Is DNA a nonlinear dynamical system where solitary conformational waves are possible?

DNA is considered as a nonlinear dynamical system in which solitary conformational waves can be excited. The history of the approach, the main results, and arguments in favour and against are presented. Perspectives are discussed pertaining to studies of DNA’s nonlinear properties.     

Persistent solutions for age-dependent pair-formation models

Conditions on the vital rates and the mating function are derived which imply existence or nonexistence of exponentially growing persistent age-distributions for age-dependent pair-formation models.     

Parametric analysis of the ratio-dependent predator–prey model

We present a complete parametric analysis of stability properties and dynamic regimes of an ODE model in which the functional response is a function of the ratio of prey and predator abundances. We show the existence of eight qualitatively different types of system behaviors realized for various parameter values. In particular, there exist areas of coexistence (which may be steady or oscillating), areas in which both populations become extinct, and areas of "conditional coexistence" depending on the initial values. One of the main mathematical features of ratio-dependent models, distinguishing this class from other predator-prey models, is that the Origin is a complicated equilibrium point, whose characteristics crucially determine the main properties of the model. This is the first demonstration of this phenomenon in an ecological model. The model is investigated with methods of the qualitative theory of ODEs and the theory of bifurcations. The biological relevance of the mathematical results is discussed both regarding conservation issues (for which coexistence is desired) and biological control (for which extinction is desired).     

Chaos and population disappearances in simple ecological models

A class of truncated unimodal discrete-time single species models for which low or high densities result in extinction in the following generation are considered. A classification of the dynamics of these maps into five types is proven: (i) extinction in finite time for all initial densities, (ii) semistability in which all orbits tend toward the origin or a semi-stable fixed point, (iii) bistability for which the origin and an interval bounded away from the origin are attracting, (iv) chaotic semistability in which there is an interval of chaotic dynamics whose compliment lies in the origin’s basin of attraction and (v) essential extinction in which almost every (but not every) initial population density leads to extinction in finite time. Applying these results to the Logistic, Ricker and generalized Beverton-Holt maps with constant harvesting rates, two birfurcations are shown to lead to sudden population disappearances: a saddle node bifurcation corresponding to a transition from bistability to extinction and a chaotic blue sky catastrophe corresponding to a transition from bistability to essential extinction. Received: 14 February 2000 / Revised version: 15 August 2000 / Published online: 16 February 2001     

Nuclear forward scattering of synchrotron radiation by deoxymyoglobin

Nuclear forward scattering of synchrotron radiation is used to determine the quadrupole splitting and the mean square displacement of the iron atom in deoxymyoglobin in the temperature range between 50 K and 243 K. Above 200 K an abnormally fast decay of the forward scattered intensity at short times after the synchrotron flash is observed, which is caused by protein-specific motions. The results strongly support the picture that protein dynamics seen at the position of the iron can be understood by harmonic motions in the low temperature regime while in the physiological regime diffusive motions in limited space are present. The shape of the resonance broadening function is investigated. An inhomogeneous broadening with a Lorentzian distribution indicating dipole interactions results in a better agreement with the experimental data than the common Gaussian distribution. Received: 30 August 1999 / Revised version: 22 October 1999 / Accepted: 6 December 1999     

Golvesin-GFP fusions as distinct markers for Golgi and post-Golgi vesicles in Dictyostelium cells

Golvesin is a new protein associated with membranes of the Golgi apparatus and post-Golgi vesicles in Dictyostelium cells. An internal hydrophobic sequence of 24 amino-acid residues is responsible for anchoring golvesin to the membranes of these organelles. In an attempt to visualize organelle dynamics in vivo, we have used specific antibody and other labels to localize golvesin-green fluorescent protein (GFP) constructs to different cellular compartments. With a GFP tag at its N-terminus, golvesin shows the same localization as the untagged protein. It is transferred to two post-Golgi compartments, the endosomal and contractile vacuole systems. Endosomes are decorated with GFP-golvesin within less than 10 min of their internalisation, and keep the label during the acidic phase of the pathway. Blockage of the C-terminus with GFP causes entrapment of the protein in the Golgi apparatus, indicating that a free C-terminus is required for transfer of golvesin to any of the post-Golgi compartments. The C-terminally tagged golvesin proved to be a reliable Golgi marker in Dictyostelium cells revealing protrusion of Golgi tubules at peak velocities of 3 to 4 microm x s(-1). The fusion protein is retained in Golgi vesicles during mitosis, visualizing Golgi disassembly and reorganization in line with cytokinesis.     

The cisproline(i - 1)-aromatic(i) interaction: folding of the Ala-cisPro-Tyr peptide characterized by NMR and theoretical approaches

Cisproline(i - 1)-aromatic(i) interactions have been detected in several short peptides in aqueous solution by analysis of anomalous chemical shifts measured by 1H-NMR spectroscopy. This formation of local structure is of importance for protein folding and binding properties. To obtain an atomic-detail characterisation of the cisproline(i - 1)-aromatic(i) interaction in terms of structure, energetics and dynamics, we studied the minimal peptide unit, blocked Ala-cisPro-Tyr, using computational and experimental techniques. Structural database analyses and a systematic search revealed two groups of conformations displaying a cisproline(i - 1)-aromatic(i) interaction. These conformations were taken as seeds for molecular dynamics simulations in explicit solvent at 278 K. During a total of 33.6 ns of simulation, all the 'folded' conformations and some 'unfolded' states were sampled. 1H- and 13C-chemical shifts and 3J-coupling constants were measured for the Ala-Pro-Tyr peptide. Excellent agreement was found between all the measured and computed NMR properties, showing the good quality of the force field. We find that under the experimental and simulation conditions, the Ala-cisPro-Tyr peptide is folded 90% of the time and displays two types of folded conformation which we denote 'a' and 'b'. The type a conformations are twice as populated as the type b conformations. The former have the tyrosine ring interacting with the alanine alpha proton and are enthalpically stabilised. The latter have the aromatic ring interacting with the proline side chain and are entropically stabilised. The combined and complementary use of computational and experimental techniques permitted derivation of a detailed scenario of the 'folding' of this peptide.     

Deuterium isotope effects on the central carbon metabolism of Escherichia coli cells grown on a D2O-containing minimal medium

In this paper it is demonstrated that cross-correlated time modulation of isotropic chemical shifts (`conformational exchange') leads to differential relaxation of double- and zero-quantum coherences, respectively. Quantitative information can be obtained from the time dependence of the interconversion between the two two-spin coherences 2I_xS_x and 2I_yS_y, induced by the differential relaxation. The effect is illustrated with an application to ¹³C,¹⁵N-labeled quail CRP2(LIM2), by studying ¹⁵N-¹H^N multiple-quantum relaxation. Significant cross-correlated fluctuations of isotropic chemical shifts were observed for residues which are part of a disordered loop region connecting two -strands in CRP2(LIM2). Differential ¹H^N and ¹⁵N exchange contributions to multiple-quantum relaxation observed at these sites illustrate the complex interplay between hydrogen bonding events and conformational reorientations in proteins.     

Backbone dynamics of free barnase and its complex with barstar determined by 15N NMR relaxation study

Backbone dynamics of uniformly ¹⁵N-labeled free barnase and its complex with unlabelled barstar have been studied at 40°C, pH 6.6, using ¹⁵N relaxation data obtained from proton-detected 2D {¹H}-¹⁵N NMR spectroscopy. ¹⁵N spin-lattice relaxation rate constants (R₁), spin-spin relaxation rate constants (R₂), and steady-state heteronuclear {¹H}-¹⁵N NOEs have been measured at a magnetic field strength of 14.1 Tesla for 91 residues of free barnase and for 90 residues out of a total of 106 in the complex (excluding three prolines and the N-terminal residue) backbone amide ¹⁵N sites of barnase. The primary relaxation data for both the cases have been analyzed in the framework of the model-free formalism using both isotropic and axially symmetric models of the rotational diffusion tensor. As per the latter, the overall rotational correlation times (_m) are 5.0 and 9.5 ns for the free and complexed barnase, respectively. The average order parameter is found to be 0.80 for free barnase and 0.86 for the complex. However, the changes are not uniform along the backbone and for about 5 residues near the binding interface there is actually a significant decrease in the order parameters on complex formation. These residues are not involved in the actual binding. For the residues where the order parameter increases, the magnitudes vary significantly. It is observed that the complex has much less internal mobility, compared to free barnase. From the changes in the order parameters, the entropic contribution of NH bond vector motion to the free energy of complex formation has been calculated. It is apparent that these motions cause significant unfavorable contributions and therefore must be compensated by many other favorable contributions to effect tight complex formation. The observed variations in the motion and their different locations with regard to the binding interface may have important implications for remote effects and regulation of the enzyme action.     

Conformational analysis of the Sda determinant-containing tetrasaccharide and two mimics in aqueous solution by using 1H NMR ROESY spectroscopy in combination with MD simulations

The conformational behaviour of the spacer-linked synthetic Sd^a tetrasaccharide -d-GalpNAc-(14)-[-Neu5Ac-(23)]--d-Galp-(14)--d-GlcpNAc-(1O)(CH₂)₅NH₂ (1) and the two mimics -d-Galp-(14)-[-Neu5Ac-(23)]--d-Galp-(14)--d-GlcpNAc-(1O)(CH₂)₅NH₂ (2) and -d-GlcpNAc-(14)-[-Neu5Ac-(23)]--d-Galp-(14)--d-GlcpNAc-(1O)(CH₂)₅NH₂ (3) were investigated by ¹H NMR spectroscopy in combination with molecular dynamics (MD) simulations in water. Experimental 2D ¹H ROESY cross-peak intensities (ROEs) of the tetrasaccharides were compared with calculated ROEs derived from MD trajectories using the CROSREL program. Analysis of these data indicated that the oligosaccharidic skeletons of the compounds 1–3 are rather rigid, especially the -d-Hex(NAc)-(14)-[-Neu5Ac-(23)]--d-Galp fragments. The - Neu5-Ac-(23)--d-Galp linkage occurred in two different energy minima in the three-dimensional structure of the compounds 1–3 in aqueous solution. Experimental data and dynamics simulations supported the finding that the higher energy rotamer (CHEAT forcefield) was abundant in compounds 1 and 3 due to the existence of a hydrogen bond between the carboxyl group of the sialic acid and the acetamido group of the terminal monosaccharide (GalNAc or GlcNAc) unit. The conformational similarity between 1 and 3 leads to the suggestion that also their activities will be alike.