Classification of certain subgraphs of the 3‐dimensional grid

We prove by “trial‐ and‐error” that up to isometry, there are exactly four different non‐empty cubic induced subgraphs of the 3‐dimensional grid with girth ≥ 10. © 2002 Wiley Periodicals, Inc. J Graph Theory 42: 34–60, 2003     

Sampling and interpolation of entire functions and exponential systems in convex domains

Research supported by the Norwegian Research Council for Science and Humanities (NAVF).     

Design and Synthesis of High‐Affinity Dimeric Inhibitors Targeting the Interactions between Gephyrin and Inhibitory Neurotransmitter Receptors

Gephyrin is the central scaffolding protein for inhibitory neurotransmitter receptors in the brain. Here we describe the development of dimeric peptides that inhibit the interaction between gephyrin and these receptors, a process which is fundamental to numerous synaptic functions and diseases of the brain. We first identified receptor‐derived minimal gephyrin‐binding peptides that displayed exclusive binding towards native gephyrin from brain lysates. We then designed and synthesized a series of dimeric ligands, which led to a remarkable 1220‐fold enhancement of the gephyrin affinity (K_D=6.8 nM ). In X‐ray crystal structures we visualized the simultaneous dimer‐to‐dimer binding in atomic detail, revealing compound‐specific binding modes. Thus, we defined the molecular basis of the affinity‐enhancing effect of multivalent gephyrin inhibitors and provide conceptually novel compounds with therapeutic potential, which will allow further elucidation of the gephyrin–receptor interplay.     

Protamine neutralisation of low molecular weight heparins and their oligosaccharide components

Protamine sulphate is an effective inhibitor of heparin and is used clinically to neutralise both low molecular weight heparins (LMWH) and unfractionated heparin (UFH). However, protamine sulphate does not fully counter the anti-Xa effect of LMWH, even in excess (>40 μg to 1 IU/ml). To investigate the molecular basis for this observation, the residual potencies in the presence and absence of plasma as well as the molecular weight profiles of commercial LMWH neutralised with increasing amounts of protamine were measured. Materials over 5000 Da are preferentially neutralised by protamine. To further investigate this molecular weight dependence, monodisperse oligosaccharides were prepared from three commercial LMWHs. The specific anti-Xa activity for the fractions increased with molecular weight, and was found to vary between the three preparations for oligosaccharides of the same molecular weight. Our results indicate that protamine sulphate neutralisation is largely dependent on molecular weight, leading to the implication that LMWHs containing a larger proportion of small oligosaccharides will not be as effectively neutralised. Protamine sulphate neutralisation of any given LMWH is also affected by the specific anticoagulant activities of its low molecular weight components, which varies between LMWH products, presumably with the method of manufacture.     

Role of nearby charges on the electronic structure of π-conjugated molecules: symmetric versus asymmetric charge distributions in oligo(p-phenyleneethynylene)

Oligo(p-phenyleneethynylene)s (OPEs) are conjugated oligomers of great interest within materials science and molecular electronics on account of their highly applicable electronic and optical properties. Here we use gas-phase action spectroscopy to elucidate how the intrinsic electronic properties of these chromophores are affected by nearby charges. An OPE3 chromophore with two nearby ammonium groups was synthesized. This molecule and a related OPE3 with only one amine protonation site were transferred to the gas phase by electrospray ionization and subjected to action spectroscopy. Ions were bunched in a 14-pole ion trap, accelerated to 50-keV kinetic energies, mass-to-charge selected by a magnet, and photoexcited in a crossed-beam configuration. Fragment ions were finally mass-analyzed by an electrostatic analyzer. The setup enables photodissociation mass spectrometry and action spectroscopy on the microsecond time scale. The gas-phase absorption of the mono- and dication was measured and compared to that of neutral chromophores in solution. Similar absorption was found for neutral chromophores (in solution) and the dication (in gas phase or solution), whereas the monocation absorbs at lower energies in the gas phase. Simple electrostatic considerations lead to an energy difference like the one found from the experiment. The work presented here addresses how the electronic properties of a π-conjugated system are affected by nearby charges, a question of fundamental interest in, for example, molecular electronics.     

One-pot synthesis of cyclopentadienyl endcapped poly(2-ethyl-2-oxazoline) and subsequent ambient temperature Diels-Alder conjugations

An efficient method for the preparation of cyclopentadienyl endcapped poly(2-ethyl-2-oxazoline) (PEtOx-Cp) via cationic ring-opening polymerization utilizing sodium cyclopentadienide as a termination agent is presented. Subsequent Diels-Alder reactions with N-substituted maleimides proceed quantitatively at ambient temperature. A block copolymer (PEtOx-b-PEG) is prepared employing maleimide terminated poly(ethylene glycol).     

Unraveling the similarity of the photoabsorption of deprotonated p-coumaric acid in the gas phase and within the photoactive yellow protein

Using advanced QM/MM methods, the surprisingly negligible shift of the lowest-lying bright electronic excitation of the deprotonated p-coumaric acid (pCA(-)) within the photoactive yellow protein (PYP) is shown to stem from a subtle balance between hypsochromic and bathochromic effects. More specifically, it is found that the change in the excitation energy as a consequence of the disruption of the planarity of pCA(-) inside PYP is nearly canceled out by the shift induced by the intermolecular interactions of the chromophore and the protein as a whole. These results provide important insights about the primary absorption and the tuning of the chromophore by the protein environment in PYP.     

Runge–Kutta Lawson schemes for stochastic differential equations

In this paper, we present a framework to construct general stochastic Runge–Kutta Lawson schemes. We prove that the schemes inherit the consistency and convergence properties of the underlying Runge–Kutta scheme, and confirm this in some numerical experiments. We also investigate the stability properties of the methods and show for some examples, that the new schemes have improved stability properties compared to the underlying schemes.