Kim Lambertsen Larsen

Minimum-Cost Reachability for Priced Time Automata

This paper introduces the model of linearly priced timed automata as an extension of timed automata, with prices on both transitions and locations. For this model we consider the minimum-cost reachability problem: i.e. given a linearly priced timed automaton and a target state, determine the minimum cost of executions from the initial state to the target state. This problem generalizes the minimum-time reachability problem for ordinary timed automata. We prove decidability of this problem by offering an algorithmic solution, which is based on a combination of branch-and-bound techniques and a new notion of priced regions. The latter allows symbolic representation and manipulation of reachable states together with the cost of reaching them.

The Role of Decorated SDS Micelles in Sub-CMC Protein Denaturation and Association

We have combined spectroscopy, chromatography, calorimetry, and small-angle X-ray scattering (SAXS) to provide a comprehensive structural and stoichiometric description of the sodium dodecyl sulfate (SDS)-induced denaturation of the 86-residue alpha-helical bovine acyl-coenzyme-A-binding protein (ACBP). Denaturation is a multistep process. Initial weak binding of 1-3 SDS molecules per protein molecule below 1.3 mM does not perturb the tertiary structure. Subsequent binding of approximately 13 SDS molecules per ACBP molecule leads to the formation of SDS aggregates on the protein and changes in both tertiary and secondary structures. SAXS data show that, at this stage, a decorated micelle links two ACBP molecules together, leaving about half of the polypeptide chain as a disordered region protruding into the solvent. Further titration with SDS leads to the additional uptake of 26 SDS molecules, which, according to SAXS, forms a larger decorated micelle bound to a single ACBP molecule. At the critical micelle concentration, we conclude from reduced mobility and increased fluorescence anisotropy that each ACBP molecule becomes associated with more than one micelle. At this point, 56-60 SDS molecules are bound per ACBP molecule. Our data provide key structural insights into decorated micelle complexes with proteins, revealing a remarkable diversity in the different conformations they can stabilize. The data highlight that a minimum decorated micelle size, which may be a key driving force for intermolecular protein association, exists. This may also provide a structural basis for the known ability of submicellar surfactant concentrations to induce protein aggregation and fibrillation.

NMR diffusion as a novel tool for measuring the association constant between cyclodextrin and guest molecules

In this paper we introduce the use of diffusion measurements by nuclear magnetic resonance (NMR) spectroscopy for determining association constants of weak and very weak interactions between cyclodextrin and guest molecules, as long as both the free and complexed guest molecules are soluble to an extent that allows good sensitivity in the NMR experiment. The experimental setup and data analysis is discussed for three different guest molecules: L-phenylalanine, L-leucine and L-valine, representing different strengths of interaction. The underlying assumptions are discussed and the scope of the method (range of K(a) values, requirements to the guest molecule) are discussed. The methods main advantage is its general applicability independent of chromogenic or electrochemical properties of the guest molecule. Whereas calorimetric methods that exhibit a similar generality, are applicable mainly to strong interactions, NMR diffusion measurements are applicable to weaker interactions down to the theoretical limit of 1 M(-1), the upper limit for K(a) values to be determined by it is approximately 200. A further advantage of the method is the low amount of sample needed. The method is in principle applicable to any case of molecular recognition between a host and guest molecule leading to weak interactions.

Structural basis for cyclodextrins' suppression of human growth hormone aggregation

Many therapeutic proteins require storage at room temperature for extended periods of time. This can lead to aggregation and loss of function. Cyclodextrins (CDs) have been shown to function as aggregation suppressors for a wide range of proteins. Their potency is often ascribed to their affinity for aromatic amino acids, whose surface exposure would otherwise lead to protein association. However, no detailed structural studies are available. Here we investigate the interactions between human growth hormone (hGH) and different CDs at low pH. Although hGH aggregates readily at pH 2.5 in 1 M NaCl to form amorphous aggregates, the presence of 25 to 50 mM of various β‐CD derivatives is sufficient to completely avoid this. α‐ and γ‐CD are considerably less effective. Stopped‐flow data on the aggregation reaction in the presence of β‐CD are analyzed according to a minimalist association model to yield an apparent hGH‐β‐CD dissociation constant of ∼6 mM. This value is very similar to that obtained by simple fluorescence‐based titration of hGH with β‐CD. Nuclear magnetic resonance studies indicate that β‐CD leads to a more unfolded conformation of hGH at low pH and predominantly binds to the aromatic side‐chains. This indicates that aromatic amino acids are important components of regions of residual structure that may form nuclei for aggregation.

Inclusion complex formation constants of α-, β-, γ-, δ-, ε-, ζ-, η- and θ-cyclodextrins determined with capillary zone electrophoresis

Abstract In contrast to the well known small cyclodextrins (CD), cyclomaltohexaose ( α -CD), cyclomaltoheptaose ( β -CD) and cyclomaltooctaose ( γ -CD), very limited information is available on larger CD and their inclusion complex forming properties. Using capillary electrophoresis, the binding constants of inclusion complexes formed with cyclomaltononaose ( δ -CD), cyclomaltodecaose ( e -CD), cyclomaltoundecaose ( ζ -CD), cyclomaltododecaose ( η -CD) and cyclomaltotridecaose ( θ -CD) and various anions were determined and compared to the corresponding binding constants of α -, β - and γ -CD. All of the large CD were capable to form inclusion complexes. Dependent on the type of guest molecules, δ - and e -CD were the weakest complex formers. The complex forming ability of e , ζ -, η -, and θ -CD increased with increasing size of the ring structure and θ -CD displayed inclusion complex formation constants comparable to γ -CD.

Hydroxypropyl-Substituted β-Cyclodextrins: Influence of Degree of Substitution on the Thermodynamics of Complexation with Tauroconjugated and Glycoconjugated Bile Salts

The effect of the degree of substitution (DS) on the ability of hydroxypropylated β-cyclodextrin (HPβCD) to form inclusion complexes with six different bile salts, found within the intestinal tracts of rats, dogs, and humans, was studied by isothermal titration calorimetry. The composition and molecular structure of the cyclodextrin samples were characterized by MALDI-TOF mass spectrometry together with 1D and 2D-NMR, and some of the complexes were studied by 2D ROESY NMR. The stability and structure of the complexes were mainly determined by the position of hydroxyl groups on the bile salts and depended relatively little on the number of hydroxypropyl side chains on the CDs. The enthalpy and entropy of complexation exhibited a strong linear increase as the DS increased from 0 to 1, and a pronounced enthalpy-entropy compensation was observed. These observations are interpreted as an increased release of ordered water from the hydration shells of the bile salts, caused by the hydroxypropyl substituents on the rim of the CD. It is estimated that each CD hydroxypropyl substituent dehydrates a hydrophobic surface area of approximately 10 Å(2).

Self-assembling microparticles with controllable disruption properties based on cyclodextrin interactions.

In this paper, we present the formation of particles by self-assembly of cyclodextrin polymers and hydrophobically modified dextran followed by a controlled disruption of the particles by addition of a trigger molecule competing for the cyclodextrin cavities. The produced particles are formed from poly(vinylpyrrolidone)-co-beta-cyclodextrin and dextran-benzoate, both biocompatible polymers, and are all in the nano-/micrometer range and hence suitable for drug delivery purposes. The particle formation was studied in different ratios of poly(vinylpyrrolidone)-co-beta-cyclodextrin and dextran-benzoate by visual inspections, dynamic light scattering, isothermal titration calorimetry and SEM. The triggering of particle disruption was achieved by addition of hydroxyadamantane which has a very strong affinity towards the beta-cyclodextrin cavities. The stepwise addition of hydroxyadamantane was followed by dynamic light scattering and SEM measurements, revealing a disruption of the particles due to the addition of this competitor. These particles are believed to be promising candidates for controlled drug delivery systems, due to their unique ability to disrupt in a controlled manner.

Methylated β-Cyclodextrins: Influence of Degree and Pattern of Substitution on the Thermodynamics of Complexation with Tauro- and Glyco-Conjugated Bile Salts

The complexation of 6 bile salts with various methylated β-cyclodextrins was studied to elucidate how the degree and pattern of substitution affects the binding. The structures of the CDs were determined by mass spectrometry and NMR techniques, and the structures of the inclusion complexes were characterized from the complexation-induced shifts of (13)C nuclei as well as by 2D ROESY NMR. Thermodynamic data were generated using isothermal titration calorimetry. The structure-properties analysis showed that methylation at O3 hinders complexation by partially blocking the cavity entrance, while methyl groups at O2 promote complexation by extending the hydrophobic cavity. Like in the case of 2-hydroxypropylated cyclodextrins, the methyl substituents cause an increased release of ordered water from the hydration shell of the bile salts, resulting in a strong increase in both the enthalpy and the entropy of complexation with increased number of methyl substituents. Due to enthalpy-entropy compensation the effect on the stability constant is relatively limited. However, when all hydroxyl groups are methylated, the rigid structure of the free cyclodextrin is lost and the complexes are severely destabilized due to very unfavorable entropies.

Analysis and characterisation of cyclodextrins and their inclusion complexes by affinity capillary electrophoresis

Abstract α-, β- and γ-cyclodextrins, which are composed of 6, 7 and 8 (1→4)-linked α- d -glucose units, are capable of forming complexes with molecules ranging from gases to proteins and other biopolymers. The physico-chemical properties of the guest molecules, such as their solubility, stability and reactivity can thereby be modified. For this reason they have found numerous applications in the agricultural, food, chemical and pharmaceutical industries. Cyclodextrins (CDs) have also been shown to be valuable as selectivity reagents for the resolution of structural, positional and stereo isomers in analytical chemistry and are important as media modifiers in the capillary electrophoretic separation of chiral biomolecules. CDs are produced from starch together with linear oligosaccharides by the extracellular microbial enzyme cyclodextrin glycosyltransferase (E.C. 2.4.1.19). Cyclodextrin glycosyltransferases are capable of producing cyclodextrins with six or more glucose units, mainly α-, β- and γ-CDs, as the major product. The analysis of the enzymatic reaction products is difficult due to the formation of a variety of both linear and cyclic oligosaccharides by cyclodextrin glycosyltransferases. Capillary electrophoresis provides a versatile and selective tool for their analysis in complex samples. Furthermore, capillary electrophoresis enables the characterisation of the inclusion complex forming properties of cyclodextrins using only minute amounts of sample.

β-Cyclodextrin-dextran polymers for the solubilization of poorly soluble drugs

The aim of this study was to assess the potential of novel β-cyclodextrin (βCD)-dextran polymers for drug delivery. The size distribution of βCD-dextrans (for eventual parenteral administration), the influence of the dextran backbones on the stability of the βCD/drug complex, the solubilization efficiency of poorly soluble drugs and drug release properties were investigated. Size analysis of different βCD-dextrans was measured by size exclusion chromatography (SEC) and asymmetrical flow field-flow fractionation (AF4). Stability of drug/βCD-dextrans was assessed by isothermal titration calorimetry (ITC) and molar enthalpies of complexation and equilibrium constants compared to some commercially available βCD derivatives. For evaluation of the solubilization efficiency, phase-solubility diagrams were made employing hydrocortisone (HC) as a model of poorly soluble drugs, whereas reverse dialysis was used to detect potential drug supersaturation (increased molecularly dissolved drug concentration) as well as controlled release effects. Results indicate that all investigated βCD-polymers are of appropriate sizes for parenteral administration. Thermodynamic results demonstrate that the presence of the dextran backbone structure does not affect the stability of the βCD/drug complex, compared to native βCD and commercially available derivatives. Solubility studies evidence higher solubilizing abilities of these new polymers in comparison to commercially available βCDs, but no supersaturation states were induced. Moreover, drug release studies evidenced that diffusion of HC was influenced by the solubilization induced by the βCD-derivatives.