Random walk through a fertile site.

We study the dynamics of random walks hopping on homogeneous hypercubic lattices and multiplying at a fertile site. In one and two dimensions, the total number N(t) of walkers grows exponentially at a Malthusian rate depending on the dimensionality and the multiplication rate µ at the fertile site. When d>d_{c}=2, the number of walkers may remain finite forever for any µ; it surely remains finite when µ≤µ_{d}. We determine µ_{d} and show that 〈N(t)〉 grows exponentially if µ>µ_{d}. The distribution of the total number of walkers remains broad when d≤2, and also when d>2 and µ>µ_{d}. We compute 〈N^{m}〉 explicitly for small m, and show how to determine higher moments. In the critical regime, 〈N〉 grows as sqrt[t] for d=3, t/lnt for d=4, and t for d>4. Higher moments grow anomalously, 〈N^{m}〉∼〈N〉^{2m-1}, in the critical regime; the growth is normal, 〈N^{m}〉∼〈N〉^{m}, in the exponential phase. The distribution of the number of walkers in the critical regime is asymptotically stationary and universal, viz., it is independent of the spatial dimension. Interactions between walkers may drastically change the behavior. For random walks with exclusion, if d>2, there is again a critical multiplication rate, above which 〈N(t)〉 grows linearly (not exponentially) in time; when d≤d_{c}=2, the leading behavior is independent on µ and 〈N(t)〉 exhibits a sublinear growth.

Universal fluctuations around typicality for quantum ergodic systems.

For a quantum system in a macroscopically large volume V, prepared in a pure state and subject to maximally noisy or ergodic unitary dynamics, the reduced density matrix of any sub-system v≪V is almost surely totally mixed. We show that the fluctuations around this limiting value, evaluated according to the invariant measure of these unitary flows, are captured by the Gaussian unitary ensemble (GUE) of random matrix theory. An extension of this statement, applicable when the unitary transformations conserve the energy but are maximally noisy or ergodic on any energy shell, allows to decipher the fluctuations around canonical typicality. According to typicality, if the large system is prepared in a generic pure state in a given energy shell, the reduced density matrix of the sub-system is almost surely the canonical Gibbs state of that sub-system. We show that the fluctuations around the Gibbs state are encoded in a deformation of the GUE whose covariance is specified by the Gibbs state. Contact with the eigenstate thermalization hypothesis is discussed.

Rimonabant dimorphism and its pressure-temperature phase diagram: a delicate case of overall monotropic behavior.

Crystalline polymorphism occurs frequently in the solid state of active pharmaceutical ingredients, and this is problematic for the development of a suitable dose form. Rimonabant, an active pharmaceutical ingredient developed by Sanofi and discontinued because of side effects, exhibits dimorphism; both solid forms have nearly the same melting temperatures, melting enthalpies, and specific volumes. Although the problem may well be academic from an industrial point of view, the present case demonstrates the usefulness of constructing pressure-temperature phase diagrams by direct measurement as well as by topological approach. The system is overall monotropic and form II is the more stable solid form. Interestingly, the more stable form does not possess any hydrogen bonds, whereas the less stable one does.

Loss of metabotropic glutamate receptor-dependent long-term depression via downregulation of mGluR5 after status epilepticus.

Synaptic plasticity is thought to be a key mechanism of information storage in the CNS. Different forms of synaptic long-term potentiation have been shown to be impaired in neurological disorders. Here, we show that metabotropic glutamate receptor (mGluR)-dependent long-term depression (LTD), but not NMDA receptor-dependent LTD at Schaffer collateral-CA1 synapses, is profoundly impaired after status epilepticus. Brief application of the group I mGluR agonist (R,S)-3,5-dihydroxyphenylglycine (100 microM; 5 min) induced mGluR LTD in control, but not in pilocarpine-treated rats. Experiments in the presence of selective inhibitors of either mGluR5 [2-methyl-6-(phenylethynyl)-pyridine] or mGluR1 [7-(hydroxyimino)cyclopropachromen-carboxylate ethyl ester and (S)-(+)-alpha-amino-4-carboxy-2-methylbenzeneacetic acid] demonstrate that loss of mGluR LTD is most likely attributable to a loss of mGluR5 function. Quantitative real-time reverse transcription PCR revealed a specific downregulation of mGluR5 mRNA, but not of mGluR1 mRNA in the CA1 region. Furthermore, we detected a strong reduction in mGluR5 protein expression by immunofluorescence and quantitative immunoblotting. Additionally, the scaffolding protein Homer that mediates coupling of mGluR5 to downstream signaling cascades was downregulated. Thus, we conclude that the reduction of mGluR LTD after pilocarpine-induced status epilepticus is the result of the subtype-specific downregulation of mGluR5 and associated downstream signaling components.

Relationship between HPLC precision and number of significant figures when reporting impurities and when setting specifications.

The rounding of an analytical result is a process that should take into account the uncertainty of the result, which is in turn assessed during the validation exercise. Rounding rules are known in physical and analytical chemistry since a long time, but are often not used or misused in pharmaceutical analysis. The paper describes the theoretical background of the most common rules and their application to fix the rounding of results and specifications. The paper makes use of uncertainty values of impurity determination acquired during studies of reproducibility and intermediate precision with regards to 22 impurities of drug substances or drug products. As a general rule, authors propose the use of sound and well-established rounding rules to derive rounding from the results of the validation package.

Checking for optimal solutions in some NP-complete problems.

For some weighted NP-complete problems, checking whether a proposed solution is optimal is a nontrivial task. Such is the case for the traveling salesman problem, or the spin-glass problem in three dimensions. In this Letter, we consider the weighted tripartite matching problem, a well known NP-complete problem. We write mean-field finite temperature equations for this model and derive their zero temperature limit. We show that any solution of the zero temperature equations provides an exact absolute ground state of the system. As a consequence, we propose a criterion which can be checked in polynomial time, and such that given a putative optimal solution, if the criterion is satisfied, then the solution is indeed optimal. This criterion is generalized to a class of variants of the multiple traveling salesmen problems.

Gene essentiality and the topology of protein interaction networks.

The mechanistic bases for gene essentiality and for cell mutational resistance have long been disputed. The recent availability of large protein interaction databases has fuelled the analysis of protein interaction networks and several authors have proposed that gene dispensability could be strongly related to some topological parameters of these networks. However, many results were based on protein interaction data whose biases were not taken into account. In this article, we show that the essentiality of a gene in yeast is poorly related to the number of interactants (or degree) of the corresponding protein and that the physiological consequences of gene deletions are unrelated to several other properties of proteins in the interaction networks, such as the average degrees of their nearest neighbours, their clustering coefficients or their relative distances. We also found that yeast protein interaction networks lack degree correlation, i.e. a propensity for their vertices to associate according to their degrees. Gene essentiality and more generally cell resistance against mutations thus seem largely unrelated to many parameters of protein network topology.

Studies on the crystallinity of a pharmaceutical development drug substance.

The crystallinity and amorphous content of a micronized pharmaceutical development drug substance have been independently determined. An evaluation of different techniques for this purpose has been carried out, and it was found that solid-state nuclear magnetic resonance (ss NMR) and X-ray powder diffraction (XRPD) were suitable for the former and latter, respectively. The baseline intensities of X-ray powder diffractograms, associated with the amorphous component of the sample, have been used to detect levels of non-crystalline material greater than 5%w/w with an absolute accuracy of +/-3%. ss NMR has been employed to quantify crystalline defects at levels of greater than 3%w/w with an estimated uncertainty of +/-2%. It is proposed that such crystalline defects arise from molecular conformational differences that only have a small effect on crystal lattice parameters and, by implication, only have small effects on X-ray powder diffractograms. In both cases the techniques are shown to be highly reproducible and require minimal sample preparation. Excellent linearity is demonstrated for the determination of amorphous material using prepared standards. The present account describes the choice of analytical method, method validation and the results obtained for typical samples of drug substance. It is demonstrated that solid-state NMR should be used as a complementary technique with respect to XRPD for studying crystallinity.

Stabilization of rasburicase and physico-chemical characterization of the resulting injectable formulation.

Rasburicase (Fasturtec/Elitek) is a new generation of recombinant urate oxidase administred therapeutically by intravenous infusion for the prevention or treatment of hyperuricemia during chemotherapy. To ensure a long storage period, a freeze-dried formulation was developed to guarantee the molecular integrity and enzyme activity. Screening of potential excipients was the first stage of the preformulation study. The selection was based on stability results (rasburicase solution with excipient) obtained with the isoelectric focusing profiles and residual enzyme activity. The different excipients were classified as stabilising, neutral or destabilising. A stability study was then carried out on different freeze-dried formulations containing the usual bulking agents for freeze-drying, excipients with a high glass transition temperature or competitive enzyme inhibitors having a stabilising effect. A mannitol/alanine mixture in phosphate buffer was selected from these preliminary results. Finally, the optimal content of mannitol and alanine in the freeze-dried powder was determined by an experimental design study. The water content and the appearance of the "cake", the osmolality, pH, clarity, and enzyme activity of the reconstituted solution were assessed. The formula with a mannitol/alanine ratio of 0.7 was found to be the best composition. Differential scanning calorimetry and ThermoStimulated Current technique experiments were carried out to study the amorphous phase. A glass transition temperature of about 45-500 degrees C was found. Glassy state is known to preserve stability, which was verified by the real stability data. X-ray diffraction studies have shown that alanine is in a crystallised state and that mannitol remains amorphous. Crystallised excipients participate in forming the structure of the powder and therefore help to prevent any collapse. Amorphous mannitol creates a surrounding medium favourable to the stability of the protein.

Molecular mobility study of amorphous and crystalline phases of a pharmaceutical product by thermally stimulated current spectrometry.

Two crystalline forms and the amorphous state of irbesartan, a pharmaceutical drug chosen as a model, were analyzed by Thermally Stimulated Current (TSC) spectroscopy, a powerful technique currently used in polymer science to investigate the molecular dynamics of heterogeneous and complex materials. Whereas no specific dielectric response was noted for the B crystalline form, the A form of irbesartan exhibited molecular motions localized inside its channel structure. The dynamics involved in the dielectric glass transition of amorphous samples followed a compensation law characteristic of highly cooperative relaxation processes. Concerning the amorphous content in physical mixtures, a calibration curve and a limit of detection (2.5%) were established. The limit of detection could be improved by optimizing the TSC experimental parameters. The amorphous sample recrystallized at a single temperature was interpreted by the "idealized one-state model" defined here to describe systems composed of identical semicrystalline particles in which amorphous and crystalline phases are independent of each other (i.e., no chemical and physical interaction between the two phases). Therefore, the idealized one-state model may be simulated by a two-state model, which is representative of the two-phase model. Other samples recrystallized through a complex annealing stage were explained by the classical one-state model in agreement with the three-phase model used to describe bulk semicrystalline systems. These results demonstrate that, as for polymers, the semicrystalline state of pharmaceutical drugs should not be considered as a single state but as a more complex system that can be described as an idealized one-state model or a one-state model depending on the applied thermal treatment. These results give a new view that should be taken into account in the development of amorphous pharmaceutical drugs and formulations.