, GTPase activity of MtFtsZ-delta C2 was comparable to that of MtFtsZ. These data suggest that MtFtsZ requires an Arg residue as the extreme C-terminal residue for polymerization in vitro. The polypeptide segment containing C-terminal 67 residues, whose coordinates were absent from MtFtsZ crystal structure, was modeled on tubulin and MtFtsZ dimers. Possibilities for the influence of the C-terminal Arg residues on the stability of the dimer and thereby on MtFtsZ polymerization have been discussed.

Two-Step Folding of Donor-Acceptor Foldamers

In a series of polymers containing alternately placed electron-rich dialkoxyilaphthalene (DAN) donors and electron-deficient pyromellitic diimide (PDI) acceptors linked by hexa(oxyethylene) (OE-6) segments, the ability to form a folded D-A stack was intentionally disrupted by random inclusion of varying amounts of a comonomer that is devoid of DAN donor units. NMR spectroscopic studies of folding in these copolymers, induced by NH4SCN that coordinates with the OE-6 segments and facilitates the charge-transfer (C-T) induced D-A stacking, clearly reveals the presence of PDI units that are isolated and those that are located at the ends of (D-A),, stacks. Similar conclusions regarding the presence of stacked and unstacked regions along the polymer chain were also inferred from UV-vis spectroscopic studies that probe the evolution of charge-transfer band. One fascinating aspect of these copolymers wits their ability to undergo it two-step folding: first, short (D-A),, stacks are formed by the interaction of the NH4+ ion with some specific regions of the polymer chain, and subsequently these Stacks are further stacked via a two-point interaction with it suitably designed external folding agent that carries a DAN unit and all ammonium group. In the second step, the interaction first occurs by the coordination of the ammonium group of the folding agent with the OE-6 segment, which in turn facilitates the C-T interaction of the DAN unit with the adjacent uncomplexed PDI units along the polymer chain, leading to an increase ill the slacking. Variations of several spectral features, during both UV-vis and NMR spectroscopic titrations, clearly reveal this novel two-step folding process.

Functional interaction of diphenols with polyphenol oxidase - Molecular determinants of substrate/inhibitor specificity SO FEBS JOURNAL

Polyphenol oxidase (PPO) catalyzes the oxidation of o-diphenols to their respective quinones. The quinones autopolymerize to form dark pigments, an undesired effect. PPO is therefore the target for the development of antibrowning and antimelanization agents. A series of phenolic compounds experimentally evaluated for their binding affinity and inhibition constants were computationally docked to the active site of catechol oxidase. Docking studies suggested two distinct modes of binding, dividing the docked ligands into two groups. Remarkably, the first group corresponds to ligands determined to be substrates and the second group corresponds to reversible inhibitors. Analyses of the complexes provide structural explanations for correlating subtle changes in the position and nature of the substitutions on o-diphenols to their functional properties as substrates and inhibitors. Higher reaction rates and binding are reckoned by additional interactions of the substrates with key residues that line the hydrophobic cavity. The docking results suggest that inhibition of oxidation stems from an interaction between the aromatic carboxylic acid group and the apical His 109 of the four coordinates of the trigonal pyramidal coordination polyhedron of CuA. The spatial orientation of the hydroxyl in relation to the carboxylic group either allows a perfect fit in the substrate cavity, leading to inhibition, or because of a steric clash flips the molecule vertically, facilitating oxidation. This is the first study to explain, at the molecular level, the determinants Of substrate and inhibitor specificity of a catechol oxidase, thereby providing a platform for the design of selective inhibitors useful to both the food and pharmaceutical industries.

Improving GPS time series for geodynamic studies

Accurate and stable time series of geodetic parameters can be used to help in understanding the dynamic Earth and its response to global change. The Global Positioning System, GPS, has proven to be invaluable in modern geodynamic studies. In Fennoscandia the first GPS networks were set up in 1993. These networks form the basis of the national reference frames in the area, but they also provide long and important time series for crustal deformation studies. These time series can be used, for example, to better constrain the ice history of the last ice age and the Earth s structure, via existing glacial isostatic adjustment models. To improve the accuracy and stability of the GPS time series, the possible nuisance parameters and error sources need to be minimized. We have analysed GPS time series to study two phenomena. First, we study the refraction in the neutral atmosphere of the GPS signal, and, second, we study the surface loading of the crust by environmental factors, namely the non-tidal Baltic Sea, atmospheric load and varying continental water reservoirs. We studied the atmospheric effects on the GPS time series by comparing the standard method to slant delays derived from a regional numerical weather model. We have presented a method for correcting the atmospheric delays at the observational level. The results show that both standard atmosphere modelling and the atmospheric delays derived from a numerical weather model by ray-tracing provide a stable solution. The advantage of the latter is that the number of unknowns used in the computation decreases and thus, the computation may become faster and more robust. The computation can also be done with any processing software that allows the atmospheric correction to be turned off. The crustal deformation due to loading was computed by convolving Green s functions with surface load data, that is to say, global hydrology models, global numerical weather models and a local model for the Baltic Sea. The result was that the loading factors can be seen in the GPS coordinate time series. Reducing the computed deformation from the vertical time series of GPS coordinates reduces the scatter of the time series; however, the long term trends are not influenced. We show that global hydrology models and the local sea surface can explain up to 30% of the GPS time series variation. On the other hand atmospheric loading admittance in the GPS time series is low, and different hydrological surface load models could not be validated in the present study. In order to be used for GPS corrections in the future, both atmospheric loading and hydrological models need further analysis and improvements.

Quantum Space-Time and Noncommutative Gauge Field Theories

Arguments arising from quantum mechanics and gravitation theory as well as from string theory, indicate that the description of space-time as a continuous manifold is not adequate at very short distances. An important candidate for the description of space-time at such scales is provided by noncommutative space-time where the coordinates are promoted to noncommuting operators. Thus, the study of quantum field theory in noncommutative space-time provides an interesting interface where ordinary field theoretic tools can be used to study the properties of quantum spacetime. The three original publications in this thesis encompass various aspects in the still developing area of noncommutative quantum field theory, ranging from fundamental concepts to model building. One of the key features of noncommutative space-time is the apparent loss of Lorentz invariance that has been addressed in different ways in the literature. One recently developed approach is to eliminate the Lorentz violating effects by integrating over the parameter of noncommutativity. Fundamental properties of such theories are investigated in this thesis. Another issue addressed is model building, which is difficult in the noncommutative setting due to severe restrictions on the possible gauge symmetries imposed by the noncommutativity of the space-time. Possible ways to relieve these restrictions are investigated and applied and a noncommutative version of the Minimal Supersymmetric Standard Model is presented. While putting the results obtained in the three original publications into their proper context, the introductory part of this thesis aims to provide an overview of the present situation in the field.

Solution structures of conformationally equilibrium forms of holo-acyl carrier protein (PfACP) from Plasmodium falciparum provides insight into the mechanism of activation of ACPs

Acyl Carrier Protein (ACP) from the malaria parasite, Plasmodium falciparum (PfACP) in its holo form is found to exist in two conformational states in solution. Unique 3D solution structures of holo-PfACP have been determined for both equilibrium conformations, using high-resolution NMR methods. Twenty high-resolution solution structures for each of the two forms of holo-PfACP have been determined on the basis of 1226 and 1218 unambiguously assigned NOEs (including NOEs between 4 '-phosphopantetheine prosthetic group (4 '-PP) and protein), 55 backbone dihedral angles and 26 hydrogen bonds. The atomic rmsd values of the determined structures of two equilibrium forms, about the mean coordinates of the backbone and heavy atoms, are 0.48 +/- 0.09 and 0.92 +/- 0.10 and 0.49 +/- 0.08 and 0.97 +/- 0.11 angstrom, respectively. The interaction of 4 '-PP with the polypeptide backbone is reported here for the first time for any of the ACPs. The structures of holo-PfACP consist of three well-defined helices that are tightly packed. The structured regions of the molecule are stabilized by extensive hydrophobic interactions. The difference between the two forms arises from a reorientation of the 4 '-PP group. The enthalpy difference between the two forms, although small, implies that a conformational switch is essential for the activation of holo-ACP. Sequence and structures of holo-PfACP have been compared with those of the ACPs from type I and type II fatty acid biosynthesis pathways (FAS), in particular with the ACP from rat and the butyryl-ACP from E. coli. The PfACP structure, thus determined has several novel features hitherto not seen in other ACPs.

Antipyrine complexes of rare-earth nitrates

Antipyrine complexes of eight rare-earth nitrates of the composition M(C11H12N2O)3 (NO3)3 where M = La, Ce, Pr, Nd, Sm, Gd, Er, and Y, have been prepared by a new, simple method and characterised. The complexes undergo exothermic decomposition at ~3oo°C. Infrared and U.V. spectral studies of the complexes indicate that antipyrine coordinates to metal through oxygen. The nature of the nitrate bonding is discussed in the light of infrared evidence, and conductivity studies in nitromethane and dimethylformamide.

Semi-supervised learning of WLAN radio maps

In this thesis a manifold learning method is applied to the problem of WLAN positioning and automatic radio map creation. Due to the nature of WLAN signal strength measurements, a signal map created from raw measurements results in non-linear distance relations between measurement points. These signal strength vectors reside in a high-dimensioned coordinate system. With the help of the so called Isomap-algorithm the dimensionality of this map can be reduced, and thus more easily processed. By embedding position-labeled strategic key points, we can automatically adjust the mapping to match the surveyed environment. The environment is thus learned in a semi-supervised way; gathering training points and embedding them in a two-dimensional manifold gives us a rough mapping of the measured environment. After a calibration phase, where the labeled key points in the training data are used to associate coordinates in the manifold representation with geographical locations, we can perform positioning using the adjusted map. This can be achieved through a traditional supervised learning process, which in our case is a simple nearest neighbors matching of a sampled signal strength vector. We deployed this system in two locations in the Kumpula campus in Helsinki, Finland. Results indicate that positioning based on the learned radio map can achieve good accuracy, especially in hallways or other areas in the environment where the WLAN signal is constrained by obstacles such as walls.

Rare-earth trichloroacetates

The rare-earth trichloroacetates having the formula Ln(Cl3CCOO)3. 3H2O, where Ln = La, Pr, Nd, Sm, Gd or Y, were investigated by conductimetric, cryoscopic and infrared methods. The results suggest a structure in which the acetate anion coordinates to the metal through both the oxygen and the water molecules remain outside the coordination sphere.