Self-Couplings and the concentration function

The concentration function of a random variable may be estimated using couplings of the variable with itself.Supported by the Göran Gustafsson Foundation for Research in Natural Sciences and Medicine.     

The random-cluster model on the complete graph

Summary The random-cluster model of Fortuin and Kasteleyn contains as special cases the percolation, Ising, and Potts models of statistical physics. When the underlying graph is the complete graph onn vertices, then the associated processes are called mean-field. In this study of the mean-field random-cluster model with parametersp=/n andq, we show that its properties for any value ofq(0, ) may be derived from those of an Erds-Rényi random graph. In this way we calculate the critical point _c (q) of the model, and show that the associated phase transition is continuous if and only ifq2. Exact formulae are given for _C (q), the density of the largest component, the density of edges of the model, and the free energy. This work generalizes earlier results valid for the Potts model, whereq is an integer satisfyingq2. Equivalent results are obtained for a fixed edge-number random-cluster model. As a consequence of the results of this paper, one obtains large-deviation theorems for the number of components in the classical random-graph models (whereq=1).     

On the history of the development of Sephadex®

Summary The creative and stimulating atmosphere in the laboratories of The Svedberg and Arne Tiselius in the Departments of Physical Chemistry and Biochemistry of Uppsala University during the 1930's, 1940's and 1950's, was a nursery for a remarkable set of both academic and industrial advances. Their pupils were to become distinguished professors at Swedish Universities, as well as abroad, and they were directly involved in the development of two successful Swedish industries, LKB-produkter AB in Stockholm and Pharmacia AB in Uppsala. This review describes the preconditions and the events which led to the development of one of the first commercially available biochemical separation products, the gel filtration medium Sephadex which was introduced by Pharmacia AB in 1959. All the necessary components of a successful transfer of academic research to industrial product development were at hand: a scientific culture of common origin and a longstanding tradition in methodological research; mutual understanding and respect combined with informal links not only between the scientists involved but also between the president of the company and the university authorities. So far, 49 products (excluding those intended for use in health care and diagnostics) have been developed based on the epichlorohydrin cross-linked dextran gel Sephadex. This review is dedicated to my teacher professor Jerker Porath on his retirement as Jacobsonian Professor of Biochemistry at Uppsala University in December 1987.     

Production, purification and characterization of recombinant human interferon gamma.

An essentially three-step chromatographic purification procedure, i.e., ion-exchange, immobilized metal ion affinity and size-exclusion chromatography, is described for the purification to homogeneity of recombinant human interferon-gamma (rhIFN-gamma) from the inclusion bodies produced in genetically transformed Escherichia coli cells. Batchwise adsorption of the cloudy solution of renatured rhIFN-gamma obviated the need for high-speed centrifugation to clarify the suspension. This step effectively removed about 70% of extraneous protein impurities. The established purification process is reproducible and leads to a total recovery of 32%. Pilot-scale processing of E. coli cells grown in a 30-l fermentor gave about 70 mg of a homogeneous preparation of rhIFN-gamma. The specific biological activity of purified rhIFN-gamma is ca. 3.4 x 10(7) I.U./mg protein, which is comparable to that of its natural counterpart. It is basic protein (pI greater than pH 9) with a monomer relative molecular mass of 15,000. It behaves, however, as a dimer on size-exclusion chromatography. Its partial NH2-terminal sequence is identical with that established for the rhIFN-gamma. However, its amino acid composition and its relative molecular mass (15,067 as determined by electrospray mass spectrometry) indicate that the purified protein is a truncated form lacking fifteen amino acid residues from its carboxyl-terminal side. This modification does not seem to have any adverse effect on its biological potency. The levels of DNA, bacterial endotoxins and Ni(II) ions in the final product were determined.     

Isolation of high purity 1-[2',4'-dihydroxy-3',5'-di-(3"-methylbut-2"-enyl)-6'-methoxy] phenylethanone from Acronychia pedunculata (L.) Miq. by high-speed counter-current chromatography

Following an initial clean-up step on silica, high-speed counter-current chromatography (HSCCC) was used to purify an aryl ketone, 1-[2',4'-dihydroxy-3',5'-di-(3"-methylbut-2"-enyl)-6'-methoxy] phenylethanone from an extract of the stem bark of the shrub Acronychia pedunculata. The two-phase solvent system used was composed of n-heptane-ethyl acetate-methanol-water at an optimized volume ratio of 4:1:4:1 (v/v/v/v). Target compound (58.1 mg) with a purity of 98.9% was obtained after HSCCC of 183.5 mg sample with a purity of 35.7% recovered after the silica clean-up step. Identification of the target compound was performed by 1H NMR, 13C NMR, two-dimensional NMR and LC-electrospray ionization MS.     

Separation and purification of puerarin using beta-cyclodextrin-coupled agarose gel media

The isoflavonoid puerarin, a well-known traditional Chinese drug, has been purified in one step from an extract of Radix puerariae (root of the plant Pueralria lobata) by adsorption chromatography on an epichlorohydrin polymerized beta-cyclodextrin ligand coupled to brominated allyl-group substituted Sepharose HP. Acetic acid (10%) was used as the mobile phase and the optimum loading capacity was around 1.2 mg crude extract/ml packed gel. The purity of the collected puerarin was about 98% with a recovery of about 62%.     

A study of atom-atom and atom-molecule interactions in the resonance extraction of sodium atoms

The formation of Na(n²L) and Na₂(A¹?_u⁺, B¹Π_u) in sodium vapour(≈10¹⁴–10¹⁵ cm^?3) irradiated by a cw dye laser tuned to the D lines has been studied. The density of excited atoms was determined by measurements of the realtive absorption of 3²P-3²D transitions. These, together with measurements of Na and Na₂ fluorescence intensities, yield rate constants for formation of Na(n²L) and Na₂(A¹?_u⁺, B¹Π_u). The experimental evidence indicates a negligible role for the photorecombination process Na(3²P) + Na(3²S) in populating A¹?_u⁺ and B¹Π_u molecular states. A new stepwise process is proposed to account for excitation to the molecular diffuse band (420–450 nm).     

The lower tail: Poisson approximation revisited

The well‐known “Janson's inequality” gives Poisson‐like upper bounds for the lower tail probability when X is the sum of dependent indicator random variables of a special form. We show that, for large deviations, this inequality is optimal whenever X is approximately Poisson, i.e., when the dependencies are weak. We also present correlation‐based approaches that, in certain symmetric applications, yield related conclusions when X is no longer close to Poisson. As an illustration we, e.g., consider subgraph counts in random graphs, and obtain new lower tail estimates, extending earlier work (for the special case ) of Janson, ?uczak and Ruciński. © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 48, 219–246, 2016     

Size characterization of green fluorescent protein inclusion bodies in E. coli using asymmetrical flow field-flow fractionation-multi-angle light scattering

The goal of this study was to investigate the applicability of asymmetrical flow field-flow fractionation-multi-angle light scattering (AsFlFFF-MALS) for size analysis of green fluorescent protein inclusion bodies (GFPIBs). The size distributions of GFPIBs prepared by various culture conditions were determined. For GFPIBs prepared at 37 degrees C the peak maximum hydrodynamic diameter (d(H)) first increased and then decreased with the increase of the induction times in the presence of 0.1 and 2 mM isopropyl-beta-D-thiogalactoside (IPTG). For GFPIBs prepared at 30 degrees C the peak maximum d(H) was constant at about 700 nm irrespectively of the induction times and IPTG concentrations.     

Mixed-mode retention mechanism for (-)-epigallocatechin gallate on a 12% cross-linked agarose gel media

The adsorption behaviour of (-)-epigallocatechin gallate (EGCG), the major polyphenolic substance in green tea extracts, on the cross-linked agarose gel Superose 12 HR 10/30, has been studied using a variety of solvent systems and shown to be based on a mixture of hydrogen bonding and hydrophobic interaction. The hydrogen bonding was studied in acetonitrile in the presence of different co-solvents possessing varying hydrogen bond donor (HBD) and/or hydrogen bond acceptor (HBA) characteristics. The HBA-value of the co-solvent had the highest effect whereas the HBD-value played a subordinate role. Retention due to hydrophobic interaction could be demonstrated when mobile phases containing high water content were applied. The retention of EGCG, and its analogues (-)-epigallocatechin (EGC) and (-)-catechin (C) were thus shown to be dependent on the polarity of the organic modifiers added. However, the elution order of EGC and C, was inversed to that observed in reversed phase chromatography, indicating that some hydrogen bonding was still in effect. The retardation of EGCG in the presence of a wide concentration range of acetonitrile in water confirmed the interpretation that the retention mechanism is of mixed-mode character based on both hydrogen bonding and hydrophobic interaction.