Parameter identification in epidemic models

Starting from a recent paper of Pollicott, Wang and Weiss we try to obtain improved representation formulas for the estimation of the time-dependent transmission rate of an epidemic in terms of either incidence or prevalence data. Although the formulas are (trivially) mathematically equivalent to previous formulas, the new representations need no additional estimates and they should be more stable numerically.We review the discrete time and the stochastic continuous time approach. We replace the assumption that recovery follows an exponential distribution and get estimates for the transmission rate for constant duration of the infectious phase.     

Linear n-compartment catenary models: Formulas to describe tracer amount in any compartment and identification of parameters from a concentration-time curve

Resolution of kinetic equations and parameter identification are discussed for n-compartment linear catenary models with elimination allowed from any compartment. For a given input, general formulas are derived to describe the tracer amount in any compartment as a function of the model parameters. Conversely, explicit procedures are given to identify the model parameters when the concentration-time curve is known in one arbitrary compartment, the tracer being injected into the same compartment. In this inverse problem, the solution is not unique: the model transfer rate constants can only be localized in a finite set of intervals.     

N,N-dimethylcarbamato complexes of zinc

By reaction of Zn₄O(O₂CNMe₂)₆ (1) with [NH₂Me₂][O₂CNMe₂] in toluene as medium, the homoleptic zinc compound [Zn(O₂CNMe₂)₂] (2) was obtained, which reverted back to the tetranuclear μ-oxo derivative by controlled hydrolysis. The reaction of ZnO in MeCN with an excess of [NH₂Me₂][O₂CNMe₂] in concentrated solution produced high yields of [Zn(O₂CNMe₂)₂] (2) or [NH₂Me₂][Zn₂(O₂CNMe₂)₅] · xMeCN, 3 · xMeCN, x = 1 or 2, depending on the experimental conditions.     

Parameter estimation in cardiac ionic models

We examine the problem of parameter estimation in mathematical models of excitable cell cardiac electrical activity using the well-known Beeler–Reuter (1977) ionic equations for the ventricular action potential. The estimation problem can be regarded as equivalent to the accurate reconstruction of ionic current kinetics and amplitudes in an excitable cell model, given only action potential experimental data. We show that in the Beeler–Reuter case, all ionic currents may be reasonably reconstructed using an experimental design consisting of action potential recordings perturbed by pseudo-random injection currents.

The Beeler–Reuter model was parameterised into 63 parameters completely defining all membrane current amplitudes and kinetics. Total membrane current was fitted to model-generated experimental data using a ‘data-clamp’ protocol. The experimental data consisted of a default action-potential waveform and an optional series of perturbed waveforms generated by current injections. Local parameter identifiability was ascertained from the reciprocal condition value (1/λ) of the Hessian at the known solution. When fitting to a single action potential waveform, the model was found to be over-determined, having a 1/λ value of 3.6e−14. This value improved slightly to 1.4e−10 when an additional 2 perturbed waveforms were included in the fitting process, suggesting that the additional data did not overly improve the identifiability problem. The additional data, however, did allow the accurate reconstruction of all ionic currents. This indicates that by appropriate experimental design, it may be possible to infer the properties of underlying membrane currents from observation of transmembrane potential waveforms perturbed by pseudo-random currents.     

N-Benzoylphenylalanine and N-Benzoylphenylalaninol,and their biosynthesis in Penicillin Brevicompactum

Penicillium brevicompactum; fungus; biosynthesis; N-benzoylphenylalanine; N-benzoylphenylalaninol     

Rotundifoline N-oxides

The N-oxides of rotundifoline are prepared for comparison with a new alkaloid from Mitragyna rubrostipulata.     

Nicotine N-oxides

Nicotine-1-N-oxide, trans and cis isomers of nicotine-1′-N-oxide and of nicotine-1,1′-di-N-oxide have been prepared and characterised by NMR, MS and reduction to nicotine. The trans and cis isomers of nicotine-1′-N-oxide have been identified in leaves, stems and roots of Nicotiana tabacum, N. affinis and N. sylvestris.     

Quantitative determination of N-arylaceto- and N-arylglycolhydroxamic acids in biochemical reaction mixtures

A high-performance liquid chromatography (hplc) solvent system was developed for use with C₁₈ bonded packings that effected the chromatographic resolution of monoaromatic hydroxamic acids in complex mixtures. The success of this hplc system resulted from the incorporation of an aliphatic hydroxamic acid additive into the elution solvent. This additive, desferal mesylate, suppressed chemisorption effects between the stationary phase of the chromatographic packing and the aromatic hydroxamic acids being analyzed. The detectability limit for acetyl-derived aromatic hydroxamic acids was about 10 ng, while that for glycolyl-derived aromatic hydroxamic acids was about 5 ng. This level of sensitivity was sufficiently low to allow for the direct detection of these components in enzymatic reaction mixutres. By manipulation of the percentage methanol in the aqueous solvent the resolution of either type of hydroxamic acid from other related metabolites was readily accomplished.     

Alkylation of isolated chromatin with N-methyl-N-nitrosourea and N-ethyl-N-nitrosourea

When isolated chromatin is incubated with the carcinogens N-methyl-N-nitrosourea (MeNU) and N-ethyl-N-nitrosourea (EtNU), DNA and chromosomal proteins become alkylated to increasingly greater extents as the carcinogen concentrations increase. With either MeNU or EtNU, the core and linker DNA of chromatin are alkylated to essentially identical extents. Alkylation of chromatin DNA as well as free DNA is drastically reduced at physiological ionic strengths (e.g. 0.15 M NaCl). The presence of 0.15 M NaCl, on the other hand, enhances alkylation of chromosomal proteins. While EtNU is much less reactive to DNA than MeNU, alkylation of chromosomal proteins relative to that of chromatin DNA has been found to be markedly greater with EtNU than with MeNU. Such a difference in their relative reactivities toward DNA and proteins may be related to the known difference of carcinogenic potency between these N-nitroso compounds.     

Parameter estimation in approximate enzyme kinetics models

Enzyme kinetic modeling is based on a very specific approximation to a more detailed model; this approximation is often called the Michaelis-Menten approximation. Its success lies not only in an initial concentration difference that is set experimentally, but also in a certain difference among kinetic rate constants. Other differences among these constants lead to additional model approximations, often much simpler than the Michaelis-Menten approximation. Under the conditions where these alternate approximations apply, the Michaelis-Menten approximation would give misleading parameter estimates.     

Identification of N, O-diacetyl-, N-acetyl- and N-glycolylneuraminyl-(2 → 3)-lactose in rat urine

The structure of three neuraminyl-oligosaccharides isolated from rat urine-have been studied by chromatographic and mass spectrometric analyses of different hydrolysis and methylation products. The structures of the oligosaccharides were identifies as O-α-N-acetyl(O-acetyl)neuraminyl-(2 → 3)-O-β-galactopyranosyl-(1 → 4)-glucopyranose, O-α-N-acetylneuraminyl-(2 → 3)-O-β-galactopyranosyl-(1 → 4)-glucopyranose and O-α-N-glycolylneuraminyl-(2 → 3)-O-β-galactopyranosyl-(1 → 4)-glucopyranose.     

Magnetic, spectroscopic, structural and biological properties of mixed-ligand complexes of copper(II) with N,N,N,N″,N″-pentamethyldiethylenetriamine and polypyridine ligands

Two new mixed ligand complexes of copper(II) with N,N,N^′,N″,N″-pentamethyldiethylenetriamine and polypyridine ligands have been prepared and characterized by means of spectroscopic, magnetic and single-crystal X-ray diffraction methods. These two complexes are isomorph and isostructure in which the coordination polyhedron about the copper(II) ion is distorted square pyramidal. [Cu(PMDT)(bipy)]²⁺ and [Cu(PMDT)(phen)]²⁺ show an absorption wavelength maximum at 625 and 678 nm, respectively, assigned to the d-d transition. Antibacterial, antifungal and superoxide dismutase activities of these complexes have also been measured. It was observed that [Cu(PMDT)(bipy)](ClO₄)₂ was more effective against P. Pyocyanea and Klebsiella sp. than S. aureus. Similarly, Fusarium sp. was highly susceptible against [Cu(PMDT)(bipy)](ClO₄)₂ but less susceptible against [Cu(PMDT)(phen)](ClO₄)₂.     

Phosphatidylserine-stimulated production of N-acyl-phosphatidylethanolamines by Ca2+-dependent N-acyltransferase

N-acyl-phosphatidylethanolamine (NAPE) is known to be a precursor for various bioactive N-acylethanolamines including the endocannabinoid anandamide. NAPE is produced in mammals through the transfer of an acyl chain from certain glycerophospholipids to phosphatidylethanolamine (PE) by Ca²⁺-dependent or -independent N-acyltransferases. The ε isoform of mouse cytosolic phospholipase A₂ (cPLA₂ε) was recently identified as a Ca²⁺-dependent N-acyltransferase (Ca-NAT). In the present study, we first showed that two isoforms of human cPLA₂ε function as Ca-NAT. We next purified both mouse recombinant cPLA₂ε and its two human orthologues to examine their catalytic properties. The enzyme absolutely required Ca²⁺ for its activity and the activity was enhanced by phosphatidylserine (PS). PS enhanced the activity 25-fold in the presence of 1?mM CaCl₂ and lowered the EC₅₀ value of Ca²⁺ >8-fold. Using a PS probe, we showed that cPLA₂ε largely co-localizes with PS in plasma membrane and organelles involved in the endocytic pathway, further supporting the interaction of cPLA₂ε with PS in living cells. Finally, we found that the Ca²⁺-ionophore ionomycin increased [¹⁴C]NAPE levels >10-fold in [¹⁴C]ethanolamine-labeled cPLA₂ε-expressing cells while phospholipase A/acyltransferase-1, acting as a Ca²⁺-independent N-acyltransferase, was insensitive to ionomycin for full activity. In conclusion, PS potently stimulated the Ca²⁺-dependent activity and human cPLA₂ε isoforms also functioned as Ca-NAT.     

Synthesis, spectroscopic, thermal and X-ray structure characterization of 1,3-propanediammonium tetrathiomolybdate and N,N,N′,N′-tetramethylethylenediammonium tetrathiomolybdate

The title compounds 1,3-propanediammonium tetrathiomolybdate, (1,3-pnH₂)[MoS₄], 1 and, N,N,N′,N′-tetramethylethylenediammonium tetrathiomolybdate, (tmenH₂)[MoS₄], 2, were prepared by reacting the ammonium salt of [MoS₄]²⁻ with the corresponding organic diamine. In 1 and 2 the organic diamines 1,3-propanediamine (1,3-pn) and N,N,N′,N′-tetramethylethylenediamine (tmen) are present in their diprotonated form. The reaction of 1 or 2 with [Ni(en)₃]Cl₂ · 2H₂O (en is ethylenediamine) results in the formation of the highly insoluble complex tris(ethylenediamine)Ni(II) tetrathiomolybdate, [Ni(en)₃][MoS₄], in quantitative yields. 1 and 2 have been characterized by chemical analysis, vibrational, UV-Vis and NMR spectroscopy, TG-DTA-MS and single crystal X-ray crystallography. Compound 1 is thermally more stable compared to 2. Both complexes decompose in a single step forming amorphous molybdenum sulfide. The structure of the title complexes can be described as consisting of tetrahedral [MoS₄]²⁻ dianions which accept a complex series of H-bonds from the organic dications. The strength and number of these hydrogen bonds affect the Mo-S bond lengths.     

Parameter estimation for bursting neural models

This paper presents work on parameter estimation methods for bursting neural models. In our approach we use both geometrical features specific to bursting, as well as general features such as periodic orbits and their bifurcations. We use the geometry underlying bursting to introduce defining equations for burst initiation and termination, and restrict the estimation algorithms to the space of bursting periodic orbits when trying to fit periodic burst data. These geometrical ideas are combined with automatic differentiation to accurately compute parameter sensitivities for the burst timing and period. In addition to being of inherent interest, these sensitivities are used in standard gradient-based optimization algorithms to fit model burst duration and period to data. As an application, we fit Butera et al.'s (Journal of Neurophysiology 81, 382-397, 1999) model of preB?tzinger complex neurons to empirical data both in control conditions and when the neuromodulator norepinephrine is added (Viemari and Ramirez, Journal of Neurophysiology 95, 2070-2082, 2006). The results suggest possible modulatory mechanisms in the preB?tzinger complex, including modulation of the persistent sodium current.     

Anion effects on ionogel formation in N,N′-dialkylimidazolium-based ionic liquids

Addition of an appropriate concentration of water to either 1-decyl-3-methylimidazolium bromide or its nitrate analog is shown to trigger the self-assembly of the ionic liquid (IL) and the concomitant formation of gel (“ionogel”) phases adopting a rich variety of structural motifs. Infrared and ¹H nuclear magnetic resonance studies indicate that water addition disrupts hydrogen bonding between the imidazolium ring and the IL anion, and that gelation involves the partial replacement of these bonds with H-bonds between the anion and water. Using small angle X-ray scattering, the relationship of the water content and the nature of the IL anion to the mesoscopic structure of the ionogels has been determined. Of particular note is the observation that by adjustment of the ionogel composition (water content or anion), near-monodomain materials can be formed with either lamellar, 2-D hexagonal or 3-D cubic structures with tunable lattice dimensions.     

Hyoscyamine N-oxide in Atropa belladonna

Separated organs of Atropa belladonna have been examined for their total alkaloid, hyoscyamine and hyoscyamine N-oxide contents during ontogenesis. Marked fluctuations in N-oxide content were observed, the highest being found in the ripe fruit. [G-³H]-atropine was fed to A. belladonna fruits and radioactively labelled hyoscyamine N-oxide isolated.     

Parameter redundancy in mark‐recovery models

We provide a definitive guide to parameter redundancy in mark‐recovery models, indicating, for a wide range of models, in which all the parameters are estimable, and in which models they are not. For these parameter‐redundant models, we identify the parameter combinations that can be estimated. Simple, general results are obtained, which hold irrespective of the duration of the studies. We also examine the effect real data have on whether or not models are parameter redundant, and show that results can be robust even with very sparse data. Covariates, as well as time‐ or age‐varying trends, can be added to models to overcome redundancy problems. We show how to determine, without further calculation, whether or not parameter‐redundant models are still parameter redundant after the addition of covariates or trends.