Solution structure of the cytotoxic RNase 4 from oocytes of bullfrog Rana catesbeiana

Cytotoxic ribonucleases with antitumor activity are mainly found in the oocytes and early embryos of frogs. Native RC-RNase 4 (RNase 4), consisting of 106 residues linked with four disulfide bridges, is a cytotoxic ribonuclease isolated from oocytes of bullfrog Rana catesbeiana. RNase 4 belongs to the bovine pancreatic ribonuclease (RNase A) superfamily. Recombinant RC-RNase 4 (rRNase 4), which contains an additional Met residue and glutamine instead of pyroglutamate at the N terminus, was found to possess less catalytic and cytotoxic activities than RNase 4. Equilibrium thermal and guanidine-HCl denaturation CD measurements revealed that RNase 4 is more thermally and chemically stable than rRNase 4. However, CD and NMR data showed that there is no gross conformational change between native and recombinant RNase 4. The NMR solution structure of rRNase 4 was determined to comprise three alpha-helices and two sets of antiparallel beta-sheets. Superimposition of each structure with the mean structure yielded an average root mean square deviation (RMSD) of 0.72(+/-0.14)A for the backbone atoms, and 1.42(+/-0.19)A for the heavy atoms in residues 3-105. A comparison of the 3D structure of rRNase 4 with the structurally and functionally related cytotoxic ribonuclease, onconase (ONC), showed that the two H-bonds in the N-terminal pyroglutamate of ONC were not present at the corresponding glutamine residue of rRNase 4. We suggest that the loss of these two H-bonds is one of the key factors responsible for the reductions of the conformational stability, catalytic and cytotoxic activities in rRNase 4. Furthermore, the differences of side-chain conformations of subsite residues among RNase A, ONC and rRNase 4 are related to their distinct catalytic activities and base preferences.     

T.T pair intercalation and duplex interconversion within i-motif tetramers

The i-motif is a four-stranded structure built by intercalation in head-to-tail orientation of two parallel duplexes associated by hemi-protonated C.C(+) pairs. Using NMR methods, we investigated the structure, the base-pair opening kinetics and the internal motions of three i-motif tetramers: [d(5mCCTCnTCC)](4) (n=1, 2, 3). These tetramers cannot accommodate the intercalation of two T.T pairs in face-to-face orientation. They are built by intercalation of two symmetrical duplexes whose contacting T3/TM thymidine bases (M=5, 6, 7) are either base-paired or unstacked. The arrangement of the unstacked/paired thymidine bases of the two T/T groups results in the formation of two different conformations. One, fully symmetric, whose thymidine bases T3 and TM are unstacked and base-paired respectively. The other is the asymmetric assembly of two duplexes: one where both thymidine bases are unstacked and the other with two T.T pairs. The proportion of the symmetric conformer increases from a value beyond the detection threshold for n=1, to 19% for n=2 and up to more than 95% for n=3. The exchange cross-peaks connecting together the intercalated duplexes of [d(5mCCTCTCC)](4) and [d(5mCCTCCTCC)](4) reveal a structural interconversion induced by the simultaneous opening/closing of the contacting T3/TM thymidine bases. In [d(5mCCTCCTCC)](4) the motion of the T3/T6 groups triggers the interconversion of the symmetric and asymmetric conformations. In [d(5mCCTCTCC)](4) the intercalated duplexes exchange their structures in an apparently concerted motion, suggesting the simultaneous opening/closing of two distant T3/T5* and T5/T3* switching groups. The spectrum of [d(5mCCTCCCTCC)](4) is fully symmetric and, for this reason, its spectrum gives no indication for duplex interconversion. Nevertheless, the imino proton exchange kinetics argues for a switching motion of the T3/T7 group. Duplex interconversion is not detectable in that case, due to the tetramer symmetry. The origin of the structural conflict hindering the intercalation of two T.T pairs into the i-motif is discussed.     

Oscillations in cyclical neutropenia: new evidence based on mathematical modeling

We present a dynamical model of the production and regulation of circulating blood neutrophil number. This model is derived from physiologically relevant features of the hematopoietic system, and is analysed using both analytic and numerical methods. Supercritical Hopf bifurcations and saddle-node bifurcations of limit cycles are shown to exist. We make the estimation of kinetic parameters for dogs and then apply the model to cyclical neutropenia (CN) in the grey collie, a rare disorder in which oscillations in all blood cell counts are found. We conclude that the major cause of the oscillations in CN is an increased rate of apoptosis of neutrophil precursors which leads to a destabilization of the hematopoietic stem cell compartment.     

An exactly solvable model of population dynamics with density-dependent migrations and the Allee effect

We consider a single-species model of population dynamics allowing for migrations and the Allee effect. Two types of migration are taken into account: one caused by environmental factors (e.g., a passive transport with the wind or water current) and the other associated with biological mechanisms. While the first type is apparently density-independent, the speed of migration in the second one can depend on the population density. Mathematically, this model consists of a non-linear partial differential equation of advection-diffusion-reaction type. Using an appropriate change of variables, we obtain an exact solution of the equation describing propagation of travelling population fronts. We show that, depending on parameter values and thus on the relative intensity of density-dependent and density-independent factors, the direction of the propagation can be different thus describing either species invasion or species retreat.     

Mathematical analysis of a model describing evolution of an asexual population in a changing environment

We investigate a mathematical model for an asexual population with non-overlapping (discrete) generations, that exists in a changing environment. Sexual populations are also briefly discussed at the end of the paper. It is assumed that selection occurs on the value of a single polygenic trait, which is controlled by a finite number of loci with discrete-effect alleles. The environmental change results in a moving fitness optimum, causing the trait to be subject to a combination of stabilising and directional selection.This model is different from that investigated by Waxman and Peck [Genetics 153 (1999) 1041] where overlapping generations and continuous effect alleles were considered. In this paper, we consider non-overlapping generations and discrete effect alleles. However in [Genetics 153 (1999) 1041] and the present work, there is the same pattern of environmental change, namely a constant rate of change of the optimum.From [Genetics 153 (1999) 1041], no rigorous theoretical conclusion can be drawn about the form of the solutions as t grows large. Numerical work carried out in [Genetics 153 (1999) 1041] suggests that the solution is a lagged travelling wave solution, but no mathematical proof exists for the continuous model. Only partial results, regarding existence of travelling wave solutions and perturbed solutions, have been established (see [Nonlin. Anal. 53 (2003) 683; An integral equation describing an asexual population in a changing environment, Preprint]). For the discrete case of this paper, under the assumption that the ratio between the unit of genotypic value and the speed of environment change is a rational number, we are able to give rigorous proof of the following conclusion: the population follows the environmental change with a small lag behind, moreover, the lag is represented using a calculable quantity.     

Periodic coexistence of four species competing for three essential resources

We show the existence of a periodic solution in which four species coexist in competition for three essential resources in the standard model of resource competition. By assuming that species i is limited by resource i for each i near the positive equilibrium, and that the matrix of contents of resources in species is a combination of cyclic matrix and a symmetric matrix, we obtain an asymptotically stable periodic solution of three species on three resources via Hopf bifurcation. A simple bifurcation argument is then employed which allows us to add a fourth species. In principle, the argument can be continued to obtain a periodic solution adding one new species at a time so long as asymptotic stability can be assured at each step. Numerical simulations are provided to illustrate our analytical results. The results of this paper suggest that competition can generate coexistence of species in the form of periodic cycles, and that the number of coexisting species can exceed the number of resources in a constant and homogeneous environment.     

Conformational preferences of the amylin nucleation site in SDS micelles: an NMR study

Human islet amyloid polypeptide (hIAPP), or amylin, is a 37 amino acid hormone secreted by pancreatic beta-cells. hIAPP constitutes approximately 90% of the amyloid deposits found in type II diabetic patients. It has been shown that the central region of the peptide (hIAPP(20-29)) constitutes the nucleation site for the amyloidogenic process with F23 playing a key role in the formation of the beta-pleated structures. In addition, it has been proposed that an important stage in the cytotoxicity of hIAPP is its interaction with the beta-cell membranes. As a first step toward the characterization of the interaction of hIAPP with cell membranes, we determined conformational preferences of hIAPP(20-29) in membrane-mimicking environments. We found that upon interacting with negatively charged micelles, the dominant conformation of hIAPP(20-29) is a distorted type I beta-turn centered on residues F23 and G24, with F23, A25, and I26 forming a small hydrophobic cluster that may facilitate the interaction of this peptide with the membrane bilayer. Moreover, we were able to elucidate the topological orientation of the peptide that is absorbed on the micelle surface, with the hydrophobic cluster oriented toward the hydrocarbon region of the micelles and both N- and C-termini exposed to the solvent.     

Conformational analysis of endomorphin-2 by molecular dynamics methods

Endomorphin-2 (EM2, H-Tyr-Pro-Phe-Phe-NH(2)) is a highly potent and selective mu-opioid receptor agonist. A conformational analysis of EM2 was carried out by simulated annealing (SA) and molecular dynamics (MD) methods. Molecular modeling was conducted on both neutral (N-terminal NH(2)) and charged (N-terminal NH(3) (+)) molecules. Based on the results of NMR investigations showing an equilibrium mixture of cis and trans Tyr(1)-Pro(2) peptide bonds for EM2 in solution, simulations were performed with restrained cis-Pro and trans-Pro peptide bonds, too. A separate SA study with unrestrained Pro peptide bonds was also conducted. Preferred conformational states are presented in Ramachandran plots. The g(+), g(-), and trans populations of the aromatic amino acid residue side chains were determined in chi(1) space. The distances between the N-terminal N atom and the other backbone N and O atoms, and the distances between the centers of the aromatic rings and the Pro(2) ring, were determined. The energy distribution of the structures obtained by SA was calculated. The preferred secondary structural elements were different kinds of beta-turns, an inverse gamma-turn located in the N-terminal region, and regular and inverse gamma-turns located in the C-terminal region. These turns were stabilized by intramolecular H-bonds and bifurcated H-bonds.