Perspectives on the reaction force constant

A synchronous, concerted chemical process is rigorously divided by the reaction force F(R), the negative gradient of V(R), into “reactant” and “product” regions which are dominated by structural changes and an intervening “transition” region which is electronically intensive. The reaction force constant κ(R), the second derivative of V(R), is negative throughout the transition region, not just at the nominal transition state, at which κ(R) has a minimum. This is consistent with experimental evidence that there is a transition region, not simply a specific point. We show graphically that significant nonsynchronicity in the process is associated with the development of a maximum of κ(R) in the transition region, which increases as the process becomes more nonsynchronous. (We speculate that for a nonconcerted process this maximum is actually positive.) Thus, κ(R) can serve as an indicator of the level of nonsynchronicity.

Measurement of the chlorophyll fluorescence induction kinetics with a 10 µs time resolution and its application in the forest decline research

Summary Measurement methods are described which determine the initial phase of the fluorescence induction kinetics with a maximum time resolution of 10 µs simultaneously for the two fluorescence componentsF ₆₈₅(t) andF ₁₃₀(t) selected by filters at the wavelengths 685 nm and 730 nm, respectively. The excitation light provided by a He-Ne laser (632.8 nm) is switched on within 0.3 µs (maximum intensityI _e=12 mW/cm²).F _o,F _p, andF _s, the initial-, peak-, and steady-state intensity and the initial valueR _o of the ratioR(t)=F ₇₃₀(t)/F ₆₈₅(t) can accurately be determined as well as the initial time derivativeF _o ^* of the fluorescence intensity.F _o andF _o ^* are related to the quantum yield _a of the antenna and to the photochemical quantum yield _pc, respectively. Spruce, oak, birch, poplar, and soy bean show a decline ofR(t) fromR _o to a first minimumR _b at some 10 ms which has a similar value as the second minimumR _p in the time range of seconds. Furthermore, the initial valueR _o and the steady-state valueR _S ofR(t) are also very similar. Measurements on spruce with water deficiency and with varying excitation light intensityI _e show effects on the initial phase of the fluorescence induction kinetics. Further measurements on spruce of different damage classes indicate that for the current year's needles the ratioF _p/F_o, is the most sensitive parameter to differentiate between the damage classes and thatF _o/F_s andR _o/R_b are also affected. As demonstrated by measurements on leaves of soy beans, the initial decrease ofR(t) fromR _o toR _b originates from a change of the fluorescence spectrum because no change of the leaf transmission can be observed in the time range between 10 µs and 1 ms.     

Chemotactic collapse for the Keller-Segel model

 This work is concerned with the system (S) {u _t =Δu − χ∇ (u∇v) for x∈Ω, t>0Γ v _t =Δv+(u−1) for x∈Ω, t>0 where Γ, χ are positive constants and Ω is a bounded and smooth open set in ℝ². On the boundary ∂Ω, we impose no-flux conditions: (N) ∂u∂n =∂v∂n =0 for x∈∂ Ω, t>0 Problem (S), (N) is a classical model to describe chemotaxis corresponding to a species of concentration u(x, t) which tends to aggregate towards high concentrations of a chemical that the species releases. When completed with suitable initial values at t=0 for u(x, t), v(x, t), the problem under consideration is known to be well posed, locally in time. By means of matched asymptotic expansions techniques, we show here that there exist radial solutions exhibiting chemotactic collapse. By this we mean that u(r, t) →Aδ(y) as t→T for some T<∞, where A is the total concentration of the species. Received 9 March 1995; received in revised form 25 December 1995     

Determination of <Superscript>13</Superscript>C CSA Tensors: Extension of the Model-independent Approach to an RNA Kissing Complex Undergoing Anisotropic Rotational Diffusion in Solution

Chemical shift anisotropy (CSA) tensor parameters have been determined for the protonated carbons of the purine bases in an RNA kissing complex in solution by extending the model-independent approach [Fushman, D., Cowburn, D. (1998) J. Am. Chem. Soc. 120, 7109–7110]. A strategy for determining CSA tensor parameters of heteronuclei in isolated X–H two-spin systems (X = ¹³C or ¹⁵N) in molecules undergoing anisotropic rotational diffusion is presented. The original method relies on the fact that the ratio κ₂=R₂^auto/R₂^cross of the transverse auto- and cross-correlated relaxation rates involving the X CSA and the X–H dipolar interaction is independent of parameters related to molecular motion, provided rotational diffusion is isotropic. However, if the overall motion is anisotropic κ₂ depends on the anisotropy D_||/D_⊥ of rotational diffusion. In this paper, the field dependence of both κ₂ and its longitudinal counterpart κ₁=R₁^auto/R₁^cross are determined. For anisotropic rotational diffusion, our calculations show that the average κ_av = 1/2 (κ₁+κ₂), of the ratios is largely independent of the anisotropy parameter D_||/D_⊥. The field dependence of the average ratio κ_av may thus be utilized to determine CSA tensor parameters by a generalized model-independent approach in the case of molecules with an overall motion described by an axially symmetric rotational diffusion tensor.     

A spectroscopic model for the high pH form of sulfite oxidase

The syntheses and spectroscopic properties of two monomeric oxo-Mo(V) complexes [NMe₄][MoO(SC₆H₄---CH=N---C₆H₄O)(SAr)₂] (Ar=Ph (2a), PhCH₃ (2b)) exhibiting a novel S₃NO coordination site are described. The EPR parameters of the Mo(V) complexes are almost identical with the parameters for the high pH form of sulfite oxidase, allowing further predictions for the unknown coordination site of the molybdenum cofactor in such molybdenum-containing enzymes. The Mo(V) compounds react with water to form a μ-oxo-bridged Mo(V) dimer, which is readily oxidized by oxygen to give the monomeric dioxo-Mo(VI) complex MoO₂(SC₆H₄---CH=N---C₆H₄O)(sol) (4) (sol=acetonitrile; dimethyl sulfoxide (DMSO)). The structure of 4 has been determined by X-ray crystallography (space group P (No. 2), a=7.855(4), b=9.530(3), c=11.676(6) Å, α=103.96(3), β=99.03(3), γ=100.73(3)°, V=814.5 ų, ρ_calc=1.79 g cm⁻³, Z=2, R(F)=0.026, R(wF)=0.026). The geometry about the molybdenum is distorted octahedral, with two terminal oxo groups cis to each other.     

Crystal structure,DNA binding studies,nucleolytic property and topoisomerase I inhibition of zinc complex with 1,10-phenanthroline and 3-methyl-picolinic acid

Crystal structure analysis of the zinc complex establishes it as a distorted octahedral complex, bis(3-methylpicolinato-κ² N,O)₂(1,10-phenanthroline-κ² N,N)-zinc(II) pentahydrate, [Zn(3-Me-pic)₂(phen)]·5H₂O. The trans-configuration of carbonyl oxygen atoms of the carboxylate moieties and orientation of the two planar picolinate ligands above and before the phen ligand plane seems to confer DNA sequence recognition to the complex. It cannot cleave DNA under hydrolytic condition but can slightly be activated by hydrogen peroxide or sodium ascorbate. Circular Dichroism and Fluorescence spectroscopic analysis of its interaction with various duplex polynucleotides reveals its binding mode as mainly intercalation. It shows distinct DNA sequence binding selectivity and the order of decreasing selectivity is ATAT > AATT > CGCG. Docking studies lead to the same conclusion on this sequence selectivity. It binds strongly with G-quadruplex with human tolemeric sequence 5′-AG₃(T₂AG₃)₃-3′, can inhibit topoisomerase I efficiently and is cytotoxic against MCF-7 cell line.     

The influence of ultraviolet-B radiation on the growth, pigment production and chlorophyll fluorescence of Norway spruce seedlings

Norway spruce (Picea abies (L.)Karst.) from seven seed sources was grown in a greenhouse with 8.3 and 14.7 kJ·m⁻²·d⁻¹ m UV-B_BE (biologically effective UV-B: 280–320 nm) irradiation, and with no supplemental irradiation as control. The seedlings total biomass (dry weight) and shoot growth decreased with high UV-B treatment but spruce from low elevation seed sources were more affected. The seedlings grown at the highest UV-B irradiance (14.7 kJ·m⁻²·d⁻¹) showed from 5 to 38% inhibition of total biomass and 15 to 70 % shoot growth inhibition. Norway spruce populations from higher altitude seed sources manifested greater tolerance to UV-B radiation compared to plants from low altitudes. Changes in phospholipids and protective pigments were also determined. The plants grown at the lower UV-B irradiance (8.3 kJ·m⁻²·d⁻¹) showed greater ability to concentrations UV-B-absorbing pigments then control plants. Chlorophyll a fluorescence parameter R_fd, (R_fd=(F_m-F_s)/F_s) showed a significant decrease in needles of UV-B treated plants and this correlated with the altitude of seed source. Exposure to UV-B affect levels of the ratio of variable to maximum fluorescence (F_v/F_m). Results from this study suggest that the response to increased levels of UV-B radiation is depended upon the ecotypic differentiation of Norway spruce and involved changes in metabolites in plant tissues.     

Synthesis and biological evaluation of tricarbonyl Re(I) and Tc(I) complexes anchored by poly(azolyl)borates: application on the design of radiopharmaceuticals for the targeting of 5-HT<Subscript>1A</Subscript> receptors

The building blocks fac-[^99mTc{κ³-HB(tim^Me)₃}(CO)₃] and fac-[^99mTc{κ³-R(μ-H)B(tim^Me)₂}(CO)₃] [R is H (4a), Ph (5a); tim^Me is 2-mercapto-1-methylimidazolyl] were obtained almost quantitatively by reacting fac-[^99mTc(CO)₃(H₂O)₃]⁺ with the corresponding scorpionate. These compounds cross the intact blood–brain barrier in mice, with significant retention in the case of 4a and 5a. Using 4a as the lead structure, we have synthesized the functionalized complexes fac-[M{κ³-H(μ-H)B(tim^Bu-pip)₂}(CO)₃] [M is Re (8), ^99mTc (8a); tim^Bu-pip is methyl[4-((2-methoxyphenyl)-1-piperazinyl)butyl](2-mercapto-1-methylimidazol-5-yl)methanamide] and fac-[M{κ ³-H(μ-H)B(tim^Me)(tim^Bu-pip)}(CO)₃] [M is Re (9), ^99mTc (9a)] and evaluated their potential as radioactive probes for the targeting of brain 5-HT_1A serotonergic receptors. The Re complexes exhibit excellent affinity [IC₅₀=0.172 ± 0.003 nM (8); IC₅₀=0.65 ± 0.01 nM (9)] for the 5-HT_1A receptor. The radioactive congeners (^99mTc) have shown an initial brain uptake of 1.38 ± 0.46%ID g⁻¹ (8a) and 0.43 ± 0.12%ID g⁻¹ (9a), but suffer from a relatively fast washout.     

Driving and retarding forces in a chemical reaction

The reaction force F(ξ) is the negative gradient of the potential energy of a chemical process along the intrinsic reaction coordinate ξ. We extend the rigorous concept of F(ξ) to the “activation strain model” of Bickelhaupt et al., to formulate the “strain” force F _str(ξ) that retards a reaction and the “interaction” force F _int(ξ) that drives it. These are investigated for a group of Diels-Alder cycloadditions. The results fully support the interpretation of the minimum of F(ξ) as defining the beginning of the transition from deformed reactants to eventual products.     

A hexanuclear iridium complex with a novel binding mode of a PCP-pincer ligand

The hexanuclear iridium complex [η⁴-(COD)Ir]₂{η⁶-[κ⁴-C₆H₂(CH₂P^tBu₂)₂]Ir₂H₂Cl₃} (1) has been prepared by the reaction of [Ir(COD)Cl]₂ with the “PCP” ligand precursor, 1,3-C₆H₄(CH₂P^tBu₂)₂ (PCP-H). Characterization by X-ray diffraction reveals that complex 1 has an unusual structure in which metalation (C-H addition) of the ligand has occurred at the 4- and 6-positions of the PCP aryl ring. This is in contrast to the widespread reactivity of this ligand precursor in which a single metalation typically occurs at the 2-position, thereby allowing coordination of both phosphino groups to a single metal center to give the κ³-meridional pincer coordination. The complex can be viewed as being composed of a dimer of two bis-metalated (Ir(III)) PCP units, held together by two bridges of three chlorides each; the aryl ring of each of the PCP ligands of this hypothetical tetra-iridium dianion is then bound to a cationic [Ir(I)(COD)]⁺ unit.The structure discussed here crystallizes as the tetra(acetone) solvate in the monoclinic space group P2₁/n with lattice parameters a=14.4154(11) Å, b=15.4435(12) Å, c=19.5181(15) Å, b=99.996(1)° and V=4279.31(6) ų. Convergence to conventional R values of R(F)=0.041 and R_w(F)=0.092 was obtained for 445 variable parameters and 8085 reflections with F>4σ(F). Complex 1 also crystallizes as the octabenzene solvate in the orthorhombic space group Pbca, with lattice parameters a=16.4247(14) Å, b=24.1695(21) Å, c=28.0460(24) Å and V=11134(1) ų. Convergence of the orthorhombic phase to R(F)=0.038 and R_w(F)=0.084 was obtained for 595 variable parameters and 12 885 reflections with F>4σ(F).     

Kinetics and mechanism for reduction of anticancer-active tetrachloroam(m)ine platinum(IV) compounds by glutathione

trans -[PtCl₄(NH₃)(thiazole)] (1), trans-[PtCl₄(cha)(NH₃)] (2), cis-[PtCl₄(cha)(NH₃)] (3) (cha =cyclohexylamine), and cis-[PtCl₄(NH₃)₂] (4) has been investigatedat 25 °C in a 1.0 M aqueous medium at pH 2.0–5.0 (1) and 4.5–6.8 (2–4) using stopped-flow spectrophotometry. The redox reactions follow the second-order rate law , where k is a pH-dependent rate constant and [GSH]_tot the total concentration of glutathione. The reduction takes place via parallel reactions between the platinum(IV) complexes and the various protolytic species of glutathione. The pH dependence of the redox kinetics is ascribed to displacement of these protolytic equilibria. The thiolate species GS⁻ is the major reductant under the reaction conditions used. The second-order rate constants for reduction of compounds 1–4 by GS⁻ are (1.43±0.01)×10⁷, (3.86±0.03)×10⁶, (1.83±0.01)×10⁶, and (1.18±0.01)×10⁶M⁻¹s⁻¹, respectively. Rate constants for reduction of 1 by the protonated species GSH are more than five orders of magnitude smaller. The mechanism for the reductive elimination reactions of the Pt(IV) compounds is proposed to involve an attack by glutathione on one of the mutually trans coordinated chloride ligands, leading to two-electron transfer via a chloride-bridged activated complex. The kinetics results together with literature data indicate that platinum(IV) complexes with a trans Cl-Pt-Cl axis are reduced rapidly by glutathione as well as by ascorbate. In agreement with this observation, cytotoxicity profiles for such complexes are very similar to those for the corresponding platinum(II) product complexes. The rapid reduction within 1 s of the platinum(IV) compounds with a trans Cl-Pt-Cl axis to their platinum(II) analogs does not seem to support the strategy of using kinetic inertness as a parameter to increase anticancer activity, at least for this class of compounds. Received: 8 December 1999 / Accepted: 15 February 2000     

Applications of the ETS-NOCV method in descriptions of chemical reactions

The present study characterizes changes in the electronic structure of reactants during chemical reactions based on the combined charge and energy decomposition scheme, ETS-NOCV (extended transition state–natural orbitals for chemical valence). Decomposition of the activation barrier, ΔE ^#, into stabilizing (orbital interaction, ΔE _orb, and electrostatic, ΔE _elstat) and destabilizing (Pauli repulsion, ΔE _Pauli, and geometry distortion energy, ΔE _dist) factors is discussed in detail for the following reactions: (I) hydrogen cyanide to hydrogen isocyanide, HCN → CNH isomerization; (II) Diels-Alder cycloaddition of ethene to 1,3-butadiene; and two catalytic processes, i.e., (III) insertion of ethylene into the metal-alkyl bond using half-titanocene with phenyl-phenoxy ligand catalyst; and (IV) B–H bond activation catalyzed by an Ir-containing catalyst. Various reference states for fragments were applied in ETS-NOCV analysis. We found that NOCV-based deformation densities (Δρ _i) and the corresponding energies ΔE _orb(i) obtained from the ETS-NOCV scheme provide a very useful picture, both qualitatively and quantitatively, of electronic density reorganization along the considered reaction pathways. Decomposition of the barrier ΔE^# into stabilizing and destabilizing contributions allowed us to conclude that the main factor responsible for the existence of positive values of ΔE ^# for all processes (I, II, III and IV) is Pauli interaction, which is the origin of steric repulsion. In addition, in the case of reactions II, III and IV, a significant degree of structural deformation of the reactants, as measured by the geometry distortion energy, plays an important role. Depending on the reaction type, stabilization of the transition state (relatively to the reactants) originating either from the orbital interaction term or from electrostatic attraction can be of vital importance. Finally, use of the ETS-NOCV method to describe catalytic reactions allows extraction of information on the role of catalysts in determination of ΔE ^#.     

Bounds on the total particle number for species governed by reaction-diffusion equations in the infinite spatial domain

Differential inequality methods are developed for establishing upper and lower bounds on the total particle numberN(t)=∫θ(x,t) d³ x associated with solutions to nonlinear reaction-diffusion equations of the form ∂θ/∂t=D∇²θ+fθ-gθ ⁿ⁺¹ , whereD(>0),n(>0),f andg are constant parameters. If finite in a neighborhood oft=0,N(t) is bounded below for allt≥0 by a certain derived function oft for equations withg≥0. An upper bound onN(t) is obtained for equations withn=1,f<0 andg<0. These results provide general preservation and extinction criteria for the total particle number.     

A New Functional Equation Analogous to CAUCHT-PEXIDER Functional Equation and its Application

The CAUCHY-PEXIDER functional equation H (x±y)=F(x) G(y) is generalized to the form H ((x^c±y^c)^1/c) = F(x) G(y), c≠0, assuming the function H(x) possesses a measurable majorant on a set of positive measure. The result is used to obtain a characterization of WEIBULL distribution. This functional equation is generalized to functions of vector variables.     

A new bisphosphonate-containing <Superscript>99m</Superscript>Tc(I) tricarbonyl complex potentially useful as bone-seeking agent: synthesis and biological evaluation

Aiming to develop new bone-seeking radiotracers based on the organometallic core fac-[^99mTc(CO)₃]⁺ with improved radiochemical and biological properties, we have prepared new conjugates with phosphonate pendant groups. The conjugates comprise a chelating unit for metal coordination, which corresponds to a pyrazolyl-containing backbone (pz) with a N,N,N donor-atom set, and a pendant diethyl phosphonate (pz-MPOEt), phosphonic acid (pz-MPOH) or a bisphosphonic acid (pz-BPOH) group for bone targeting. Reactions of the conjugates with the precursor [^99mTc(H₂O)₃(CO)₃]⁺ yielded (mote than 95%) the single and well-defined radioactive species [^99mTc(CO)₃(κ³-pz-MPOEt)]⁺ (1a), [^99mTc(CO)₃(κ³-pz-MPOH]⁺ (2a) and [^99mTc(CO)₃(κ³-pz-BPOH)]⁺ (3a), which were characterized by reversed-phase high-performance liquid chromatography . The corresponding Re surrogates (1–3), characterized by the usual analytical techniques, including X-ray diffraction analysis in the case of 1, allowed for macroscopic identification of the radioactive conjugates. These radioactive complexes revealed high stability both in vitro (phosphate-buffered saline solution and human plasma) and in vivo, without any measurable decomposition. Biodistribution studies of the complexes in mice indicated a fast rate of blood clearance and high rate of total radioactivity excretion, occurring primarily through the renal–urinary pathway in the case of complex 3a. Despite presenting moderate bone uptake (3.04 ± 0.47% injected dose per gram of organ, 4 h after injection), the high stability presented by 3a and its adequate in vivo pharmacokinetics encourages the search for new ligands with the same chelating unit and different bisphosphonic acid pendant arms.     

Kinetics and DFT studies on the reaction of copper(II) complexes and H2O2

Copper(II) complexes supported by bulky tridentate ligands L1^H (N,N-bis(2-quinolylmethyl)-2-phenylethylamine) and L1^Ph (N,N-bis(2-quinolylmethyl)-2,2-diphenylethylamine) have been prepared and their crystal structures as well as some physicochemical properties have been explored. Each complex exhibits a square pyramidal structure containing a coordinated solvent molecule at an equatorial position and a weakly coordinated counter anion (or water) at an axial position. The copper(II) complexes reacted readily with H₂O₂ at a low temperature to give mononuclear hydroperoxo copper(II) complexes. Kinetics and DFT studies have suggested that, in the initial stage of the reaction, deprotonated hydrogen peroxide attacks the cupric ion, presumably at the axial position, to give a hydroperoxo copper(II) complex retaining the coordinated solvent molecule (H ^R ·S). H ^R ·S then loses the solvent to give a tetragonal copper(II)-hydroperoxo complex (H ^R ), in which the –OOH group may occupy an equatorial position. The copper(II)–hydroperoxo complex H ^R exhibits a relatively high O–O bond stretching vibration at 900 cm⁻¹ compared to other previously reported examples.Electronic Supplementary Material Supplementary material is available for this article at     

A fitness function for optimal life history in relation to density effects,competition, predation and stability of the environment

A fitness function (function maximized under natural selection) is studied in a population model in which the growth of a population is suppressed by crowding, density-independent continuous mortality (by euryphagous predators) and periodic disturbances. The dynamics of the population density between occurrence of disturbance can be expressed as,dN/dt=(F(N/K)−D)N, whereN is the population density,K is the carrying capacity,D is the density-independent continuous mortality, andF is the growth regulation factor described as a function of crowding (N/K). The period of disturbance isS. The survival rate under disturbance isu. It is concluded that the fitness function is (approximately) a product of competitive ability (C), carrying capacity, and degree of saturation, and is given byCKF ⁻¹(D−(lnu)/S). The degree of saturation is the inverse function of regulation factor (F) at the death rate due to predators and disturbance. I assume a population in which density is regulated only through survival. In this case, a low survival rate at the critical age-group means a high value ofCKF ⁻¹(D−(lnu)/S). Therefore, the reciprocal of the density-dependent survival rate at critical age-group is a measure of the fitness function. Using this measure, I predict the optimal age (body size) at first reproduction of a species of salamander. I also found that fitness calculated from observed values ofl(x) andm(x) includes a tautology. When the concept of fitness function is compared with the ESS method, the latter is more flexible. However, there is a possibility that an ESS is at the minimum of fitness function.     

Heterologous expression of polyhydroxyalkanoate depolymerase from <Emphasis Type="Italic">Thermobifida</Emphasis> sp. in <Emphasis Type="Italic">Pichia pastoris</Emphasis> and catalytic analysis by surface plasmon resonance

A polyhydroxyalkanote depolymerase gene from Thermobifida sp. isolate BCC23166 was cloned and expressed as a C-terminal His₆-tagged fusion in Pichia pastoris. Primary structure analysis revealed that the enzyme PhaZ-Th is a member of a proposed new subgroup of SCL-PHA depolymerase containing a proline–serine repeat linker. PhaZ-Th was expressed as two glycosylated forms with apparent molecular weights of 61 and 70 kDa, respectively. The enzyme showed esterase activity toward p-nitrophenyl alkanotes with V _max and K _m of 3.63 ± 0.16 μmol min⁻¹ mg⁻¹ and 0.79 ± 0.12 mM, respectively, on p-nitrophenyl butyrate with optimal activity at 50–55°C and pH 7–8. Surface plasmon resonance (SPR) analysis demonstrated that PhaZ-Th catalyzed the degradation of poly-[(R)-3-hydroxybutyrate] (PHB) films, which was accelerated in (R)-3-hydroxyvalerate copolymers with a maximum degradation rate of 882 ng cm⁻² h⁻¹ for poly[(R)-3-hydroxybutyrate-co-3-hydroxyvalerate] (12 mol% V). Surface deterioration, especially on the amorphous regions of PHB films was observed after exposure to PhaZ-Th by atomic force microscopy. The use of P. pastoris as an alternative recombinant system for bioplastic degrading enzymes in secreted form and a sensitive SPR analytical technique will be of utility for further study of bioplastic degradation.     

Interaction of maturation delay and nonlinear birth in population and epidemic models

 A population with birth rate function B(N) N and linear death rate for the adult stage is assumed to have a maturation delay T>0. Thus the growth equation N′(t)=B(N(t−T)) N(t−T) e⁻ d ₁ T−dN(t) governs the adult population, with the death rate in previous life stages d ₁≧0. Standard assumptions are made on B(N) so that a unique equilibrium N _e exists. When B(N) N is not monotone, the delay T can qualitatively change the dynamics. For some fixed values of the parameters with d ₁>0, as T increases the equilibrium N _e can switch from being stable to unstable (with numerically observed periodic solutions) and then back to stable. When disease that does not cause death is introduced into the population, a threshold parameter R ₀ is identified. When R ₀<1, the disease dies out; when R ₀>1, the disease remains endemic, either tending to an equilibrium value or oscillating about this value. Numerical simulations indicate that oscillations can also be induced by disease related death in a model with maturation delay. Received: 2 November 1998 / Revised version: 26 February 1999