Theoretical and fuzzy modelling of a pharmaceutical batch reactor

This paper deals with the development of a batch-reactor model with a theoretical and a locally affine fuzzy model. The batch reactor is used in the pharmaceutical industry for the production of drugs, where a rapid and precise temperature control is necessary. The model has to be built to include all the main features necessary for the purposes of modelling. The development of the model for the reactor is designed for further control development and simulation purposes, without doing any further experiments on the real process. In our case we use the model for simulating the reactor’s jacket temperature and the reactor’s core temperature. The theoretical model describes all the nonlinearities of the process of heating and cooling the content of the batch reactor. The main contribution of the theoretical model is in the modelling of the heat transfer between the reactor’s jacket and the reactor’s core, mainly caused by the change in the overall heat transfer, which also covers the main nonlinearity. Because of the complexity of the theoretical model a locally affine fuzzy model is also developed.     

Zinc-phosphate nanoparticles with reversibly attached TNF-α analogs: an interesting concept for potential use in active immunotherapy

The authors’ intention was to prepare nanometer-sized zinc-phosphate nanoparticles that would be capable of binding histidine-rich TNF-α analogs onto their surface via a coordinative bond. Zinc-phosphate nanoparticles with a size of around 60 nm were prepared by a wet precipitation method and characterized using SEM, EDX, XRD, and DLS. First, BSA was bound as a testing protein, afterward two TNF-α analogs with decreased activity were bound to the described nanoparticles. The efficiency of binding and the existence of coordinative bond were confirmed with SDS-PAGE analysis. During binding, particle storage, and release experiments, the prepared TNF-α analogs retained their biological activity—hence the epitopes necessary for formation of antibodies stayed intact. The particle size did not change within a period of 2 weeks. No significant agglomeration was observed, the particles could be quickly dispersed in ultrasound. The present nanoparticles and the general approach of coordinative binding are widely applicable for natural and engineered histidine-rich proteins. The nanoparticles bearing appropriate TNF-α analogs could also be potentially used for active immunotherapy to tackle the chronic inflammatory diseases associated with pathogenically elevated levels of TNF-α.     

Diverse polymorphism of G-quadruplexes as a kinetic phenomenon

Knowledge of forces that drive conformational transitions of G-quadruplexes is crucial for understanding the molecular basis of several key cellular processes. It can only be acquired by combining structural, thermodynamic and kinetic information. Existing biophysical and structural evidences on polymorphism of intermolecular G-quadruplexes have shown that the formation of a number of these structures is a kinetically controlled process. Reported kinetic models that have been used to describe the association of single strands into quadruplex structures seem to be inappropriate since the corresponding model-predicted activation energies turn out to be negative. By contrast, we propose here a novel kinetic model that successfully describes experimentally monitored folding/unfolding transitions of G-quadruplexes and gives positive activation energies for all elementary steps, including those describing association of two single strands into bimolecular quadruplex structures. It is based on a combined thermodynamic and kinetic investigation of polymorphic behavior of bimolecular G-quadruplexes formed from d(G4T4G4) and d(G4T4G3) strands in the presence of Na(+) ions, monitored by spectroscopic (UV, CD) and calorimetric (DSC) techniques. According to our experiment and model analysis the topology of the measured G-quadruplexes is clearly flexible with the conformational forms that respond to the rate of temperature change at which global unfolding/folding transitions occur.     

Energetic basis of human telomeric DNA folding into G-quadruplex structures

Recent theoretical studies performed on the folding/unfolding mechanism of the model telomeric human DNA, 5'-AGGGTTAGGGTTAGGGTTAGGG-3' (Tel22), have indicated that in the presence of K(+) ions Tel22 folds into two hybrid G-quadruplex structures characterized by one double and two reversal TTA loops arranged in a different way. They predicted a new unfolding pathway from the initial mixture of hybrid G-quadruplexes via the corresponding intermediate triplex structures into the final, fully unfolded state. Significantly, no experimental evidence supporting the suggested pathway has been reported. In the current work, we performed a comprehensive global thermodynamic analysis of calorimetric (DSC, ITC) and spectroscopic (CD) data obtained on monitoring the folding/unfolding of Tel22 induced by changes of temperature and K(+) concentration. We show that unfolding of Tel22 may be described as a monomolecular equilibrium three-state process that involves thermodynamically distinguishable folded (F), intermediate (I), and unfolded (U) state. Considering that calorimetric methods cannot distinguish between energetically similar G-quadruplex or triplex conformations predicted by the theoretical model one can conclude that our results represent the first experimental support of the suggested unfolding/folding mechanism of Tel22. This conclusion is confirmed by the fact that the estimated number of K(+) ions released upon each unfolding step in our thermodynamic model agrees well with the corresponding values predicted by the theoretical model and that the observed changes in enthalpy, entropy, and heat capacity accompanying the F → I and I → U transitions can be reasonably explained only if the intermediate state I is considered to be a triplex structural conformation.     

Differentiation of Borrelia burgdorferi sensu lato species by temperature gradient gel electrophoresis

Borrelia burgdorferi sensu lato is a multispecies complex of pathogenic spirochetes, causing Lyme borreliosis. Due to clinical, epidemiological, and taxonomical implications, there is a need for identification of isolated Borrelia strains. In the present study, we have optimized TGGE for B. burgdorferi sensu lato species differentiation and the results were compared with two reference methods, namely PFGE and restriction of 5S-23S intergenic space region PCR product. A differentiation of B. garinii, B. afzelii, and B. burgdorferi senso stricto species with TGGE was possible and intraspecies variation was detected. Results compared between TGGE, PFGE, and restriction of 5S-23S intergenic space region PCR product showed no difference in specificity of species identification.     

Mathematical modeling of the relation between myosin phosphorylation and stress development in smooth muscles

In this paper the 4-state latch bridge model proposed by Rembold and Murphy is expanded; first by incorporation of the analytical expression of Ca2+ dependent MLCK activation from the work of Kato et al. and second, by inclusion of the myosin dephosphorylation based on the Michaelis-Menten kinetics. The analysis of the proposed model and the comparison with the original model results as well as with the experimental data is presented. The model is able to predict the steady-state isometric stress and the myosin phosphorylation in dependence on steady cytosolic [Ca2+] as well as the temporal evolution of the system in dependence on the input Ca2+ signal in the form of biphasic transient, whereby our model results are in several aspects in better agreement with experimental observations.     

Continuous multiplicative mappings on

Let and be compact Hausdorff topological spaces, and let and be real Banach algebras of all real-valued continuous functions on and , respectively. The general form of continuous multiplicative mappings is given.

     

Simplified approach to modelling the catalytic degradation of low-density polyethylene (LDPE) by applying catalyst-free LDPE-TG profiles and the Friedman method

The course of the thermogravimetric degradation of LDPE in the presence of different aluminosilicate catalysts was modelled by applying a differential isoconversional Friedman approach. An analysis of catalyst-free PE-TG profiles confirmed that the degradation profiles predicted by various reaction models overlap over the entire conversion range once the data are analysed using a differential isoconversional Friedman approach. The results demonstrate that the catalytic degradation of LDPE can be predicted by a correlation twin, i.e. the two specific functional relations between the activation energy, pre-exponential factor and conversion. The crucial step for ensuring good agreement between the predicted and the measured profiles is to extrapolate the discrete values of the activation energies and pre-exponential factors to the zero conversion. It turns out that linear extrapolation and interpolation from the discrete values outperforms regression functions based on various order polynomials, and that apparent deviations from the global trend at lower conversions are not a consequence of the misinterpretation of the experimental results but are an experimental fact. The assumption about the compensation effect between the pre-exponential factor and activation energy holds within the conversion range from 10 to 90%. However, it is generally unsuitable for modelling purposes due to the uncertain extrapolation of the kinetic parameters to the zero conversion.

     

Evaluations of Low-Energy Physical Quantities in QCD with IR Freezing of the Coupling

The \({{\overline{\rm MS}}}\) -like schemes in QCD have in general the running coupling which contains Landau singularities, i.e., singularities outside the timelike semi-axis, at low squared momenta. As a consequence, evaluation of the spacelike quantities, such as current correlators, in terms of (powers of) such a coupling then results in quantities which contradict the basic principles of quantum field theories. On the other hand, in those QCD frameworks where the running coupling remains finite at low squared momenta (IR freezing), the coupling usually does not have Landau singularities in the complex plane of the squared momenta. I argue that in such QCD frameworks the spacelike quantities should not be evaluated as a power series, but rather as a series in derivatives of the coupling with respect to the logarithm of the squared momenta. Such series show considerably better convergence properties. Moreover, Padé-related resummations of such logarithmic derivative series give convergent series, thus eliminating the practical problem of series divergence due to renormalons.     

A fast algorithm for numerical solutions to Fortet's equation

A fast algorithm for computation of default times of multiple firms in a structural model is presented. The algorithm uses a multivariate extension of the Fortet's equation and the structure of Toeplitz matrices to significantly improve the computation time. In a financial market consisting of M1 firms and N discretization points in every dimension the algorithm uses O(nlogn·M·M!·N^M(M-1)/2) operations, where n is the number of discretization points in the time domain. The algorithm is applied to firm survival probability computation and zero coupon bond pricing.