Use of high-throughput tools to optimise polishing-chromatography sequences for complex feed mixtures

Polishing chromatography is a critical element of a bioprocess, because it is currently the only scalable separation technique that can remove process-related impurities, thereby achieving the high purity required of a biotherapeutic. Optimising the polishing chromatography of complex feeds has not been systematically addressed in the literature. This thesis identified a novel, academically affordable ternary protein mixture and systematically developed an optimal two-column polishing train for it. The ternary protein feed mixture was selected using many criteria, but had no special feature to aid identification, such as a chromophore, making it more difficult to characterise. The resulting analytical chromatogram could not be fully resolved, which is typical of industrially relevant products, such as glycoproteins. The selected HPLC column produced fast separations, resulting in a comparatively rapid quantification of preparative chromatograms. Many chromatographic resins and operating conditions were screened, resulting in the non-obvious sequence a hydrophobic interaction (HIC) followed by an anion-exchange (AX) adsorbent. Systematic experimental studies optimised the sequence with respect to yield, purity and amount recovered. Although the loading exceeded the binding capacity of the HIC column, runs at extremely high loadings (60 — 150 g/L) gave very efficient separation in an unusual combination of flow-through and bind-and-elute modes. It was found to achieve >200 mg of acceptably pure product from a single run. A variety of problems were encountered during the development of this polishing train, to which solutions were developed. While these problems are not uncommon, the literature does not contain systematic solutions to them. Examples include decisions about sequence design, protein solubility issues, and the detailed characterisation of samples from preparative runs (not achieved by analytical HPLC). In particular, a system-specific deconvolution methodology was developed that allowed complete characterisation of the mixture; the approach is likely to be widely applicable to industrially relevant biological feed mixtures

Scaling limits of coupled continuous time random walks and residual order statistics through marked point processes

A continuous time random walk (CTRW) is a random walk in which both spatial changes represented by jumps and waiting times between the jumps are random. The CTRW is coupled if a jump and its preceding or following waiting time are dependent random variables, respectively. The aim of this paper is to explain the occurrence of different limit processes for CTRWs with forward- or backward-coupling in Straka and Henry (2011) using marked point processes. We also establish a series representation for the different limits. The methods used also allow us to solve an open problem concerning residual order statistics by LePage (1981).Comment: revised version, to appear in: Stoch. Process. App

Generalized Fractal Kinetics in Complex Systems (Application to Biophysics and Biothechnology)

We derive a universal function for the kinetics of complex systems. This kinetic function unifies and generalizes previous theoretical attempts to describe what has been called "fractal kinetic".The concentration evolutionary equation is formally similar to the relaxation function obtained in the stochastic theory of relaxation, with two exponents a and n. The first one is due to memory effects and short-range correlations and the second one finds its origin in the long-range correlations and geometrical frustrations which give rise to ageing behavior. These effects can be formally handled by introducing adequate probability distributions for the rate coefficient. We show that the distribution of rate coefficients is the consequence of local variations of the free energy (energy landscape) appearing in the exponent of the Arrhenius formula. We discuss briefly the relation of the (n,a) kinetic formalism with the Tsallis theory of nonextensive systems.Comment: 15 pages, 3 figures, submitted to Physica

Glass transition of an epoxy resin induced by temperature, pressure and chemical conversion: a configurational entropy rationale

A comparative study is reported on the dynamics of a glass-forming epoxy resin when the glass transition is approached through different paths: cooling, compression, and polymerization. In particular, the influence of temperature, pressure and chemical conversion on the dynamics has been investigated by dielectric spectroscopy. Deep similarities are found in dynamic properties. A unified reading of our experimental results for the structural relaxation time is given in the framework of the Adam-Gibbs theory. The quantitative agreement with the experimental data is remarkable, joined with physical values of the fitting parameters. In particular, the fitting function of the isothermal tau(P) data gives a well reasonable prediction for the molar thermal expansion of the neat system, and the fitting function of the isobaric-isothermal tau(C) data under step- polymerization conforms to the prediction of diverging tau at complete conversion of the system.Comment: 16 pages, 8 figures, from the talk given at the 4th International Discussion Meeting on Relaxations in Complex Systems (IDMRCS), Hersonissos, Helaklion, Crete (Greece), 17-23 June 200

Solvable non-Markovian dynamic network

Non-Markovian processes are widespread in natural and human-made systems, yet explicit modeling and analysis of such systems is underdeveloped. We consider a non-Markovian dynamic network with random link activation and deletion (RLAD) and heavy-tailed Mittag-Leffler distribution for the interevent times. We derive an analytically and computationally tractable system of Kolmogorov-like forward equations utilizing the Caputo derivative for the probability of having a given number of active links in the network and solve them. Simulations for the RLAD are also studied for power-law interevent times and we show excellent agreement with the Mittag-Leffler model. This agreement holds even when the RLAD network dynamics is coupled with the susceptible-infected-susceptible spreading dynamics. Thus, the analytically solvable Mittag-Leffler model provides an excellent approximation to the case when the network dynamics is characterized by power-law-distributed interevent times. We further discuss possible generalizations of our result

Continuous-time statistics and generalized relaxation equations

Using two simple examples, the continuous-time random walk as well as a two state Markov chain, the relation between generalized anomalous relaxation equations and semi-Markov processes is illustrated. This relation is then used to discuss continuous-time random statistics in a general setting, for statistics of convolution-type. Two examples are presented in some detail: the sum statistic and the maximum statistic

On the book ``An Introduction to Differential Equations: Stochastic Modeling, Methods and Analysis'' by A.G.Ladde and G.S.Ladde

Niniejsza książka stanowi kontynuację podręcznika, tych samych autorów, przedstawiającego tematykę równań różniczkowych. Tom 1. (Deterministic Modeling, Methods and Analysis) dotyczył teorii klasycznych, natomiast omawiany tu tom 2. prezentuje ideę równań różniczkowych stochastycznych i ich zastosowania w modelowaniu matematycznym. Książka adresowana jest głównie do studentów i doktorantów kierunków interdyscyplinarnych.The book under review presents advanced tools of stochastic calculus and stochastic differential equations of Ito type, illustrated by several problems and applications. It is a continuation of Volume 1: Deterministic Modeling, Methods and Analysis. It is addressed to interdisciplinary graduate/undergraduate students and to interdisciplinary young researchers